Tuesday, April 22, 2008

Grid Systems, a brief introduction

Let there be grids

Outside of ZIP codes, there are other methods we like to utilize to map our data. One of these is the use of a grid of some arbitrary size over a large area. Many types of data can be mapped to a grid. Temperature, precipitation, elevation each lends themselves to grids due to their continuous nature over a surface. Sometimes other types of data are projected onto grids that are not necessarily continuous, population, geologic formations and income for instance. Grids are also useful for simply indicating locations of geographic features, and have most often been exploited historically for that purpose.

The grid system is probably the easiest method for determining a location on the surface of the earth.There are two types of grids we like to employ, each has strengths and weaknesses. The first is the most common, the Cartesian Coordinate System.

Cartesian Coordinate System

If you have ever played the board game Battleship, then you understand Cartesian Coordinates. With Cartesian system, each cell in the grid is referenced by a pair of X and Y coordinates and measured using linear distance. Cartesian Coordinates are useful only when tied to some geographic unit, (a datum) usually indicated by the (0,0) X/Y coordinates may be arbitrarily located prior to developing the grid, or fixed to a point of cultural or geographic significance.

Ordinarily, the grid is broken into 4 quadrants, with Quadrant 1 holding all positive coordinates. Aside from being easy to read, the usefulness of this gird is increased since we can keep all coordinates positive by setting the datum ahead of time. The Universal Transverse Mercator grid uses this technique to remove the need for negative x and y coordinates, but that is for another entry.

Cartesian Coordinate System
The Cartesian Coordinate System

When using a grid of this nature, we would usually indicate the size of each cell in specific squared units. You might use a 1 square mile grid over a city, or as I utilized years ago-1 square meter grid cells over an archaeological site. In each of these examples, each cell is precisely 1 mile or 1 meter squared. This system works well for small areas of no more than a few dozen miles, but any more and we need to take into consideration the curvature of the earth.

To consider the nature of the curvature of the earth, we need to set a projection that would compensate for the distortion in each grid cell size as you moved north and south. For larger areas, even an equidistant projection would not suffice for a national or continental grid of visually equidistant cells. We need a spatial reference system to which all measurements can relate, the Geographic Coordinate System (GCS) must be employed.

Geographic Coordinate System (GCS)

The GCS is a spherical coordinate system that represents position with angles instead of distances. The system uses a network of latitude and longitude lines or graticule to fix surface positions of features or routes. Unlike the Cartesian Coordinate System, the GCS relies on angular measurements from two reference points, as opposed to linear distance from a single reference point. There are two primary reference points of the GCS: North/South Poles and the Equator.
The Geographic Coordinate System

Illustrated above, you notice the angular measurements start from the center of the earth and extend to the surface from two imaginary lines, the Equator and the Prime Meridian. Those two imaginary lines form the datum for the grid (see image below).
Key Great and Small Circles

Starting at zero, any point above the equator is positive, below is negative. This line is fairly easy to understand since it marks widest point of the earth along its rotation, it's in the middle. The angular distance is measured starting at the equator (0˚) and moving to the poles at 90˚ for the north pole and -90˚ for the south pole. Lines of latitude mark the degrees moving away from the equator. These latitude lines are spaced roughly 60 nautical miles apart (69 statute miles) or 111 kilometers.

Prime Meridian

The prime meridian is an arbitrary demarcation of a line that cleanly divides the earth into two equal east/west hemispheres; the line opposite the prime meridian is known as the International Date Line. The position of this prime meridian passes through Greenwich, England for no other reason than England was the prevailing naval power at the time the line was set in 1851. To the east of the prime meridian, all coordinates are positive; to the west the coordinates are negative. Unlike the equator, there are 180˚ from the prime meridian to the International Date Line. Lines of longitude mark the degrees moving away from the prime meridian. The distance between these lines start at roughly 60 nautical miles at the equator, but gradually move closer together until meeting at the poles.

Like a clock, with 360 hours

The coordinates in a GCS are measured in Degrees/MInutes/Seconds, touched on in the illustrations above. When measuring from the equator, the degrees can be anywhere between -90 and 90; from the prime meridian you have -180˚ to 180˚ which are the same line, roughly the international date line. Each degree is broken down into minutes; minutes are further broken into seconds. Just like a clock, there are 60 minutes in the degree and 60 seconds per minute. These coordinates may be denoted in several ways, two of the most popular are Degree/Minutes/Seconds (DMS) and Decimal Degrees (DD).

Often, these GCS coordinates are expressed much like the Catesian Coordinate System. This can be problematic as they do not represent linear distance. However, for purposes of arithmetical computation, they may be treated as cartesian though they represent an angular measurement from the center of the earth expressed on the surface.

DMS is formatted: 42˚ 22' 06". This is the oldest format and historically the most common. Many GPS unists will still display this format since it is "human readable" and makes sense to us. However, it is not readily machine readable for GIS software. Software requires the DD format. Using the example above, the equivalent DD format is: 42.36824. In the decimal format, the GIS can readily digest it, interpret the coordinate as a point and plot it on your map. All coordinates must be in DD format to plot in AWhere as well, whether read in from a spreadsheet or manually entered using the point editor add-in. There are many web conversion tools available, or you may make the conversion or manually using the following formula:
Degrees + (minutes / 60) + (seconds / 3600) = Decimal Degree

42 + 22/60 + 6/3600

42 + .366 + .00166

42.36832 (which is a little off from the web tool due to decimal precision)

Which is best?

That depends solely on what the purpose of the grid is. Using a GCS grid is a better option for global data as you can easily and accurately visualize multiple locations around the world for comparison. The GCS makes no claims at showing equal area grid cells. For smaller projects, over part of a city or small region, a Cartesian grid would suffice; they are easy to set up and you can compare areas and linear distance more easily across the surface. Cartesian grids are less flexible than the GCS, however. There are hybrid grids such as the Universal Transverse Mercator and the State Planes, each set their datums in such as way so as to allow for only positive coordinates, but they are designed for specific areas and are best discussed in a future article.

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