Estimating Watershed Runoff and

Sediment Yield

Using a GIS 

Interface to Curve

Number and

MUSLE Models

By Jacek Blaszczynski

Physical Scientist, BLM, National

Science and Technology Center

Background

Increased sediment yield from a watershed is usually a sign that the condition of the watershed is degrading.

Geographic information systems (GIS)

offer a unique opportunity to generate

otherwise difficult-to-obtain data that

can be utilized in various models of

natural processes that occur throughout large areas of landscape. It can

perform some of the mathematical

operations of the existing models using

spatial data processing algorithms and

can help test the models’ effectiveness

for describing and predicting the actual situation. It also allows us to visualize the results of modeling as maps

rather than mere columns of numbers.

A relatively simple GIS procedure can

be used to generate input and output

data for the Modified Universal Soil

Loss Equation (MUSLE) model to

calculate sediment yield. The GIS

methods permit the generation of

detailed information from digital

maps about the many environmental

parameters required to run MUSLE.

Using GIS enables easier derivation of

difficult-to-obtain key data for large

areas which, when used with the

MUSLE model, can provide estimates

of sediment yield for a storm. These

estimates, provided in tabular and map

format, can be used to locate and

design sediment yield control methods

that include the building of structures such as dams and spreaders, the

digging of pits, contour plowing, and

revegetation.

Calculating Sediment Yield

Using the MUSLE/GIS

Interface

Two steps are used to calculate sediment yield by using the MUSLE/GIS

interface:

• The calculation of a runoff hydrograph for a particular storm using

rainfall and watershed characteristics

data such as the average slopes, areas

of the hydrologic response units, and

lengths of the longest channels in

subwatersheds; and

• The calculation of sediment yield

using the MUSLE with the runoff

factor calculated from the runoff

hydrograph.

The Modified Universal Soil Loss

Equation follows the structure of the

Universal Soil Loss Equation (USLE),

with the exception that the rainfall factor is replaced with the runoff factor.

The equation calculates sediment yield

for a storm within a watershed that

does not exceed 5 square miles. The

structure of the MUSLE is

SY = R * K * L * S * C * P

where

R = a(Q * qp )b

therefore

SY = a(Q * qp)b * K * L * S * C * P.

SY is the sediment yield per calculation

unit (watershed) in tons, a is a constant, b is a constant, Q is the volume

of runoff in acre-feet, and qp is the

peak flow rate in cubic feet per second.

The other factors are precisely the same

as the Revised Universal Soil Loss

Equation (RUSLE) factors and include

K, which is the the soil erodibility factor—the soil loss rate per erosion index

unit for a specified soil, as measured on

a unit plot, which is defined as a 72.6-

foot length of uniform 9% slope continuously in clean, tilled fallow; L is the

slope-length factor—the ratio of soil

loss from the field slope length to that

of a 72.6-foot length under identical

conditions; S is the slope gradient

factor—the ratio of soil loss from the

field slope gradient to that from a 9%

slope under otherwise identical conditions; C is the cover and management

factor—the ratio of soil loss from an

area with specified cover and management to that of an identical area in

tilled continuous fallow; and P is the

support practice factor—the ratio of

soil loss with a support practice like

contouring, strip-cropping, or terracing

to that with straight-row farming up

and down the slope.

Discussion

The function of GIS in the modeling

procedure is to obtain input data on

subwatershed characteristics for calculation of a storm hydrograph from

watershed and storm data. GIS capabilities allow for calculation per subwatershed of average slope gradients,

determination of the length of the

longest channel in each subwatershed,

integration of soil and vegetation

information to develop hydrologic

response units (HRUs), and estimation

of the areas of the HRUs. This information is used as input to develop a

runoff hydrograph using hydrograph

software. From the hydrograph, data

can be obtained that permit derivation

of the runoff (R) factor. A map of the

R factors can be generated and then

combined with maps of other relevant

environmental parameters to develop a

sediment yield map for the storm.

Sediment yield maps show the modeled distribution of sediment output

from various locations and can be used

to estimate sediment yield for each

subwatershed, and then for the entire

watershed. A sediment yield map can

also be calculated for each cell, and

this map will show the areas of the

greatest likely runoff. Potentially, a

series of sediment yield maps for a

sequence of storms can be used to

derive locations of areas with highest

contributions of sediment over a time

period and for a variety of different

types of storms. Since MUSLE

permits calculation of sediment yield

based on curve number model runoff

NO. 66 DATE 05/01/03

Range

Soils/geology

Resource Note 66

page 1
estimates for a single storm only, it

would also be useful to get an annual

perspective of the project area’s

response to rainfall. We can get an

understanding of the type of storms

on the landscape over the duration of

a year by applying basic statistics and

modeling the biggest storm, the smallest storm, the mean storm, and the

median storm. These storms also have

a frequency associated with them,

which will tell us how often they occur

over several years of time.

The versions of the National Resource

Conservation Service (NRCS) runoff

hydrograph generation program and

of the Modified Universal Soil Loss

Equation sediment yield calculation

program on which this discussion is

based consist of two programs used at

the center: WILDCAT4 for NRCS

runoff hydrograph calculation, and the

RUSLE (which also contains calculations for MUSLE) program. The

runoff hydrograph program WILDCAT4 was based on the SCS “Curve

Number” method using triangular

unit hydrographs, as outlined in the

SCS National Engineering Handbook,

Section 4, Hydrology (“NEH-4”).

The sediment yield program is the

combined Revised Universal Soil Loss

Equation and the Modified Universal

Soil Loss Equation package prepared

by Richard Moore. This program is

based on the work of K. G. Renard,

D. K. McCool, and G. R. Foster,

which can be referenced in Predicting

Soil Erosion by Water: A Guide to

Conservation Planning With the

Revised Universal Soil Loss Equation,

and J. R. Simanton from the U.S.

Agricultural Research Service.

Values for the constants a and b can

vary depending on sources and areas

of application. I used the constants

provided in the BLM MUSLE DOS

program, in which a = 11.8 and b =

0.56. These constants were originally

derived on the basis of individual

storm data from 18 basins in Texas

and Nebraska and validated on 102

basins throughout the United States.

One of the benefits of using the

GIS/MUSLE methodology is that it is

flexible in adjustment of the constant

values used in calculation if scientists

believe that they have better estimates

from previous research into the

MUSLE in their areas. The K, L, S, C,

and P factors can be obtained by looking up their values in the soil surveys

for the area of study, generating them

by using GIS processes, or calculating

them by using the instructions in the

DOS RUSLE/MUSLE program.

A list of steps of the MUSLE/GIS

procedure for generating sediment

yield maps is as follows:

• Prepare a map of subwatersheds

from the Digital Elevation Model for

the area of study using GIS hydrologic

terrain analysis capabilities.

• Generate a vector map of line segments representing the longest stream

or channel courses for each subwatershed and determine the total length of

the stream.

• Intersect raster maps of soil hydrologic groups and range condition units

from the soil or vegetation surveys for

the project area to create a map of

Hydrologic Response Units (HRUs).

• Intersect the HRU map with the

subwatershed map to obtain a map of

HRUs for each of the subwatersheds. 

• Produce an area listing for each of

the HRUs for each subwatershed.

• Prepare a listing of the average slopes

for each subwatershed. 

• Prepare a table that contains all the

information you just generated. The

table should include, for each subwatershed: average slope, length of the

longest channel, number of HRUs,

area of each HRU in square miles,

and the curve number of each HRU.

• Input this information into the

WILDCAT4 runoff hydrograph program together with storm data, generating a unique watershed file for

each subwatershed, and a unique

storm file for each storm. Generate a

hydrograph for each subwatershed,

which will give you the volume of

runoff (Q) and peak flow (qp) data.

• Generate a volume of runoff (Q)

and peak flow (qp) maps, and relate

them mathematically to produce a

runoff (R) factor map for each subwatershed.

• Prepare maps of other factors,

namely the soil erodibility (K), the

terrain (LS), surface cover factor (C)

and erosion control practice (P) factor maps (these factors are the same

as the Revised Universal Soil Loss

Equation factors).

• Generate a runoff (R) factor map

representing partial value of the R

factor per cell. This will permit calculating sediment yield for each cell

making use of the cell-by-cell calculation of the terrain (LS) factor.

• Multiply the cell runoff (R) factor

map by the other factor maps to produce the sediment yield (S) map for

the area of study using the simplifying

assumption that runoff is distributed

evenly for each watershed. 

• Add the tonnage values contained in

each acre cell for each subwatershed in

the sediment yield map to produce

estimates of sediment yield per storm

from each subwatershed. Add the values for all the subwatersheds to produce sediment yield per storm for the

entire watershed under study.

Contact

Jacek Blaszczynski, Physical Scientist

National Science and 

Technology Center

Denver Federal Center, Building 50

P.O. Box 25047

Denver, CO 80225-0047

Phone: 303-236-5263

Fax: 303-236-0358 

Email: jblaszcz@blm.gov

Range

Resource Note 66

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