cee 795 water resources modeling and gis learning objectives: demonstrate the concepts of spatial...
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CEE 795Water Resources Modeling and GIS
Learning Objectives:• Demonstrate the concepts of spatial fields as a way to represent geographical
information• Use raster and vector representations of spatial fields• Perform raster calculations in hydrology• Perform raster based watershed delineation from digital elevation models
Handouts: Assignments:Exercise #3
Lecture 4: Spatial Fields and DEM Processing
(some material from Dr. David Maidment, University of Texas and Dr. David Tarboton, Utah State University)
February 6, 2006
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Vector and Raster Representation of Spatial Fields
Vector Raster
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Numerical representation of a spatial surface (field)
Grid
TIN Contour and flowline
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Six approximate representations of a field used in GIS
Regularly spaced sample points Irregularly spaced sample points Rectangular Cells
Irregularly shaped polygons Triangulated Irregular Network (TIN) Polylines/Contours
from Longley, P. A., M. F. Goodchild, D. J. Maguire and D. W. Rind, (2001), Geographic Information Systems and Science, Wiley, 454 p.
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A grid defines geographic space as a matrix of identically-sized square cells. Each cell holds a
numeric value that measures a geographic attribute (like elevation) for that unit of space.
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The grid data structure
• Grid size is defined by extent, spacing and no data value information– Number of rows, number of column– Cell sizes (X and Y) – Top, left , bottom and right coordinates
• Grid values – Real (floating decimal point)– Integer (may have associated attribute table)
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Definition of a Grid
Numberof
rows
Number of Columns(X,Y)
Cell size
NODATA cell
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Points as Cells
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Line as a Sequence of Cells
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Polygon as a Zone of Cells
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NODATA Cells
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Cell Networks
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Grid Zones
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Floating Point Grids
Continuous data surfaces using floating point or decimal numbers
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Value attribute table for categorical (integer) grid data
Attributes of grid zones
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Raster Sampling
from Michael F. Goodchild. (1997) Rasters, NCGIA Core Curriculum in GIScience, http://www.ncgia.ucsb.edu/giscc/units/u055/u055.html, posted October 23, 1997
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Raster Generalization
Central point ruleLargest share rule
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Raster Calculator
Cell by cell evaluation of mathematical functions
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Example
Precipitation-
Losses (Evaporation,
Infiltration)=
Runoff5 22 3
2 43 3
7 65 6
-
=
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Runoff generation processesInfiltration excess overland flowaka Horton overland flow
Partial area infiltration excess overland flow
Saturation excess overland flow
PP
P
qrqs
qo
PP
P
qo
f
PP
P
qo
f
f
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Runoff generation at a point depends on
• Rainfall intensity or amount
• Antecedent conditions
• Soils and vegetation
• Depth to water table (topography)
• Time scale of interest
These vary spatially which suggests a spatial geographic approach to runoff estimation
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Modeling infiltration excessEmpirical, e.g. SCS Curve Number
method
Runoff from SCS Curve Number
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12
Precipitation (in)
Dir
ect
Ru
no
ff (
in)
CN=10090 80
70
60
50
40
3020
S8.0P
)S2.0P(R
2
10CN
1000S
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Cell based discharge mapping flow accumulation of generated runoff
Radar Precipitation grid
Soil and land use grid
Runoff grid from raster calculator operations implementing runoff generation formula’s
Accumulation of runoff within watersheds
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Raster calculation – some subtleties
Analysis extent
+
=
Analysis cell size
Analysis mask
Resampling or interpolation (and reprojection) of inputs to target extent, cell size, and projection within region defined by analysis mask
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Spatial Snowmelt Raster Calculation ExampleThe grids below depict initial snow depth and average temperature over a day for an area.
40 50 55
42 47 43
42 44 41
100 m
100
m
(a) Initial snow depth (cm)
4 6
2 4
150 m
150
m
(b) Temperature (oC)
One way to calculate decrease in snow depth due to melt is to use a temperature index model that uses the formula
TmDD oldnew
Here Dold and Dnew give the snow depth at the beginning and end of a time step, T gives the temperature and m is a melt factor. Assume melt factor m = 0.5 cm/OC/day. Calculate the snow depth at the end of the day.
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Snow Depth and Temperature
4
2 4
640 50 55
4347
414442
42
Initial Snow Depth (cm) Temperature (º C)
100 m
100
m
150 m
150
m
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New depth calculation using Raster Calculator
[snow100m] - 0.5 * [temp150m]
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The Result
38 52
41 39
• Outputs are on 150 m grid.
• How were values obtained ?
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Nearest Neighbor Resampling with Cellsize Maximum of Inputs
40 50 55
4347
414442
42
100
m
4
2 4
6150
m
40-0.5*4 = 38
55-0.5*6 = 5238 52
41 39
42-0.5*2 = 41
41-0.5*4 = 39
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Scale issues in interpretation of measurements and modeling results
The scale triplet
From: Blöschl, G., (1996), Scale and Scaling in Hydrology, Habilitationsschrift, Weiner Mitteilungen Wasser Abwasser Gewasser, Wien, 346 p.
a) Extent b) Spacing c) Support
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From: Blöschl, G., (1996), Scale and Scaling in Hydrology, Habilitationsschrift, Weiner Mitteilungen Wasser Abwasser Gewasser, Wien, 346 p.
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Spatial analyst options for controlling the scale of the output
Extent Spacing & Support
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Raster Calculator “Evaluation” of temp150
4 6
2 4
6
2
4
44
4 6
Nearest neighbor to the E and S has been resampled to obtain a 100 m temperature grid.
2 4
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Raster calculation with options set to 100 m grid
• Outputs are on 100 m grid as desired.
• How were these values obtained ?
38 52
41 39
47
41
42
4145
[snow100m] - 0.5 * [temp150m]
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100 m cell size raster calculation
40 50 55
4347
414442
42
100
m15
0 m
40-0.5*4 = 38
42-0.5*2 = 4138 52
41 39
43-0.5*4 = 41
41-0.5*4 = 39
47
41 45 41
42
50-0.5*6 = 47
55-0.5*6 = 52
47-0.5*4 = 45
42-0.5*2 = 41
44-0.5*4 = 42
Nearest neighbor values resampled to 100 m grid used in raster calculation
4
6
2 4
6
2
4
44
4
6
2 4
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What did we learn?
• Spatial analyst automatically uses nearest neighbor resampling
• The scale (extent and cell size) can be set under options
• What if we want to use some other form of interpolation?
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InterpolationEstimate values between known values.
A set of spatial analyst functions that predict values for a surface from a limited number of sample points creating a continuous raster.
Apparent improvement in resolution may not be justified
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Interpolation methods
• Nearest neighbor• Inverse distance
weight• Bilinear
interpolation• Kriging (best linear
unbiased estimator)• Spline
ii
zr
1z
)dyc)(bxa(z
iizwz
ii eei yxcz
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Nearest Neighbor “Thiessen” Polygon Interpolation Spline Interpolation
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Spatial Surfaces used in Hydrology
Elevation Surface — the ground surface elevation at each point
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3-D detail of the Tongue river at the WY/Mont border from LIDAR.
Roberto GutierrezUniversity of Texas at Austin
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Topographic Slope
• Defined or represented by one of the following– Surface derivative z (dz/dx, dz/dy)
– Vector with x and y components (Sx, Sy)
– Vector with magnitude (slope) and direction (aspect) (S, )
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Standard Slope Function
a b c
d e f
g h i
cingx_mesh_spa * 8
i) 2f (c - g) 2d (a
dx
dz
acing y_mesh_sp* 8
i) 2h (g - c) 2b (a
dy
dz
22
dy
dz
dx
dz
run
rise
dy/dz
dx/dzatan
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Aspect – the steepest downslope direction
dx
dz
dy
dz
dy/dz
dx/dzatan
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Example30
80 74 63
69 67 56
60 52 48
a b c
d e f
g h i229.0
30*8
)2456*263()6069*280(
cingx_mesh_spa * 8
i) 2f (c - g) 2d (a
dx
dz
329.030*8
)6374*280()4852*260(
acing y_mesh_sp* 8
c) 2b (a -i) 2h (g
dy
dz
o8.21)401.0(atan
o8.34329.0
229.0atanAspect
o
o
2.145
180
145.2o
401.0
329.0229.0Slope 22
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80 74 63
69 67 56
60 52 48
80 74 63
69 67 56
60 52 48
30
45.0230
4867
50.0
30
5267
Slope:
Hydrologic Slope - Direction of Steepest Descent
30
ArcHydro Page 70
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32
16
8
64
4
128
1
2
Eight Direction Pour Point Model
ESRI Direction encoding
ArcHydro Page 69
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?
Limitation due to 8 grid directions.
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Length on Meridians and Parallels
0 N
30 N
Re
Re
RR
A
BC
(Lat, Long) = (, )
Length on a Meridian:AB = Re (same for all latitudes)
Length on a Parallel:CD = R Re Cos(varies with latitude)
D
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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 = 3.1416/180 = 0.0175 radians
• For the meridian, L = Re km
• For the parallel, L = Re CosCoskm• Parallels converge as poles are approached
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Summary Concepts
• Grid (raster) data structures represent surfaces as an array of grid cells
• Raster calculation involves algebraic like operations on grids
• Interpolation and Generalization is an inherent part of the raster data representation
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Summary Concepts (2)
• The elevation surface represented by a grid digital elevation model is used to derive surfaces representing other hydrologic variables of interest such as– Slope– Drainage area (more details in later classes)– Watersheds and channel networks (more details
in later classes)
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Summary Concepts (3)
• The eight direction pour point model approximates the surface flow using eight discrete grid directions.