# Basic GIS Coordinates

Coordinates are integral building tools for GIS, cartography, surveying and are vital to the many applications we use today such as smart phones, car navigation systems and driverless cars. Basic GIS Coordinates, Third Edition grants readers with a solid understanding of coordinates and coordinate systems and how they operate as well as valuable insight into what causes them to malfunction. This practical and comprehensive guide lays out the foundation of a coordinate system and the implications behind building it as it elaborates on heights, two coordinate systems, and the rectangular system.The previous editions described horizontal and vertical datums such as the North American Datum 1983 (NAD 83) and the North American Vertical Datum 1988 (NAVD 88). Both will be replaced in 2022 or thereabouts. The National Geodetic Survey (NGS) plans to replace NAD83 with a new semi-dynamic terrestrial reference frame for North America and a new vertical datum will replace NAVD88. The foundation of the new vertical datum will be a temporally tracked gravimetric geoid. The interim period is intended to smooth the transition to the new paradigm and this new edition explores the changes and provides assistance in understanding them.

## Basic GIS coordinates

Coordinates are integral building tools for GIS, cartography, surveying and are vital to the many applications we use today such as smart phones, car navigation systems and driverless cars. Basic GIS Coordinates, Third Edition grants readers with a solid understanding of coordinates and coordinate systems and how they operate as well as valuable insight into what causes them to malfunction. This practical and comprehensive guide lays out the foundation of a coordinate system and the implications behind building it as it elaborates on heights, two coordinate systems, and the rectangular system.The previous editions described horizontal and vertical datums such as the North American Datum 1983 (NAD 83) and the North American Vertical Datum 1988 (NAVD 88). Both will be replaced in 2022 or thereabouts. The National Geodetic Survey (NGS) plans to replace NAD83 with a new semi-dynamic terrestrial reference frame for North America and a new vertical datum will replace NAVD88. The foundation of the new vertical datum will be a temporally tracked gravimetric geoid. The interim period is intended to smooth the transition to the new paradigm and this new edition explores the changes and provides assistance in understanding them.

In 1854, John Snow, an epidemiologist and physician, was able to determine the source of a cholera outbreak in London through the use of spatial analysis. Snow achieved this through plotting the residence of each casualty on a map of the area, as well as the nearby water sources. Once these points were marked, he was able to identify the water source within the cluster that was responsible for the outbreak. This was one of the earliest successful uses of a geographic methodology in pinpointing the source of an outbreak in epidemiology. While the basic elements of topography and theme existed previously in cartography, Snow's map was unique due to his use of cartographic methods, not only to depict, but also to analyze clusters of geographically dependent phenomena.

The earth can be represented by various models, each of which may provide a different set of coordinates (e.g., latitude, longitude, elevation) for any given point on the Earth's surface. The simplest model is to assume the earth is a perfect sphere. As more measurements of the earth have accumulated, the models of the earth have become more sophisticated and more accurate. In fact, there are models called datums that apply to different areas of the earth to provide increased accuracy, like North American Datum of 1983 for U.S. measurements, and the World Geodetic System for worldwide measurements.

The latitude and longitude on a map made against a local datum may not be the same as one obtained from a GPS receiver. Converting coordinates from one datum to another requires a datum transformation such as a Helmert transformation, although in certain situations a simple translation may be sufficient.[29]

Geocoding is interpolating spatial locations (X,Y coordinates) from street addresses or any other spatially referenced data such as ZIP Codes, parcel lots and address locations. A reference theme is required to geocode individual addresses, such as a road centerline file with address ranges. The individual address locations have historically been interpolated, or estimated, by examining address ranges along a road segment. These are usually provided in the form of a table or database. The software will then place a dot approximately where that address belongs along the segment of centerline. For example, an address point of 500 will be at the midpoint of a line segment that starts with address 1 and ends with address 1,000. Geocoding can also be applied against actual parcel data, typically from municipal tax maps. In this case, the result of the geocoding will be an actually positioned space as opposed to an interpolated point. This approach is being increasingly used to provide more precise location information.

Cartographers write spherical coordinates (latitudes and longitudes) in degrees-minutes-seconds (DMS) and decimal degrees. For degrees-minutes-seconds, minutes range from 0 to 60. For example, the geographic coordinate expressed in degrees-minutes-seconds for New York City is:

For those referring to (land?) Plot plans, these use a different datum(?) than geographic coordinates. They are based on bearings, not locations in (x,y,z), and depend on a fixed starting point other than (0,0,0).

Ultimately, the goal is very straightforward relating each position on one surface, the reference ellipsoid, to a corresponding position on another surface as faithfully as possible and then flattening that second surface to accommodate Cartesian coordinates. In fact, the whole procedure is in the service of moving from geographic to Cartesian coordinates and back again. These days, the complexities of the mathematics are handled with computers. Of course, that was not always the case. Map projections in which shape is preserved are known as conformal or orthomorphic. Orthomorphic means right shape. In a conformal projection, the angles between intersecting lines and curves retain their original form on the map. In other words, between short lines, meaning lines under about 10 miles, a 45º angle on the ellipsoid is a 45º angle on the map. It also means that the scale is the same in all directions from a point; in fact, it is this characteristic that preserves the angles. These aspects were certainly a boon for all State Plane Coordinate users. On long lines, angles on the ellipsoid are not exactly the same on the map projection. Nevertheless, the change is small and systematic. Actually, all three of the projections that were used in the designs of the original State Plane Coordinate Systems were conformal. Each system was originally based on the North American Datum 1927, NAD27. Along with the Oblique Mercator projection, which was used on the panhandle of Alaska, the two primary projections were the Lambert Conic Conformal Projection and the Transverse Mercator projection. Today, they're in North American Datum of 1983, NAD83 2011 (2010.0).

The original State Plane Coordinate System (SPCS) was so successful in North Carolina, similar systems were devised for all the states in the Union within a year or so. The system was successful because, among other things, it overcame some of the limitations of mapping on a horizontal plane while avoiding the imposition of strict geodetic methods and calculations. It managed to keep the distortion of the scale ratio under 1 part in 10,000 and preserved conformality. It did not disturb the familiar system of ordered pairs of Cartesian coordinates, and it covered each state with as few zones as possible whose boundaries were constructed to follow county lines. County lines were generally used, so that those relying on State Plane Coordinates could work in one zone throughout a jurisdiction.

In several instances, the boundaries of State Plane Coordinate Zones today, SPCS83, the State Plane Coordinate System based on NAD83 2011 (2010.0) and its reference ellipsoid GRS80, differ from the original zone boundaries. The foundation of the original State Plane Coordinate System, SPCS27 was NAD27 and its reference ellipsoid Clarke 1866. As mentioned earlier, NAD27 geographical coordinates, latitudes and longitudes, differ significantly from those in NAD83 2011 (2010.0). In fact, conversion from geographic coordinates, latitude and longitude, to grid coordinates, y and x, and back is one of the three fundamental conversions in the State Plane Coordinate system. It is important because the whole objective of the SPCS is to allow the user to work in plane coordinates, but still have the option of expressing any of the points under consideration in either latitude and longitude or State Plane Coordinates without significant loss of accuracy. Therefore, when geodetic control was migrated from NAD27 to NAD83 2011 (2010.0), the State Plane Coordinate System had to go along. When the migration was undertaken in the 1970s, it presented an opportunity for an overhaul of the system. Many options were considered, but in the end, just a few changes were made. One of the reasons for the conservative approach was the fact that 37 states had passed legislation supporting the use of State Plane Coordinates. Nevertheless, some zones got new numbers, and some of the zones changed. The zones are numbered in the SPCS83 system known as FIPS. FIPS stands for Federal Information Processing Standard, and each SPCS83 zone has been given a FIPS number. These days, the zones are often known as FIPS zones. SPCS27 zones did not have these FIPS numbers. As mentioned earlier, the original goal was to keep each zone small enough to ensure that the scale distortion was 1 part in 10,000 or less, but when the SPCS83 was designed, that scale was not maintained in some states. In five states, some SPCS27 zones were eliminated altogether and the areas they had covered were consolidated into one zone or added to adjoining zones. In three of those states, the result was one single large zone. Those states are South Carolina, Montana, and Nebraska. In SPCS27, South Carolina and Nebraska had two zones; in SPCS83, they have just one, FIPS zone 3900 and FIPS zone 2600, respectively. Montana previously had three zones. It has one, FIPS zone 2500. Therefore, because the area covered by these single zones has become so large, they are not limited by the 1 part in 10,000 standard. California eliminated zone 7 and added that area to FIPS zone 0405, formerly zone 5. Two zones previously covered Puerto Rico and the Virgin Islands. They have one. It is FIPS zone 5200. In Michigan, three Transverse Mercator zones were entirely eliminated. 041b061a72