May 31, 2022

# All About Geoids and How to Set Up a Geoid Model Transformation in Geographic Calculator

When new geoid models and vertical coordinate systems are implemented in Geographic Calculator, they cross my path, as a Quality Assurance analyst, for verification. Through this process, I have observed that new or updated geoid models are a more and more common occurrence. I am most familiar with the US National Geodetic Survey modernization efforts to produce the new vertical datum NAPGD2022 and geoid model NAPGD2022 (which will be time-dependent too!), but numerous international authorities are also releasing new geoids and vertical coordinate systems. We add these new objects and definitions to Geographic Calculator as quickly as we can, which depends on both the format of the grid and the availability of a validation reference data.

The increasing availability of accurate and precise geoid models, and our ability to implement them into Geographic Calculator, allows end-users to transform between ellipsoidal height and height in a vertical datum easily and accurately. Advanced aerial and ground-based gravimetric surveys allow for ever-improving estimates of the ellipsoid and the creation of both regional and global geoid models to support these transformations. While the ability to create accurate geoid models is relatively new, the geoid is nothing new to geodesy, with its conceptualization and formulation having largely taken place during the 19th century.

Before looking at how we can make use of geoid models, ellipsoids, and vertical coordinate systems to work with height data, let’s first look at what a geoid is conceptually.

A geoid represents a hypothetical surface (mean sea level) that the earth’s oceans would follow based solely on gravitational and rotational forces. The geoid surface extends under or over the landmasses and is irregular as it “undulates” above and below the ellipsoid due to irregularities in the mass distribution within the earth. This undulation is also known as “geoid height” or “geoid separation.” A bit more technically speaking, the geoid is a surface of equal geopotential and gravity always acts perpendicular to the geoid surface.

Now that we have a description of the geoid, how is a geoid model derived and summarized for use in geodetic software?

The geoid model is an estimate of the geoid calculated from measurements of gravitational anomalies. The resulting modeled surface is then sampled on a horizontal grid and stored as one or more files from which a geoid height for any location within the domain of the model can be interpolated. A geoid model is particular for a specific ellipsoid and vertical datum.

The process of implementing a geoid model in Geographic Calculator is a matter of defining the transformation in accordance with the issuing authority, reading the grid file(s) supplied by the authority, and validating the transform calculations. It can take some time to accomplish these tasks, most notably in the reading of the data. Grids are not always provided in a standard format, in which case we must make modifications to support the file(s).

How is a geoid model transformation defined and how is software configured to use one?

A geoid model vertical transformation can at first be a little tricky to set up if unfamiliar with how the geoid models are defined. First, I should state that while most coordinate transformations are referred to as datum transformations, the source and target of a transformation are defined with coordinate reference systems rather than the datums that they are based upon. The reason for this is that a coordinate reference system has a few additional pieces of useful information that the datum does not. Area of use is one example.

Now in the case of geoid models, the ellipsoid is the reference to which the geoid separations are taken. And in the transformation definition, we need to specify which ellipsoid was used, but we do that by specifying a horizontal geodetic coordinate reference system, which has a horizontal datum that is based on the appropriate ellipsoid. This is customarily specified as the source side of the transformation, but keep in mind that the source and target are reversible in a transformation at the time of usage.

Finally, in the Geographic Calculator interface, to specify the ellipsoid side of the transformation, we select the correct geodetic coordinate reference system, then select Ellipsoidal Height as the vertical system, and now the software knows which ellipsoid you are referencing. The target side of the transformation is more intuitively just the vertical coordinate reference system (and datum) for which the geoid was developed.

What are some of the more recent geoid models that are in common use today and available for use in Geographic Calculator?

Examples of recent geoid models include, but are not limited to the following (sometimes these are more recent than the release year in the name implies):

• “Canadian Gravimetric Geoid Model of 2013”
• “Earth Geopotential Model of 2008 (1′ grid)”
• “Japanese GSI Geoid Model of 2011 (version 2)”
• “LHN95 via the CHGeo2004 geoid”
• “Mexican Gravimetric Geoid Model of 2010”
• “Netherlands Geoid Model of 2004”
• “NZGD2000 to NZVD2016 height (1)”
• “Ordnance Survey Geoid Model of 2015/Great Britain”
• “South African Geoid Model of 2010”
• “Swedish Geoid Model of 2008 for RH2000”
• “US Geoid Model of 2018”

While the science of geodesy and the concept of geoids, ellipsoids, and vertical reference systems is complex, our team at Blue Marble is chock-full of experts. We gladly take on the task of researching, implementing, verifying, and testing new geoid models in Geographic Calculator as the program is continually updated to provide you, the user, with the latest and greatest geodetic tools for all coordinate transformation needs.