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GIS in Water Resources

GIS in Water Resources. Review for Midterm Exam. Latitude and Longitude in North America. Austin: (30 ° N, 98 ° W) Logan: (42 ° N, 112 ° W). 60 N. 30 N. 60 W. 120 W. 90 W. 0 N. Length on Meridians and Parallels. (Lat, Long) = ( f , l ). Length on a Meridian: AB = R e Df

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GIS in Water Resources

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  1. GIS in Water Resources Review for Midterm Exam

  2. Latitude and Longitude in North America Austin: (30°N, 98°W) Logan: (42°N, 112°W) 60 N 30 N 60 W 120 W 90 W 0 N

  3. Length on Meridians and Parallels (Lat, Long) = (f, l) Length on a Meridian: AB = ReDf (same for all latitudes) R Dl D R 30 N C B Re Df 0 N Re Length on a Parallel: CD = R Dl = ReDl Cos f (varies with latitude) A

  4. Example: What is the length of a 1º increment along • on a meridian and on a parallel at 30N, 90W? • Radius of the earth = 6370 km. • Solution: • A 1º angle has first to be converted to radians • p radians = 180 º, so 1º = p/180 = 3.1416/180 = 0.0175 radians • For the meridian, DL = ReDf = 6370 * 0.0175 = 111 km • For the parallel, DL = ReDl Cos f • = 6370 * 0.0175 * Cos 30 • = 96.5 km • Parallels converge as poles are approached

  5. Horizontal Earth Datums • An earth datum is defined by an ellipse and an axis of rotation • NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non geocentric axis of rotation • NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation • WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83

  6. Vertical Earth Datums • A vertical datum defines elevation, z • NGVD29 (National Geodetic Vertical Datum of 1929) • NAVD88 (North American Vertical Datum of 1988) • takes into account a map of gravity anomalies between the ellipsoid and the geoid

  7. Coordinate System A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin Y X Origin (xo,yo) (fo,lo)

  8. Universal Transverse Mercator • Uses the Transverse Mercator projection • Each zone has a Central Meridian(lo), zones are 6° wide, and go from pole to pole • 60 zones cover the earth from East to West • Reference Latitude (fo), is the equator • (Xshift, Yshift) = (xo,yo) = (500000, 0) in the Northern Hemisphere, units are meters

  9. UTM Zone 14 -99° -102° -96° 6° Origin Equator -90 ° -120° -60 °

  10. Defined for a feature dataset in ArcCatalog Coordinate System Projected Geographic X/Y Domain Z Domain M Domain ArcInfo 8 Reference Frames

  11. X/Y Domain (Max X, Max Y) Long integer max value of 231 = 2,147,483,645 (Min X, Min Y) Maximum resolution of a point = Map Units / Precision e.g. map units = meters, precision = 1000, then maximum resolution = 1 meter/1000 = 1 mm on the ground

  12. Network Definition • A network is a set of edges and junctions that are topologically connected to each other.

  13. Flow to a sink

  14. 32 64 128 16 1 8 4 2 Eight Direction Pour Point Model Water flows in the direction of steepest descent

  15. 32 64 128 16 1 8 4 2 Flow Direction Grid

  16. Stream cell Cell to Cell Grid Network Through the Landscape

  17. 1 1 1 1 1 1 1 1 1 1 1 4 3 3 1 4 3 1 1 3 1 1 2 1 1 12 1 2 1 12 1 1 1 2 16 1 1 2 1 16 2 1 3 6 25 3 6 1 2 25 Contributing Area Grid Drainage area threshold > 5 Cells

  18. Delineation ofStreams and Watersheds on a DEM

  19. Hortons Laws: Strahler system for stream ordering 1 3 • most upstream is order 1 • when two streams of a order i join, a stream of order i+1 is created • when a stream of order i joins a stream of order i+1, stream order is unaltered 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1 1 1 1

  20. A Mesh of Triangles Triangle is the only polygon that is always planar in 3-D Lines Surfaces Points

  21. Tin Triangles in 3-D (x3, y3, z3) (x1, y1, z1) (x2, y2, z2) z y Projection in (x,y) plane x

  22. Delauney Triangulation Maximize the minimum interior angle of triangles No point lies within the circumcircle of a triangle Yes No

  23. 13.0 10.0 9.0 5.0 2.0 Flow On a Triangle

  24. Flow On a TIN

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