A horizontal datum is a collection of specific points on the Earth’s surface that have been accurately identified according to their precise northerly or southerly location (latitude) and easterly or westerly location (longitude).
To create the network of horizontal positions, surveyors marked each of the positions they had identified with a brass, bronze, or aluminum disk known as a survey benchmark. Because surveyors wanted to see one marked position from another, the benchmarks were usually placed on mountaintops or at high elevations. If they were on flat land, surveyors would have towers built to help locate them.
In order to create a horizontal datum, these monument locations were connected using mathematical techniques like triangulation. The result of triangulation from the unified network of survey monuments was North American Datum of 1927 (NAD 27) and later the more accurate NAD 83, which is still used today. NAD 27 and NAD 83 provide a frame of reference for latitude and longitude locations on Earth.
What is a Horizontal Datum?
A horizontal (geometric) datum (or reference frame) forms a basis for computations of horizontal positions on the Earth.
Real world objects are defined by coordinate systems. Various coordinate reference systems exist. In each coordinate system, geographic locations or features are described mathematically using coordinate values. A geographic coordinate system defines three-dimensional coordinates based on the Earth’s surface. It contains an angular unit of measure, prime meridian and datum (which contains the spheroid).
Longitudes:
X-coordinates are between -180 and +180, which are called longitudes.
Longitude Coordinates
Latitudes:
Y-values are between -90 and +90 degrees, which are called latitudes.
Latitude Coordinates
Most horizontal datums define a zero line at the equator. The equator is where we measure north and south.
The Greenwich Meridian (or prime meridian) is a zero line of longitude from which we measure east and west. The zero line passes through the Royal Observatory in Greenwich, England – which is how it earned its name. In a geographical coordinate system, it is a line of longitude defined to be 0°.
Together, these lines provide a reference for latitude and longitude. This system is also known as a geographic grid
.
A datum describes the shape of the Earth. In mathematical terms, it defines the radius, major and minor axis and flattening for an ellipsoid. Datums are used in projections, monitoring the Earth’s crust, survey boundary delineation and more.
All coordinates are referenced to a datum – including the one you are standing on right now.
Locate ANYTHING on Earth with Coordinates
Coordinates are pairs (X, Y) or triplets (X, Y, Z) of values that are used to represent points and features on a two and three-dimensional space. The X-value represents the horizontal position and Y-value represents the vertical position. The Z-value generally refers to the elevation at that point location.
Latitude / Longitude Geographic Coordinate System
Geographic coordinate systems (latitudes and longitudes) are based on a spheroid surface. Spheroids are approximate locations on the surface of the earth. The datum defines the surface. The major axis (longest diameter of an ellipse) and minor axis (shortest diameter of an ellipse) and radius represent the position of the surface relative to the center of the earth.
What is a Coordinate Reference System?
Reference ellipsoids are mathematical models of the shape of the Earth with the major axis along the equatorial radius. A geographic coordinate system uses longitude and latitude expressed in decimal degrees. WGS 1984 and NAD 1983 are examples of datums.
Coordinates are pairs (X, Y) or triplets (X, Y, Z) of values that are used to represent points and features on a two and three-dimensional space.
Spherical coordinates (latitudes and longitudes) are often written as degrees-minutes-seconds (DMS). Minutes range from 0 to 60. For example, the geographic coordinate expressed in degrees-minutes-seconds for New York City is:
Geographic coordinate can also be expressed in decimal degrees. Here is New York City in decimal degrees:
What is an Ellipsoid in GIS?
Reference ellipsoids are mathematical models of the shape of the Earth with the shape of flattened sphere. The major axis of an ellipse is the equatorial radius. The minor axis is from the poles to the center. Reference ellipsoids are primarily used as a surface to specify point coordinates such as latitudes (north/south), longitudes (east/west) and elevations (height).
The most common reference ellipsoid in cartography and surveying is the World Geodetic System WGS 84. The Clarke Ellipsoid of 1866 and was recomputed in 1927 as NAD27. When comparing NAD27 and NAD84, latitude and longitude coordinates can be displaced on the degree of tens of meters (with the same latitude and longitude coordinates).
Reference Ellipsoid / Spheroid
How Do Horizontal Datums Relate to Ellipsoids?
Horizontal datums give us the capability to measure distances and directions across the surface of the earth. Most horizontal datums define a zero line at the equator from which we measure north and south (latitudes). There is also a zero line at the Greenwich Meridian from which we measure east and west (longitudes). Together these lines provide a reference for latitude and longitude expressed in decimal degrees. These latitudes and longitude positions (Geographic Coordinate Systems) are based on a spheroid or ellipsoid surfaces that approximate the surface of the earth – a datum.
All coordinates are referenced to a datum. A datum describes the shape of the Earth in mathematical terms. A datum defines the radius, inverse flattening, semi-major axis and semi-minor axis for an ellipsoid. Here is the WGS84 datum:
Semi-major axis: 6,378,137.0 m
Semi-minor axis: 6,356,752.3 m
Inverse flattening: 294.978698214
Earth is Flattened Because of Rotational Forces
Sir Isaac Newton and others proposed that the Earth flattens at the poles because of rotational forces. As the Earth spins on its axis, the centrifugal force causes the Earth to bulge out at the equator. This is why the Earth is better modeled as an ellipsoid, which is a sphere slightly flattened at the poles.
In the 19th and 20th centuries, different ellipsoids were adopted in various parts of the world. Surveys were being performed on different continents. Each survey produced different ellipsoidal parameters. For example, surveys in Australia yielded a “best” ellipsoid. Europe’s “best” ellipsoid was different South America and Asia. There wasn’t a unifying global ellipsoid. Each continental survey was isolated with it’s own ellipsoid parameters. There was no clear way how to combine these global survey measurements. There was a scarcity of survey points in specific areas and a lack of computational resources that prevented a global ellipsoid.
Earth Bulging at Equator
How Are Horizontal Datums Created?
Over the past two centuries, surveyors have measured extremely precise latitude and longitude locations on the Earth’s surface. These locations are called benchmarks and are identified with a brass or aluminum disk in the ground. Networks of benchmarks have been placed in higher altitude locations so they can be viewed from one-another.
In order to create a horizontal datum, several methods have been established to connect these benchmark locations. First-order triangulation was used to connect horizontal monuments into a unified network with the end result being North American Datum of 1927 (NAD27). But the network of points in 1927 was sparse in comparison.
The Elements of Geodesy: The Horizontal Datum. National Oceanic and Atmospheric Administration
A datum describes the shape of the Earth. In mathematical terms, it defines the radius, major and minor axis and flattening for an ellipsoid. Datums are used in projections, monitoring the Earth’s crust, survey boundary delineation and more.
All coordinates are referenced to a datum – including the one you are standing on right now.
Locate ANYTHING on Earth with Coordinates
Coordinates are pairs (X, Y) or triplets (X, Y, Z) of values that are used to represent points and features on a two and three-dimensional space. The X-value represents the horizontal position and Y-value represents the vertical position. The Z-value generally refers to the elevation at that point location.
Latitude / Longitude Geographic Coordinate System
Geographic coordinate systems (latitudes and longitudes) are based on a spheroid surface. Spheroids are approximate locations on the surface of the earth. The datum defines the surface. The major axis (longest diameter of an ellipse) and minor axis (shortest diameter of an ellipse) and radius represent the position of the surface relative to the center of the earth.
What is a Coordinate Reference System?
Reference ellipsoids are mathematical models of the shape of the Earth with the major axis along the equatorial radius. A geographic coordinate system uses longitude and latitude expressed in decimal degrees. WGS 1984 and NAD 1983 are examples of datums.
Coordinates are pairs (X, Y) or triplets (X, Y, Z) of values that are used to represent points and features on a two and three-dimensional space.
Spherical coordinates (latitudes and longitudes) are often written as degrees-minutes-seconds (DMS). Minutes range from 0 to 60. For example, the geographic coordinate expressed in degrees-minutes-seconds for New York City is:
- Latitude: 40 degrees, 42 minutes, 51 seconds N
- Longitude: 74 degrees, 0 minutes, 21 seconds W
Geographic coordinate can also be expressed in decimal degrees. Here is New York City in decimal degrees:
- Latitude: 40.714
- Longitude: -74.006
What is an Ellipsoid in GIS?
Reference ellipsoids are mathematical models of the shape of the Earth with the shape of flattened sphere. The major axis of an ellipse is the equatorial radius. The minor axis is from the poles to the center. Reference ellipsoids are primarily used as a surface to specify point coordinates such as latitudes (north/south), longitudes (east/west) and elevations (height).
The most common reference ellipsoid in cartography and surveying is the World Geodetic System WGS 84. The Clarke Ellipsoid of 1866 and was recomputed in 1927 as NAD27. When comparing NAD27 and NAD84, latitude and longitude coordinates can be displaced on the degree of tens of meters (with the same latitude and longitude coordinates).
Reference Ellipsoid / Spheroid
How Do Horizontal Datums Relate to Ellipsoids?
Horizontal datums give us the capability to measure distances and directions across the surface of the earth. Most horizontal datums define a zero line at the equator from which we measure north and south (latitudes). There is also a zero line at the Greenwich Meridian from which we measure east and west (longitudes). Together these lines provide a reference for latitude and longitude expressed in decimal degrees. These latitudes and longitude positions (Geographic Coordinate Systems) are based on a spheroid or ellipsoid surfaces that approximate the surface of the earth – a datum.
All coordinates are referenced to a datum. A datum describes the shape of the Earth in mathematical terms. A datum defines the radius, inverse flattening, semi-major axis and semi-minor axis for an ellipsoid. Here is the WGS84 datum:
Semi-major axis: 6,378,137.0 m
Semi-minor axis: 6,356,752.3 m
Inverse flattening: 294.978698214
Earth is Flattened Because of Rotational Forces
Sir Isaac Newton and others proposed that the Earth flattens at the poles because of rotational forces. As the Earth spins on its axis, the centrifugal force causes the Earth to bulge out at the equator. This is why the Earth is better modeled as an ellipsoid, which is a sphere slightly flattened at the poles.
In the 19th and 20th centuries, different ellipsoids were adopted in various parts of the world. Surveys were being performed on different continents. Each survey produced different ellipsoidal parameters. For example, surveys in Australia yielded a “best” ellipsoid. Europe’s “best” ellipsoid was different South America and Asia. There wasn’t a unifying global ellipsoid. Each continental survey was isolated with it’s own ellipsoid parameters. There was no clear way how to combine these global survey measurements. There was a scarcity of survey points in specific areas and a lack of computational resources that prevented a global ellipsoid.
Earth Bulging at Equator
How Are Horizontal Datums Created?
Over the past two centuries, surveyors have measured extremely precise latitude and longitude locations on the Earth’s surface. These locations are called benchmarks and are identified with a brass or aluminum disk in the ground. Networks of benchmarks have been placed in higher altitude locations so they can be viewed from one-another.
In order to create a horizontal datum, several methods have been established to connect these benchmark locations. First-order triangulation was used to connect horizontal monuments into a unified network with the end result being North American Datum of 1927 (NAD27). But the network of points in 1927 was sparse in comparison.
The Elements of Geodesy: The Horizontal Datum. National Oceanic and Atmospheric Administration
In 1983, NAD83 replaced NAD27 because of its inaccuracies. According to NOAA, the geographic coordinates given relative to the NAD 27 datum might represent a position hundreds of meters different than those same coordinates given relative to the NAD 83 datum. The average correction between NAD27 and NAD84 is an average of 0.349″ northward an 1.822″ eastward.
NAD27 Shift to NAD83 (Image credit: NADCON – North American Datum Conversion Utility)
NAD27, NAD83 and WGS84 Are Commonly Datums in North America
In order to create a horizontal datum, monument locations were connected using mathematical techniques like triangulation. The result of triangulation from the unified network of survey monuments was North American Datum of 1927 (NAD 27) and later the more accurate NAD 83, which is still used today. NAD 27 and NAD 83 provide a frame of reference for latitude and longitude locations on Earth.
Meades Ranch Triangulation Station, fundamental station for the North American Datum of 1927
The North American datum of 1983 (NAD 83)is the most current datum being used in North America. It provides latitude and longitude and some height information. Several datums have existed over the years. Many maps were created using different datums and starting points in the past. For example, the North American datum of 1927 used Kansas as a starting point. Horizontal datums are continuously being improved even today.
Surveyors now rely almost exclusively on the Global Positioning System (GPS) to identify locations on the Earth and incorporate them into existing datums.
The North American Datum of 1927 (NAD27) is one of the main three horizontal datums used in North America. NAD27 uses the Clarke Ellipsoid of 1866 with a fixed latitude and longitude at Meade’s Ranch, Kansas (39° 13’26.686″ north latitude, 98° 32’30.506″ west longitude). This means that all points in North America used this fixed point as a reference measuring direction and distance away. All latitudes and longitudes could be measured on the Clarke Ellipsoid of 1866.
The North American Datum of 1983 (NAD 83) is a unified horizontal or geometric datum and successor to NAD27 providing a spatial reference for Canada and the United States. NAD83 corrects some of the distortions from NAD27 over distance by using a more sense set of positions from terrestrial and Doppler satellite data. NAD83 is a geocentric datum (referenced to the center of Earth’s mass) offset by about 2 meters.
The World Geodetic System (WGS84) is the reference coordinate system used by the Global Positioning System. It comprises of a reference ellipsoid, a standard coordinate system, altitude data and a geoid. Similar to NAD 83, it uses the Earth’s center mass as the coordinate origin. The error is believed to be less than 2 centimeters.
Fitting the Ellipsoid with the Geoid
NAD27 Shift to NAD83 (Image credit: NADCON – North American Datum Conversion Utility)
NAD27, NAD83 and WGS84 Are Commonly Datums in North America
In order to create a horizontal datum, monument locations were connected using mathematical techniques like triangulation. The result of triangulation from the unified network of survey monuments was North American Datum of 1927 (NAD 27) and later the more accurate NAD 83, which is still used today. NAD 27 and NAD 83 provide a frame of reference for latitude and longitude locations on Earth.
Meades Ranch Triangulation Station, fundamental station for the North American Datum of 1927
The North American datum of 1983 (NAD 83)is the most current datum being used in North America. It provides latitude and longitude and some height information. Several datums have existed over the years. Many maps were created using different datums and starting points in the past. For example, the North American datum of 1927 used Kansas as a starting point. Horizontal datums are continuously being improved even today.
Surveyors now rely almost exclusively on the Global Positioning System (GPS) to identify locations on the Earth and incorporate them into existing datums.
The North American Datum of 1927 (NAD27) is one of the main three horizontal datums used in North America. NAD27 uses the Clarke Ellipsoid of 1866 with a fixed latitude and longitude at Meade’s Ranch, Kansas (39° 13’26.686″ north latitude, 98° 32’30.506″ west longitude). This means that all points in North America used this fixed point as a reference measuring direction and distance away. All latitudes and longitudes could be measured on the Clarke Ellipsoid of 1866.
The North American Datum of 1983 (NAD 83) is a unified horizontal or geometric datum and successor to NAD27 providing a spatial reference for Canada and the United States. NAD83 corrects some of the distortions from NAD27 over distance by using a more sense set of positions from terrestrial and Doppler satellite data. NAD83 is a geocentric datum (referenced to the center of Earth’s mass) offset by about 2 meters.
The World Geodetic System (WGS84) is the reference coordinate system used by the Global Positioning System. It comprises of a reference ellipsoid, a standard coordinate system, altitude data and a geoid. Similar to NAD 83, it uses the Earth’s center mass as the coordinate origin. The error is believed to be less than 2 centimeters.
Fitting the Ellipsoid with the Geoid
Geoid (Image courtesy of NASA/JPL)
A horizontal coordinate system gives us the side-by-side that is our latitude and longitude. A vertical datum is another component of your typical horizontal coordinate system. We are on a three-dimensional planet which has ups-and-downs in addition to the side-to-side in a horizontal coordinate system on the surface. To handle the ups-and-downs, we have the vertical datum which gives a place to put the zero measurement. Mean sea level is often understood as the basis for our ups-and-downs. This is called the geoid.
Vertical datums are lumpy and irregular. This is because of the varying densities in the Earth in different places. There are gravity anomalies. Mean sea level is not a smooth thing that everyone likes to think it is. Geoids are not constant and they differ from place-to-place. Geoids have undulations as you move around on the Earth. The Earth is not as round as we like to pretend it is. We have lumps or undulations on them as they come back to us in the form of a geoid. The geoids put the lumps back into our nice smooth horizontal datum coordinate system.
Ellipsoid Height is the most basic version of up-and-down. The ellipsoid uses the size and shape of the horizontal datum such as WGS84. It gives a smooth surface without bumps or irregularities. The geoid is complex to describe it mathematically. Therefore, we fit different Ellipsoids to approximate it such as WGS84.
Flatten the Sphere with Map Projections
A projection on a map is basically the method by which the mapmaker translates a sphere or a globe into a two-dimensional representation. Projected coordinate systems converts the spheroid-based coordinates to a flat plane.
Imagine peeling an orange and flattening it on a two-dimensional surface. Universal Transverse Mercator coordinate system is an example of a map projection that divides the Earth into sixty zones. Each zone flattens the spheroid surface to a flat plane.
There are multiple ways to represent a sphere on a two-dimensional surface. Every projection has a strength and a weakness. It is up to the map maker to determine what projection it most favorable for its purpose.
The Mercator projection distortions and are so that it is no longer used in Atlases. For most of us, the projection is common enough that it looks fine for us. But if you take a closer look, Greenland is presented as having roughly as much land area as Africa. However, Africa (11.67 million square kilometers) is roughly 14 times larger than Greenland (2.16 million square kilometers)
Conclusion
Coordinates reference systems, geoids, latitudes and longitudes, projections, datums, ellipsoids…
Every GIS analyst needs a good base understanding of what they are and how it relates to location.
Because you can’t just put anything on a map without understanding its horizontal reference system.
Source: GIS Geography
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