Validation of NGS Geoid Models in the U.S. by Geoid Slope Validation Surveys and Satellite Altimetry over the Great Lakes Compiled by Xiaopeng Li Email: [email protected]Airborne Gravity for Geodesy Summer School May 23-27 2016 Silver Spring, MD, U.S.A.
Transcript
Validation of NGS Geoid Models in the U.S. by Geoid Slope Validation Surveys and Satellite
Airborne Gravity for Geodesy Summer School May 23-27 2016 Silver Spring, MD, U.S.A.
Acknowledgements:
Simon A. Holmes1
1 = Stinger Ghaffarian Technologies, Inc. 2 = NOAA’s National Geodetic Survey 3=Nature Resources Canada
Dru A. Smith2 Yan M. Wang2
Dan R. Roman2 John W. Crowley3
Presenter
Presentation Notes
Thanks to my colleagues. Really appreciate the opportunity to present these great results here. Also thank to many other persons from the OAD department and NRCan for providing some of the gravity data and oceanic models
GSVS11 (The breakthrough) Smith, D.A., Holmes, S.A., Li, X., Guillaume, S., Wang, Y.M., Burki, B., Roman, D.R., Damiani, T.M., 2013. Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011. J. Geodes. 87, 885–907.
GSVS14 (a follow up study) Wang, Y.-M., et Al., 2016. The Geoid Slope Validation Survey 2014, in press.
Great Lakes (Using Satellite Altimetry) Xiaopeng Li, John W. Crowley, Simon A. Holmes, Yan‐Ming Wang* (2016) The Contribution of the GRAV‐D Airborne Gravity to Geoid Determination in the Great Lakes Region. GEOPHYSICAL RESEARCH LETTERS, SOLID EARTH
Outlook (DoV, NAVD88)
Summary
Contents:
A simple equation:
In CONUS, the geoid is actually below the ellipsoid, N is negative.
N=h-H
Presenter
Presentation Notes
Courtesy of http://www.ngs.noaa.gov/GEOID/PRESENTATIONS/2007_02_24_CCPS/Roman_A_PLSC2007notes.pdf Orthometric height is the height on the surface above the geoid along the plumb line. Ellipsoidal height is the height above the reference ellipsoidal surface along the ellipsoidal normal. Neglecting the plumb line and ellipsoidal normal differences, we can use this simple equation to check the quality of the geoid models. But we cannot directly measure it from the geoid. So we do levelling. So errors come.
A simple equation:
Level Surfaces and Orthometric Heights
Level Surfaces
Plumb Line
“Geoid”
PO
P
Level Surface = Equipotential Surface (W)
H (Orthometric Height) = Distance along plumb line (PO to P)
Ocean
Mean Sea Level
Geopotential Number (CP) = WP -WO
WO
WP
High density rocks Low density rocks
• Normal Height (NGVD 29) H* = C / γ – γ = Average normal gravity along plumb line
• Dynamic Height (IGLD 55, 85) Hdyn
= C / γ45
– γ45 = Normal gravity at 45° latitude
• Orthometric Height H = C / g – g = Average gravity along the plumb line
• Helmert Height (NAVD 88) H = C / (g + 0.0424 H0) – g = Surface gravity measurement (mgals)
Presenter
Presentation Notes
Courtesy of http://www.ngs.noaa.gov/GEOID/PRESENTATIONS/2007_02_24_CCPS/Roman_A_PLSC2007notes.pdf Orthometric height is the height on the surface above the geoid along the plumb line. Ellipsoidal height is the height above the reference ellipsoidal surface along the ellipsoidal normal. Neglecting the plumb line and ellipsoidal normal differences, we can use this simple equation to check the quality of the geoid models. But we cannot directly measure it from the geoid. So we do levelling. So errors come.
Why do we need Geoid Slope Validation Surveys?
W0
Dru A. Smith (1998) There is no such thing as "The" EGM96 geoid: Subtle points on the use of a global geopotential model IGeS Bulletin No. 8, p. 17-28
Presenter
Presentation Notes
The geopotential differences between EGM2008 and the NAVD88 have clear extreme (meter level) systematic errors
Geoid differences between NAVD88 and EGM2008 (cm) Geoid differences between NAVD88 and DIR5 (cm)
Why do we need Geoid Slope Validation Surveys?
Presenter
Presentation Notes
Same thing for the geoid As a result, historical leveling surveys cannot be used for the purpose of geoid validation. New leveling surveys have to be carried out.
GSVS11 Differences between new GSVS11 leveled heights and
published NAVD 88 heights on 23 existent bench marks used in GSVS11
Presenter
Presentation Notes
The majority of differences are scattered within a vertical band of 5 cm. This 2.5 cm (1σ) scatter of points over relatively short distances is much larger than would be expected solely from the propagation of measurement error from geodetic leveling
GSVS11
325 km 218 points 1.5 km spacing
Fall completely under already-flown. At least 200 km long to compare against GRACE&GOCE Be low in absolute elevation, minimizing the assumptions
about density of rock and curvature of the plumb line between the earth’s surface and the geoid
Not have any significant water crossing (for leveling) Have relatively open sky views (for GPS) Be during a time with minimum cloud cover (for DoVs) Have some existing geodetic marks Run along a roadway Be in a location that is not expensive to travel to
Presenter
Presentation Notes
The survey was to be in a low, flat, gravimetrically benign coastal area, for which reason the coastal area of Texas was chosen. The final line was a 325 km stretch from downtown Austin, Texas (North end) to Rockport, Texas (South end). There were 218 official survey points along the line, with an average spacing of 1.5 km between them. The shaded areas in the above picture were the existing GRAV-D data at the time of planning GSVS11. Although the weather report looks extreme, most surveying was done in the milder times of day. To avoid problematic definitional, and relatively unproductive, concerns involved with evaluating ‘absolute’ geoid heights, this survey concentrated on differential accuracy between observed geoidal stations, and so this survey was termed the Geoid SlopeValidation Survey (GSVS) of 2011, or GSVS11.
• sDh (OPUS-S) : 2 - 6 cm – GPSCOM adjustment : ~
4 mm – (no significant baseline
dependency)
• => 12.6 mm RMS
GSVS11
Zilkoski and Richards (1998) gave the following error estimate for first order, class II leveling
Weston et al. (2007) & Mader et al. (2012) gave the following error estimates for GPS survey Smith DA (2011) True Zero. Point of Beginning
The primary purpose of the survey was to collect differential ellipsoid heights with GPS, differential orthometric height with leveling and deflections of the vertical, all coincident in time (4 months) and space (at 218 geodetic control marks distributed along roads running 325 km generally North/South between the cities of Austin and Rockport in the US state of Texas, where recent airborne gravity was also available). This allowed for a direct comparison between differential heights from geoid models and GPS and leveling data GPS error : No statistically significant distance correlation. This supports the presumption that differential ellipsoidal heights between any two of the 218 points on GSVS11 are known to about 4–5 mm accuracy, as shown by black bars. Leveling : First order, Class 2 geodetic surveys can achieve a differential orthometric height accuracy of 0.7 mm per square root of traverse-length in kilometers. For the current survey, which is 325 km long, NGS expected to achieve 12.7 mm of differential orthometric height accuracy (1σ) from one end of the line to the other.
All separation distances show improvement with GSVS11 survey when airborne gravity are introduced.
Presenter
Presentation Notes
This chart speaks to the ability of a gravimetric geoid model to be as accurate over distances as GPS and leveling combined. The basic messages here are that currently, gravimetric geoids aren’t as accurate as GPS and leveling, but they aren’t bad either. They are certainly cheaper than leveling! Furthermore, it shows that for this survey, at least, USGG2009 has some improvements to make to beat EGM2008. As such, NGS embarked on a rigorous re-examination of their geoid modeling methods. New experimental geoids with the new software show an improvement over USGG2009, but still not quite as good as EGM2008. The real story of columns 3/4/5 can be summarized as follows: “No matter what software is used, massaging the same old, uncorrected terrestrial gravity data isn’t going to improve the geoid precision. However, when adding in airborne gravity from GRAV-D, these new geoids blow everything else away.
GSVS11
0
0.5
1
1.5
2
2.5
3
3.5
"Geo
id O
nly"
RM
SE (c
m)
Distance Bins (km)
Predicted errors of various geoid models over GSVS11 after removal of
GPS/leveling error budget
USGG2009 (1'x1')DRMS (cm)
EGM2008 (5'x5')DRMS (cm)
USGG2012x01 (1’x1’) New software DRMS(cm)
USGG2012x02 (1’x1’) New software + Airborne data DRMS (cm)
Predicted errors of various geoid models over GSVS11 after removal of GPS/leveling error budget
Presenter
Presentation Notes
Geoid Models computed using existing terrestrial gravity, combined with digital elevation models (DEMs) and GRACE and GOCE data, differential geoid accuracy of 1 to 3 cm (1 σ) over distances from 0.4 to 325 km were currently being achieved. However, the addition of a contemporaneous airborne gravity data set, flown at 11 km altitude, brought the estimated differential geoid accuracy down to 1 cm over nearly all distances from 0.4 to 325 km.
GSVS11
Agreement with DIADEM DoVs (arcseconds)
Model Mean STD Extreme Values
USGG09 -0.028 0.195 -0.525/0.551
EGM08 -0.074 0.218 -0.659/0.462
USGG2012x02 (new software, with airborne data)
-0.075 0.199 -0.652/1.079 ξ
Model Mean STD Extreme Values
USGG09 -0.030 0.183 -0.599/0.531
EGM08 -0.047 0.225 -0.527/0.535
USGG2012x02 (new software, with airborne data)
0.020 0.164 -0.483/0.507
η
N/S
E/W
Smith, D.A., Holmes, S.A., Li, X., Guillaume, S., Wang, Y.M., Burki, B., Roman, D.R., Damiani, T.M., 2013. Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011. J. Geodes. 87, 885–907.
Presenter
Presentation Notes
Note that the new software and airborne gravity data don’t have a significant improvement in the north south deflections, but do improve the east-west deflections.
GSVS14
Presenter
Presentation Notes
GSVS14 was selected to a moderate terrain area with some geological features called the mid continent rift system Courtesy of http://geo.msu.edu/extra/geogmich/rift_zone.html And http://www.earth.northwestern.edu/people/seth/research/mcr.html
GSVS14 Flight trajectories
Topography
EGM2008 Geoid
GSVS14 Surface & Airborne Gravity Anomalies in the Target Area
Presenter
Presentation Notes
Left panel: Dots represent the surface gravity anomaly and the lines in the east-west and north south directions are the GRAV-D data collected. Note: the 4 slanted lines that cross the Midcontinent Rift are surface gravity measurements. The east-west black line is the GSVS14 traverse. Right panel: 3d plots of the surface and airborne data
GSVS14 Gravity model changes in the Target Area
Presenter
Presentation Notes
Considering that the EIGEN6c4 (Förste et al 2014) has already “optimally” combined all satellite observable, including SLR, SST, and SGG, by a FULL (all variances and co-variances) adjustment up to degree and order 370, I used this global gravity field model as the reference field in the compute-remove-restore procedure, rather than the kind of outdated EGM2008 model that does not contain any GOCE information and very limited GRACE data. The Figures show the gravity differences and the geoid differences between these two models, respectively, both of which show very clear systematic features omitted (or miss modeled?) by EGM2008. For instance, the geoid differences at the west end of GSVS14 reached to almost 10cm. This kind of magnitude and spatial pattern cannot be artifacts or random noise, if we consider the success of the full least square adjustment up to degree and order 370 in the EIGEN6c4 model.
GSVS14 Residual airborne gravity power distribution w.r.t. the
reference field over the target area
Presenter
Presentation Notes
Spatial and frequency distributions of the residual gravity anomalies with respect to the reference field: EIGEN6c4
The slope validation results show 1-2cm precision in most of the bins
GSVS14 The gravity comparisons along the survey
Jekeli, Yang, Kwon (2013)has also shown that “the most critical aspect of the combination is the gravitational effect of the topographic masses above the geoid, which, if not properly taken into account, introduces a significant bias of about 8 mgal in the gravity anomalies, and which can lead to geoid height bias errors of up to 10 cm”.
Presenter
Presentation Notes
Gravity comparisons further indict the importance of topographic modeling and agree with independent studies such as Jekeli et al 2013.
The Great Lakes The GRAV-D data contribution to the XGeoid models
Presenter
Presentation Notes
One of the Biggest Geoid improvements due to GRAV-D
The Great Lakes
Very mature technique (> 20 years), it can have accuracy of a few cm in open ocean area.
Courtesy of http://www.star.nesdis.noaa.gov/sod/lsa/AltBathy/ Fitting the shape of the echo waveform to a model function that represents the form of the echo plus averaging over a large number of echoes
The Great Lakes
Summer School 2016 05/01/2016 28
TPJO multi-mission & multi-year merged products (Beckley et al 2013)
Presenter
Presentation Notes
Beckley, B., R. Ray, S. Holmes, N. Zelensky, F. Lemoine, X. Yang, S. Brown, S. Desai, G. Mitchum, and J. Hausman (2013), Integrated multimission ocean altimeter data for climate research complete time series version 2. [Available at ftp://podaac.jpl.nasa.gov/allData/merged_ alt/preview/L2/docs/multi_alt_handbook_v2.pdf.]
The Great Lakes
Summer School 2016 05/01/2016 29
Data editing strategies
Presenter
Presentation Notes
There are few things in the above figure that directly impact and determine the data editing strategies of the altimetry data for geoid models comparison. (1) Outliers need to be detected and removed (2) Different cycles have different biases. These biases need to be removed or minimized as much as possible. (3) There are missing data in some cycles As such, at the first step the outliers need to be detected and removed. Considering the characteristic of the profiles, simply taking the “3-sigma” rule along the track cannot be applied because there are trends and no linear features along the track. Thus, a regression analysis was used to achieve a 95% fit of the data, whose residuals serve a good indicator for outlier detection. If there are no significant missing data, the “cycle bias” can be easily removed by normalizing into some “mean” height through iteration: Averaging the outlier free data at each location as the initial mean values Taking the mean at each location as the mean height of each cycle Normalizing each cycle to this mean height (point by point)/average so that the shape of each cycle get preserved
The Great Lakes Geoid validation along altimetry tracks
Presenter
Presentation Notes
Both EIGEN6C4 and xGeoid15Aref show a 10 cm improvement over EGM2008 along track 1, and a 20 cm improvement (from 43.5o to 44o latitude) along track 2. The standard deviation (STD) along each track provides a metric for assessing the quality of the model, with low values indicating the desired level lake surface and large values indicating significant departures from a level surface. The GOCE data helped to reduce the STD of the dynamic height from ±14.1 cm for EGM2008 to ±12.8 cm for xGeoid15Aref along track 1, and from ±20.2 cm for EGM2008 to ±11.4 cm for xGeoid15Aref along track 2. However, the most significant improvement comes from incorporating the GRAV-D data into xGEOID15Bref. For xGEOID15Bref, the STD of the dynamic heights across the lake is reduced to merely ±1.3 cm and ±2.2 cm for tracks 1 and 2, respectively. This is an order of magnitude improvement over all other gravity models. The standard errors of altimetric data are estimated at 1.5 cm. The discrepancies of 1.3 and 2.2 cm between the altimetric data and xGeoid15Bref for tracks 1 and 2 imply that the accuracy of xGeoid15Bref should be at the level of 1–2 cm.
The Great Lakes GRAV-D & Surface Gravity data
Presenter
Presentation Notes
The comparisons are extended to the remaining tracks of the Great Lakes.
The Great Lakes Geoid model precision over all Lakes
Presenter
Presentation Notes
The STD of the dynamic height across each track was used as a metric for comparing the different models. It was shown that the addition of GOCE data to EGM2008, yielding xGeoid15Aref and EIGEN6C4, improved both models over Lake Michigan. A more significant improvement, however, came from augmenting xGeoid15Aref with GRAV-D gravity data, yielding xGeoid15Bref. Here the standard deviation in dynamic height was reduced by an order of magnitude from previous models and a ±1–2 cm relative accuracy was achieved. Here again, GRAV-D data are shown to improve the xGeoid15Bref GGM over the lakes, even if these results are not as significant as over Lake Michigan. These show clearly that the xGeoid15Bref GGM agrees with altimetric data to 2–3 cm or better along all the tracks, except track 12 over Lake Erie. The large discrepancy over Lake Erie for xGeoid15Bref is likely due to poor terrestrial data that supported EGM2008, but which lies beyond the resolution of GRAV-D data to correct. Even so, improvement shown by the xGeoid15Bref GGM is clear: the GRAV-D data reduce the STD of the dynamic heights from 7.5 cm in xGeoid15Aref to 4.1 cm.
The Great Lakes Using GRAV-D data to identify problems in the surface gravity surveys
Presenter
Presentation Notes
Why it is only Lake Michigan? Because the surface data are very bad.
Summer School 2016 05/01/2016 34 Daniel ROMAN, and Xiaopeng Li (2016) Physical Heights from GNSS-Derived Geometric Coordinates and a Geophysical Model, FIG Working Week 2016 Recovery from Disaster Christchurch, New Zealand, May 2–6, 2016
Site IGLD 85 ht Dynamic Heights (m) from Geopotential Numbers (Wi) EGM2008 EIGEN6c4 xGEOID15A_REF xGEOID15B_REF
Grand Marais 183.613 182.890 182.891 182.908 182.919
The Great Lakes
Presenter
Presentation Notes
The CORS network has about 2,000 stations. NGS is responsible for 39 with a few of those being WLS. Six were selected: three on Lake Erie and three on Lake Superior at the west, middle and east of each Lake. The red circles for the following sites moving from east to west: Buffalo, Cleveland, Marblehead (Sandusky), Point Iroquois, Marquette, and Grand Marais. The coordinates or the CORS ARP at each site are available from the site file. The metadata for the WLS provides the distance between the ARP and water level (WL). Table shows the dynamic heights developed for these locations using four different geopotential models. This slope in Lake Erie may be a function of physical water surface.
Outlook
Deflection component USGG2009 EGM08 ξ Mean = 0.02529 Mean=−0.09113 SD = 0.87338 SD = 0.97803 Min=−5.84741 Min=−5.34600 Max = 5.28829 Max = 5.36200 η Mean = 0.16115 Mean = 0.18889 SD = 0.94117 SD = 1.03344 Min=−5.79390 Min=−5.62400 Max = 5.91816 Max = 5.97300
Jekeli C (1999) An analysis of the vertical deflections derived from high-degree spherical harmonic models. J Geod 73(1):10–22
Using DoV data
Outlook
Foreman et al (2008) Dynamic ocean topography for the northeast Pacific and its Geocontinental margins. phys.
Roman, DR, and ND Weston (2012) Beyond GEOID12: Implementing a New Vertical Datum for North America, FIG Working Week 2012
Outlook Using GRAV-D data to “clean” surface gravity surveys
Presenter
Presentation Notes
Jarir Saleh, Xiaopeng Li, Yan MingWang, Daniel R. Roman and Dru A. Smith (2013): “Error analysis of the NGS’ surface gravity database (J Geod 87:203-221 DOI 10.1007/s00190-012-0589-9) Surface gravity data needs to be somehow “Cleaned” up
Outlook Generating a “correcting” surface of NAVD88 by parametric modeling
Generating a “correcting” surface of NAVD88 by parametric modeling
Outlook
Presenter
Presentation Notes
Regression of parametric modeling using predefined basis functions needs extra statistical tests in determining the model coefficients
Outlook Generating a “correcting” surface of NAVD88 by BSS
Geoid differences between NAVD88 and DIR5 (cm)
Presenter
Presentation Notes
After the systematic error is removed (estimated from the geoid differences obtained by using DIR5 as the reference model), the standard deviation of the residuals is 16.3cm. If the same systematic error is removed in the DIR4 model, the standard deviation of the residuals becomes 19.5cm. This represents a relative 55% improvement from DIR4 to DIR5 and is much more significant than the previously found mm-level change based on systematic errors analyzed by regression.
Summary
GSVS11 demonstrated the possibility of obtaining accurate geoid models by using airborne gravity data
GSVS14 provided a further test in a moderate terrain area
Great Lakes results showed up to 40cm geoid improvement by using the NGS airborne geoid modeling approach
Terrain effects need to be further studied
NGS surface gravity data need to be “cleaned”
References:
o Holmes, S.A., Li, X., and Kinsman, N (2016) Alaska Geoid in preparation
o Xiaopeng Li, John W. Crowley, Simon A. Holmes, Yan‐Ming Wang (2016) The Contribution of the GRAV‐D Airborne Gravity to Geoid Determination in the Great Lakes Region. GEOPHYSICAL RESEARCH LETTERS, SOLID EARTH (Accepted)
o Jarir Saleh, Xiaopeng Li, Yan MingWang, Daniel R. Roman and Dru A. Smith (2013): “Error analysis of the NGS’ surface gravity database (J Geod 87:203-221 DOI 10.1007/s00190-012-0589-9)
o Jekeli, Yang, Kwon (2013) Geoid Determination in South Korea from a Combination of Terrestrial and Airborne Gravity Anomaly Data
