book08coords - Weather Observation and Analysis John...

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Weather Observation and Analysis John Nielsen-Gammon Course Notes These course notes are copyrighted. If you are presently registered for ATMO 251 at Texas A&M University, permission is hereby granted to download and print these course notes for your personal use. If you are not registered for ATMO 251, you may view these course notes, but you may not download or print them without the permission of the author. Redistribution of these course notes, whether done freely or for profit, is explicitly prohibited without the written permission of the author. Chapter 8. COORDINATE SYSTEMS 8.1 Conventional Coordinate Systems In all of your math classes up to this point, you have worked mostly in what are called orthogonal coordinate systems. Orthogonal here means that each coordinate axis is perpendicular to every other coordinate axis. The simplest such example is Cartesian coordinates. In three- dimensional Cartesian coordinates, the three coordinate axes perfectly ATMO 251 Chapter 8 page 1 of 15
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straight and exactly perpendicular to each other. Each axis extends to infinity. The horizontal coordinates are labeled x and y , and the vertical coordinate is labeled z . The second most common coordinate system is polar coordinates (in two dimensions) or spherical coordinates (in three dimensions). These coordinates are orthogonal everywhere except at the origin, where directions are undefined. In polar or spherical coordinates, only the radial axis is straight. Unlike Cartesian coordinates, where the orientation of the axes is the same throughout the known universe, polar and spherical coordinates are oriented differently at different locations. The most common use of spherical coordinates in meteorology is with the Earth itself. Longitude corresponds to the azimuthal angle in spherical coordinates, with the origin defined arbitrarily as the Greenwich Meridian. Latitude corresponds to the elevation angle, with the origin defined as the Equator. Longitudes West are equivalent to negative azimuthal angles. ATMO 251 Chapter 8 page 2 of 15
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ATMO 251 Chapter 8 page 3 of 15
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The next most common use of spherical coordinates in meteorology is with radar data. The coordinate system origin is defined as the radar transmitter location, the elevation angle is zero along a direction parallel to the horizontal, and the azimuthal angle is defined to be similar to compass headings, with a zero azimuth corresponding to a beam pointing toward the north, a 90 degree azimuth corresponding to a beam pointing toward the east, etc. The two different applications of spherical coordinates, Earth and radar, illustrate the arbitrary nature of coordinate systems in general. When applied to the Earth, the center of the Earth is the origin of the coordinate system. When applied to radar data, the radar location is the origin of the coordinate system. In practice, one can define the origin of a coordinate system to be anywhere.
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This note was uploaded on 04/02/2008 for the course ATMO 251-501/50 taught by Professor Alcorn during the Fall '07 term at Texas A&M.

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book08coords - Weather Observation and Analysis John...

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