watershed and stream network delineation – geomorphological considerations
DESCRIPTION
Watershed and Stream Network Delineation – Geomorphological Considerations. David G. Tarboton [email protected]. http://www.engineering.usu.edu/dtarb. Overview. Review of flow direction, accumulation and watershed delineation Topographic texture and drainage density - PowerPoint PPT PresentationTRANSCRIPT
Watershed and Stream Network Delineation – Geomorphological Considerations
David G. [email protected]
http://www.engineering.usu.edu/dtarb
Overview Review of flow direction, accumulation and
watershed delineation Topographic texture and drainage density Channel network geomorphology and Hortons
Laws Stream drop test to objectively oelect channel
delineation threshold Curvature and slope based methods to
represent variable drainage density The D approach Specialized grid accumulation functions TauDEM software
Elevation Surface — the ground surface elevation at each point
Digital Elevation Model — A digital representation of an elevation surface. Examples include a (square) digital elevation grid, triangular irregular network, set of digital line graph contours or random points.
Digital Elevation Grid — a grid of cells (square or rectangular) in some coordinate system having land surface elevation as the value stored in each cell.
Square Digital Elevation Grid — a common special case of the digital elevation grid
67 56 49
52 48 37
58 55 22
30
67 56 49
52 48 37
58 55 22
30
45.02304867
50.030
5267
Slope:
Direction of Steepest Descent
32
16
8
64
4
128
1
2
Eight Direction Pour Point Model
ESRI Direction encoding
4
5
6
3
7
2
1
8
Eight Direction Pour Point Model D8
Band/GRASS/TARDEM Direction encoding
Grid Network
1 1 111
1
1
1
1
1
1
1
1
14 3 3
12 2
2 163 6
25 2
1 1 11 1
1
1
1
1
1
1
1
1
1
4 3 3
12 1
2
23
16
256
Contributing Area Grid
TauDEM convention includes the area of the grid cell itself.
Programming the calculation of contributing
area
5 1
8 7 6
3 2
4
5 6
5 6
7 7 6
7
7
Direction encoding
2
2
6
3 1
1
1
2
3
1 2 3
Contributing area
1 1 11 1
1
1
1
1
1
1
1
1
1
4 3 3
12 2
2
23
16
256
Contributing Area > 10 Cell Threshold
Watershed Draining to This Outlet
100 grid cell constant support area threshold stream delineation
1 0 1 KilometersConstant support area threshold100 grid cell9 x 10E4 m^2
200 grid cell constant support area based stream delineation
1 0 1 Kilometersconstant support area threshold200 grid cell18 x 10E4 m^2
How to decide on support area threshold ?
AREA 1AREA 1
AREA 2AREA 2
3
12
Why is it important?
Hydrologic processes are different on hillslopes and in channels. It is important to recognize this and account for this in models.
Drainage area can be concentrated or dispersed (specific catchment area) representing concentrated or dispersed flow.
Delineation of Channel Networks and Subwatersheds
500 cell theshold
1000 cell theshold
Examples of differently textured topography
Badlands in Death Valley.from Easterbrook, 1993, p 140.
Coos Bay, Oregon Coast Range. from W. E. Dietrich
Logged Pacific Redwood Forest near Humboldt, California
Canyon Creek, Trinity Alps, Northern California.
Photo D K Hagans
Gently Sloping Convex Landscape
From W. E. Dietrich
Mancos Shale badlands, Utah. From Howard, 1994.
0 1 Kilometers 0 1 KilometersDriftwood, PA Sunland, CA
Topographic Texture and Drainage DensitySame scale, 20 m contour interval Sunland, CADriftwood, PA
Lets look at some geomorphology.• Drainage Density• Horton’s Laws• Slope – Area scaling• Stream Drops
“landscape dissection into distinct valleys is limited by a threshold of channelization that sets a finite scale to the landscape.” (Montgomery and Dietrich, 1992, Science, vol. 255 p. 826.)
Suggestion: One contributing area threshold does not fit all watersheds.
Drainage Density• Dd = L/A
• Hillslope length 1/2Dd
L
BB
Hillslope length = B
A = 2B L
Dd = L/A = 1/2B
B= 1/2Dd
Drainage Density for Different Support Area ThresholdsEPA Reach Files 100 grid cell threshold 1000 grid cell threshold
Drainage Density Versus Contributing Area Threshold
Support Area km^2
Dd
km
^-1
0.05 0.10 0.50 1.00
0.8
2.0
3.0
Dd=0.792 A^(-0.434)
Hortons Laws: Strahler system for stream ordering
1
1
1
1
11
111
1
1
1
1
1
2
2
2
2
3
Bifurcation Ratio
Order
Num
ber o
f Stre
ams
1 2 3 4 5
15
1050Rb = 3.58
Area Ratio
Order
Mea
n S
tream
Are
a
1 2 3 4 5
10^6
5*10
^65*
10^7 Ra = 4.65
Length Ratio
Order
Mea
n S
tream
Len
gth
1 2 3 4 5
900
2000
4000
Rl = 1.91
Slope Ratio
Order
Mea
n S
tream
Slo
pe
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.05
0.10
Rs = 1.7
Slope-Area scaling
Link Contributing Area
Link
Slo
pe
5*10^4 5*10^5 5*10^6 5*10^7
0.00
50.
050
0.50
0S ~ A^-0.35
Data from Reynolds Creek 30 m DEM, 50 grid cell threshold, points, individual links, big dots, bins of size 100
Constant Stream Drops Law
Order
Mea
n S
tream
Dro
p
1.0 1.5 2.0 2.5 3.0 3.5 4.0
5010
050
0Rd = 0.944
Broscoe, A. J., (1959), "Quantitative analysis of longitudinal stream profiles of small watersheds," Office of Naval Research, Project NR 389-042, Technical Report No. 18, Department of Geology, Columbia University, New York.
Stream DropElevation difference between ends of stream
Note that a “Strahler stream” comprises a sequence of links (reaches or segments) of the same order
NodesLinks
Single Stream
Suggestion: Map channel networks from the DEM at the finest resolution consistent with observed channel
network geomorphology ‘laws’.
• Look for statistically significant break in constant stream drop property
• Break in slope versus contributing area relationship
• Physical basis in the form instability theory of Smith and Bretherton (1972), see Tarboton et al. 1992
Statistical Analysis of Stream Drops
Elevation Drop for Streams
0
100
200
300
400
500
600
0 1 2 3 4 5 6
Strahler Order
Dro
p (m
eter
s)
DropMean Drop
T-Test for Difference in Mean Values
72 130
Order 1 Order 2-4Mean X 72.2 Mean Y 130.3Std X 68.8 Std Y 120.8Var X 4740.0 Var Y 14594.5Nx 268 Ny 81
0
T-test checks whether difference in means is large (> 2)when compared to the spread of the data around the mean values
Constant Support Area Threshold
Strahler Stream Order
Stra
hler
Stre
am D
rop
(m)
050
100
150
200
250
1 3 5 1 3 5 1 3 5 1 3 5 1 3 5
Support Area threshold (30 m grid cells) 50 100 200 300 500
Drainage Density (km-1) 3.3 2.3 1.7 1.4 1.2
t statistic for difference between lowest order and higher order drops
-8.8 -5 -1.8 -1.1 -0.72
200 grid cell constant support area based stream delineation
1 0 1 Kilometersconstant support area threshold200 grid cell18 x 10E4 m^2
Local Curvature Computation(Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375)
43
41
48
47
48
47 54
51
54
51 56
58
Contributing area of upwards curved grid cells only
Topsrc01 - 55-2020-5050-30000No Data
50mcont.shp 1 0 1 2 Kilometers
Upward Curved Contributing Area Threshold
Strahler Stream Order
Stra
hler
Stre
am D
rop
(m)
050
100
150
200
250
1 3 5 1 3 5 1 3 5 1 3 5
Upward curved support area threshold (30 m grid cells) 10 15 20 30
Drainage Density (km-1) 2.2 1.8 1.6 1.4
t statistic for difference between lowest order and higher order drops
-4.1 -2.2 -1.3 -1.2
1 0 1 KilometersCurvature basedStream delineation
Curvature based stream delineation
Channel network delineation, other options
4
5
6
3
7
2
1
8
1 1 11 1
1
1
1
1
1
1
1
1
1
4 3 3
12 2
2
23
16
256
Contributing Area
1 1 11 1
1
1
1
1
1
1
1
1
1
2 2 2
3 1
1
12
3
32
Grid Order
1 0 1 Kilometers Grid networkpruned to 4thorder
Grid network pruned to order 4 stream delineation
Slope area threshold (Montgomery and Dietrich, 1992).
Addressing the limitations imposed by 8 grid directions
Topographic Slope
?
Topographic Definition Drop/Distance
Limitation imposed by 8 grid directions.
Flow Direction Field — if the elevation surface is differentiable (except perhaps for countable discontinuities) the horizontal component of the surface normal defines a flow direction field.
Flowdirection.
Steepest directiondownslope
1
2
1
234
5
67
8
Proportion flowing toneighboring grid cell 3is 2/(1+
2)
Proportionflowing toneighboringgrid cell 4 is
1/(1+2)
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)
Specific catchment area a is the upslope area per unit contour length [m2/m m]
Upslope contributing area a
Stream line
Contour line
Unit contourlength b
Contributing area A
Specific Catchment Area a = A/b
Contributing Area using D8
Contributing Area using D
Downslope Influence The contributing area only of points in a target set y. I(x;y) says what the contribution from points y are at each mapped point x.
Useful for example to track where sediment or contaminant moves
1
0
Influence function of grid cell y
0.5 0.5
1 0
0.6 0.4
0
0 0
0
0 0.6 0.4
Grid cell y
Upslope Dependence. Quantifies the amount a point x contributes to the point or zone y. The inverse of the influence function D(x;y) = I(y;x)
Dependence function of grid cells y
0 1 0
0 1 0
0 0.6 0
0.3 0.3 0
0.6 0 0
Grid cells y
Useful for example to track where a contaminant may come from
Decayed Accumulation A decayed accumulation operator DA[.] takes as input a mass loading field m(x) expressed at each grid location as m(i, j) that is assumed to move with the flow field but is subject to first order decay in moving from cell to cell. The output is the accumulated mass at each location DA(x). The accumulation of m at each grid cell can be numerically evaluated
DA[m(x)] = DA(i, j) = m(i, j)2 +
neighborsngcontributikkkkkk )j,i(DA)j,i(dp
Here d(x) = d(i ,j) is a decay multiplier giving the fractional (first order) reduction in mass in moving from grid cell x to the next downslope cell. If travel (or residence) times t(x) associated with flow between cells are available d(x) may be evaluated as ))x(texp( where is a first order decay parameter.
Useful for a tracking contaminant or compound
subject to decay or attenuation
Transport limited accumulationErodability
e.g. E = a0.7 S0.6 Transport Capacity e.g. Tcap = a2 S2
Transport Flux, T
Deposition, D
)T,TEmin(T capinout outin TTEDUseful for modeling erosion and sediment delivery, the spatial
dependence of sediment delivery ratio and contaminant that adheres to sediment
Reverse Accumulation
Reverse accumulation of field weights indicated in red
0 0.8 0.6
0 0.4
0.6
0 1.8 0
0.9 0.9 0
1.8 0 0
1.2
0.8 0.6
Useful for destabilization sensitivity in landslide
hazard assessmentwith Bob Pack
TauDEM Software Functionality Pit removal (standard flooding approach) Flow directions and slope
D8 (standard) D (Tarboton, 1997, WRR 33(2):309) Flat routing (Garbrecht and Martz, 1997, JOH 193:204)
Drainage area (D8 and D) Network and watershed delineation
Support area threshold/channel maintenance coefficient (Standard)
Combined area-slope threshold (Montgomery and Dietrich, 1992, Science, 255:826)
Local curvature based (using Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375)
Threshold/drainage density selection by stream drop analysis (Tarboton et al., 1991, Hyd. Proc. 5(1):81)
Wetness index and distance to streams Specialized grid analysis functions (Upslope influence, Downslope
dependence, Decaying accumulation, Concentration limited accumulation, Downslope accumulation, Transport limited accumulation)
TauDEM in ArcGIS
ESRI binarygrid
ASCII text grid
ESRI gridio API (Spatial analyst)
USU TMDLtoolkit modules(grid, shape, image, dbf, map, mapwin)
TauDEM C++ library Fortran (legacy)components
Standalone command line
applications
C++ COM DLL interface
Visual Basic GUI
application
Visual Basic ESRI ArcGIS 8.1
Toolbar
Vector shape files
Data formats
Available from http://www.engineering.usu.edu/dtarb/
Binary direct access grid
Demonstration