# Elevation Concepts for GIS

Blog Post created by Matt Morris on Apr 3, 2020

This blog post discusses the basic concept of elevation, and the various ways that it can be expressed - particularly as it relates to GNSS receivers. We will cover terminology including ellipsoids, HAE, mean sea level, MSL height, geoids, geoid height, and orthometric height. After reading this article you should understand what these terms mean, and how to best interpret the data from your Trimble GNSS receiver so that you can be confident in the data you base your decision making on.

A common support request received by our Global Services team is to provide an explanation as to why the elevation output from a GNSS receiver doesn’t match what the user expects to see - sometimes with differences of tens of meters in elevation between an observed GNSS elevation and the elevation of a reference coordinate compared to the published coordinates recorded for historic reference monuments such as those available through the National Geodetic Survey for users in the USA.

The answer is normally that a user is comparing apples with oranges. Both elevation coordinates are usually correct - but are measured against different points and frames of reference. To understand what we mean, we need to understand how GNSS receivers normally work, and what frame of reference they are using. .

# Ellipsoidal Height (Height Above Ellipsoid, or HAE)

Elevation is the vertical difference between two points. GNSS elevation refers to the height you are measuring with your GNSS receiver, relative to a known reference surface.

However because the earth’s surface is highly irregular (e.g. due to geology), and ever changing (e.g. due to tectonic motion) making accurate calculations from this surface at a global scale is very difficult. So to simplify the calculation of elevations, geodesists use geometrical approximations of the earth’s surface to base the calculations on.

The approximated geometric shape used to represent the earth’s surface is a type of “vertical datum” called an ellipsoid (which is another word for a three-dimensional ellipse). Elevation at the surface of the ellipsoid is zero. Elevations measured above the ellipsoid surface are reported as positive elevations, and elevations measured below the ellipsoid surface are reported as negative elevations.

Ellipsoid surfaces can be defined very accurately using mathematical formulae, and so provide a very convenient way for mapping and surveying devices (like Trimble GNSS receivers) to create highly accurate digital measurements of the physical world.

Question: I thought the earth was a globe. Why do we use an ellipsoid, and not a sphere to represent the earth?
Answer: The earth is not perfectly round - and is in fact slightly wider (by about 42.7km) than it is tall. Ellipsoids allow a more accurate approximation of the earth’s surface.

Using a highly accurate mathematical model of the earth’s ellipsoid (the most common of which is referred to as the WGS84 ellipsoid), elevations relative to the ellipsoid based on a current GNSS position can be very accurately measured. Elevations using this method of measurement are referred to as heights above ellipsoid (HAE), or ellipsoidal height. HAE values can be either positive (for elevations above the ellipsoid surface) or negative (for elevations below the ellipsoid surface). HAE is the default value output by most GNSS receivers, and depending on the type and accuracy of your receiver, HAE can be computed to very precise values.

But there is a problem with HAE values - they are not very practical in real-world terms. Most practical use of GNSS is done relative to real-world features. And in the real-world the earth’s surface is not a perfect ellipsoid. The earth’s surface has mountains, valleys, and oceans and lakes (which also have mountains and valleys and other surface deformations). For most practical purposes the most intuitive elevation reference surface is “sea level.”
For example, it is not uncommon for a GNSS receiver to report an elevation (while standing on the beach) of +10 metres HAE. For the measured elevation to make sense it needs to be transformed to a different reference datum.

# Mean Sea Level Height (MSL)

The most common vertical reference used in everyday language to represent altitude or elevation is the idea of mean sea level or MSL. For example, Denver, CO, is often referred to as the Mile High City. By an amazing stroke of good luck, the 13th step on the west side of the State Capitol Building is exactly 5,280 feet above mean sea level – one mile high.

Fun fact: Because the earth is dynamic (due to tectonics), and due to improving technology for measuring elevations, measured elevations change over time, based on redefinition of where sea level is and better surveying technology. Because of this, there are actually three separate 5,280 feet markers on the Capitol steps. The original, one from 1969, and another one from 2003.

Your GNSS receiver usually outputs a global MSL in the standard NMEA receiver output. Global MSL on a traditional GNSS receiver is generally based on a relatively coarse (and therefore imprecise) 10-minute by 10-minute grid, which is used to determine the offset between the reference ellipsoid and MSL at any given location on the earth. This relatively low resolution calculation can make the reported MSL elevations output by GNSS receivers off by several meters or more. This is fine for some applications, but for others (e.g. high accuracy mapping of underground assets) that’s a problem as local deformations and changes are not sufficiently accounted for.

## Geoids

A geoid is a highly accurate model of the local gravitational forces in a specific region of the world. Gravity force is affected by the density and structure of the earth’s surface. This means that in denser, and higher areas of the world the measured gravitational force is different to that of low-lying, less dense areas. This change in local gravity has an effect on the observed sea level at any given location.

Geoids measure the effects of variances in the local gravity on MSL using a sophisticated geometric representation of the actual physical shape of the earth. Each location or region in the world has its own local geoid(s), and these get updated from time to time; as measuring techniques change, or as the land deforms, local geoids are updated and re-released.

The current vertical datum in the United States is called NAVD88 (North American Vertical Datum of 1988) which incorporates the latest geoid model (see below; GEOID18). This will be changing in the next couple years.

Elevations, computed against localised vertical datums are computed using a highly accurate reference height (usually the ellipsoidal height calculated by your GNSS receiver), and this is referenced against the geoid model for the local area.

The geoid can be thought of as the detailed 3D surface of the earth. The shape of the geoid is the shape that the ocean surface would take under the influence of the gravity and rotation of the earth alone, assuming all other influences (such as winds and tides) were absent. The geoid surface is extended through the continents. Because of the massive size of our planet, it is difficult to visually distinguish the variance in surface gravity, and so digital renderings of the geoid tend to exaggerate the differences (by a factor of up to x10,000 or more) so that they can be visually seen. Below is an example of the visual representation of the Geoid showing the undulations and variations in the surface of the earth’s gravitational field. Here, geoid undulation is rendered in false color, with shaded relief and a vertical exaggeration scale factor of x10,000.

Image credit: By International Centre for Global Earth Models (ICGEM) - http://icgem.gfz-potsdam.de/vis3d/longtime / Ince, E. S., Barthelmes, F., Reißland, S., Elger, K., Förste, C., Flechtner, F., Schuh, H. (2019): ICGEM – 15 years of successful collection and distribution of global gravitational models, associated services and future plans. - Earth System Science Data, 11, pp. 647-674,DOI: http://doi.org/10.5194/essd-11-647-2019., CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=81462823

## Geoid models

A geoid model is a grid of numeric values representing the geoid in a given region. It is similar to the MSL grid found in a GNSS receiver, but is defined with much higher resolution, is far more accurate, but is only applicable to a specific geographic region. Geoid models allow accurate conversion between ellipsoid height (HAE) and a mean sea level height based on a specific, local vertical datum. The geoid model can be interpolated to calculate an offset value called the “geoid height” or “geoid undulation" at the specific location being measured/calculated. This is the number we must use to convert between a global height referenced to a reference ellipsoid and a local height. This elevation is called orthometric height and is a much more usable and relevant height reference for most applications.

Fun fact: The etymological root of the word “orthometric” is the Greek prefix “ortho”, meaning “straight”, “upright”, “right” or “correct”.

## Calculating orthometric height

Orthometric height is a relatively simple calculation:

H = h - N

Where:
H = Orthometric Height, the elevation value that is defined in terms of the local target vertical datum
h = Ellipsoidal Height, the elevation above or below the reference ellipsoid of the GNSS receiver
N = Geoid Height / Undulation, the difference between the geoid and ellipsoid in the current location

Orthometric height is the type of elevation data that surveyors, engineers, and other field workers need to work practically and accurately.

Depending on your field application or workflow, your software may calculate orthometric heights for you. Trimble Mobile Manager allows you to specify the latest geoid for your region, and the geoid file will be automatically downloaded to the app. Using the undulation information in the geoid file, the orthometric height is calculated directly in the app, and output alongside the ellipsoidal height.

For more information on using geoids and calculating orthometric heights in Trimble Mobile Manager, check out our 4 part series of blog posts: Orthometric Heights with Trimble GNSS & Esri Collector.

Banner image credit: https://medium.com/swlh/the-earths-weird-gravity-86449f8cb3e7