Spatial Fields in GIS and Hydrology

1
Spatial Fields in GIS and Hydrology

• David G. Tarboton
• dtarb_at_cc.usu.edu

http//www.engineering.usu.edu/dtarb
2
Learning Objectives

• The concepts of spatial fields as a way to
  represent geographical information
• Raster and vector representations of spatial
  fields
• Raster calculation concepts and their use in
  hydrology
• Raster based watershed delineation from digital
  elevation models

3
Two fundamental ways of representing geography
are discrete objects and fields.
The discrete object view represents the real
world as objects with well defined boundaries in
empty space.
Points
Lines
Polygons
The field view represents the real world as a
finite number of variables, each one defined at
each possible position.
Continuous surface
4
Raster and Vector Data
Raster data are described by a cell grid, one
value per cell
Vector
Raster
Point
Line
Zone of cells
Polygon
5
Raster and Vector are two methods of representing
geographic data in GIS

• Both represent different ways to encode and
  generalize geographic phenomena
• Both can be used to code both fields and discrete
  objects
• In practice a strong association between raster
  and fields and vector and discrete objects

6
Vector and Raster Representation of Spatial Fields
Vector
Raster
7
Numerical representation of a spatial surface
(field)
Grid
TIN
Contour and flowline
8
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.
9
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.
10
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)

11
Definition of a Grid
Cell size
Number of rows
NODATA cell
(X,Y)
Number of Columns
12
Points as Cells
13
Line as a Sequence of Cells
14
Polygon as a Zone of Cells
15
NODATA Cells
16
Cell Networks
17
Grid Zones
18
Floating Point Grids
Continuous data surfaces using floating point or
decimal numbers
19
Value attribute table for categorical (integer)
grid data
Attributes of grid zones
20
Raster Sampling
from Michael F. Goodchild. (1997) Rasters, NCGIA
Core Curriculum in GIScience, http//www.ncgia.ucs
b.edu/giscc/units/u055/u055.html, posted October
23, 1997
21
Scale issues in the interpretation of data
The scale triplet
a) Extent
b) Spacing
c) Support
From Blöschl, G., (1996), Scale and Scaling in
Hydrology, Habilitationsschrift, Weiner
Mitteilungen Wasser Abwasser Gewasser, Wien, 346
p.
22
From Blöschl, G., (1996), Scale and Scaling in
Hydrology, Habilitationsschrift, Weiner
Mitteilungen Wasser Abwasser Gewasser, Wien, 346
p.
23
Raster Generalization
Central point rule
Largest share rule
24
Spatial Surfaces used in Hydrology

• Elevation Surface the ground surface elevation
  at each point

25
Topographic Slope

• Defined or represented by one of the following
• Surface derivative ?z
• Vector with x and y components
• Vector with magnitude (slope) and direction
  (aspect)

26
Standard Slope Function
27
Aspect the steepest downslope direction
28
Hydrologic Slope - Direction of Steepest Descent
30
30
67
56
49
52
48
37
58
55
22
Slope
29
Eight Direction Pour Point Model
ESRI Direction encoding
30
Eight Direction Pour Point Model D8
Band/GRASS/TARDEM Direction encoding
31
Topographic Slope
Limitation imposed by 8 grid directions.

• Topographic Definition Drop/Distance

32
The D? Algorithm
?
Tarboton, D. G., (1997), "A New Method for the
Determination of Flow Directions and Contributing
Areas in Grid Digital Elevation Models," Water
Resources Research, 33(2) 309-319.)
(http//www.engineering.usu.edu/cee/faculty/dtarb/
dinf.pdf)
33
The D? Algorithm
34
Raster Calculator
Cell by cell evaluation of mathematical functions
35
Raster calculation some subtleties
Resampling or interpolation (and reprojection) of
inputs to target extent, cell size, and
projection within region defined by analysis mask


Analysis mask
Analysis cell size
Analysis extent
36
Interpolation

• Estimate 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
37
Interpolation methods

• Nearest neighbor
• Inverse distance weight
• Bilinear interpolation
• Kriging (best linear unbiased estimator)
• Spline

38
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 formulas
Accumulation of runoff within watersheds
39
Runoff generation processes
P
Infiltration excess overland flow aka Horton
overland flow
f
P
qo
P
f
Partial area infiltration excess overland flow
P
P
qo
P
f
P
Saturation excess overland flow
P
qo
P
qr
qs
40
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
41
Modeling infiltration excess

• Empirical, e.g. SCS Curve Number method

CN100
80
90
70
60
50
40
30
20
42
DEM Based Watershed and Stream Network Delineation

• Study Area in West Austin with a USGS 30m DEM
  from a 124,000 scale map
• Eight direction pour point model (flow direction
  and flow accumulation grids)
• Stream network definition
• Watershed delineation

43
Eight Direction Pour Point Model
ESRI Direction encoding
44
Flow Direction Grid
45
Flow Direction Grid
46
Grid Network
47
Contributing Area Grid
TauDEM convention. The area draining each grid
cell.
48
Flow Accumulation Grid. ESRI convention. Area
draining in to a grid cell
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
3
2
0
2
0
0
1
0
0
11
0
1
0
11
0
0
0
1
15
0
0
1
0
15
1
0
2
24
5
2
5
0
1
24
Link to Grid calculator
49
Flow Accumulation gt 5 Cell Threshold
50
Stream Network for 5 cell Threshold Drainage Area
0
0
0
0
0
0
3
2
0
2
0
0
1
0
11
0
0
1
0
15
2
5
0
1
24
51
Streams with 200 cell Threshold(gt18 hectares or
13.5 acres drainage area)
52
Watershed Outlet
53
Watershed Draining to This Outlet
54
Watershed and Drainage Paths Delineated from 30m
DEM
Automated method is more consistent than hand
delineation
55
Filling in the Pits

• DEM creation results in artificial pits in the
  landscape
• A pit is a set of one or more cells which has no
  downstream cells around it
• Unless these pits are filled they become sinks
  and isolate portions of the watershed
• Pit filling is first thing done with a DEM

56
(No Transcript)
57
Burning In the Streams
? Take a mapped stream network and a DEM ? Make a
grid of the streams ? Raise the off-stream DEM
cells by an arbitrary elevation increment ?
Produces "burned in" DEM streams mapped streams


58
AGREE Elevation Grid Modification Methodology
59
Stream Segments
60
Stream Segments in a Cell Network
5
5
61
Subwatersheds for Stream Segments
Same Cell Value
62
Vectorized Streams Linked Using Grid Code to Cell
Equivalents
Vector Streams
Grid Streams
63
Delineated Subwatersheds and Stream Networks
64
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

65
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
• Watersheds and channel networks

66
Summary Concepts (3)

• The eight direction pour point model approximates
  the surface flow using eight discrete grid
  directions.
• The D? vector surface flow model approximates the
  surface flow as a flow vector from each grid cell
  apportioned between down slope grid cells.