9 10 11 12 and ICESat-2 Project Science Office · 4 2017 September Modified 500 canopy photon...

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Ice, Cloud, and Land Elevation Satellite 2 (ICESat-2) 1 2

Algorithm Theoretical Basis Document (ATBD) 3 4

for 5 6

Land - Vegetation Along-Track Products (ATL08) 7 8

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Contributions by Land/Vegetation SDT Team Members 11and ICESat-2 Project Science Office 12

(Amy Neuenschwander, Katherine Pitts, Benjamin Jelley, John Robbins, 13Brad Klotz, Sorin Popescu, Ross Nelson, David Harding, Dylan Pederson, 14

and Ryan Sheridan) 15

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ATBD prepared by 18

Amy Neuenschwander and 19

Katherine Pitts 20

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15 January 2020 23

(Corresponds to release 003 of the ICESat-2 ATL08 data) 24

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Contentreviewed:technicalapproach,assumptions,scientificsoundness,27

maturity,scientificutilityofthedataproduct28

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ATL08algorithmandproductchangehistory3334ATBDVersion Change2016Nov Productsegmentsizechangedfrom250signalphotonsto

100musingfive20msegmentsfromATL03(Sec2)2016Nov Filteredsignalclassificationflagremovedfrom

classed_pc_flag(Sec2.3.2)2016Nov DRAGANNsignalflagadded(Sec2.3.4)2016Nov Donotreportsegmentstatisticsiftoofewgroundphotons

withinsegment(Sec4.15(3))2016Nov Productparametersadded:h_canopy_uncertainty,

landsat_flag,d_flag,delta_time_beg,delta_time_end,night_flag,msw_flag(Sec2)

2017May Revisedregionboundariestobeseparatedbycontinent(Sec2)

2017May AlternativeDRAGANNparametercalculationadded(Sec4.3.1)

2017May Setcanopyflag=0whenL-kmsegmentisoverAntarcticaorGreenlandregions(Sec4.4(1))

2017May Changeinitialcanopyfiltersearchradiusfrom3mto15m(Sec4.9(6))

2017May Productparametersremoved:h_rel_ph,terrain_thresh2017May Productparametersadded:segment_id,segment_id_beg,

segment_id_end,dem_flag,surf_type(Sec2)2017July Urbanflagadded(Sec2.4.17)2017July Dynamicpointspreadfunctionadded(Sec4.11(6))2017July MethodologyforprocessingL-kmsegmentswithbuffer

added(Sec4.1(2),Sec4.17)2017July RevisedalternativeDRAGANNmethodology(seeboldedtext

inSec4.3.1)2017July Addedpost-DRAGANNfilteringmethodology(Sec4.7)2017July UpdatedSNRtobeestimatedfromsupersetofATL03and

DRAGANNfoundsignalusedforprocessingATL08(Sec2.5.18)

2017September MoredetailsaddedtoDRAGANNdescription(Sec4.3),andcorrectionstoDRAGANNimplementation(Sec3.1.1,Sec4.3(9))

2017September AddedAppendixA–verydetailedDRAGANNdescription2017September RevisedalternativeDRAGANNmethodology(seeboldedtext

inSec4.3.1)2017September ClarifiedSNRcalculation(Sec2.5.18,Sec4.3(18))2017September Addedcloudflagfilteringoption(SecError!Reference

sourcenotfound.)2017September Addedtopofcanopymediansurfacefilter(Sec3.5(a),Sec

4.10(3),Sec4.12(1-3))

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2017September Modified500canopyphotonsegmentfilter(Sec3.5(c),Sec4.12(6))

2017November Addedsolar_azimuth,solar_elevation,andn_seg_phtoReferenceDatagroup;parameterswerealreadyinproduct(Sec2.4)

2017November Specifiednumberofgroundphotonsthresholdforrelativecanopyproductcalculations(Sec4.16(2));nonumberofgroundphotonsthresholdforabsolutecanopyheights(Sec4.16.1(1))

2017November ChangedtheATL03signalusedinsupersetfromallATL03signal(signal_conf_phflags1-4)tothemedium-highconfidenceflags(signal_conf_phflags3-4)(Sec3.1,Sec4.3(17))

2017November RemovedDateparameterfromTable2.4sinceUTCdateisinfilemetadata

2018March Clarifiedthatcloudflagfilteringoptionshouldbeturnedoffbydefault(SecError!Referencesourcenotfound.)

2018March Changedh_diff_refQAthresholdfrom10mto25m(Table5.2)

2018March Addedabsolutecanopyheightquartiles,canopy_h_quartile_abs(Laterremoved)

2018March Removedpsf_flagfrommainproduct;psf_flagwillonlybeaQAQCalert(Sec5.2)

2018March AddedanAsmoothfilterbasedonthereferenceDEMvalue(Sec4.6(4-5))

2018March Changedreliefcalculationto95th–5thsignalphotonheights.(Sec4.6(6))

2018March AdjustedtheAsmoothsmoothingmethodology(Sec4.6(8))2018March RecalculatetheAsmoothsurfaceafterfilteringoutlyingnoise

fromsignal,thendetrendsignalheightdata(Sec4.7(3-4))2018March AddedoptiontorunalternativeDRAGANNprocessagainin

highnoisecases(Sec4.3.3)2018March ChangedgloballandcoverreferencetoMODISGlobal

Mosaicsproduct(Sec2.4.14)2018March Adjustedthetopofcanopymedianfilterthresholdsbasedon

SNR(Sec4.12(1-2))2018March AddedafinalphotonclassificationQAcheck(Sec4.14,Table

5.2)2018March Addedslopeadjustedterrainparameters(Laterremoved)2018June Replacedslopeadjustedterrainparameterswithterrainbest

fitparameter(Sec2.1.14,4.15(2.e))2018June Clarifiedsourceforwatermask(Sec2.4.15)2018June Clarifiedsourceforurbanmask(Sec2.4.17)2018June Addedexpansiontotheterrain_slopecalculation(Sec4.15)2018June Removedcanopy_d_quartile

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2018June Removedcanopy_quartile_heightsandcanopy_quartile_heights_abs,replacedwithcanopy_h_metrics(Secs2.2.3,4.16(6),4.16.1(5))

2018***draft1 Delta_timespecifiedasmid-segmenttime,ratherthanmeansegmenttime(Sec2.4.5)

2018***draft1 QA/QCproductstobereportedonaperorbitbasis,ratherthanperregion(Sec5.2)

2018***draft1 Addedmoredetailtolandsat_flagdescription(Sec2.2.23)2018***draft1 Addedpsf_flagbackintoATL08product,asitisalsoneeded

fortheQAproduct(Sec2.5.12)2018***draft1 Specifiedthatthesigma_hvaluereportedhereisthemeanof

theATL03reportedsigma_hvalues(Sec2.5.7)2018***draft1 Removedn_photonsfromallsubgroups2018***draft1 Betterdefinedtheinterpolationandsmoothingmethods

usedthroughout:• Error!Referencesourcenotfound.(3):

Interpolation–nearest• 4.6(5):Interpolation–PCHIP• 4.6(8):Smoothing–movingaverage• 4.7(3):Interpolation–PCHIP• 4.7(3):Smoothing–movingaverage• 4.8(10):Smoothing–movingaverage• 4.8(11):Interpolation–linear• 4.8(12):Smoothing–movingaverage• 4.8(13):Interpolation–linear• 4.8(14):Smoothing–movingaverage• 4.8(15):Smoothing–Savitzky-Golay• 4.8(16):Interpolation–linear• 4.8(21):Interpolation–PCHIP• 4.10(10):Interpolation–linear• 4.11(all):Smoothing–movingaverage• 4.10(6.b):Interpolation–linear• 4.12(1.a):Interpolation–linear• 4.12(1.c):Smoothing–lowess• 4.12(4):Interpolation–PCHIP• 4.12(7):Interpolation–PCHIP• 4.12(9):Smoothing–movingaverage• 4.15(2.e.i.1):Interpolation–linear

2018***draft1 Addedref_elevandref_azimuthbackin(itwasmistakenlyremovedinapreviousversion;Secs2.5.3,2.5.4)

2018***draft1 Clarifiedwordingofh_canopy_quaddefinition(Sec2.2.17)2018***draft1 Updatedsegment_snowcoverdescriptiontomatchthe

ATL09snow_iceparameteritreferences(Sec2.4.16)andaddedproductreferencetoTable4.2

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2018***draft1 Addedph_ndx_beg(Sec2.5.22);parameterwasalreadyonproduct

2018***draft1 Addeddem_removal_flagforQApurposes(Sec2.4.11;Table5.2)

2018***draft2 ReformattedQA/QCtrendingandtriggeralertlistintoatableforbetterclarification(Table5.3)

2018***draft2 Replacedn_photonsinTable5.2withn_te_photons,n_ca_photons,andn_toc_photons

2018***draft2 Removedbeam_numberfromTable2.5.Beamnumberandweak/strongdesignationwithingtxgroupattributes.

2018***draft2 Clarifiedcalculationofh_te_best_fit(Sec4.15(2.e))2018***draft2 Changedh_canopyandh_canopy_abstobe98thpercentile

height(Table2.2,Sec2.2.5,Sec2.2.6,Sec4.16(4),Sec4.16.1(3))

2018***draft2 Separatedh_canopy_metrics_absfromh_canopy_metrics(Table2.2,Sec2.2.3,Sec4.16.1(5))

2018October Removed99thpercentilefromh_canopy_metricsandh_canopy_metrics_abs(Table2.2,Sec2.2.3,Sec2.2.4,Sec4.16(4),Sec4.16.1(5))

2018December RenamedandrewordedSection4.3.1tobetterindicatethattheDRAGANNpreprocessingstepisnotoptional

2018December SpecifiedthatDRAGANNshouldusealong-tracktime,andaddedtimerescalingstep(Sec4.3(1-4))

2018December AddedDRAGANNchangesmadetobettercapturesparsecanopyincasesoflownoiserates(Sec4.3,AppendixA)

2018December MadecorrectionstoDRAGANNdescriptionregardingthedeterminationofthenoiseGaussian(Sec3.1.1,Sec4.3)

2018December Removedh_median_canopyandh_median_canopy_abs,astheyareequivalenttocanopy_h_metrics(50)andcanopy_h_metrics_abs(50)(Table2.2,Sec4.16(5),Sec4.16.1(4))

2018December Removedtherequirementthat>5%groundphotonsrequiredtocalculaterelativecanopyheightparameters(Table2.2,Sec4.16(2))

2018December Addedcanopyrelativeheightconfidenceflag(canopy_rh_conf)basedonthepercentageofgroundandcanopyphotonsinasegment(Table2.2,Sec4.16(2))

2018December AddedATL09layer_flagtoATL08output(Table2.5,Table4.2)

2019February AdjustedcloudfilteringtobebasedonATL09backscatteranalysisratherthancloudflags(Sec4.1)

2019March5 UpdatedATL09-basedproductdescriptionsreportedonATL08product(Secs2.5.13,2.5.14,2.5.15,2.5.16)

2019March5 Updatedcloud-basedlowsignalfiltermethodology,andmovedtofirststepofATL08processing(Sec4.1)

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2019March13 Replacecanopy_closurewithnewlandsat_percparameter(Table2.2,Sec2.2.24)

2019March13 ChangeATL08productoutputregionstomatchATL03regions(Sec2),butkeepATL08regionsinternallyandreportinnewparameteratl08_regions(Table2.4,Sec2.4.19)

2019March13 AddmethodologyforhandlingshortATL08processingsegmentsattheendofanATL03granule(Sec4.2),andoutputdistancetheprocessingsegmentlengthisextendedintonewparameterlast_seg_extend(Table2.4,Sec2.4.20)

2019March13 AddpreprocessingstepforremovingatmosphericandoceantidecorrectionsfromATL03heights(Laterremoved)

2019March27 RemovepreprocessingstepforremovingatmosphericandoceantidecorrectionsfromATL03heights,sincethosevaluesarenowremovedfromtheATL03photonheights.

2019March27 ReplacedATL03regionfigurewithcorrectedversion(Figure2.2)

2019March27 Specifiedthatatleast50classedphotonsarerequiredtocreatethe100mlandandcanopyproducts(Secs2,4.15(1),4.16(1))

2019March27 Clarifiedthatanynon-extendedsegmentswouldreportaland_seg_extendvalueof0(Sec4.2,Sec2.4.20)

2019April30 FixedtheerrorinEqn1.4forthesigmatopovalue2019May13 Specifiedforcloudflagcarry-overfromATL09thatATL08

willreportthehighestcloudflagifan08segmentstraddlestwo09segments.(Section2.5)

2019May13 Changedparametercloud_flag_asrtocloud_flag_atmsincethecloud_flag_asrislikelynottoworkoverlandduetovaryingsurfacereflectance(Sec,2.5)

2019May13 AddATL09parametercloud_fold_flagtotheATL08dataproductforfutureqa/qcchecksforlowclouds.(Secs,2.5)

2019May13 Clarificationonthecalculationofgradientforslopethatfeedsintothecalculationofthepointspreadfunction(Sec4.11)

2019July8 ChangedLandsatcanopycoverpercentageto3%(fromoriginalvalueof5%)(Section4.4)

2019July8 AddedaQAmethodforDRAGANNflagstohelpremovefalsepositives(nowSection4.3.1)

2019July8 Setthewindowsizeto9ratherthanSmoothSizeforthefinalgroundfindingstep.(Section4.11and4.12)

2019July8 Addedabrightnessflagtolandsegments.(Section2.4.21)2019November12

Addedsubset_te_flagto(Section2.1)whichindicate100msegmentsthatarepopulatedbylessthan100mworthofdata

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2019November12

Addedsubset_can_flag(section2.2)whichindicate100msegmentsthatarepopulatedbylessthan100mworthofdata

2020January5 Clarifiedtheinterpolationofvalues(latitude,longitude,deltatime)whenthe100msegmentsarepopulatedbylessthan100mworthofdata.(Section2.4.3and2.4.4)

2020January13 Fine-tunedthemethodologytoimprovegroundfindingbyfirsthistogrammingthephotonstoimprovedetectingthegroundincasesofdensecanopy.(Section4.8)

2020January13 UpdatedATL08HDF5fileorganizationfigureinSection2.153 54

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Contents82

ListofTables.............................................................................................................................................15 83

ListofFigures...........................................................................................................................................16 84

1 INTRODUCTION.............................................................................................................................18 85

1.1. Background..............................................................................................................................19 86

1.2 PhotonCountingLidar........................................................................................................21 87

1.3 TheICESat-2concept...........................................................................................................22 88

1.4 HeightRetrievalfromATLAS...........................................................................................25 89

1.5 AccuracyExpectedfromATLAS.....................................................................................27 90

1.6 AdditionalPotentialHeightErrorsfromATLAS.....................................................29 91

1.7 DenseCanopyCases.............................................................................................................29 92

1.8 SparseCanopyCases...........................................................................................................30 93

2. ATL08:DATAPRODUCT............................................................................................................31 94

2.1 Subgroup:LandParameters.............................................................................................34 95

2.1.1 Georeferenced_segment_number_beg................................................................35 96

2.1.2 Georeferenced_segment_number_end................................................................35 97

2.1.3 Segment_terrain_height_mean...............................................................................36 98

2.1.4 Segment_terrain_height_med..................................................................................36 99

2.1.5 Segment_terrain_height_min...................................................................................36 100

2.1.6 Segment_terrain_height_max..................................................................................37 101

2.1.7 Segment_terrain_height_mode...............................................................................37 102

2.1.8 Segment_terrain_height_skew................................................................................37 103

2.1.9 Segment_number_terrain_photons......................................................................37 104

2.1.10 Segmentheight_interp...............................................................................................37 105

2.1.11 Segmenth_te_std..........................................................................................................38 106

2.1.12 Segment_terrain_height_uncertainty...................................................................38 107

2.1.13 Segment_terrain_slope...............................................................................................38 108

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2.1.14 Segment_terrain_height_best_fit............................................................................38 162

2.2 Subgroup:VegetationParameters.................................................................................39 163



2.2.3 Canopy_height_metrics_abs.....................................................................................42 166

2.2.4 Canopy_height_metrics..............................................................................................43 167

2.2.5 Absolute_segment_canopy_height........................................................................43 168

2.2.6 Segment_canopy_height............................................................................................43 169

2.2.7 Absolute_segment_mean_canopy..........................................................................44 170

2.2.8 Segment_mean_canopy..............................................................................................44 171

2.2.9 Segment_dif_canopy....................................................................................................44 172

2.2.10 Absolute_segment_min_canopy.............................................................................44 173

2.2.11 Segment_min_canopy.................................................................................................44 174

2.2.12 Absolute_segment_max_canopy.............................................................................44 175

2.2.13 Segment_max_canopy.................................................................................................45 176

2.2.14 Segment_canopy_height_uncertainty..................................................................45 177

2.2.15 Segment_canopy_openness......................................................................................46 178

2.2.16 Segment_top_of_canopy_roughness.....................................................................46 179

2.2.17 Segment_canopy_quadratic_height......................................................................46 180

2.2.18 Segment_number_canopy_photons......................................................................46 181

2.2.19 Segment_number_top_canopy_photons.............................................................46 182

2.2.20 Centroid_height.............................................................................................................47 183

2.2.21 Segment_rel_canopy_conf.........................................................................................47 184

2.2.22 Canopy_flag.....................................................................................................................47 185

2.2.23 Landsat_flag....................................................................................................................47 186

2.2.24 Landsat_perc..................................................................................................................47 187

2.3 Subgroup:Photons...............................................................................................................48 188

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2.3.1 Indices_of_classed_photons.....................................................................................49 243

2.3.2 Photon_class...................................................................................................................49 244

2.3.3 Georeferenced_segment_number..........................................................................49 245

2.3.4 DRAGANN_flag...............................................................................................................50 246

2.4 Subgroup:Referencedata.................................................................................................50 247



2.4.3 Segment_latitude..........................................................................................................52 250

2.4.4 Segment_longitude......................................................................................................53 251

2.4.5 Delta_time........................................................................................................................53 252

2.4.6 Delta_time_beg...............................................................................................................53 253

2.4.7 Delta_time_end..............................................................................................................54 254

2.4.8 Night_Flag........................................................................................................................54 255

2.4.9 Segment_reference_DTM..........................................................................................54 256

2.4.10 Segment_reference_DEM_source...........................................................................54 257

2.4.11 Segment_reference_DEM_removal_flag..............................................................54 258

2.4.12 Segment_terrain_difference.....................................................................................54 259

2.4.13 Segment_terrainflag...................................................................................................55 260

2.4.14 Segment_landcover.....................................................................................................55 261

2.4.15 Segment_watermask...................................................................................................55 262

2.4.16 Segment_snowcover...................................................................................................55 263

2.4.17 Urban_flag........................................................................................................................55 264

2.4.18 Surface_type...................................................................................................................56 265

2.4.19 ATL08_region.................................................................................................................56 266

2.4.20 Last_segment_extend..................................................................................................56 267

2.5 Subgroup:Beamdata..........................................................................................................57 268


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2.5.3 Beam_coelevation........................................................................................................60 325

2.5.4 Beam_azimuth...............................................................................................................60 326

2.5.5 ATLAS_Pointing_Angle...............................................................................................60 327

2.5.6 Reference_ground_track............................................................................................60 328

2.5.7 Sigma_h.............................................................................................................................61 329

2.5.8 Sigma_along....................................................................................................................61 330

2.5.9 Sigma_across..................................................................................................................61 331

2.5.10 Sigma_topo......................................................................................................................61 332

2.5.11 Sigma_ATLAS_LAND....................................................................................................62 333

2.5.12 PSF_flag.............................................................................................................................62 334

2.5.13 Layer_flag.........................................................................................................................62 335

2.5.14 Cloud_flag_atm...............................................................................................................62 336

2.5.15 MSW...................................................................................................................................62 337

2.5.16 CloudFoldFlag..............................................................................................................63 338

2.5.17 Computed_Apparent_Surface_Reflectance........................................................63 339

2.5.18 Signal_to_Noise_Ratio.................................................................................................63 340

2.5.19 Solar_Azimuth................................................................................................................63 341

2.5.20 Solar_Elevation..............................................................................................................64 342

2.5.21 Number_of_segment_photons.................................................................................64 343

2.5.22 Photon_Index_Begin....................................................................................................64 344

3 ALGORITHMMETHODOLOGY.................................................................................................65 345

3.1 NoiseFiltering........................................................................................................................65 346

3.1.1 DRAGANN........................................................................................................................66 347

3.2 SurfaceFinding......................................................................................................................70 348

3.2.1 De-trendingtheSignalPhotons.............................................................................72 349

3.2.2 CanopyDetermination...............................................................................................72 350

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3.2.3 VariableWindowDetermination..........................................................................74 405

3.2.4 Computedescriptivestatistics...............................................................................75 406

3.2.5 GroundFindingFilter(Iterativemedianfiltering)........................................77 407

3.3 TopofCanopyFindingFilter............................................................................................78 408

3.4 ClassifyingthePhotons.......................................................................................................79 409

3.5 RefiningthePhotonLabels...............................................................................................79 410

3.6 CanopyHeightDetermination.........................................................................................84 411

3.7 LinkScaleforDataproducts............................................................................................84 412

4. ALGORITHMIMPLEMENTATION...........................................................................................85 413

4.1 Cloudbasedfiltering............................................................................................................88 414

4.2 PreparingATL03dataforinputtoATL08algorithm............................................90 415

4.3 NoisefilteringviaDRAGANN...........................................................................................91 416

4.3.1 DRAGANNQualityAssurance.................................................................................94 417

4.3.2 PreprocessingtodynamicallydetermineaDRAGANNparameter........95 418

4.3.3 IterativeDRAGANNprocessing..............................................................................98 419

4.4 IsCanopyPresent.................................................................................................................99 420

4.5 ComputeFilteringWindow..............................................................................................99 421

4.6 De-trendData..........................................................................................................................99 422

4.7 Filteroutliernoisefromsignal.....................................................................................100 423

4.8 Findingtheinitialgroundestimate............................................................................101 424

4.9 Findthetopofthecanopy(ifcanopy_flag=1).....................................................104 425

4.10 Computestatisticsonde-trendeddata.....................................................................105 426

4.11 RefineGroundEstimates................................................................................................106 427

4.12 CanopyPhotonFiltering.................................................................................................107 428

4.13 ComputeindividualCanopyHeights.........................................................................110 429

4.14 FinalphotonclassificationQAcheck.........................................................................110 430

4.15 ComputesegmentparametersfortheLandProducts.......................................111 431

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4.16 ComputesegmentparametersfortheCanopyProducts..................................113 467

4.16.1 CanopyProductscalculatedwithabsoluteheights....................................115 468

4.17 Recordfinalproductwithoutbuffer..........................................................................115 469

5 DATAPRODUCTVALIDATIONSTRATEGY.....................................................................117 470

5.1 ValidationData....................................................................................................................117 471

5.2 InternalQCMonitoring....................................................................................................120 472

6 REFERENCES................................................................................................................................126 473

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ListofTables497

Table2.1.SummarytableoflandparametersonATL08......................................................34 498

Table2.2.SummarytableofcanopyparametersonATL08................................................40 499

Table2.3.SummarytableforphotonparametersfortheATL08product....................48 500

Table2.4.SummarytableforreferenceparametersfortheATL08product...............50 501

Table2.5.SummarytableforbeamparametersfortheATL08product........................57 502

Table3.1.Standarddeviationrangesutilizedtoqualifythespreadofphotonswithin503movingwindow.......................................................................................................................................76 504

Table4.1.InputparameterstoATL08classificationalgorithm.........................................85 505

Table4.2.AdditionalexternalparametersreferencedinATL08product.....................86 506

Table5.1.Airbornelidardataverticalheight(Zaccuracy)requirementsfor507validationdata.......................................................................................................................................117 508

Table5.2.ATL08parametermonitoring...................................................................................120 509

Table5.3.QA/QCtrendingandtriggers.....................................................................................124 510

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ListofFigures553

Figure1.1.Variousmodalitiesoflidardetection.AdaptedfromHarding,2009........22 554

Figure1.2.Schematicof6-beamconfigurationforICESat-2mission.Thelaser555energywillbesplitinto3laserbeampairs–eachpairhavingaweakspot(1X)anda556strongspot(4X).......................................................................................................................................24 557

Figure1.3.Illustrationofoff-nadirpointingscenarios.Overland(greenregions)in558themid-latitudes,ICESat-2willbepointedawayfromtherepeatgroundtracksto559increasethedensityofmeasurementsoverterrestrialsurfaces.......................................25 560

Figure1.4.Illustrationofthepointspreadfunction,alsoreferredtoasZnoise,fora561seriesofphotonsaboutasurface....................................................................................................27 562

Figure2.1.HDF5datastructureforATL08products............................................................32 563

Figure2.2.ATL03granuleregions;graphicfromATL03ATBD(Neumannetal.).....33 564

Figure2.3.ATL08productregions..................................................................................................34 565

Figure2.4.Illustrationofcanopyphotons(reddots)interactioninavegetatedarea.566Relativecanopyheights,Hi,arecomputedbydifferencingthecanopyphotonheight567fromaninterpolatedterrainsurface..............................................................................................40 568

Figure3.1.Combinationofnoisefilteringalgorithmstocreateasupersetofinput569dataforsurfacefindingalgorithms.................................................................................................66 570

Figure3.2.Histogramofthenumberofphotonswithinasearchradius.This571histogramisusedtodeterminethethresholdfortheDRAGANNapproach................68 572

Figure3.3.OutputfromDRAGANNfiltering.Signalphotonsareshownasblue.......70 573

Figure3.4.Flowchartofoverallsurfacefindingmethod.......................................................71 574

Figure3.5.PlotofSignalPhotons(black)from2014MABELflightoverAlaskaand575de-trendedphotons(red)....................................................................................................................72 576

Figure3.6.ShapeParameterforvariablewindowsize..........................................................75 577

Figure3.7.Illustrationofthestandarddeviationscalculatedforeachmoving578windowtoidentifytheamountofspreadofsignalphotonswithinagivenwindow.579.........................................................................................................................................................................77 580

Figure3.8.ThreeiterationsofthegroundfindingconceptforL-kmsegmentswith581canopy..........................................................................................................................................................78 582

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17

Figure3.9.Exampleoftheintermediategroundandtopofcanopysurfaces616calculatedfromMABELflightdataoverAlaskaduringJuly2014.....................................81 617

Figure3.10.ExampleofclassifiedphotonsfromMABELdatacollectedinAlaska6182014.Redphotonsarephotonsclassifiedasterrain.Greenphotonsareclassifiedas619topofcanopy.Canopyphotons(shownasblue)areconsideredasphotonslying620betweentheterrainsurfaceandtopofcanopy.........................................................................82 621



Figure5.1.ExampleofL-kmsegmentclassificationsandinterpolatedground630surface.......................................................................................................................................................123 631

632

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18

1 INTRODUCTION 638

This document describes the theoretical basis and implementation of the639

processingalgorithmsanddataparametersforLevel3landandvegetationheights640

forthenon-polarregionsoftheEarth.TheATL08productcontainsheightsforboth641

terrain and canopy in the along-track direction as well as other descriptive642

parametersderivedfromthemeasurements.Atthemostbasiclevel,aderivedsurface643

heightfromtheATLASinstrumentatagiventimeisprovidedrelativetotheWGS-84644

ellipsoid.HeightestimatesfromATL08canbecomparedwithothergeodeticdataand645

usedas input tohigher-level ICESat-2products,namelyATL13andATL18.ATL13646

will provide estimates of inland water-related heights and associated descriptive647

parameters.ATL18willconsistofgriddedmapsforterrainandcanopyfeatures.648

TheATL08productwillprovideestimatesofterrainheights,canopyheights,649

and canopy cover at fine spatial scales in the along-trackdirection.Along-track is650

defined as the direction of travel of the ICESat-2 satellite in the velocity vector.651

Parametersfortheterrainandcanopywillbeprovidedatafixedstep-sizeof100m652

alongthegroundtrackreferredtoasasegment.Afixedsegmentsizeof100mwas653

chosentoprovidecontinuityofdataparametersontheATL08dataproduct.Froman654

analysisperspective,itisdifficultandcumbersometoattempttorelatecanopycover655

overvariablelengths.Furthermore,asegmentsizeof100mwillfacilitateasimpler656

combinationofalong-trackdatatocreatethegriddedproducts.657

Weanticipatethatthesignalreturnedfromtheweakbeamwillbesufficiently658

weak andmay prohibit the determination of both a terrain and canopy segment659

height,particularlyoverareasofdensevegetation.However,inmorearidregionswe660

anticipateproducingaterrainheightforboththeweakandstrongbeams.661

Inthisdocument,section1providesabackgroundoflidarintheecosystem662

communityaswellasdescribingphotoncountingsystemsandhowtheydifferfrom663

discrete return lidar systems. Section 2 provides an overview of the Land and664

Vegetation parameters and how they are defined on the data product. Section 3665

describesthebasicmethodologythatwillbeusedtoderivetheparametersforATL08.666

19

Section4describestheprocessingsteps,inputdata,andproceduretoderivethedata667

parameters. Section 5 will describe the test data and specific tests that NASA’s668

implementation of the algorithm should pass in order to determine a successful669

implementationofthealgorithm.670

671

1.1. Background672

TheEarth’s landsurface isa complexmosaicofgeomorphicunitsand land673

covertypesresultinginlargevariationsinterrainheight,slope,roughness,vegetation674

height and reflectance, oftenwith the variationsoccurringover very small spatial675

scales.Documentationoftheselandscapepropertiesisafirststepinunderstanding676

theinterplaybetweentheformativeprocessesandresponsetochangingconditions.677

Characterizationofthelandscapeisalsonecessarytoestablishboundaryconditions678

for models which are sensitive to these properties, such as predictive models of679

atmosphericchangethatdependon land-atmosphere interactions.Topography,or680

landsurfaceheight,isanimportantcomponentformanyheightapplications,bothto681

thescientificandcommercialsectors.Themostaccurateglobalterrainproductwas682

produced by the Shuttle Radar Topography Mission (SRTM) launched in 2000;683

however, elevation data are limited to non-polar regions. The accuracy of SRTM684

derivedelevationsrangefrom5–10m,dependingupontheamountoftopography685

andvegetationcoveroveraparticulararea.ICESat-2willprovideaglobaldistribution686

ofgeodeticmeasurements(ofboththeterrainsurfaceandrelativecanopyheights)687

whichwillprovideasignificantbenefittosocietythroughavarietyofapplications688

including sea level change monitoring, forest structural mapping and biomass689

estimation,andimprovedglobaldigitalterrainmodels.690

Inadditiontoproducingaglobalterrainproduct,monitoringtheamountand691

distribution of above ground vegetation and carbon pools enables improved692

characterizationof the global carbonbudget. Forestsplay a significant role in the693

terrestrial carbon cycle as carbon pools. Events, such as management activities694

(Krankinaetal.2012)anddisturbancescanreleasecarbonstored in forestabove695

20

groundbiomass(AGB)intotheatmosphereascarbondioxide,agreenhousegasthat696

contributestoclimatechange(Ahmedetal.2013).Whilecarbonstocks innations697

withcontinuousnationalforestinventories(NFIs)areknown,complicationswithNFI698

carbonstockestimatesexist, including:(1)ground-basedinventorymeasurements699

are time consuming, expensive, and difficult to collect at large-scales (Houghton700

2005; Ahmed et al. 2013); (2) asynchronously collected data; (3) extended time701

betweenrepeatmeasurements(Houghton2005);and(4)thelackofinformationon702

thespatialdistributionofforestAGB,requiredformonitoringsourcesandsinksof703

carbon(Houghton2005).Airbornelidarhasbeenusedforsmallstudiestocapture704

canopyheightandinthosestudiescanopyheightvariationformultipleforesttypes705

ismeasuredtoapproximately7mstandarddeviation(Halletal.,2011).706

Althoughthespatialextentandchangestoforestscanbemappedwithexisting707

satelliteremotesensingdata,thelackofinformationonforestverticalstructureand708

biomasslimitstheknowledgeofbiomass/biomasschangewithintheglobalcarbon709

budget.Basedontheglobalcarbonbudgetfor2015(Quereetal.,2015),thelargest710

remaining uncertainties about the Earth’s carbon budget are in its terrestrial711

components, the global residual terrestrial carbon sink, estimated at 3.0 ± 0.8712

GtC/yearforthelastdecade(2005-2014).Similarly,carbonemissionsfromland-use713

changes, including deforestation, afforestation, logging, forest degradation and714

shiftingcultivationareestimatedat0.9±0.5GtC/year.Byprovidinginformationon715

vegetation canopyheight globallywithahigher spatial resolution thanpreviously716

afforded by other spaceborne sensors, the ICESat-2 mission can contribute717

significantlytoreducinguncertaintiesassociatedwithforestvegetationcarbon.718

AlthoughICESat-2isnotpositionedtoprovideglobalbiomassestimatesdue719

to its profiling configuration and somewhat limited detection capabilities, it is720

anticipatedthatthedataproductsforvegetationwillbecomplementarytoongoing721

biomassandvegetationmappingefforts.SynergisticuseofICESat-2datawithother722

space-based mapping systems is one solution for extended use of ICESat-2 data.723

PossibilitiesincludeNASA’sGlobalEcosystemsDynamicsInvestigation(GEDI)lidar724

21

plannedtoflyonboardtheInternationalSpaceStation(ISS)orimagingsensors,such725

asLandsat8,orNASA/ISRO–NISARradarmission.726

727

1.2 PhotonCountingLidar728

Ratherthanusingananalog,fullwaveformsystemsimilartowhatwasutilized729

ontheICESat/GLASmission,ICESat-2willemployaphotoncountinglidar.Photon730

countinglidarhasbeenusedsuccessfullyforrangingforseveraldecadesinboththe731

science and defense communities. Photon counting lidar systems operate on the732

concept that a low power laser pulse is transmitted and the detectors used are733

sensitiveatthesinglephotonlevel.Duetothistypeofdetector,anyreturnedphoton734

whetherfromthereflectedsignalorsolarbackgroundcantriggeraneventwithinthe735

detector.Adiscussionregardingdiscriminatingbetweensignalandbackgroundnoise736

photonsisdiscussedlaterinthisdocument.Aquestionofinteresttotheecosystem737

community is to understand where within the canopy is the photon likely to be738

reflected.Figure1.1 isanexampleof threedifferent laserdetectormodalities: full739

waveform,discretereturn,andphotoncounting.Fullwaveformsensorsrecordthe740

entiretemporalprofileofthereflectedlaserenergythroughthecanopy.Incontrast,741

discrete return systems have timing hardware that record the time when the742

amplitudeofthereflectedsignalenergyexceedsacertainthresholdamount.Aphoton743

counting system, however, will record the arrival time associated with a single744

photon detection that can occur anywhere within the vertical distribution of the745

reflectedsignal.Ifaphotoncountinglidarsystemweretodwelloverasurfacefora746

significantnumberofshots(i.e.hundredsormore),theverticaldistributionofthe747

reflectedphotonswill resemblea fullwaveform.Thus,whilean individualphoton748

could be reflected from anywhere within the vertical canopy, the probability749

distribution function (PDF) of that reflected photon would be the full waveform.750

Furthermore, the probability of detecting the top of the tree is not as great as751

detecting reflective surfaces positioned deeper into the canopywhere the bulk of752

leavesandbranchesarelocated.Asonemightimagine,thePDFwilldifferaccording753

22

tocanopystructureandvegetationphysiology.Forexample,thePDFofaconifertree754

willlookdifferentthanbroadleaftrees.755

756

Figure 1.1. Various modalities of lidar detection. Adapted from Harding, 2009. 757

Acautionarynote,thephotoncountingPDFthatisillustratedinFigure1.1is758

merelyanillustrationifenoughphotons(i.e.hundredsofphotonsormore)wereto759

bereflectedfromatarget.Inreality,duetothespacecraftspeed,ATLASwillrecord0760

–4photonspertransmitlaserpulseovervegetation.761

762

1.3 TheICESat-2concept763

The Advanced Topographic Laser Altimeter System (ATLAS) instrument764

designed for ICESat-2willutilizeadifferent technology than theGLAS instrument765

usedforICESat.Insteadofusingahigh-energy,single-beamlaseranddigitizingthe766

entire temporal profile of returned laser energy, ATLAS will use a multi-beam,767

micropulselaser(sometimesreferredtoasphoton-counting).Thetraveltimeofeach768

detectedphotonisusedtodeterminearangetothesurfacewhich,whencombined769

withsatelliteattitudeandpointinginformation,canbegeolocatedintoauniqueXYZ770

locationonornear theEarth’ssurface.Formore informationonhowthephotons771

fromICESat-2aregeolocated,refertoATL03ATBD.TheXYZpositionsfromATLAS772

23

are subsequently used to derive surface and vegetation properties. The ATLAS773

instrumentwilloperateat532nminthegreenrangeoftheelectromagnetic(EM)774

spectrumandwillhavealaserrepetitionrateof10kHz.Thecombinationofthelaser775

repetition rate and satellite velocity will result in one outgoing laser pulse776

approximatelyevery70cmontheEarth’ssurfaceandeachspotonthesurfaceis~13777

mindiameter.Eachtransmittedlaserpulseissplitbyadiffractiveopticalelementin778

ATLAS to generate six individualbeams, arranged in threepairs (Figure1.2).The779

beamswithineachpairhavedifferenttransmitenergies(‘weak’and‘strong’,withan780

energyratioofapproximately1:4)tocompensateforvaryingsurfacereflectance.The781

beampairsareseparatedby~3.3kmintheacross-trackdirectionandthestrongand782

weakbeamsareseparatedby~2.5kminthealong-trackdirection.AsICESat-2moves783

alongitsorbit,theATLASbeamsdescribesixtracksontheEarth’ssurface;thearray784

isrotatedslightlywithrespecttothesatellite’sflightdirectionsothattracksforthe785

fore and aft beams in each column produce pairs of tracks – each separated by786

approximately90m.787

24

788

789Figure 1.2. Schematic of 6-beam configuration for ICESat-2 mission. The laser energy will 790

be split into 3 laser beam pairs – each pair having a weak spot (1X) and a strong spot (4X). 791

Themotivation behind thismulti-beam design is its capability to compute792

cross-track slopes on a per-orbit basis, which contributes to an improved793

understandingoficedynamics.Previously,slopemeasurementsoftheterrainwere794

determinedviarepeat-trackandcrossoveranalysis.Thelaserbeamconfigurationas795

proposedforICESat-2isalsobeneficialforterrestrialecosystemscomparedtoGLAS796

asitenablesadenserspatialsamplinginthenon-polarregions.Toachieveaspatial797

samplinggoalofnomorethan2kmbetweenequatorialgroundtracks,ICESat-2will798

be off-nadir pointed a maximum of 1.8 degrees from the reference ground track799

duringtheentiremission.800

2.5 km* 3.305 km*

Weak (1)

Strong (4)

Strong (4)

Weak (1)

Strong (4)

Weak (1)

25

801

Figure 1.3. Illustration of off-nadir pointing scenarios. Over land (green regions) in the 802

mid-latitudes, ICESat-2 will be pointed away from the repeat ground tracks to increase the 803

density of measurements over terrestrial surfaces. 804

ICESat-2 is designed to densely sample the Earth’s surface, permitting805

scientists to measure and quantitatively characterize vegetation across vast806

expanses, e.g., nations, continents, globally. ICESat-2 will acquire synoptic807

measurements of vegetation canopy height, density, the vertical distribution of808

photosyntheticallyactivematerial,leadingtoimprovedestimatesofforestbiomass,809

carbon,andvolume.Inaddition,theorbitaldensity,i.e.,thenumberoforbitsperunit810

area, at theendof the threeyearmissionwill facilitate theproductionof gridded811

globalproducts.ICESat-2willprovidethemeansbywhichanaccurate“snapshot”of812

globalbiomassandcarbonmaybeconstructedforthemissionperiod.813

814

1.4 HeightRetrievalfromATLAS815

LightfromtheATLASlasersreachestheearth’ssurfaceasflatdisksofdown-816

traveling photons approximately 50 cm in vertical extent and spread over817

approximately14mhorizontally.Uponhittingtheearth’ssurface,thephotonsare818

reflected and scattered in every direction and a handful of photons return to the819

26

ATLAS telescope’s focal plane. The number of photon events per laser pulse is a820

functionofoutgoinglaserenergy,surfacereflectance,solarconditions,andscattering821

andattenuationintheatmosphere.Forhighlyreflectivesurfaces(suchaslandice)822

and clear skies, approximately 10 signal photons from a single strong beam are823

expectedtoberecordedbytheATLASinstrumentforagiventransmitlaserpulse.824

Overvegetatedlandwherethesurfacereflectanceisconsiderablylessthansnowor825

ice surfaces,we expect to see fewer returned photons from the surface.Whereas826

snow and ice surfaces have high reflectance at 532 nm (typical Lambertian827

reflectancebetween0.8and0.98(Martino,GSFCinternalreport,2010)),canopyand828

terrainsurfaceshavemuchlowerreflectance(typicallyaround0.3forsoiland0.1for829

vegetation)at532nm.Asaconsequenceweexpecttosee1/3to1/9asmanyphotons830

returned from terrestrial surfaces as from ice and snow surfaces. For vegetated831

surfaces,thenumberofreflectedsignalphotoneventspertransmittedlaserpulseis832

estimatedtorangebetween0to4photons.833

Thetimemeasuredfromthedetectedphotoneventsareusedtocomputea834

range,ordistance,fromthesatellite.Combinedwiththeprecisepointingandattitude835

informationaboutthesatellite,therangecanbegeolocatedintoaXYZpoint(known836

as a geolocated photon) above the WGS-84 reference ellipsoid. In addition to837

recording photons from the reflected signal, the ATLAS instrument will detect838

backgroundphotons fromsunlightwhicharecontinuallyenteringthetelescope.A839

primary objective of the ICESat-2 data processing software is to correctly840

discriminate between signal photons and background photons. Some of this841

processingoccursattheATL03levelandsomeofitalsooccurswithinthesoftware842

forATL08.AtATL03,thisdiscriminationisdonethroughaseriesofthreestepsof843

progressivelyfinerresolutionwithsomeprocessingoccurringonboardthesatellite844

priortodownlinkoftherawdata.TheATL03dataproductproducesaclassification845

betweensignalandbackground(i.e.noise)photons,andfurtherdiscussiononthat846

classificationprocess canbe read in theATL03ATBD. In addition, all geophysical847

corrections (e.g. ocean tide, solid earth tide models, etc.) are not applied to the848

position of the individual geolocated photons at the ATL03 level, but they are849

27

providedon thedataproduct if thereexistsaneed toapply them.Thus,allof the850

heightsprocessedintheATL08algorithmconsistsoftheATL03heightswithrespect851

totheWGS-84ellipsoid.852

853

1.5 AccuracyExpectedfromATLAS854

Thereareavarietyofelementsthatcontributetotheelevationaccuracythat855

are expected from ATLAS and the derived data products. Elevation accuracy is a856

composite of ranging precision of the instrument, radial orbital uncertainty,857

geolocationknowledge,forwardscatteringintheatmosphere,andtroposphericpath858

delayuncertainty.TherangingprecisionseenbyATLASwillbeafunctionofthelaser859

pulsewidth,thesurfaceareapotentiallyilluminatedbythelaser,anduncertaintyin860

thetimingelectronics.Therequirementonradialorbitaluncertaintyisspecifiedto861

belessthan4cmandtroposphericpathdelayuncertaintyisestimatedtobe3cm.In862

the case of ATLAS, the ranging precision for flat surfaces, is expected to have a863

standarddeviationofapproximately25cm.Thecompositeofeachoftheerrorscan864

alsobethoughtofasthespreadofphotonsaboutasurface(seeFigure1.4)andis865

referredtoasthepointspreadfunctionorZnoise.866

867

Figure 1.4. Illustration of the point spread function, also referred to as Znoise, for a series 868

of photons about a surface. 869

The estimates of 𝜎!"#$% , 𝜎%"&'&(')*"* , 𝜎+&",-".(/-%%*"$01, 𝜎'&$0%$01, 𝑎𝑛𝑑𝜎%$2$01870

foraphotonwillberepresentedontheATL03dataproductasthefinalgeolocated871

accuracy in theX,Y, andZ (orheight)direction. In reality, theseparametershave872

differenttemporalandspatialscales,howeveruntilICESat-2isonorbit,itisuncertain873

howtheseparameterswillvaryovertime.Assuch,Equation1.1maychangeoncethe874

28

temporal aspects of these parameters are better understood. For a preliminary875

quantificationoftheuncertainties,Equation1.1isvalidtoincorporatetheinstrument876

relatedfactors.877

𝜎3 = (𝜎!"#$%4 + 𝜎%"&'4 + 𝜎+&",-".(/-%%*"$014 + 𝜎'&$0%$014 + 𝜎%$2$014 Eqn.1.1878

879

Although𝜎3ontheATL03productrepresentsthebestunderstandingofthe880

uncertainty for each geolocated photon, it does not incorporate the uncertainty881

associatedwithlocalslopeofthetopography.Theslopecomponenttothegeolocation882

uncertaintyisafunctionofboththegeolocationknowledgeofthepointing(whichis883

requiredtobelessthan6.5m)multipliedbythetangentofthesurfaceslope.Inacase884

offlattopography(<=1degreeslope),𝜎3<=25cm,whereasinthecaseofa10degree885

surfaceslope,𝜎3 =119cm.Theuncertaintyassociatedwith the local slopewillbe886

combinedwith𝜎3toproducetheterm𝜎5%6-(!"#$ .887

𝜎5%6-(!"#$ = (𝜎34 + 𝜎%&'&4 Eqn.1.2888

𝜎%&'& = Eqn.1.3889

Ultimately,theuncertaintythatwillbereportedonthedataproductATL08890

willincludethe𝜎5%6-(!"#$termandthelocalrmsvaluesofheightscomputedwithin891

each data parameter segment. For example, calculations of terrain height will be892

made on photons classified as terrain photons (this process is described in the893

followingsections).Theuncertaintyoftheterrainheightforasegmentisdescribed894

inEquation1.4,where the rootmeansquare termof𝜎5%6-(!"#$ andrmsof terrain895

heightsarenormalizedbythenumberofterrainphotonsforthatgivensegment.896

𝜎589:;%&'(&#) = (𝜎5%6-(!"#$4 + 𝜎3"2(%&'(&#)_+,"%%

4 Eqn.1.4897

898

29

1.6 AdditionalPotentialHeightErrorsfromATLAS899

Someadditional potential height errors in theATL08 terrain and vegetation900

productcancomefromavarietyofsourcesincluding:901

a. Vertical sampling error. ATLAS height estimates are based on a902

randomsamplingof thesurfaceheightdistribution.Photonsmay903

bereflectedfromanywherewithinthePDFofthereflectingsurface;904

more specifically, anywhere fromwithin the canopy. A detailed905

lookatthepotentialeffectofverticalsamplingerrorisprovidedin906

NeuenschwanderandMagruder(2016).907

b. Background noise. Random noise photons are mixed with the908

signalphotonssoclassifiedphotonswillincluderandomoutliers.909

c. Complex topography. The along-track product may not always910

represent complex surfaces, particularly if the density of ground911

photonsdoesnotsupportanaccuraterepresentation.912

d. Vegetation. Dense vegetation may preclude reflected photon913

eventsfromreachingtheunderlyinggroundsurface.Anincorrect914

estimationoftheunderlyinggroundsurfacewillsubsequentlylead915

toanincorrectcanopyheightdetermination.916

e. Misidentified photons. The product from ATL03 combinedwith917

additionalnoise filteringmaynot identify the correctphotonsas918

signalphotons.919

920

1.7 DenseCanopyCases921

Although the height accuracy produced from ICESat-2 is anticipated to be922

superior to other global height products (e.g. SRTM), for certain biomes photon923

countinglidardataasitwillbecollectedbytheATLASinstrumentpresentachallenge924

for extractingboth the terrain and canopyheights, particularly for areasof dense925

30

vegetation.Duetotherelativelylowlaserpower,weanticipatethatthealong-track926

signal fromATLASmay lose ground signal under dense forest (e.g. >96% canopy927

closure)andinsituationswherecloudcoverobscurestheterrestrialsignal.Inareas928

havingdensevegetation,itislikelythatonlyahandfulofphotonswillbereturned929

fromthegroundsurfacewiththemajorityofreflectionsoccurringfromthecanopy.930

Apossiblesourceoferrorcanoccurwithboththecanopyheightestimatesandthe931

terrainheightsifthevegetationisparticularlydenseandthegroundphotonswere932

notcorrectlyidentified.933

934

1.8 SparseCanopyCases935

Conversely, sparse canopy cases also pose a challenge to vegetation height936

retrievals. In these cases, expected reflected photon events from sparse trees or937

shrubsmaybedifficulttodiscriminatebetweensolarbackgroundnoisephotons.The938

algorithms being developed for ATL08 operate under the assumption that signal939

photonsareclosetogetherandnoisephotonswillbemoreisolatedinnature.Thus,940

signal(inthiscasecanopy)photonsmaybeincorrectlyidentifiedassolarbackground941

noise on the data product. Due to the nature of the photon counting processing,942

canopyphotonsidentifiedinareasthathaveextremelylowcanopycover<15%will943

befilteredoutandreassignedasnoisephotons.944

945

31

2. ATL08:DATAPRODUCT946

TheATL08productwillprovideestimatesof terrainheight, canopyheight,947

andcanopycoveratfinespatialscalesinthealong-trackdirection.Inaccordancewith948

the HDF-driven structure of the ICESat-2 products, the ATL08 product will949

characterize each of the six Ground Tracks (GT) associated with each Reference950

GroundTrack(RGT)foreachcycleandorbitnumber.Eachgroundtrackgrouphasa951

distinct beam number, distance from the reference track, and transmit energy952

strength,andallbeamswillbeprocessedindependentlyusingthesamesequenceof953

stepsdescribedwithinATL08.Eachgroundtrackgroup(GT)ontheATL08product954

contains subgroups for land and canopy heights segments as well as beam and955

referenceparametersusefulintheATL08processing.Inaddition,thelabeledphotons956

thatareusedtodeterminethedataparameterswillbeindexedbacktotheATL03957

productssuchthattheyareavailableforfurther, independentanalysis.Alayoutof958

theATL08HDFproductisshowninFigure2.1.ThesixGTsarenumberedfromleftto959

right,regardlessofsatelliteorientation.960

32

961

Figure 2.1. HDF5 data structure for ATL08 products 962

963

Foreachdataparameter,terrainsurfaceelevationandcanopyheightswillbe964

providedatafixedsegmentsizeof100metersalongthegroundtrack.Basedonthe965

satellitevelocityandtheexpectednumberofreflectedphotonsforlandsurfaces,each966

segmentshouldhavemorethan100signalphotons,butinsomeinstancestheremay967

belessthan100signalphotonspersegment.Ifasegmenthaslessthan50classed968

(i.e., labeled by ATL08 as ground, canopy, or top of canopy) photonswe feel this969

wouldnotaccuratelyrepresentthesurface.Thus,aninvalidvaluewillbereportedin970

33

allheightfields.Intheeventthattherearemorethan50classedphotons,butaterrain971

heightcannotbedeterminedduetoaninsufficientnumberofgroundphotons,(e.g.972

lackofphotonspenetratingthroughdensecanopy),theonlyreportedterrainheight973

willbetheinterpolatedsurfaceheight.974

TheATL08productwillbeproducedpergranulebasedontheATL03defined975

regions(seeFigure2.2).Thus,theATL08file/nameconventionschemewillmatch976

thefile/namingconventionforATL03–inattemptforreducingcomplexitytoallow977

userstoexaminebothdataproducts.978

979

Figure 2.2. ATL03 granule regions; graphic from ATL03 ATBD (Neumann et al.). 980

The ATL08 product additionally has its own internal regions, which are981

roughly assigned by continent, as shown by Figure 2.3. For the regions covering982

Antarctica(regions7,8,9,10)andGreenland(region11),theATL08algorithmwill983

assumethatnocanopyispresent.TheseinternalATL08regionswillbenotedinthe984

ATL08product(seeparameteratl08_regioninSection2.4.19).Notethattheregions985

foreachICESat-2productarenotthesame.986

34

987

Figure 2.3. ATL08 product regions. 988

989

2.1 Subgroup:LandParameters990

ATL08terrainheightparametersaredefinedintermsoftheabsoluteheight991

abovethereferenceellipsoid.992

Table 2.1. Summary table of land parameters on ATL08. 993

Group Datatype Description Sourcesegment_id_beg Integer Firstalong-tracksegment_id

numberin100-msegmentATL03

segment_id_end Integer

Lastalong-tracksegment_idnumberin100-msegment

ATL03

h_te_mean Float Meanterrainheightforsegment

computed

h_te_median Float Medianterrainheightforsegment

computed

h_te_min Float Minimumterrainheightforsegment

computed

h_te_max Float Maximumterrainheightforsegment

computed

h_te_mode Float Modeofterrainheightforsegment

computed

h_te_skew Float Skewofterrainheightforsegment

computed

35

n_te_photons Integer Numberofgroundphotonsinsegment

computed

h_te_interp Float Interpolatedterrainsurfaceheightatmid-pointofsegment

computed

h_te_std Float Standarddeviationofgroundheightsabouttheinterpolatedgroundsurface

computed

h_te_uncertainty Float Uncertaintyofgroundheightestimates.Includesallknownuncertaintiessuchasgeolocation,pointingangle,timing,radialorbiterrors,etc.

computedfromEquation1.4

terrain_slope Float Slopeofterrainwithinsegment

computed

h_te_best_fit Float Bestfitterrainelevationatthe100msegmentmid-pointlocation

computed

subset_te_flag Integer Qualityflagindicatingtheterrainphotonspopulatingthe100msegmentstatisticsarederivedfromlessthan100mworthofphotons

computed

994

2.1.1 Georeferenced_segment_number_beg995

(parameter=segment_id_beg).Thefirstalong-tracksegment_idineach100-m996

segment.Each100-msegmentconsistsof fivesequential20-msegmentsprovided997

fromtheATL03product,whicharelabeledassegment_id.Thesegment_idisaseven998

digitnumberthatuniquelyidentifieseachalongtracksegment,andiswrittenatthe999

along-track geolocation segment rate (i.e. ~20m along track). The four digit RGT1000

numbercanbecombinedwiththesevendigitsegment_idnumbertouniquelydefine1001

anyalong-tracksegmentnumber.Valuesaresequential,with0000001referringto1002

thefirstsegmentaftertheequatorialcrossingoftheascendingnode.1003

2.1.2 Georeferenced_segment_number_end1004

(parameter=segment_id_end).Thelastalong-tracksegment_idineach100-m1005




36





2.1.3 Segment_terrain_height_mean1013

(parameter = h_te_mean). Estimatedmean of the terrain height above the1014

referenceellipsoidderivedfromclassifiedgroundphotonswithinthe100msegment.1015

Ifaterrainheightcannotbedirectlydeterminedwithinthesegment(i.e.therearenot1016

asufficientnumberofgroundphotons),onlytheinterpolatedterrainheightwillbe1017

reported.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledaseither1018

canopyorgroundintheATL08processing).Thisparameterwillbederivedfromonly1019

classifiedgroundphotons.1020

2.1.4 Segment_terrain_height_med1021

(parameter = h_te_median). Median terrain height above the reference1022

ellipsoidderived fromtheclassifiedgroundphotonswithin the100msegment. If1023

therearenotasufficientnumberofgroundphotons,aninvalidvaluewillbereported1024

–no interpolation will be done. Required input data is classified point cloud (i.e.1025

photonslabeledaseithercanopyorgroundintheATL08processing).Thisparameter1026

willbederivedfromonlyclassifiedgroundphotons.1027

2.1.5 Segment_terrain_height_min1028

(parameter=h_te_min).Minimumterrainheightabovethereferenceellipsoid1029

derivedfromtheclassifiedgroundphotonswithinthe100msegment.Ifthereare1030

not a sufficient number of ground photons, an invalid valuewill be reported –no1031

interpolationwillbedone.Requiredinputdataisclassifiedpointcloud(i.e.photons1032

labeledaseithercanopyorgroundintheATL08processing).Thisparameterwillbe1033

derivedfromonlyclassifiedgroundphotons.1034

37

2.1.6 Segment_terrain_height_max1035

(parameter = h_te_max). Maximum terrain height above the reference1036

ellipsoidderived fromtheclassifiedgroundphotonswithin the100msegment. If1037

therearenotasufficientnumberofgroundphotons,aninvalidvaluewillbereported1038

–no interpolationwill be done. Required input data is classified point cloud (i.e.1039

photonslabeledaseithercanopyorgroundintheATL08processing).Thisparameter1040

willbederivedfromonlyclassifiedgroundphotons.1041

2.1.7 Segment_terrain_height_mode1042

(parameter=h_te_mode).Modeoftheclassifiedgroundphotonheightsabove1043

thereferenceellipsoidwithinthe100msegment.Iftherearenotasufficientnumber1044

ofgroundphotons,aninvalidvaluewillbereported–nointerpolationwillbedone.1045

Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledaseithercanopyor1046

groundintheATL08processing).Thisparameterwillbederivedfromonlyclassified1047

groundphotons.1048

2.1.8 Segment_terrain_height_skew1049

(parameter=h_te_skew).Theskewoftheclassifiedgroundphotonswithinthe1050

100msegment. If therearenotasufficientnumberofgroundphotons,an invalid1051

valuewillbereported–nointerpolationwillbedone.Requiredinputdataisclassified1052

pointcloud(i.e.photonslabeledaseithercanopyorgroundintheATL08processing).1053

Thisparameterwillbederivedfromonlyclassifiedgroundphotons.1054

2.1.9 Segment_number_terrain_photons1055

(parameter=n_te_photons).Numberofterrainphotonsidentifiedinsegment.1056

2.1.10 Segmentheight_interp1057

(parameter = h_te_interp). Interpolated terrain surface height above the1058

referenceellipsoid fromATL08processingat themid-pointof each segment.This1059

interpolatedsurfaceistheFINALGROUNDestimate(describedinsection4.9).1060

38

2.1.11 Segmenth_te_std1061

(parameter = h_te_std). Standard deviations of terrain points about the1062

interpolatedground surfacewithin the segment.Providesan indicationof surface1063

roughness.1064

2.1.12 Segment_terrain_height_uncertainty1065

(parameter=h_te_uncertainty).Uncertaintyofthemeanterrainheightforthe1066

segment. This uncertainty incorporates all systematic uncertainties (e.g. timing,1067

orbits,geolocation,etc.)aswellasuncertaintyfromerrorsofidentifiedphotons.This1068

parameterisdescribedinSection1,Equation1.4.Iftherearenotasufficientnumber1069

ofgroundphotons,aninvalidvaluewillbereported–nointerpolationwillbedone.1070


groundintheATL08processing).Thisparameterwillbederivedfromonlyclassified1072

ground photons. The 𝜎(*12*0%/6-((term in Equation 1.4 represents the standard1073

deviationoftheterrainheightresidualsabouttheFINALGROUNDestimate.1074

2.1.13 Segment_terrain_slope1075

(parameter= terrain_slope). Slopeof terrainwithineachsegment.Slope is1076

computedfromalinearfitoftheterrainphotons.Itestimatestherise[m]inrelief1077

overeachsegment[100m];e.g.,iftheslopevalueis0.04,thereisa4mriseoverthe1078

100msegment.Requiredinputdataaretheclassifiedterrainphotons.1079

2.1.14 Segment_terrain_height_best_fit1080

(parameter = h_te_best_fit). The best fit terrain elevation at the mid-point1081

locationofeach100msegment.Themid-segmentterrainelevationisdeterminedby1082

selectingthebestofthreefits–linear,3rdorderand4thorderpolynomials–tothe1083

terrainphotonsandinterpolatingtheelevationatthemid-pointlocationofthe1001084

m segment. For the linear fit, a slope correction andweighting is applied to each1085

groundphotonbasedonthedistancetotheslopeheightatthecenterofthesegment.1086

39

2.1.15 Subset_te_flag{1:5}1087

(parameter = subset_te_flag). This flag indicates the quality distribution of1088

identifiedterrainphotonswithineach100monagesegmentbasis.Thepurposeof1089

thisflagistoprovidetheuserwithanindicationwhetherthephotonscontributingto1090

theterrainestimateareevenlydistributedoronlypartiallydistributed(i.e.dueto1091

cloudcoverorsignalattenuation).A100mATL08segmentiscomprisedof5geo-1092

segmentsandwearepopulatingaflagforeachgeosegment.subset_te_flags:1093

-1:nodatawithingeosegmentavailableforanalysis1094

0:indicatesnogroundphotonswithingeosegment1095

1:indicatesgroundphotonswithingeosegment1096

For example, an 100 m ATL08 segment might have the following1097

subset_te_flags:{-1-1011}whichwouldtranslatethatnosignalphotons(canopyor1098

ground)wereavailableforprocessing inthefirsttwogeosegments.Geosegment31099

wasfoundtohavephotons,butnonewerelabeledasgroundphotons.Geosegment41100

and5hadvalidlabeledgroundphotons.Again,themotivationbehindthisflagisto1101

informtheuserthat,inthisexample,the100mestimatearebeingderivedfromonly1102

40mworthofdata.1103

1104

2.2 Subgroup:VegetationParameters1105

CanopyparameterswillbereportedontheATL08dataproductintermsofboth1106

theabsoluteheightabovethereferenceellipsoidaswellastherelativeheightabove1107

anestimatedground.Therelativecanopyheight,Hi,iscomputedastheheightfrom1108

an identified canopy photonminus the interpolated ground surface for the same1109

horizontalgeolocation(seeFigure2.3).Thus,eachidentifiedsignalphotonabovean1110

interpolated surface (including a buffer distance based on the instrument point1111

spreadfunction)isbydefaultconsideredacanopyphoton.Canopyparameterswill1112

40

only be computed for segmentswheremore than 5% of the classed photons are1113

classifiedascanopyphotons.1114

1115

1116

Figure 2.4. Illustration of canopy photons (red dots) interaction in a vegetated area. 1117

Relative canopy heights, Hi, are computed by differencing the canopy photon height from 1118

an interpolated terrain surface. 1119

Table 2.2. Summary table of canopy parameters on ATL08. 1120

Group Datatype

Description Source

segment_id_beg Integer Firstalong-tracksegment_idnumberin100-msegment

ATL03

segment_id_end Integer Lastalong-tracksegment_idnumberin100-msegment

ATL03

canopy_h_metrics_abs Float Absolute(H##)canopyheightmetricscalculatedatthefollowingpercentiles:25,50,60,70,75,80,85,90,95.

computed

canopy_h_metrics Float Relative(RH##)canopyheightmetricscalculatedatthefollowingpercentiles:25,50,60,70,75,80,85,90,95.

computed

h_canopy_abs Float 98%heightofalltheindividualabsolutecanopyheightsforsegment.

computed

41

h_canopy Float 98%heightofalltheindividualrelativecanopyheightsforsegment.

computed

h_mean_canopy_abs Float Meanofindividualabsolutecanopyheightswithinsegment

computed

h_mean_canopy Float Meanofindividualrelativecanopyheightswithinsegment

computed

h_dif_canopy Float Differencebetweenh_canopyandcanopy_h_metrics(50)

computed

h_min_canopy_abs Float Minimumofindividualabsolutecanopyheightswithinsegment

computed

h_min_canopy Float Minimumofindividualrelativecanopyheightswithinsegment

computed

h_max_canopy_abs Float Maximumofindividualabsolutecanopyheightswithinsegment.ShouldbeequivalenttoH100

computed

h_max_canopy Float Maximumofindividualrelativecanopyheightswithinsegment.ShouldbeequivalenttoRH100

computed

h_canopy_uncertainty Float Uncertaintyoftherelativecanopyheight(h_canopy)

computed

canopy_openness Float STDofrelativeheightsforallphotonsclassifiedascanopyphotonswithinthesegmenttoprovideinferenceofcanopyopenness

computed

toc_roughness Float STDofrelativeheightsofallphotonsclassifiedastopofcanopywithinthesegment

computed

h_canopy_quad Float Quadraticmeancanopyheight computedn_ca_photons Integer4 Numberofcanopyphotonswithin100

msegmentcomputed

n_toc_photons Integer4 Numberoftopofcanopyphotonswithin100msegment

computed

centroid_height Float Absoluteheightabovereferenceellipsoidassociatedwiththecentroidofallsignalphotons

computed

canopy_rh_conf Integer Canopyrelativeheightconfidenceflagbasedonpercentageofgroundandcanopyphotonswithinasegment:0(<5%canopy),1(>5%canopy,<5%ground),2(>5%canopy,>5%ground)

computed

canopy_flag Integer FlagindicatingthatcanopywasdetectedusingtheLandsatTreeCoverContinuousFieldsdataproduct

computed

landsat_flag Integer FlagindicatingthatLandsatTreeCoverContinuousFieldsdataproducthadmorethan50%values>100forL-kmsegment

computed

42

landsat_perc Float Averagepercentagevalueofthevalid(value<=100)LandsatTreeCoverContinuousFieldsproductforeach100msegment

subset_can_flag Integer Qualityflagindicatingthecanopyphotonspopulatingthe100msegmentstatisticsarederivedfromlessthan100mworthofphotons

computed

1121



















2.2.3 Canopy_height_metrics_abs1140

(parameter = canopy_h_metrics_abs). The absolute heightmetrics (H##) of1141

classifiedcanopyphotonsabovetheellipsoid.Theheightmetricsaresortedbasedon1142

acumulativedistributionandcalculatedatthefollowingpercentiles:25,50,60,70,1143

43

75,80,85,90,95.Theseheightmetricsareoftenusedintheliteraturetocharacterize1144

vertical structure of vegetation. One important distinction of these canopy height1145

metricscomparedtothosederivedfromotherlidarsystems(e.g.,LVISorGEDI)is1146

thattheICESat-2canopyheightmetricsareheightsabovethegroundsurface.These1147

metrics do not include the ground photons. Required input data are the absolute1148

canopyheightsofallcanopyphotons.1149

2.2.4 Canopy_height_metrics1150

(parameter=canopy_h_metrics).Relativeheightmetricsabovetheestimated1151

terrainsurface(RH##)ofclassifiedcanopyphotons.Theheightmetricsaresorted1152

basedonacumulativedistributionandcalculatedatthefollowingpercentiles: 25,1153

50,60,70,75,80,85,90,95.Theseheightmetricsareoftenusedintheliteratureto1154

characterize vertical structure of vegetation. One important distinction of these1155

canopyheightmetricscomparedtothosederivedfromotherlidarsystems(e.g.,LVIS1156

orGEDI) is that the ICESat-2 canopyheightmetrics areheights above theground1157

surface.Thesemetricsdonotincludethegroundphotons.Requiredinputdataare1158

relativecanopyheightsabovetheestimatedterrainsurfaceforallcanopyphotons.1159

2.2.5 Absolute_segment_canopy_height1160

(parameter = h_canopy_abs). The absolute 98%height of classified canopy1161

photon heights above the ellipsoid. The absolute height from classified canopy1162

photonsaresortedintoacumulativedistribution,andtheheightassociatedwiththe1163

98%heightisreported.1164

2.2.6 Segment_canopy_height1165

(parameter=h_canopy).Therelative98%heightofclassifiedcanopyphoton1166

heights above the estimated terrain surface. Relative canopy heights have been1167

computed by differencing the canopy photon height from the estimated terrain1168

surface in the ATL08 processing. The relative canopy heights are sorted into a1169

cumulativedistribution,andtheheightassociatedwiththe98%heightisreported.1170

44

2.2.7 Absolute_segment_mean_canopy1171

(parameter=h_mean_canopy_abs).Theabsolutemeancanopyheightforthe1172

segment. Absolute canopy heights are the photons heights above the reference1173

ellipsoid.Theseheightsareaveraged.1174

2.2.8 Segment_mean_canopy1175

(parameter = h_mean_canopy). The mean canopy height for the segment.1176

Relative canopy heights have been computed by differencing the canopy photon1177

heightfromtheestimatedterrainsurfaceintheATL08processing.Theseheightsare1178

averaged.1179

2.2.9 Segment_dif_canopy1180

(parameter=h_dif_canopy).Differencebetweenh_canopyand1181

canopy_h_metrics(50).Thisparameterisonemetricusedtodescribethevertical1182

distributionofthecanopywithinthesegment.1183

2.2.10 Absolute_segment_min_canopy1184

(parameter=h_min_canopy_abs).Theminimumabsolutecanopyheightfor1185

the segment. Required input data is classified point cloud (i.e. photons labeled as1186

eithercanopyorgroundintheATL08processing).1187

2.2.11 Segment_min_canopy1188

(parameter=h_min_canopy). Theminimumrelative canopyheight for the1189

segment.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledaseither1190

canopyorgroundintheATL08processing).1191

2.2.12 Absolute_segment_max_canopy1192

(parameter=h_max_canopy_abs).Themaximumabsolutecanopyheightfor1193

thesegment.ThisproductisequivalenttoH100metricreportedintheliterature.This1194

parameter,however,hasthepotentialforerrorasrandomsolarbackgroundnoise1195

maynothavebeenfullyrejected.Itisrecommendedthath_canopyorh_canopy_abs1196

45

(i.e., the 98% canopy height) be considered as the top of canopy measurement.1197


groundintheATL08processing).1199

2.2.13 Segment_max_canopy1200

(parameter=h_max_canopy). Themaximumrelativecanopyheight for the1201

segment.ThisproductisequivalenttoRH100metricreportedintheliterature.This1202

parameter,however,hasthepotentialforerrorasrandomsolarbackgroundnoise1203

maynothavebeenfullyrejected.Itisrecommendedthath_canopyorh_canopy_abs1204

(i.e., the 98% canopy height) be considered as the top of canopy measurement.1205



2.2.14 Segment_canopy_height_uncertainty1208

(parameter = h_canopy_uncertainty). Uncertainty of the relative canopy1209

height for the segment. This uncertainty incorporates all systematic uncertainties1210

(e.g.timing,orbits,geolocation,etc.)aswellasuncertaintyfromerrorsofidentified1211

photons.Thisparameter isdescribed inSection1,Equation1.4. If therearenota1212

sufficient number of ground photons, an invalid value will be reported –no1213

interpolationwillbedone.Inthecaseforcanopyheightuncertainty,theparameter1214

𝜎(*12*0%/6-((iscomprisedofboththeterrainuncertaintywithinthesegmentbutalso1215

thetopofcanopyresiduals.Requiredinputdataisclassifiedpointcloud(i.e.photons1216

labeledaseithertopofcanopyorgroundintheATL08processing).Thisparameter1217

will be derived from only classified top of canopy photons. The canopy height1218

uncertaintyisderivedfromEquation1.4,shownbelowasEquation1.5,represents1219

thestandarddeviationoftheterrainpointsandthestandarddeviationofthetopof1220

canopyheightphotons.1221

𝜎589:;%&'(&#)_/) = Eqn1.51222

1223

46

2.2.15 Segment_canopy_openness1224

(parameter = canopy_openness). Standard deviation of relative canopy1225

heightswithineachsegment.Thisparameterwillpotentiallyprovideanindicatorof1226

canopy openness as a greater standard deviation of heights indicates greater1227

penetrationofthelaserenergyintothecanopy.Requiredinputdataisclassifiedpoint1228

cloud(i.e.photonslabeledaseithercanopyorgroundintheATL08processing).1229

2.2.16 Segment_top_of_canopy_roughness1230

(parameter = toc_roughness). Standard deviation of relative top of canopy1231

heightswithineachsegment.Thisparameterwillpotentiallyprovideanindicatorof1232

canopyvariability.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeled1233

asthetopofthecanopyintheATL08processing).1234

2.2.17 Segment_canopy_quadratic_height1235

(parameter=h_canopy_quad).Thequadraticmeanrelativeheightofclassified1236

canopyphotons.Thequadraticmeanheightiscomputedas:1237

𝑞𝑚ℎ = - .ℎ$4

𝑛_𝑐𝑎_𝑝ℎ𝑜𝑡𝑜𝑛𝑠

0_/-_')&%&0(

$=>

1238

2.2.18 Segment_number_canopy_photons1239

(parameter=n_ca_photons).Numberofcanopyphotonswithineachsegment.1240



2.2.19 Segment_number_top_canopy_photons1243

(parameter=n_toc_photons).Numberoftopofcanopyphotonswithineach1244

segment.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledastopof1245

canopyintheATL08processing).1246

47

2.2.20 Centroid_height1247

(parameter= centroid_height). Optical centroidof all photons classifiedas1248

eithercanopyorgroundpointswithinasegment.Theheightsusedinthiscalculation1249

areabsoluteheightsabovethereferenceellipsoid.Thisparameterisequivalenttothe1250

centroidheightproducedonICESatGLA14.1251

2.2.21 Segment_rel_canopy_conf1252

(parameter=canopy_rh_conf).Canopyrelativeheightconfidenceflagbased1253

onpercentageofgroundphotonsandpercentageofcanopyphotons,relativetothe1254

totalclassified(groundandcanopy)photonswithinasegment:0(<5%canopy),11255

(>5%canopyand<5%ground),2(>5%canopyand>5%ground).Thisisameasure1256

basedonthequantity,notthequality,oftheclassifiedphotonsineachsegment.1257

2.2.22 Canopy_flag1258

(parameter=canopy_flag).Flagindicatingthatcanopywasdetectedusingthe1259

LandsatContinuousCoverproductfortheL-kmsegment.Currently,ifmorethan3%1260

of the Landsat CC pixels along the profile have canopy in them, we make the1261

assumptioncanopyispresentalongtheentireL-kmsegment.1262

2.2.23 Landsat_flag1263

(parameter=landsat_flag).Flagindicatingthatmorethan50%oftheLandsat1264

Tree Cover Continuous Fields product have values >100 (indicatingwater, cloud,1265

shadow,orfilledvalues)fortheL-kmsegment.Canopyisassumedpresentalongthe1266

L-kmsegmentiflandsat_flagis1.1267

2.2.24 Landsat_perc1268

(parameter= landsat_perc). Averagepercentagevalueof thevalid(value<=1269

100)LandsatTreeCoverContinuousFieldsproductpixelsthatoverlapwithineach1270

100msegment.1271

48

2.2.25 Subset_can_flag{1:5}1272

(parameter=subset_can_flag).Thisflagindicatesthedistributionofidentified1273

canopyphotonswithineach100m.Thepurposeofthis flag istoprovidetheuser1274

withanindicationwhetherthephotonscontributingtothecanopyheightestimates1275

areevenlydistributedoronlypartiallydistributed(i.e.duetocloudcoverorsignal1276

attenuation). A 100 m ATL08 segment is comprised of 5 geo-segments.1277

subset_can_flags:1278

-1:nodatawithingeosegmentavailableforanalysis1279

0:indicatesnocanopyphotonswithingeosegment1280

1:indicatescanopyphotonswithingeosegment1281

For example, a 100 m ATL08 segment might have the following1282

subset_can_flags: {-1 -1 -111}whichwould translate thatnophotons (canopyor1283

ground)wereavailableforprocessinginthefirstthreegeosegments.Geosegment41284

and5hadvalidlabeledcanopyphotons.Again,themotivationbehindthisflagisto1285

informtheuserthat,inthisexample,the100mestimatearebeingderivedfromonly1286

40mworthofdata.1287

1288

1289

2.3 Subgroup:Photons1290

The subgroup for photons contains the classified photons thatwere used to1291

generatetheparameterswithinthelandorcanopysubgroups.Eachphotonthatis1292

identifiedasbeinglikelysignalwillbeclassifiedas:0=noise,1=ground,2=canopy,1293

or3=topofcanopy.Theindexvaluesforeachclassifiedphotonwillbeprovidedsuch1294

thattheycanbeextractedfromtheATL03dataproductforindependentevaluation.1295

Table 2.3. Summary table for photon parameters for the ATL08 product. 1296

Group DataType Description Source

49

classed_PC_indx Float IndicesofphotonstrackingbacktoATL03thatsurfacefindingsoftwareidentifiedandusedwithinthecreationofthedataproducts.

ATL03

classed_PC_flag Integer Classificationflagforeachphotonaseithernoise,ground,canopy,ortopofcanopy.

computed

ph_segment_id Integer Georeferencedbinnumber(20-m)associatedwitheachphoton

ATL03

d_flag Integer FlagindicatingwhetherDRAGANNlabeledthephotonasnoiseorsignal

computed

1297

2.3.1 Indices_of_classed_photons1298

(parameter=classed_PC_indx).IndicesofphotonstrackingbacktoATL03that1299

surfacefindingsoftwareidentifiedandusedwithinthecreationofthedataproducts1300

foragivensegment.1301

2.3.2 Photon_class1302

(parameter = classed_PC_flag).Classification flags for a given segment. 0 =1303

noise, 1 = ground, 2 = canopy, 3 = top of canopy. The final ground and canopy1304

classificationareflags1-3.Thefullcanopyisthecombinationofflags2and3.1305

2.3.3 Georeferenced_segment_number1306

(parameter=ph_segment_id).Thesegment_idassociatedwitheveryphotonin1307

each100-msegment.Each100-msegmentconsistsoffivesequential20-msegments1308

providedfromtheATL03product,whicharelabeledassegment_id.Thesegment_id1309

is a seven digit number that uniquely identifies each along track segment, and is1310

writtenatthealong-trackgeolocationsegmentrate(i.e.~20malongtrack).Thefour1311

digit RGT number can be combined with the seven digit segment_id number to1312

uniquely define any along-track segment number. Values are sequential, with1313

50

0000001referringtothefirstsegmentaftertheequatorialcrossingoftheascending1314

node.1315

2.3.4 DRAGANN_flag1316

(parameter=d_flag).FlagindicatingthelabelingofDRAGANNnoisefilteringfor1317

agivenphoton.0=noise,1=signal.1318

1319

2.4 Subgroup:Referencedata1320

Thereferencedatasubgroupcontainsparametersand information thatare1321

useful for determining the terrain and canopy heights that are reported on the1322

product.Inadditiontopositionandtiminginformation,theseparametersincludethe1323

referenceDEMheight,referencelandcovertype,andflagsindicatingwaterorsnow.1324

Table 2.4. Summary table for reference parameters for the ATL08 product. 1325

Group DataType

Description Source


ATL03


ATL03

latitude Float Centerlatitudeofsignalphotonswithineachsegment

ATL03

longitude Float Centerlongitudeofsignalphotonswithineachsegment

ATL03

delta_time Float Mid-segmentGPStimeinsecondspastanepoch.Theepochisprovidedinthemetadataatthefilelevel

ATL03

delta_time_beg Float Deltatimeofthefirstphotoninthesegment

ATL03

delta_time_end Float Deltatimeofthelastphotoninthesegment

ATL03

night_flag Integer Flagindicatingwhetherthemeasurementswereacquiredduringnighttimeconditions

computed

dem_h Float4 ReferenceDEMelevation externaldem_flag SourceofreferenceDEM external

51

dem_removal_flag Integer Qualitycheckflagtoindicate>20%photonsremovedduetolargedistancefromdem_h

computed

h_dif_ref Float4 Differencebetweenh_te_mediananddem_h

computed

terrain_flg Integer TerrainflagqualitychecktoindicateadeviationfromthereferenceDTM

computed

segment_landcover Integer4 Referencelandcoverforsegmentderivedfrombestgloballandcoverproductavailable

external

segment_watermask Integer4 Watermaskindicatinginlandwaterproducedfrombestsourcesavailable

external

segment_snowcover Integer4 Dailysnowcovermaskderivedfrombestsources

external

urban_flag Integer Flagindicatingsegmentislocatedinanurbanarea

external

surf_type Integer1 Flagsdescribingsurfacetypes:0=nottype,1=istype.Orderofarrayisland,ocean,seaice,landice,inlandwater.

ATL03

atl08_region Integer ATL08region(s)encompassedbyATL03granulebeingprocessed

computed

last_seg_extend Float Thedistance(km)thatthelastATL08processingsegmentinafileiseitherextendedoroverlappedwiththepreviousATL08processingsegment

computed

brightness_flag Integer Flagindicatingthatthegroundsurfaceisbright(e.g.snow-coveredorotherbrightsurfaces)

computed

1326






52














2.4.3 Segment_latitude1345

(parameter=latitude).Centerlatitudeofsignalphotonswithineachsegment.1346

Each100msegmentconsistsof520mATL03geosegments.Inmostcases,therewill1347

besignalphotonsineachofthe5geosegmentsnecessaryforcalculatingalatitude1348

value.Forinstanceswherethe100mATL08isnotfullypopulatedwithphotons(e.g.1349

photonsdropoutduetocloudsorsignalattenuation),thelatitudewillbeinterpolated1350

tothemid-pointofthe100msegment.Toimplementthisinterpolation,weconfirm1351

thateach100msegmentiscomprisedofatleast3uniqueATL03geosegmentsIDs,1352

indicatingthatdataisavailablenearthemid-pointofthelandsegment.Iflessthan31353

ATL03segmentsareavailable, thecoordinate is interpolatedbasedontheratioof1354

deltatimeatthecentermostATL03segmentandthatofthecentermostphoton,thus1355

applyingthecentermostphoton’scoordinatestorepresentthelandsegmentwitha1356

slight adjustment. In some instances, the latitude and longitude will require1357

extrapolationtoestimateamid-100msegmentlocation.Itispossiblethatinthese1358

extremelyrarecases,thelatitudeandlongitudecouldnotrepresentthetruecenter1359

of the 100 m segment. We encourage the user to investigate the parameters1360

53

segment_te_flagandsegment_can_flagwhichprovideinformationastothenumber1361

anddistributionofsignalphotonswithineach100msegment.1362

2.4.4 Segment_longitude1363

(parameter = longitude). Center longitude of signal photons within each1364

segment.Each100msegmentconsistsof520mgeosegments.Inmostcases,there1365

will be signal photons in each of the 5 geosegments necessary for calculating a1366

longitudevalue.For instanceswherethe100mATL08 isnot fullypopulatedwith1367

photons(e.g.photonsdropoutduetocloudsorsignalattenuation),thelatitudewill1368

be interpolated to the mid-point of the 100 m segment. To implement this1369

interpolation,weconfirmthateach100msegmentiscomprisedofatleast3unique1370

ATL03geosegmentsIDs, indicatingthatdata isavailablenearthemid-pointofthe1371

land segment. If less than 3 ATL03 segments are available, the coordinate is1372

interpolatedbasedontheratioofdeltatimeatthecentermostATL03segmentand1373

thatofthecentermostphoton,thusapplyingthecentermostphoton’scoordinatesto1374

representthelandsegmentwithaslightadjustment.Insomeinstances,thelatitude1375

andlongitudewillrequireextrapolationtoestimateamid-100msegmentlocation.It1376

ispossible that in theseextremelyrarecases, the latitudeand longitudecouldnot1377

representthetruecenterofthe100msegment.Weencouragetheusertoinvestigate1378

theparamterssegment_te_flagandsegment_can_flagwhichprovideinformationasto1379

thenumberanddistributionofsignalphotonswithineach100msegment.1380

2.4.5 Delta_time1381

(parameter=delta_time).Mid-segmentGPStimeforthesegmentinseconds1382

pastanepoch.Theepochislistedinthemetadataatthefilelevel.1383

2.4.6 Delta_time_beg1384

(parameter=delta_time_beg).Deltatimeforthefirstphotoninthesegment1385

insecondspastanepoch.Theepochislistedinthemetadataatthefilelevel.1386

54

2.4.7 Delta_time_end1387

(parameter=delta_time_end).Deltatimeforthelastphotoninthesegment1388

insecondspastanepoch.Theepochislistedinthemetadataatthefilelevel.1389

2.4.8 Night_Flag1390

(parameter = night_flag). Flag indicating the data were acquired in night1391

conditions: 0=day, 1=night.Night flag is setwhen solar elevation is below0.01392

degrees.1393

2.4.9 Segment_reference_DTM1394

(parameter=dem_h).Referenceterrainheightvalueforsegmentdetermined1395

by the “best” DEM available based on data location. All heights in ICESat-2 are1396

referencedtotheWGS84ellipsoidunlessclearlynotedotherwise.DEMistakenfrom1397

avarietyofancillarydatasources:GIMP,GMTED,MSS.TheDEMsourceflagindicates1398

whichsourcewasused.1399

2.4.10 Segment_reference_DEM_source1400

(parameter=dem_flag).IndicatessourceofthereferenceDEMheight.Values:1401

0=None,1=GIMP,2=GMTED,3=MSS.1402

2.4.11 Segment_reference_DEM_removal_flag1403

(parameter = dem_removal_flag). Quality check flag to indicate > 20%1404

classifiedphotonsremovedfromlandsegmentduetolargedistancefromdem_h.1405

2.4.12 Segment_terrain_difference1406

(parameter=h_dif_ref).Differencebetweenh_te_mediananddem_h.Sincethe1407

meanterrainheightismoresensitivetooutliers,themedianterrainheightwillbe1408

evaluatedagainstthereferenceDEM.Thisparameterwillbeusedasaninternaldata1409

qualitycheckwiththenotionbeingthatifthedifferenceexceedsathreshold(TBD)a1410

terrainqualityflag(terrain_flg)willbetriggered.1411

55

2.4.13 Segment_terrainflag1412

(parameter= terrain_flg).Terrain flag to indicateconfidence in thederived1413

terrain height estimate. If h_dif_ref exceeds a threshold (TBD) the terrain_flg1414

parameterwillbesetto1.Otherwise,itis0.1415

2.4.14 Segment_landcover1416

(parameter=segment_landcover).Segmentlandcoverwillbebasedonbest1417

availablegloballandcoverproductusedforreference.Onepotentialsourceisthe0.51418

kmglobalmosaicsofthestandardMODISlandcoverproduct(Channanetal,2015;1419

Friedletal,2010;availableonlineathttp://glcf.umd.edu/data/lc/index.shtml).Here,1420

17 classes are defined ranging from evergreen (needle and broadleaf forest),1421

deciduous (needle and broadleaf forest), shrublands, woodlands, savanna and1422

grasslands,agriculture,tourban.Themostcurrentyearprocessedforthisproductis1423

basedonMODISmeasurementsfrom2012.1424

2.4.15 Segment_watermask1425

(parameter=segment_watermask).Watermask(i.e., flag) indicating inland1426

waterasreferencedfromtheGlobalRasterWaterMaskat250mspatialresolution1427

(Carrolletal,2009;availableonlineathttp://glcf.umd.edu/data/watermask/).0=1428

nowater;1=water.1429

2.4.16 Segment_snowcover1430

(parameter = segment_snowcover). Daily snowcover mask (i.e., flag)1431

indicatingalikelypresenceofsnoworicewithineachsegmentproducedfrombest1432

availablesourceusedforreference.Thesnowmaskwillbethesamesnowmaskas1433

used for ATL09 Atmospheric Products: NOAA snow-ice flag. 0=ice free water;1434

1=snowfreeland;2=snow;3=ice.1435

2.4.17 Urban_flag1436

(parameter = urban_flag). The urban flag indicates that a segment is likely1437

locatedoveranurbanarea.Intheseareas,buildingsmaybemisclassifiedascanopy,1438

56

andthusthecanopyproductsmaybeincorrect.Theurbanflagissourcedfromthe1439

“urbanandbuiltup”classificationontheMODISlandcoverproduct(Channanetal,1440

2015; Friedl et al, 2010; available online at1441

http://glcf.umd.edu/data/lc/index.shtml).0=noturban;1=urban.1442

2.4.18 Surface_type1443

(parameter=surf_type).Thesurfacetypeforagivensegmentisdeterminedat1444

themajor framerate(every200shots,or~140metersalong-track)and isa two-1445

dimensionalarraysurf_type(n,nsurf),wherenisthemajorframenumber,andnsurf1446

isthenumberofpossiblesurfacetypessuchthatsurf_type(n,isurf) issetto0or11447

indicatingifsurfacetypeisurf ispresent(1)ornot(0),whereisurf=1to5(land,1448

ocean,seaice,landice,andinlandwater)respectively.1449

2.4.19 ATL08_region1450

(parameter = atl08_region). The ATL08 regions that encompass the ATL031451

granulebeingprocessedthroughtheATL08algorithm.TheATL08regionsareshown1452

by Figure 2.3. In ATL08 regions 11 (Greenland) and 7 – 10 (Antarctica), the1453

canopy_flagisautomaticallysettofalseforATL08processing.1454

2.4.20 Last_segment_extend1455

(parameter= last_seg_extend).Thedistance (km) that the lastATL0810km1456

processingsegmentiseitherextendedbeyond10kmorusesdatafromtheprevious1457

10kmprocessingsegmenttoallowforenoughdataforprocessingtheATL03photons1458

throughtheATL08algorithm.IfthelastportionofanATL03granulebeingprocessed1459

wouldresultinasegmentwithlessthan3.4km(170geosegments)worthofdata,1460

thatlastportionisaddedtotheprevious10kmprocessingwindowtobeprocessed1461

togetherasoneextendedATL08processingsegment.Theresultinglast_seg_extend1462

valuewouldbeapositivevalueofdistancebeyond10kmthattheATL08processing1463

segmentwasextendedby.IfthelastATL08processingsegmentwouldbelessthan1464

10kmbutgreaterthan3.4km,aportionextendingfromthestartofcurrentATL081465

processingsegmentbackwardsintothepreviousATL08processingsegmentwould1466

57

beaddedtothecurrentATL08processingsegmenttomakeit10kminlength.The1467

distanceofthisbackwarddatagatheringwouldbereportedinlast_seg_extendasa1468

negativedistancevalue.Onlynew100mATL08segmentproductsgeneratedfrom1469

thisbackwardextensionwouldbereported.Allothersegmentsthatarenotextended1470

willreportalast_seg_extendvalueof0.1471

2.4.21 Brightness_flag1472

(parameter = brightness_flag). Based upon the classification of the photons1473

withineach100m,thisparameterflagsATL08segmentswherethemeannumberof1474

groundphotonspershotexceedavalueof3.Thiscalculationcanbemadeasthetotal1475

numberofgroundphotonsdividedbythenumberofATLASshotswithinthe100m1476

segment. A value of 0 = indicates non-bright surface, value of 1 indicates bright1477

surface,andavalueof2indicates“undetermined”duetocloudsorotherfactors.The1478

brightness is computed initially on the 10 km processing segment. If the ground1479

surfaceisdeterminedtobebrightfortheentire10kmsegment,thebrightnessisthen1480

calculatedatthe100msegmentsize.1481

1482

2.5 Subgroup:Beamdata1483

Thesubgroupforbeamdatacontainsbasicinformationonthegeometryand1484

pointingaccuracyforeachbeam.1485

Table 2.5. Summary table for beam parameters for the ATL08 product. 1486

Group DataType

Units Description Source


ATL03


ATL03

ref_elev Float Elevationoftheunitpointingvectorforthereferencephotoninthe

ATL03

58

localENUframeinradians.TheangleismeasuredfromEast-Northplaneandpositivetowardsup

ref_azimith Float AzimuthoftheunitpointingvectorforthereferencephotonintheENUframeinradians.TheangleismeasuredfromNorthandpositivetowardEast.

ATL03

atlas_pa Float Offnadirpointingangleofthespacecraft

ATL03

rgt Integer Thereferencegroundtrack(RGT)isthetrackontheearthatwhichthevectorbisectinglaserbeams3and4ispointedduringrepeatoperations

ATL03

sigma_h Float TotalverticaluncertaintyduetoPPDandPOD

ATL03

sigma_along Float Totalalong-trackuncertaintyduetoPPDandPODknowledge

ATL03

sigma_across Float Totalcross-trackuncertaintyduetoPPDandPODknowledge

ATL03

sigma_topo Float Uncertaintyofthegeolocationknowledgeduetolocaltopography(Equation1.3)

computed

sigma_atlas_land Float Totaluncertaintythatincludessigma_hplusthegeolocationuncertaintyduetolocalslopeEquation1.2

computed

psf_flag integer Flagindicatingsigma_atlas_land(akaPSF)ascomputedinEquation1.2exceedsavalueof1m.

computed

layer_flag Integer Cloudflagindicatingpresenceofcloudsorblowingsnow

ATL09

59

cloud_flag_atm Integer CloudconfidenceflagfromATL09indicatingclearskies

ATL09

msw_flag Integer MultiplescatteringwarningproductproducedonATL09

ATL09

cloud_fold_flag integer Cloudflagtoindicatepotentialofhighcloudsthathave“folded”intothelowerrangebins

ATL09

asr Float Apparentsurfacereflectance

ATL09

snr Float Backgroundsignaltonoiselevel

Computed

solar_azimuth Float Theazimuth(indegrees)ofthesunpositionvectorfromthereferencephotonbouncepointpositioninthelocalENUframe.TheangleismeasuredfromNorthandispositivetowardsEast.

ATL03g

solar_elevation Float TheelevationofthesunpositionvectorfromthereferencephotonbouncepointpositioninthelocalENUframe.TheangleismeasuredfromtheEast-NorthplaneandispositiveUp.

ATL03g

n_seg_ph Integer Numberofphotonswithineachlandsegment

computed

ph_ndx_beg Integer Photonindexbegin computed1487







60













2.5.3 Beam_coelevation1506

(parameter=ref_elev).Elevationoftheunitpointingvectorforthereference1507

photon in the localENU frame in radians.Theangle ismeasured fromEast-North1508

planeandpositivetowardsup.1509

2.5.4 Beam_azimuth1510

(parameter = ref_azimuth). Azimuth of the unit pointing vector for the1511

referencephotonintheENUframeinradians.TheangleismeasuredfromNorthand1512

positivetowardEast.1513

2.5.5 ATLAS_Pointing_Angle1514

(parameter=atlas_pa).Offnadirpointingangle(inradians)ofthesatelliteto1515

increasespatialsamplinginthenon-polarregions.1516

2.5.6 Reference_ground_track1517

(parameter=rgt).Thereferencegroundtrack(RGT)isthetrackontheearth1518

atwhich thevectorbisecting laserbeams3and4 (orGT2LandGT2R) ispointed1519

61

duringrepeatoperations.EachRGTspansthepartofanorbitbetweentwoascending1520

equatorcrossingsandarenumberedsequentially. TheICESat-2missionhas13871521

RGTs,numberedfrom0001xxto1387xx.Thelasttwodigitsrefertothecyclenumber.1522

2.5.7 Sigma_h1523

(parameter=sigma_h).TotalverticaluncertaintyduetoPPD(PrecisePointing1524

Determination), POD (Precise Orbit Determination), and geolocation errors.1525

Specifically, this parameter includes radial orbit error,𝜎!"#$% , tropospheric errors,1526

𝜎8"&',forwardscatteringerrors,𝜎+&",-".(/-%%*"$01,instrumenttimingerrors,𝜎%$2$01,1527

and off-nadir pointing geolocation errors. The component parameters are pulled1528

fromATL03andATL09.Sigma_histherootsumofsquaresofthesetermsasdetailed1529

inEquation1.1.Thesigma_hreportedhereisthemeanofthesigma_hvaluesreported1530

withinthefiveATL03geosegmentsthatareusedtocreatethe100mATL08segment.1531

2.5.8 Sigma_along1532

(parameter=sigma_along).Totalalong-trackuncertaintyduetoPPDandPOD1533

knowledge.ThisparameterispulledfromATL03.1534

2.5.9 Sigma_across1535

(parameter = sigma_across).Total cross-track uncertainty due to PPD and1536

PODknowledge.ThisparameterispulledfromATL03.1537

2.5.10 Sigma_topo1538

(parameter=sigma_topo).Uncertaintyinthegeolocationduetolocalsurface1539

slope as described in Equation 1.3. The local slope is multiplied by the 6.5 m1540

geolocation uncertainty factor that will be used to determine the geolocation1541

uncertainty.Thegeolocationerrorwillbecomputedfroma100msampleduetothe1542

localslopecalculationatthatscale.1543

62

2.5.11 Sigma_ATLAS_LAND1544

(parameter = sigma_atlas_land). Total vertical geolocation error due to1545

ranging,andlocalsurfaceslope.TheparameteriscomputedforATL08asdescribed1546

inEquation1.2.Thegeolocationerrorwillbecomputedfroma100msampledueto1547

thelocalslopecalculationatthatscale.1548

2.5.12 PSF_flag1549

(parameter = psf_flag). Flag indicating that the point spread function1550

(computedassigma_atlas_land)hasexceeded1m.1551

2.5.13 Layer_flag1552

(parameter= layer_flag).Flag isacombinationofmultipleATL09 flagsand1553

takesdaytime/nighttime intoconsideration.Avalueof1meanscloudsorblowing1554

snowislikelypresent.Avalueof0indicatesthelikelyabsenceofcloudsorblowing1555

snow.IfnoATL09productisavailableforanATL08segment,aninvalidvaluewillbe1556

reported.SincethecloudflagsfromtheATL09productarereportedatanalong-track1557

distanceof250m,wewillreportthehighestvalueoftheATL09flagsattheATL081558

resolution (100m). Thus, if a 100m ATL08 segment straddles two values from1559

ATL09,thehighestcloudflagvaluewillbereportedonATL08.Thisreportingstrategy1560

holdsforallthecloudflagsreportedonATL08.1561

2.5.14 Cloud_flag_atm1562

(parameter=cloud_flag_atm).CloudconfidenceflagfromATL09thatindicates1563

thenumberofcloudoraerosollayersidentifiedineach25Hzatmosphericprofile.If1564

theflagisgreaterthan0,aerosolsorcloudscouldbepresent.1565

2.5.15 MSW1566

(parameter=msw_flag).Multiplescatteringwarningflagwithvaluesfrom-1to1567

5ascomputedintheATL09atmosphericprocessinganddeliveredontheATL09data1568

product.IfnoATL09productisavailableforanATL08segment,aninvalidvaluewill1569

bereported.MSWflags:1570

63

-1=signaltonoiseratiotoolowtodeterminepresenceof1571

cloudorblowingsnow1572

0=no_scattering1573

1=cloudsat>3km1574

2=cloudsat1-3km1575

3=cloudsat<1km1576

4=blowingsnowat<0.5opticaldepth1577

5=blowingsnowat>=0.5opticaldepth1578

2.5.16 CloudFoldFlag1579

(parameter=cloud_fold_flag).Cloudsoccurringhigherthan14to15kminthe1580

atmospherewillbefoldeddownintothelowerportionoftheatmosphericprofile. 1581

2.5.17 Computed_Apparent_Surface_Reflectance1582

(parameter = asr). Apparent surface reflectance computed in the ATL091583

atmospheric processing and delivered on the ATL09 data product. If no ATL091584

productisavailableforanATL08segment,aninvalidvaluewillbereported.1585

2.5.18 Signal_to_Noise_Ratio1586

(parameter = snr). The Signal to Noise Ratio of geolocated photons as1587

determinedbytheratioofthesupersetofATL03signalandDRAGANNfoundsignal1588

photonsused forprocessing theATL08segments to thebackgroundphotons (i.e.,1589

noise)withinthesameATL08segments.1590

2.5.19 Solar_Azimuth1591

(parameter=solar_azimuth).Theazimuth(indegrees)ofthesunposition1592

vectorfromthereferencephotonbouncepointpositioninthelocalENUframe.The1593

angleismeasuredfromNorthandispositivetowardsEast.1594

64

2.5.20 Solar_Elevation1595

(parameter=solar_elevation).Theelevationofthesunpositionvectorfrom1596

thereferencephotonbouncepointpositioninthelocalENUframe.Theangleis1597

measuredfromtheEast-Northplaneandispositiveup.1598

2.5.21 Number_of_segment_photons1599

(parameter=n_seg_ph).Numberofphotonsineachlandsegment.1600

2.5.22 Photon_Index_Begin1601

(parameter=ph_ndx_beg).Index(1-based)withinthephoton-ratedataof1602

thefirstphotonwithinthiseachlandsegment.1603

1604

1605

65

3 ALGORITHMMETHODOLOGY1606

Fortheecosystemcommunity,identificationofthegroundandcanopysurface1607

isbyfarthemostcriticaltask,asmeetingthescienceobjectiveofdeterminingglobal1608

canopy heights hinges upon the ability to detect both the canopy surface and the1609

underlyingtopography.Sinceaspace-basedphotoncountinglasermappingsystem1610

is a relatively new instrument technology for mapping the Earth’s surface, the1611

software to accurately identify and extract both the canopy surface and ground1612

surface is described here. The methodology adopted for ATL08 establishes a1613

frameworktopotentiallyacceptmultipleapproaches forcapturingboththeupper1614

and lower surface of signal photons. Onemethod used is an iterative filtering of1615

photons in thealong-trackdirection.Thismethodhasbeen found topreserve the1616

topographyandcapturecanopyphotons,whilerejectingnoisephotons.Anadvantage1617

of this methodology is that it is self-parameterizing, robust, and works in all1618

ecosystemsifsufficientphotonsfromboththecanopyandgroundareavailable.For1619

processingpurposes,along-trackdatasignalphotonsareparsedintoL-kmsegment1620

oftheorbitwhichisrecommendedtobe10kminlength.1621

1622

3.1 NoiseFiltering 1623

Solar background noise is a significant challenge in the analysis of photon1624

counting laser data. Rangemeasurement data created fromphoton counting lidar1625

detectors typically contain far higher noise levels than themore common photon1626

integrating detectors available commercially in the presence of passive, solar1627

background photons. Given the higher detection sensitivity for photon counting1628

devices,abackgroundphotonhasagreaterprobabilityoftriggeringadetectionevent1629

over traditional integralmeasurementsandmaysometimesdominate thedataset.1630

Solar background noise is a function of the surface reflectance, topography, solar1631

elevation, and atmospheric conditions. Prior to running the surface finding1632

algorithms used for ATL08 data products, the superset of output from the GSFC1633

medium-highconfidenceclassedphotons(ATL03signal_conf_ph:flags3-4)andthe1634

66

output fromDRAGANNwillbeconsideredas the inputdataset.ATL03 inputdata1635

requirementsincludethelatitude,longitude,height,segmentdeltatime,segmentID,1636

and a preliminary signal classification for each photon. The motivation behind1637

combiningtheresultsfromtwodifferentnoisefilteringmethodsistoensurethatall1638

of the potential signal photons for land surfaceswill be provided as input to the1639

surface finding software. The description of the methodology for the ATL031640

classificationisdescribedseparatelyintheATL03ATBD.Themethodologybehind1641

DRAGANNisdescribedinthefollowingsection.1642

1643

1644

Figure 3.1. Combination of noise filtering algorithms to create a superset of input data for 1645

surface finding algorithms. 1646

1647

3.1.1 DRAGANN1648

The Differential, Regressive, and Gaussian Adaptive Nearest Neighbor1649

(DRAGANN)filteringtechniquewasdevelopedtoidentifyandremovenoisephotons1650

fromthephotoncountingdatapointcloud.DRAGANNutilizesthebasicpremisethat1651

signalphotonswillbecloserinspacethanrandomnoisephotons.Thefirststepofthe1652

filteringistoimplementanadaptivenearestneighborsearch.Byusinganadaptive1653

method, different thresholds can be applied to account for variable amounts of1654

backgroundnoiseandchangingsurfacereflectancealongthedataprofile.Thissearch1655

findsaneffectiveradiusbycomputingtheprobabilityoffindingPnumberofpoints1656

withinasearcharea.ForMABELandmATLAS,P=20pointswithinthesearcharea1657

67

was empirically derived but found to be an effective and efficient number of1658

neighbors.1659

Theremaybecases,however,wherethevalueofPneedstobechanged.For1660

example,duringnightacquisitionsitisanticipatedthatthebackgroundnoiseratewill1661

be considerably low. Since DRAGANN is searching for two distributions in1662

neighborhoodsearchingspace,thesoftwarecouldincorrectlyidentifysignalphotons1663

asnoisephotons.TheparameterP,however,canbedetermineddynamically from1664

estimations of the signal and noise rates from the photon cloud. In cases of low1665

background noise (night), P would likely be changed to a value lower than 20.1666

Similarly,incasesofhighamountsofsolarbackground,Pmayneedtobeincreased1667

tobetter capture the signal andavoid classifying small, dense clustersofnoise as1668

signal.Inthiscase,however,itislikelythatnoisephotonsnearsignalphotonswill1669

alsobemisclassifiedassignal.ThemethodfordynamicallydeterminingaPvalueis1670

explainedfurtherinsection4.3.1.1671

AfterP isdefined, ahistogramof thenumberofneighborswithin a search1672

radiusforeachpointisgenerated.Thedistributionofneighborradiusoccurrencesis1673

analyzedtodeterminethenoisethreshold.1674

!"!"!#$

= ##!"!#$

Eqn.3.11675

1676

whereNtotalisthetotalnumberofphotonsinthepointcloud,Visthevolumeofthe1677

nearestneighborhoodsearch,andVtotalistheboundingvolumeoftheenclosedpoint1678

cloud.Fora2-dimensionaldataset,Vbecomes1679

1680

𝑉 = 𝜋𝑟4 Eqn.3.21681

1682

wherer is theradius.Agoodpractice is to firstnormalize thedatasetalongeach1683

dimensionbeforerunningtheDRAGANNfilter.Normalizationpreventsthealgorithm1684

from favoring one dimension over the others in the radius search (e.g.,when the1685

latitudeandlongitudeareindegreesandheightisinmeters).1686

68

1687

1688Figure 3.2. Histogram of the number of photons within a search radius. This histogram is 1689

used to determine the threshold for the DRAGANN approach. 1690

1691

Oncetheradiushasbeencomputed,DRAGANNcountsthenumberofpoints1692

withintheradiusforeachpointandhistogramsthatsetofvalues.Thedistributionof1693

thenumberofpoints,Figure3.2,revealstwodistinctpeaks;anoisepeakandasignal1694

peak.ThemotivationofDRAGANNistoisolatethesignalphotonsbydetermininga1695

thresholdbasedonthenumberofphotonswithinthesearchradius.Thenoisepeak1696

ischaracterizedashavingalargenumberofoccurrencesofphotonswithjustafew1697

neighboringphotonswithinthesearchradius.Thesignalphotonscomprisethebroad1698

secondpeak.Thefirststepindeterminingthethresholdbetweenthenoiseandsignal1699

is to implement Gaussian fitting to the number of photons distribution (i.e., the1700

distributionshowninFigure3.2).TheGaussianfunctionhastheform1701

1702

𝑔(𝑥) = 𝑎𝑒 ?(A?#)-

4/- Eqn.3.31703

1704

0 100 200 300 400 500 6000

500

1000

1500

2000

2500

3000

# of points in search radius

# of

occ

uren

ces

Noisepeak

Otherfeatures

69

whereaistheamplitudeofthepeak,bisthecenterofthepeak,andcisthestandard1705

deviationofthecurve.Afirstderivativesigncrossingmethodisoneoptiontoidentify1706

peakswithinthedistribution.1707

TodeterminethenoiseandsignalGaussians,uptotenGaussiancurvesarefit1708

to the histogram using an iterative process of fitting and subtracting the max-1709

amplitudepeakcomponentfromthehistogramuntilallpeakshavebeenextracted.1710

Then,thepotentialGaussianspassthrougharejectionprocesstoeliminatethosewith1711

poorstatisticalfitsorotherapparenterrors(GoshtasbyandO’Neill,1994;Chauveet1712

al.2008).AGaussianwithanamplitudelessthan1/5ofthepreviousGaussianand1713

withintwostandarddeviationsofthepreviousGaussianshouldberejected.Oncethe1714

errantGaussiansarerejected,thefinaltworemainingareassumedtorepresentthe1715

noise and signal. These are separated based on the remaining two Gaussian1716

componentswithinthehistogramusingthelogicthattheleftmostGaussianisnoise1717

(lowneighborcounts)andtheotherissignal(highneighborcounts).1718

TheintersectionofthesetwoGaussians(noiseandsignal)determinesadata1719

thresholdvalue.Thethresholdvalueistheparameterusedtodistinguishbetween1720

noisepointsandsignalpointswhenthepointcloudisre-evaluatedforsurfacefinding.1721

Intheeventthatonlyonecurvepassestherejectionprocess,thethresholdissetat1722

1𝜎abovethecenterofthenoisepeak.1723

AnexampleofthenoisefilteredproductfromDRAGANNisshowninFigure1724

3.3.Thesignalphotonsidentifiedinthisprocesswillbecombinedwiththecoarse1725

signalfindingoutputavailableontheATL03dataproduct.1726

70

1727

Figure 3.3. Output from DRAGANN filtering. Signal photons are shown as blue. 1728

Figure3.3providesanexampleofalong-track(profiling)heightdatacollected1729

inSeptember2012fromtheMABEL(ICESat-2simulator)overvegetationinNorth1730

Carolina.Thephotonshavebeenfilteredsuchthatthesignalphotonsreturnedfrom1731

vegetationandthegroundsurfaceareremaining.Noisephotonsthatareadjacentto1732

thesignalphotonsarealsoretainedintheinputdataset;however,theseshouldbe1733

classifiedasnoisephotonsduringthesurfacefindingprocess.Itispossiblethatsome1734

additionaloutlyingnoisemayberetainedduringtheDRAGANNprocesswhennoise1735

photonsaredenselygrouped,and thesephotonsshouldbe filteredoutbefore the1736

surfacefindingprocess.Estimatesofthegroundsurfaceandcanopyheightcanthen1737

bederivedfromthesignalphotons.1738

1739

3.2 SurfaceFinding1740

Once the signal photonshavebeendetermined, the objective is to find the1741

groundandcanopyphotonsfromwithinthepointcloud.Withtheexpectationthat1742

one algorithm may not work everywhere for all biomes, we are employing a1743

frameworkthatwillallowustocombinethesolutionsofmultiplealgorithmsintoone1744

final composite solution for the ground surface. The composite ground surface1745

solutionwillthenbeutilizedtoclassifytheindividualphotonsasground,canopy,top1746

71

ofcanopy,ornoise.Currently,theframeworkdescribedhereutilizesonealgorithm1747

for finding the ground surface and canopy surface. Additionalmethods, however,1748

couldbeintegratedintotheframeworkatalatertime.Figure3.4belowdescribesthe1749

framework.1750

1751

1752

1753

Figure 3.4. Flowchart of overall surface finding method. 1754

1755

72

3.2.1 De-trendingtheSignalPhotons1756

Animportantstepinthesuccessofthesurfacefindingalgorithmistoremove1757

theeffectof topographyonthe inputdata, thus improving theperformanceof the1758

algorithm. This is done by de-trending the input signal photons by subtracting a1759

heavilysmoothed“surface”thatisderivedfromtheinputdata.Essentially,thisisa1760

lowpassfilteroftheoriginaldataandmostoftheanalysistodetectthecanopyand1761

ground will subsequently be implemented on the high pass data. The amount of1762

smoothingthatisimplementedinordertoderivethisfirstsurfaceisdependentupon1763

the relief. For segments where the relief is high, the smoothing window size is1764

decreasedsotopographyisn’tover-filtered.1765

1766

Figure 3.5. Plot of Signal Photons (black) from 2014 MABEL flight over Alaska and de-1767

trended photons (red). 1768

1769

3.2.2 CanopyDetermination1770

Akeyfactorinthesuccessofthesurfacefindingalgorithmisforthesoftware1771

toautomaticallyaccountforthepresenceofcanopyalongagivenL-kmsegment.1772

Duetothelargevolumeofdata,thisprocesshastooccurinanautomatedfashion,1773

allowingthecorrectmethodologyforextractingthesurfacetobeappliedtothedata.1774

In theabsenceof canopy, the iterative filteringapproach to findinggroundworks1775

73

extremelywell,butifcanopydoesexist,weneedtoaccommodateforthatfactwhen1776

wearetryingtorecoverthegroundsurface.1777

Currently, theLandsatTreeCoverContinuousFieldsdataset fromthe20001778

epochisusedtosetacanopyflagwithintheATL08algorithm.EachoftheseLandsat1779

Tree Cover tiles contain 30 m pixels indicating the percentage canopy cover for1780

vegetationover5mhighinthatpixelarea.The2000epochisusedoverthenewer1781

2005epochdueto“striping”inthe2005tiles,causedbythefailureofthescanline1782

corrector (SLC) in 2003. The striping artifacts result in inconsistent pixel values1783

across a landscapewhich in turn can result in a tenfold difference in the average1784

canopycoverpercentagecalculatedbetweentheepochsforaflightsegment.Thereis1785

currentlyavailablea2015TreeCoverBetaReleasethatutilizesLandsat8data.This1786

newreleaseofthe2015TreeCoverproductwillreplacethe2000epochforsetting1787

thecanopyflagintheATL08algorithm.TheTreeCoverdataareavailableviaftpat1788

http://glcf.umd.edu/data/landsatTreecover/.1789

For eachL-km segment of ATLAS data, a comparison ismade between the1790

midpointlocationofthesegmentandthemidpointlocationsoftheWRSLandsattiles1791

tofindtheclosesttilethatencompassestheL-kmsegment.Usingtheclosestfound1792

tile,eachsignalphoton’sX-YlocationisusedtoidentifythecorrespondingLandsat1793

pixel.MultipleinstancesofthesamepixelsfoundfortheL-kmsegmentarediscarded,1794

andthepercentagecanopyvaluesoftheuniquepixelsdeterminedtobeundertheL-1795

kmsegmentareaveragedtoproduceanaveragecanopycoverpercentageforthat1796

segment.Iftheaveragecanopycoverpercentageforasegmentisover3%(threshold1797

subjecttochangeunderfurthertesting),thentheATL08algorithmwillassumethe1798

presence of canopy and identify both ground and vegetation photons in that1799

segment’soutput.Else,theATL08algorithmusesasimplifiedcalculationtoidentify1800

onlygroundphotonsinthatsegment.1801

Thecanopyflagdeterminesifthealgorithmwillcalculateonlygroundphotons1802

(canopyflag=0)orbothgroundandvegetationphotons(canopyflag=1)foreachL-1803

kmsegment.1804

74

ForATL08productregionsoverAntarctica(regions7,8,9,10)andGreenland1805

(region11),thealgorithmwillassumeonlygroundphotons(canopyflag=0)(see1806

Figure2.2).1807

1808

3.2.3 VariableWindowDetermination1809

Themethodforgeneratingabestestimatedterrainsurfacewillvarydepending1810

uponwhethercanopyispresent.L-kmsegmentswithoutcanopyaremucheasierto1811

analyze because the ground photons are usually continuous. L-km segmentswith1812

canopy,however,requiremorescrutinyasthenumberofsignalphotonsfromground1813

arefewerduetoocclusionbythevegetation.1814

Therearesomecommonelementsforfindingtheterrainsurfaceforbothcases1815

(canopy/nocanopy)andwithbothmethods. Inbothcases,wewilluseavariable1816

windowing span to compute statistics as well as filter and smooth the data. For1817

clarification, thewindowsize isvariable foreachL-km segment,but it is constant1818

within the L-km segment. For the surface finding algorithm, we will employ a1819

Savitzky-Golaysmoothing/medianfilteringmethod.Usingthisfilter,wecomputea1820

variablesmoothingparameter(orwindowsize).It isimportanttoboundthefilter1821

appropriatelyastheoutputfromthemedianfiltercanlosefidelityifthescanisover-1822

filtered.1823

Wehavedevelopedanempirically-determinedshapefunction,boundbetween1824

[551],thatsetsthewindowsize(Sspan)basedonthenumberofphotonswithineach1825

L-kmsegment.1826

𝑆𝑠𝑝𝑎𝑛 = 𝑐𝑒𝑖𝑙[5 + 46 ∗ (1 − 𝑒?-∗6*01%))] Eqn.3.41827

𝑎 =DEFG>? -.

/.0/H

?4;>>I ≈ 21𝑥10?J Eqn.3.51828

whereaistheshapeparameterandlengthisthetotalnumberofphotonsintheL-km1829

segment.Theshapeparameter,a,wasdeterminedusingdatacollectedbyMABELand1830

75

is shown in Figure 3.6. It is possible that themodel of the shape function, or the1831

filtering bounds, will need to be adjusted once ICESat-2/ATLAS is on orbit and1832

collectingdata.1833

1834

Figure 3.6. Shape Parameter for variable window size. 1835

1836

3.2.4 Computedescriptivestatistics1837

Tohelpcharacterizetheinputdataandinitializesomeoftheparametersused1838

inthealgorithm,weemployamovingwindowtocomputedescriptivestatisticson1839

the de-trended data. Themovingwindow’swidth is the smoothing span function1840

computed in Equation 5 and the window slides¼ of its size to allow of overlap1841

betweenwindows.Bymovingthewindowwithalargeoverlaphelpstoensurethat1842

the approximate ground location is returned. The statistics computed for each1843

windowstepinclude:1844

• Meanheight1845

• Minheight1846

• Maxheight1847

• Standarddeviationofheights1848

1849

76

Dependentupontheamountofvegetationwithineachwindow,theestimated1850

ground height is estimated using different statistics. A standard deviation of the1851

photon elevations computedwithin eachmovingwindow are used to classify the1852

verticalspreadofphotonsasbelongingtooneoffourclasseswithincreasingamounts1853

ofvariation:open,canopylevel1,canopylevel2,canopylevel3.Thecanopyindices1854

aredefinedinTable3.1.1855

1856

Table 3.1. Standard deviation ranges utilized to qualify the spread of photons within 1857

moving window. 1858

Name Definition LowerLimit UpperLimit

Open Areas with little orno spread in signalphotons determineddue to lowstandarddeviation

N/A Photons fallingwithin1stquartileofStandarddeviation

CanopyLevel1 Areas with smallspread in signalphotons

1stquartile Median

CanopyLevel2 Areas with amedium amount ofspread

Median 3rdquartile

CanopyLevel3 Areas with highamountofspread insignalphotons

3rdquartile N/A

1859

1860

77

1861

Figure 3.7. Illustration of the standard deviations calculated for each moving window to 1862

identify the amount of spread of signal photons within a given window. 1863

1864

3.2.5 GroundFindingFilter(Iterativemedianfiltering)1865

Acombinationofan iterativemedian filteringandsmoothing filterapproach1866

will be employed to derive the output solution of both the ground and canopy1867

surfaces. The input to this process is the set of de-trended photons. Finding the1868

ground in thepresenceof canopyoftenposesa challengebecauseoften thereare1869

fewergroundphotonsunderneaththecanopy.Thealgorithmadoptedhereusesan1870

iterativemedianfilteringapproachtoretain/eliminatephotonsforgroundfindingin1871

thepresenceof canopy.When canopy exists, a smoothed linewill lay somewhere1872

betweenthecanopytopandtheground.Thisfactisusedtoiterativelylabelpoints1873

abovethesmoothedlineascanopy.Theprocessisrepeatedfivetimestoeliminate1874

canopypointsthatfallabovetheestimatedsurfaceaswellasnoisepointsthatfall1875

belowthegroundsurface.AnexampleofiterativemedianfilteringisshowninFigure1876

3.8.Thefinalmedianfilteredlineisthepreliminarysurfaceestimate.Alimitationof1877

thisapproach,however,isincasesofdensevegetationandfewphotonsreachingthe1878

groundsurface.Intheseinstances,theoutputofthemedianfiltermayliewithinthe1879

canopy.1880

78

1881

1882 1883

1884Figure 3.8. Three iterations of the ground finding concept for L-km segments with canopy. 1885

1886

3.3 TopofCanopyFindingFilter1887

Findingthetopofthecanopysurfaceusesthesamemethodologyasfinding1888

thegroundsurface, exceptnow thede-trendeddataare “flipped”over. The “flip”1889

occursbymultiplyingthephotonsheightsby-1andaddingthemeanofalltheheights1890

backtothedata.Thesameprocedureusedtofindthegroundsurfacecanbeusedto1891

findtheindicesofthetopofcanopypoints.1892

1893

4400 4600 4800 5000 5200 5400 5600 5800 6000 6200 64002690

2700

2710

2720

2730

2740

2750

2760

2770

2780

Estimate Lower Bound: Iteration 1

Along-track distance (m)

Elev

atio

n (m

)

Original DataSmoothing InputSmoothed Line

4400 4600 4800 5000 5200 5400 5600 5800 6000 62002690

2700

2710

2720

2730

2740

2750

2760

2770

2780

Estimate Lower Bound: Iteration 2

Along-track Distance (m)

Elev

atio

n (m

)


4600 4800 5000 5200 5400 5600 5800 6000 6200

2700

2710

2720

2730

2740

2750

2760

2770

2780

2790Estimate Lower Bound: Iteration 3

Along-track Distance (m)

Elev

atio

n (m

)


79

3.4 ClassifyingthePhotons1894

Once a composite ground surface is determined, photons fallingwithin the1895

point spread function of the surface are labeled as groundphotons. Based on the1896

expectedperformanceofATLAS,thepointspreadfunctionshouldbeapproximately1897

35cmrms.Signalphotonsthatarenotlabeledasgroundandarebelowtheground1898

surface(bufferedwiththepointspreadfunction)areconsiderednoise,butkeepthe1899

signallabel.1900

Thetopofcanopyphotonsthatareidentifiedcanbeusedtogenerateanupper1901

canopysurfacethroughashape-preservingsurfacefittingmethod.Allsignalphotons1902

thatarenotlabeledgroundandlieabovethegroundsurface(bufferedwiththepoint1903

spreadfunction)andbelowtheuppercanopysurfaceareconsideredtobecanopy1904

photons (and thus labeled accordingly). Signal photons that lie above the top of1905

canopysurfaceareconsiderednoise,butkeepthesignallabel. 1906

1907

FLAGS, 0=noise1908

1=ground1909

2=canopy1910

3=TOC(topofcanopy)1911

1912

Thefinalgroundandcanopyclassificationsareflags1–3.Thefullcanopyis1913

thecombinationofflags2and3.1914

1915

3.5 RefiningthePhotonLabels1916

Duringthefirstiterationofthealgorithm,itispossiblethatsomephotonsare1917

mislabeled;mostlikelythiswouldbenoisephotonsmislabeledascanopy.Toreject1918

thesemislabeledphotons,weapplythreecriteria:1919

a) If top of canopy photons are 2 standard deviations above a1920

smoothedmediantopofcanopysurface1921

b) Iftherearelessthan3canopyindiceswithina15mradius1922

80

c) If,for500signalphotonsegments,thenumberofcanopyphotons1937

is<5%ofthetotal(whenSNR>1),or<10%ofthetotal(whenSNR1938

<=1).Thisminimumnumberofcanopyindicescriterionimpliesa1939

minimumamountofcanopycoverwithinaregion.1940

There are also instances where the ground points will be redefined. This1941

reassigningofgroundpointsisbasedonhowthefinalgroundsurfaceisdetermined.1942

Following the “iterate” steps in the flowchart shown in Figure3.4, if there areno1943

canopy indices identified for the L-km segment, the final ground surface is1944

interpolatedfromtheidentifiedgroundphotonsandthenwillundergoafinalround1945

ofmedianfilteringandsmoothing.1946

Ifcanopyphotonsareidentified,thefinalgroundsurfaceisinterpolatedbased1947

uponthelevel/amountofcanopyatthatlocationalongthesegment.Thefinalground1948

surfaceisacompositeofvariousintermediategroundsurfaces,definedthusly:1949

ASmooth heavilysmoothedsurfaceusedtode-trendthesignaldata

Interp_Aground interpolatedgroundsurfacebasedupontheidentifiedground

photons

AgroundSmooth medianfilteredandsmoothedversionofInterp_Aground

1950

Deleted: Figure3.41951

81

1952

Figure 3.9. Example of the intermediate ground and top of canopy surfaces calculated from 1953

MABEL flight data over Alaska during July 2014. 1954

1955

Duringthefirstroundofgroundsurfacerefinement,wheretherearecanopy1956

photonsidentifiedinthesegment,thegroundsurfaceatthatlocationisdefinedby1957

the smoothed ground surface (AgroundSmooth) value. Else, if there is a location1958

along-trackwherethestandarddeviationoftheground-onlyphotonsisgreaterthan1959

the75%quartileforallsignalphotonstandarddeviations(i.e.,canopylevel3),then1960

thegroundsurfaceatthatlocationisaweightedaveragebetweentheinterpolated1961

groundsurface(Interp_Aground*1/3)andthesmoothedinterpolatedgroundsurface1962

(AgroundSmooth*2/3). For all remaining locations long the segment, the ground1963

surfaceistheaverageoftheinterpolatedgroundsurface(Interp_Aground)andthe1964

heavilysmoothedsurface(Asmooth).1965

The second round of ground surface refinement is simpler than the first.1966

Wheretherearecanopyphotonsidentifiedinthesegment,thegroundsurfaceatthat1967

locationisdefinedbythesmoothedgroundsurface(AgroundSmooth)valueagain.1968

For all other locations, the ground surface is defined by the interpolated ground1969

surface(Interp_Aground).Thiscompositegroundsurfaceisrunthroughthemedian1970

andsmoothingfiltersagain.1971

82

Thepseudocodeforthissurfacerefiningprocesscanbefoundinsection4.11.1972

Examples of the ground and canopy photons for several MABEL lines are1973

showninFigures3.10–3.12.1974

1975

Figure 3.10. Example of classified photons from MABEL data collected in Alaska 2014. 1976

Red photons are photons classified as terrain. Green photons are classified as top of canopy. 1977

Canopy photons (shown as blue) are considered as photons lying between the terrain 1978

surface and top of canopy. 1979

83

1980





1985

1986



84



1991

3.6 CanopyHeightDetermination1992

Once a final ground surface is determined, canopy heights for individual1993

photons are computed by removing the ground surface height for that photon’s1994

latitude/longitude.Theserelativecanopyheightvalueswillbeusedtocomputethe1995

canopystatisticsontheATL08dataproduct.1996

1997

3.7 LinkScaleforDataproducts1998

Thelinkscaleforeachsegmentwithinwhichvaluesforvegetationparameters1999

willbederivedwillbedefinedoverafixeddistanceof100m.Afixedsegmentlength2000

ensuresthatcanopyandterrainmetricsareconsistentbetweensegments,inaddition2001

toincreasedeaseofuseofthefinalproducts.Asizeof100mwasselectedasitshould2002

provideapproximately140photons(astatisticallysufficientnumber)fromwhichto2003

makethecalculationsforterrainandcanopyheight.2004

2005

85

4. ALGORITHMIMPLEMENTATION2006

Prior to running the surface finding algorithms used for ATL08 data products, the 2007

superset of output from the GSFC medium-high confidence classed photons (ATL03 2008

signal_conf_ph: flags 3-4) and the output from DRAGANN will be considered as the input 2009

data set. ATL03 input data requirements include the along-track time, latitude, longitude, 2010

height, and classification for each photon. The motivation behind combining the results 2011

from two different noise filtering methods is to ensure that all of the potential signal 2012

photons for land surfaces will be provided as input to the surface finding software. 2013

Table 4.1. Input parameters to ATL08 classification algorithm. 2014

Name Data Type Long Name

Units Description Source

delta_time DOUBLE GPS elapsed time

seconds Elapsed GPS seconds since start of the granule for a given photon. Use the metadata attribute granule_start_seconds to compute full gps time.

ATL03

lat_ph FLOAT latitude of photon

degrees Latitude of each received photon. Computed from the ECEF Cartesian coordinates of the bounce point.

ATL03

lon_ph FLOAT longitude of photon

degrees Longitude of each received photon. Computed from the ECEF Cartesian coordinates of the bounce point.

ATL03

h_ph FLOAT height of photon

meters Height of each received photon, relative to the WGS-84 ellipsoid.

ATL03

sigma_h FLOAT height uncertainty

m Estimated height uncertainty (1-sigma) for the reference photon.

ATL03

signal_conf_ph

UINT_1_LE

photon signal confidence

counts Confidence level associated with each photon event selected as signal (0-noise. 1- added to allow for buffer but algorithm classifies as background, 2-low, 3-med, 4-high).

ATL03

segment_id UNIT_32 along-track

unitless A seven-digit number uniquely identifying each along-track segment. These are sequential, starting with one for the first

ATL03

86

segment ID number

segment after an ascending equatorial crossing node.

cab_prof FLOAT Calibrated Attenuated Backscatter

unitless Calibrated Attenuated Backscatter from 20 to -1 km with vertical resolution of 30m

ATL09

dem_h FLOAT DEM Height

meters Best available DEM (in priority of GIMP/ANTARCTIC/GMTED/MSS) value at the geolocation point. Height is in meters above the WGS84 Ellipsoid.

ATL09

Landsat tree cover

UINT_8 Landsat Tree Cover Continuous Fields

percentage

Percentage of woody vegetation greater than 5 meters in height across a 30 meter pixel

Global Land Cover Facility (Sexton, 2013)

2015

Table 4.2. Additional external parameters referenced in ATL08 product. 2016

Name Data Type Long Name Units Description Source

atlas_pa Off nadir pointing angle of the spacecraft

ground_track Ground track, as numbered from left to right: 1 = 1L, 2 = 1R, 3 = 2L, 4 = 2R, 5 = 3L, 6 = 3R

dem_h Reference DEM height ANC06

ref_azimuth FLOAT azimuth radians Azimuth of the unit pointing vector for the reference photon in the local ENU frame in radians. The angle is measured from north and positive towards east.

ATL03

ref_elev FLOAT elevation radians Elevation of the unit pointing vector for the reference photon in the local ENU frame in radians. The angle is measured from east-north plane and positive towards up.

ATL03

rgt INTEGER_2

reference ground track

unitless The reference ground track (RGT) is the track on the Earth at which a specified unit vector within the

ATL03

87

observatory is pointed. Under nominal operating conditions, there will be no data collected along the RGT, as the RGT is spanned by GT2L and GT2R. During slews or off-pointing, it is possible that ground tracks may intersect the RGT. The ICESat-2 mission has 1,387 RGTs.

sigma_along DOUBLE along-track geolocation uncertainty

meters Estimated Cartesian along-track uncertainty (1-sigma) for the reference photon.

ATL03

sigma_across DOUBLE across-track geolocation uncertainty

meters Estimated Cartesian across-track uncertainty (1-sigma) for the reference photon.

ATL03

surf_type INTEGER_1

surface type unitless Flags describing which surface types this interval is associated with. 0=not type, 1=is type. Order of array is land, ocean, sea ice, land ice, inland water.

ATL03, Section 4

layer_flag Integer Consolidated cloud flag

unitless Flag indicating the presence of clouds or blowing snow with good confidence

ATL09

cloud_flag_asr Integer(3) Cloud probability from ASR

unitless Cloud confidence flag, from 0 to 5, indicating low, med, or high confidence of clear or cloudy sky

ATL09

msw_flag Byte(3) Multiple scattering warning flag

unitless Flag with values from 0 to 5 indicating presence of multiple scattering, which may be due to blowing snow or cloud/aerosol layers.

ATL09

asr Float(3) Apparent surface reflectance

unitless Surface reflectance as modified by atmospheric transmission

ATL09

snow_ice INTEGER_1

Snow Ice Flag

unitless NOAA snow-ice flag. 0=ice free water; 1=snow free land; 2=snow; 3=ice

ATL09

2017

88

4.1 Cloudbasedfiltering2018

Itispossibleforthepresenceofcloudstoaffectthenumberofsurfacephoton2019

returnsthroughsignalattenuation,ortocausefalsepositiveclassificationsof2020

groundorcanopyphotonsonlowcloudreturns.Eitherofthesecaseswouldreduce2021

theaccuracyoftheATL08product.ToimprovetheperformanceoftheATL082022

algorithm,ideallyallcloudswouldbeidentifiedpriortoprocessingthroughthe2023

ATL08algorithm.Therewillbeinstances,however,wherelowlyingclouds(e.g.2024

<800mabovethegroundsurface)maybedifficulttoidentify.Currently,ATL082025

providesanATL09derivedcloudflag(layer_flag)onits100mproductand2026

encouragestheusertomakenoteofthepresenceofcloudswhenusingATL082027

output.Unfortunatelyatpresent,areviewofon-orbitdatafromATL03andATL092028

indicatethatthecloudlayerflagisnotbeingsetcorrectlyintheATL09algorithm.2029

Ultimately,thefinalcloudbasedfilteringprocessusedintheATL08algorithmwill2030

mostlikelybederivedfromparameters/flagontheATL09dataproduct.Untilthe2031

ATL09cloudflagsareprovenreliable,however,apreliminarycloudscreening2032

methodispresentedbelow.Thismethodologyutilizesthecalibratedattenuated2033

backscatterontheATL09dataproducttoidentify(andsubsequentlyremovefor2034

processing)cloudsorotherproblematicissues(i.e.incorrectlytelemetered2035

windows).Usingthisnewmethod,telemeteredwindowsidentifiedashavingeither2036

lowornosurfacesignalduetothepresenceofclouds(likelyabovethetelemetered2037

band),aswellasphotonreturnssuspectedtobecloudsinsteadofsurfacereturns,2038

willbeomittedfromtheATL08processing.Thisprocess,however,willnotidentify2039

theextremelylowclouds(i.e.<800m).Thestepsareasfollows:2040

1. MatchuptheATL09calibratedattenuatedbackscatter(cab_prof)columnsto2041

theATL03granulebeingprocessedusingsegmentID.2042

2. Flipthematchingcab_profverticalcolumnssothattheelevationbinsgo2043

fromlowtohigh.2044

3. ForeachofthematchingATL09cab_profverticalcolumns,performacubic2045

Savitsky-Golaysmoothingfilterwithaspansizeof15verticalbins.Callthis2046

cab_smooth.2047

89

4. Performthesamesmoothingfilteroneachhorizontalrowofthecab_smooth2048

output,thistimeusingaspansizeof7horizontalbins.Callthis2049

cab_smoother.2050

5. Createalow_signallogicalarraythelengthofthenumberofmatchingATL092051

columnsandsettofalse.2052

6. Foreachcolumnofcab_smoother:2053

a. Setanyvaluesbelow0to0.2054

b. Setalogicalarrayofcab_smootherbinsthatarebelow15kmin2055

elevationtotrue.Callthiscab15.2056

c. UsingtheATL09dem_hvalueforthatcolumn,findtheATL092057

cab_smootherbinsthatare240maboveand240mbelow(~8ATL092058

verticalbinseachdirection)thedem_hvalue.Thebinsfoundherethat2059

arealsowithincab15aredesignatedassfc_bins.2060

d. Findthemaximumpeakvalueofcab_smootherwithinthesfc_bins,if2061

any.Thiswillrepresentthesurfacepeak.2062

e. Findthemaximumvalueofcab_smootherthatishigherinelevation2063

thanthesfc_binsandwithincab15,ifany.Thiswillrepresentthe2064

cloudpeak.2065

f. Ifthereisnosurfacepeak,setthelow_signalflagtotrue.2066

g. Iftherearebothsurfaceandcloudpeakvaluesreturned,determinea2067

surfacepeak/cloudpeakratio.Ifthatratioislessthanorequalto0.4,2068

setlow_signalflagforthatcolumntotrue.2069

7. AftereachmatchingATL09columnofcab_smootherhasbeenanalyzedfor2070

lowsignal,assignthelow_signalflagtoanATL03photonresolutionlogical2071

arraybymatchinguptheATL03photonsegment_idvaluestotheATL092072

rangeofsegmentIDsforeachATL09cab_profcolumn.2073

8. ForeachATL09cab_profcolumnwherethelow_signalflagwasnotset,check2074

foranyATL03photonsgreaterthan800meters(TBD)inelevationaway2075

(higherorlower)fromtheATL09dem_hvalue.AssignanATL03photon2076

resolutiontoo_far_signalflagtotruewhenthisconditionalismet.2077

90

9. AlogicalarraymaskiscreatedforanyATL03photonsthathaveeitherthe2078

low_signalflagorthetoo_far_signalflagsettotruesuchthatthosephotons2079

willnotbefurtherprocessedbytheATL08function.2080

2081

4.2 PreparingATL03dataforinputtoATL08algorithm2082

1. BreakupdataintoL-kmsegments.Segmentsequivalentof10kminalong-2083

trackdistanceofanorbitwouldbeappropriate.2084

a. IfthelastportionofanATL03granulebeingprocessedwouldresult2085

inanL-kmsegmentwithlessthan3.4km(170geosegments)worthof2086

data,thatlastportionisaddedtothepreviousL-kmprocessing2087

windowtobeprocessedtogetherasoneextendedL-kmprocessing2088

segment.2089

i. Theresultinglast_seg_extendvaluewouldbereportedasa2090

positivevalueofdistancebeyond10kmthattheATL082091

processingsegmentwasextendedby.2092

b. IfthelastL-kmsegmentwouldbelessthan10kmbutgreaterthan3.42093

km,aportionextendingfromthestartofcurrentL-kmprocessing2094

segmentbackwardsintothepreviousL-kmprocessingsegmentwould2095

beaddedtothecurrentATL08processingsegmenttomakeit10km2096

inlength.Onlynew100mATL08segmentproductsgeneratedfrom2097

thisbackwardextensionwouldbereported.2098

i. Thedistanceofthisbackwarddatagatheringwouldbe2099

reportedinlast_seg_extendasanegativedistancevalue.2100

c. Allothersegmentsthatarenotextendedwillreportalast_seg_extend2101

valueof0.2102

2. Addabufferof200m(or10segment_id's)tobothendsofeachL-km2103

segment.Thetotalprocessingsegmentlengthis(L-km+2*buffer),butwill2104

bereferredtoasL-kmsegmentsforsimplicity.2105

91

a. ThefirstL-kmsegmentfromanATL03granulewouldonlyhavea2106

bufferattheend,andthelastL-kmsegmentfromanATL03granule2107

wouldonlyhaveabufferatthebeginning.2108

3. TheinputdataforATL08algorithmisX,Y,Z,T(whereTistime).2109

2110

4.3 NoisefilteringviaDRAGANN2111

DRAGANNwilluseATL03photonswithallsignalclassificationflags(0-4).These2112

willincludebothsignalandnoisephotons.Thissectiongiveabroadoverviewofthe2113

DRAGANNfunction.SeeAppendixAformoredetails.2114

1. Determinetherelativealong-tracktime,ATT,ofeachgeolocatedphoton2115

fromthebeginningofeachL-kmsegment.2116

2. RescaletheATTwithequal-timespacingbetweeneachdataphoton,keeping2117

therelativebeginningandendtimevaluesthesame.2118

3. NormalizetheheightandrescaledATTdatafrom0–1foreachL-km2119

segmentbasedonthemin/maxofeachfield.So,normtime=(time-2120

mintime)/(maxtime-mintime).2121

4. Buildakd-treebasedonnormalizedZandnormalizedandrescaledATT.2122

5. DeterminethesearchradiusstartingwithEquation3.1.P=[determinedby2123

preprocessor;seeSec4.3.1],andVtotal=1.Ntotalisthenumberofphotons2124

withinthedataL-kmsegment.SolveforV.2125

6. NowthatyouknowV,determinetheradiususingEquation3.2.2126

7. Computethenumberofneighborsforeachphotonusingthissearchradius.2127

8. Generateahistogramoftheneighborcountdistribution.Asillustratedin2128

Figure3.2,thenoisepeakisthefirstpeak(usuallywiththehighest2129

amplitude).2130

9. Determinethe10highestpeaksofthehistogram.2131

10. FitGaussianstothe10highestpeaks.Foreachpeak,2132

a. Computetheamplitude,a,whichislocatedatpeakpositionb.2133

92

b. Determinethewidth,c,bysteppingonebinatatimeawayfromband2134

findingthelasthistogramvaluethatis>½theamplitude,a.2135

c. UsetheamplitudeandwidthtofitaGaussiantothepeakofthe2136

histogram,asdescribedinEquation3.3.2137

d. SubtracttheGaussianfromthehistogram,andmoveontocalculate2138

thenexthighestpeak’sGaussian.2139

e. RejectGaussiansthataretoonear(<2standarddeviations)and2140

amplitudetoolow(<1/5previousamplitude)fromtheprevious2141

signalGaussian.2142

11. RejectanyofthereturnedGaussianswithimaginarycomponents.2143

12. DetermineifthereisanarrownoiseGaussianatthebeginningofthe2144

histogram.Thesetypicallyoccurwhenthereislittlenoise,suchasduring2145

nighttimepasses.2146

a. SearchfortheGaussianwiththehighestamplitude,a,inthefirst5%2147

ofthehistogram2148

b. Checkifthehighestamplitudeis>=1/10ofthemaximumofall2149

Gaussianamplitudes2150

c. Checkifthewidth,c,oftheGaussianwiththehighestamplitudeis<=2151

4bins2152

d. Ifthesethreeconditionsaremet,savethe[a,b,c]valuesas[a0,b0,c0].2153

e. Ifthethreeconditionsarenotmet,searchagainwithinthefirst10%.2154

Repeattheprocess,incrementingthepercentageofhistogram2155

searchedby5%upto30%.Assoonastheconditionsaremet,save2156

the[a0,b0,c0]valuesandbreakoutofthepercentagehistogramsearch2157

loop.2158

13. Ifanarrownoisepeakwasfound,sorttheremainingGaussiansfromlargest2159

tosmallestarea,estimatedbya*c,thenappend[a0,b0,c0]tothebeginningof2160

thesorted[a,b,c]arrays.Ifanarrownoisepeakwasnotfound,sortall2161

Gaussiansbylargesttosmallestarea.2162

93

a. Ifanarrownoisepeakwasnotfound,checkinsortedorderifoneof2163

theGaussiansareinthefirst10%ofthehistogram.Ifso,itbecomes2164

thefirstGaussian.2165

b. RejectanyGaussiansthatarefullycontainedwithinanother.2166

c. RejectGaussianswhosecentersarewithin3standarddeviationsof2167

another,unlessonlytwoGaussiansremain2168

14. IftherearetwoormoreGaussiansremaining,theyarereferredtoas2169

Gaussian1andGaussian2,assumedtobethenoiseandsignalGaussians.2170

15. Determinethethresholdvaluethatwilldefinethecutoffbetweennoiseand2171

signal.2172

a. IftheabsolutedifferenceofthetwoGaussiansbecomesnearzero,2173

definedas<1e-8,setthefirstbinindexwherethatoccurs,pastthe2174

firstGaussianpeaklocation,asthethreshold.Thiswouldtypicallybe2175

setifthetwoGaussiansarefarawayfromeachother.2176

b. Else,thethresholdvalueistheintersectionofthetwoGaussians,2177

whichcanbeestimatedasthefirstbinindexpastthefirstGaussian2178

peaklocationwherethereisaminimumabsolutedifferencebetween2179

thetwoGaussians.2180

c. IfthereisonlyoneGaussian,itisassumedtobethenoiseGaussian,2181

andthethresholdissettob+c.2182

16. Labelallphotonshavinganeighborcountabovethethresholdassignal.2183

17. Labelallphotonshavinganeighborcountbelowthethresholdasnoise.2184

18. Rejectnoisephotons.2185

19. Retainsignalphotonsforfeedingintonextstepofprocessing.2186

20. UseLogicalORtocombineDRAGANNsignalphotonswithATL03medium-2187

highconfidencesignalphotons(flags3-4)asATL08signalphotons.2188

21. Calculateasignaltonoiseratio(SNR)fortheL-kmsegmentbydividingthe2189

numberofATL08signalphotonsbythenumberofnoise(i.e.,all–signal)2190

photons.2191

94

4.3.1 DRAGANNQualityAssurance2192

Baseduponon-orbitdata,thereareinstanceswherenoisephotonsareselectedas2193

signalphotonsfollowingrunningthroughDRAGANN.Theseinstancesusuallyoccur2194

totelemeteredwindowswithlowsignal,signalattenuationnearthesurfacedueto2195

fog,haze(orotheratmosphericproperties).Ifanyd_flagresultsinthe10km=12196

1. Foreach20msegment_idthathasad_flag=1,buildahistogramof5m2197

heightbinsusingtheheightofonlytheDRAGANN-flaggedphotons2198

(d_flag=1)2199

2. Ifthenumberofbinsindicatesthatalld_flagphotonsfallwithinthesame2200

vertical60m,donothingandmovetothenextgeosement.2201

3. Ifthed_flagphotonsfalloutsideof60m,calculatethemedianand2202

standarddeviationofthehistogramcounts.2203

4. Ifthemaximumvalueofthehistogramcountsisgreaterthanthemedian2204

+3*standarddeviation,asurfacepeakhasbeendetectedbasedonthe2205

relativephotondensitywithinthe5metersteps.Else,setalld_flag=02206

forthisgeosegment.2207

5. Setalld_flag=0from3heightbinsbelowthedetectedpeaktothebottom2208

ofthetelemetrywindow.2209

6. Startingwiththepeakcountbin(surface),stepupwardsbinbybinand2210

checkif12bincounts(60metersofheightbins)abovesurfaceareless2211

than0.5*histogrammedian.Ifso,forallphotonsabovecurrentheightin2212

loop+60meters,setalld_flag=0andexitbin-by-binloop.2213

7. Startingwithonebinabovethepeakcountbin(surface),againstep2214

upwardsbinbybin.Foreachiteration,calculatethestandarddeviationof2215

thebincountsincludingonlythecurrentbintothehighestheightbinand2216

callthisnoisestandarddeviation.Ifallremainingverticalheightbins2217

fromcurrentbintohighestheightbinarelessthan2*histogram2218

standarddeviation,orifthenoisestandarddeviationislessthan1.0,orif2219

thisbinandthenext2higherbinseachhavecountslessthanthepeakbin2220

95

count(entirehistogram)–3*histogramstandarddeviation,thensetall2221

d_flag=0forallheightsabovethislevel.2222

8. Forafinalcheck,constructanewhistogram,withmedianandstandard2223

deviation,usingthecorrectedd_flagresultsandonlywhered_flag=1.If2224

thehistogrammedianisgreaterthan0.0andthestandarddeviationis2225

greaterthan0.75*median,setalld_flaginthisgeosegment=0.This2226

indicatesresultsnotwellconstrainedaboutadetectiblesurface.2227

2228

4.3.2 PreprocessingtodynamicallydetermineaDRAGANNparameter2229

WhileadefaultvalueofP=20wasfoundtoworkwellwhentestingwithMABEL2230

flightdata,furthertestingwithsimulateddatashowedthatP=20isnotsufficientin2231

casesofveryloworveryhighnoise.AdditionaltestingwithrealATL03datahave2232

shownthegroundsignaltobemuchstronger,andthecanopysignaltobemuch2233

weaker,thanoriginallyanticipated.Therefore,apreprocessingstepfordynamically2234

calculatingPandrunningthecoreDRAGANNfunctionisdescribedinthis2235

subsection.ThisassumesL-kmtobe10km(withadditionalL-kmbuffering).2236

1. DefineaDRAGANNprocessingwindowof170segments(~3.4km),2237

andabufferof10segments(~200m).2238

2. ThebufferisappliedtobothsidesofeachDRAGANNprocessing2239

windowtocreatebufferedDRAGANNprocessingwindows2240

(referencedas“bufferedwindow”fortherestofthissection)thatwill2241

overlaptheDRAGANNprocessingwindowsnexttothem.2242

3. ForeachbufferedwindowwithintheL-kmsegment,calculatea2243

histogramofpointswith1melevationbins.2244

4. Foreachbufferedwindowhistogram,calculatethemediancounts.2245

5. Binswithcountsbelowthebufferedwindowmediancountvalueare2246

estimatedtobenoise.Calculatethemeancountofnoisebins.2247

6. Binswithcountsabovethebufferedwindowmediancountvalueare2248

estimatedtobesignal.Calculatethemeancountofsignalbins.2249

7. Determinethetimeelapsedoverthebufferedwindow.2250

96

8. Calculateestimatednoiseandsignalratesforeachbufferedwindow2251

bymultiplyingeachwindow’smeancountsofnoisebinsandsignal2252

bins,determinedfromsteps5and6above,by1/(elapsedtime)to2253

returntheratesintermsofpoints/meter[elevation]/second[across].2254

9. Calculateanoiseratioforeachwindowbydividingthenoiserateby2255

thesignalrate.2256

10. If,forallthebufferedwindowsintheL-kmsegment,thenoiserateis2257

lessthan20andthenoiseratioislessthan0.15;ORanynoiserateis2258

0;ORanysignalrateisgreaterthan1000:re-calculatesteps3-92259

usingtheentireL-kmsegment.Continuewiththefollowingsteps2260

usingresultsfromtheoneL-kmwindow(insteadofmultiplebuffered2261

windows).2262

11. Now,determinetheDRAGANNparameter,P,foreachbuffered2263

windowbasedonthefollowingconditionals:2264

a. IfthesignalrateisNaN(i.e.,aninvalidvalue),setthesignal2265

indexarraytoemptyandmoveontothenextbuffered2266

window.2267

b. Ifnoiserate<20||noiseratio<0.15:2268

P=signalrate2269

Ifsignalrateis<5,P=5;ifsignalrate>20,P=202270

c. ElseP=20.2271

12. RunDRAGANNonthebufferedwindowpointsusingthecalculatedP.2272

13. IfDRAGANNfailstofindasignal(i.e.,onlyoneGaussianfound),run2273

DRAGANNagainwithP=10.2274

14. IfDRAGANNstillfailstofindasignal,trytodeterminePasecondtime2275

usingthefollowingconditionals:2276

a. If(noiserate>=20)…2277

&&(signalrate>100)…2278

&&(signalrate<250),2279

P=(signalrate)/22280

97

b. Elseifsignalrate>=250,2281

ifnoiserate>=250,2282

P=(noiserate)*1.12283

else,2284

P=2502285

c. Else,P=mean(noiserate,signalrate)2286

15. RunDRAGANNonthebufferedwindowpointsusingthenewly2287

calculatedP.2288

a. Ifstillnosignalpointsarefound,setadragannErrorflag.2289

16. IfsignalpointswerefoundbyDRAGANN,foreachbufferedwindow2290

calculateasignalcheckbydividingthenumberofsignalpointsfound2291

viaDRAGANNbythenumberoftotalpointsinthebufferedwindow.2292

17. IfdragannErrorhasbeenset,ortherearesuspectsignalstatistics,the2293followingsnippetofpseudocodewillcheckthoseconditionalsandtry2294toiterativelyfindabetterPvaluetorunDRAGANNwith:22952296try_count=022972298WhiledragannError…2299||((noiserate>=30)…2300&&(signalcheck>noiseratio)…2301&&(noiseratio>=0.15))…2302||(signalcheck<0.001):23032304ifP<3,2305break2306else,2307P=P*0.752308end23092310iftry_count<22311ClearoutsignalindexresultsfrompreviousDRAGANNrun2312Re-runDRAGANNwithnewPvalue2313Recalculatethesignalcheck2314end23152316ifnosignalindexresultsarereturned2317P=P*0.752318end23192320

98

try_count=try_count+123212322end23232324

18. IfnosignalphotonsarefoundbyDRAGANNbecauseonlyone2325

Gaussianwasfound,setthethresholdasb+c(i.e.,onestandard2326

deviationawayfromtheGaussianpeaklocation)forafinalDRAGANN2327

run.Otherwise,setthesignalindexarraytoemptyandmoveontothe2328

nextbufferedwindow.2329

19. AssignthesignalvaluesfoundfromDRAGANNforeachbuffered2330

windowtotheoriginalDRAGANNprocessingwindowrangeofpoints.2331

20. CombinesignalpointsfromeachDRAGANNprocessingwindowback2332

intooneL-kmarrayofsignalpointsforfurtherprocessing.2333

2334

4.3.3 IterativeDRAGANNprocessing2335

ItispossibleinprocessingsegmentswithhighnoiseratesthatDRAGANNwill2336

incorrectlyidentifyclustersofnoiseassignal.Onewaytoreducethesefalsepositive2337

noiseclustersistorunthealternativeDRAGANNprocess(Sec4.3.1)againwiththe2338

inputbeingthesignaloutputphotonsfromthefirstrunthroughalternative2339

DRAGANN.Notethatthismethodologyisstillbeingtested,sobydefaultthisoption2340

shouldnotbeset.2341

1. IfSNR<1(TBD)fromalternativeDRAGANNrun,runalternativeDRAGANN2342

processagainusingtheoutputsignalphotonsfromfirstDRAGANNrunasthe2343

inputtothesecondDRAGANNrun.2344

2. RecalculateSNRbasedonoutputofsecondDRAGANNrun.2345

2346

99

4.4 IsCanopyPresent2347

1. IfL-kmsegmentiswithinanATL08regionencompassingAntarctica(regions2348

7,8,9,10)orGreenland(region11),assumenocanopyispresent:canopy2349

flag=0.Else:2350

2. DeterminethecenterLatitude/LongitudepositionfortheL-kmsegment.2351

3. DeterminethecorrespondingtilefromtheLandsatcontinuouscover2352

product.2353

4. ForeachuniqueXYpositionintheATLASsegment,extractthecanopycover2354

valuefromtheLandsatCCproduct2355

5. ComputetheaveragecanopycovervaluefortheL-kmsegment(basedonthe2356

Landsatvalues).2357

6. Ifcanopycover>3%,setcanopyflag=1(assumescanopyispresent)2358

7. Ifcanopycover<=3%,setcanopyflag=0(assumesnocanopyispresent)2359

2360

4.5 ComputeFilteringWindow2361

1. Nextstepistorunasurfacefilterwithavariablewindowsize(variablein2362

thatitwillchangefromL-kmsegmenttoL-kmsegment).Thewindow-sizeis2363

denotedasWindow.2364

2. 𝑊𝑖𝑛𝑑𝑜𝑤 = 𝑐𝑒𝑖𝑙[5 + 46 ∗ (1 − 𝑒?-∗6*01%))], wherelengthisthenumberof2365

photonsinthesegment.2366

3. 𝑎 =DEFG>? -.

/.0/H

?4;>>I ≈ 21𝑥10?J, whereaistheshapeparameterforthewindow2367

span. 2368 2369

4.6 De-trendData2370

1. TheinputdataarethesignalphotonsidentifiedbyDRAGANNandtheATL032371

classification(signal_conf_ph)valuesof3-4.2372

2. Generatearoughsurfacebyconnectingallunique(time)photonstoeach2373

other.Let’scallthissurfaceinterp_A.2374

100

3. Runamedianfilterthroughinterp_Ausingthewindowsizesetbythe2375

software.Output=Asmooth.2376

4. DefineareferenceDEMlimit(ref_dem_limit)as120m(TBD).2377

5. RemoveanyAsmoothvaluesfurtherthantheref_dem_limitthresholdfrom2378

thereferenceDEM,andinterpolatetheAsmoothsurfacebasedonthe2379

remainingAsmoothvalues.Theinterpolationmethodtouseistheshape2380

preservingpiecewisecubicHermiteinterpolatingpolynomial–hereafter2381

labeledas“pchip”(Fritsch&Carlson,1980).2382

6. ComputetheapproximatereliefoftheL-kmsegmentusingthe95th-5th2383

percentileheightsofthesignalphotons.WearegoingtofilterAsmoothagain2384

andthesmoothingisafunctionoftherelief.2385

7. DefinetheSmoothSizeusingtheconditionalstatementsbelow.The2386

SmoothSizewillbeusedtodetrendthedataaswellastocreatean2387

interpolatedgroundsurfacelater.2388

SmoothSize=2*Window2389

• Ifrelief>=900,SmoothSize=round(SmoothSize/4)2390

• Ifrelief>=400&&<=900,SmoothSize=round(SmoothSize/3)2391

• Ifrelief>=200&&<=400,SmoothSize=round(SmoothSize/2)2392

8. GreatlysmoothAsmoothbyfirstrunningAsmooth10timesthrougha2393

medianfilterthenasmoothingfilterwithamovingaveragemethodonthe2394

result.Boththemedianfilterandthesmoothingfilteruseawindowsizeof2395

SmoothSize.2396

2397

4.7 Filteroutliernoisefromsignal2398

1. Ifthereareanysignaldatathatare150metersaboveAsmooth,removethem2399

fromthesignaldataset.2400

101

2. Ifthestandarddeviationofthedetrendedsignalisgreaterthan10meters,2401

removeanysignalvaluefromthesignaldatasetthatis2timesthestandard2402

deviationofthedetrendedsignalbelowAsmooth.2403

3. CalculateanewAsmoothsurfacebyinterpolating(pchipmethod)asurface2404

fromtheremainingsignalphotonsandmedianfilteringusingtheWindow2405

size,thenmedianfilterandsmooth(movingaveragemethod)10timesagain2406

usingtheSmoothSize.2407

4. Detrendthesignalphotonsbysubtractingthesignalheightvaluesfromthe2408

Asmoothsurfaceheightvalues.Usethedetrendedheightsforsurfacefinding.2409

2410

4.8 Findingtheinitialgroundestimate2411

1. Atthispoint,theinitialsignalphotonshavebeennoisefilteredandde-2412

trendedandshouldhavethefollowingformat:X,Y,detrendedZ,T(T=time).2413

Fromthis,theinputdataintothegroundfindingwillbetheATD(alongtrack2414

distance)metric(suchastime)andthedetrendedZheightvalues.2415

2. DefineamedianSpanasWindow*2/3.2416

3. Calculatethebackgroundneighbordensityofthesubsurfacephotonsusing2417

ALLavailablephotons(thenon-detrendeddata).Thisstepisrunonall2418

photonsincludingnoisephotons.Histogramthephotonsin0.5mvertical2419

binsanda60mhorizontalbin.2420

4. Toavoidincludingzeropopulationbinsinthehistogramsignaltracking2421

process,identifythebinwiththemaximumbincountamongbins3–72422

(startingatthelowestheight)acrosseach60mwithinthe10-kmprocessing2423

window.2424

5. Calculatethemeanofthosemaximumbinvaluestorepresentthenoisecount2425

forthe10-kmwindow.2426

6. Thefollowingstepsarerunonthedetrendedsignalphotons.2427

102

7. Calculatethebrightnessofthesurfaceforeach60mtobehistogrammedvia2428

thecalculationinSection2.4.21.Ifabrightsurfaceisdetected,skipsteps72429

and82430

8. Determinethelowest0.5mhistogramheightbinforeach60malongtrack,2431

inthedetrendedheightswhere:2432

a. Theneighbordensityis10xgreaterthanthebackgrounddensityand2433

b. Theneighbordensityisgreaterthanthehistogrampopulationmedian2434

plus1/3ofthepopulationstandarddeviation.2435

9. Thephotonswithdetrendedheightsabovethisbinaremaskedfrom2436

considerationintheinitialgroundheightestimate.Detrendedsignalphotons2437

impliesthatthed_flagphotons.2438

10. Identifyingthegroundsurfaceisaniterativeprocess.Startbyassumingthat2439

alltheinputsignalheightphotonsaretheground.Thefirstgoalisthecut2440

outthelowerheightexcessphotonsinordertofindalowerboundfor2441

potentialgroundphotons.Thisprocessisdone5timesandanoffsetof42442

metersissubtractedfromtheresultinglowerbound.Thesmoothingfilter2443

usesamovingaverageagain:2444

forj=1:52445

cutOff=medianfilter(ground,medianSpan)2446

cutOff=smoothfilter(cutOff,Window)2447

ground=ground((cutOff–ground)>-1)2448

end2449

lowerbound=medianfilter(ground,medianSpan*3)2450

middlebound=smoothfilter(lowerbound,Window)2451

lowerbound=smoothfilter(lowerbound,Window)–42452

end;2453

11. Createalinearlyinterpolatedsurfacealongthelowerboundpointsandonly2454

keepinputphotonsabovethatlineaspotentialgroundpoints:2455

top=input(input>interp(lowerbound))2456

103

12. Thenextgoalistocutoutexcesshigherelevationphotonsinordertofindan2457

upperboundtothegroundphotons.Thisprocessisdone3timesandan2458

offsetof1meterisaddedtotheresultingupperbound.Thesmoothingfilter2459

usesamovingaverage:2460

forj=1:32461

cutOff=medianfilter(top,medianSpan)2462


top=top((cutOff–top)>-1)2464

end2465

upperbound=medianfilter(top,medianSpan)2466

upperbound=smoothfilter(upperbound,Window)+12467

13. Createalinearlyinterpolatedsurfacealongtheupperboundpointsand2468

extractthepointsbetweentheupperandlowerboundsaspotentialground2469

points:2470

ground=input((input>interp(lowerbound))&…2471

(input<interp(upperbound)))2472

14. Refinetheextractedgroundpointstocutoutmorecanopy,againusingthe2473

movingaveragesmoothing:2474

Forj=1:22475

cutOff=medianfilter(ground,medianSpan)2476


ground=ground((cutOff–ground)>-1)2478

end2479

15. Runthegroundoutputoncemorethroughamedianfilterusingwindowside2480

medianSpanandasmoothingfilterusingwindowsizeWindow,butthistime2481

withtheSavitzky-Golaymethod.2482

16. Finally,linearlyinterpolateasurfacefromthegroundpoints.2483

104

17. Thefirstestimateofcanopypointsarethoseindicesofpointsthatare2512

between2and150metersabovetheestimatedgroundsurface.Savethese2513

indicesforthenextsectiononfindingthetopofcanopy.2514

18. Theoutputfromthefinaliterationofgroundpointsistemp_interpA–an2515

interpolatedgroundestimate.2516

19. Findgroundindicesthatliewithin10mbelowand0.5maboveof2517

temp_interpAonlywhenthecanopy_flagindicatescanopyshouldbepresent.2518

Otherwise,(i.e.nocanopy)useathresholdof0.5maroundtemp_interpA.2519

20. Applythegroundindicestotheoriginalheights(i.e.,notthede-trendeddata)2520

tolabelgroundphotons.2521

21. Interpolateagroundsurfaceusingthepchipmethodbasedontheground2522

photons.Outputisinterp_Aground.2523

2524

4.9 Findthetopofthecanopy(ifcanopy_flag=1)2525

1. TheinputaretheATDmetric(i.e.,time),andthede-trendedZvaluesindexed2526

bythecanopyindicesextractedfromstep4.8(17).2527

2. Flipthisdataoversothatwecanfindacanopy“surface”bymultiplyingthe2528

de-trendedcanopyheightsby-1.0andaddingthemean(heights).2529

3. Findingthetopofcanopyisalsoaniterativeprocess.Followthesamesteps2530

describedin4.8(2)–4.8(16),butusethecanopyindexedandflippedZ2531

valuesinplaceofthegroundinput.2532

4. Finalretainedphotonsareconsideredtopofcanopyphotons.Usetheindices2533

ofthesephotonstodefinetopofcanopyphotonsintheoriginal(notde-2534

trended)Zvalues.2535

5. Buildakd-treeoncanopyindices.2536

6. Iftherearelessthanthreecanopyindiceswithina15mradius,reassign2537

thesephotonstonoisephotons.2538

2539

Deleted: 102540

Deleted: 92541

105

4.10 Computestatisticsonde-trendeddata2542

1. Theinputdatahavebeennoisefilteredandde-trendedandshouldhavethe2543

followinginputformat:X,Y,detrendedZ,T.2544

2. Theinputdatawillcontainsignalphotonsaswellasafewnoisephotons2545

nearthesurface.2546

3. Computestatisticsofheightsinthealong-trackdirectionusingasliding2547

window.Usingthewindowsize(window),computeheightstatisticsforall2548

photonsthatfallwithineachwindow.Theseincludemaxheight,median2549

height,meanheight,minheight,andstandarddeviationofallphotonheights.2550

Additionally,ineachwindowcomputethemedianheightandstandard2551

deviationofjusttheinitiallyclassifiedtopofcanopyphotons,andthe2552

standarddeviationofjusttheinitiallyclassifiedgroundphotonheights.2553

Currentlyonlythemediantopofcanopy,andallSTDvariablesarebeing2554

utilized,butit’spossiblethatotherstatisticsmaybeincorporatedas2555

changes/improvementsaremadetothecode.2556

4. Slidethewindow¼ofthewindowspanandrecomputestatisticsalongthe2557

entireL-kmsegment.Thisresultsinonevalueforeachstatisticforeach2558

window.2559

5. Determinecanopyindexcategoriesforeachwindowbaseduponthetotal2560

distributionofSTDvaluesforallsignalphotonsalongtheL-kmsegment2561

basedonSTDquartiles.2562

6. OpencanopyhaveSTDvaluesfallingwithinthe1stquartile.2563

7. CanopyLevel1hasSTDvaluesfallingfrom1stquartiletomedianSTDvalue.2564

8. CanopyLevel2hasSTDvaluesfallingfrommedianSTDvalueto3rdquartile.2565

9. CanopyLevel3hasSTDvaluesfallingfrom3rdquartiletomaxSTD.2566

10. LinearlyinterpolatethewindowSTDvalues(bothforallphotonsand2567

ground-onlyphotons)backtothenativealong-trackresolutionandcalculate2568

theinterpolatedall-photonSTDquartilestocreateaninterpolatedcanopy2569

levelindex.Thiswillbeusedlaterforinterpolatingagroundsurface.2570

2571

106

4.11 RefineGroundEstimates2572

1. Smooththeinterpolatedgroundsurface10times.Allfurthergroundsurface2573

smoothingusethemovingaveragemethod:2574

Forj=1:102575

AgroundSmooth=medianfilter(interp_Aground,SmoothSize*5)2576

AgroundSmooth=smoothfilter(AgroundSmooth,SmoothSize)2577

End2578

2579

2. Thisoutput(AgroundSmooth)fromthefiltering/smoothingfunctionisan2580

intermediategroundsolutionanditwillbeusedtoestimatethefinal2581

solution.2582

3. Iftherearenocanopyindicesidentifiedalongtheentiresegment(OR2583

canopy_flag=0)ANDrelief>400m2584

FINALGROUND=medianfilter(Asmooth,SmoothSize)2585

FINALGROUND=smoothfilter(FINALGROUND,SmoothSize)2586

Else2587

FINALGROUND=AgroundSmooth2588

end2589

4. Iftherearecanopyindicesidentifiedalongthesegment:2590

Ifthereisacanopyphotonidentifiedatalocationalong-trackabovethe2591

groundsurface,thenatthatlocationalong-track2592

FINALGROUND=AgroundSmooth2593

elseifthereisalocationalong-trackwheretheinterpolatedgroundSTDhas2594

aninterpolatedcanopylevel>=32595

FINALGROUND=Interp_Aground*1/3+AgroundSmooth*2/32596

else2597

FINALGROUND=Interp_Aground*1/2+Asmooth*1/22598

end2599

107

5. Smooththeresultinginterpolatedgroundsurface(FINALGROUND)once2600

usingamedianfilterwithwindowsizeof9thenasmoothingfiltertwicewith2601

windowsizeof9.Selectgroundphotonsthatliewithinthepointspread2602

function(PSF)ofFINALGROUND.2603

6. PSFisdeterminedbysigma_atlas_land(Eq.1.2)calculatedatthephoton2604

resolutionandthresholdedbetween0.5to1m.2605

a. EstimatetheterrainslopebytakingthegradientofFINALGROUND.2606

Gradientisreportedatthecenterof((finalground(n+1)-2607

finalground(n-1))/(dist_x(n+1)-dist_x(n-1))/22608

b. Linearlyinterpolatethesigma_hvaluestothephotonresolution.2609

c. Calculatesigma_topo(Eq.1.3)atthephotonresolution.2610

d. Calculatesigma_atlas_landatthephotonresolutionusingthesigma_h2611

andsigma_topovaluesatthephotonresolution.2612

e. SetPSFequaltosigma_atlas_land.2613

i. AnyPSF<0.5missetto0.5mastheminimumPSF.2614

ii. AnyPSF>1missetto1masthemaximumPSF.Setpsf_flagto2615

true.2616

2617

4.12 CanopyPhotonFiltering2618

1. Thefirstcanopyfilterwillremovephotonsclassifiedastopofcanopythat2619

aresignificantlyaboveasmoothedmediantopofcanopysurface.To2620

calculatethesmoothedmediantopofcanopysurface:2621

a. Linearlyinterpolatethemedianandstandarddeviationcanopy2622

windowstatistics,calculatedfrom4.10(3),tothetopofcanopy2623

photonresolution.Outputvariables:interpMedianC,interpStdC.2624

b. CalculateacanopywindowsizeusingEq.3.4,wherelength=number2625

oftopofcanopyphotons.Outputvariable:winC.2626

108

c. Createthemedianfilteredandsmoothedtopofcanopysurface,2627

smoothedC,usingalocallyweightedlinearregressionsmoothing2628

method,“lowess”(Cleveland,1979):2629

smoothedC=medianfilter(interpMedianC,winC)2630

2631

ifSNR>1,canopySmoothSpan=winC*2;2632

else,canopySmoothSpan=smoothSpan;2633

2634

smoothedC=smoothfilter(smoothedC,canopySmoothSpan)2635

d. AddthedetrendedheightsbackintothesmoothedCsurface:2636

smoothedC=smoothedC+Asmooth2637

2. SetcanopyheightthresholdsbasedontheinterpolatedtopofcanopySTD:2638

IfSNR>1,canopySTDthresh=3;else,canopySTDthresh=2;2639

canopy_height_thresh=canopySTDthresh*interpStdC2640

high_cStd=canopy_height_thresh>102641

low_cStd=canopy_height_thresh<32642

canopy_height_thresh(high_cStd)=2643

canopy_height_thresh(high_cStd)/22644

canopy_height_thresh(low_cStd)=32645

3. RelabelasnoiseanytopofcanopyphotonsthatarehigherthansmoothedC+2646

canopy_height_thresh.2647

4. Next,interpolateatopofcanopysurfaceusingtheremainingtopofcanopy2648

photons(herewearetryingtocreateanupperboundoncanopypoints).The2649

interpolationmethodusedispchip.Thisoutputisnamedinterp_Acanopy.2650

5. Photonsfallingbelowinterp_AcanopyandaboveFINALGROUND+PSFare2651

labeledascanopypoints.2652

109

6. For500signalphotonsegments,ifnumberofallcanopyphotons(i.e.,canopy2653

andtopofcanopy)is:2654

<5%ofthetotal(whenSNR>1),OR2655

<10%ofthetotal(whenSNR<=1),2656

relabelthecanopyphotonsasnoise.2657

7. Interpolate,usingthepchipmethod,anewtopofcanopysurfacefromthe2658

filteredtopofcanopyphotons.Thisoutputisagainnamedinterp_Acanopy.2659

8. Again,labelphotonsthatliebetweeninterp_Acanopyand2660

FINALGROUND+PSFascanopyphotons.2661

9. Sincethecanopypointshavebeenrelabeled,weneedtodoafinal2662

refinementofthegroundsurface:2663

Ifcanopyispresentatanylocationalong-track2664

FINALGROUND=AgroundSmooth(atthatlocation)2665

Elseifcanopyisnotpresentatalocationalong-track2666

FINALGROUND=interp_Aground2667

Smooththeresultinginterpolatedgroundsurface(FINALGROUND)once2668

usingamedianfilterwithwindowsizeofSmoothSize(SmoothSize=9),then2669

amovingaveragesmoothingfiltertwicewithwindowsizeofSmoothSize2670

(SmoothSize=9)2671

10. Relabelgroundphotonsbasedonthisnew(andlast)FINALGROUNDsolution2672

+/-arecalculatedPSF(viastepsin4.11(6)).Pointsfallingbelowthebuffer2673

arelabeledasnoise.2674

11. UsingInterp_AcanopyandthislastFINALGROUNDsolution+PSFbuffer,2675

labelallphotonsthatliebetweenthetwoascanopyphotons.2676

12. Repeatthecanopycoverfiltering:For500signalphotonsegments,if2677

numberofallcanopyphotons(i.e.,canopyandtopofcanopy)is:2678

<5%ofthetotal(whenSNR>1),OR2679

110

<10%ofthetotal(whenSNR<=1),2680

relabelthecanopyphotonsasnoise.Thisisthelastcanopylabelingstep.2681

2682

4.13 ComputeindividualCanopyHeights2683

1. Atthispoint,eachphotonwillhaveitsfinallabelassignedin2684

classed_pc_flag:0=noise,1=ground,2=canopy,3=topofcanopy.2685

2. Foreachindividualphotonlabeledascanopyortopofcanopy,subtracttheZ2686

heightvaluefromtheinterpolatedterrainsurface,FINALGROUND,atthat2687

particularpositioninthealong-trackdirection.2688

3. Therelativeheightforeachindividualcanopyortopofcanopyphotonwill2689

beusedtocalculatecanopyproductsdescribedinSection4.16.Additional2690

canopyproductswillbecalculatedusingtheabsoluteheights,asdescribedin2691

Section4.16.1.2692

2693

4.14 FinalphotonclassificationQAcheck2694

1. Findanyground,canopy,ortopofcanopyphotonsthathaveelevations2695

furtherthantheref_dem_limitfromthereferenceDEMelevationvalue.2696

Convertthesetothenoiseclassification.2697

2. Findanyrelativeheightsofcanopyortopofcanopyphotonsthataregreater2698

than150mabovetheinterpolatedgroundsurface,FINALGROUND.Convert2699

thesetothenoiseclassification.2700

3. FindanyFINALGROUNDelevationsthatarefurtherthantheref_dem_limit2701

fromthereferenceDEMelevationvalue.ConvertthoseFINALGROUND2702

elevationstoaninvalidvalue,andconvertanyclassifiedphotonsatthesame2703

indicestonoise.2704

4. Ifmorethan50%ofphotonsareremovedinasegment,setph_removal_flag2705

totrue.2706

2707

111

4.15 ComputesegmentparametersfortheLandProducts2708

1. Foreach100msegment,determinetheclassedphotons(photonsclassified2709

asground,canopy,ortopofcanopy).2710

a. Iftherearefewerthan50classedphotonsina100msegment,donot2711

calculatelandorcanopyproducts.2712

b. Ifthereare50ormoreclassedphotonsina100msegment,extract2713

thegroundphotonstocreatethelandproducts.2714

2. Ifthenumberofgroundphotons>5%ofthetotalnumberofclassedphotons2715

withinthesegment(thiscontrolvalueof5%canbemodifiedonceonorbit):2716

a. Computestatisticsonthegroundphotons:mean,median,min,max,2717

standarddeviation,mode,andskew.Theseheightswillbereported2718

ontheproductash_te_mean,h_te_median,h_te_min,h_te_max,2719

h_te_mode,andh_te_skewrespectivelydescribedinTable2.1.2720

b. Computethestandarddeviationofthegroundphotonsaboutthe2721

interpolatedterrainsurface,FINALGROUND.Thisvalueisreportedas2722

h_te_stdinTable2.1.2723

c. ComputetheresidualsofthegroundphotonZheightsaboutthe2724

interpolatedterrainsurface,FINALGROUND.Theproductistheroot2725

sumofsquaresofthegroundphotonresidualscombinedwiththe2726

sigma_atlas_landterminTable2.5asdescribedinEquation1.4.This2727

parameterreportedash_te_uncertaintyinTable2.1.2728

d. Computealinearfitonthegroundphotonsandreporttheslope.This2729

parameteristerrain_slopeinTable2.1.2730

e. Calculateabestfitterrainelevationatthemid-pointlocationofthe2731

100msegment:2732

i. Calculateeachterrainphoton’sdistancealong-trackintothe2733

100msegmentusingthecorrespondingATL0320mproducts2734

segment_lengthanddist_ph_along,anddeterminethemid-2735

segmentdistance(expectedtobe50m±0.5m).2736

112

1. Usethemid-segmentdistancetolinearlyinterpolatea2737

mid-segmenttime(delta_timeinTable2.4).Usethe2738

mid-segmenttimetolinearlyinterpolateothermid-2739

segmentparameters:interpolatedterrainsurface,2740

FINALGROUND,ash_te_interp(Table2.1);latitude2741

andlongitude(Table2.4).2742

ii. Calculatealinearfit,aswellas3rdand4thorderpolynomialfits2743

totheterrainphotonsinthesegment.2744

iii. Createaslope-adjustedandweightedmid-segmentvariable,2745

weightedZ,fromthelinearfit:Useterrain_slopetoapplya2746

slopecorrectiontoeachterrainphotonbysubtractingthe2747

terrainphotonheightsfromthelinearfit.Determinethemid-2748

segmentlocationofthelinearfit,andaddthatheighttothe2749

slopecorrectedterrainphotons.Applyalinearweightingto2750

eachphotonbasedonitsdistancetothemid-segmentlocation:2751

1/sqrt((photondistancealong–mid-segmentdistance)^2).2752

Calculatetheweightedmid-segmentterrainheight,weightedZ:2753

sum(eachadjustedterrainheight*itsweight)/sum(all2754

weights).2755

iv. Determinewhichofthethreefitsisbestbycalculatingthe2756

meanandstandarddeviationofthefiterrors.Ifoneofthefits2757

hasboththesmallestmeanandstandarddeviations,usethat2758

fit.Else,usethefitwiththesmalleststandarddeviation.If2759

morethanonefithasthesamesmallestmeanand/orstandard2760

deviation,usethefitwiththehigherpolynomial.2761

v. Usethebestfittodefinethemid-segmentelevation.This2762

parameterish_te_best_fitinTable2.1.2763

1. Ifh_te_best_fitisfartherthan3mfromh_te_interp(best2764

fitdiffthreshold),checkif:thereareterrainphotonson2765

bothsidesofthemid-segmentlocation;ortheelevation2766

differencebetweenweightedZandh_te_interpis2767

113

greaterthanthebestfitdiffthreshold;orthenumberof2768

groundphotonsinthesegmentis<=5%oftotal2769

numberofclassifiedphotonspersegment.Ifanyof2770

thosecasesarepresent,useh_te_interpasthecorrected2771

h_te_best_fit.OtherwiseuseweightedZasthecorrected2772

h_te_best_fit.2773

f. Computethedifferenceofthemediangroundheightfromthe2774

referenceDTMheight.Thisparameterish_dif_refinTable2.4.2775

2776

3. Ifthenumberofgroundphotonsinthesegment<=5%oftotalnumberof2777

classifiedphotonspersegment,2778

a. Reportaninvalidvalueforterrainproducts:h_te_mean,2779

h_te_median,h_te_min,h_te_max,h_te_mode,h_te_skew,h_te_std,2780

andh_te_uncertaintyrespectivelyasdescribedinTable2.1.2781

b. Ifthenumberofgroundphotonsinthesegmentis<=5%oftotal2782

numberofclassifiedphotonsinthesegment,computeterrain_slope2783

viaalinearfitoftheinterpolatedgroundsurface,FINALGROUND,2784

insteadofthegroundphotons.2785

c. Reportthemid-segmentinterpolatedterrainsurface,FinalGround,as2786

h_te_interpasdescribedinTable2.1,andreporth_te_best_fitasthe2787

h_te_interpvalue.2788

2789

4.16 ComputesegmentparametersfortheCanopyProducts2790

1. Foreach100msegment,determinetheclassedphotons(photonsclassifiedas2791

ground,canopy,ortopofcanopy).2792

a) Iftherearefewerthan50classedphotonsina100msegment,donot2793

calculatelandorcanopyproducts.2794

b) Ifthereare50ormoreclassedphotonsina100msegment,extractall2795

canopyphotons(i.e.,canopyandtopofcanopy;henceforthreferredto2796

as“canopy”unlessotherwisenoted)tocreatethecanopyproducts.2797

114

2. Onlycomputecanopyheightproductsifthenumberofcanopyphotonsis>2798

5%ofthetotalnumberofclassedphotonswithinthesegment(thiscontrol2799

valueof5%canbemodifiedonceonorbit).2800

a) Ifthenumberofgroundphotonsisalso>5%ofthetotalnumberof2801

classedphotonswithinthesegment,setcanopy_rh_confto2.2802

b) Ifthenumberofgroundphotonsis<5%ofthetotalnumberofclassed2803

photonswithinthesegment,continuewiththerelativecanopyheight2804

calculations,butsetcanopy_rh_confto1.2805

c) Ifthenumberofcanopyphotonsis<5%ofthetotalnumberofclassed2806

photons within the segment, regardless of ground percentage, set2807

canopy_rh_confto0andreportaninvalidvalueforeachcanopyheight2808

variable.2809

3. Again, the relative heights (height above the interpolated ground surface,2810

FINALGROUND)havebeencomputedalready.Allparametersderivedinthe2811

sectionarebasedonrelativeheights.2812

4. Sorttheheightsandcomputeacumulativedistributionoftheheights.Select2813

theheightassociatedwiththe98%maximumheight.Thisvalueish_canopy2814

listedinTable2.2.2815

5. Computestatisticsontherelativecanopyheights.Min,Mean,Median,Maxand2816

standard deviation. These values are reported on the product as2817

h_min_canopy, h_mean_canopy, h_max_canopy, and canopy_openness2818

respectivelyinTable2.2.2819

6. Usingthecumulativedistributionofrelativecanopyheights,selecttheheights2820

associatedwiththecanopy_h_metricspercentiledistributions(25,50,60,70,2821

75,80,85,90,95),andreportaslistedinTable2.2.2822

7. Compute the difference between h_canopy and canopy_h_metrics(50). This2823

parameterish_dif_canopyreportedinTable2.2andrepresentsanamountof2824

canopydepth.2825

8. Compute the standarddeviationof all photons thatwere labeledasTopof2826

Canopy(flag3)inthephotonlabelingportion.Thisvalueisreportedonthe2827

dataproductastoc_roughnesslistedinTable2.2.2828

115

9. Thequadraticmeanheight,h_canopy_quadiscomputedby2829

𝑞𝑚ℎ = (∑ )1-

K/-K/-$=> 2830

whereNca is the number of canopy photons in the segment and hi are the2831

individualcanopyheights.2832

2833

4.16.1 CanopyProductscalculatedwithabsoluteheights2834

1. Theabsolutecanopyheightproductsarecalculatedifthenumberofcanopy2835

photonsis>5%ofthetotalnumberofclassedphotonswithinthesegment.2836

Nonumberofgroundphotonsthresholdisappliedforthese.2837

2. Thecentroid_heightparameterinTable2.2isrepresentedbyalltheclassed2838

photonsforthesegment(canopy&ground).Todeterminethecentroid2839

height,computeacumulativedistributionofallabsoluteclassifiedheights2840

andselectthemedianheight.2841

3. Calculateh_canopy_abs,the98thpercentileoftheabsolutecanopyheights.2842

4. Computestatisticsontheabsolutecanopyheights:Min,Mean,Median,and2843

Max.Thesevaluesarereportedontheproductash_min_canopy_abs,2844

h_mean_canopy_abs,andh_max_canopy_abs,respectively,asdescribedin2845

Table2.2.2846

5. Again,usingthecumulativedistributionofabsolutecanopyheights,select2847

theheightsassociatedwiththecanopy_h_metrics_abspercentile2848

distributions(25,50,60,70,75,80,85,90,95),andreportaslistedinTable2849

2.2.2850

4.17 Recordfinalproductwithoutbuffer2851

1. NowthatallproductshavebedeterminedviaprocessingoftheL-km2852

segmentwiththebufferincluded,removetheproductsthatliewithinthe2853

bufferzoneoneachendoftheL-kmsegment.2854

2. RecordthefinalL-kmproductsandmoveontoprocessthenextL-km2855

segment.2856

116

2857

2858

117

5 DATAPRODUCTVALIDATIONSTRATEGY2859

AlthoughtherearenoLevel-1requirementsrelatedtotheaccuracyandprecision2860

oftheATL08dataproducts,wearepresentingamethodologyforvalidatingterrain2861

height, canopy height, and canopy cover once ATL08 data products are created.2862

Parametersfortheterrainandcanopywillbeprovidedatafixedsizeof100malong2863

thegroundtrackreferredtoasasegment.Validationofthedataparametersshould2864

occuratthe100msegmentscaleandresidualsofuncertaintiesarequantified(i.e.2865

averaged)atthe5-kmscale.This5-kmlengthscalewillallowforquantificationof2866

errors and uncertainties at a local scale which should reflect uncertainties as a2867

functionofsurfacetypeandtopography.2868

2869

5.1 ValidationData2870Swathmappingairbornelidaristhepreferredsourceofvalidationdataforthe2871

ICESat-2missionduetothefactthatitiswidelyavailableandtheerrorsassociated2872

with most small-footprint, discrete return data sets are well understood and2873

quantified.Profilingairbornelidarsystems(suchasMABEL)aremorechallengingto2874

useforvalidationduetothelowprobabilityofexactoverlapofflightlinesbetween2875

twoprofilingsystems(e.g.ICESat-2andMABEL).InorderfortheICESat-2validation2876

exercisetobestatisticallyrelevant,theairbornedatashouldmeettherequirements2877

listedinTable5.1.Validationdatasetsshouldpreferablyhaveaminimumaverage2878

pointdensityof5pts/m2. In some instances,however,validationdata setswitha2879

lowerpointdensitythatstillmeettherequirementsinTable5.1maybeutilizedfor2880

validationtoprovidesufficientspatialcoverage.2881

Table 5.1. Airborne lidar data vertical height (Z accuracy) requirements for validation data. 2882

ICESat-2ATL08Parameter Airbornelidar(rms)

Terrainheight <0.3moveropenground(vertical)

<0.5m(horizontal)

118

Canopyheight <2mtemperateforest,<3mtropicalforest

Canopycover n/a

2883

Terrainandcanopyheightswillbevalidatedbycomputingtheresidualsbetweenthe2884

ATL08terrainandcanopyheightvalue,respectively,foragiven100msegmentand2885

the terrain height (or canopy height) of the validation data for that same2886

representativedistance.CanopycoverontheATL08dataproductshallbevalidated2887

bycomputingtherelativecanopycover(cc=canopyreturns/totalreturns)forthe2888

samerepresentativedistanceintheairbornelidardata.2889

Itisrecommendedthatthevalidationprocessincludetheuseofancillarydatasets2890

(i.e.Landsat-derivedannualforestchangemaps)toensurethatthevalidationresults2891

arenoterrantlybiasedduetonon-equivalentcontentbetweenthedatasets.2892

Using a synergistic approach, we present two options for acquiring the required2893

validationairbornelidardatasets.2894

2895

Option1:2896

Wewill identifyandutilizefreelyavailable,opensourceairbornelidardataasthe2897

validation data. Potential repositories of this data include OpenTopo (a NSF2898

repositoryorairbornelidardata),NEON(aNSFrepositoryofecologicalmonitoring2899

in theUnited States), andNASAGSFC (repository of G-LiHTdata). In addition to2900

small-footprintlidardatasets,NASAMissiondata(i.e.ICESatandGEDI)canalsobe2901

usedinavalidationeffortforlargescalecalculations.2902

2903

Option2:2904

Option2willincludeOption1aswellastheacquisitionofadditionalairbornelidar2905

datathatwillbenefitmultipleNASAefforts.2906

119

GEDI:WiththelaunchoftheGlobalEcosystemsDynamicInvestigation2907

(GEDI)missionin2018,therearetremendoussynergisticactivitiesfor2908

datavalidationbetweenboththeICESat-2andGEDImissions.Sincethe2909

GEDI mission, housed on the International Space Station, has a2910

maximumlatitudeof51.6degrees,muchoftheBorealzonewillnotbe2911

mapped by GEDI. The density of GEDI datawill increase as latitude2912

increasesnorthto51.6degrees.SincethedatadensityforGEDIwould2913

be at its highest near 51.6 degrees, we would propose to acquire2914

airborne lidar data in a “GEDI overlap zone” that would ample2915

opportunitytohavesufficientcoverageofbenefittobothICESat-2and2916

GEDIforcalibrationandvalidation.2917

Werecommendtheacquisitionofnewairbornelidarcollectionsthatwillmeetour2918

requirementstobestvalidateICESat-2aswellasbebeneficialfortheGEDImission.2919

Inparticular,wewouldliketoobtaindataoverthefollowingtwoareas:2920

1) Borealforest(asthisforesttypewillNOTbemappedwithGEDI)2921

2) GEDIhighdensityzone(between50to51.6degreesN).Airbornelidardata2922

intheGEDI/ICESat-2overlapzonewillensurecross-calibrationbetween2923

these two critical datasetswhichwill allow for the creationof a global,2924

seamless terrain, canopy height, and canopy cover product for the2925

ecosystemcommunity.2926

Inbothcases,wewouldflydatawiththefollowingscenario:2927

Small-footprint,full-waveform,dualwavelength(greenandNIR),highpointdensity2928

(>20pts/m2)and,overlowandhighrelieflocations.Inaddition,thenewlyacquired2929

lidardatamustmeettheerroraccuracieslistedinTable5.1.2930

Potentialcandidateacquisitionareasinclude:SouthernCanadianRockyMountains2931

(near Banff), Pacific Northwest mountains (Olympic National Park, Mt. Baker-2932

Snoqualmie National Forest), and Sweden/Norway. It is recommended that the2933

120

airbornelidaracquisitionsoccurduringthesummermonthstoavoidsnowcoverin2934

either2016or2017priortolaunchofICESat-2.2935

2936

5.2 InternalQCMonitoring2937

In addition to the data product validation, internal monitoring of data2938

parameters and variables is required to ensure that the final ATL08 data quality2939

outputistrustworthy.Table5.2listsafewofthecomputedparametersthatshould2940

provide insight into the performance of the surface finding algorithm within the2941

ATL08processingchain.2942

Table 5.2. ATL08 parameter monitoring. 2943

Group Description Source Monitor ValidateinField

h_te_median Medianterrainheightforsegment computed Yesagainstairbornelidardata.Theairbornelidardatashouldhaveanabsoluteaccuracyof<30cmrms.

n_te_photonsn_ca_photonsn_toc_photons

Numberofclassed(sumofterrain,canopy,andtopofcanopy)photonsina100msegment

computed Yes.Buildaninternalcounterforthenumberofsegmentsinarowwheretherearen’tenoughphotons(currentlyaminimumof50photons

121

per100msegmentisused)

h_te_interp Interpolatedterrainsurfaceheight,FINALGROUND

computed Differenceh_te_interpandh_te_mediananddetermineifthevalueis>aspecifiedthreshold.2missuggestedasthethresholdvalue.Thisisaninternalchecktoevaluatewhetherthemedianelevationforasegmentisroughlythesameastheinterpolatedsurfaceheight.

h_dif_ref Differencebetweenh_te_medianandref_dem

computed Thisvaluewillbecomputedandflaggedifthedifferenceis>25m.ThereferenceDEMistheonboardDEM.

h_canopy 95%heightofindividualcanopyheightsforsegment

computed Yes,>aspecifiedthreshold(e.g.60m)

Yesagainstairbornelidardata.The

122

canopyheightsderivedfromairbornelidardatashouldhavearelativeaccuracy<2mintemperateforest,<3mintropicalforest

h_dif_canopy Differencebetweenh_canopyandcanopy_h_metrics(50)

computed Yes,thisisaninternalchecktomakesurethecalculationsoncanopyheightarenotsuspect

psf_flag FlagissetifcomputedPSFexceeds1m computed Yes,thisisaninternalchecktomakesurethecalculationsarenotsuspect

ph_removal_flag Flagissetifmorethan50%ofclassifiedphotonsinasegmentisremovedduringfinalQAcheck

computed

dem_removal_flag Flagissetifmorethan20%ofclassifiedphotonsinasegmentisremovedduetoalargedistancefromthereferenceDEM

computed Yes,thiswillcheckifbadresultsareduetobadDEMvaluesorbecausetoomuchnoisewaslabeledassignal

2944

123

InadditiontothemonitoringparameterslistedinTable5.2,aplotsuchaswhatis2945

showninFigure5.1wouldbehelpfulforinternalmonitoringandquality2946

assessmentoftheATL08dataproduct.Figure5.1illustratesingraphicalformwhat2947

theinputpointcloudlooklikeinthealong-trackdirection,theclassificationsofeach2948

photon,andtheestimatedgroundsurface(FINALGROUND).2949

2950

Figure 5.1. Example of L-km segment classifications and interpolated ground surface. 2951

2952

124

ThefollowingparametersaretobecalculatedandplacedintheQA/QCgrouponthe2953

HDF5datafile,basedonTable5.2oftheATL08ATBD.Statisticsshallbecomputed2954

onaper-granulebasisandreportedonthedataproduct.Ifanyparametermeetsthe2955

QAtriggerconditional,analertwillbesenttotheATL08ATBDteamforproduct2956

review.2957

Table 5.3. QA/QC trending and triggers. 2958

QA/QCtrendingdescription QAtriggerconditional

Percentageofsegmentswith>50classedphotons None

Max,median,andmeanofthenumberofcontiguous

segmentswith<50classedphotons

None

Numberandpercentageofsegmentswithdifferencein

h_te_interp–h_te_medianisgreaterthanaspecified

threshold(2mTBD)

>50segmentsinarow

Max,median,andmeanofh_diff_refoverallsegments None

Percentageofsegmentswhereh_diff_ref>25m Percentage>75%

Percentageofsegmentswheretheh_canopyis>60m None

Max,median,andmeanofh_diff None

NumberandpercentageofLandsatcontinuoustree

coverpixelsperprocessing(L-km)segmentwith

values>100

None

Percentageofsegmentswherepsf_flagisset Percentage>75%

Percentageofclassifiedphotonsremovedinasegment

duringfinalphotonQAcheck

Percentage>50%

(i.e.,ph_removal_flagis

settotrue)

125

Percentageofclassifiedphotonsremovedinasegment

duringthereferenceDEMthresholdremovalprocess

Percentage>20%

(i.e.,dem_removal_flagis

settotrue)

2959

2960

126

6 REFERENCES2961

2962

Carroll,M.L.,Townshend,J.R.,DiMiceli,C.M.,Noojipady,P.,&Sohlberg,R.A.2963

(2009).Anewglobalrasterwatermaskat250mresolution.InternationalJournalof2964

DigitalEarth,2(4),291–308.http://doi.org/10.1080/175389409029514012965

Channan,S.,K.Collins,andW.R.Emanuel(2014).Globalmosaicsofthestandard2966

MODISlandcovertypedata.UniversityofMarylandandthePacificNorthwest2967

NationalLaboratory,CollegePark,Maryland,USA.2968

Chauve,Adrien,etal.(2008).Processingfull-waveformlidardata:modellingraw2969

signals.Internationalarchivesofphotogrammetry,remotesensingandspatial2970

informationsciences2007,102-107.2971

Cleveland,W.S.(1979).RobustLocallyWeightedRegressionandSmoothing2972

Scatterplots.JournaloftheAmericanStatisticalAssociation,74(368),829–836.2973

http://doi.org/10.2307/22864072974

Friedl,M.A.,D.Sulla-Menashe,B.Tan,A.Schneider,N.Ramankutty,A.SibleyandX.2975

Huang(2010).MODISCollection5globallandcover:Algorithmrefinementsand2976

characterizationofnewdatasets,2001-2012,Collection5.1IGBPLandCover,2977

BostonUniversity,Boston,MA,USA.2978

Fritsch,F.N.,andCarlson,R.E.(1980).MonotonePiecewiseCubicInterpolation.2979

SIAMJournalonNumericalAnalysis,17(2),238–246.2980

http://doi.org/10.1137/07170212981

Goshtasby,A.,andO’Neill,W.D.(1994).CurvefittingbyaSumofGaussians.2982

GraphicalModelsandImageProcessing,56(4),281-288.2983

GoetzandDubayah(2011).Advancesinremotesensingtechnologyand2984

implicationsformeasuringandmonitoringforestcarbonstocksandchange.Carbon2985

Management,2(3),231-244.doi:10.4155/cmt.11.182986

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Hall,F.G.,Bergen,K.,Blair,J.B.,Dubayah,R.,Houghton,R.,Hurtt,G.,Kellndorfer,J.,2987

Lefsky,M.,Ranson,J.,Saatchi,S.,Shugart,H.,Wickland,D.(2011).Characterizing3D2988

vegetationstructurefromspace:Missionrequirements.Remotesensingof2989

environment,115(11),2753-27752990

Harding,D.J.,(2009).Pulsedlaseraltimeterrangingtechniquesandimplicationsfor2991

terrainmapping,inTopographicLaserRangingandScanning:Principlesand2992

Processing,JieShanandCharlesToth,eds.,CRCPress,Taylor&FrancisGroup,173-2993

194.2994

Neuenschwander,A.L.andMagruder,L.A.(2016).Thepotentialimpactofvertical2995

samplinguncertaintyonICESat-2/ATLASterrainandcanopyheightretrievalsfor2996

multipleecosystems.RemoteSensing,8,1039;doi:10.3390/rs81210392997

Neuenschwander,A.L.andPitts,K.(2019).TheATL08LandandVegetationProduct2998

fortheICESat-2Mission.RemoteSensingofEnvironment,221,247-259.2999

https://doi.org/10.1016/j.rse.2018.11.0053000

Neumann,T.,Brenner,A.,Hancock,D.,Robbins,J.,Saba,J.,Harbeck,K.(2018).ICE,3001

CLOUD,andLandElevationSatellite–2(ICESat-2)ProjectAlgorithmTheoretical3002

BasisDocument(ATBD)forGlobalGeolocatedPhotons(ATL03).3003

Olson,D.M.,Dinerstein,E.,Wikramanayake,E.D.,Burgess,N.D.,Powell,G.V.N.,3004

Underwood,E.C.,D'Amico,J.A.,Itoua,I.,Strand,H.E.,Morrison,J.C.,Loucks,C.J.,3005

Allnutt,T.F.,Ricketts,T.H.,Kura,Y.,Lamoreux,J.F.,Wettengel,W.W.,Hedao,P.,3006

Kassem,K.R.(2001).Terrestrialecoregionsoftheworld:anewmapoflifeonEarth.3007

Bioscience,51(11),933-938.3008

Sexton,J.O.,Song,X.-P.,Feng,M.Noojipady,P.,Anand,A.,Huang,C.,Kim,D.-H.,3009

Collins,K.M.,Channan,S.,DiMiceli,C.,Townshend,J.R.G.(2013).Global,30-m3010

resolutioncontinuousfieldsoftreecover:Landsat-basedrescalingofMODIS3011

VegetationContinuousFieldswithlidar-basedestimationsoferror.International3012

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128

3014

129

AppendixA 3015DRAGANNGaussianDeconstruction3016JohnRobbins30172015102130183019UpdatesmadebyKatherinePitts:30202017080830212018121830223023

Introduction3024

ThisdocumentprovidesaverbaldescriptionofhowtheDRAGANN(Differential,3025Regressive,andGaussianAdaptiveNearestNeighbor)filteringsystemdeconstructs3026ahistogramintoGaussiancomponents,whichcanalsobecallediterativelyfittinga3027sumofGaussianCurves.ThepurposeistoprovideenoughdetailforASAStocreate3028operationalICESat-2coderequiredfortheproductionoftheATL08,Landand3029Vegetationproduct.ThisdocumentcoversthefollowingMatlabfunctionswithin3030DRAGANN:3031

• mainGaussian_dragann3032• findpeaks_dragann3033• peakWidth_dragann3034• checkFit_dragann3035

3036

Componentsofthek-dtreenearest-neighborsearchprocessingandhistogram3037creationwerecoveredinthedocument,DRAGANNk-dTreeInvestigations,andhave3038beendeterminedtofunctionconsistentlywithUTexasDRAGANNMatlabsoftware.3039

3040

HistogramCreation3041

Stepstoproduceahistogramofnearest-neighborcountsfromanormalizedphoton3042cloudsegmenthavebeencompletedandconfirmed.FigureA.1providesanexample3043ofsuchahistogram.Thedevelopment,below,isspecifictothetwo-dimensional3044caseandisprovidedasareview.3045

Thehistogramrepresentsthefrequency(count)ofthenumberofnearbyphotons3046withinaspecifiedradius,asascertainedforeachpointwithinthephotoncloud.The3047radius,R,isestablishedbyfirstnormalizingthephotoncloudintime(x-axis)andin3048height(y-axis),i.e.,bothsetsofcoordinates(time&height)runfrom0to1;thenan3049averageradiusforfinding20pointsisdeterminedbasedonformingtheratioof203050tothetotalnumberofthephotonsinthecloud(Ntotal):20/Ntotal.3051

3052

130

3053

FigureA.1.HistogramforMabeldata,channel43fromSE-AKflightonJuly30,20143054at20:16.3055

Giventhatthetotalareaofthenormalizedphotoncloudis,bydefinition,1,thenthis3056ratiogivestheaveragearea,A,inwhichtofind20points.Acorrespondingradiusis3057foundbythesquarerootofA/π.Asingleequationdescribingtheradius,asa3058functionofthetotalnumberofphotonsinthecloud(rememberingthatthisisdone3059inthecloudnormalized,two-dimensionalspace),isgivenby3060

𝑅 = (4: K)2)",⁄M

(A.1)3061

FortheexampleinFigureA.1,Rwasfoundtobe0.00447122.Thenumberof3062photonsfallingintothisradius,ateachpointinthephotoncloud,isgivenalongthe3063x-axis;acountoftheirnumber(orfrequency)isgivenalongthey-axis.3064

3065

GaussianPeakRemoval30663067Atthispoint,thefunction,mainGaussian_dragann,iscalled,whichpassesthe3068histogramandthenumberofpeakstodetect(typicallysetto10).3069

Thisfunctionessentiallyestimates(i.e.,fits)asequenceofGaussiancurves,from3070largertosmaller.ItdeterminesaGaussianfitforthehighesthistogrampeak,then3071removesitbeforedeterminingthefitforthenexthighestpeak,etc.Inconcept,the3072processisaniterativesequential-removalofthetenlargestGaussiancomponents3073withinthehistogram.3074

131

Intheprocessofsequentialleast-squares,parametersarere-estimatedwheninput3075dataisincrementallyincreasedand/orimproved.Thepresentproblemoperatesin3076aslightlyreverseway:thedatasetisfixed(i.e.,thehistogram),butcomponents3077withinthehistogram(independentGaussiancurvefits)areremovedsequentially3078fromthehistogram.ThepaperbyGoshtasby&O’Neill(1994)outlinestheconcepts.3079

RecallthataGaussiancurveistypicallywrittenas3080

𝑦 = 𝑎 ∙ 𝑒𝑥𝑝(−(𝑥 − 𝑏)4 2𝑐4⁄ ) (A.2)3081

wherea=theheightofthepeak;b=positionofthepeak;andc=widthofthebell3082curve.3083

Thefunction,mainGaussian_dragann,computesthe[a,b,c]valuesfortheten3084highestpeaksfoundinthehistogram.Atinitialization,these[a,b,c]valuesaresetto3085zero.Theprocessbeginsbylocatinghistogrampeaksviathefunction,3086findpeaks_dragann.3087

3088

PeakFinding3089

Asinputarguments,thefindpeaks_dragannfunctionreceivesthehistogramanda3090minimumpeaksizeforconsideration(typicallysettozero,whichmeansallpeaks3091willbefound).Anarrayofindexnumbers(i.e.,the“numberofneighboringpoints”,3092valuesalongx-axisofFigureA.1)forallpeaksisreturnedandplacedintothe3093variablepeaks.3094

Themethodologyforlocatingeachpeakgoeslikethis:Thefunctionfirstcomputes3095thederivativesofthehistogram.InMatlabthereisanintrinsicfunction,calleddiff,3096whichcreatesanarrayofthederivatives.Diffessentiallycomputesthedifferences3097alongsequential,neighboringvalues.“Y=diff(X)calculatesdifferencesbetween3098adjacentelementsofX.”[fromMatlabReferenceGuide]Oncethederivativesare3099computed,thenfindpeaks_dragannentersaloopthatlooksforchangesinthesign3100ofthederivative(positivetonegative).Itskipsanyderivativesthatequalzero.3101

Forthekthderivative,the“next”derivativeissettok+1.Atestismadewherebyif3102thek+1derivativeequalszeroandk+1islessthanthetotalnumberofhistogram3103values,thenincrement“next”tok+2(i.e.,findthenextnegativederivative).Thetest3104isiterateduntilthestartofthe“downside”ofthepeakisfound(i.e.,theseiterations3105handlecaseswhenthepeakhasaflattoptoit).3106

Whenasignchange(positivetonegative)isfound,thefunctionthencomputesan3107approximateindexlocation(variablemaximum)ofthepeakvia3108

𝑚𝑎𝑥𝑖𝑚𝑢𝑚 = 𝑟𝑜𝑢𝑛𝑑 T0*A%?N4

U + 𝑘 (A.3)3109

132

Thesevaluesofmaximumareretainedinthepeaksarray(whichcanbegrownin3110Matlab)andreturnedtothefunctionmainGaussian_dragann.3111

Next,backwithinmainGaussian_dragann,therearetwoteststodeterminewhether3112thefirstorlastelementsofthehistogramarepeaks.Thisisdonesincethe3113findpeaks_dragannfunctionwillnotdetectpeaksatthefirstorlastelements,based3114solelyonderivatives.Thetestsare:3115

If(histogram(1)>histogram(2)&&max(histogram)/histogram(1)<20)then3116insertavalueof1totheveryfirstelementofthepeaksarray(again,Matlabcan3117easily“grow”arrays).Here,max(histogram)isthehighestpeakvalueacrossthe3118wholehistogram.3119

Forthecaseofthelasthistogramvalue(saythereareN-bins),wehave3120

If(histogram(N)>histogram(N-1)&&max(histogram)/histogram(N)<4)then3121insertavalueofNtotheverylastelementofthepeaksarray.3122

Onemoretestismadetodeterminewhetherthereanypeakswereactuallyfound3123forthewholehistogram.Ifnonewerefound,thenthefunction,3124mainGaussian_dragann,merelyexits.3125

3126

IdentifyingandProcessingupontheTenHighestPeaks3127

Thefunction,mainGaussian_dragann,nowbeginsalooptoanalyzethetenhighest3128peaks.Itbeginsthenthloop(wherengoesfrom1to10)bysearchingforthelargest3129peakamongallremainingpeaks.Theindexnumber,aswellasthemagnitudeofthe3130peak,areretainedinavariable,calledmaximum,withdimension2.3131

Ineachpassintheloop,the[a,b,c]values(seeeq.2)areretainedasoutputofthe3132function.Thevaluesofaandbaresetequaltotheindexnumberandpeak3133magnitudesavedinmaximum(1)andmaximum(2),respectively.Thec-valueis3134determinedbycallingthefunction,peakWidth_dragann.3135

DeterminationofGaussianCurveWidth3136

Thefunction,peakWidth_dragann,receivesthewholehistogramandtheindex3137number(maximum(1))ofthepeakforwhichthevaluecisneeded,asarguments.3138Foraspecificpeak,thefunctionessentiallysearchesforthepointonthehistogram3139thatisabout½thesizeofthepeakandthatisfurthestawayfromthepeakbeing3140investigated(leftandrightofthepeak).Ifthetwosides(leftandright)are3141equidistantfromthepeak,thenthesidewiththesmallestvalueischosen(>½3142peak).3143

Uponentry,itfirstinitializesctozero.Thenitinitializestheindexvaluesleft,xLand3144right,xRasindex-1andindex+1,respectively(thesewillbeusedinaloop,3145

133

describedbelow).Itnextcheckswhetherthenthpeakisthefirstorlastvalueinthe3146histogramandtreatsitasaspecialcase.3147

Atinitialization,firstandlasthistogramvaluesaretreatedasfollows:3148

Iffirstbinofhistogram(peak=1),setleft=1andxL=1.3149

Iflastbinofhistogram,setright=mandxR=m,wheremisthefinalindexofthe3150histogram.3151

Next,asearchismadetotheleftofthepeakforanearbyvaluethatissmallerthan3152thepeakvalue,butlargerthanhalfofthepeakvalue.Awhile-loopdoesthis,with3153thefollowingconditions:(a)left>0,(b)histogramvalueatleftis≥halfofhisto3154valueatpeakand(c)histovalueatleftis≤histovalueatpeak.Whenthese3155conditionsarealltrue,thenxLissettoleftandleftisdecrementedby1,sothatthe3156testcanbemadeagain.Whentheconditionsarenolongermet(i.e.,we’vemovedto3157abininthehistogramwherethevaluedropsbelowhalfofthepeakvalue),thenthe3158programbreaksoutofthewhileloop.3159

Thisisfollowedbyasimilarsearchmadeuponvaluestotherightofthepeak.When3160thesetwowhile-loopsarecomplete,wethenhavetheindexnumbersfromthe3161histogramrepresentingbinsthatareabovehalfthepeakvalue.Thisisshownin3162FigureA.2.3163

3164

FigureA.2.SchematicrepresentationofahistogramshowingxLandxRparameters3165determinedbythefunctionpeakWidth_dragann.3166

Atestismadetodeterminewhichoftheseisfurthestfromthemiddleofthepeak.In3167FigureA.2,xLisfurthestawayandthevariablexissettoequalxL.Thehistogram3168

134

“height”atx,whichwecallVx,isused(aswellasx)inaninversionofEquationA.23169tosolveforc:3170

𝑐 = W?(A?#)-

4DOG34" H (A.4)3171

Thefunction,peakWidth_dragann,nowreturnsthevalueofcandcontrolreturnsto3172thefunction,mainGaussian_dragann.3173

ThemainGaussian_dragannfunctionthenpicks-upwithatestonwhetherthe3174returnedvalueofciszero.Ifso,thenuseavalueof4,whichisbasedonanapriori3175understandingthatcusuallyfallsbetween4and6.Ifthevalueofcisnotzero,then3176add0.5toc.3177

Atthispoint,wehavethe[a,b,c]valuesoftheGaussianforthenthpeak.Basedon3178thesevalues,theGaussiancurveiscomputed(viaEquationA.2)anditisremoved3179(subtracted)fromthecurrenthistogram(andputintoanewvariablecalled3180newWave).3181

AfteraGaussiancurveisremovedfromthecurrenthistogram,thefollowingpeak3182widthcalculationscouldpotentiallyhaveaVxvaluelessthan1froma.Thiswould3183causethewidth,c,tobecalculatedasunrealisticallylarge.Therefore,acheckisput3184inplacetodetermineifa-Vx<1.Ifso,Vxissettoavalueofa-1.3185

NumericOptimizationSteps3186

ThefirstoftheoptimizationstepsutilizesaFullWidthHalfMax(FWHM)approach,3187computedvia3188

𝐹𝑊𝐻𝑀 = 2𝑐√2𝑙𝑛2 (A.5)3189

Aleftrange,Lr,iscomputedbyLr=round(b-FWHM/2).Thistestedtomakesureit3190doesn’tgoofftheleftedgeofthehistogram.Ifso,thenitissetto1.3191

Similarly,arightrange,Rr,iscomputedbyRr=round(b+FWHM/2).Thisisalsotested3192tobesurethatitdoesn’tgoofftherightedgeofthehistogram.Ifso,thenitissetto3193theindexvaluefortheright-mostedgeofthehistogram.3194

Usingthesenewrangevalues,createatemporarysegment(betweenLrandRr)of3195thenewWavehistogram,thisiscallederrorWave.Also,setthreedeltaparameters3196forfurtheroptimization:3197

DeltaC=0.05; DeltaB=0.02; DeltaA=13198

Thetemporarysegment,errorWaveispassedtothefunctioncheckFit_dragann,3199alongwithasetofzerovalueshavingthesamenumberofelementsaserrorWave,3200theresult,atthispoint,issavedintoavariablecalledoldError.Thefunction,3201checkFit_dragann,computesthesumofthesquaresofthedifferencebetweentwo3202

135

histogramsegments(inthiscase,errorWaveandzeroswiththesamenumberof3203elementsaserrorWave).Hence,theresult,oldError,isthesumofthesquaresofthe3204valuesoferrorWave.Thisfunctionisappliedinoptimizationloops,torefinethe3205valuesofbandc,describedbelow.3206

Optimizationoftheb-parameter.Thedo-loopoperatesatamaximumof1000times.3207It’spurposeistorefinethevalueofb,in0.02increments.Itincrementsthevalueof3208bbyDeltaB,totheright,andcomputesanewGaussiancurvebasedonb+∆b,which3209isthenremovedfromthehistogramwiththeresultgoingintothevariable3210newWave.Asbefore,checkFit_draganniscalledbypassingtherange-limitedpartof3211newWave(errorWave)andreturninganewestimateoftheerror(newError)which3212isthencheckedagainstoldErrortodeterminewhichissmaller.IfnewErroris≥3213oldError,thenthevalueofbthatproducedoldErrorisretained,andthetestingloop3214isexited.3215

Optimizationofthec-parameter.Nowthevalueofcisoptimized,firsttotheleft,3216thentotheright.Itisperformedindependentlyof,butsimilarly,totheb-parameter,3217usingdo-loopswithamaximumof1000passes.Theseloopsincrement(toright)or3218decrement(toleft)byavalueof0.05(DeltaC)andusecheckFit_dragannto,again,3219checkthequalityofthefit.Theloops(rightandleft)kick-outwhenthefitisfoundto3220besmallest.3221

Thefinal,optimizedGaussiancurveisnowremoved(subtracted)fromthe3222histogram.Afterremoval,astatement“corrects”anyhistogramvaluesthatmay3223dropbelowzero,bysettingthemtozero.Thiscouldhappenduetoanymis-fitofthe3224Gaussian.3225

Thenthloopisconcludedbyexaminingthepeaksremaininginthehistogram3226withoutthepeakjustprocessedbysendingthenth-residualhistogrambackintothe3227functionfindpeaks_dragann.Ifthereturnofpeakindexnumbersfrom3228findpeaks_dragannrevealsmorethan1peakremaining,thentheindexnumbersfor3229peaksthatmeetthesethreecriteriaareretainedinanarrayvariablecalledthese:3230

1. Thepeakmustbelocatedaboveb(n)-2*c(n),and32312. Thepeakmustbelocatedbelowb(n)+2*c(n),and32323. Theheightofthepeakmustbe<a(n)/5.3233

3234

Thepeaksmeetingallthreeofthesecriteriaaretobeeliminatedfromfurther3235consideration.Whatthisaccomplishesiseliminatethenearbypeaksthathaveasize3236lowerthanthepeakjustpreviouslyanalyzed;thus,aftertheirelimination,only3237leavingpeaksthatarefurtherawayfromthepeakjustprocessedandare3238presumably“real”peaks.Thenthiterationendshere,andprocessingbeginswiththe3239revisedhistogram(afterhavingremovedthepeakjustanalyzed).3240

3241

136

GaussianRejection3242

ThefunctionmainGaussian_dragannreturnsthe[a,b,c]parametersfortheten3243highestpeaksfromtheoriginalhistogram.Theremainingcodeindragannexamines3244eachofthetenGaussianpeaksandeliminatestheonesthatfailtomeetavarietyof3245conditions.Thissectiondetailshowthisisaccomplished.3246

First,anapproximatearea,area1=a*c,iscomputedforeachfoundpeakandb,forall3247tenpeaks,beingtheindexofthepeaks,areconvertedtoanactualvaluevia3248b+min(numptsinrad)-1(callthisallb).3249

Next,arejectionismadeforallpeaksthathaveanycomponentof[a,b,c]thatare3250imaginary(Matlabisrealfunctionisusedtoconfirmthatallthreecomponentsare3251real,inwhichcaseitpasses).3252

Tocheckforanarrownoisepeakatthebeginningofthehistogramincasesoflow3253noiserates,suchasduringnighttimepasses,acheckismadetofirstdetermineifthe3254highestGaussianamplitude,a,withinthefirst5%ofthehistogramis>=1/10*the3255maximumamplitudeofallGaussians.Ifso,thatpeak’sGaussianwidth,c,ischecked3256todetermineifitis<=4bins.Ifneitherofthoseconditionsaremetinthefirst5%,3257theconditionsarerecheckedforthefirst10%ofthehistogram.Thisprocessis3258repeatedupto30%ofthehistogram,in5%intervals.Onceanarrownoisepeakis3259found,theprocessbreaksoutoftheincremental5%histogramchecks,andthe3260noisepeakvaluesarereturnedas[a0,b0,c0].3261

Ifanarrownoisepeakwasfound,theremainingpeakareavalues,area1(a*c),then3262passthroughadescendingsort;ifnonarrownoisepeakwasfound,allpeakareasgo3263throughthedescendingsort.Sonow,the[a,allb,c]-valuesaresortedfromlargest3264“area”tosmallest,theseareplacedinarrays[a1,b1,c1].Ifanarrownoisepeakwas3265found,itisthenappendedtothebeginningofthe[a1,b1,c1]arrays,suchthata1=3266[a0a1],b1=[b0b1],c1=[c0c1].3267

Inthecasethatanarrownoisepeakwasnotfound,atestismadetocheckthatat3268leastoneofthepeaksiswithinthefirst10%ofthewholehistogram.Itisdone3269insidealoopthatworksfrompeak1tothenumberofpeaksleftatthispoint.This3270loopfirsttestswhetherthefirst(sorted)peakiswithinthefirst10%ofthe3271histogram;ifso,thenitsimplykicksoutoftheloop.Ifnot,thenitplacestheloop’s3272currentpeakintoaholder(ihold)variable,incrementsthelooptothenextpeakand3273runsthesametestonthesecondpeak,etc.Here’saMatlabcodesnippet:3274

inds = 1:length(a1); 3275for i = 1:length(b1) 3276 if b1(i) <= min(numptsinrad) + 1/10*max(numptsinrad) 3277 if i==1 3278 break; 3279 end 3280 ihold = inds(i); 3281 for j = i:-1:2 3282 inds(j) = inds(j-1); 3283 end 3284 inds(1) = ihold; 3285

137

break 3286 end 3287end 3288

3289

Thej-loopexpressiongivestheinit_val:step_val:final_val.Thesemi-colonattheend3290ofstatementscausesMatlabtoexecutetheexpressionwithoutprintouttotheuser’s3291screen.Whenthisloopiscomplete,thentheindexes(inds)arere-orderedand3292placedbackintothe[a1,b1,c1]andarea1arrays.3293

Next,areteststorejectanyGaussianpeakthatisentirelyencompassedbyanother3294peak.AMatlabcodesnippethelpstodescribetheprocessing.3295

% reject any gaussian if it is fully contained within another 3296isR = true(1,length(a1)); 3297for i = 1:length(a1) 3298 ai = a1(i); 3299 bi = b1(i); 3300 ci = c1(i); 3301 aset = (1-(c1/ci).^2); 3302 bset = ((c1/ci).^2*2*bi - 2*b1); 3303 cset = -(2*c1.^2.*log(a1/ai)-b1.^2+(c1/ci).^2*bi^2); 3304 realset = (bset.^2 - 4*aset.*cset >= 0) | (a1 > ai); 3305 isR = isR & realset; 3306end 3307a2 = a1(isR); 3308b2 = b1(isR); 3309c2 = c1(isR); 3310

3311

ThelogicalarrayisRisinitializedtoallbetrue.Thei-do-loopwillrunthroughall3312peaks.Thecomputationsaredoneinarrayformwiththevariablesaset,bset,csetall3313beingarraysoflength(a1).Atthebottomoftheloop,isRremains“true”when3314eitheroftheconditionsintheexpressionforrealsetismet(thesingle“|”isalogical3315“or”).Also,thenomenclature,“.*”and“.^”,denoteelement-by-elementarray3316operations(notmatrixoperations).Uponexitingthei-loop,thearrayvariables3317[a2,b2,c2]aresettothe[a1,b1,c1]thatremainas“true.”[Atthispoint,inourtest3318casefromchannel43ofEast-AKMableflighton20140730@20:16,sixpeaksare3319stillretained:18,433,252,33,44.4and54.]3320

Next,rejectGaussianpeakswhosecenterslaywithin3σofanotherpeak,unlessonly3321twopeaksremain.Thecodesnippetlookslikethis:3322

isR = true(1, length(a2)); 3323for i = 1:length(a2) 3324 ai = a2(i); 3325 bi = b2(i); 3326 ci = c2(i); 3327 realset = (b2 > bi+3*ci | b2 < bi-3*ci | b2 == bi); 3328 realset = realset | a2 > ai; 3329 isR = isR & realset; 3330end 3331if length(a2) == 2 3332 isR = true(1, 2); 3333end 3334a3 = a2(isR); 3335

138

b3 = b2(isR); 3336c3 = c2(isR); 3337

3338

Onceagain,theisRarrayisinitiallysetto“true.”Now,thearray,realset,istested3339twice.Inthefirstline,oneofthreeconditionsmustbetrue.Inthesecondline,if3340realsetistrueora2>ai,thenitremainstrue.Atthispoint,we’vepareddown,from3341tenGaussianpeaks,totwoGaussianpeaks;onerepresentsthenoisepartofthe3342histogram;theotherrepresentsthesignalpart.3343

Iftherearelessthantwopeaksleft,athresholding/histogramerrormessageis3344printedout.IfthelastTryFlagisnotset,DRAGANNendsitsprocessingandanempty3345IDXvalueisreturned.ThelastTryFlagissetinthepreprocessingfunctionwhich3346callsDRAGANN,asmultipleDRAGANNrunsmaybetrieduntilsufficientsignalis3347found.3348

Iftherearetwopeaksleft,thensetthearray[a,b,c]tothosetwopeaks.[Atthis3349point,inourtestcasefromchannel43ofEast-AKMableflighton20140730@335020:16,thetwopeaksare:18and433.]3351

3352

GaussianThresholding3353

WiththetwoGaussianpeaksidentifiedasnoiseandsignal,allthatisleftisto3354computethethresholdvaluebetweentheGaussians.3355

Anarrayofxvalsisestablishedrunningfrommin(numptsinrad)to3356max(numptsinrad).Inourexample,xvalshasindicesbetween0and653.Foreach3357ofthesexvals,Gaussiancurves(allGauss)arecomputedforthetwoGaussianpeaks3358[a,b,c]determinedattheendoftheprevioussection.Thiscomputationisperformed3359viaafunctioncalledgaussmakerwhichreceives,asinput,thexvalsarrayandthe3360[a,b,c]parametersforthetwoGaussiancurves.AnarrayofheightsoftheGaussian3361curvesisreturnedbythefunction,computedwithEquationA.2.InMatlab,the3362allGaussarrayhasdimension2x654.Anarray,noiseGaussissettobeequaltothe33631stcolumnofallGauss.3364

Anif-statementcheckswhetherthebarrayhasmorethan1element(i.e.,consisting3365oftwopeaks),ifso,thennextGaussissettothe2ndcolumnofallGauss,anda3366difference,noiseGauss-nextGauss,iscomputed.3367

Thefollowingstepsarerestrictedtobebetweenthetwomainpeaks.First,thefirst3368indexoftheabsolutevalueofthedifferencethatisnear-zero(definedas1e-8)is3369found,ifitexists,andputintothevariablediffNearZero.Thisisexpectedtobefound3370ifthetwoGaussiansarefarawayfromeachotherinthehistogram.3371

Second,thepoint(i.e.,index)isfoundoftheminimumoftheabsolutevalueofthe3372difference;thisindexisputintovariable,signchanges.Thispointiswherethesign3373changesfrompositivetonegativeasonemovesleft-to-right,uptheGaussiancurve3374

139

differences(noiseminusnextwillbepositiveunderthepeakofthenoisecurve,and3375negativeunderthenext(signal)curve).FigureA.3(top)showsthetwoGaussian3376curves.Thebottomplotshowstheirdifferences.3377

3378

FigureA.3.Top:tworemainingGaussiancurvesrepresentingthenoise(blue)and3379signal(red)portionsofthehistograminF1gureA.1.Bottom:differencenoise–3380signalofthetwoGaussiancurves.Thethresholdisdefinedasthepointwherethe3381signofthedifferenceschange.3382

IfthereisanyvaluestoredindiffNearZero,thatvalueisnowsavedintothevariable3383threshNN.Else,thevalueofthethresholdinsignchangesissavedintothreshNN,3384concludingtheif-statementforbhavingmorethan1element.3385

0

200

400

Gauss

ian V

alu

e

0 100 200 300 400 500 600

number of points inside radius

Noise GaussianSignal Gaussian

−200

0

200

400

Gauss

ian D

iffere

nce

s

0 100 200 300 400 500 600

number of points inside radius

Threshold

140

Anelseclause(b!>1),merelysetsthreshNNtob+c,i.e.,1-standarddeviationaway3386frommeanofthe(presumably)noisepeak.3387

Thefinalstepismaskthesignalpartofthehistogramwhereallindicesabovethe3388threshNNindexaresettological1(true).Thisisappliedtothenumptsinradarray,3389whichrepresentsthephotoncloud.Afterapplication,dragannreturnsthecloud3390withpointsinthecloudidentifiedas“signal”points.3391

TheMatlabcodehasafewdebugstatementsthatfollow,alongwithabout40lines3392forplotting.3393

3394

References3395

Goshtasby,A&W.D.O’Neill,CurveFittingbyaSumofGaussians,CVGIP:Graphical3396ModelsandImageProcessing,V.56,No.4,281-288,1994.3397

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