Use of Numerical Simulations in Surface-Water Studies

by the U.S. Geological Survey in Missouri

—David C. Heimann, Paul H. Rydlund, Jr., and Susan S. Licher

Introduction

Numerical simulations of surface-water systems can be a useful 

tool to predict and understand a 

variety of physical, chemical, and 

ecological processes. A number of 

applications have been conducted 

by the U.S. Geological Survey 

Missouri Water Science Center in 

conjunction with ecological and 

flood studies in Missouri. Numerical simulations can provide a 

physically based method to predict 

natural processes in situations 

where it is impractical to measure 

the results directly as a result of 

cost, time, or infrequent occurrence. 

Numerical simulations provide 

a means of analyzing “What if?” 

scenarios. For example, a simulation can be used to estimate the 

effects of reservoirs in a basin on 

the timing and magnitude of 

downstream streamflows. Simulations also may provide a better 

understanding of a complex process, such as sediment transport 

and deposition during a large 

flood. Alternatively, numerical 

simulations can be used to quantify aquatic habitat that is defined 

by the hydraulic (depth and velocity) characteristics of streamflow. 

This report provides information 

on recent applications of numerical simulations of hydraulic, 

floodplain, and watershed processes.

Numerical Simulation of 

Riverine Processes

Technological advancements in 

computer capabilities have made 

computationally intensive modeling applications, including twodimensional simulations, more feasible for widespread application. 

Two-dimensional simulations

often replace one-dimensional simulations to determine hydraulic processes in stream channels, and thereby 

provide hydraulic information at a 

greater level of detail. The twodimensional hydraulic simulations 

use a developed computation mesh to 

represent stream channel geometry 

and solve calculations for water depth 

(fig. 1) and velocity at each mesh

U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet 2006–3075

Printed on recycled paper April 2006

Depth, in meters

0

1.61

1.45

1.29

1.13

0.97

0.81

0.64

0.48

0.32

0.16

0

node

mesh

FIgure 1. (A) A natural site (undetermined streamflow) simulated by a twodimensional model. (B) Model mesh and simulated depths at the same site, 

at a streamflow of 16.4 cubic meters per second.

EXPLANATION
node. Hydraulic characteristics are 

determined for either steady-state 

(streamflow and water level conditions do not vary with time) or 

transient (streamflow and/or water 

levels vary with time) conditions 

depending on the simulation 

objective. General input requirements for two-dimensional 

models include topography/

bathymetry, channel roughness, 

upstream discharge, and downstream stage. Observed depth and 

velocity information are required 

for calibration and validation of 

the hydraulic simulations. Accurate representation of the channel 

topography in the model mesh is 

the most time-consuming, yet 

most critical, of the input requirements. Simulation output consists 

of two horizontal velocity components and a depth at each computational model mesh node providing 

a planar view of flow direction. 

The number and placement of the 

computational nodes in the simulation mesh are dependent on the 

scale of the reach being simulated 

and the scale of desired hydraulic 

information.

To obtain accurate and reliable 

output data from a two-dimensional model application, the simulation velocity and depth results 

need to be compared to observed 

measurements. This is achieved 

through a calibration and validation process. Calibration is the 

process by which the differences 

between observed and simulated 

velocity and depth characteristics 

for a particular streamflow are 

minimized through adjustment of 

model parameters. Ideally, model 

calibration is conducted for a range 

of streamflows including the working range of flows desired in the 

application. Model validation is an 

important step by which the calibrated model is applied to an independent flow condition (other than 

calibrated streamflows) to test the 

reliability of the model and to see if 

the differences between observed 

and simulated data are within 

acceptable limits.

One application of two-dimensional streamflow models has 

been to determine the location and 

size of fish habitat areas. Fish 

habitat in the upper Osage River 

Basin in Missouri has been simulated using the two-dimensional 

model River2D (Ghanem and others, 1995, 1996; Steffler and 

Blackburn, 2002). Fish habitat 

area is calculated based on the distribution of water velocity, depth, 

and channel bottom material characteristics compared to known 

species’ requirements for these 

physical attributes (Heimann and 

others, 2005; fig. 2). 

Figure 2. Velocity, depth, and substrate layers are combined using Geographic Information System software 

to produce a habitat distribution map for paddlefish based on known habitat requirements.

Habitat distribution

Depth

Velocity 

Channel bottom material
The Federal Highway Administration’s Finite Element SurfaceWater Modeling System (FESWMS) (Froehlich, 1989) has been 

used to simulate the movement of 

water and sediment in rivers, lakes, 

and coastal waters. FESWMS is a 

two-dimensional streamflow 

model that provides water-surface 

elevation and velocity information 

around buildings (fig. 3), levees, 

bridge abutments, spur dikes, and 

meander bends, and also has been 

used to provide flow distributions 

at confluences of rivers. FESWMS 

commonly is used at highway river 

crossings where complex flow 

conditions exist (Froehlich, 1989). 

In addition, the model has utilities 

that allow detailed analysis of

flow over roadway embankments, as well as

pressure flow through

bridges, culverts, gate 

structures, and dropinlet spillways. One of

the more important aspects of modeling flow

through structures is the

potential for backwater.

Backwater (elevated

water-level conditions)

can be caused by structures, hydraulic inefficiencies, or channel 

constrictions and may contribute

to road inundations and flood damage. Knowing when backwater 

exists and the extent can be difficult 

to measure in a complex river reach.

FESWMS has been used by the 

USGS in Missouri to simulate a 

complex 2-mile reach along the 

Blue River in Kansas City, Missouri, in 2005 to determine water 

levels and areas of inundation associated with various streamflows 

(Kelly and Rydlund, 2006). 

FESWMS is a useful tool for simulating water levels, turbulence 

parameters, and pressure flow 

through bridge openings, and was 

used to analyze three bridge structures in the reach. In addition to 

analyzing bridge structures, the 

two-dimensional approach was 

beneficial in defining flow directions and velocities in sharp meander bends and at tributary junctions.

Flood simulations from the 

FESWMS model produced watersurface elevations that were used in 

the development of flood profiles 

and inundation maps for the Blue 

River in Kansas City, Missouri 

(Kelly and Rydlund, 2006). A 

library of inundation maps for 

selected water-surface elevations 

are available on the internet (http://

mo.water.usgs.gov/indep/kelly/

Example of complex riverine flow that can be modeled by the Finite 

Element Surface-Water Modeling System.

Figure 3. Visualization of numerical 

model output for a flood along the Blue 

River in Kansas City, Missouri, as simulated by the Finite Element SurfaceWater Modeling System. (Red represents the slowest water velocities and 

green represents the fastest water

velocities).

blueriver/index.htm), which allows 

the user to identify the estimated 

extent of flood inundation by selecting the appropriate inundation map 

for the water-surface elevation 

measured at the stream gage (fig. 4).

If river-channel sediments are 

characterized, the FESWMS flow 

results can determine the effects of 

flow on river channel bed and 

banks. Bottom shear stress in natural channels and those constricted 

by waterway crossings are analyzed to aid in stream-bank stability 

and abutment protection countermeasures. An additional utility that 

allows for the computation of erosion or “scour” in bridge openings 

during floods also is available.

RMA2 is a two-dimensional 

hydraulic model (U.S. Army Corps 

of Engineers, 1996) that has been 

used to simulate steady-state and 

transient streamflow conditions in 

Missouri rivers. RMA2 has been 

used in conjunction with the U.S. 

Army Corps of Engineers model 

SED2D (Roig and others, 1996) to 

simulate sediment transport and 

flood plain deposition (fig. 5) along 

Long Branch Creek in northeast 

Missouri (Heimann, 2001). In this 

application the two-dimensional 

distribution of water velocity, 

direction, and depth derived from 
Stage

28 feet 

Satellite

Inundation map selection

from website

Real-time

water-surface

elevation

Stream

gage

house

Radio

transmission

Repeated satellite

transmissions Stored flow 

simulations

(stage, in feet)

32

30

28

26

Internet

Downlink

NOTE: In this example, the user selected the appropriate inundation map from a library of 

stored flow simulations on a web site, based on a stage of 28 feet measured at the stream 

gage and transmitted to the U.S. Geological Survey satellite downlink. Stage is the watersurface elevation above the gage datum.

Figure 4. Schematic depicting communication links that occur when accessing estimated flood inundation maps from the internet. 

RMA2 was used as the input to 

determine sediment transport and 

changes in bed elevation in SED2D 

simulations (fig. 5). Data requirements for SED2D included sediment concentration time series and 

streambed characteristics such as 

bottom material particle size, water 

depth, and spatial distribution of 

bottom material.

Numerical Simulation of 

Watershed Processes

Precipitation-runoff models are 

used to simulate the quantity and 

timing of streamflow or the quality 

of stream water at select points in a 

watershed resulting from the 

cumulative effects of precipitation, 

land use, soils, and topography. 

The key inputs of a watershed 

model are precipitation, temperature, land-use information, topog1.50

-.77

NA

NA

.18

.10 -.25 .66

1.97

-.23

.10

.10

0

-.45 .58

1.85

.80 .05

.48

.30 .10 .20

1.44

-.20 .45 .20

.70

0

-.27

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-.55

.20

-.10 -.11

-.69 1.82 -.20

-1.90

-.2.01

1.21

.83

.22

.90

-2.00

-1.68

2.33

1.30 8.00

-3.64

1.67 .40

.10

.10

.05

-.20 .17

NOTE: Bed change locally

may exceed shown

range.

Bed change, in centimeters

-2.5

-3.0

-2.0

-1.5

-1.0

-0.5

 0

 0.5

 1.0

 1.5

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 2.5

3.0

Observed value

Data not available

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NA

EXPLANATION

Figure 5. Comparison of observed and simulated spatial distributions of changes in bed elevation along Long Branch Creek 

(northwest Missouri) following a 2-year recurrence interval flood.
raphy, soils, and point-source discharges and withdrawals. 

Additional data required for modeling sediment transport and waterquality variables are temperature, 

dissolved oxygen, total nitrogen, 

total phosphorus, pesticides, and 

other constituents. Simulation outputs may include total streamflow 

(fig. 6), the proportions of run off, 

interflow, and baseflow that contribute to the total streamflow, sediment transport and deposition, and 

water-quality constituent concentrations. To ensure that precipitation-runoff models are reliable, the 

model output must be calibrated to 

observed data. Parameters that 

help determine the model output 

are adjusted within realistic bounds 

to improve the match between simulated output and observed data. 

Once model parameters have been 

adjusted to minimize differences, 

an independent set of observed 

data are compared to simulated 

output to validate that the model 

will correctly simulate different 

conditions.

The Hydrologic Simulation Program-Fortran (HSPF) is a precipitation-runoff model that can be 

used to simulate the hydrologic 

(streamflow quantity and timing) 

and water-quality processes within 

a watershed (Bicknell and others, 

2004). HSPF is being used in 2006 

within the USGS Missouri Water 

Science Center to understand the 

effect of many small flood-retarding impoundments on streamflow 

at selected downstream locations. 

Some other applications of HSPF 

(and similar numerical models) 

include predicting flow at ungaged 

locations, extending missing 

record, understanding how landuse changes affect hydrology and 

water quality (Duncker and others, 

1995; Duncker and Melching, 

1998; Coon, 2003), how wetland 

restoration affects hydrology 

(Jones and Winterstein, 1999), the 

effects of withdrawals on hydrology (Zarriello and Ries, 2000), and 

simulation of water quality and 

nutrient loads (Stigall and others, 

1993; Laroche and others, 1996).

In conclusion, a number of different numerical models have been 

used by the USGS Missouri Water 

Science Center to simulate hydraulic and hydrologic conditions in 

surface-water systems in Missouri. 

Increases in computing capabilities 

have resulted in a greater prevalence of two-dimensional numerical simulations, and for some 

applications, three-dimensional 

numerical simulations may provide the most appropriate means of 

obtaining suitable answers. These 

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10 1020 2031 30 10 20 31 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30

October November December January February March April May June July August September

STREAMFLOW, IN CUBIC FEET PER SECOND PRECIPITATION, 

IN INCHES

OBSERVED

SIMULATED 

DAILY MEAN FLOW

Figure 6. Comparison of observed and simulated streamflow as predicted by the Hydrologic Simulation Program-Fortran.

2003 2004
tools continue to undergo further 

development and enhancements in 

capabilities and will continue to 

provide an effective means for the 

USGS to answer “What if ?” questions regarding the surface-water 

resources of Missouri.

Selected References

Bicknell, B.R., Imhoff, J.C., Kittle, J.L., 

Jr., Jobes, T.H. and Donigian, A.S., Jr., 

2004, Hydrological Simulation Program-Fortran, users manual version 

12.1: Athens, Ga., U.S. Environmental 

Protection Agency Research Laboratory, 885 p.

Coon, W.F., 2003, Simulating land-use 

changes and stormwater-detention 

basins and evaluating their effect on 

peak streamflows and stream-water 

quality in Irondequoit Creek Basin, 

New York: U.S. Geological Survey 

Open-File Report 03–136, 96 p.

Duncker, J.J., and Melching, C.S., 1998, 

Regional rainfall-runoff relations for 

simulation of streamflow for watersheds in Du Page County, Illinois: U.S. 

Geological Survey Water-Resources 

Investigations Report 98–4035, 80 p.

Duncker, J.J., Vail, T.J., and Melching, 

C.S., 1995, Regional rainfall-runoff 

relations for watersheds in Lake 

County, Illinois: U.S. Geological 

Survey Water-Resources Investigations 

Report 95–4023, 71 p.

Froehlich, D.C., 1989, HW031.D—Finite 

Element Surface-Water Modeling System: Two-dimensional flow in a horizontal plane—users manual: Federal 

Highway Administration Report 

FHWA-RD–88–177. 285 p.

Ghanem, A.H., Steffler, P.M., Hicks, F.E., 

and Katopodis, C., 1995, Two dimensional finite element model for aquatic 

habitats: Edmonton, Alberta Canada, 

University of Alberta, Department of 

Civil Engineering, Water Resources 

Engineering Report 95–S1, 189 p. 

Ghanem, A.H., Steffler, P.M., Hicks, F.E., 

and Katopodis, C., 1996, Two dimensional finite element flow modeling of 

physical fish habitat: Regulated Rivers: 

Research and Management, v. 12, pp. 

185–200.

Heimann, D.C., 2001, Numerical simulation of streamflow distribution, sediment transport, and sediment deposition along Long Branch Creek in 

northeast Missouri: U.S. Geological 

Survey Water-Resources Investigations 

Report 01–4269, 61 p.

Heimann, D.C., Richards, J.M., Brewer, 

S.H., and Norman, R.D., 2005, Quantification of fish habitat in selected 

reaches of the Marmaton and Marais 

des Cygnes Rivers, Missouri, 2004: 

U.S. Geological Survey Scientific 

Investigations Report 05–5180, 58 p.

Huizinga, R.J., and Rydlund, P.H., Jr., 

2001, Simulation of flow and evaluation of bridge scour at Horse Island 

Chute Bridge near Chester, Illinois: 

U.S. Geological Survey WaterResources Investigations Report 

01–4269, 28 p.

Kelly, B.P., and Rydlund, P.H., Jr., 2006, 

Estimated flood-inundation mapping 

for the lower Blue River in Kansas City, 

Missouri, 2003–05: U.S. Geological 

Survey Scientific Investigations Report 

06–5089, 29 p. plus appendixes.

Jones, P.M, and Winterstein, T.A., 1999, 

Characterization of rainfall-runoff 

response and estimation of the effect of 

wetland restoration on runoff, Heron 

Lake Basin, Southwestern Minnesota, 

1991–97: U.S. Geological Survey 

Water-Resources Investigations Report 

00–4095, 48 p.

Laroche, A., Gallichand, J., Lagacé, R., 

and Pesant, A., 1996, Simulating atrazine transport with HSPF in an agricultural watershed: Journal of Environmental Engineering, vol. 122, no. 7, 

622–630 p.

Roig, L.C., Donnell, B.P., Thomas, W.A., 

McAnally, W.H., and Adamec, Jr. S.A., 

1996, A users manual for SED2DWES—a generalized computer program for two-dimensional, vertically 

average sediment transport: Vicksburg, 

Miss., U.S. Army Corps of Engineers 

Waterways Experiment Station, 75 p.

Southard, R.E., 1997, Simulation of the 

effect of traffic barricades on backwater 

along U.S. Highway 54 at Jefferson 

City, Missouri—1993 flood on the Missouri River: U.S. Geological Survey 

Water-Resources Investigations Report 

97–4213, 13 p.

Steffler, P., and Blackburn, J., 2002, Twodimensional depth averaged model of 

river hydrodynamics and fish habitat: 

Introduction to depth averaged modeling 

and users manual: Edmunton, Alberta, 

Canada, University of Alberta, 119 p.

Stigall, E., Linker, L.C., and Donigian, 

A.S., 1993, Application of the Hydrologic Simulation Program-Fortran 

(HSPF) Model to the Potomac River 

Basin: Proceedings of WATERSHED 

’93 A National Conference on Watershed Management, March 21–24, 1993, 

Alexandria, Va., 776–775 p.

U.S. Army Corps of Engineers, 1996, 

Users guide to RMA2, version 4.3: 

Vicksburg, Miss., Waterways experiment Station, 226 p.

Zarriello, P.J., and Ries K.G., III, 2000, A 

precipitation-runoff model for analysis 

of the effects of water withdrawals on 

streamflow, Ipswich River Basin, Massachusetts: U.S. Geological Survey 

Water-Resources Investigation Report 

00–4029, 99 p.

For more information contact any of the following:

For water information:

U.S. Geological Survey, Director

1400 Independence Road, Mail Stop 100

Rolla, Missouri 65401

(573) 308-3667 or “http://mo.water.usgs.gov”.

For more information on all USGS

reports and products (including maps,

images, and computerized data), call

1-888-ASK-USGS.

Additional earth science information

can be found by accessing the USGS

“Home Page” on the Internet at

“http://www.usgs.gov”.