GIS in Water Resources Review for Midterm Exam

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

Length on Meridians and Parallels 0 N 30 N  ReRe ReRe R R A B C  (Lat, Long) = ( , ) Length on a Meridian: AB = R e  (same for all latitudes) Length on a Parallel: CD = R  R e  Cos  (varies with latitude) D

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  radians = 180 º, so 1º =  /180 = /180 = radians For the meridian,  L = R e  km For the parallel,  L = R e  Cos   Cos   km Parallels converge as poles are approached

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

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

Coordinate System (  o, o ) (x o,y o ) X Y Origin A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin

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

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

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

X/Y Domain (Min X, Min Y) (Max X, Max 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 Long integer max value of 2 31 = 2,147,483,645

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

Flow to a sink

Eight Direction Pour Point Model Water flows in the direction of steepest descent

Flow Direction Grid

Cell to Cell Grid Network Through the Landscape Stream cell

Contributing Area Grid Drainage area threshold > 5 Cells

Delineation of Streams and Watersheds on a DEM

Hortons Laws: Strahler system for stream ordering 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

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

Tin Triangles in 3-D (x 3, y 3, z 3 ) (x 1, y 1, z 1 ) (x 2, y 2, z 2 ) x y z Projection in (x,y) plane

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

Flow On a Triangle

Flow On a TIN