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GEOID12/GEOID12A
Yan Ming Wang
Geosciences Research Division
GeoTech 2012 Conference
Fair Oaks, Fairfax VA
October 25-26, 2012
OUTLINE
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Geoid modeling at NGS
USGG12
GEOID12
Erroneous data
GEOID12A
DEFLEC12A & USDOV2012
Outlook
Fundamentals of Geoid Computation
1. Newton’ gravitation law (integration)
Difficulty: the density of the Earth’s interior masses is
never known accurately
2. Geodetic boundary value problems: from free boundary
to fix-boundary (differentiation)
One solution: Stokes integral: requires gravity measured
on the Earth’s surface everywhere
Another solution: Spherical harmonic series as solution
of GBVPs
……
History of geoid modeling at NGS
1.
GEOID90 (Milbert D.G., 1991)
2.
Geoid96 (Smith, D.A. and D.G. Milbert, 1999)
3.
Geoid99 (Smith, D.A. and D.G. Milbert)
4.
USGG03/GEOID03 (Roman, D. R., Y. M. Wang, W.
Henning, J. Hamilton, 2004)
5.
USGG09/GEOID09 (Wang Y.M., J. Saleh, XP Li and D.
Roman, 2012)
6.
USGG2012/GEOID12/GEOID12A (today)
NGS geoid computation methods
Before USGG09:
1. Simplified Helmert 2nd condensation
Terrain correction (30”+3” DEMs)
Bouguer anomaly for gravity gridding
Stokes integral of Faye anomaly
2. Remove-restore of a global gravity model (EGM96)
Computations on the sea level
3. Linearized formula of the indirect effect added ,
ellipsoidal effect added
USGG12 Computation Method
1. Method of harmonic continuation
Residual free-air anomaly computed on the
Earth’s surface
Stokes integral of residual free-air anomaly
Harmonic continuation effects on mm level
3” SRTM DEM used for RTM effect (gravity and
geoid)
2. Remove-restore of a global gravity model
(EGM08+GRACE+GOCE)
Stokes kernel truncated at n=120, 360
GRACE(Gravity Recovery and Climate Experiment)
GOCE(Gravity field and steady-state Ocean Circulation
Explorer)
Objective: a geoid of accuracy in 1-2cm in a spatial resolution of 100 km
Long wavelength geoid from GRACE
Difference between NAVD88 and GRACE
• Geoid height difference:
dN=N(NAVD88)-N(GRACE)
where
N(NAVD88)=H(BM)-h(BM)
N(GRACE) is computed to degree and order 120
Long wavelength diff (5°) NAVD88-GRACE
EGM08
• GRACE satellite only at low degree and order
• Using global terrestrial/altimetry gravity data in 5’
mean, geophysical model fill-in in areas with no
data
• Using SRTM elevation for topographic reduction
and geoid conversion
• Model developed to degree and order 2160
Geoid Difference: EGM08-EGM96
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
RTM effect on gravity (mGal)
FA-EGM08
FA-EGM08-RTM
Mean
-1.9
0.6
STD
10.6
5.4
RTM Geoid (5’ -3”)
USGG12 Gravimetric Geoid Model
• Satellite gravity models (GRACE+GOCE) + EGM08
• 2.6 million terrestrial, ship, and altimetric gravity
measurements
• 30 arc second Digital Elevation Data
• 3 arc second DEM for the Northwest USA
– Decimated from 1 arc second NGSDEM99
• Computed on 1 x 1 arc minute grid spacing
• GRS-80 ellipsoid centered at ITRF00 origin
Gravity Coverage for USGG12
USGG2012(Gravimetric Model)
• Satellite Gravity Models + EGM08
• 2.6 million terrestrial, ship-borne, and altimetric gravity
measurements
• 30 arc second Digital Elevation Data
• 3 arc second DEM for the Northwest USA
– Decimated from 1 arc second NGSDEM99
• Computed on 1 x 1 arc minute grid spacing
• GRS-80 ellipsoid
GEOID12(operational model)
• Start with a gravimetric geoid (USGG2012)
• Use control data to fit to local datums
– Appropriate versions of NAD 83
– Respective local Vertical Datum (if one exists)
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Use LSC to determine correlated signal
For complex areas (e.g., CONUS), use MMLSC
Apply grid of correlated signal to USGG2012
Results in GEOID12 with high frequency
nature from USGG2012 but fit to local control
Hybrid Geoid Height Models (e.g., GEOID12), Gravimetric Geoid Height Models (e.g.,
USGG2012) and Conversion Surfaces using GPS on BM data
Earth’s Surface
h
h
h
h
H Ellipsoid
H
H
N
N
N
h
H
N
H
N
Hybrid Geoid
Gravimetric Geoid
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Gravimetric Geoid systematic misfit to BM’s but best fits “true” heights
Hybrid Geoid “converted” to fit local BM’s, so best fits NAVD 88 heights
Conversion Surface model of systematic misfit derived from BM’s in IDB
USGG2012 – USGG2009
Control Data for GEOID12 Modeling
Region
Reference
Frame
Vertical Datum # GPSBM used
(# Rejected)
CONUS
NAD 83 (2011)
NAVD 88
NAD 83 (2011)
Alaska
#OPUSDB used
(# Rejected)
* 24,003 (868)
478 (258)
NAVD 88/VTDP
357 (153)
1 (17)
NAD 83 (2011)
NAVD 88
** 105 (4)
2 (1)
Puerto Rico
NAD 83 (2011)
PRVD 02
38
0
U.S. Virgin Islands
NAD 83 (2011)
VIVD 09
21 (3)
0
Hawaii
NAD 83 (PA11)
Geoid (W0)
n/a
n/a
American Samoa
NAD 83 (PA11)
ASVD 02
19 (3)
0
Guam
NAD 83 (MA11) GUVD 04
33
0
CNMI
NAD 83 (MA11) NMVD 03
55
0
- VTDP Region
* Supplemented by 574 (5 rejected) in Canada and 674 (70 rejected) in Mexico
** Supplemented by 88 (2 rejected) in Canada
http://www.ngs.noaa.gov/GEOID/GEOID12/GPSonBM12.shtml
Ellipsoid Height Changes
(NA2011-NA2007)
Rejections based on adjustment error
(NA2011 => ‘h’ Reject code)
Rejections based on adjustment error
(NA2011 => ‘h’ Reject code)
Orthometric Height Changes (mm)
Orthometric Height Changes (mm)
Large error points (‘H’ Reject)
Distribution of OPUSDBBM12
Distribution of OPUSDBBM12
MMLSC for CONUS with and
without (w/o) OPUSDBBM12
GEOID12 with OPUS
GEOID12 without OPUS
The Impact of OPUS
GEOID12 Error Map for Southwest
Triangles show
locations of
GPSBM2012 &
OPUSDBBM12
control points.
Error increases
based on the
size of the gap.
Dense coverage
yields < 1 cm.
Errors will be
provided with
GEOID12 hts.
Inverse Distance Plot to Control Data
(Interpolation Gap Magnitude)
Inverse Distance Plot to Control Data
(Interpolation Gap Magnitude)
An additional 6,000 points?
GEOID12 – GEOID09
GEOID12 – GEOID03
Same
Scale
as 12-9
So … What Went Wrong?
• Erroneous Data
– VTDP exclusion region – what’s in/out? (MS, LA)
– Transposed numbers (AL)
– Recent adjustment and superseding data (WI)
– Miscoded error flags (Canada)
– Judgment call – keep or reject? (OK)
• Miscommunication/Misunderstanding
– No-check GPS: NGSIDB vs. OPUS-DB (TX)
– Hybrid to use minimal number of points (LA)
What Went Wrong:
A Picture’s Worth a 1000 Words
What Went Wrong:
Erroneous Data & Judgment Calls
GEOID12
Ellipsoidal Orthometric Rejected from
PID
Name
State Height (m)
Height (m)
Modeling?
Change orthometric height to published leveled value (do not use VTDP value)
1
BJ0021 F 207
LA
-12.789
14.224
NO
2
BJ0026 H 207
LA
-13.742
13.335
NO
3
BJ0055 V 207
LA
-15.691
11.516
NO
4
BW0051 E 208
LA
-12.149
14.767
NO
5
BX0822 OPUS :U 238
LA
-4.805
21.936
NO
6
BX0916 Q 239
LA
-2.543
23.346
NO
7
CO1081 L 251
MS
55.539
82.182
NO
8
DM5373 COUNTY ENG OFFICE CORS ARP
AL
238.544
263.305
YES
9
NG0372 RACINE
WI
161.637
196.386
NO
10
NH0083 VEEN
WI
259.555
293.637
NO
11
PM0119 AIRPORT
WI
162.024
198.146
NO
12
PO0408 D 125
WI
173.401
203.859
NO
Reject in GPSBM list
1
BH3160 49 11
AL
-22.709
5.734
NO
2
BH3161 49 12
AL
-24.751
3.693
NO
3
AT0681 876 1724 C TIDAL
LA
-23.228
0.769
NO
4
AT0760 V 375
LA
-25.230
0.799
NO
5
AU0174 VERDUN
LA
-23.759
1.928
NO
6
AU0178 J 168
LA
-22.741
2.846
NO
7
AU0189 TECHE
LA
-23.654
1.987
NO
8
AU0245 T 298
LA
-24.199
1.295
NO
9
AU1117 LAROSE
LA
-23.085
1.928
NO
10
AU1300 H 233
LA
-24.543
0.352
NO
11
AU1304 M 233
LA
-23.541
1.255
NO
12
AU1307 Q 233
LA
-24.257
0.500
NO
13
AU1314 X 233
LA
-21.401
3.150
NO
14
AU1317 Y 233
LA
-24.224
0.300
NO
15
AU1396 F 227
LA
-24.090
1.301
NO
16
AU1399 ARSENAUX
LA
-24.242
1.098
NO
17
AU1404 K 227
LA
-23.828
1.422
NO
18
AU1406 L 227
LA
-24.251
0.934
NO
GEOID12A
Orthometric Rejected from
Height (m)
Modeling?
CHANGE (m)
Ellipsoidal
Height (m)
OH: 0.129
OH: 0.132
OH: 0.098
OH: 0.093
OH: 0.046
OH: 0.572
OH: 0.630
OH: 4.320
OH: 0.024
OH: 0.032
OH: 0.047
OH: 0.007
-12.789
-13.742
-15.691
-12.149
-4.805
-2.543
55.539
238.544
161.637
259.555
162.024
173.401
14.353
13.467
11.614
14.860
21.982
23.918
82.812
267.625
196.41
293.669
198.193
203.866
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
NO
Outside VTDP exclusion area; use published value instead
Outside VTDP exclusion area; use published value instead
Outside VTDP exclusion area; use published value instead
Outside VTDP exclusion area; use published value instead
Outside VTDP exclusion area; use published value instead
Outside VTDP exclusion area; use published value instead
Outside VTDP exclusion area; use published value instead
Wrong Orthometric height posted; value corrected to fix 4.3 m bust
Incorrect OH loaded in NGSIDB
Incorrect OH loaded in NGSIDB
Incorrect OH loaded in NGSIDB
Incorrect OH loaded in NGSIDB
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
-22.709
-24.751
-23.228
-25.230
-23.759
-22.741
-23.654
-24.199
-23.085
-24.543
-23.541
-24.257
-21.401
-24.224
-24.090
-24.242
-23.828
-24.251
5.734
3.693
0.769
0.799
1.928
2.846
1.987
1.295
1.928
0.352
1.255
0.500
3.150
0.300
1.301
1.098
1.422
0.934
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because near primary only station
Inside VTDP exclusion area; reject because does not match nearby neighbors
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Comments
What Went Wrong:
Erroneous Data & Judgment Calls
19
AU1418 S 227
LA
-23.847
1.284
NO
20
AU1424 T 227
LA
-22.170
2.924
NO
21
AU1433 Y 227
LA
-22.945
2.203
NO
22
AU1440 T 221
LA
-23.962
1.142
NO
23
AU1505 B 233
LA
-22.304
2.839
NO
24
AU1507 D 233
LA
-22.878
2.259
NO
25
AU1508 E 233
LA
-23.322
1.717
NO
26
AU2085 T 359
LA
-22.814
2.324
NO
27
AU2087 V 359
LA
-23.059
2.056
NO
28
AU2089 W 359
LA
-24.508
0.465
NO
29
AU2090 X 359
LA
-23.355
1.854
NO
30
BJ2124 28 A 013
LA
-15.764
11.438
NO
31
BJ2147 D 171
LA
-16.803
9.973
NO
32
BJ2167 Y 266
LA
-18.519
8.243
NO
33
BK0159 X 267
LA
-22.996
4.112
NO
34
BK0182 416
LA
-21.288
6.063
NO
35
BK1611 10 V 27
LA
-22.301
4.840
NO
36
BW0007 E 254
LA
-10.488
16.338
NO
37
AJ6426 ADDICKS 1795 CORS ARP
TX
4.035
31.500
NO
38
AF9213 ENID RESET
TX
357.109
385.210
NO
39
AB6370 LAKE HOUSTON CORS L1
OK
-7.137
20.220
NO
40
BH3164 49 15
AL
-13.221
15.279
NO
41
BH3165 49 16
AL
-14.151
14.339
NO
42
EF0792 B 182
AL
148.544
175.25
NO
Change ellipsoid height to OPUS value
1
DO0454 C 281
TX
353.930
383.465
NO
2
DO0454 OPUS: C 281
TX Not Previously Used
YES
Duplicate station in GPSBM file; delete one with OHT = 35.664 m (keep one with ADJUSTED source)
1
BK1060 A 16
LA
8.608
35.664
NO
2
BK1060 A 16
LA
8.608
35.994
NO
Currently rejected OPUS points to remain rejected (but has ortho height change)
1
BH1732 OPUS :21 D 2 D
AL
-26.488
1.756
YES
oint not originally in GEOID12
1
DL7331 FOLEY CORS ARP
AL Not Previously Used
YES
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
'S' reject code
-23.847
-22.170
-22.945
-23.962
-22.304
-22.878
-23.322
-22.814
-23.059
-24.508
-23.355
-15.764
-16.803
-18.519
-22.996
-21.288
-22.301
-10.488
4.035
357.109
-7.137
-13.221
-14.151
148.544
1.284
2.924
2.203
1.142
2.839
2.259
1.717
2.324
2.056
0.465
1.854
11.438
9.973
8.243
4.112
6.063
4.840
16.338
31.500
385.210
20.220
15.279
14.339
175.22
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because large residual, VTDP rate suspect
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because of large residual and rank
Inside VTDP exclusion area; reject because large residual, no rate validation
Inside VTDP exclusion area; reject because large sigma and secondary
Inside VTDP exclusion area; reject because opposite sign resid of neighbor
Reject; duplicate CORS tied only with old GPS vectors
Reject; duplicate CORS tied only with old GPS vectors
Reject due to large residual and superseded 3rd BM
Inside VTDP exclusion area; reject at request of AL representatives
Inside VTDP exclusion area; reject at request of AL representatives
Near DM2662 with a 11 cm difference; keep DM2662 and drop this one
EH: 0.501
353.930
354.431
383.465
383.465
YES
NO
Single shot-no check GPS from 1995 - 50 cm error
Still fills interpolation void
'S' reject code
Keep only this
8.608
8.608
35.664
35.994
YES
NO
Outside VTDP Exclusion area; reject VTDP Keep/Add value
Outside VTDP Exclusion area; keep ADJUSTED Value
1.681
YES
Inside VTDP exclusion area; continue to reject but change VTDP orthometric height
32.259
NO
Missed CORS site from first round; should have been included
OH: -0.075
ADD NEW
-26.488
4.461
What Went Right?
• Big changes in Alexandria, LA & Meridian, MS
were reported shortly after GEOID12’s release
• These were quickly checked and GEOID12 was
found to be consistent with the control data
• The control data (GPSBM2012) were then rechecked and a number of errors detected
• Notices went up quickly & GEOID12 pulled
• A new SOP was developed for a more public
vetting of the final product (Beta release)
There are Valid Big Changes
Ignore changes
outside CONUS
VTDP region does
see 50 cm change
Can see the effect
of 3”-5’ RTM in
the mountains
200-400 km
features are due
to GOCE in
USGG2012
Bigger Differences with GEOID03
GEOID03 built on
USGG2003
USGG2003 built
using EGM96
EGM96 had no
GRACE data
Most significant
changes are all
offshore or
OCONUS
Note: same color
scale as before
Coming Soon: Error Maps …
GEOID03 made
using a Cholesky
Decomposition
Rigorous LSC was
used in GEOID12A
This ensured we
had a var-cov
matrix to estimate
errors on a regular
grid
This means errors
can be provided
with geoid heights
… Minimum Distance to Control Data
One of the main
factors affecting
errors is distance
to control
This plot will
provide the
distance to the
closest point
This provides an
estimate of
interpolation
error impact
Deflections of the Vertical
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DoV’s are related to geoid heights
Describe local plumb variations from ellipsoid
Geoid models can determine DoV models
USGG2012 => USDOV2012
GEOID12A => DEFLEC12A
USDOV2012 is in the IGS08 reference frame
DEFLEC12A is in the NAD 83 reference frame
DoV models are useful for IMU applications
DEFLEC12A – Xi (ξ)
DEFLEC12A – Eta (η)
USDOV2012 – Xi (ξ)
USDOV2012 – Eta (η)
Summary
• GEOID12A is complete for all regions
• It converts between NAD 83 (**11) and the
local vertical datum (NAVD 88 in CONUS)
• Modeling is much the same as before (MMLSC)
• Incorporation of data in Mexico and
OPUSDBBM12 is new and has had an impact
• Error maps will be available to provide
estimated errors along with geoid heights
Summary (continued)
•
•
•
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Erroneous data were identified & corrected
Corrected data were used to make GEOID12A
This primarily affected Conterminous U.S.
For consistency, GEOID12 for other regions
renamed to GEOID12A (i.e., they’re the same)
• No impact on USGG2012
• DEFLEC12A derived from GEOID12A
• USDOV2012 derived from USGG2012
Near Term Goals
• Error and interpolation grids
– Online interpolation geodetic tool
– OPUS results
• Updates to FAQ and Technical Details
• Paper, likely on GEOID09, USGG2012,
GEOID12 & GEOID12A
Questions?
• Geoid Models Page:
– http://www.ngs.noaa.gov/GEOID/
• GRAV-D Page:
– http://www.ngs.noaa.gov/GRAV-D/
• Geoid Team: 301-713-3202
– Dan Roman (x161), Yan Wang (x127), Xiaopeng Li
(x210)