Are you an engineer? Did you study linear algebra in college? Perhaps you have an advanced mathematics degree? If so, you might not find this blog helpful. If you’re like many folks in the GIS industry today who did not take a heavy math load in college and are not working as a surveyor or engineer, then this blog hopefully will help you to understand one of the fundamental principles of mapping. Geodesy is that area in GIS that is a bit of a dirty secret in that many people try to avoid it or don’t understand it. Technically it’s the branch of mathematics and science focused on accurately measuring and understanding the size and shape of the earth, its orientation in space, and its gravity field. It is a $100,000 word that even sounds intimidating, but break it down and it will hopefully make sense. It’s the underpinning of all mapping but it can be the most difficult to understand and the most intimidating to the unindoctrinated. I am here to help with my top ten list of geodetic fundamentals, explained in an easy to understand and hopefully easy to remember approach. So let’s dive in to the deep end, shall we?

## Number 1: It’s Coordinate “Reference” System not Coordinate System

This is an important point, no pun intended, to remember. The Coordinate Reference System (CRS) is a reference model that packages up everything we need to communicate locations, sizes, and shapes. It is a toolkit that gives us a language to accurately enumerate positions on the earth. Some of the tools in the CRS toolbox are Ellipsoid, Datum, Map Projection, Units, and Origin. A CRS is defined by these concepts, which allows us to talk geodesy. Just remember that we are using a math model to reference the earth. Blue Marble has a tag line: Mind the Gap Between World and Map. That is what we are talking about. Unfortunately there is not a good acronym for these terms. EDPUO does not have a good ring to it. I’ve tried switching them around, nothing works. But you usually need them all to make a CRS.

## Number 2: Transform not Convert

When I first started working at Blue Marble, we used to use the phrase “coordinate conversion”. Over the years, we have moved away from that phrase simply because it implies a process that is exact and easily reversible when that is not always the case. When we change coordinate reference systems we are actually transforming the data. We are moving all of the points to a new system and, if we were to reverse that process, we are actually transforming the data again and on some small level those points will not be exactly where they were before. The concept here is that there is much more going on behind the scenes.

## Number 3: Three types of Coordinate Reference Systems

There are three main types of CRS that we work with ̶ the Geographic, the Projected, and the Geocentric. Geographic coordinate systems can be thought of as a globe, a whole-earth model. The units are angular like degrees as opposed to feet and are focused on rotation around an axis. This type of system gets us close to the shape of the planet without a lot of distortion. But it is not practical for talking about directions, distances and relative locations. That is why we have the projected systems. Think of the projected systems as taking the round globe and projecting it on to a flat plane. These behave like planar Cartesian systems that allow us to map x and y on a grid in linear units like feet, meters or miles. The third type of system is called geocentric or earth centered/earth fixed (ECEF). This is a model that is based on an origin that is at the center of the planet (the geocenter) as opposed to the surface. Many of these are gravity-based and they were used for GPS satellite technology.

## Number 4: The Types of Datum Transformations

Datum Transformations are probably the most difficult concepts for people to understand. Actually, it’s the concept of a datum itself that trips people up. I like to think of the datum as a tie-down point. It is the point that ties a specific location on the globe to your mapping surface. So, if the datum is where we begin a mapping process, envision moving from that point in one direction. We will call that X. Then we turn to a perpendicular direction that we will call Y. If we introduce a change in height, that is Z. So now we take all three position changes (change in X, change in Y, change in Z) and we move them together to arrive at a different reference surface. In order to mathematically move X, Y, and Z together, we use a datum transformation. A simple, linear, three-parameter transformation tries to leave our point in one place and swap out the surface they are on by lining up a new model under it. The simplicity of the shift has tradeoffs in terms of accuracy. If we add more complexity we add more parameters like rotations and scale and we can move into seven, ten, and even 14 parameter shifts. This process is very complex, mathematically speaking, and not easily summed up in a brief blog. But the point (once again, no pun intended) is that we have to transform our data in a precise and accurate manner and this process starts with the datum from which we are transforming.

## Number 5: Geoids – Getting Vertical

So many concepts, so little time. OK, so the term geoid literally means Earth model. In today’s geodetic world (seriously, not a pun) we consider geoids in conjunction with vertical datums. Vertical datums add a new dimension to horizontal datums. Think of a horizontal datum as mainly dealing with the x and y, based on an ellipsoid. With a vertical datum we introduce a z value for height. With a vertical datum we introduce ‘up’ and ‘down’. The vertical datums allow us to map mountains, valleys, changes in the terrain, by giving us a good zero height from which we start measuring. Mean Sea Level comes into play when we talk about geoids as well. Geoids are typically models approximating where sea level is supposed to be to create an even more accurate reference for height measurement. They of course have a whole bag of assumptions and challenges to bring to the table as the ocean is an ever moving target. It’s important to remember that when talking about sea level, there are multiple models of it and they aren’t all the same!

## Number 6: Not just Where but When is your data?

By this stage, I’ve either confused you even more than you were at the start, or perhapsbe you are beginning to understand some of these concepts a little more so that you have a deeper appreciation of where your data is. Well, I’m sorry but for modern mapping it is no longer just about where, but it is also about when. When is your data? Coordinate reference systems can now also carry a value of when the system was measured; a time stamp if you will. Also known as an epoch. Think of the areas of the earth’s surface that are relatively active (moving) due to tectonic activity. The island of Japan is a great example. After a major earth quake in Japan, the entire island can actually move or change its location. There are now time-dependent transformations available, such as HTDP, to address this challenge. Another way to think of this concept is our friend WGS84 ̶ World Geodetic System 1984. The first iteration of this GPS-measured system was way back in 1984. For our millennial friends, that is ancient history. For today’s mapping, if we are concerned with modern measurement, the original WGS 84 is not going to get it done. It’s been realized (revised) six times over the years; we now use WGS84 (G1762), which was realized 1762 weeks (33 years!) after the original and is now several meters away from positions on surface-based models from that time.

## Number 7: Process Assumptions – aka Garbage in Garbage out!

So now you have some of the basic concepts in your list checked off. Now you should be able to look at your mapping data, review these issues and know that, if they are all accounted for, you are all set. Your data is accurate. It is where it is supposed to be and you can move on to more cartographic pursuits such as contour generation and buffering. No, sorry it is not that easy. We cannot assume that the process used to create the data we are working with was executed properly. A common problem in modern mapping is we load in secondary data to our map. Many GIS tools will automatically place that data over the base data. If it appears to line up, we assume it is correct. When we bring in our data, if that data was corrupted by a poor transformation process or mis-labeled geodetically when it comes through that process it will still be bad. We may never know. That is why we always have to be on alert for geodetically corrupted data or processes where assumptions are made.

## Number 8: The challenge of that last Meter

Today’s GIS and Survey work often encompasses data in the centimeter level of precision or resolution. Data products like high-resolution LiDAR data with multiple points collected per square meter are common place. Working at high-precision levels requires a great deal of care and persistence. The work is far from complete when the data is collected. There are assumptions to question, data manipulations to understand, and limitations to acknowledge. All of the concepts in our top ten come into play.

## Number 9: Metadata, metadata, metadata

One way to help battle garbage in/garbage out is the often overlooked, admittedly boring process of metadata. Metadata is data about the data. It is a key to understanding the CRS involved in our map. Information like coordinate reference system, projections, sources, and assumptions are all important forms of metadata. Mapping folks have been talking about metadata for as long as I can remember. Yet it is still often overlooked. We took delivery of a large, high-resolution, and extremely expensive-to-collect LiDAR data set not too long ago and when we attempted to transform the data we realized there was absolutely no coordinate metadata information. Because it was terrestrial LiDAR and intended to be quite accurate, it used a local CRS, but there was no metadata in the files. An easy fix would have been a text file in the folder directory but that was nowhere to be found either. And this data was collected by a licensed land surveyor. Unacceptable! We all have to do better than that.

## Number 10: Education on the Science/ Training on the Software

Let’s remember, whether it’s geography, surveying, geology, physics, ecology, or any number of other disciplines, collectively we are talking about science. One cannot simply become an expert on all facets of applied GIS. One can learn the tools involved but the science of mapping itself is the responsibility of the GIS professional and that science is founded on positioning. Additionally, there are any number of software tools that can be used to create maps. All of those software titles address our top ten list and the question of whether or not they do a good job is up to the GIS professional. We said earlier, garbage in means garbage out. We must all work to stay current on the various tools we use for mapping, and thus by extension geodesy, so that we can understand how those tools address our top ten issues. If we are diligent, we can provide accurate mapping. If we are not, the follies and foils of inaccurate data rest on our shoulders.

*Patrick Cunningham is the President of Blue Marble Geographics. He has two decades of experience in software development, marketing, sales, consulting, and project management. Under his leadership, Blue Marble has become the world leader in coordinate conversion software (the Geographic Calculator) and low cost GIS software with the 2011 acquisition of Global Mapper. Cunningham is Chair of the Maine GIS Users Group, a state appointed member of the Maine Geolibrary Board, a member of the NEURISA board, a GISP and holds a masters in sociology from the University of New Hampshire.*