Datums, Projections, CRS + Desktop GIS

Part 1 - Datums, Projections, CRS

The Process of building a mathematical model of the surface of the Earth

Because of the Earth’s Geoid’s irregularity Geodesists have chosen to use Ellipsoids (or Spheroids) to calculate the location of latitude and longitude.

Ellipsoid (aka spheroid) = idealized shape of Earth - used for calculations.  

An XY datum is built on top of the selected spheroid and can incorporate local variations in elevation. With the spheroid, the rotation of the ellipse creates a totally smooth surface across the world. Because this doesn't reflect reality very well, a local datum can incorporate local variations in elevation.  The spheroid defines the size and shape of the earth model, while the datum connects the spheroid to the earth's surface.

Vertical Datum:  To get your x-y position, datums usually use a spheroid/ellipsoid.  For vertical position, some variation on the geoid is used.

Coordinate Reference Systems - unprojected & projected

Examples of map datums are:

• WGS 84, 72, 66 and 60 of the World Geodetic System

• NAD83, the North American Datum which is very similar to WGS 84

• NAD27, the older North American Datum, of which NAD83 was basically a readjustment [1]

• OSGB36 of the Ordnance Survey of Great Britain

• ETRS89, the European Datum, related to ITRS

• ED50, the older European Datum

• GDA94, the Australian Datum[8]

• JGD2011, the Japanese Datum, adjusted for changes caused by 2011 Tōhoku earthquake and tsunami[9]

• Tokyo97, the older Japanese Datum[10]

• KGD2002, the Korean Datum[11]

• TWD67 and TWD97, different datum currently used in Taiwan.[12]

• BJS54 and XAS80, old geodetic datum used in China[13]

• GCJ-02 and BD-09, Chinese encrypted geodetic datum.

• PZ-90.11, the current geodetic reference used by GLONASS[14]

• GTRF, the geodetic reference used by Galileo; currently defined as ITRF2005[15]

• CGCS2000, or CGS-2000, the geodetic reference used by BeiDou Navigation Satellite System; based on ITRF97[15][16][17]

• International Terrestrial Reference Frames (ITRF88, 89, 90, 91, 92, 93, 94, 96, 97, 2000, 2005, 2008, 2014), different realizations of the ITRS.[18][19]

• Hong Kong Principal Datum, a vertical datum used in Hong Kong.[20][21]

• SAD69 - South American Datum 1969

NOTE....The Earth's tectonic plates move relative to one another in different directions at speeds on the order of 50 to 100 mm (2.0 to 3.9 in) per year.[22] Therefore, locations on different plates are in motion relative to one another. For example, the longitudinal difference between a point on the equator in Uganda, on the African Plate, and a point on the equator in Ecuador, on the South American Plate, increases by about 0.0014 arcseconds per year.[citation needed] These tectonic movements likewise affect latitude.

If a global reference frame (such as WGS84) is used, the coordinates of a place on the surface generally will change from year to year. Most mapping, such as within a single country, does not span plates. To minimize coordinate changes for that case, a different reference frame can be used, one whose coordinates are fixed to that particular plate. Examples of these reference frames are "NAD83" for North America and "ETRS89" for Europe.

General Approach to Producing Map Projections

The process of projection is often described as follows:  Imagine that you have a globe that is hollow.  Light can shine through the globe such that it would illuminate a surface outside the globe.  If the continents are drawn on the globe in a non-transparent material - when the light is turned on inside the globe - you will see the outline of the continents on the surface outside the globe.  Let's say the surface outside the globe is a cylinder (a piece of poster board wrapped in a cylinder around the globe).  When the light at the center of the globe is turned on the continents will be projected onto the poster board. Areas nearest the light will have little distortion whereas areas farther from the light will have more distortion.  In reality...we can make the projected surface intersect with the globe wherever we want (red line in images below).  Distortions are small close to this line of intersection (red line) and get larger as you move away from the red line.

Distortion from Projection

A Special Case - The Universal Transverse Mercator

Remember now that in a Geographic Coordinate System you must measure in degrees because it is not projected.  The distance that a degree covers varies widely from the equator to the pole.  Now with a projected GCS it becomes possible to measure distance is standard units (m, km, and miles) - but we still have to be careful about distortions depending on where we are on the Earth and what projection we are using.  For most work - a standard go-to is the Universal Transverse Mercator (UTM).

Coordinate Reference System + Projection - UTM

The Universal Transverse Mercator (UTM) conformal projection uses a 2-dimensional Cartesian coordinate system to give locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, i.e. it is used to identify locations on the Earth independently of vertical position. However, instead of lat and long in an unprojected framework you can now measure distance.

TAKE NOTE:  The UTM system is not a single map projection. The system instead divides the Earth into sixty zones, each being a six-degree band of longitude, and uses a secant transverse Mercator projection in each zone.  UTM must always use Transverse Mercator (the projection) but can still use other datums (WGS 84, NAD 27, etc.) -- but -- WGS 84 is standard in the USA.  These bands work great for most of the world except the poles...here the Universal polar stereographic coordinate system is used.

Dynamic Map - Which UTM Zone am I In?

Google Maps and Google Earth

Google Maps

Google Maps use a quasi Spherical Normal (equatorial) variant of the Mercator projection based on the World Geodetic System (WGS) 1984 geographic coordinate system (datum) → this is called the “Web Mercator” projection

Web Mercator (aka Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator or WGS 84/Pseudo-Mercator) is a variant of the Mercator projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted it in 2005.

It uses the same formulas as the standard Mercator as used for small-scale maps. However, the Web Mercator uses the spherical formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection. The discrepancy is imperceptible at the global scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale. This deviation becomes more pronounced further from the equator, and can reach as much as 35 km on the ground.

Web Mercator shares some of the same properties of the standard Mercator projection: north is up everywhere, meridians are equally spaced vertical lines, but areas near the poles are greatly exaggerated.

Unlike the ellipsoidal Mercator and spherical Mercator, the Web Mercator is not quite conformal due to its use of ellipsoidal datum geographical coordinates against a spherical projection. Rhumb lines are not straight lines. The benefit is that the spherical form is much simpler to calculate, saving many computing cycles.

But WHY does GM use this projection?!?!?! 

Maps uses Mercator because it preserves angles.  The first launch of Maps actually did not use Mercator, and streets in high latitude places like Stockholm did not meet at right angles on the map the way they do in reality. While this distorts a 'zoomed-out view' of the map, it allows close-ups (street level) to appear more like reality. The majority of our users are looking down at the street level for businesses, directions, etc.

By certain measures, such as area, the Mercator map is probably the most distorted, so the question is legitimate. All projections from a sphere to a plane are, of course, distorted. When you fix one kind of distortion, you increase another kind of distortion. The choice of projection, then, is about selecting what kind of distortion you would dislike the least. For example, if it is important to you that areas of countries are shown accurately, an equal-are projection is certainly preferable. The Mercator projection seems at first glance to be an odd choice because its solution to latitudinal distortion is to make sure that longitudinal distortion is just as bad.

The primary purpose of Google Maps is to provide local navigation, street maps and directions, rather than to provide a planetary view of the Earth. Within the context of local street searches (e.g. where is the closest shoe store), angles and compass directions are very important, as well as ensuring that distances in all directions are shown at the same scale (locally). Consistent area is less important, since local scale is easily dealt with by providing a distance indicator (assuming the region being viewed is relatively small). Also, it is highly advantageous to make panning work correctly in conjunction with zooming, without the application of linear or non-linear transforms. It turns out that there is exactly one kind of planar projection with these properties. That projection is the Mercator projection. The choice to use this projection is not arbitrary, but rather is motivated by practical mathematical considerations. These properties make Mercator the standard for nearly all navigation applications. 

A good alternative to Mercator is to not use any projection at all (i.e. map all the data to a three dimensional mesh). This is what Google Earth uses, and it is great for large scale (e.g. planetary) geological applications.  Any alternative to Mercator will remove certain properties such as the ability to pan continuously such that only the newly exposed map needs to be redrawn.

A great discussion on this topic can be found here → https://productforums.google.com/forum/#!topic/maps/A2ygEJ5eG-o

Google Earth

The elevations on google earth refer to EGM96 and are, therefore, Geoidal heights. The lat/long are referred to the WGS 84 ellipsoid.

Helpful Resources

• https://en.wikipedia.org/wiki/List_of_map_projections

• http://geokov.com/education/map-projection.aspx

• https://en.wikipedia.org/wiki/Geographic_coordinate_system#Expressing_latitude_and_longitude_as_linear_units

• https://courses.washington.edu/gis250/lessons/projection/

• http://www.icsm.gov.au/education/fundamentals-mapping

• https://en.wikipedia.org/wiki/Tissot%27s_indicatrix

Practical Advice on Managing Projections in a GIS (special attention to QGIS)

Managing CRS’s in a GIS can get very confusing very quickly.  This is just a short note to help you sort out which datums/projections are good to use and when and how to convert between datums/projections in GIS.  The first distinction you have to make is between geographic and projected CRS’s.  Geographic reference systems treat the map as if it is still on the surface of the earth and thus uses latitude and longitude.  Geographic reference systems tend to work well for most places on Earth but can only measure distances in degrees (except when using the MMQGIS plugin which allows for creating buffers in meters, miles, etc. on geographic layers).  

Examples of commonly used Geographic reference systems are as follows:  

• WGS 84, EPSG:4326

• NAD 83, EPSG:4269

By themselves, these CRS’s are good to use across the entire globe, but remember that these are geographic CRS’s and therefore no good for measuring distances.  To be able to measure distances, we have to use local projections of these broad geographic reference systems to come up with local projected CRS’s.  This type of approach works well if you are looking at an area the size of a state or smaller.  For example, if I want to work on the central Rocky Mountains of Colorado, I would look of the corresponding UTM zone (13N) and project my data to this zone .  Any of these would work:

• WGS 84 / UTM zone 13N, (found within “Universal Transverse Mercator”)

• NAD83 works in a very similar way.  You can choose from a suite of options to project your NAD83 dataset given your particular area:

  • • • NAD83 / Colorado Central, EPSG:26954 (found within “Lambert Conformal Conic”)

Notice for both of these that we have to use some sort of mathematical method to project our data.  These mathematical methods are defined by the “Universal Transverse Mercator” and the “Lambert Conformal Conic” portions of these projections respectively.

**NOTE** People sometimes have issues in QGIS when one of their layers was produced in NAD83 and the other was produced in WGS84.  Hypothetically, let us imagine that I have QGIS open and I have a layer displaying mines in the Colorado mountains.  This layer is projected to WGS 84 / UTM zone 13N because I want to measure the distance from abandoned mines inside National Parks to the park boundaries in meters.  Now, I add my park boundary layers to QGIS and notice that this layer is in a geographic coordinate system (NAD83).  These layers overlap just fine in my display because I have “on the fly projection” selected in my “Project Properties”, but when I go to subset the mine layer by the National Park layer, I get an empty layer (nothing shows up, no attributes, etc.).  This is because, although they appear to overlap in my display, they actually have two very different coordinate systems (one is geographic, the other is projected)!  Therefore, I know I have to convert the NAD83 file to a WGS 84 / UTM zone 13N projection if I am ever going to reach my goal.  However, when I resave the National Parks layer with a WGS 84 / UTM zone 13N projection I find that this has resulted in my layers not overlapping at all...THIS IS WHERE THE TRICK COMES IN.  For some reason in QGIS if you want to take something in a geographic reference system with a certain datum (like NAD83) and project it with a different datum (datum = WGS 84, projection = UTM zone 13N), you can not go all the way on the first conversion (i.e. you cannot go datum 1 to datum 2 + projection).  Instead, you have to first convert just the datum (NAD83 [geographic] to WGS 84 [geographic] = datum 1 to datum 2).  THEN you can go ahead and project the geographically referenced layer that you have converted to your preferred datum (WGS 84) to your preferred projection (UTM zone 13N)...(i.e. datum 2 to datum 2 + projection).  Now you are free to use this layer to create buffers, subset other layers, etc. 

Sometimes though our data span more than one of these small zones, that is when we need a regional or global projection.  For example, if you are looking at mapping the Oregon Trail, which reaches across most of the United States, you might what to try this projection:

• Lambert Conformal Conic, EPSG:102009 for North America

And further yet, you might be mapping earthquake locations across the entire world.  For that you need a projection that works across the entire globe (though it probably won’t work well for the poles, you need a different projection for that!).  Here are a couple of good choices:

• World Azimuthal Equidistant, EPSG:54032

• WGS 84 / Pseudo Mercator, EPSG:3857 

Why don’t we always use global projections you ask?  Well, if we are just working on a small definable area, then if we use a projection specific for that area we will get better mapping precision than if we used a global projection.  For many projections it might not make a difference (Google Maps and Carto only use global projections), but for some projections, this increased precision may be important.

Now, for the person who has a global data set but needs the precision of the local projections, you have no choice but to split up your data and display it piecemeal.  Here are some options along that route with the task of creating a buffer in mind:

1. Create a custom CRS using aeqd (or tmerc) for each one, and draw just that one buffer with it. Practically, you only have to create the buffer once, and exchange the CRS information in the .prj and .qpj file. The coordinates of the buffer with respect to its center will always be the same.

2. Group the data according to the UTM zones, and use the UTM CRS of that zone for those points respectively.

3. Similar to UTM, group your points into zones of latitude (e.g. every 10 degrees), and create custom Lambert conformal conical 2SP CRS for each group. This will be significantly faster than using all northern and southern UTM zones of the world.

4. Use pseudo mercator EPSG:3857 for all. The buffers will look like nice circles, but the real size will get smaller and distorted the more to the poles you come.

Summing Up Coordinate Systems

1. You need to define the surface of the Earth in a way that is computationally feasible (ellipsoid for x,y location; geoid for z elevation)

   • Once you define an ellipsoid and geoid combo that you like for your mapping needs...you package that up and call it your datum (i.e. WGS84, NAD83, NAD27, etc.)

2. You need some way of communicating location on your spherioid/ellipsoid

   • you can impose a grid (lat / long) → this is your Geographic Reference System

   • This system is degrees-based and distance per degree changes depending where you are on Earth

3. You need to flatten this spheroid out on a flat surface

   • This is where you choose a projection based on your specific purpose (cylindrical, conic, azimuthal)

     • You want to avoid distortion in your area of interest - UTM

4. You can then apply a coordinate system onto this projected map to measure xy distances (in meters) - northings and eastings

   • https://www.youtube.com/watch?v=HnWNhyxyUHg

Georeferencing

Exercise C:  Processing Raster Data in QGIS

• Different Indices

• Supervised vs. Unsupervised classification

• Other Raster analyses....

List of Raster Analyses Tutorials in QGIS - for reference

• QGIS manual section on “working with raster data”

  • • https://docs.qgis.org/3.4/en/docs/user_manual/working_with_raster/index.html

• NDVI

  • • https://www.youtube.com/watch?v=j61X3l6LvxY

• clipping rasters

  • • https://www.youtube.com/watch?v=h8g9IgxWwqw

• suitability map

  • • https://www.youtube.com/watch?v=HWeWVKgjkro

• raster calculator

  • • https://www.youtube.com/watch?v=mCyNRf_olkw

• reclassify and convert raster to shp

  • • https://www.youtube.com/watch?v=LyjI0jD2WUs

• raster stats

  • • https://www.youtube.com/watch?v=Ej4Ucz3GgSQ

• Raster Zonal Statistics

  • • https://www.youtube.com/watch?v=dOZrtgpVOMU

• resampling rasters

  • • https://www.youtube.com/watch?v=JBiqsK03xVA

• Landsat & Sentinel Data - pan sharpening

  • • https://www.youtube.com/watch?v=GwaDSfJ1pk4&t=381s

• SCP tool (1) - download and preprocess data

  • • https://www.youtube.com/watch?v=v-xj2SkAWdg

• SCP tool (2) - landcover classification

  • • https://www.youtube.com/watch?v=fUZgYxgDjsk

• SCP tool (3) - entire channel...take your pick

  • • https://www.youtube.com/user/fromgistors

• Load IMERG precip

  • • https://www.youtube.com/watch?v=S-TILW0OI3E