Prepare yourself for possibly one of the most interesting and potentially most boring blog posts you have ever read! Today, we are talking about projections and coordinate systems. |
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Now, hopefully your brain isn’t spinning yet, as this can be a very tricky and confusing topic. But never fear because modern technology has made working with spatial reference systems (SRS) surprisingly easy. Historically, cartography in general has been very mathematics heavy; with modern advancements you no longer need to be a math whiz to be a Cartographer.
So, what are these components that we are collectively referring to as SRS? What do they do? What purpose do they serve? And most importantly, why should you care? Let’s start at the top.
There are several key components to representing the earth as a flat surface, it isn’t just one variable, but multiple variables. Each of these variables plays a key component in what the map can be used for, and what it cannot be used for.
Projection – The method in which you transform the 3-dimensonal earth into a 2-dimensional, flat surface
Coordinate System – How you find your location on your new, 2D surface.
Datum/Geoid – How the surface of the earth is represented. The earth is not round, it is referred to as an oblate spheroid or oblate ellipsoid, meaning that it bulges at the equator due to the spinning of the planet. A datum is the basis of determining your elevation and position on the earth. Datums attempt to normalize mean sea level across the globe. There are global datums (WGS84, EGM2008) and local datums (NAVD88).
Transformations – The formulas used to convert between one SRS to another SRS. For example, when going from WGS84, Web Mercator, Meters to NAD83, State Plane Coordinate System, US Survey Feet, there are some mathematical transformations that need to happen. In the image to the right, you can see the equation at the bottom of the dialog box that is needed to transform between WGS84 and NAD83. Defining an SRS – SRS can be defined using a few different methods, including, but not limited to: EPSG Code (European Petroleum Survey Group), WKID (Well-Known ID), and WKT (Well-Known Text). These are codes, usually just numbers, between 4-6 digits. They collectively tell you the Projection, Coordinate System, and Units of measure in one simple code. This is especially important to know your EPSG code, because even slight differences, like US Feet vs. Meters results in a different EPSG code. |
Example of a Transformation in ArcMap |
Simply put, this is how you take the 3D shape of the earth, and turn it into a flat, 2D surface in which you place your imagery. A common way this is explained is to visualize an orange, or even better, go get a real orange! Now peel the orange and flatten it out onto a table. You have just taken a round object (Earth) and turned it into a flat object. Whatever method you used to flatten out your orange is your projection. There are many ways to get from a 3D object to a 2D object, and none of them are perfect. Later we will break down some of the different projections that are out there, and what the pro’s and con’s are of some of the more popular projections in use today. |
https://www.lexico.com/en/definition/projection |
The first step was to figure out how to take a round object and make it flat (projection), your next step is to figure out where you are standing on your newly created flat map. To do this you will need a coordinate system. There are really two main types of coordinate systems in geography: Cartesian and Geographic.
While the term Cartesian might not ring a bell, I promise that you are very knowledgeable on Cartesian coordinate systems. Have you ever used one of those old paper atlases? Okay, maybe that is a bad example and I am old, but I am going to go with it anyway. In the example to the right, what would you say the coordinates are for Denmark?
In this example Denmark would be in H-9. In this map the letters are on the X-Axis, and the numbers are on the Y-Axis. The format for how to write that out would be X, Y (letter, number). This is an example of a simple cartesian coordinate system. See, I told you! You already knew what cartesian coordinate systems were! So now let’s look at how these work in the real world of cartography, and what coordinate systems fall under the category of Cartesian coordinate systems.
A common example of a Cartesian coordinate system is Universal Transverse Mercator. Most coordinate systems only work with a very specific projection and UTM is no different – this coordinate system uses the Transverse Mercator projection. The term Transverse is of Latin origin and means “turned across”. Since that isn’t very helpful, maybe the below image will be.
What you are looking at here depicts a representation on how this projection is created. You see that line down the middle? That line is touching the globe. Wherever that line is touching the globe there is very limited distortion; however, if you look at the ends of the cylinder they are nowhere close to touching the surface of the globe. So, guess what? Those areas are going to be useless for determining your location. Instead, UTM divides the world into 6^{o }zones which results in 60 UTM zones totaling 360^{o}. So, imagine that cylinder pivoting around the globe on the North and South Pole’s axis, 6^{o }at a time. Every 6^{o }a new UTM Zone is created.
The result of that would look something like the image to the right. Now you can see with that many zones distortion will be minimized.
Now, let’s get back on topic and discuss coordinate systems again.
So that’s straight forward, right? Now how do you explain to someone where the heck you are on the Earth using UTM?
Well, it uses what is called a false easting and false northing. Think of this as an arbitrary starting point, referred to as a central meridian. For UTM, the central meridian has an easting value of 500,000 meters. As you move east of the central meridian, that number will increase. As you move west, that number will decrease. However, it will never turn into a negative number. So, if your false easting is 400,000 meters for example, you know that you are west of the central meridian.
To measure how far north or south you are, UTM uses a false northing. In the Southern Hemisphere the false northing begins at the equator with a value of 10 million meters. As you move south that number will decrease. Once you get to about 80^{o }south, your false northing would be around 1.1 million meters. In the Northern Hemisphere, the equator is at 0 meters and increases from there.
UTM is just one example of a Cartesian coordinate system. For simplicity, I’ve used UTM as my shining example, but perhaps the most popular is State Plane Coordinate System (SPCS). So, I will briefly give SPCS the respect it deserves and provide a quick overview. SPCS has a lot of differences across the US - each state has their own SPCS flavor, making it a bit tricky (see why I stuck with UTM now?).
With over 100 different variations in the United States, things can quickly become murky. It also uses two different projections. Ever notice how some SPCS zones run East-West (i.e. Colorado), while others run North-South (i.e. New Mexico)? Well, the ones with vertical lines use a Transverse Mercator Projection (not the same Transverse Mercator that UTM uses though), while the zones with horizontal lines use the Lambert Conformal Projection.
However, the underlying principles remain the same as they are with UTM. They are both cartesian coordinate systems, so SPCS uses a false easting and northing just like UTM does.
Clear as mud? Great.
Wow, okay, who else is ready to move on to geographic coordinate systems?! Yeah, me too!
Give yourself some credit, you know what this SRS is all about too! Geographic coordinate systems are super common, especially when dealing with data that spans continents or the entire globe. Unlike Cartesian type coordinate systems, which are localized and somewhat arbitrary, geographic coordinate systems work worldwide. The numbers within the geographic coordinates can give the experienced geographer an instant idea of where those coordinates point to on the globe. You can think of Geographic Coordinate Systems as breaking the globe up into 4 sectors, or hemispheres. Lat/Long coordinates can quickly tell you what hemisphere you are in. The basis of this is latitude and longitude. Lines of latitude are the horizontal lines on a globe, representing how far north or south you are from the equator (northern and southern hemisphere). These lines are often referred to as parallels.
The lines that run vertically are for measuring longitude, this means they tell you how far east or west you are of the Prime Meridian (eastern or western hemisphere) which is located at 0^{o}. As you may have imagined, lines showing longitude are referred to as meridians. The Prime Meridian could be anywhere, as it is just an arbitrary starting point, but the official Prime Meridian was designated in 1884 and is located at the Royal Observatory in Greenwich, England, which is in London.
Geographic coordinate systems measure out from the center of the earth and find the angle between the core and the surface (see the image to the upper left) which results in your location being represented in either degrees, minutes, and seconds, or in decimal degrees.
Degrees, minutes, and seconds are units of measurements going from largest to smallest, allowing you to get very granular with your location, or just keep it general. There are 360^{o }(surprise, surprise!) in the sphere that represents the earth. Degrees can then be can be broken down into 60 minutes, and a minute can be broken down into 60 seconds. So, if you are familiar with the format, you can get a general idea of where you are just based on the numbers. For example, in the image to the right, taken from Nearmap’s MapBrowser^{TM}, we provide geographic coordinates in both decimal degrees, and degrees, minutes, and seconds. In this example, I can see that the first number is positive, which means northern hemisphere. 38.9 degrees tells me it is in the mid-latitudes. The next number is negative, that tells me it is in the western hemisphere, and since it is -77^{o} I know from experience it is on the east coast of the US. As you may have picked up on from the address, this is the White House in Washington D.C.. This is much different than the Cartesian coordinate system – coordinates from those, such as UTM, are arbitrary (remember that false easting conversation?). Decimal degrees are like degrees, minutes, and seconds, just in a different format. Nearmap can provide you with both coordinates just by dropping a pin on the map within MapBrowser^{TM.} |
Well, simply put, if you don’t understand this topic then you can easily confuse projection/coordinate system issues with horizontal accuracy issues. Some programs, like web-based mapping applications (ArcGIS Online, MapBrowser^{TM}, Google, etc.) only support Web Mercator (EPSG 3857). This is because everything comes through in square tiles using Web Mercator – the earth is broken up into a series of grid squares. Web Mercator, despite its popularity, is a very poor projection and introduces a lot of size and distortion errors which we will discuss further. Ironically, the Mercator projection was never meant to be a projection used to map land. The unique advantage of the Mercator projection is that azimuth lines are constant – this means that you could follow your compass in a straight line and never have to make any other adjustments. In a nutshell, Mercator was meant for navigating the seas, but has become the universal standard projection for most web mapping applications!
There are some neat applications out there that do a really good job of showing that distortion from Web Mercator. One of my personal favorites is thetruesize.com which allows you to select a country and drag it towards the equator, showing how large it really is. This is because with Web Mercator, as you move away from the equator, either north or south, areas will get stretched out and appear larger than they should be.
With that being said, you can see how this might cause some issues for end-users. When you are using imagery in an SRS that is different than your usual SRS you are going to see some horizontal accuracy issues.
Nearmap recently added the ability to download images from our MapBrowser product in NAD83, US State Plane Coordinate System, US Survey feet; we also introduced GDA2020 support for Australia. You can also stream these products through our newly released Custom WMS Service. This allows you to geofence an area, bring in historical imagery, and consume the imagery natively using NAD83 SPCS, or GDA 2020.
Previously, we only supported Web Mercator, WGS84, WGS84 UTM, and NAD83 UTM. End users were still able to consume our imagery in their native SRS, but it had to be reprojected/transformed which can introduce errors. Now that it is being consumed directly in the native SRS directly from Nearmap’s servers, there are no longer horizontal accuracy issues being introduced due to reprojections or transformations.
Additionally, different SRS configurations can introduce errors to measurements as well. For instance, if I take the entire US, and calculate the area in square miles using the Web Mercator projection (EPSG 3857) I get a total of 8,308,294 square miles.
Here at Nearmap, we have several products that we offer which are priced based on the size of an area, so it is important that we calculate areas accurately. Because of this we use an Equal Area projection which preserves area, but sacrifices in other areas, like distortion or linear measurements. Remember when I said before that no SRS is perfect? This is a good example of that. I need a particular SRS just to get an accurate area measurement. So, at Nearmap, we use NAD83 Contiguous USA Albers (EPSG 5070) projection in the US for area measurements.
When I did the area measurement of the US with the Web Mercator projection, the total area was 8,308,294 square miles – any guesses to what it will be with the Albers projection?
3,611,961 square miles! That is a difference of over 56%! You can see why this could cause so many issues. So, for measurements, including area and lines, you need to be using the correct SRS.
In the below images, you will also see how the shape and size of the areas changes between Web Mercator and Albers Equal Area.
Screenshot from Esri’s ArcMap showing Web Mercator Area Measurements |
Screenshot from Esri’s ArcMap showing Albers Equal Area Measurements |
You can start with the following charts as a starting point. These charts will tell you which projection and coordinate system should be used for different use cases (such as measuring area vs. measuring a linear feature like a road).
Thank you for hanging in there! I know it was a long one (how do you think I feel, I had to write it!) but hopefully you are leaving us with a little more knowledge under that fedora. If you have any questions please reach out to us:
or check out some of our publicly available resources at docs.nearmap.com.
Happy Nearmapping!
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