# Section Five: Geodetic Datums: Combining Reference Ellipsoids and Geoids

In Section Three, we looked at the idea that the Earth is not best represented by a sphere (or even a spheroid a sphere-like 3D object where the radius in one direction is longer than the radius in a direction at a right angle to the first ), but a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , which is a model of the variation in gravitational pull over the surface of the Earth. This variation allows for a modeling of true mean sea level at any single location on the Earth's surface, since an assumption could be made between the strength of the pull of gravity and where water would pool (higher gravitational pull, more water pooling).

We also noted the best way to simplify the shape is to match it to a 3D reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , one which either was best-fit for the whole world (global reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid ) or one which was best-fit for a local area (local reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid - which could be regional, continental, state-wide, county wide, or city wide). We also learned that the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid was great for laying out the 2D portion of the map and we mentioned that the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." is the base for the Z value or elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface portion for making maps. In order to make useful maps, we need combine the 2D, XY half of the map and the 3D, Z half of the map. This is accomplished with the creation of a geodetic datum the result of attaching a "free-floating" reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid to a specifically measured geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points and benchmarks. , or really just "datum" for short.

### 2.5.1: Geodetic Datums

So far, we understand 2D maps, consisting of the shapes of continents, states, counties, or city limits (among a whole boatload of other features), drawn on the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , while the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface values are stored with the geodetic datums, or - what most people say - just "datums".

Reference ellipsoids come in two varieties - global, containing a map of all of the continents and oceans, and local, which consist of any are smaller than the whole globe. Geoids are almost always, and in our studies here will always, consists of the entire globe. When we create datums, the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid is the half of the equation that decides the extent of the datum. If the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid only covers North America, it most likely fits inside the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." pretty darn good in North America but doesn't touch anywhere else in the world (or if it does, by chance, it is ignored). When the datum is created, the extent - the boundaries of the datum - is limited to North America, regardless of the fact that the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." maps the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface of the entire planet. If the extent of the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid is the entire globe, it will fit mostly okay everywhere on Earth (the extent of the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." ) - some place will be very close, some will be quite a bit off, and some will be average. But that is nature of global datums - kinda good everywhere, but not really great anywhere.

As we will see in the next section, the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid is not blank to start, but actually covered with an evenly spaced Cartesian Coordinate System specifically called a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. . This grid is used to start the process of labeling exact locations on the Earth's surface, but in this section, we will just remember the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid is not blank like a piece of printer paper, but covered in a grid like engineer's paper.

We haven't really talked much about the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." - the surface upon which we walk around and observe the Earth's landforms the descriptive words for individual features on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , such as "hills", "valley", and "ridgelines" , but we need to remember that all of these mathematical models are created and used with the goal of labeling and navigating to locations on the Earth's surface. Since that is our goal, we need something to connect the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." to the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." to the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , and that real-world object is a benchmark. Benchmarks are, as we said, real world objects that are placed and maintained at specific and known locations of the Earth's surface. Some benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . are labeled monuments, some are chunks of rebar sunk into concrete, and some are just chunks of concrete, but all of them are scattered about world-wide and are used to connect the three surfaces together.

As, I'm sure you've noticed, there are not benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . covering the entire surface of the Earth, and most likely, you've never actually noticed a benchmark in real life ever. Since they are not covering the Earth at every location, we use the ones which do exist, then mathematically infer the rest.

Every benchmark is at a known location upon an existing Cartesian Coordinate System, we can use them as a connection point between the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." (a model of the difference between GMSL and LMSL via a model of gravitational acceleration) and the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid (a gridded 3D shape with the oceans and land areas drawn upon it). If, for example, a benchmark existing on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." in the real world has an "address" (the exact known location) of -114.03, 34.42 which has been carefully surveyed and recorded, the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." is created with GPS (an electronic means of finding Earth "addresses"), and the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid has a point marked on it's grid found by counting 34.42 intersections east of the 0,0 origin and 114.03 intersections south, we can simply connect the same location between the three different surfaces, creating beginning of a geodetic datum the result of attaching a "free-floating" reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid to a specifically measured geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points and benchmarks. , or just datum. If we connect several benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . between the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." with the matching, known coordinates located on a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." and some specific reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , we have a pretty good start to the datum. If we know the "address" of each connected benchmark/ geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." coordinates/ reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid 's Cartesian Coordinate System coordinates, using simple counting we can label all the remaining intersections on the datum and call those mathematically derived connections control points. And you thought you'd never use Cartesian Coordinate Systems again.....

• NOTE: Benchmarks are used for the basis of all datums. Once a benchmark is used to make the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." - geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." - reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid connection, it is "converted" into a control point aka: tie point  mathematically derived points that connect a two spatial objects together, such as a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." and a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid . The difference between the two is a benchmark an actual object which resides in the real world and is used over and over to create lots of datums and a control point aka: tie point  mathematically derived points that connect a two spatial objects together, such as a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." and a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid is a mathematically determined connection between a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." and a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid which "resides" in the datum. So, within a datum, all benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . become control points, but not all control points started out as benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . .

FIGURE 2.17: An Example of a Benchmark
An example of a benchmark. While there is no single standard benchmark, they all include what they are, a height above sea level, and a cross or point in the middle for a surveyor to place the point of their survey equipment.

The Main Point...
Datums are: reference ellipsoids that have been linked to a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points, which connect real-world points called benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . with mathematically derived points on the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid .

### 2.5.2: Horizontal and Vertical Datums

We've explored the idea that the geodetic datum the result of attaching a "free-floating" reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid to a specifically measured geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points and benchmarks. is the product of combining a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." with a selected reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , starting with the benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . , and establishing all the remaining control points utilizing the principles of labeling intersections with a Cartesian Coordinate System. We noted that the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid - covered with a grid and with the 2D land and ocean masses drawn upon it - is connected to a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." - a mathematical derivation of local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features at any point on the Earth's surface via the specific gravitational pull at said point, which stores our 3D elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface values.

Looking at the creation of the datum in this way makes it seem like there are only "2D datums" and "3D geoids", when in reality, the two work together to produce three kinds of 3D datums: three-dimensional datums. All three come from the initial product: combine a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid with a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points (both benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . and mathematically derived intersections) and each serves a specific purpose in Geospatial Sciences. All three are actually a 3 dimensional product, regardless of the fact that only one is called "three dimensional". Everything we have looked at up to this point is really a 3D object. Reference ellipsoids, datums, geoids ... all three dimensional objects.

Horizontal datums contain only XY values upon a 3D Earth, vertical datums used to reference locations and distances above mean sea level; elevation. contain only Z values upon a 3D Earth, and three-dimensional datums contain XY and Z values upon a 3D Earth.

Horizontal datums assume that every point on the Earth's surface is at an equal zero elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface - including the tops of mountains, the bottoms of oceans, and everything in between. Horizontal datums assume there is no change in topography or relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , and that the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." is totally flat and level at every point on the Earth's surface.

Vertical datums come in three varieties: three-dimensional datums, which combine horizontal datums used to reference location on the Earth's surface, regardless of elevation with ellipsoidal height.

Three-dimensional datums are used by GPS units to determine a personal elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface at any given time. Introduction to GIS doesn't work with vertical or three-dimensional datums at all, and GPS for GIS only looks at the fact the if you stand at any given point on the Earth's surface, the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface is known, so for now, just understand that there are a few products of the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid + geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." process.

### 2.5.3: Geodetic Height and Elevation

Elevation is defined as the measured distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . (as we've looked at while examining the geoid creation method, local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features is specified because of the varied effects of the Earth’s gravitational pull; using a global mean sea level the average of the sea level as affected by the pull of gravity when there is a finite amount of water upon a model of the Earth. would create accurate measurements in some places and incorrect measurements in others.)

Altitude is defined as the height of an independent object, such as an aircraft, above ground level (AGL) or Above Sea Level (ASL). If an aircraft was flying at 2,000 feet AGL, it would be 2,000 feet above the ground right below it, no matter the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface of that location. Aircraft can also record values Above Sea Level (ASL), where elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface and altitude the height of an independent object, such as an aircraft, above ground level (AGL) are combined. Regardless of how an aircraft is recording measurements, it is not possible for a person to hike to an altitude the height of an independent object, such as an aircraft, above ground level (AGL) , only an elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface .

Orthometric height is defined as measured distance between the geoid and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . Elevation measurements are created from and stored within vertical datums used to reference locations and distances above mean sea level; elevation. for accurate Z-values within a geographic coordinate system for accurate analysis.

Ellipsoid height is defined as the measured distance between the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . GPS receivers use ellipsoidal height since the calculation is easier to obtain on the fly. If the GPS knows where it is in relation to the XY positions on the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , it can easily calculate it's height above that established zero. For a GPS receiver, to calculate elevations based on the geoid is much more labor intensive.

Geoid separation (geoid height) is defined as the measured difference between the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid and the geoid. Worldwide, geoid separation the measured difference between the ellipsoid and the geoid varies from +278.87 feet (85 meters) to -351.05 feet (-107 meters), based on the WGS84 reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid and the Earth Gravitational Model 1996 (EGM96) geoid. Geoid separation is used to increase the accuracy of GPS measurements in the post-processing phase of data collection since the GPS receiver uses elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface established between the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , but accurate measurements are between the geoid and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." (or the orthometric height the measured distance between the geoid and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . ). In order to convert from ellipsoidal height to orthometric height the measured distance between the geoid and the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . , the geoid separation the measured difference between the ellipsoid and the geoid needs to be a known value. Notice how these height determination definitions can be related back to the kinds of vertical datums used to reference locations and distances above mean sea level; elevation. .

Figure 2.18: A Graphical Explanation of Ellipsoid Height, Orthometric Height, and Geoid Height

Figure 2.19: Deviation of the Geoid and Reference Ellipsoid in For the World Geodetic Datum, 1984 (WGS84)
This image shows the areas where the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid and geoid deviate in the WGS84 Geographic Coordinate System. We see that there are really only a few places where the two meet exactly; just the places where the pink and the blue meet in a single line. Most areas of the geoid fall either above or below the surface of the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , where the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid is a smooth, even shape and the geoid is the undulating weirdo shape./td>

The Main Point...
Representing the Earth in three ways, geoid, reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , and topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , leads us to a need to know the measured distances between each of them. Each surface serves a different purpose in geodesy the science of measuring and monitoring the size and shape of the Earth and the location of points on its surface , so eliminating one is impossible.

### 2.5.4: Datum Shifts

Over time, data collection technology improves, while at the same time land and ocean masses are in constant flux - moving, shifting, and boogieing down. As a response to these changes, datum measurements regarding the precision of control points must also be changed to keep up with the shifting world. While it might seem rather obvious, it is a gazillion times easier to move the mathematical points on the datum then to go out, dig up, and physically replace the benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . . And since we know that benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . are used for several different datums, moving them to repair the accuracy of one datum would be catastrophic to all of the others.

A datum shift when control points are adjusted via better mathematical calculations or real-world surveying. Benchmarks cannot move, but control points can change via datum shifts.  ''Major'' Large effort; many points change; expensive and time-consuming. Noted with a two-digit year (ie NAD83)  ''Minor'' Just a few points change. Less expensive; less involved. Noted with a four-digit year (ie. NAD83(1985)) is when the coordinate associated with a benchmark (and the resulting control points) is adjusted or changed based upon either better surveying techniques, better mathematical calculations, or adjustments for continental shift. Datum shifts can be major, noted with a two-digit year following the datum name — i.e. NAD27 to NAD83 — or minor, noted with a four-digit year in parenthesis following the datum name (i.e. WGS84(1988)). Major datum shifts are extremely involved, and usually include a major survey project and mathematical calculations, while minor datum shifts are usually completed when just a few control points are deemed incorrect.