Watershed and Stream Network Delineation – Geomorphological Considerations David G. Tarboton

Overview n Review of flow direction, accumulation and watershed delineation n Topographic texture and drainage density n Channel network geomorphology and Hortons Laws n Stream drop test to objectively oelect channel delineation threshold n Curvature and slope based methods to represent variable drainage density n The D  approach n Specialized grid accumulation functions n 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

Slope: Direction of Steepest Descent

Eight Direction Pour Point Model ESRI Direction encoding

Eight Direction Pour Point Model D8 Band/GRASS/TARDEM Direction encoding

Grid Network

Contributing Area Grid TauDEM convention includes the area of the grid cell itself.

Programming the calculation of contributing area Direction encoding Contributing area

Contributing Area > 10 Cell Threshold

Watershed Draining to This Outlet

100 grid cell constant support area threshold stream delineation

200 grid cell constant support area based stream delineation

How to decide on support area threshold ? AREA 1 AREA 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.

Topographic Texture and Drainage Density Same scale, 20 m contour interval Sunland, CA Driftwood, 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 D d = L/A Hillslope length  1/2D d L B B Hillslope length = B A = 2B L D d = L/A = 1/2B  B= 1/2D d

Drainage Density for Different Support Area Thresholds EPA Reach Files100 grid cell threshold1000 grid cell threshold

Drainage Density Versus Contributing Area Threshold

Hortons Laws: Strahler system for stream ordering

Bifurcation Ratio

Area Ratio

Length Ratio

Slope Ratio

Slope-Area scaling Data from Reynolds Creek 30 m DEM, 50 grid cell threshold, points, individual links, big dots, bins of size 100

Constant Stream Drops Law Broscoe, A. J., (1959), "Quantitative analysis of longitudinal stream profiles of small watersheds," Office of Naval Research, Project NR , Technical Report No. 18, Department of Geology, Columbia University, New York.

Stream Drop Elevation difference between ends of stream Note that a “Strahler stream” comprises a sequence of links (reaches or segments) of the same order Nodes Links 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

T-Test for Difference in Mean Values 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

200 grid cell constant support area based stream delineation

Local Curvature Computation (Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375)

Contributing area of upwards curved grid cells only

Upward Curved Contributing Area Threshold

Curvature based stream delineation

Channel network delineation, other options Contributing Area Grid Order

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.

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): ) (

Specific catchment area a is the upslope area per unit contour length [m 2 /m  m] Upslope contributing area a Stream line Contour line

Contributing Area using D8 Contributing Area using D 

Useful for example to track where sediment or contaminant moves

Useful for example to track where a contaminant may come from

Useful for a tracking contaminant or compound subject to decay or attenuation

Transport limited accumulation 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 assessment with Bob Pack

TauDEM Software Functionality n Pit removal (standard flooding approach) n Flow directions and slope u D8 (standard) u D  (Tarboton, 1997, WRR 33(2):309) u Flat routing (Garbrecht and Martz, 1997, JOH 193:204) n Drainage area (D8 and D  ) n Network and watershed delineation u Support area threshold/channel maintenance coefficient (Standard) u Combined area-slope threshold (Montgomery and Dietrich, 1992, Science, 255:826) u Local curvature based (using Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375) n Threshold/drainage density selection by stream drop analysis (Tarboton et al., 1991, Hyd. Proc. 5(1):81) n Wetness index and distance to streams n Specialized grid analysis functions (Upslope influence, Downslope dependence, Decaying accumulation, Concentration limited accumulation, Downslope accumulation, Transport limited accumulation)

TauDEM in ArcGIS ESRI binary grid 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 Binary direct access grid

Demonstration