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

3. 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

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 = /180 = radians
For the meridian, DL = Re Df = 6370 * = 111 km
For the parallel, DL = Re Dl Cos f
= 6370 * * 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
-120°
-90 °
-60 °

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

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. 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!!

14. Polylines and Edges

15. 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

16. 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”

17. Flow to a sink

18. Eight Direction Pour Point Model32 16 8 64 4
128 1 2
Water flows in the direction of steepest descent

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

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

21. Contributing Area Grid1 4 3 12 2 16 25 6 1 4 3 12 2 16 6 25
Drainage area threshold > 5 Cells

22. Delineation of Streams and Watersheds on a DEM

23. Stream Segments 3 2 11 1 15 5 24

24. Stream Segments in a Cell Network1 3 2 4 5 6 5 5

25. Watershed Outlet

26. Watershed Draining to This Outlet

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

28. 1000 Cell Threshold Exceeded at Stream Junction
510
989
1504 (>1000)

29. Subwatersheds for Stream Segments
Same Cell Value

30. Vectorized Streams Linked Using Grid Code to Cell Equivalents

31. Delineated Subwatersheds and Stream Networks

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

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

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

35. 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.

36. 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.