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

32

16

8

64

4

128

1

2

Eight Direction Pour Point Model

Grid Network

1 1 111

1

1

1

1

1

1

1

1

14 3 3

12 2

2 163 6

25 2

1 1 11 1

1

1

1

1

1

1

1

1

1

4 3 3

12 1

2

23

16

256

Contributing Area Grid

TauDEM convention includes the area of the grid cell itself.

1 1 11 1

1

1

1

1

1

1

1

1

1

4 3 3

12 2

2

23

16

256

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

3

12

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

1

1

1

1

11

1

11

1

1

1

1

1

2

2

2

2

3

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

400

500

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)

43

41

48

47

48

47 54

51

54

51 56

58

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

4

5

6

3

7

2

1

8

1 1 11 1

1

1

1

1

1

1

1

1

1

4 3 3

12 2

2

23

16

256

Contributing Area

1 1 11 1

1

1

1

1

1

1

1

1

1

2 2 2

3 1

1

12

3

32

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

3

12