A Dynamic Geoid-based Vertical Datum for Canada: Recent Models Developments and Prospective Implementation
With the considerable improvement in the accuracy of the newest Canadian geoid model ranging from few centimeters in the flat terrain areas to few decimeters in the mountainous areas, a need emerges to account for and incorporate the dynamic geoid variations in the region, mainly due to the large postglacial rebound effects, in the future geoid-based vertical datum in Canada. The realization of this dynamic reference surface for orthometric heights will be crucial for a large number of engineering and science applications that require precize vertical positioning including environmental and climate hazards monitoring, hydrology, oceanography and sea level studies, among many others. Therefore, constant efforts are made to model the dynamic variations of the geoid and heights in Canada using data provided by terrestrial and space-based techniques and geodynamic modelling. In this paper, we present the newest models of the dynamic geoid variations in North America, together with an analysis of the models' errors, derived by means of traditional and novel techniques from GRACE gravity field time series. To mitigate certain limitations of the latter, high accuracy GNSS vertical velocities are incorporated into the GRACE models, and these improved models are compared with postglacial rebound model outputs. The dynamic geoid is imputed into a GNSS/leveling/geoid height optimal combination analysis to estimate the frequency of the necessary update of the geoid-based height reference surface. Our results show that in order to maintain a reference surface with a centimeter level of accuracy, such updates should be undertaken at a decadal rate.
Geodetic Modeling With Realistic Geology
Crustal structure has significant impact on the gravity field in short to intermediate wavelengths and lateral variations in density at or near the surface also affect the field. The U.S. Naval Research Laboratory will begin in FY2010 a research program to develop advanced geodetic modeling techniques utilizing realistic geologic and geophysical constraints to improve gravity anomaly estimation in mountainous terrains. The effort is facilitated by several new high-altitude airborne gravity data sets that will provide ground truth for modeling in several different geologic environments. Data sets collected over the Himalayas, the Alps and the mountains of Taiwan will be used to develop, calibrate and test regional models having different geologic conditions including crustal thickness and flexural rigidity, average regional sediment thickness, fault geometry, geomorphology and local density variations. Medium wavelength satellite gravity such as the Gravity Recovery and Climate Experiment (GRACE) data will allow comparison with the upward continued models as a check on the accuracy of the estimates and can also be used to estimate longer wavelength components due to the crust-mantle interface from either remove-restore methods of modeling or from two dimensional loaded plate theory under appropriate assumptions of flexural rigidity. Buried basement topography masked by sediments is a primary contributor to unknown short wavelength features and will be of great importance in stream-cut mountain valleys and depositional plains adjacent to exposed mountain ridges: we will use existing data sets to test the effects of various basement morphologies. Our modeling strategies will be tested for biases in medium and short wavelength components against existing ground truth, airborne and satellite data sets. Some of the proposed modeling has been previously done for specific and limited areas but we propose to examine to what extent it is possible to determine regional parameterizations that can be used to forward model large areas.
Practical Aspects of Terrain Correction Calculations for Airborne Gravimetry
Calculating terrain corrections for airborne gravity surveys would seem to be a straightforward procedure: however, as with many such procedures, practical computations involving large datasets can be truly challenging. In this presentation, I will discuss some of these challenges and techniques for meeting them. My viewpoint on these questions is shaped by my background in exploration geophysics, but much of this presentation should be applicable in other areas as well. Three major aspects of airborne gravity terrain corrections will be considered: 1) Modifying Parker's FFT computation technique to handle terrain rising above the flight height. A relatively simple modification using mirror-image masses works well in this case. Possible concerns with accuracy and convergence in areas of the computational grid where the terrain surface passes through the flight height can be eased by consideration of the operational aspects of the survey. 2) Combining regional-scale DTMs outside of the survey area with detailed local DTMs within the survey area, and making this combination work well with Parker's method. Calculation of terrain corrections using a fine-mesh grid is obviously important for the terrain inside the survey area, and terrain closely adjacent to the survey, but becomes impractical (and unnecessary) when the fine-mesh grid is used to model topography extending well outside the survey area. A detailed terrain correction grid can be embedded within a more regional terrain correction grid in a way which exploits the periodic nature of the FFT-based algorithms. 3) Demonstrating the relative lack of importance of detailed terrain profiling using aircraft-borne laser or radar altimeters, and the relative importance of synoptic terrain modeling using satellite radar (and similar) DTMs. Many airborne gravity survey contracts specify detailed flight-path terrain profiling. Acquiring, operating, and processing the data from these types of instruments can be a considerable, and (from a gravity viewpoint) unnecessary expense. Given the inherent filtering due to upward continuation from surface to flight height and the explicit filtering required in airborne gravity data processing, the fine details of the topography are irrelevant. The effects of terrain between flight paths, and immediately adjacent to the survey area, are highly relevant. This is particularly true in cases where parts of the survey are naturally bounded by terrain above the flight height.
Combination of Marine Gravity Data for Geoid Modelling
The approach for the realization of national vertical datum is currently moving from geodetic levelling to geoid modelling. The geoid model allows access to an accurate vertical datum anywhere over land, lakes and oceans through space-based positioning technology (e.g., GPS, satellite altimetry). Furthermore, it can ensure datum compatibility at the continental and global scale. Naturally, the accuracy of the geoid model can only be as good as its theory and data. Over the years, various national and international institutions have developed geoid-modelling theory to achieve the millimetre level. However, the quality of the data remains in question in terms of the required accuracy. This presentation focuses on determining a precise geoid model for the North Atlantic by combining shipborne gravity measurements and altimetry-derived gravity data. The investigation makes use of six gravity data sets derived from satellite. The sea surface topography is determined from two mean sea surface height models (height of the sea surface above the ellipsoid). The precision of the geoid models is assessed by estimating the speed of the oceanic currents (Labrador and Gulf Stream) using the equation describing local geostrophic approximation. The speed of the currents is very sensitive to the slope of the geoid model. Small errors in the slope of geoid model translate into significant speed inaccuracy. The results indicate that each dataset has advantages and disadvantages in terms of accuracy (absolute), precision (relative) and resolution. In order to derive proper current speed, the geoid model and mean sea surface height must have identical high spatial resolution. A mismatch in spatial resolution will create artifacts.
Program Update for GRAV-D (Gravity for the Redefinition of the American Vertical Datum): Recent Airborne Surveys
The mission of NOAA's National Geodetic Survey (NGS) is to "define, maintain and provide access to the
National Spatial Reference System" (NSRS). NAVD 88 (North American Vertical Datum of 1988) provides the
vertical reference for the NSRS. However, comparisons of NAVD 88 with the Gravity Recovery and Climate
Experiment (GRACE) satellite gravity data have demonstrated significant problems with the vertical reference,
with an average difference between the two of 0.98 m and std dev of 0.37m. As repairing NAVD 88 through a
massive leveling effort is impractical, our approach will be to establish a gravimetric geoid as the vertical
reference. The linchpin in NGS's effort is the Gravity for the Redefinition of the American Vertical Datum (GRAV-
D) program, which will ultimately incorporate satellite, airborne and terrestrial gravity data to build the 1-2 cm
geoid that the U.S. surveying public is demanding. The program involves both an airborne component, for
measuring a "baseline" gravity field, and a relative and absolute terrestrial program, for monitoring time
variations of the gravity field.
The GRAV-D aerogravity program commenced with a survey based from Anchorage, AK in the summer of
2008, additionally in support of NOAA's Hydropalooza program. Starting in October, the GRAV-D team has
undertaken a concerted effort to survey Puerto Rico/US Virgin Islands, and then the Gulf Coast for the US Army
Corps of Engineers. Gulf operations were from New Orleans, Lake Charles, and Austin, TX. This survey
provides a continuous airborne field measurement at 10 km line spacing from the GA/AL state line to the
Mexican border. We will present the results of these data collection efforts and outline the plans for the GRAV-
D program during the remainder of 2009.
EVRF2007 as Realization of the European Vertical Reference System
Since 1994 the IAG Sub-commission for Europe (EUREF) has continuously enhanced the Unified European Leveling Network (UELN). On the basis of the UELN (status 1998), the first realization of the European Vertical Reference System (EVRS) was computed and released under the name EVRF2000. After that, more than half of the participating countries have provided new national leveling data to the UELN computing centre. Using these data a new realization of the EVRS has now been computed and published under the name EVRF2007. The datum of EVRF2007 is the Normaal Amsterdams Peil (NAP) which is realized by 13 datum points distributed over the stable part of Europe. Prior to adjustment, the measurements in the main area of the Fennoscandian Postglacial Rebound (i.e., Nordic and Baltic countries, northern Poland, northern Germany) were reduced to the common epoch 2000 using the land uplift model NKG2005LU of the Nordic Geodetic Commission (NKG). The results of the adjustment are provided as geopotential numbers and normal heights, which are reduced to the zero tidal system. The EUREF symposium in Brussels (June 2008) approved Resolution No. 3 which proposes to the European Commission that the EVRF2007 is adopted as the vertical reference for pan-European geo-information. Transformation parameters between national European height systems and the EVRF2007 will be calculated and provided through a web-based information and transformation service on coordinate reference systems.
Upcoming replacements for NAD83, NAVD88 and IGLD85
The National Geodetic Survey (NGS), part of the National Oceanic and Atmospheric Administration (NOAA) is responsible for defining, maintaining and providing access to the National Spatial Reference System (NSRS) for the United States. The NSRS is the official system to which all civil federal mapping agencies should refer, and contains, amongst other things, the official geopotential (historically "vertical") datum of NAVD 88, the 3-D geometric reference system (historically "horizontal datum") of NAD 83 and great lakes datum (IGLD 85). Although part of the United States NSRS, all three of these datums have been created through international partnerships across North America. Unfortunately, time has shown both the systematic errors existent within these datums, as well as the inherent weaknesses of relying exclusively on passive monuments to define and provide access to these datums. In recognition of these issues, the National Geodetic Survey has issued a "10 year plan", available online, which outlines steps which will be taken to update NAD 83, NAVD 88 and IGLD 85 concurrently around the year 2018. The primary source of success will be in the refinement of the CORS network and the upcoming execution of the GRAV-D project (Gravity for the Re-definition of the American Vertical Datum). Conversations are ongoing with colleagues in Canada, Mexico, Central America and the Caribbean in order to coordinate all of these efforts across the entire continent. The largest changes expected to occur are the removal of over 2 meters of non-geocentricity in NAD 83; the removal of decimeters of bias and over a meter of tilt in NAVD 88; the addition of the ability to track crustal motions (subsidence, tectonics, etc) in the datums; the removal of leveling as a tool for long-line height differencing; the use of a "best" geoid as the orthometric height reference surface; the addition of datum velocities (motions of the 3-D geometric reference system origin and motions of the geoid); and the use of GNSS technology as the way to access both orthometric and dynamic heights in the vertical datum. This talk will outline the broad plan of action and invite further collaboration along these lines.