Hydrologic Properties of the Landscape David G Tarboton Utah State University http://www.engineering.usu.edu/dtarb/ david.tarboton@usu.edu

Outline Slope and Contributing Area The D Algorithm TOPMODEL Wetness Index Terrain Stability Mapping SINMAP ArcView Extension Topographic texture and drainage density TARDEM programs for watershed and channel network delineation

Topographic Slope ? Limitation imposed by 8 grid directions. Topographic Definition Drop/Distance Limitation imposed by 8 grid directions.

Contributing Area Grid Based Evaluation Topographic Definition Upslope contributing area a Stream line Contour line Grid Based Evaluation Topographic Definition Specific catchment area a is the upslope area per unit contour length [m2/m  m]

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)

Contributing Area using D

Topmodel - Assumptions The soil profile at each point has a finite capacity to transport water laterally downslope. e.g. or S Dw D

Topmodel - Assumptions Specific catchment area a [m2/m  m] (per unit coutour length) The actual lateral discharge is proportional to specific catchment area. R is Proportionality constant may be interpreted as “steady state” recharge rate, or “steady state” per unit area contribution to baseflow. S Dw D

Topmodel - Assumptions Specific catchment area a [m2/m  m] (per unit coutour length) Relative wetness at a point and depth to water table is determined by comparing qact and qcap Saturation when w > 1. i.e. S Dw D

Topmodel z D Dw S Specific catchment area a [m2/m  m] (per unit coutour length) S Dw D z

Slope Specific Catchment Area Wetness Index ln(a/S) from Map Calculator. Average, l = 6.91

Numerical Example K=10 m/hr T=2 m2/hr f=5 m-1 R=0.0002 m/hr l=6.91 Map calculator -( [ln(sca/S)] - 6.91)/5+0.46

6/12/2018 SINMAP - Terrain Stability Mapping Arcview Extension R T Pack, D G Tarboton, C.N. Goodwin Illustrates GIS as a spatial modeling environment Illustrates tight integration of model into GIS Utilizes GRIDIO application programmers interface to access Grids from external programs Utilizes customizability of ArcView to provide easy to use interface

Where is it Used Forest and watershed management, forestry and forest engineering. Determine volume of harvestable timber in annual allowable cut calculations. Better plan timber development to minimize occurrence of landslides and resulting impacts.

Lardeau Creek, BC

Norrish Watershed, BC.

Norrish Watershed, BC.

Theoretical Basis 6/12/2018 The infinite plane slope stability model with wetness (pore pressure) obtained from a topographically based steady state hydrology model has been used to map terrain stability (e.g. Montgomery and Dietrich, 1994, WRR p1153) Stream line Contour line Stream tube Upslope contributing area a 1. Relative Wetness h q 2. Dimensionless Cohesion Density Ratio (assumed a constant of 0.5)

Area-Slope Plot FS > 1 w = 1 Stable, Saturated FS < 1 Unstable Stable, Unsaturated

But Define Stability Index SI = Prob(FS > 1) Soil parameters, C, f, T are uncertain and spatially variable. Recharge parameter R is spatially and temporally variable. range P Define Stability Index SI = Prob(FS > 1) C1 C2

Area-Slope plot with uncertainty FS* > 1 SI = FS* *(using most conservative end of each parameter range) FS < 1 for all possible parameters SI = 0 Most conservative parameter limits Most destabilizing parameter limits SI = Prob(FS >1)

SI derived analytically for each region e.g. for region 2

Stability Class Definitions

SINMAP Inputs Topography (dictated by DEM) a - specific catchment area θ - slope angle Soil Parameters (given as a range) C - dimensionless cohesion tan Φ- tan of soil internal friction angle R/T - soil hydraulic parameter

SINMAP Outputs 1. Specific Catchment Area Map 2. Stability Index Map 3. Soil Wetness Map 4. Calibration Plot 5. Statistical Tables

Stability Index Map

Slope-Area plot interactive calibration

SINMAP Implementation Spatial Analyst includes a C programming API (Application Programming Interface) that allows you to read and write ESRI grid data sets directly. Excerpt from gioapi.h / * GetWindowCell - Get a cell within the window for a layer, * Client must interpret the type of the output 32 Bit Ptr * to be the type of the layer being read from. * * GetWindowCellFloat - Get a cell within the window for a layer as a 32 Bit Float * GetWindowCellInt - Get a cell within the window for a layer as a 32 Bit Integer * PutWindowCell - Put a cell within the window for a layer. * Client must ensure that the type of the input 32 Bit Ptr * is the type of the layer being read from. * PutWindowCellFloat - Put a cell within the window for a layer as a 32 Bit Float * PutWindowCellInt - Put a cell within the window for a layer as a 32 Bit Integer */ int GetWindowCell(int channel, int rescol, int resrow, CELLTYPE *cell); int GetWindowCellFloat(int channel, int rescol, int resrow, float *cell); int GetWindowCellInt(int channel, int rescol, int resrow, int *cell); int PutWindowCellFloat(int channel, int col, int row, double fcell); int PutWindowCellInt(int channel, int col, int row, int icell); int PutWindowCell(int channel, int col, int row, CELLTYPE cell);

' SINMAP.c.area ' BaseName is the full directory path name of the input DEM grid BaseName = Self.Get(0) 'get the procedure from the dll library area = DLLProc.Make(_avlsmDLL,"area",#DLLPROC_TYPE_INT16, {#DLLPROC_TYPE_STR,#DLLPROC_TYPE_STR,#DLLPROC_TYPE_INT32, #DLLPROC_TYPE_INT32}) if (area = NIL) then av.Run("SINMAP.Error.OpFail",{2}) end error = area.Call({BaseName+"ang",BaseName+"sca", 0, 0}) if (error > 0) then av.Run("SINMAP.Error.OpFail",{"Grid and/or memory error reading/writing in area.c"})

Customizing the GUI

Examples of differently textured topography Badlands in Death Valley. from Easterbrook, 1993, p 140. Coos Bay, Oregon Coast Range. from W. E. Dietrich

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 Driftwood, PA Same scale, 20 m contour interval Sunland, CA

Channel network delineation options 6/12/2018 Channel network delineation options 4 5 6 3 7 2 1 8 Accumulation Area 1 4 3 12 2 16 25 6

Streams from 1:250,000 blue lines

100 grid cell constant support area threshold stream delineation

200 grid cell constant support area based stream delineation

Constant Support Area Threshold

Channel network delineation options 6/12/2018 Channel network delineation options 4 5 6 3 7 2 1 8 Accumulation Area 1 2 3 Grid Order 1 4 3 12 2 16 25 6

Grid network pruned to order 4 stream delineation

Curvature based stream delineation

Local Curvature Computation (Peuker and Douglas, 1975, Comput Local Curvature Computation (Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375) 6/12/2018 43 48 48 51 51 56 41 47 47 54 54 58

Contributing area of upwards curved grid cells only 6/12/2018

Upward Curved Contributing Area Threshold 6/12/2018

TARDEM Components Grid Processing Flood D8 Dinf Aread8 Areadinf Gridnet Grid to Hierarchical Vector Network Netsetup Hierarchical Vector to Arc Coverage Arclinks Arcstreams Network and Subwatershed Analysis Linkan Streaman Asfgrid Subbasinsetup

Questions and Demo? AREA 1 AREA 2 3 12