SUPPLEMENTAL INFORMATION...IN GREATER DEPTH

Wednesday, 24 August 2016

GEOGRAPHIC COORDINATES AND MAP PROJECTIONS


Meteorologists like other earth scientists routinely use many different graphical representations for their data to permit easier interpretation. One of the graphical representations that we will use frequently in this course is the surface weather map. A weather map is a graphical model that assembles and displays weather data in a manner that can be readily interpreted to determine the location of weather systems, such as low and high-pressure systems and frontal boundaries between air masses. A surface weather map is a two-dimensional representation of the weather conditions that have been observed at the spherical Earth's surface. Like all models, a surface weather map is an approximation of the actual weather conditions. Throughout our study, we will also encounter other weather data depictions such as upper-air weather maps, together with radar charts and satellite images. The national maps and satellite images used in the course have been designed to have similar scales and map projections so as to permit easy comparison.

COORDINATE SYSTEM: LATITUDE AND LONGITUDE

A map needs a coordinate system in order not only to identify a point on a map but also on the Earth's surface. Most maps use a familiar latitude/longitude grid. This geographic coordinate system is based upon the Earth's axis of rotation, which defines the poles and the equator. The North and South Poles are the two points where the spin axis intersects the Earth's surface. The equator is the primary great circle that is along the equatorial plane perpendicular to the axis, making it halfway between the poles. The concept of latitude and longitude as imaginary reference lines on the globe dates to the Egyptian geographer Ptolemy about A.D. 150. Consult a globe and note that lines of latitude called "parallels" run east-west forming circles that parallel the equator, while longitude lines, called "meridians" converge toward the poles.

Latitude describes the angular displacement that a point on the Earth's surface is with respect to the equator, while longitude is the angular displacement that the point would be from some reference meridian, usually taken as the Greenwich Prime Meridian. For centuries, angular measurements describing the geographic coordinates of latitude and longitude were expressed in sexagesimal (base-sixty) units. In this numerical system, which originated with the ancient Sumerians (ca. 2000 BC), each degree is divided into 60 minutes of arc (identified by the symbol ') and each minute is divisible by 60 seconds of arc (identified by the symbol "). Therefore, latitude is expressed in degrees where 1 degree = 60 minutes and 1 minute = 60 seconds. The equator is assigned a latitude of 0 degrees. Latitude increases north and south of the equator reaching 90 degrees N at the North Pole and 90 degrees S at the South Pole. Lines of longitude (also called meridians) run north-south and converge toward the North Pole and South Pole. By convention, the 0-degree longitude line (the prime meridian) runs through Greenwich, England. Longitude is measured in degrees west and east of the prime meridian to 180 degrees. (Again, 1 degree of longitude = 60 minutes and 1 minute = 60 seconds.) We described the importance of the Greenwich Prime Meridian to time keeping in Tuesday's Weather Topic in Greater Depth.

With the development of computers and the widespread use of global positioning system (GPS) technology, geographic coordinates are expressed often in terms of degrees and decimal equivalents. Thus, the latitude of the current Tropic of Cancer, which was 23 degrees 26 minutes 22 seconds, could be expressed as 23.4394 degrees. Furthermore, in most computer usage, the designation of N and S are dropped, with latitudes of locations in the Northern Hemisphere expressed with positive (+) numbers, while Southern Hemisphere locations have negative (-) latitude values. Longitude is sometimes counted in such a way that locations in the Eastern Hemisphere have a positive value, while Western Hemisphere longitudes are negative.

MAP SCALE

By definition, map scale represents the ratio of distance on a map to the actual distance on the Earth's surface. A map of the continental United States used in the course would be considered a small-scale map, since the fractional equivalent of the scale ratio would be relatively small, at approximately 1:25,000,000. Conversely, a map overlay on a local National Weather Service radar image would be called a large-scale map, as the fractional scale ratio would be larger at 1:5,000,000.

Helpful hint: You can estimate distances on a map of the United States by scaling the distance against that along the western boundary of Colorado or Wyoming. The differences between the northern and southern boundaries of each of these two states are four degrees, which would be 444 km or 275 mi.

Since a map is a two-dimensional representation of a three-dimensional sphere, distortions will occur. The distortions will be minimal on a large-scale map, which means that the local radar chart will not show the convergence of the longitude meridians. However, a small-scale map could have considerable distortion, as the distance between meridians change significantly between the southern and northern borders of the United States. Therefore, one would need to become familiar with the various map projections employed to adjust for these distortions.

MAP PROJECTIONS

A map projection is the formal representation of the geographical coordinate system on a two-dimensional piece of paper or computer screen. Depending on the purpose of the map, some distortions are acceptable, while others are not. At least 20 map projections have been developed by cartographers to account for the distortions on small-scale maps.

Let us inspect the blank base map that appears on the course homepage. This map projection, along with all the national maps for the course, would have parallels of latitude that are curved. We will have to imagine these latitude parallels from those that correspond to various state boundaries (such as between Colorado and New Mexico) and the US-Canadian border, which represents the 49th parallel of latitude. These borders appear curved on the map. On the other hand, the meridians of longitude that form several state boundaries would appear as straight lines; take for example the borders between Colorado and Utah. However, these meridians would converge as you would move toward the pole. Our base map is oriented so that the central meridian (oriented in a vertical direction) would be at approximately 105 degrees West, which would run through the Denver (CO) metropolitan area.

Helpful hint: When using this type of map projection, you should orient yourself to the imaginary latitude parallels and longitude meridians in attempting to determine directions.

One additional note is needed for map projections. A link is made from the course homepage to the Hawaiian map links. The weather map for the Pacific Ocean is centered on tropical and subtropical latitudes. Since distortion of the map is small at these latitudes, the map has all meridians remaining parallel. For more on map projections, see USGS Map Projections.


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Prepared by Edward J. Hopkins, Ph.D., email hopkins@aos.wisc.edu
© Copyright, 2016, The American Meteorological Society.