Spatial Fields in GIS and Hydrology

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Spatial Fields in GIS and Hydrology

• David G. Tarboton
• dtarb_at_cc.usu.edu

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

• The concepts of spatial fields as a way to
  represent geographical information
• Raster and vector representations of spatial
  fields
• Raster based watershed delineation from digital
  elevation models
• Reading ArcHydro Chapter 4

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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
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Raster and Vector Data
Raster data are described by a cell grid, one
value per cell
Vector
Raster
Point
Line
Zone of cells
Polygon
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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

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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
Cell size
Number of rows
NODATA cell
(X,Y)
Number of Columns
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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.ucs
b.edu/giscc/units/u055/u055.html, posted October
23, 1997
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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.
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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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Raster Generalization
Central point rule
Largest share rule
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Spatial Surfaces used in Hydrology

• Elevation Surface the ground surface elevation
  at each point

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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
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Aspect the steepest downslope direction
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Example
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Hydrologic Slope - Direction of Steepest Descent
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Slope
ArcHydro Page 70
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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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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)
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The D? Algorithm
?
If ?1 is not fit within the triangle the angle is
chosen along the steepest edge or diagonal
resulting in a slope and direction equivalent to
D8
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D8 Example
eo
e8
e7
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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

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Watershed Delineation by Hand Digitizing
Watershed divide
Drainage direction
Outlet
ArcHydro Page 57
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DEM Elevations
720
720
Contours
740
720
700
680
680
700
720
740
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Flow Direction Grid
ArcHydro Page 71
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Flow Direction Grid
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Grid Network
ArcHydro Page 71
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Contributing Area Grid
TauDEM convention. The area draining each grid
cell including the grid cell itself.
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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
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Link to Grid calculator
ArcHydro Page 72
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Flow Accumulation gt 5 Cell Threshold
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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
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Streams with 200 cell Threshold(gt18 hectares or
13.5 acres drainage area)
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Watershed Outlet
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Watershed Draining to This Outlet
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Watershed and Drainage Paths Delineated from 30m
DEM
Automated method is more consistent than hand
delineation
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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

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(No Transcript)
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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


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AGREE Elevation Grid Modification Methodology
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Stream Segments
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Stream Links in a Cell Network
5
5
ArcHydro Page 74
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Stream links grid for the San Marcos subbasin
201
172
202
203
206
204
Each link has a unique identifying number
209
ArcHydro Page 74
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Catchments for Stream Links
Same Cell Value
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Vectorized Streams Linked Using Grid Code to Cell
Equivalents
Vector Streams
Grid Streams
ArcHydro Page 75
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DrainageLines are drawn through the centers of
cells on the stream links. DrainagePoints are
located at the centers of the outlet cells of the
catchments
ArcHydro Page 75
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Catchments, DrainageLines and DrainagePoints of
the San Marcos basin
ArcHydro Page 75
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Adjoint catchment the remaining upstream area
draining to a catchment outlet.
ArcHydro Page 77
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Catchment, Watershed, Subwatershed.
Subwatersheds
Catchments
Watershed
Watershed outlet points may lie within the
interior of a catchment, e.g. at a USGS
stream-gaging site.
ArcHydro Page 76
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Summary Concepts

• Grid (raster) data structures represent surfaces
  as an array of grid cells
• 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
• Watersheds and channel networks

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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.