Review for Midterm Exam 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 120 W 60 W 90 W 0 N

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

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 = Re Df = 6370 * 0.0175 = 111 km For the parallel, DL = Re Dl Cos f = 6370 * 0.0175 * Cos 30 = 96.5 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 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)

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

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

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 (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

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

Edges and Junctions Simple feature classes: points and lines Network feature classes: junctions and edges Edges can be Simple: one attribute record for a single edge Complex: one attribute record for several edges in a linear sequence A single edge cannot be branched No!!

Polylines and Edges

Junctions Junctions exist at all points where edges join If necessary they are added during network building (generic junctions) Junctions can be placed on the interior of an edge e.g. stream gage Any number of point feature classes can be built into junctions on a single network

Connectivity Table p. 132 of Modeling our World J125 Junction Adjacent Junction and Edge J123 J124, E1 J124 J123, E1 J125, E2 J126, E3 J125 J124, E2 J126 J124, E3 E2 J124 E3 E1 J123 J126 This is the “Logical Network”

Flow to a sink

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

Flow Direction Grid 32 16 8 64 4 128 1 2

Cell to Cell Grid Network Through the Landscape Stream cell

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

Delineation of Streams and Watersheds on a DEM

Stream Segments 3 2 11 1 15 5 24

Stream Segments in a Cell Network 1 3 2 4 5 6 5 5

Watershed Outlet

Watershed Draining to This Outlet

Watershed and Drainage Paths Delineated from 30m DEM Automated method is more consistent than hand delineation

1000 Cell Threshold Exceeded at Stream Junction 510 989 1504 (>1000)

Subwatersheds for Stream Segments Same Cell Value

Vectorized Streams Linked Using Grid Code to Cell Equivalents

Delineated Subwatersheds and Stream Networks

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

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

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

Flow On a Triangle 2.0 13.0 9.0 10.0 5.0 Any three XYZ points that make up a triangle form a planar surface. Contouring a triangle is straightforward since we only need to linearly interpolate along each edge to discover where a specified contour interval lies (such as 5.0 and 10.0 in this figure). Flow will always be in the direction of steepest descent, or perpendicular to the contours.

Flow On a TIN Flow can be traced across a TIN (series of triangles) by repeatedly tracing flow across individual triangles as explained in the previous slide. In this example flow begins at the point marked with an X. The path of steepest descent is determined from the planar surface defined by the triangle and is traced until it intersects with one of the triangle edges. From the intersection point flow is traced across the adjacent triangle in a similar manner. Flow may also follow a triangle edge if the two adjacent triangles slope together as is the case with the last two flow path segments in this slide.