Some Potential Terrain Analysis Tools for ArcGIS

David G. Tarboton

dtarb@cc.usu.edu

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

Overview Review of digital elevation model

grid based flow direction, accumulation and watershed delineation

Channel network delineation. Objective selection of channel delineation threshold and representation of variable drainage density.

Terrain flow fields and their numerical representation. Multiple flow direction approaches.

Specialized grid accumulation functions

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 Model Based Flow Path Analysis

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Drainage Area

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Eight direction pour point model D8

Grid network

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Grid Order

100 grid cell constant support area threshold stream delineation

1 0 1 KilometersConstant support area threshold100 grid cell9 x 10E4 m^2

1 0 1 Kilometers Grid networkpruned to 4thorder

Grid network pruned to order 4 stream delineation

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 drainage area threshold ?

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Drainage Area Threshold (m2)

Dra

inag

e D

ensi

ty (

1/km

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Mawheraiti

Gold Creek

Choconut and Tracy Creeks

Drainage density (total channel length divided by drainage area) as a function of drainage area support threshold used to define channels for the three study watersheds.

Dd = 760 A-0.507

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.

Objective determination of channel network drainage density

Delineation of Channel Networks and Subwatersheds

500 cell theshold

1000 cell theshold

0 1 Kilometers 0 1 KilometersDriftwood, PA Sunland, CA

Examples of differently textured topographySame scale, 20 m contour interval

Sunland, CADriftwood, PA

Logged Pacific Redwood Forest near Humboldt, California

Gently Sloping Convex Landscape

From W. E. Dietrich

Mancos Shale badlands, Utah. From Howard, 1994.

Suggestion: Map channel networks from the DEM at the finest resolution consistent with observed channel network geomorphology ‘laws’.

“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.)

One contributing area threshold does not fit all watersheds.

Constant Stream Drops Law based on Strahler Stream Ordering

Order

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n S

trea

m D

rop

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5010

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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.

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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

Statistical Analysis of Stream Drops

Elevation Drop for Streams

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Strahler Order

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Mean Drop

Constant Support Area Threshold

Strahler Stream Order

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rop

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Support Area threshold (30 m grid cells)

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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

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Upward curved support area threshold (30 m grid cells)

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Drainage Density (km-1) 2.2 1.8 1.6 1.4

t statistic for difference between lowest order and higher order drops

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1 0 1 KilometersCurvature basedStream delineation

Curvature based stream delineation

Addressing the limitations imposed by 8 grid directions

Topographic Slope

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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.

Single Flow Direction Grid — A numerical representation of the flow direction field in which each cell takes on one of eight values depending on which of its eight neighboring cells is in the direction of steepest descent

Multiple Flow Direction Grid — A numerical representation of the flow direction field in which flow is partitioned between one or more or the eight neighboring cells such that proportions add up to one

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Flowdirection.

Steepest directiondownslope

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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

Multiple flow direction grid accumulation functions

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

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Influence function of grid cell y

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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

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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

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

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Suggestions for Terrain Analysis Tools for ArcGIS

All of the above Of course !

Already available as TauDEM ArcGIS toolbar but lacking in support and robustness

Things that could be implemented quickly Generalized channel network delineation Geomorphologically based routing of flow

across flats (Garbrecht and Martz, 1997) Multiple flow direction data structure – more

general than D angles (and not in radians) D flow directions Slope proportioned flow directions

MFD derived functions Contributing area (accumulation,

weighted, downslope influence) Upslope dependence

Edge contamination

Intermediate term or more specialized functions

Additional MFD derived functions Transport limited accumulation Concentration limited accumulation Reverse accumulation "average" distance to streams Wetness index Decaying accumulation Partial contributing area

Generalized drainage correction Hydrologic model integration

Are there any questions ?

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