watershed and stream network delineation including geomorphology
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Watershed and Stream Network Delineation Including Geomorphology
David G. Tarboton
dtarb@cc.usu.edu
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
TOPMODEL
Specialized grid accumulation functions
TauDEM software
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.
Elevation Surface — the ground surface elevation at each point
67 56 49
52 48 37
58 55 22
30
67 56 49
52 48 37
58 55 22
30
45.0230
4867
50.0
30
5267
Slope:
Direction of Steepest Descent
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16
8
64
4
128
1
2
Eight Direction Pour Point Model
Grid Network
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25 2
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256
Contributing Area Grid
TauDEM convention includes the area of the grid cell itself.
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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
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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 Thresholds
EPA 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
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Bifurcation Ratio
Order
Num
ber
of S
trea
ms
1 2 3 4 5
15
1050Rb = 3.58
Area Ratio
Order
Mea
n S
trea
m A
rea
1 2 3 4 5
10^6
5*10
^65*
10^7 Ra = 4.65
Length Ratio
Order
Mea
n S
trea
m L
engt
h
1 2 3 4 5
900
2000
4000
Rl = 1.91
Slope Ratio
Order
Mea
n S
trea
m S
lope
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
trea
m D
rop
1.0 1.5 2.0 2.5 3.0 3.5 4.0
5010
050
0
Rd = 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
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600
0 1 2 3 4 5 6
Strahler Order
Dro
p (
me
ters
)
Drop
Mean 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
Str
ah
ler
Str
ea
m D
rop
(m
)
05
01
00
15
02
00
25
0
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)
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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
Str
ah
ler
Str
ea
m D
rop
(m
)
05
01
00
15
02
00
25
0
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
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256
Contributing Area
1 1 11 1
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1
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3 1
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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).
Topographic Slope
?
Topographic Definition Drop/Distance
Limitation imposed by 8 grid directions.
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
TOPMODEL
Beven, K., R. Lamb, P. Quinn, R. Romanowicz and J. Freer, (1995), "TOPMODEL," Chapter 18 in Computer Models of Watershed Hydrology, Edited by V. P. Singh, Water Resources Publications, Highlands Ranch, Colorado, p.627-668.
“TOPMODEL is not a hydrological modeling package. It is rather a set of conceptual tools that can be used to reproduce the hydrological behaviour of catchments in a distributed or semi-distributed way, in particular the dynamics of surface or subsurface contributing areas.”
TOPMODEL and GIS• Surface saturation and soil
moisture deficits based on topography– Slope– Specific Catchment Area– Topographic Convergence
• Partial contributing area concept
• Saturation from below (Dunne) runoff generation mechanism
Saturation in zones of convergent topography
Slope
Specific Catchment Area
ln(a/S) or ln(a/tan) [tan=S] is a wetness index that determines the locations of saturation from below and soil moisture deficit.
TOPMODEL soil moisture deficit exampleGiven • Ko=10 m/hr• f=5 m-1
• Qb = 0.8 m3/s• A (from GIS)• ne = 0.2
m46.0z
Sa
lnf1
zz
Raster calculator -( [ln(sca/S)] - 6.90)/5+0.46
-3 - 0 (7.8%)0 - 0.1 (2.5%)0.1 - 0.2 (4.0%)0.2 - 0.5 (29%)0.5 - 1 (56%)1 - 1.5 (0.2%)
Flat (0.5%)Depth to saturation z
Compute• R=0.0002 m/h• =6.90• T=2 m2/hr
Contributing Area using D8
Contributing Area using D
Weighted Accumulation.
CA
dx)x(r)]x(r[A
A[.] is a functional operator that takes as input a spatial field r(x), and the topographic flow direction field (not denoted) and produces a field A(x) representing the accumulation of r(x) up to each point x. Numerical evaluation
A[r(x)] = A(i,j) = r( i, j)2+ neighborsngcontributik
kkk )j,i(Ap
pk is the proportion of flow from neighbor k contributing to the grid cell (i,j).
kp =1 is required to ensure ‘conservation’.
Flow directions must not have loops.
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. I(x|y)=A[i(x|y)]
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
Decaying 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
Concentration Limited Accumulation An unlimited supply of a substance that is loaded into flow at a concentration or solubility threshold Csol. The set of points y, delineating the area of the substance supply are mapped using the (0,1) indicator field i(x;y). 1. Flow (weighted accumulation)
Q(x)=A[w(x)] 2. Supply area concentration at threshold
If i(x; y) = 1 C(x) = Csol L(x) = Csol Q(x)
3. Remaining locations by load accumulation and dilution L(x) = L(i, j) =
neighborsngcontributikkkk )j,i(Lp
C(x) = L(x)/Q(x) Useful for a tracking a contaminant released or partitioned to flow at a
fixed threshold concentration
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 TTED
Useful for modeling erosion and sediment delivery, the spatial dependence of sediment delivery ratio and contaminant that adheres to
sediment
Reverse Accumulation
Useful for destabilization sensitivity in landslide
hazard assessmentwith Bob Pack
Reverse accumulation of field weights indicated in red
0 0.8 0.6
0 0.4
0.6
0 1.8 0
0.9 1.8 0
1.35 1.8 0
1.2
0.8 0.6
TauDEM in ArcGIS
ESRI binarygrid
ASCII text grid
ESRI gridio API (Spatial analyst)
USU TMDLtoolkit modules(grid, shape, image, dbf, map, mapwin)
TauDEM C++ libraryFortran (legacy)
components
Standalone command line
applications
C++ COM DLL interface
Visual Basic GUI
application
Visual Basic ESRI ArcGIS 8.x
Toolbar
Vector shape files
Data formats
Available from http://www.engineering.usu.edu/dtarb/
Binary direct access grid
Are there any questions ?
AREA 1AREA 1
AREA 2AREA 2
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