Projection  

MAP PROJECTIONS and COORDINATE SYSTEMS

In order to represent the surface of the earth on a flat piece of paper, the map area is projected onto the paper.  There are many different types of projections, each with its own strengths and weaknesses. GTM topographic maps use either a Lambert Conformal Conic or a UTM (Universal Transverse Mercator) projection both of which are known to preserve shape. (Individual GTM map projections can be found here).

LATITUDE LONGITUDE

The Geographic Coordinate System, one of the most commonly known coordinate systems, uses degrees of latitude and longitude to describe a location on the earth’s surface. Lines of latitude run parallel to the equator and divide the earth into 180 equal portions from north to south (or south to north). The reference latitude is the equator and each hemisphere is divided into ninety equal portions, each representing one degree of latitude.

In the Northern Hemisphere degrees of latitude are measured from zero at the equator to ninety at the north pole. In the Southern Hemisphere degrees of latitude are measured from zero at the equator to ninety degrees at the south pole.    To simplify the digitization of maps, degrees of latitude in the southern hemisphere are often assigned negative values (0 to -90°).  Wherever you are on the earth’s surface, the distance between lines of latitude is the same (60 nautical miles,), so they conform to the uniform grid criterion assigned to a useful grid system.




To be truly useful, a map grid must divided into small enough sections that they can be used to describe with an acceptable level of accuracy the location of a point on the map.  To accomplish this, degrees are divided into minutes (') and seconds ("). There are sixty minutes in a degree, and sixty seconds in a minute (3600 seconds in a degree).  At the equator, one second of latitude or longitude = 101.3 feet. For Example, the summit of Mt Rainer has a latitude of 46° 51' N and a longitude of 121° 46' W.



An alternative method of notation in the geographic coordinate system, often used for many GIS/GPS applications (Geographic Information Systems, Global Positioning System), is the decimal degree system.  In the decimal degree system the major (degree) units are the same, but rather than using minutes and seconds, smaller increments are represented as a percentage (decimal) of a degree.

The decimals can be carried out to four places, resulting in a notation of DD.XXXX, DDD.XXX.  When using four decimal places, the decimal degree system is accurate to within ± 36.5 feet (11.12 m). For Example, the summit of Mt Rainer in decimal degrees has a latitude of 46.852947N and a longitude of -121.760424W.

The GTM 15 Minutes Series cover 15 Minutes of Latitude North/South and15 minutes of longitude East/West.Latitude longitude- tics and points are noted on all GTM.


UNIVERSAL TRANSVERSE MERCATOR - UTM

UTM Projections are used on GTM because they preserve shape, their grids are the easiest to use with a GPS and allow precise measurements in meters to within 1 meter.

What a transverse mercator projection does, is orient the ‘equator’ north-south (through the poles), thus providing a north-south oriented swath of little distortion. By changing slightly the orientation of the cylinder onto which the map is projected, successive swaths of relatively undistorted regions can be created. 

Each of these swaths is called a UTM zone and is six degrees of longitude wide. The first zone begins at the International Date Line (180°, using the geographic coordinate system). The zones are numbered from west to east, so zone 2 begins at 174°W and extends to 168°W. The last zone (zone 60) begins at 174°E and extends to the International Date Line.

The zones are then further subdivided into an eastern and western half by drawing a line, representing a transverse mercator projection, down the middle of the zone. This line is known as the ‘central meridian’ and is the only line within the zone that can be drawn between the poles and be perpendicular to the equator (in other words, it is the new ‘equator’ for the projection and suffers the least amount of distortion).  For this reason, vertical grid lines in the UTM system are oriented parallel to the central meridian.  The central meridian is also used in setting up the origin for the grid system.



Any point can then be described by its distance east of the origin (its ‘easting’ value).  By definition the Central Meridian is assigned a false easting of 500,000 meters. Any easting value greater than 500,000 meters indicates a point east of the central meridian. Any easting value less than 500,000 meters indicates a point west of the central meridian. Distances (and locations) in the UTM system are measured in meters, and each UTM zone has its own origin for east-west measurements.

To eliminate the necessity for using negative numbers to describe a location, the east-west origin is placed 500,000 meters west of the central meridian. This is referred to as the zone’s ‘false origin’.  The zone doesn't extend all the way to the false origin.

UTM coordinates are typically given with the zone first, then the Easting, then the Northing.  So, in UTM coordinates, the summit of Mount Rainer is located in Zone 10 at E, The UTM system may seem a difficult to understand at first, once one become familiar with it, it becomes an extremely fast and efficient means of finding exact locations and approximating locations on a GTM map especially with a GPS.


LAMBERT CONFORMAL CONIC

The Lambert Conformal Conic projection superimposes a cone over the sphere of the Earth, with two reference parallels secant to the globe and intersecting it. This minimizes distortion from projecting a three dimensional surface to a two-dimensional surface. Distortion is least along the standard parallels, and increases further from the chosen parallels.

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