Article history:Received 29 April 2015Received in revised form 26 January 2016Accepted 11 February 2016Available online 19 February 2016
Long time series of accurate Sea Surface Temperatures (SSTs) are needed to resolve subtle signals that may beindicative of a changing climate. Motivated by the stringent requirements on SST accuracy required for ClimateData Records (CDR) we quantify sampling errors in satellite SSTs. Infrared sensors, including the Moderate Res-olution Imaging Spectroradiometer (MODIS), have sampling errors caused by incomplete coverage primarily dueto clouds and inter-swath gaps (gaps between successive swaths/orbits). Unlike retrieval errors, the sampling er-rors are introduced when calculating mean values and in generating gap-free SST fields. We generate MODIS-sampled SST fields by superimposing MODIS cloud masks on top of the Multi-scale Ultrahigh Resolution(MUR) SST field for the same day. Based on the MODIS-sampled fields, we calculate sampling errors at differenttemporal and spatial resolutions to examine the impacts at different scales. Our results indicate that sampling er-rors are significant,more so in the high latitudes, especially the Arctic. The 30°N–30°S zonal band is found to havethe smallest errors; a notable exception is the persistent negative errors found in the Tropical Instability Wavearea, where the mesoscale ocean–atmosphere interaction leads to a more frequently satellite sampling abovethe cold sections of the wave area. The global mean sampling error is generally positive and increases approxi-mately exponentially with missing data fraction at a fixed averaging interval, while error variability is mainlycontrolled by SST variability. Areaswith persistent cloud cover have large sampling errors in temporally averagedSSTs.We conclude that the sampling error can be an important or even dominant component of the error budgetof mean and gap-free SST fields. Climate data generation and interpretation of satellite-derived SST CDRs andtheir application must be conducted with due regard to the sampling error.
Keywords:Sea Surface Temperature (SST)Climate Data Records (CDR)MODISSampling errors
1. Introduction
Global Sea Surface Temperature (SST) is an essential climate variable(ECV, listed by theGlobal ClimateObserving System) that can be used toassess climate change. In order to resolve the subtle signals that maybeindicative of a changing climate, long time-series of accurate, spatiallyand temporally averaged SSTs are needed. Specifically, an SST ClimateData Record (CDR) (National Research Council, 2004) requires an abso-lute temperature uncertainty of 0.1 K and stability of 0.04 K per decade(Ohring, Wielicki, Spencer, Emery, & Datla, 2005). Such stringent re-quirements are intended to enable the detection of the likely regionalor global signals of 0.2 K per decade. Hence, the correct quantificationof errors and uncertainties in observed SSTs has become a critical need.
Among all the SST observing methods, satellites provide the mostconsistent global coverage. Infrared (IR) sensors in particular providemeasurements of a fine resolution as well as having a long history.
Therefore, for generating SST CDRs from satellite measurements(Minnett & Corlett, 2012), IR measured SSTs are a potentially valuablesource. The Moderate Resolution Imaging Spectroradiometer (MODIS(Esaias et al., 1998)) on board the NASA Earth Observing System satel-lites Terra and Aqua obtain SST retrievals in a 2330 km swath. SST is de-rived from MODIS measurements of top-of-atmosphere radiances inmid- and thermal-IR bands (centered at wavelengths of 3.7, 3.9, 4.0,11 and 12 μm), at which the atmosphere is relatively transparent tothe transmission of surface IR emission. The comparison with indepen-dentmeasurements from shipboard spectroradiometers (Minnett et al.,2001) confirms that the derived SSTs fromMODIS generally have meanbiases b0.1 K and scatter b0.5 K (Minnett, 2010).
However, in a general satellite data processing flow, errors from dif-ferent sources are produced at each of the successive data levels (Level 0(digitized detector output) to Level 4 (bias corrected, geo-located,gridded, and gap-free SSTs in lat/lon coordinates) and accumulate to-ward higher levels, as discussed by the Interim Sea Surface TemperatureScience TeamWhite Paper (ISSTST, 2010). As with other satellite mea-surements, the MODIS SST accuracy refers to the retrieval error pro-duced at Level 2 (derived SSTs at pixel bases), but Level 3 (binned,gridded and averaged Level 2 values) and Level 4 fields are extensively
used in climate and modeling studies, mainly because of the desirablefeatures of being “gridded and gap-free”. Another important error inLevel 4 fields, independent of the retrieval error, is the sampling errorcaused by incomplete coverage of satellite measurements, and this isthe focus of this paper.
There are two main reasons for this incomplete coverage. First, forany IR sensors such as MODIS, the presence of clouds causes gaps inthe sampling, or ‘undersampling’, of SSTs. Cloudy pixels rejected bymany currently used SST cloud masks constitute up to 90% of the totalpixels sampled. Instead of being random, clouds around the globeform geographical patternswhere some regions are prone to cloudinesswhile others are not. Some regions are even found with cloud-SST rela-tions due to physical (e.g. Ramanathan and Collins (1991)) and dynam-ical mechanisms (e.g. Xie (2004) and Klein (1997)). Second, gapsbetween successive swaths of some sensors also lead to sampling errors.Sensors with narrower swaths are subject to a larger gap than others.The relatively broad swath of MODIS indicates that a scan gap of432.8 km exists at the equator every 98.8min. This gap narrows as it ex-tends to themid-latitudes of 32.3° poleward ofwhich there is overlap ofsuccessive swaths. Consequently, these two factors become the funda-mental issues in generating gap-free SST fields and lead to samplingerrors.
In early studies, incomplete sampling issues were highlighted to as-certain the sampling errors of averaged climate data (Parker, 1984;Trenberth, 1984a, 1984b; Wigley, Briffa, & Jones, 1984). Recent sam-pling error studies for climatic time–space grid box averages of in-situmeasured Surface Air Temperature (SAT) (Parker & Horton, 2005;Shen, Yin, & Smith, 2007) and SST (Brohan, Kennedy, Harris, Tett, &Jones, 2006) are based on the quantification framework proposed byJones, Osborn, and Briffa (1997) (referred to here as J97). In J97, thesampling error was expressed as the additional variance contributingto the grid box long-term temporal variance due to spatially incompletesampling. Certain assumptions were made about the data statistics(e.g., homogeneity and stationarity) and the data spatial correlationcurve. The sampling uncertainty was calculated by estimating averagedvariance of stations and the inter-correlation between stations in thegrid box. The SST data were mostly from ship and buoy observationsand control run outputs frommodels. Morrissey and Greene (2009) de-veloped a more general quantification framework by includingtemporally-insufficient sampling associated with ship measurements,assuming observations are randomly distributed. Kennedy, Rayner,Smith, Parker, and Saunby (2011) updated the work of J97 by applyingan isotropic correlation decay function in both time and space. Thesepreviousworks relied on the assumptionmade for the spatial or tempo-ral inter-correlation curves within a grid box; additionally, the in-situSSTs were used. Most recently, Hearty et al. (2014) quantified samplingbiases in climatologies of atmospheric temperature and water vapor bycomparing two MERRA (Modern Era Retrospective-Analysis for Re-search Applications; Rienecker et al. (2011)) climatologies sampledseparately by the time and quality components of AIRS (AtmosphericInfrared Sounder) (Aumann et al., 2003) with a MERRA climatologysampled like a climatemodel, assuming that theMERRAdata representsthe real atmospheric state.
The sampling error of IR SSTs remains to be determined. Therefore,this paper will initiate the sampling error quantification for satellite IRSSTs. Furthermore, IR SSTs have different sampling structures (not ran-dom) and known sources of the sampling error (i.e., clouds and inter-swath gaps). The aforementioned statistical assumptions may not benecessary nor appropriate for determining sampling error magnitudes,and they may smooth sampling error variations which in fact can giveinformation on how the errors are generated and whether they can bereduced. In this study, we calculate the MODIS sampling errors withoutpresuming SST spatial or temporal correlations. Instead,we assume thata reasonable Level 4 field can be the reference, or ‘true’ field to helpquantify the impact of the under-sampling in IR fields. For the purposeof this work, we calculate the difference between the sampled fields
and the corresponding gap-free reference fields as an ‘error’ instead of‘uncertainty’ because of our assumption about the reference fields. Themerit of this approach is that we can suggest possible causes and im-pacts that can be physical and predictable, instead of just statistical,which can further help develop solutions or predictions of the samplingerror. We show the sampling errors found in monthly IR SST fields arelarge at O(1 K), especially in regions sensitive to climate change, andhave geographical distributions due to natural and artificial causes.We conclude that sampling errors can be an important or even domi-nant component in the error budget of Level 4 SSTs, compared withthe typical magnitudes of retrieval error (b0.5 K). Hence, climate datageneration and interpretation of satellite-derived SST CDRs and theirapplication must be conducted with due regard to the sampling error.
2. Data and methods
We used masks from the thermal IR daytime and mid-IR nighttimeLevel 3 fields of TerraMODIS SSTs. These data are globally gridded fieldsat 4 km spatial resolution and were generated from the MODIS Collec-tion 6 retrievals, which is the most recent reprocessing of the MODISSST. Global day and night cloud masks (i.e., quality mask, referred toas cloud mask in this paper, with flags = 0 indicating the best quality)were derived by considering quality flags N1 as missing data primarilydue to cloud cover and gaps between successive orbits. These Level 3fields were generated for this study at the University of Miami, and isavailable at http://oceancolor.gsfc.nasa.gov/.
We selected as the Level 4 reference field, the Multi-scale UltrahighResolution (MUR) SST product (Chin, Jorge, & Armstrong, 2010), whichis a 1 km resolution daily SST analysis derived using observations frommultiple sources including both satellite skin and subskin SSTs and in-situ SSTs. The satellite input fields include: 1) IR SST retrievals frompolar orbiting satellite sensors AVHRR and MODIS; 2) microwave SSTretrievals from AMSR-E and Windsat. The interpolated in situ data arefrom iQuam (in situ SST quality monitoring; Xu and Ignatov (2014)),and are used as references for bias correction (Chin et al., 2010). MURdata can be retrieved freely from the NASA JPL PO.DAAC website:http://podaac.jpl.nasa.gov/dataset/JPL-L4UHfnd-GLOB-MUR. In orderto match the MODIS cloud mask resolution, we aggregated MUR fieldsinto 4 km daily maps.
Due to the occasional satellite instrument outages such as resultfrom satellite maneuvers, a year-round continuously scanned globalMODIS SST field is not achieved. Therefore, for each season, a 30-dayperiod was selected as being a representative to determine theseasonal sampling error characteristics: winter: 20101228–20110125(yyyymmdd); spring: 20110407–20110506; summer: 20110721–20110819; fall: 20111001–20111030. Any mean quantities calculatedby averaging the four seasonal periods will be referred to here as anannual mean.
The errors in any satellite Level 4 product are an accumulation oferrors from different sources, and the quantification of onecomponent—the sampling error—requires us to focus on this errorsource alone. Therefore, theMODIS-sampledMUR is generated by elim-inating the 4 kmMUR pixels which are identified as cloudy or fall in aninter-swath gap. In other words, the MODIS sampling is represented bysuperimposing daily cloud masks on the daily MUR reference field. TheMODIS retrieval errors, assessed using Level 2 data (e.g. Kilpatrick et al.,2015) do not contribute to our results. Fig. 1 shows an illustration of themethod.We superimposed the MODIS cloud mask (Fig. 1b) to theMURfield (Fig. 1a) to generate the sampledfield (Fig. 1c). Note that the globalSST density (Fig. 1d) ofMUR and theMODIS-sampledMUR are quite dif-ferent. By utilizing this approach, the undersampling impact. i.e. thesampling error is represented and quantified as the difference betweenspatial or temporal mean fields of the MODIS-sampled-reference SSTsand the reference SSTs. We assessed the sampling errors of seasonaland 4-month means and compared day and night fields.
Fig. 1.Methodology. a: Reference field ofMURon 2011/04/07. b: Daymask of TerraMODIS SST on the same day. Green colors showwhere quality 0 and 1 SSTs are derived. c: The sampledMUR after superimposing b on a. d: SST probability density of a and c. Note the difference between the two histograms shows the incompleteness of sampling.
50 Y. Liu, P.J. Minnett / Remote Sensing of Environment 177 (2016) 48–64
In this approach the MUR fields are assumed to be a possiblerealization of the global SST field, so the effects of sampling errors canbe isolated and quantified. This is not to say that the MUR fields areerror-free representations of daily SSTs. In fact, there certainly areinherent errors and uncertainties in MUR due to the blending of SSTsof different scales. We build our assumption on MUR's potential of pro-viding realistic, if not perfectly accurate, representations of the smallscale SST variability in dynamic regions (Vazquez-Cuervo et al., 2013).The consequence of the uncertainties in MUR errors can be testedthrough the application of the methods developed here to a differentLevel 4 field. Preliminary results show that the spatial sampling errorsdiffer by b0.1 K over nearly all of the oceans. The causes of these differ-ences are a topic of continuing research and will be the subject of afuture paper.
3. Sampling error quantification framework
Let SST0ref represent the reference data at a base resolution R0 of0.04°and 1 day (1d), which is the Level 4 field, MUR. Then, for agrid box centered at location i and time j, the averaged referencefield is
SSTrefi; j Rð Þ ¼ 1R∭R
0SSTref0 dxdydt ¼ 1
NR∑NR
n¼1SSTref0 n ð1Þ
where the averaging for space and time is denoted in a new resolu-tion size R. R is selected as every combination of spatial resolutionsof 0.04° (4 km, here after as ‘4 k’), 0.12° (12 k), 0.25°, 0.5°, 1°, 2.5°,and 5° and temporal resolutions of 1 day (1d), 3 days (3d), 1 week(1w), 2 weeks (2w) and 1 month (mon). This selection is based onthe commonly used resolutions of SST fields. Resolutions of manysatellite products can be found at https://www.ghrsst.org/products-and-services/r-gts/; climate modelers and others also useother lower resolutions. NR is the number of reference SSTs in the
grid box. The averaged sampled field for the same grid box isexpressed as
SSTi; j Rð Þ ¼ 1nR
∑nRn¼1SST
ref0 n ð2Þ
where nR is the number of sampled reference SSTs; 0 b nR ≤ NR.The sampling error due to cloud and inter-swath gap at grid box i, j is
given by
εi; j Rð Þ ¼ SSTi; j Rð Þ � SSTrefi; j Rð Þ: ð3Þ
This is the difference from the ‘true’ grid box mean and can be eval-uated at any given time, location, and resolution.
In general, it can be expected that SST sampling errors are affectedby two factors. One is the fraction of cloud ormissing data (gap fraction)in the grid box.
f i; j Rð Þ ¼ 1:0� nR
NRð4Þ
Here, 0≤ fi ,jb1. For the grid box statistics, we only use those with atleast one SST value being sampled.
One important aspect of the gap fraction in this study is how long thegap persists, especially in cases of sampling errors due tomonthly aver-aging. It is intuitive that even though the temporal gap fraction is large,the gaps might be short intervals that frequently occur during themonth or clouds leading to the same gap fraction may occur in a singleevent. These cases may lead to different sampling errors. To examinethis, we define the cloud persistence as the largest number of consecu-tive days during which the grid i, j was detected to be cloudy in a tem-poral averaging period. We will return to this aspect of sampling errorsin monthly averaged SSTs in Section 4.4.
The other essential factor for sampling error is the variance of theSSTs in the grid box, which is represented by the standard deviation ofthe reference SST in the grid box:
σ refi; j Rð Þ ¼ 1
NR � 1∑NR
n¼1 SSTref0 n � SSTrefi; j
� �2� �1
2
: ð5Þ
To assess this error, statisticswill be calculated for global and region-al ocean areas, primarily in terms of the three quantities below: meansampling error, root mean square error and difference of mean SST ina region of interest, A, and during a time interval, t. lati in the equationsbelow is the latitude of each sample.
εA;t Rð Þ ¼ 1∑nt
j¼1∑nAi¼1 cos latið Þ∑
nt
j¼1∑nA
i¼1εi; j Rð Þ � cos latið Þ ð6Þ
RMSEA;t Rð Þ ¼ 1∑nt
j¼1∑nAi¼1 cos latið Þ∑
nt
j¼1∑nA
i¼1ε2i; j Rð Þ � cos latið Þ
" #1=2
ð7Þ
δSSTA;t Rð Þ ¼ 1∑nt
j¼1∑nAi¼1 cos latið Þ∑
nt
j¼1∑nA
i¼1SSTi; j Rð Þ � cos latið Þ
� 1
∑Ntj¼1∑
NAi¼1 cos latið Þ
∑Nt
j¼1∑NA
i¼1SSTrefi; j Rð Þ � cos latið Þ ð8Þ
Regional gap fraction is defined as themissing data fraction that can-not be filled even by averaging into a low resolution of R:
f A;t Rð Þ ¼ 1:0�∑nti¼1 ∑
nAj¼1 lat j
∑Nti¼1 ∑
NAj¼1 lat j
ð9Þ
Fig. 2. a, b, and c: Global annual mean (t = 4 seasonal periods) sampling error distribution usresolution; White color in ocean areas indicates zero error, which is denoted in the middle ofgrid scale clouds, thus is excluded when generating the probability density. Note the color scaleis displayed in the upper right corner.
By gridding the sampled and reference SSTs into a range of temporaland spatial resolutions, the undersampling impacts are reflected in differ-ent temporal and spatial averaging situations. One way to consider thedifference between the grid box statistics (εA;t and RMSEA ,t) and theregional statistics (δSSTA;t) is that the statistics calculated based on gridbox i, j gives an evaluation of impacts from the “subgrid scale clouds”(clouds or gaps that have scales less than the box size defined by R; alsodefined as fi ,j), while the statistics based on region A and time intervalt provides additional impacts from grids that are not filled, or, from the“super-grid scale clouds” (clouds or gaps that have scales at least thebox size; also defined as fA ,t). The impacts due to certain scale cloudsand SST temporal and spatial variation are therefore revealed in thedifferent resolution fields. Changes in global error magnitude and errorpatterns from one resolution to another can be attributed to the impactsfrom the inclusion of oceanic features and clouds on these scales.
4. Results
4.1. Sampling error annual mean characteristics
Annualmeans of the sampling error are estimated by averaging overthe full time period at a certain resolution R, and are shown in Fig. 2.Generally for these three cases, global sampling errors are prevalentlywithin±0.5 K. Regions where fronts and upwelling occur have somevalues at about±1.0 K. Extreme values of ±1.0 K to ±6.0 Konly occur in the Hudson Bay and other seasonally open water regionsat high latitudes. The error pattern varies with resolution. In the[4 k, mon] map, positive errors (~0.5 K) are evident off the west coastsof North and South America and South Africa, wheremaritime stratocu-mulus clouds are common. There is a largewarm (~0.5 K) pattern in theSouth-Central Pacific (SCP, 175°W–135°W, 25°S–45°S) region. This is
ing MODIS (Terra) cloud masks in 2011. White labels on the Asian continent indicate thethe color bar; Black indicates either land or sea ice; Gray indicates the region with super-is non-linear. d: SST probability density of the maps shown. The number of grids counted
52 Y. Liu, P.J. Minnett / Remote Sensing of Environment 177 (2016) 48–64
due to a significant warming event in this area in January of 2011, sim-ilar to the SCPwarming of the previous year. The 2009–10 SCPwarmingwas associated with a strong divergence of circumpolar westerlies, lowwind speed (Lee et al., 2010) and stronger solar radiation at the surface(Liu, Tang, Pinker, Niu, & Lee, 2014), which are usually accompanied bygradually clearer skies and therefore lead to warm sampling errors. Thecold (~−1.0 K) zonally stripe-like patterns at the eastern equatorial Pa-cific and Atlantic oceans exist along the tropical instability waves (TIW,details in Section 4.5.2). The error distributions along the westernboundary currents are rather diverse (details in Section 4.5.3). Similarlyvariable are those errors in the high latitude regions usually covered bystratus. However, the [5°, 1d] error distribution shows somedifferences.Tropical regions are prevalently filled with negative errors of ~0.1 K.Warm patterns in the west coast stratocumulus regions are variable.The positive error region in the SCP is absent. Errors along the oceanfronts and western boundary currents are more coherent, with cold er-rors to the warmer side of the current and warm errors to the cold side.The [5°, mon] map has the above-mentioned features with larger errors,except that the error signs in the tropics have changed to bemore positivethan in the [5°, 1d] case, yet the cold error in the TIW remains. Hence, amore interesting La-Niña-like error pattern becomes apparent in the trop-ical Pacific. The changing error sign in the tropics is reflected in the SSTdensity in Fig. 2d. The SST error distribution shifts toward the positiveas the resolution shifts from the spatial averaging case of [5°, 1d] to thetemporal averaging case of [4 k, mon]. The [5°, mon] case shows evenwarmer errors than the [4 k, mon] because of the including of monthlypersistent cloudy regions that were excluded from [4 k, mon]. Xie(2004) summarized the global low-level boundary layer clouds responseto SST changes that over most regions result in a negative SST-cloudinesscorrelation due to basin-wide dominant static stability. That more warmsampling errors are found in [4 k, mon] fields supports the concept ofthe long-term basin-wide negative correlation, while the sampling errorsin [5°, 1d] are associated with weather scale SST-cloud correspondence.
The zonal and annual means of the sampling error are shown inFig. 3. The mean error generally increases with a decrease of resolutionor increase of latitude in both spatial and temporal averaging cases. Thisis because the Rossby radius and eddy scales decrease with increasinglatitude (Høyer, Karagali, Dybkjær, & Tonboe, 2012), and the lower theresolution, the more scales of variability become involved and affectthe sampling errors. The maximum appears at high latitudes for bothhemispheres. The secondary peak exists in the northern hemispheremid latitudes, where SST variability is influenced by western boundarycurrent systems and along storm tracks. The increase of mean errorwith latitudes does not apply to the spatial averaging in the tropics,where zonal mean cold errors exist with the maximum (~−0.15 K
Fig. 3. The zonal mean of the annual sampling errors (A = per latitude line,
at 5°) close to the equator for all spatial averaging cases, and decreaseaway from the equator. This is associated with the significant colderror along the TIWs shown in Fig. 1.
In order to assess the sampling error at all resolutions in different lat-itude bands, the regional and annual statistics of the RMSE, the meansampling error, the difference between the regional mean SST, and theregional gap fraction are generated for 5 zonal bands (Fig. 4). By exam-ining the evolution of RMSE in the resolution domain, one finds the dis-tribution follows a saddle-like pattern with extremely large valuesfalling into either the spatial averaging or temporal averaging case(the bottom-right and upper left corners) and smaller values appearalong the diagonal indicatingmore symmetrically spatiotemporal aver-aging. The difference of mean SST (δSSTA;t) is mostly positive and ismaximum at the highest resolution, primarily because of the sparsestdata coverage for cold SSTs. This suggests large scale data loss cancause significant highmean SST sampling errors. Going to lower resolu-tions, themissing data become filled by averaging and theδSSTA;t growssmaller and closer to εA;t. This illustrates that eliminating the significantpositive biases in the regional or global mean SSTs often comes at thecost of coarser resolution. The regional gap fraction decreasesmonoton-icallywhen going to the lower resolution or lower latitudes, which is as-sociated with the more super-grid clouds in the high latitudes. In the30°S–30°N region, the RMSEs and mean sampling errors are thesmallest among the latitude zones. The mean errors are within±0.05 K, and the RMSEs are within 0.3 K except in the [5°, 1d] case.The sampled mean SST does not differ greatly from the true mean asshown in the δSSTA;t . Even though this is the region affected by bothclouds and inter-swath gaps, gap fraction in this region remains thelowest when compared to others. These indicate the relative reliabilityof sampling within 30°S–30°N for most gridded SSTs. Going to thehigher latitudes, the RMSE and δSSTA;t distributions exhibit more com-plexity. RMSE values are larger in the northern hemisphere than inthe southern. The δSSTA;t is remarkably large (N2.5 K) in the 30°N–50°N zone.
4.2. Global sampling error dependence
The results above show sampling errors vary substantially over theglobe. As one might expect, natural SST variation and gap fraction arethe two reasons. However the extent of such expected dependence asyet remains to be quantified. So, for the global sampling error, we exam-ine its dependence on natural SST variation (represented by MUR Level4 SST standard deviation) and on the gap fraction. Only the [4 k, mon]and [5°, 1d] cases are shown as representations (Fig. 5 a and b). In
Fig. 4. Variation of the 4 quantities (columns) in the resolution domain (x: spatial; y: temporal) are evaluated at different latitude bands (rows). First column: RMSE (contour interval =0.1 K); Second column: the zonal-band and 4-month averaged sampling error εA;t (contour interval = 0.05 K); Third column: The difference between the sampled annual mean SST andthe annual mean MUR SST of the zonal band (contour interval = 0.2 K); Fourth column: The regional gap fraction of the field due to super-grid clouds/gaps. Definitions are given inEqs. (6)-(9).
these cases, the sampling errormagnitude increases substantially as SSTstandard deviation or gap fraction increases. Note that the portionwhere sampling errors are within 0.1 K is limited to: monthly standarddeviation of b0.3 K or 5° spatial standard deviation of b0.7 K; monthlygap fraction of b10% or 5° spatial gap fraction of b4%. Such restrictionscan be relaxed when assessing cases averaged more symmetrically, orsingle averaging cases at higher resolutions (Fig. 6). Fig. 5, c and d,show the mean sampling error is positive and increases approximatelyexponentially with gap fraction. On the contrary, averaging over stan-dard deviation intervals (not shown) does not indicate any dominantdependence.
The spread of the sampling error depends on SST variability as wellas the gap fraction. The RMSE shows stronger dependence on the refer-ence SST variability (Fig. 6 c and d) than on the sampling gap fraction(Fig. 6 a and b). Note that the RMSE varies approximately linearlywith the reference standard deviation. Increasing spatial resolution re-duces the RMSE dependence on spatial gap fraction, while differenttemporal resolutions barely change the RMSE dependence on temporalgap fraction. Nonetheless, the change of resolution makes minimal dif-ference to the near-linear dependence of RMSE on reference SST vari-ability. This demonstrates that as long as the gap-free SST variability isknown, the RMSE generated by the current cloudmasks can be predict-ed regardless of the resolution selected.
4.3. Sampling errors seasonal and day–night variability
Mid- (30°–50°) and high- (50°–70°) latitudes are found to have largesampling error variability (Fig. 4). The sampling error in these regions isfurther decomposed by seasons and day–night sampled fields. Monthlyerror variation in the resolution domain does not necessarily follow thepatterns of annual mean statistics shown in Fig. 4. For example, spatio-temporal averaging might cause the RMSE in some seasons to exceedthat in the single dimension averaging case. Monthlymean errors no lon-ger necessarily increase monotonically with decreases of spatial or tem-poral resolution. Details of the seasonal error statistics are included inthe supplementary figures (Figs. S1–S4). In this section, we continue topresent [4 k, mon] and [5°, 1d] monthly statistics (Fig. 7) as examples,and compare the seasonal variation of sampling error statistics amongdifferent zonal bands, and between time (day or night cloud masks).
4.3.1. Seasonal variabilityEvidently, RMSEs and mean errors (the first and second rows in
Fig. 7) of the Northern Hemisphere (NH) show more in-phase fluctua-tions regardless of latitude, resolution, and day–night sampled fields.The maximum RMSE and mean error generally exist in the summermonth of the NH mid- and high-latitudes, due to the larger SST
Fig. 5. The dependence of sampling errors on reference SST standard deviation (color) and gap fraction (x-axis). a: Temporal averaging case of [4 k, mon]; b: Spatial averaging case of [5°,1d]. Note that the width of each colored rectangle indicates the logarithmic linearized number of SSTs that fall into the range of the corresponding gap fraction and error (y-axis) interval(4% and 0.08 K). Scaling of such a linearization is denoted in the upper left corner of each figure. c and d: The mean sampling error averaged over gap fraction intervals.
54 Y. Liu, P.J. Minnett / Remote Sensing of Environment 177 (2016) 48–64
variability andhigher amounts of cloud, probably stratus. One exceptionis the spatial averaging case in the NH mid-latitude band, where thelargest RMSE occurs in the spring month, possibly due to a Pacificstorm. The high-latitude summer peak is due to the increased SST vari-ability brought by open water around the ice edge (Fig. S5). Also in thisarea, the mean sampling error is negative in the winter month, primar-ily due to the large amount of negative sampling errors of −0.5–1.0 Kthat occur in the Gulf Stream and Kuroshio in this season. On theother hand, RMSEs of the Southern Hemisphere (SH) exhibit small var-iation across the 4 months. The time of the weak RMSE peaks differsfrom one to another. The mean sampling error of the SH high latitudesat [5°, 1d] shows a large variability among the seasons. In aspects ofthe regionalmean temperature (δSSTA;t) and the super-grid scale clouds(fA ,t), seasonal variations of these two quantities are generally in phase(Fig. 7 the third and fourth rows). This indicates again the significance oflarge scale cloud coverage on causing highmean sampling errors in SST.Seasonal variations of the δSSTA;t and fA , t in the NH generally peak insummer except for the temporal averaged case in the high-latitudeband. In the SH, seasonal variations of the δSSTA;t and fA , t present alarge spread across different resolutions and sampling time.
4.3.2. Day–night variabilityDay and night differences of the 4 statistical quantities in the NH are
small, compared with the SH. Note only the NH high-latitude band
shows considerable differences in the δSSTA;t and fA ,t between day andnight. On the contrary, notable inconsistencies in the aspect of the sea-sonal peak of the SHRMSE andmean sampling error exists between dayand night field. Especially, the daytime δSSTA;t and fA ,t generally peak inthe winter month, while the nighttime values peak in the summermonth. The most significant day–night difference remains in the SHhigh latitude band, and thus blurs the seasonality. Since the samedailyMURfield is used for both this difference cannot result fromSST di-urnal variability and the diurnal differences are therefore caused by di-urnal cloud variability, and possibly indicate an imperfection in thecloud masks. This will be discussed in Section 4.6.
4.4. Cloud persistence
Themaximumcloud persistence at each grid box around the globe isextracted from both day and night cloud masks (Fig. 8). Long persis-tence is found in the high latitudes. Also, regions known to have prevail-ing stratus and stratocumulus clouds, for example, the north Pacific andregions off-shore of California, Peru, and Namibia, are shown to havelong cloud persistence. In addition, the Indian-Pacific warm pool andthe ITCZ, which generally are expected to have long-time presence ofconvective systems, and do indeed display long cloud persistence inFig. 8. From the previous figures, large sampling errors correspond tothose regions with long cloud persistence. Seasonally, the ice-edge-
Fig. 6.Dependence of the RMSE on gap fraction (a. temporal averaging of: [4 k, 3d], [4 k, 1w], [4 k, 2w] and [4 k, mon]; b. spatial averaging of: [12 k, 1d], [0.25°, 1d], [0.5°, 1d], [1°, 1d], [2.5°,1d], and [5°, 1d].) and reference standard deviation (c. temporal and d. spatial). Resolutions are represented by the size of the circles. The smaller the circle is, the higher the resolution.
region of the Arctic Ocean shows high variability. The summer and fallmonths arewhen the persistence can be less than 25 days in this region,while in the winter and spring, some areas are covered by ice, the re-maining areas have very long persistence of almost 30 days. FromFig. 8, it is also notable that Pacific mid-latitudes have a persistencepeak in summer. This area is known to have pronounced stratus cloudsin summer.
However, large differences exist between day and night cloud per-sistence around Antarctica. The difference is more evident in the australautumn and winter (boreal spring and summer in Fig. 8), when someareas are determined to be consistently cloudy in the daytime for almostthe whole month, but cloud-free at night for most of the days. This isconsistent with the diurnal variation in the statistics of sampling error(Fig. 7 δSSTA;t ) due to super-grid scale clouds (Fig. 7 fA ,t ) in this region.Again, we believe this is related to imperfections in the cloud masks,which will be discussed in Section 4.6.
A larger sampling error is expected in areaswith longer cloudpersis-tence. But, a large gap fraction does not necessarily dictate long persis-tence. Therefore, for the sampling error in temporal averaged SSTs,even though gap fraction is suggested as a source of error (Fig. 5a), thedominant cause is shown to be the cloud persistence (Fig. 9). Themean absolute sampling errors are calculated at each gap fraction andpersistence for the 4 months. For the same gap fraction, the samplingerror tends to increase as the persistence increases.
4.5. Regional characteristics
The magnitudes and dominant causes of the sampling errors varyglobally. In this section, we characterize and interpret the samplingerror in 4 important types of region (Fig. 10). Firstly, theWestern PacificWarm Pool (WPWP: 140°E–160°W, 10°S–15°N) is known to have thehighest SSTs, consistently ≥28 °C. In this convective region, prevalentclouds include precipitating mid- to high-level stratiform clouds thatheat the upper troposphere and cool the lower troposphere, and cirrusclouds close to the tropopause; SSTs have relatively low variability
due to small horizontal temperature gradients. Secondly, the TropicalInstability Wave (TIW: 160°W–80°W, 5°S–10°N) region is selected be-cause the marked SST gradients are associated with distinct forcingthe atmosphere above. Thirdly, the two important NH western bound-ary currents regions are defined as 120°E–150°E and 15°N–50°N forthe Kuroshio (KS), and 80°W–45°W and 25°N–55°N for the Gulf Stream(GS). SST variability in these two regions is greater than in many otherareas, and with strong and more complex air–sea interactions present.Lastly, we analyze the two most pronounced marine stratocumulus re-gions, where satellite sampling of SST is rather scarce: the off-shorecoastal regions of Peru (90°W–80°W, 20°S–10°S), and of Namibia(0°W–10°E, 20°S–10°S).
4.5.1. Western pacific warm poolOverall, sampling errors in theWPWP are relatively small, as the SST
variability is small (standard deviation b1 K, calculated from onemonthof daily SST fields). Although the sampling error magnitude is not aslarge as in the high latitudes, there is a difference of sign between themeans of the temporal and spatial sampling errors (suggested in Fig. 2and shown in Fig. 11a). Also, the mean sampled SST of this region islower than themean of the reference SST field (Fig. 11b), which is oppo-site to the global sampled mean (Fig. 4 δSSTA;t). The preponderance ofnegative sampling errors on daily spatial averaged SSTs might indicatethe significance of local convergence to the SST-cloud relationship(Xie, 2004), or the spatial correspondence between deep convectionand warmer SSTs indicative of the local regulation of SSTs by cirrusclouds being part of the thermodynamical constraint (Ramanathan &Collins, 1991). For non-weather scales (monthly, as considered here),the radiative cooling effect of clouds on SST plays a role (Ramanathan& Collins, 1991; Ramanathan et al., 1995), so that the long-term meansampling error tends to be positive.
4.5.2. Tropical instability wave regionAs seen from previous figures, the TIW region is the exception in the
tropics regarding the sign of the sampling error. This region has
Fig. 7. Seasonal and day–night variation. Columns represent SouthernHemisphere and NorthernHemisphere. The seasons in the x-axes refer to those in each hemisphere. Mid- and high-latitude bands are differentiated by color: Orange: mid-latitude; blue: high-latitude. Resolution is represented by line style: Solid:[4 k, mon]; Dot: [5°, 1d]. Circled and starred linesrepresent daytime and night time cloud masks respectively.
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significant horizontal SST gradients to which the atmosphere boundarylayer strongly responds. The vertical mixing mechanism in the atmo-sphere (Hayes, McPhaden, & Wallace, 1989; Wallace, Mitchell, &Deser, 1989) dominates the mesoscale ocean–atmosphere coupling inthis area. To the north of the TIW, where the SST gradients in thiscusp-shaped front are stronger, the surface wind converges slightlynortheast of the warm SST anomalies, which results in the formationof low level clouds because of the convergence of surface moisture(Chelton et al., 2001; Chelton, Schlax, Freilich, & Milliff, 2004; Chelton& Xie, 2010; Hashizume, Xie, Liu, & Takeuchi, 2001; Hashizume et al.,2002; Mason, Sheather, Bowles, & Davies, 1996; Small et al., 2008; Xie,2004). The gap fraction shown in Fig. 12 b can be deemed as cloud frac-tion, except that the inter-swath gaps may generate striped patternsthat are more obvious in regions where cloud occurrence is low. Twophenomena can be observed. First, the significantwarm sampling errorsare found in the offshore region of Ecuador and Peru, where the SSTs arethe coolest, due to upwelling and the cloud fraction is large. Second, inthe downstream region further away from the shore, significant coldsampling errors can be found along the larger SST gradient, northernside of the TIW. Thewarmsampling errors can be attributed to themod-ulation of SST on the lower troposphere static stability. The decrease ofSST can stabilize the frequent atmospheric temperature inversions,
which in most cases favor greater occurrence of low-level stratus(Klein & Hartmann, 1993). This usually can be found in a stratocumulusdeck above ocean upwelling. Note that fog forms frequently in such up-welling regions and is treated as cloud in the satellite SST retrieval pro-cess, so thewarm errors could also be caused by the presence of fog. Thelarge negative sampling errors along the north side of the TIW indicatethat there are more colder-than-average SST measurements, whichsupport the robust SST-cloud coupling suggested by the atmosphericvertical mixing mechanism. Fig. 12 shows the monthly mean SST,which does not perfectly reveal the instantaneous coupling of warmSSTs beneath low-level clouds. The dynamic activity (e.g. meridionalshifts and westward wave propagation) in a grid box, among thefixed grids defined for any resolution in this study, can lead to tem-poral changes of both clouds and SST variations. Although notshown in Fig. 12, it has been seen in satellite images that cloudspropagate westward along with the SST warm anomalies in theTIW (Chang, 1970; Legeckis, 1977). Thus, mean sampling errors oftemporal averaged SSTs in this region are negative. Similarly, nega-tive sampling errors can be found along the strong SST gradient inthe spatial averaged fields as well. Simply put, when the skies areclear and SSTs can be measured from satellite in the infrared, theSSTs are lower than average, as the warmer-than-average SSTs
Fig. 8. The maximum cloud persistence at each grid point. The boreal season and time of sampling (D: day; N: night) are denoted on the Asian continent.
tend to be associated with cloudy skies when SST cannot be derivedfrom infrared satellite measurements.
4.5.3. Gulf stream and KuroshioSampling errors of the spatially averaged SSTs vary substantially in
the GS and KS regions and among seasons (Fig. 13). According to theaforementioned linear relation between SST standard deviation andRMSE for the globe (Section 4.2), errors here seem to be largelydetermined by the SST variability. Nonetheless, several well-knownprocesses in these regions indicate: the sampling errors can be relatedto the complex coupled ocean–atmosphere system rather than decidedby variability in the ocean, primarily SST, alone. First, and also inconcert with the TIW, atmospheric response to SSTs in these twoocean frontal regions involves the ubiquitous vertical momentum
mixing mechanisms and the resultant wind convergence as well aslow level cloud forming above the downwind warm water (Chelton &Xie, 2010; Kilpatrick, Schneider, & Qiu, 2013). Here direct pressure ad-justment is also found (Lindzen & Nigam, 1987), in which a good corre-spondence exists betweenwind convergence and the sea level pressureLaplacian (Minobe, Kuwano-Yoshida, Komori, Xie, & Small, 2008). Lowlevel clouds show a sharp transition across the GS front due to the sec-ondary circulation induced by pressure adjustment (Liu, Xie, Norris, &Zhang, 2014). Li et al. (2004) reported a cloud line forming rightabove the GS axis, where the pressure-induced wind curl is the maxi-mum. Similar adjustments were found in the KS region (Kawai,Tomita, Cronin, & Bond, 2014; Liu, Zhang, & Xie, 2013; Tokinaga et al.,2009). Both mechanisms suggest that the SST-cloud relationship, if itexists, should be positively correlated and thus leads to negative
Fig. 9. Large sampling errors (shown in color) are caused by long cloud persistence (y-axis) for those grid boxes with the same gap fraction (x-axis).
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sampling errors. Second, seasonal variations of the direct pressure ad-justment have been shown to strongly affect the cloud distribution inthe GS area: in winter, wind convergence is strongest right over theGS between Cape Hatteras and the Grand Banks, and is accompaniedby enhanced precipitation and more midlevel clouds (Minobe,Miyashita, Kuwano-Yoshida, Tokinaga, & Xie, 2010). Indeed, in Fig. 13,the GS region shows strong negative sampling errors over the northernsector in winter, yet the dominant negative errors are missing in theother seasons. Regardless of the mechanisms, the pathways of thesetwo western boundary currents can affect synoptic variability. The GSfront is more intense and confined to a narrow meridional band ofabout 100 km,while the KS front appears to bemore diffusely distribut-ed. This geographical feature influences atmospheric variables, such aslatent and sensible heat release and horizontal divergence (Joyce,
Fig. 10.Geographic locations of the regions:Western PacificWarmPool (WPWP: 140°E–160°W(KS: 120°E–150°E, 15°N–50°N); Gulf StreamCurrent (GS: 80°W–45°W, 25°N–55°N); Peruvian C
Kwon, & Yu, 2009).We found similar features in the sampling error pat-terns with large errors in the KS spread wider in the meridional direc-tion (Fig. 13). It is also widely known that frequent fog and haze formover the slope waters. Fog can be identified as clouds in IR and thus af-fect the sampling errors. To summarize, the strong variability in thesampling error results from the concurrent coupled air-sea processesand the error cannot be attributed to any single process.
4.5.4. Stratocumulus regionsThe Peruvian and Namibian coasts are recognized as being covered
by persistent stratocumulus clouds. As seen in Fig. 8, the maximummonthly persistence can be ~25 days in these areas. In Fig. 14, weshow that generally sampling errors become warmer as the cloud per-sistence becomes longer in both regions (also in seasonal statistics(Fig. S6)). In other words, the longer the sampled cloudiness, the colderthe sampled mean SST for that grid box. Causes for this relationshipcould be several. Klein andHartmann (1993) found that themodulationof SST on the lower troposphere static stability is important for the low-level stratus cloud cover in these two regions. The decrease of SST canstabilize the frequent temperature inversions, which in most casesfavor high cloud occurrence. Later Klein (1997) pointed out that sucha modulation also exists at synoptic time scales. The prevalence of pos-itive sampling error here can possibly be due to such a modulation,which gives a negative correlation between SST and cloud fraction.But it could also be due to advections of colder SSTs with cloudsabove. Besides, if the reduced solar radiation at the sea surface due topersistent cloudiness decreases the SST in these regions, the variationin the amplitude of the SST could be magnified by a positive feedbackand warmer sampling errors can be found at longer cloud persistence.The amplification of the SST annual cycle by cloud “shading” effectswas found in oceanic observations off the Peruvian coast (Takahashi,2005). Kubar, Waliser, Li, and Jiang (2012) found that starting fromthe time scale of ~15 days the low-topped cloud fraction (LCF) andSST show negative correlation comparable to annual cycle statistics;where the primary LCF variance is explained by the annual cycle, themaximum LCF leads the minimum SST by 15–30 days. The domainswhere this was found include the two stratocumulus regions here. Webelieve that the time scale of 15–30 days indicates the dominant
Fig. 11. The dependence of mean sampling error on gap fraction in the WPWP. The single temporal and single spatial cases are shown. b. The WPWP δSSTA;t ̅ variation in the resolutiondomain.
warm sampling errors commonly starting from 20-day cloud persis-tence and the likely internal positive feedback. But more research isneeded to support this mechanism. Note that in the Peruvian coastalarea a positive feedback exists between negatively correlated low-level cloud amount and SST on a decadal time scale (Clement,Burgman, & Norris, 2009). Our findings here suggest that any longterm relationship between SSTs that include IR measurements andclouds in these regions could be potentially obscured, especially duringperiods of cold SSTs, because of the cloud induced sampling errors in IRmeasurements.
4.6. MODIS cloud mask
One noticeable feature in our results is the day and night inconsis-tency of sampling error statistics, especially in the Southern Ocean.The reference field (MUR) is the same for both day and night sampling;the only source of the different day and night statistics is the differentday and night cloud masks of MODIS. Therefore, unless the diurnal var-iability in cloud cover is substantial, the diurnal difference in gap frac-tion should be small. However, note that the MODIS SST cloud masksnot only flag pixels identified as clouds, but also flag pixels with poorquality level due to radiometric errors. For the cloud flags, the day–night difference can be related to the use of a visible band for cloud de-tection during the daytime but which cannot be used at night; for otherlow quality level flags, the day–night difference is related to the differ-ent thresholds used in the quality tests. Consequently, even if therewere no diurnal changes of clouds in reality, differences between dayand night cloudmasks could be introduced simply through themethodsof cloud identification.
In fact, the day–night gap fraction difference shows meridional andseasonal variations (Fig. 15). The winter hemisphere shows higher day-time gap fraction than the summer hemisphere, while in spring and fall,mid and high latitudes show higher daytime gap fraction than the tro-pics. The daytime gap fraction in high latitudes is about 30% higherthan the nighttime, especially in the Southern Ocean. However, thetropical daytime gap fraction is lower than the night-time in all four sea-sons. Interestingly, over the North and South Pacific Ocean gyre centers,where it is mostly “clear”, the daytime gap fraction is higher than at thenighttime. For sampling errors, the day–night difference does not showanalogous patterns to the mask difference. Instead, large differencesmostly occur in the cloudy regions. There can be multiple causes of
the day–night cloud mask meridional and seasonal differences, but theidentification of the causes needs further investigation into the cloudscreening algorithm.
The sampling error day–night differences show different patternsnot only by seasons but also by resolutions. In the [4 k, mon] case (sec-ond column in Fig. 15), the sampling error pattern shows large day–night differences in regions with frequent cloudiness. The error differ-ence in the “clear” regions is essentially negligible. On the other hand,the error difference in the [5°, 1d] case shows more correspondencewith the gap fraction difference. Particularly in the Southern Ocean,where clouds are oftenmultilayer, warmer daytime sampling errors co-exist with higher daytime gap fraction and vice versa.
Mesoscale SST anomalies associated with oceanic eddies modify theatmospheric boundary layer, including in the Southern Ocean: Frenger,Gruber, Knutti, and Munnich (2013) found a positive correlation be-tween SST anomalies and cloud fraction in this area; Chelton (2013)commented that the surface expression of eddies imprinted on the sur-facewind, low-level clouds, and precipitation are omnipresent. Such ro-bust dynamical links can bemanifested in the sampling error, but only iftheMODIS cloudmask represents realistic cloud fraction and if low levelcloud dominates. However, it seems that both conditions apparently donot hold in the Southern Ocean. Taken together, an SST-cloud correla-tion is less likely reflected in the high latitude sampling errors becauseof the enhanced uncertainty in the cloud mask, and this uncertainty ismost likely generated by intrinsic cloud screening algorithm instead ofphysical causes.
5. Discussion
Weanalyzed the effects of dailyMODIS SST cloudmasks of 4monthsto characterize the resulting sampling errors. Note that because theMODIS swath width is insufficient to provide overlap of successiveswaths equatorward of 32.3° latitude, the resulting, systematic gaps inthe SST fields are included in this analysis with themissing data that re-sult from the presence of clouds. The annual mean sampling error mag-nitudemight fluctuate around the values we calculated for the 4 samplemonths. Similarly, the seasonal variation extracted from the 4 monthsmight be less representative of the error seasonality, which connectsto complete seasonal cycles of clouds and SSTs. Sampling errors alsooccur in generating Level 3 fields (4 km as used here) from Level 2swaths (1 km for MODIS), but we anticipate these errors to be small,
Fig. 12. The 2011 October mean SST (a), gap fraction (b) and the resulting sampling error (c) in the TIW region. SST contours (1 K interval) are shown in b. and c. for comparison.
Fig. 13.Monthly mean sampling errors of 5° spatially averaged daytime sampled SSTs in: the Kuroshio region (first row) and the Gulf Stream region (second row). The 4 columns showdifferent seasons.
60 Y. Liu, P.J. Minnett / Remote Sensing of Environment 177 (2016) 48–64
Fig. 14. Box-whisker plots of sampling errors at different cloud persistence. Peruvian (left) and Namibian (right) coasts are shown.
as the error growth is very flat from 4 km to 0.25° (Fig. 4). Thereforesampling errors in 4 km fields are neglected in this work. However,the results shown here are indicative of how large are the error magni-tudes, comparedwith theCDR target accuracies of 0.1 K anddecadal sta-bility of 0.04 K (Ohring et al., 2005).
We selected one Level 4 field, MUR, as the reference, assuming it tobe a reasonable, not necessarily a perfectly accurate, realization of thedaily SST fields. For example, MUR has unresolved SST variability onscales b25 km in regions where extensive clouds are present, due toonly microwave SSTs being used. To assess the error in the estimate ofthe mean that is caused by unresolved variability in microwave SSTs,we selected the grid boxes at [0.25°, 1d] resolution that are identified
Fig. 15.Day–night difference of the gap fraction and the sampling error during the 4months. Theof the monthly averaged variables at [5°, 1d]. White color shows the zero difference. Gray indi
with gap fraction f = 0, and use these to represent the SST fields thatwould be given by on the microwave (AMSR-E) SST retrieval grid, i.e.the SST variability in these grid cells is taken as the sub-cloud SST vari-ability missing fromMUR in cases where the cloud extent totally coversa 25 km grid cell. The standard error of the estimate of themean of sam-pled [4 k, 1d] sub-grids in the [0.25°, 1d] areas is then considered to bethe error in the SST that is caused by unresolved variability in themicro-wave SST retrieval grid cell. We show the global standard error cumula-tive histogram of the 4 months (Fig. 16). These are day time statistics,but those from night time is very similar. In all cases, more than two-thirds of the error is less than 0.02 K.We anticipate the error due to un-resolved variability to be very small and thus can be neglected. Being
left two columns show resolution at [4 k,mon]; the right two columns show the differencecates the region with super-grid scale clouds, thus is excluded.
Fig. 16. The cumulative histogram of estimated errors in MUR that are caused by unresolved SST variability underneath clouds. SE is the standard error of the estimate of the mean.
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aware that the input ofMODIS data in generatingMURfieldmight causecloud mask coupling with the underlying SSTs, we conducted two testsshifting the cloud masks by ±1 day, in order to decouple MUR andMODIS. The two tests yield very similar sampling error patterns, magni-tudes and statistics (not shown). There might also be differences in thesampling error if other Level 4 reference fields were to be used.Wewillcompare the difference of sampling error referenced to different Level 4fields in future work.
Although also affected by the inter-swath gaps, the 30°S–30°N zoneshows small sampling errors primarily due to the low SST variability inthis region. Here the absence of the anticipated striped pattern in themonthly averaged SST fields indicates a relatively adequate samplingof MODIS for monthly SSTs. This is also a reason for the small samplingerror found in this region.
For mesoscale applications, which require SSTs at spatial resolutionsof higher than 1°, our analysis is able to reveal possible sampling errorimpacts on the data quality and we have described possible physicaland dynamical causes. An interesting question is, can we rely on anSST-cloud correlation to anticipate or even correct the sampling error?The previously reported SST-cloud relationships involve several mecha-nisms at various scales in the lower atmospheric boundary layer. Ouranalysis implies that over some regions where the vertical system isstrongly coupled, for example the TIW region, sampling errors can beexplicitly anticipated. However, in most cases, an SST–cloud relation-ship does not hold linearly or may not be manifested, because thesub-seasonal cloud variability might be more related to surface meteo-rological variables than to the SST. In fact, many factors in microphysicsmore directlymodulate the cloud formation. Therefore, more analysis isneeded before the SST and cloud attributions to the sampling error ofmany regions can be made in a quantitative fashion.
Cloud detection in IR imagery is difficult and has its own issues. Asmentioned in Section 4.6, there appears to be some imperfections inthe MODIS cloud masks. Although improving cloud masks is a subjectbeyond the sampling errors discussed here, we believe that the furtherunderstanding of sampling errors in the high latitudes is obstructed bythis additional cloudmask uncertainty. Nonetheless the type of analysispresented here can illuminate some of the possible causes of failures inthe cloud screening algorithms.
Our results show warm sampling errors in the monthly averagedSSTs dominating in most regions around the globe. Without analyzinga longer period, it is unclear whether the long-term climate signal inthe current IR SST climatologies is also affected. In a related study onsampling errors in climatology, Hearty et al. (2014) found that sampling
biases in climatologies of air temperature andwater vapormeasured byAIRS can be up to 2 K cold and N30% dry over mid-latitude storm tracksand deep convective regions, and N20% wet over stratus regions. Theyalso found seasonal and diurnal variations in the sampling biases andmentioned that clouds might be the main cause for these since thebias pattern resembles the cloud distribution. Here we argue that overregions with possible SST-cloud feedbacks and longtime cloud persis-tence, a climate trend can even be biased by the possibly weakeneddata stability. Although the small SST sampling error in the tropics im-plies good data quality, the La-Niña-like sampling error pattern of strik-ing negative errors in the cold tongue region potentially depresses thequality of IR SSTs for ENSO studies.
However, there is one component of the sampling error that can bequantified and separated from the overall sampling error: the samplingerror caused by the known seasonal climatological cycle of SSTs.We ex-pect for regions with long cloud persistence, the sampling error can bereduced by eliminating the climatological seasonal variation in thedata. Future work will include elucidating which part of the samplingerror can or cannot be corrected or at least reduced.
Using microwave SSTs can reduce the sampling error caused byclouds, but there are sampling errors caused by precipitation. For re-gions like the GS, where precipitation tends to line upwith ocean fronts(Chelton & Xie, 2010; Liu, Xie, Norris, & Zhang, 2014; Minobe et al.,2010; Small, Xie, & Wang, 2003), sampling errors can be expected.
Total errors in Level 4 fields include those inherited from Level 2 andadditional contributions from the sophisticated interpolation algo-rithms and physical models, which could either introduce more errorsor reduce the final error. The propagation and evolution of total errorscannot be simply assessed by using the method in this study, but willbe the subject of further research.
6. Summary and conclusions
Motivated by the demanding accuracy of SSTs required for the SSTCDR generation, we quantified the sampling errors of MODIS SSTs. Wefound that theMODISmonthly sampling error, usingMURSSTs as refer-ence fields, is up to O(1 K), which far exceeds the error threshold need-ed for climate research andmonitoring. Although the high latitudes aremeasured the most frequently by satellites, the largest sampling error(N5 K) is found in the Arctic, which is believed to be themost vulnerableto climate change (Serreze & Barry, 2011). The 30°N–30°S zonal band,exclusive of the TIW region, is found to have the smallest sampling er-rors. Although the error magnitudes are very diverse globally,
essentially the sampling error distribution is decided by both the gapfraction and the SST variability. Our results show that the samplingerror increases approximately exponentially with the gap fraction at afixed averaging interval, while the RMSE correlates approximately line-arly with the SST variability. By comparing sampling errors at 34 differ-ent spatiotemporal averaging scales, we found that the global meanerror increases monotonically with averaging scales, yet the RMSE canbe decreased by averaging over a more symmetrical spatiotemporalscale. Based on this, we suggest that gridding pixel measurements intoa resolution with relatively equivalent sub-resolution variability in thespatial and temporal dimension generates lower error uncertainty. Wealso investigated the seasonal and diurnal changes of the samplingerror. Not surprisingly, seasonal error changes are related to the season-ality of SSTs and clouds. Diurnal error changes are relatively small ex-cept for those in the high latitudes. We defined a new quantity—thecloud persistence—for error source attribution in regions of long dura-tion cloudiness. Imperfections in the cloud masks are seen in the unre-alistic diurnal changes in the cloud persistence and can explain theapparent errors that are not attributable to either physical or dynamicalcauses, especially those around Antarctica. For the regionswhere strongocean–atmosphere interactions exist, our results demonstrate remark-able geophysical error patterns, which can be explained by previouslydescribed mechanisms.
This research is the first attempt to quantify the sampling error of IRSSTs. The sampling error found is substantial and can be the primarycomponent in the Level 3 and Level 4 SST error budget. Regional sam-pling errors even exhibit geophysical patterns, which indicate potentialrisks of misinterpretation in a number of applications. Therefore, wesuggest that, the SST CDRs generated from IR SSTs should include thesampling error in the final error budget. Climate applications of IR SSTfields should be conducted with due regard to the sampling errors.
Acknowledgments
The initial stages of this researchwere supported by a grant from theNASA Physical Oceanography Program (NNX11AF26G) and then by aNASA Graduate Fellowship to Y. Liu (NNX14AL28H). This work hasbenefited from discussions with colleagues at RSMAS, including R. H.Evans, S. Walsh, K.A. Kilpatrick, D. Putrasahan, P. Zuidema and A.Adebiyi.
Appendix A. Supplementary data
Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.rse.2016.02.026.
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