PowerPoint Presentation
GRAV-D for Puerto Rico and the U.S. Virgin IslandsDaniel R
Roman1 Xiaopeng Li2 and Dru A. Smith1 1. NOAA's National Geodetic
Survey, Silver Spring, MD, United States. 2 Earth Resource
Technology, Inc. Silver Spring, MD 20910
The intent of GRAV-D is to use aerogravity to bridge the gap
between satellite data and surface gravity. Data from satellite
missions such as GRACE (Tapley et al. 2004) and GOCE (Pail et al.
2011) provide the basis for determining the largest features of the
Earths gravity field and provide a common basis for developing a
World Height System (WHS). Any model developed for a region, such
as all of North America, using such data would be largely
consistent with other regional models. The GOCO03S model (Mayer-Grr
et al. 2012) is very useful for this analysis because it
incorporates GRACE, GOCE, CHAMP (Reigber et al. 2002), and
Satellite Laser Ranging (SLR) data.
However such global models omit significant portions of the
gravity field. Surface gravity observations contain all aspects of
the Earths gravity field, but they are limited in scope and subject
to systematic errors ; many of which have been identified in data
used to make models for the United States (Saleh et al. 2013, Roman
et al. 2010). Many global models , such as EGM2008 (Pavlis et al.
2012) rely upon methods of synthetic harmonic analysis (SHA) to
blend satellite models in with terrestrial data sets. GRAV-D seeks
to collect aerogravity to provide supplemental information between
the longest wavelengths (satellite data) and the shortest surface
gravity and terrain models. Much work has already by been completed
on this in the Gulf Coast (Roman et al. 2006, Roman et al. 2007,
Saleh et al. 2009) and in central Texas (Smith et al. 2013).
The work here represents a continuation of these previous
efforts with a focus on Puerto Rico and the U.S. Virgin Islands,
where data collection has already been completed. This region is
self-contained and provides a test case for implementing a future
vertical datum based on aerogravity enhancements. Figure 2 shows
the extent of the aerogravity collections performed in 2009. Flight
heights were at about 11 km (35,000 ft) and spaced at 10 km.
Documentation on the particulars of data collection and processing
are available from the GRAV-D Science Team (2012a, 2012b, 2012c) on
the website.
Figure 1. Map Key - Airborne Gravity DataGreen: Available data
and metadata, Blue: Data being processed,Orange: Data collection
underway, White: Planned for data collection.
ABSTRACT
NOAAs National Geodetic Survey began the Gravity for the
Redefinition of the American Vertical Datum (GRAV-D) program in an
effort to modernize and unify vertical datums in all states and
territories. As a part of this program, NGS collected aerogravity
profiles over the islands of Puerto Rico and the U.S. Virgin
Islands in January 2009. A Citation II aircraft was equipped with
an airborne gravimeter, GPS receiver, and a GPS/Inertial unit.
Absolute gravity and GPS ties were made to multiple ground sites to
ensure consistency in the results. The main survey covered a region
of approximately 400 km by 500 km with flight altitudes of 10,668 m
(35,000ft) and with 10 km track spacing. Cross-track profiles at 40
km spacing were also collected to establish an accuracy of 1.34
mGals RMSE. Additionally, terrestrial surveys were also conducted
to better tie ground sites and to serve as control for later
analysis for available but older terrestrial and marine gravity
data in the region already held by NGS. The aerogravity data were
analyzed and at least internally compared to obtain the optimal
results before being published on the web. In this study, the
aerogravity data were compared to available global gravity models
derived from satellite missions (GRACE & GOCE) to evaluate
their long wavelength character (e.g., potential biases and
trends). The vetted satellite-aerogravity data were then combined
and used to evaluate surface data (terrestrial and marine) in the
region to remove any potential systematic effects. Finally, all
these data were combined into a gravimetric geoid height model and
evaluated with an eye to use as a GNSS-accessed vertical datum.
INTRODUCTION
The Gravity for the Redefinition of the American Vertical Datum
(GRAV-D) Program (Smith 2007) intends to develop a consistent,
accurate and seamless gravity field model over the United States
for use as a cm-level accurate vertical datum. Figure 1 highlights
data collected thus far, including over Puerto Rico and the U.S.
Virgin Islands (green box in SE corner). The data in Figure 1 are
available from the National Geodetic Surveys GRAV-D webpage:
http://www.ngs.noaa.gov/GRAV-D/.
Figure 2. GRAV-D aerogravity Profiles collected in 2009. Flight
height was 11 km and data spacing was at about 10 km. SYNTHETIC
HARMONIC ANALYSIS
Greater detail on SHA will be provided in a forthcoming paper
(Smith et al. 2013). However, the essential elements are to analyze
the satellite model with respect to some trusted terrestrial data
set, such as GNSS on leveled heights, and ascertain as to what
spectral band the additional signal from the model actually causes
a degradation in the comparison. This process is conducted for both
GOCO03S and the aerogravity data in the study area. For a test set
of data, Puerto Rico (PR) and the U.S. Virgin Islands (USVI) have
some limited data. Figure 3 shows the distribution of available
data on PR and Table 1 (bottom poster) lists all 65 points in the
region.
While a bit circuitous in logic, the data in Table 1 are
analyzed with an eye to determining which of them are best utilized
for further refining the gravity modeling in order to further
assess the quality of the resulting models against the data. While
this is somewhat less than the desired level of independence in
data, it does assure that extremely poor data are not used to
refine the gravity field model. The data along the northern
shoreline of PR were collected and processed by NGS and formed the
basis for the Puerto Rico Vertical Datum of 2002 (PRVD02). The more
recently collected data has heights that are not yet complete,
which are termed field heights. Figure 3. Locations of Control Data
(GPS on leveled bench marks) located in Puerto Rico. Values
represent the misfit with respect to EGM2008 (W0 = 62,636,855.60
m2/s2) in the IGS08 reference frame and centered at -34.60 cm. Data
in box are new since GEOID12A.Much of the new GPS positioning is
also not processed following NGS Bluebook procedures and are the
results of submissions to the Online Positioning User Service
(OPUS) database (Roman and Weston 2011) . Both the field heights
and are likely accurate to the cm-level based on the quality of
OPUS products and a personal communication with Tim Hanson (2013)
regarding the quality of field heights. The main benefit of the
data on PR is that they provide coverage around a significant
portion of the island. The data on the three USVI are congregated
closely together and do not provide adequate spatial distribution
to analyze the spectral characteristics of any geoid height models.
For this reason then, these data were selected to analyze the
potential enhancements that both GOCO03S and the aerogravity might
bring to any solution.
While a bit circuitous in logic, the data in Table 1 are
analyzed with an eye to determining which of them are best utilized
for further refining the gravity modeling in order to further
assess the quality of the resulting models against the data. While
this is somewhat less than the desired level of independence in
data, it does assure that extremely poor data are not used to
refine the gravity field model. The data along the northern
shoreline of PR were collected and processed by NGS and formed the
basis for the Puerto Rico vertical Datum of 2002 (PRVD02). The more
recently collected data has heights that are not yet complete,
which are termed field heights. Much of the new GPS positioning is
also not processed following NGS Bluebook procedures and are the
results of submissions to the Online Positioning User Service
(OPUS) database. Both the field heights and are likely accurate to
the cm-level based on the quality of OPUS products and a personal
communication with Tim Hanson (2013) regarding the quality of field
heights. The main benefit of the data on PR is that they provide
coverage around a significant portion of the island. The data on
the three USVI are congregated closely together and do not provide
adequate spatial distribution to analyze the spectral
characteristics of any geoid height models. For this reason then,
these data were selected to analyze the potential enhancements that
both GOCO03S and the aerogravity might bring to any solution.
Focusing on the green line in Figure 4, comparisons are made
between the PR GPS/leveling and the EGM2008 model as the GOCO03S
model is blended through progressively higher degrees in the SHA.
Inclusion of the GOCO03S data achieves the best agreement at about
degree 205, where the misfit between GPS/leveling and gravity model
is given at about 2.0 cm RMSE. Based on this, the optimal blend
between EGM2008 and GOCO03S for this region is at degree 205. This
then represents the XGG13A model in Table 1 below.Figure 4.
Comparison between PR GPS/leveling and geoid height models.
Developed from a progressively higher combination of GOCO03S into
the EGM2008 model. Misfit errors on the right go to a minimum at
about degree 205.Figure 5. SHA of GRAV-D aerogravity combined with
the XGG13A model in comparison to PR GPS/leveling. Arrow marks
degree 280 where the combination provides the best agreement
(lowest geoid error/misfit).IMPACT OF GOCO03S THROUGH SHA
Figure 6 shows the impact of incorporating GOCO03S into EGM2008.
The top figure shows the changes in gravity anomaly residuals and
the bottom image shows the equivalent impact in geoid heights. The
impact here is quite profound and represents the improved
observations over the Puerto Rico Trench to the North. GOCE had
increased sensitivity to the signal and better resolved it.
Figure 6. Impact of GOCO03S on reference field model through
SHA. Significant gains were made over the Puerto Rico Trench due to
GOCEs increased sensitivity.IMPACT OF GRAV-D AEROGRAVITY THROUGH
SHA
Figure 7 shows the impact of incorporating aerogravity into the
XGG13A model. The top figure shows the impact in gravity signal
while the bottom shows the equivalent signal in geoid height. While
the impact of aerogravity is about an order of magnitude smaller
than that seen from the inclusion GOCO03S, the impacts are still
significant. The amplitude of the features seen oscillating from
West to East are at about 160 km (full wavelength), which is below
the effective resolution of GOCE. An aspect of this the 10 cm slope
seen along the southern shore of PR. Not including these data would
likely result in omission error related to this signal. While the
effects of these features are shown at the edge of the figures,
note the density of tracks in Figure 2. The 10 km track spacing in
the West-East direction means that there is sufficient data to
resolve these features. There are also three cross-tracks (one
along the southern shoreline and two further South from that) to
control the data lines. The signal seen in Figure 7 represents
value added by the GRAV-D aerogravity data.
Figure 7. Impact of GRAV-D aerogravity on reference field model
through SHA. A 10 cm slope is seen along the southern shoreline of
PR at a scale of 160 km. IMPACT OF SURFACE GRAVITY DATA
The XGG13B model was developed from EGM2008 blended via SHA with
GOCO03S and GRAV-D aerogravity over the PR/USVI region. This model
was removed from available surface data in the region to produce
residuals for further analysis. The top image in Figure 8 shows the
residual signal in gravity anomalies. Note that significant
systematic effects are seen in these residuals, particularly in the
ship track data. Using the aerogravity to resolve these and any
differences with satellite altimeter-implied gravity anomalies
represents crucial future work.
A regional geoid height model was developed using established
techniques (Wang et al. 2012). This methodology uses a modified
kernel at about degree 70 for this region. The terrestrial data
were permitted to modify the wavelengths of the gravity field that
were shorter than about 600 km. In the lower image of Figure 8, a
significant systematic effect is seen in the resulting residual
geoid height model as a result of the signal present in the surface
data that did not agree with the satellite or airborne gravity
missions. This final model then is the XGG13C model listed in the
last column of Table 1.A similar process was then followed for the
aerogravity. SHA was used to develop a model of the aerogravity for
this region. While the aerogravity are in regular grids over a
limited region of the Earth, they can be analyzed using methods
more often used for global models. Residual values are formed over
the region where the data exist and null values exist outside the
region. When a set of coefficients is generated, the resulting
statistics are useful for determining if the combination represents
an improvement over the original model when compared to ground
truth or some other external data.
Starting at about degree 200 and progressing to higher harmonic
combinations. Figure 5 demonstrates that the aerogravity improve
the comparisons through about degree 280 and then the comparisons
become progressively worse there after. Hence the optimal
combination is GOCO03S through degree 205 and then aerogravity
through degree 280, which results in the XGG13B model in Table
1.
Figure 8. Residual gravity anomalies and residual using XGG13B
for reference model. Significant systematic effects are in surface
gravity data. A significant trend also exists where surface data
were permitted to modify the reference model.1NAD 83
CoordinatesIGS08 Coordinatesexpressed in NAD 83expressed in
IGS08expressed in
IGS08XGG13A=EGM2008+GOCO03SXGG13B=XGG13A+AerogravityXGG13C=XGG13B+Surface
GravitySTATION NAMEST IDPIDORTHO. HEIGHTLATITUDELONGITUDEELLIPS.
HEIGHThH83 (h-H)LATITUDELONGITUDEELLIPS. HEIGHTh - HGEOID12A
(m)USGG2012 (m)EGM2008 (m)XGG13A (m)XGG13B (m)XGG13C
(m)metersDMSHDMSHmetersmetersDMSHDMSHmetersmetersNh-H-N+/-
Ave.Nh-H-N+/- Ave.Nh-H-N+/-
Ave.Nh-H-N+/-Ave.Nh-H-N+/-Ave.Nh-H-N+/-Ave.Existing GPSBM in Puerto
Rico (Adjusted ellipsoid and leveling heights)1ZSU
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USCG
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GPS
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5371 A
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JUAN SIG APT
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GPSBM Points in Puerto Rico (GPS is Adjusted but Leveling are Field
Heights)Ave. (m)0.0000.3010.282-0.021-0.0280.016S.D.
(m)0.0200.0680.0770.0570.0630.06037new: GPS
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EL
OJOPRAB984354.45118044.39947N662311.07036W15.361-39.09018044.41345N662311.06826W13.478-40.973-39.1160.026-0.127-41.3340.361-0.047-41.3530.380-0.018-40.892-0.081-0.115-40.926-0.047-0.087-40.9850.012-0.086New
OPUS-DB points (Ellipsoid heights are from OPUS solutions and
Leveling is Field Heights)Ave.
(m)0.1520.4080.3990.0340.0410.098S.D.
(m)0.1790.0660.0260.1630.1240.12239OPUS: E
1009PRDK74347.37418239.80838N67914.21463W-35.593-42.96718239.82259N67914.21349W-37.467-44.841-43.0490.0820.018-45.1950.354-0.004-45.1460.305-0.040-44.8770.0360.043-44.8580.0170.027-44.9160.0750.02940OPUS:
GPS
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R
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C
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T
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F
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GPSBM on the U.S. Virgin Islands (Adjusted ellipsoid and leveling
heights) (the three in red on St. Croix were rejected from GEOID12A
Modeling)Ave. (m)0.0640.3580.345-0.007-0.0110.046S.D.
(m)0.0930.0490.0520.0960.0650.065St. Thomas45STT
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1639
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STA
BVQTV15322.843182017.64492N645831.31856W-39.337-42.180182017.65956N645831.31493W-41.217-44.060-42.1900.0100.011-44.4980.4380.026-44.4660.4060.025-44.1840.1240.027-44.1450.0850.027-44.1670.1070.02951STT
CVQTV15333.515182020.56975N645759.66542W-38.654-42.169182020.58439N645759.66178W-40.534-44.049-42.1910.0220.023-44.4920.4430.031-44.4640.4150.034-44.1820.1330.036-44.1430.0940.036-44.1620.1130.03552STT
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BM 1639
MVQTV15482.35618201.30444N645515.33530W-39.846-42.20218201.31909N645515.33160W-41.726-44.082-42.184-0.018-0.017-44.4640.382-0.030-44.4280.346-0.035-44.1410.059-0.038-44.1040.022-0.036-44.1260.044-0.03455WESTONVQTV15490.830182022.82635N645552.97813W-41.373-42.203182022.84100N645552.97445W-43.253-44.083-42.2030.0000.001-44.4810.398-0.014-44.4430.360-0.021-44.1570.074-0.023-44.1190.036-0.022-44.1470.064-0.014Ave.
(m)-0.0010.4120.3810.0970.058St. JohnS.D.
(m)0.0230.0300.0280.0290.02956C
1001VQDL36337.472181913.47692N644338.37690W-34.774-42.246181913.49160N644338.37298W-36.654-44.126-42.225-0.021-44.4700.344-44.4320.306-44.123-0.003-44.090-0.036-44.112-0.014St.
Croix57VIKH
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1002VQDK714838.742174328.12176N644526.45927W-2.593-41.335174328.13579N644526.45524W-4.486-43.228-41.327-0.008-0.042-43.7180.490-0.063-43.7150.487-0.067-43.2520.024-0.068-43.3050.077-0.067-43.3290.101-0.06560B
1012VQDK715369.962174413.54122N644312.61855W28.672-41.290174413.55528N644312.61448W26.780-43.182-41.2920.002-0.032-43.6630.481-0.072-43.6740.492-0.062-43.2040.022-0.070-43.2610.079-0.065-43.2730.091-0.07561975
1364 C
TIDALVQDK71601.658174448.83227N644157.11124W-39.650-41.308174448.84634N644157.10714W-41.542-43.200-41.3090.001-0.033-43.6830.483-0.070-43.6870.487-0.067-43.2140.014-0.078-43.2720.072-0.072-43.2900.090-0.07662975
1401 M
TIDALVQDK71653.111174141.17939N644513.64834W-38.102-41.213174141.19339N644513.64429W-39.995-43.106-41.2210.008-0.026-43.6250.519-0.034-43.6160.510-0.044-43.1460.040-0.052-43.2030.097-0.047-43.2420.136-0.03063STX
CVQTV151215.845174156.87029N644833.30930W-25.366-41.211174156.88428N644833.30532W-27.259-43.104-41.3030.0920.058-43.7290.6250.072-43.7310.6270.073-43.2790.1750.083-43.3250.2210.077-43.3470.2430.07764ST
CROIX APT ARP
STXVQTV153510.97217425.66903N644752.96240W-30.220-41.19217425.68303N644752.95841W-32.113-43.085-41.2800.0880.054-43.7130.6280.075-43.7170.6320.078-43.2610.1760.084-43.3090.2240.080-43.3290.2440.07865ST
CROIX APT AP STA
BVQTV15366.39017429.31371N644717.30046W-34.770-41.16017429.32771N644717.29646W-36.663-43.053-41.2680.1080.074-43.7000.6470.094-43.6990.6460.092-43.2400.1870.095-43.2910.2380.094-43.3180.2650.099Ave.
(m)0.0340.5530.5540.0920.1440.166S.D.
(m)0.0470.0660.0660.0720.0680.069GEOID12AUSGG2012EGM2008XGG13AXGG13BXGG13CPuerto
Rico Average (m)0.0160.3130.296-0.017-0.0220.024Puerto Rico S.D.
(m)0.0590.0710.0780.0670.0660.065U.S.V.I. Average
(m)0.0130.4690.4510.0900.0900.111U.S.V.I. S.D.
(m)0.0390.0890.1030.0540.0700.072Cum. Average
(m)0.0150.3590.3420.0190.0150.052Cum. S.D.
(m)0.0520.1120.1180.0800.0840.077ReferencesGRAV-D Science Team
(2012a). GRAV-D General Airborne Gravity Data User Manual, Theresa
Damiani, ed., v. 1, Available 10 May 2013,
www.ngs.noaa.gov/GRAV-D/data_TS01.shtmlGRAV-D Science Team (2012b).
"Gravity for the Redefinition of the American Vertical Datum
(GRAV-D) Project, Airborne Gravity Data; Block TS01". Available 10
May 2013. Online at:
http://www.ngs.noaa.gov/GRAV-D/data_TS01.shtml
GRAV-D Science Team (2012c). "Block TS01 (Atlantic South 01);
GRAV-D Airborne Gravity Data User Manual." Monica A. Youngman and
Carly A. Weil, ed. Version 1. Available: 10 May 2013. Online at:
http://www.ngs.noaa.gov/GRAV-D/data_TS01.shtmlJacob T, J Wahr, R
Gross, and S Swenson (2012) estimating geoid height change in North
America: past, present and future, J. Geodesy, 86 (5), 337-358,
DOI: 10.1007/s00190-011-0522-7.Mayer-Grr T, D Rieser, E. Hoeck, JM
Brockman, W-D Schuh, I Krasbutter, J Kusche, A Maier, S Krauss, W
Hausleitner, O Baur, A Jaeggi, U Meyer, L Prange, R Pail, T Fecher,
and T Gruber. (2012) The new combined satellite only model GOCO03S.
Paper S2-183, GGHS Meeting in Venice, Italy 9-12 OCT 2012.Pail R, S
Bruinsma, F Migliaccio, C Foerste, H Goiginger, W-D Schuh, E Hck, M
Reguzzoni, JM Brockmann, O Abrikosov, M Veicherts, T Fecher, R
Mayrhofer, I Krasbutter, F Sans, CC Tscherning (2011) First GOCE
gravity field models derived by three different approaches, J.
Geodesy, 85 (11), 819-843, DOI: 10.1007/s00190-011-0467-x.Pavlis,
NK, SA Holmes, SC Kenyon, and JK Factor (2012) The development and
evaluation of the Earth Gravitational Model 2008 (EGM2008), JGR,
117 (B4), Article Number: B04406, DOI: 10.1029/2011JB008916.
Reigber, Ch., Balmino, G., Schwintzer, P., Biancale, R., Bode,
A., Lemoine, J.-M., Koenig, R., Loyer, S., Neumayer, H.,
Marty,J.-C., Barthelmes, F., Perosanz, F. and Zhu, S. Y. (2002). A
high quality global gravity field model from CHAMP GPS tracking
data and Accelerometry (EIGEN-1S), Geophysical Research Letters,
29(14), 10.1029/2002GL015064.Roman DR, YM Wang, JM Brozena, VA
Childers, DL Rabine, SB Lutcke, J Blair, SA Martinka, MA Hofton
(2006) Gravity-Lidar Study for 2006: Refined Gravity Field for the
North-Central Gulf of Mexico, Proceedings of the 1st International
Symposium of the International Gravity Field Service, Istanbul,
Turkey, available at:
http://www.hgk.msb.gov.tr/dergi/makaleler/18ozelsayi.asp.
Roman D.R., and N.D. Weston (2011). OPUS-Database: Supplemental
Data for Better Datum Conversion Models, presented at the F.I.G
Working Week in Marrakech, Morocco, May 18-22, 2011,
http://www.fig.net/pub/fig2011/papers/ts04a/ts04a_roman_weston_4860.pdf.
Roman DR, YM Wang, JM Brozena, VA Childers, DL Rabine, SB
Lutcke, SA Martinka, and MA Hofton (2007) Regional Geoid Modeling
Compared to Ocean Surface Observations, Eos Trans. AGU, 88(23), Jt.
Assem. Suppl., Abstract G33B-04.Roman DR, D Winester, and J Saleh
(2010) Surface gravity observations define gravity field change
over 30 years, Abstract G41A-0789 presented at 2010 Fall Meeting,
AGU, San Francisco, Calif., 13-17 Dec.Saleh J, X Li, YM Wang, DR
Roman, and DA Smith (2013) Error analysis of the NGS surface
gravity database, J. Geodesy, 87 (3), 203-221, DOI
10.1007/s00190-012-0589-9Saleh J, YM Wang, DR Roman, X Li (2009)
Validation and inter-comparison of GRAV-D airborne gravity
anomalies at three flight altitudes over the coast of Western
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Abstract G51A-0651.Smith DA (2007) The GRAV-D project: gravity for
the redefinition of the American Vertical Datum. Available online
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DA, M Vronneau, DR Roman, J Huang, YM Wang, and MG Sideris (2012)
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10.1007/s00190-011-0506-7Table 1. GPS/Leveling data in the Puerto
Rico (PR) and the U.S. Virgin Islands (USVI) versus various geoid
height models. There are a total of 65 bench marks on the islands:
44 total points on PR and 21 on the USVI. Of the 44 on PR: 36
points have fully adjusted ellipsoid and orthometric heights and
were used to make the GEOID12A model; 2 are new points with
adjusted ellipsoid heights but only Field quality leveling heights;
and 6 more have ellipsoid heights from resolved through OPUS and
Field heights. All 21 points in the USVI are fully adjusted and
were available for GEOID12A though three were dropped (text in red
for St. Croix) due to high residual values. These data sets are
compared in the above groups and collectively at the bottom of the
Table to: GEOID12A, USGG2012, EGM2008, XGG13A, XGG13B, and XGG13C.
Coordinates for NAD 83 were used for GEOID12A, while all others
were given in the IGS08 reference frame using a GRS-80 ellipsoid.
For each comparison: the geoid height for the respective model at
that location is in the first column; the difference between the
ellipsoid height and orthometric height (h-H) and the geoid height
(N) is given in the middle column; and the third column removes the
average for the subset region to show the distribution of points
around the regional mean. No stats are available for St. John since
there was only one point. Overall, GEOID12A does very well, but
these data were used to make it. It does poorer in regions where
new data are added. The best comparison data remains all the
aggregate GPS/leveling for PR as this forms a loop with significant
spatial extent. Those statistics are highlighted in bold at the
bottom of Table 1. USGG2012 does slightly better than EGM2008 but
this is expected because USGG2012 has higher resolution
information. Adding in GOCO03S (XGG13A) helped improve EGM2008
significantly. Adding in aerogravity (XGG13B) further refined the
solution and inclusion of the terrestrial data yielded the best
result. Clearly adding in the aerogravity along with GOCO03Shelped
the solution. Additionally, the most optimal results come from use
of surface data, so this cannot just be rejected or ignored in
future models (i.e., aerogravity by itself is not the optimal
solution).ANALYSIS
All models are compared to the 65 GPS/leveling points available
in the region. Refer to the Table 1 legend for details as to how
the Table is organized. However, the first 44 stations were those
used to develop the Synthetic Harmonic Analysis that developed the
subject models. While the individual stations are useful to isolate
potential outliers, the summary statistics by region and by geoid
model provide the most succinct insight. Those GPS/leveling points
on PR represent the best spatial distribution of data on a single
common datum. All points in the USVI are tied to the Virgin Islands
Vertical Datum of 2009 (VIVD09) and in fact each island has its own
tide gauge and, therefore, own datum. Rather than deal with such
disparity, the focus is on those points on PR. There at the bottom
below Table 1 in bold are the summary statistics for all points (in
the database, new, and OPUS-derived), where a steady improvement is
seen going to models that incorporate all signal.SUMMARY
GPS/leveling data, particularly that available on the island of
Puerto Rico, were used to develop optimal filters for Synthetic
Harmonic Analysis. Filters for combing GOCO03S at degree 205 and
aerogravity through degree 280 were implemented on the EGM2008
model to generate a revised reference model (XGG13B). This model
was used to a more traditional approach to regional geoid modeling
and compared against all GPS/leveling points.
Naturally, the comparison was best at the points on PR since it
was used in determining the filters. However, these filters were
against data that had significant (for this region) spatial extents
and could optimally determine the local gravity field at
intermediate to long wavelengths. The most optimal combination came
from using all available information to develop regional geoid
height model.OUTLOOK
A great deal of interest has been expressed in developing such a
model for at least the region of North America (Smith et al. 2012,
Jacob et al. 2012). Such a model should be a subset or at least
easily tied into a World Height System. Collections by satellite
systems remains the likely avenue for WHS unification. However,
they are insufficient to resolve systematic errors due omission or
commission in terrestrial data. This paper has explored the
potential for using aerogravity to refine and improve the local
gravity field and subsequent geoid height model.
Future work will include incorporating data flown at 1.67 km
(5000 ft), cleaning the surface data, changing the blending ranges
in SHA, and adjusting the degree used in the kernel modification.
With little data improvement, the model determined here meets or
exceeds all others. With further work, it should achieve the
desired goal of cm-level accuracy.