Geoid Evaluation
Research question: How can we evaluate a geoid model or a geopotential surface?
Once a geoid model has been developed, it is important to evaluate the model and check it against independent data sets, including survey marks where heights have been measured with both Global Navigation Satellite System (GNSS) measurements and leveling. The National Geodetic Survey has also conducted evaluation of spatial trends of the geoid. These evaluations include survey campaigns, like the using a suite of survey technologies that include: GNSS, leveling, and celestial observation to measure the deflections of the vertical (the slope of the geoid model). The quality of a gravity model for the Earth depends on the available gravity observations collected on the Earth's surface (e.g., land and shipborne gravity), and above the surface (airborne and satellite). A key focus in the evaluation is on the deviation of the geopotential surface from the water over the ocean and other water bodies.
Because it is possible to calculate the deflection of the vertical directly using an astro-geodetic system (using stars for location and orientation) without gravimeters, this approach provides an independent approach to validate the NOAA geoid model. It is also important to note that deflection of the vertical products support other applications that are beyond the scope of geoid modeling, such as precise calculation of survey networks and geophysical applications that investigate the physical structure of the Earth's crust and mantle. The two key product components of the deflection of the vertical are the north–south component ξ (xi) and an east–west component η (eta). The xi and eta components represent the difference between astronomical and geodetic latitudes and longitudes, respectively.
Direct evaluation of the geoid with respect to water level observation is constrained to the geographic location of the water level stations, where most of these stations are located along the coast lines. It is crucial that these stations are referenced to the national network and water level observations have been collected for at least five years. For water level observations in riverine environments, there are additional factors contributing to the water levels and are not related to oceanographic processes, such as water run off, surge from extreme weather events. As a result, the height difference between the geopotential surface to the water levels in rivers is large and is greater than 1 m difference.
As such, it is more practical to observe trends along a geopotential surface of the geoid model. These trends are the slopes of the geoid (first derivative of the geopotential surface). In other words, the gravity field of the geoid can be described, and illustrated, as a vector. For any given location above the Earth’s surface, the gravity field can be quantified based on: 1) the strength (magnitude of attraction) and 2) the direction of the gravity to the Earth’s center of mass. Gravity observations focus on strength of the gravity field, where the deflection of the vertical evaluates direction of the gravity field with respect to the ellipsoidal surface and is typically inferred indirectly.
NOAA’s National Geodetic Survey (NGS), have been conducting geoid model evaluation using both direct comparisons of the geoid using water level observations and indirect trend evaluations using deflection of the vertical observation and other field survey observations. In the past, NOAA’s NGS validated the geoid models by performing independent measurements through three field campaigns called “The Geoid Slope Validation Survey (GSVS)”that evaluated the accuracy of geoid as a slope function of the model ("geoid undulations slopes"). In addition to astro-geodetic deflections of the vertical from observations, the geoid slopes of the baseline were independently computed using differential orthometric heights and differential ellipsoid heights from leveling and GPS campaigns, respectively (both minimally constrained). The trend observations from the field campaigns were compared to the calculated geoid slope of a gravimetric geoid created with and without data from NOAA’s national airborne gravity data, GRAV-D. As such, the design of field surveys was in areas that overlapped existing GRAV-D surveys in order to test the impact of the aerial gravity on the gravimetric geoid model, and the distance needed to be at least 200 km long in order to compare directly to satellite-only (GRACE and/or GOCE) geoid models. A secondary design requirement was that elevations should be close to the geopotential surface for reducing the amount of corrections needed in order to compare the survey results with the geoid model.
The areas selected for the deflection of the vertical evaluation were based on the geographic characteristics:
- Texas 2011 - Evaluation of geoid accuracy in a flat and gravimetrically simple region.
- Iowa 2014 - Evaluation of geoid accuracy in a flat, high elevation, and gravimetrically complex region.
- Colorado 2017 - Evaluation of geoid accuracy in a rugged, high elevation, gravimetrically and topographically complex region.
Due to the large amount of resources needed to conduct these surveys (the surveys were labor intensive and prohibitively expensive to repeat), NGS modernized their astro-geodetic approach in order to conduct repeatable deflection of the vertical observations with high accuracy comparable to leveling observations with denser measurements along a profile line. NGS developed a system, known as the Total Station Astrogeodetic Control System (TSACS), which is a compact deployable system that enables a single operator to conduct repeated surveys with a commercially available robotic total station. This system has been tested in several field campaigns and has transitioned into operations. Today, there are several TSACS instruments at NOAA and with NOAA’s academic partners. The system has been used also to revisit historical sites to examine how the deflection of the vertical has changed over the past century.
NGS has deployed TSACS in multiple projects since 2020 and included surveys such as:
- NGS’s IERS Site Survey program uses deflections of the vertical and astronomic azimuths to provide unambiguous orientations for their terrestrial surveys that establish local vector ties between fundamental space geodesy stations. By measuring both azimuths and deflections of the vertical with the stars, TSACS provides the three rotation angles necessary for orienting these local surveys in a global frame to a degree that outperforms GNSS methods by an order of magnitude.
- Another notable deployment of TSACS was during the Geoid Monitoring Service Validation Survey in 2021 in Alaska. TSACS was used to observe temporal changes in the geoid in two ways: First, TSACS was used to repeat historical astronomic latitude and longitude measurements near glaciers from the 1940s. Second, TSACS observations were used to assemble a geoid profile across 600 km of Alaskan roadway near these glaciers. The snapshot of the 2021 geoid in Alaska was used to compare present-day orthometric heights to historical leveling to reveal orthometric height changes. The geoid profile is also a record of the current state of the geoid that may be compared with future geoid profiles to reveal geoid change.
- Most recently, TSACS was deployed in Louisiana in 2024 as part of an academic collaboration to measure a geoid profile along the Mississippi River between Baton Rouge and New Orleans. Deflections of the vertical fill a key validation gap in the geoid in Louisiana, where gravity data are sparse, and rapid changes in land elevation create problems with traditional methods of geoid validation like GNSS/leveling. The combination of volume of commercial traffic, vulnerability to flooding, and population density of this corridor drive an urgent need for additional geopotential data in this region.
Another approach for evaluating the deflection of the vertical is comparing the slope of the geopotential surface and comparing to simulated water surfaces produced from circulation models. NGS has been collaborating with ocean models at NOAA’s Office of Coast Survey (OCS). NGS is currently evaluating Local Mean Sea Level marine grids that are generated from their Global coverage of the Surge and Tide Operational Forecast System using a depth-averaged water density model based on the ADvanced CIRCulation (ADCIRC) engine. Multi-year water level products generated from the ocean models are averaged, where the first derivative slope of the multi-year water surface is compared to the geoid’s slope. The ADCIRC model grid provides global coverage. Using the marine grids, it is possible to infer a higher degree of accuracy by inferring ocean currents from measurements of the sea surface height (by combined satellite altimetry and gravimetry). Oceanographers describe these currents as geostrophic currents, oceanic current in which the pressure gradient force is balanced by the Coriolis effect. The major currents that NGS uses to evaluate the geoid include Gulf Stream and the Kuroshio Current.
Peer Review Publications and Conference Presentations
Erickson, B.T. 2022. Astrogeodetic Investigations of the Gravity Field in Central Ohio, Master Thesis, The Ohio State University, 87 pp.
Hardy, R.A. 2021. “Geodetic Astronomy at NGS: Past and Present” NGS Webinar Series, March 10. https://geodesy.noaa.gov/web/science_edu/webinar_series/geodetic-astronomy.shtml
Hardy, R., K. Fancher, K. Ahlgren, B. Erickson, C. Geoghegan, S. Breidenbach,, and S. Hilla. 2020. “Geodetic astronomy with an imaging robotic total station,” American Geophysical Union 2020 Fall Meeting, Silver Spring, MD, November 20. https://agu.confex.com/agu/fm20/meetingapp.cgi/Paper/674689
Hardy, R.A., K. Fancher, B. Erickson, S. Breidenbach, K. Ahlgren, D. van Westrum, C. Geoghegan, S.Hilla, and K. Jordan. 2021. “Performance Assessment of the Total Station Astrogeodetic Control System (TSACS),” AGU Fall Meeting, December 15, San Fansisco, CA. https://agu.confex.com/agu/fm21/meetingapp.cgi/Paper/813173
Saleh, J., X. Li, Y.M. Wang, D.R. Roman, and D.A. Smith. 2013. “Error analysis of the NGS’ surface gravity database,” J Geod 87, 203–221 (2013). https://doi.org/10.1007/s00190-012-0589-9
Seroka, S., Y. Wang, R. Hardy, K. Ahlgren, S. Pe’eri, L. Tang, E. Myers, J. Zhang. 2024. “Marine Geoid Validation Using Ocean Modeling Sea Surface Topography,” American Meteorological Society 2024, February 1. https://ams.confex.com/ams/104ANNUAL/meetingapp.cgi/Paper/434052
Smith, D., S. Holmes, X. Li, S. Guillaume, Y.M. Wang, B. Bürki, D.R. Roman, and T. Damiani. 2013. “Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011.” J Geod 87, 885–907 (2013). https://doi.org/10.1007/s00190-013-0653-0
van Westrum, D., K. Ahlgren, C. Hirt, S. Guillaume. 2021. “A Geoid Slope Validation Survey (2017) in the rugged terrain of Colorado, USA,” J Geod 95, 9. https://doi.org/10.1007/s00190-020-01463-8
Wang, Y.M., C. Becker, G. Mader, D. Martin, X. Li, T. Jiang, S. Breidenbach, C. Geoghegan, D. Winester, S. Guillaume, and B. Bürki. 2017. “The Geoid Slope Validation Survey 2014 and GRAV-D airborne gravity enhanced geoid comparison results in Iowa,” J Geod 91, 1261–1276. https://doi.org/10.1007/s00190-017-1022-1
Wang, Y.M., M. Veronneau, J. Huang, K. Ahlgren, J. Krcmaric, X. Li, and D. Avalos-Naranjo. 2022. NOAA Technical Report NOS NGS 78 National Oceanic and Atmospheric Administration National Geodetic Survey Technical Details of the Experimental GEOID 2020, https://geodesy.noaa.gov/library/pdfs/NOAA_TR_NOS_NGS_0078.pdf
