Advanced Terrain Analysis Concepts n Specific Catchment Area n The D Surface Flow Model n Topmodel u Terrain based calculations of saturated areas and.

Advanced Terrain Analysis Concepts

Specific Catchment Area The D Surface Flow Model Topmodel

Terrain based calculations of saturated areas and soil moisture deficit

Generalized flow accumulation functions Flow algebra

Extending ArcGIS Scripts and Programming

Drainage area can be concentrated or dispersed (specific catchment area) representing concentrated or

dispersed flow.

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

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)

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.”

Hydrological processes within a catchment are complex, involving:

• Macropores

• Heterogeneity

• Fingering flow

• Local pockets of saturation

The general tendency of water to flow downhill is however subject to macroscale conceptualization

Map of saturated areas showing expansion during a single rainstorm. The solid black shows the saturated area at the beginning of the rain; the lightly shaded area is saturated by the end of the storm and is the area over which the water table had risen to the ground surface. [from Dunne and Leopold, 1978]

Seasonal variation in pre-storm saturated area [from Dunne and Leopold, 1978]

TOPMODEL Key Ideas

• 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

Topmodel - Assumptions

Specific catchment area a [m2/m m] (per unit contour length)

tan

• The soil profile at each point has a finite capacity to transport water laterally downslope based on slope and transmissivity, qcap=T tan.

• The actual lateral discharge is proportional to specific catchment area, q=Ra

• Relative wetness at a point and depth to water table is determined by comparing q and qcap

• The dynamics of the saturated zone can be approximated by successive steady state representations involving the depth to water table adjusting to accommodate q that results in expansion and contraction of the variable source area contributing to saturation excess runoff

VSA

Slope

Specific Catchment Area

Wetness Index ln(a/tan)

from Raster Calculator.

Average, = 6.9

TOPMODEL and GIS

Numerical ExampleGiven • Ko=10 m/hr• f=5 m-1

• Qb = 0.8 m3/s• a (from GIS)• ne = 0.2

m46.0z

tan

aln

f

1zz

Raster calculator -( [ln(sca/S)] - 6.9)/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• =6.9• T=2 m2/hr

Continuum Definition.

Area ngContributi

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.

Generalized Flow Accumulation

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

Extending ArcGIS via programming

Why Programming Automation of repetitive tasks Implementation of functionality not

available Programming functionality

Scripts (AML, VB, Python, Avenue) Interfaces for application programmers Model Builder ArcObjects COM Integration

Geodatabase view: Structured data sets that represent geographic information in terms of a generic GIS data model.

Geovisualization view: A GIS is a set of intelligent maps and other views that shows features and feature relationships on the earth's surface. "Windows into the database" to support queries, analysis, and editing of the information.

Geoprocessing view: Information transformation tools that derives new geographic data sets from existing data sets.

Three Views of GIS

adapted from www.esri.com

Examples

• TauDEM – ArcMap toolbar using Visual Basic/C++ (implementation of functionality not available in ArcGIS)

• Visual Basic Programming of simple grid calculations

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 Water Quality Functions

TauDEM in ArcGIS

ESRI binarygrid

ASCII text grid

ESRI gridio API (Spatial analyst)

Data Access libraries(grid, shape, image, dbf)

TauDEM C++ libraryFortran (legacy)

components

Standalone command line

applications

C++ COM DLL interface

Visual Basic MapWindow plugin

Visual Basic ESRI ArcGIS 8.x+9.x

Toolbar

Vector shape files

Data formats

Available from http://www.engineering.usu.edu/dtarb/

Binary direct access grid

Implementation Details

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. * * 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. * */int GetWindowCell(int channel, int rescol, int resrow, CELLTYPE *cell);

int PutWindowCell(int channel, int col, int row, CELLTYPE cell);

STDMETHODIMP CtkTauDEM::Areadinf(BSTR angfile, BSTR scafile, long x, long y, int doall, BSTR wfile, int usew, int contcheck, long *result){ USES_CONVERSION; //needed to convert from BSTR to Char* or String *result = area( OLE2A(angfile), OLE2A(scafile), x,y,doall, OLE2A(wfile),

usew, contcheck); return S_OK;}

C++ COM Methods used to implement functionality using Microsoft Visual C++

Visual Basic for the GUI and ArcGIS linkage

Private TarDEM As New tkTauDEM…

Private Function runareadinf(Optional toadd As Boolean = False) As Boolean Dim i As Long runareadinf = False i = TarDEM.Areadinf(tdfiles.ang, tdfiles.sca, 0, 0, 1, "", 0, 1) If TDerror(i) Then Exit Function If toadd Then AddMap tdfiles.sca, 8 End If runareadinf = TrueEnd Function

Visual Basic Programming in ArcMAP

ReferencesESRI, (1999), ArcObjects Developers Guide:

ArcInfo 8, ESRI Press, Redlands, California.

Zeiler, M., (2001), Exploring ArcObjects. Vol 1. Applications and Cartography. Vol 2. Geographic Data Management, ESRI, Redlands, CA.

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