U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5107 

Prepared in cooperation with the Greater Cincinnati Water Works and 

the American Water Works Association Research Foundation 

An Initial Investigation of Multidimensional Flow and 

Transverse Mixing Characteristics of the Ohio River 

near Cincinnati, Ohio 
Cover: Meldahl Dam on the Ohio River near Neville, Ohio. (Photograph by U.S. Army Corps of Engineers (http://www.lrh.usace.army.mil/_

storage/Photos/1951.jpg, accessed March 2, 2006). Used with permission.)
An Initial Investigation of Multidimensional 

Flow and Transverse Mixing Characteristics 

of the Ohio River near Cincinnati, Ohio 

By David J. Holtschlag 

Prepared in cooperation with the Greater Cincinnati Water Works and 

the American Water Works Association Research Foundation 

Scientific Investigations Report 2009–5107 

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Holtschlag, D.J., 2009, An initial investigation of multidimensional flow and transverse mixing characteristics of the 

Ohio River near Cincinnati, Ohio: U.S. Geological Survey Scientific Investigations Report 2009–5107, 56 p. 
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................2

Model Area ............................................................................................................................................2

Summary of Hydrologic, Bathymetric, and Hydraulic Data Used in Models.......................................2

Water Levels and Flows within the Model Area..............................................................................2

Bathymetry and Acoustic Doppler Current Profiler Surveys ........................................................8

Dye-Injection Studies.........................................................................................................................11

Modeling Approach.....................................................................................................................................11

Dye-Mixing and Transport Rates......................................................................................................13

Hydrodynamic Simulation .................................................................................................................14

RMA2 Hydrodynamic Code ......................................................................................................15

Greater Cincinnati Hydrodynamic Model of the Ohio River ...............................................16

Finite-Element Mesh ........................................................................................................17

Boundary-Condition Scenarios ......................................................................................18

Water-Quality Simulations.................................................................................................................23

RMA4 Water-Quality Transport Code .....................................................................................23

Greater Cincinnati Water-Quality Transport Model of the Ohio River ..............................23

Mesh Refinement..............................................................................................................24

Boundary-Condition Scenarios ......................................................................................24

Parameter Estimation and Model Calibration................................................................................24

Nonlinear Regression ...............................................................................................................26

UCODE Analyses........................................................................................................................27

Hydrodynamic-Model-Calibration Strategy .................................................................27

Water-Quality-Transport Model-Calibration Strategy ................................................28

Greater Cincinnati Hydrodynamic Model of the Ohio River .................................................................29

Parameter Estimation.........................................................................................................................29

Simulation.............................................................................................................................................30

Greater Cincinnati Water-Quality-Transport Model of the Ohio River................................................30

Parameter Estimation.........................................................................................................................30

Dye-Decay Parameters ............................................................................................................34

RMA4 Peclet Numbers .............................................................................................................37

Simulation.............................................................................................................................................37

Hydrodynamic Model Limitations and Impacts on Water-Quality-Transport Simulations ..............42
iv

Figures

1. Map showing the Ohio River Basin, excluding the Tennessee River, in 

northeastern United States.........................................................................................................3

2. Map showing the study area of the Ohio River from Meldahl Dam to 

Cincinnati, Ohio .............................................................................................................................4

3–5. Graphs showing:

3. Daily mean gage heights on the Ohio River at Cincinnati, Ohio, at the 

U.S. Geological Survey water-level gaging station 03255000, 

January 2000–06 ..................................................................................................................5

4. Average monthly flow on the Ohio River at Cincinnati, Ohio, at the 

U.S. Geological Survey streamgaging station 03255000, 1940–75 ...............................5

5. Historical stage-discharge relation at the U.S. Geological Survey 

streamgaging station at Cincinnati, Ohio, 03255000.......................................................6

6. Photograph showing Meldahl Dam on the Ohio River near Neville, Ohio ..........................7

7–11. Graphs showing:

7. Histogram of hourly gate openings at Meldahl Dam near Neville, Ohio, 

2000–05.........................................................................................................................................7

8. Gate and tailwater ratings at Meldahl Dam on the Ohio River near 

Neville, Ohio..........................................................................................................................9

9. Relation between hourly flows on the Ohio River at Meldahl Dam near 

Neville, Ohio, estimated from the tailwater and the gate-opening ratings 

maintained by the U.S. Army Corps of Engineers Huntington District........................9

10. Flow-exceedance characteristics on the Ohio River at Meldahl Dam near 

Neville, Ohio, estimated by gate and tailwater ratings maintained by the 

U.S. Army Corps of Engineers Huntington District.......................................................10

11. Relation between measured flows and flows estimated from the gate 

rating on the Ohio River at Meldahl Dam near Neville, Ohio, 2004–06 .....................10

12. Map showing the location of transects related to dye-tracer studies..............................12

13–37. Graphs showing:

13. Distribution of depth-averaged flow-velocity magnitudes at dyemeasurement transects on the Ohio River, August 2–4, 2005 ....................................13

14. Flows and dye concentrations at OH 15 on the Ohio River from the 

Twelvemile Creek dye-injection study, near California, Ohio, August 2, 2005 .........14

Summary and Conclusions.........................................................................................................................48

Acknowledgments.......................................................................................................................................49

References Cited..........................................................................................................................................49

Appendix 1. Regimen of the gate-opening sequence for individual gates as a function 

of total gate opening at Meldahl Dam, near Neville, Ohio..........................................52

Appendix 2. Miscellaneous water-level measurements on the Ohio River between 

Cincinnati and Meldahl Dam obtained during 2004–06 bathymetry surveys...........55
v

15. Image of the finite-element mesh near the confluence of Little Miami 

River and the Ohio River...................................................................................................17

16. Water levels and flows in the Ohio River model area, October 4–8, 2004, 

scenario (Oct2004).............................................................................................................18

17. Water levels and flows on the Ohio River, August 1–5, 2005, scenario 

(Aug2005).............................................................................................................................19

18. Water levels and flows on the Ohio River, October 21–29, 2005, 

scenario (Oct2005).............................................................................................................19

19. Water levels and flows on the Ohio River, November 2–5, 2005, scenario 

(Nov2005).............................................................................................................................20

20. Water levels and flows on the Ohio River, March 20–23, 2006, scenario 

(Mar2006) ............................................................................................................................20

21. Water-level measurements during the 2004–06 bathymetry surveys.......................22

22. Refined mesh areas that surround dye-injection sites near Twelvemile 

Creek and Big Indian Creek on the Ohio River..............................................................25

23. Relation between computed and simulated flow depths on the Ohio River 

near Cincinnati, Ohio, October 2004–March 2006 ........................................................32

24. Relation between systematically measured and simulated water levels 

on the Ohio River downstream from Meldahl Dam near Neville, Ohio, 

October 2004–March 2006................................................................................................33

25. Relation between miscellaneous measurements and simulated water 

levels at miscellaneous sites measured during bathymetry surveys .......................33

26. Relation between measured and simulated flows on the Ohio River 

near Cincinnati, Ohio, October 2004–March 2006 ........................................................34

27. Relation between computed and simulated easting velocities on the 

Ohio River near Cincinnati, Ohio, October 2004–March 2006.....................................35

28. Relation between computed and simulated northing velocities on the 

Ohio River near Cincinnati, Ohio, October 2004–March 2006.....................................36

29. Dye-decay characteristics inferred from dye-injection sites near 

Twelvemile and Big Indian Creeks on the Ohio River upstream from 

Cincinnati, Ohio, August 2005 ..........................................................................................38

30. Measured and simulated dye concentrations at vertically mixed 

transects within the Twelvemile Creek injection reach of the Ohio River 

near Cincinnati, Ohio, August 2, 2005 .............................................................................39

31. Measured and simulated dye concentrations at vertically mixed 

transects within the Big Indian Creek dye-injection reach of the Ohio River 

near Cincinnati, Ohio, August 4, 2005 .............................................................................41

32. Relation between distance downstream from dye-injection points near 

Twelvemile Creek and Big Indian Creek and percent mixing on the 

Ohio River near Cincinnati, Ohio, August 2–4, 2005 .....................................................42

33. Variation in depth-averaged velocities, November 3, 2005, near acoustic 

Doppler current profiler transect OR 64 in a reach of the Ohio River near 

Cincinnati, Ohio, that curves to the left..........................................................................43
vi

Tables

1. Computed mean dye concentrations, percent mixing, and transport rates 

at selected Ohio River transects, August 2–4, 2005..............................................................15

2. Sites of water-level measurements during bathymetry surveys........................................21

3. Drainage areas of the Ohio River and selected tributaries.................................................21

4. Number of measurements used in the estimation of RMA2 parameters 

for the hydrodynamic model of the Ohio River near Cincinnati, Ohio, by 

scenario, 2004–06 .......................................................................................................................28

5. Parameter estimates for the two-dimensional hydrodynamic and transport 

models of the Ohio River near Cincinnati, Ohio.....................................................................30

6. Summary statistics describing the match between simulated and computed 

flow depths, heads, flows, and velocities for the hydrodynamic model of the 

Ohio River near Cincinnati, Ohio, October 2004–March 2006..............................................31

34. Variation in depth-averaged velocities, November 3, 2005, near acoustic 

Doppler current profiler transect OR 69 in straight reach of the Ohio River 

near Cincinnati, Ohio.........................................................................................................44

35. Variation in depth-averaged velocities, October 7, 2004, near acoustic 

Doppler current profiler transect OR 20 in a reach of the Ohio River near 

Cincinnati, Ohio, that curves to the right .......................................................................45

36. Variation of speed of flow with depth below the water surface at OR 20, 

Ohio River near Cincinnati, Ohio, October 7, 2004........................................................46

37. Relation between flow depth and flow-velocity azimuth from selected 

acoustic Doppler current profiler surveyed cross sections on the 

Ohio River near Cincinnati, Ohio, 2004–05 .....................................................................47
vii

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

square foot (ft2) 0.09290 square meter (m2)

square inch (in2) 6.452 square centimeter (cm2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 3.785 liter (L) 

gallon (gal) 0.003785 cubic meter (m3) 

million gallons (Mgal) 3,785 cubic meter (m3)

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

gallon per minute (gal/min) 0.06309 liter per second (L/s)

gallon per day (gal/d) 0.003785 cubic meter per day (m3/d)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

million gallons per day per square mile 

[(Mgal/d)/mi2] 

1,461 cubic meter per day per square 

kilometer [(m3/d)/km2] 

mile per hour (mi/h) 1.609 kilometer per hour (km/h) 

Mass

ounce, avoirdupois (oz) 28.35 gram (g) 

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

Vertical coordinate information is referenced to North American Vertical Datum of 1988 (NAVD 

88) in feet. 

Horizontal coordinate information is referenced to the Ohio South (zone 3402) State Plane 

Coordinate System of 1983 (Ohio South SPCS 83) in U.S. Survey Feet. A U.S. Survey Foot is 

1200/3937 of a meter. 

Altitude, as used in this report, refers to distance above the vertical datum. 

Conversion Factors 
viii

Abbreviations 

2D Two Dimensional

ADCP acoustic Doppler current profiler

AwwaRF American Water Works Association Research Foundation

BIC Big Indian Creek

EST Eastern Standard Time

FORTRAN Formula Translation (computer language)

GCWW Greater Cincinnati Water Works

GPS Global Positioning System

NAD 83 North American Datum of 1983

NAVD 88 North American Vertical Datum of 1988

NGVD 29 National Geodetic Vertical Datum of 1929

OHRFC Ohio River Forecast Center

ORD Ohio River Datum

RM River Mile

RMA2 Resource Management Association 2D hydrodynamic model

RMA4 Resource Management Association 2D transport model

SMS Surface Water Modeling System by Environmental Modeling Systems, Inc.

SPCS State Plane Coordinate System

TMC Twelvemile Creek

UCODE universal parameter estimation code

USACE U.S. Army Corps of Engineers

USGS U.S. Geological Survey
An Initial Investigation of Multidimensional Flow and 

Transverse Mixing Characteristics of the Ohio River near 

Cincinnati, Ohio 

By David J. Holtschlag 

Abstract

Two-dimensional hydrodynamic and transport models 

were applied to a 34-mile reach of the Ohio River from Cincinnati, Ohio, upstream to Meldahl Dam near Neville, Ohio. 

The hydrodynamic model was based on the generalized finiteelement hydrodynamic code RMA2 to simulate depth-averaged velocities and flow depths. The generalized water-quality 

transport code RMA4 was applied to simulate the transport of 

vertically mixed, water-soluble constituents that have a density 

similar to that of water. Boundary conditions for hydrodynamic simulations included water levels at the U.S. Geological 

Survey water-level gaging station near Cincinnati, Ohio, and 

flow estimates based on a gate rating at Meldahl Dam. Flows 

estimated on the basis of the gate rating were adjusted with 

limited flow-measurement data to more nearly reflect current 

conditions. An initial calibration of the hydrodynamic model 

was based on data from acoustic Doppler current profiler 

surveys and water-level information. These data provided 

flows, horizontal water velocities, water levels, and flow 

depths needed to estimate hydrodynamic parameters related to 

channel resistance to flow and eddy viscosity. Similarly, dye 

concentration measurements from two dye-injection sites on 

each side of the river were used to develop initial estimates of 

transport parameters describing mixing and dye-decay characteristics needed for the transport model. 

A nonlinear regression-based approach was used to estimate parameters in the hydrodynamic and transport models. 

Parameters describing channel resistance to flow (Manning’s 

“n”) were estimated in areas of deep and shallow flows as 

0.0234, and 0.0275, respectively. The estimated RMA2 Peclet 

number, which is used to dynamically compute eddy-viscosity 

coefficients, was 38.3, which is in the range of 15 to 40 that 

is typically considered appropriate. Resulting hydrodynamic 

simulations explained 98.8 percent of the variability in depthaveraged flows, 90.0 percent of the variability in water levels, 

93.5 percent of the variability in flow depths, and 92.5 percent 

of the variability in velocities. 

Estimates of the water-quality-transport-model parameters describing turbulent mixing characteristics converged to 

different values for the two dye-injection reaches. For the Big 

Indian Creek dye-injection study, an RMA4 Peclet number 

of 37.2 was estimated, which was within the recommended 

range of 15 to 40, and similar to the RMA2 Peclet number. 

The estimated dye-decay coefficient was 0.323. Simulated dye 

concentrations explained 90.2 percent of the variations in measured dye concentrations for the Big Indian Creek injection 

study. For the dye-injection reach starting downstream from 

Twelvemile Creek, however, an RMA4 Peclet number of 173 

was estimated, which is far outside the recommended range. 

Simulated dye concentrations were similar to measured concentration distributions at the first four transects downstream 

from the dye-injection site that were considered vertically 

mixed. Farther downstream, however, simulated concentrations did not match the attenuation of maximum concentrations or cross-channel transport of dye that were measured. 

The difficulty of determining a consistent RMA4 Peclet was 

related to the two-dimension model assumption that velocity 

distributions are closely approximated by their depth-averaged 

values. Analysis of velocity data showed significant variations in velocity direction with depth in channel reaches with 

curvature. Channel irregularities (including curvatures, depth 

irregularities, and shoreline variations) apparently produce 

transverse currents that affect the distribution of constituents, 

but are not fully accounted for in a two-dimensional model. 

The two-dimensional flow model, using channel resistance to 

flow parameters of 0.0234 and 0.0275 for deep and shallow 

areas, respectively, and an RMA2 Peclet number of 38.3, and 

the RMA4 transport model with a Peclet number of 37.2, may 

have utility for emergency-planning purposes. Emergencyresponse efforts would be enhanced by continuous streamgaging records downstream from Meldahl Dam, real-time waterquality monitoring, and three-dimensional modeling. Decay 

coefficients are constituent specific. 
2 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Introduction

The Ohio River is formed by the confluence of the 

Allegheny and Monongahela Rivers in Pittsburgh, Pa. (fig. 1). 

It flows 891 mi westward to the Mississippi River near Cairo, 

Ill. The U.S. Army Corps of Engineers (USACE) operates a 

series of 20 locks and dams along the Ohio River to maintain 

a minimum 9-ft depth of flow to support commercial navigation and recreational activities. The Ohio River is a source 

of drinking water for more than 3 million people (more than 

25 million people live in the Ohio River Basin). The total 

drainage area of the Ohio River is 203,940 mi2 (Ohio River 

Valley Water Sanitation Commission, 2006). 

Water-related problems in the Ohio River Basin include 

spills and accidental discharges, effluent from municipal 

wastewater-treatment plants, combined-sewage and stormwater overflows, urban stormwater, mine drainage, runoff from 

agricultural and forest lands, sedimentation, brines associated 

with oil and gas recovery, reservoir sedimentation, drinkingwater contamination, and invasive aquatic species. 

The U.S. Geological Survey (USGS), in cooperation with 

the Greater Cincinnati Water Works (GCWW) and the American Water Works Association Research Foundation, made an 

initial investigation of flow and mixing characteristics of the 

Ohio River near Cincinnati, Ohio, to facilitate the protection 

of drinking-water supplies from contamination. 

Purpose and Scope

This report documents an initial investigation of flow and mixing characteristics along a 34-mi reach of the Ohio River from 

a water-level gaging station at Cincinnati, Ohio, upstream 

to the Meldahl Dam. Acoustic Doppler current profiler 

(ADCP) surveys and ancillary data provided flow, velocity, 

flow-depth, and water-level information needed to estimate 

channel roughness and eddy-viscosity parameters associated 

with a two-dimensional (2D) hydrodynamic model, and two 

dye-injection studies provided concentration data needed to 

estimate turbulent mixing and dye-decay parameters in a 2D 

water-quality transport model. Boundary conditions for model 

simulations included water-level data from the USGS gaging 

station at Cincinnati, Ohio, and available flow information at 

Meldahl Dam. 

Model Area

The model area extends about 34 mi along the Ohio 

River from Cincinnati, Ohio, upstream to Meldahl Dam, near 

Neville, Ohio (fig. 2). The downstream limit of the model is 

at the USGS water-level gaging station Ohio River at Cincinnati, Ohio (station number 03255000), which is near river 

mile (RM) 471 on the Roebling suspension bridge that crosses 

the Ohio River. The drainage area of the Ohio River at the 

Cincinnati gaging station is 76,580 mi2. The upstream model 

limit is near the Meldahl Dam, operated by the Huntington 

District of the USACE near RM 436. River miles (RM), as 

shown on navigational charts of the Ohio River (U.S. Army 

Corps of Engineers, 2008), reference distances downstream 

from zero at the confluence of the Allegheny and Monongahela Rivers to 891 mi at the mouth at the Mississippi River 

near Cairo, Ill. 

Summary of Hydrologic, Bathymetric, 

and Hydraulic Data Used in Models

Water Levels and Flows within the Model Area

Operations at Markland Dam, downstream from Cincinnati at RM 531.3, exert primary control over normal water 

levels in the 95.3-mi reach that extends upstream to Meldahl 

Dam (fig. 2). Water levels at Cincinnati, however, also respond 

to storms, typically causing an annual 25-ft excursion over 

the project-pool elevation of 455 ft above the Ohio River 

Datum for Markland Dam (fig. 3). Of the 123 annual peak 

flows recorded on the Ohio River at the Cincinnati water-level 

gaging station, 1773–1975, the maximum flow of 894,000 ft3/s 

was recorded on January 26, 1937, with a gage height of 80 ft. 

Water levels referenced to the National Geodetic Vertical 

Datum of 1929 (NGVD 29) are obtained by adding 428.88 ft 

to the gage heights; water levels referenced to the North 

American Vertical Datum of 1988 (NAVD 88) are obtained by 

adding 428.227 ft to the gate heights. 

Prior to its conversion to a water-level-only gaging station, the USGS Cincinnati gaging station also provided flow 

information. Based on USGS flow data from 1940 to 1975, 

the average flow of about 91,900 ft3/s varies monthly from 

about 25,000 ft3/s in October to about 215,000 ft3/s in March 

(fig. 4). These historical flows at the USGS Cincinnati gaging 

station were computed from an empirically derived relation 

between water level and flow, which is commonly referred 

to as a stage-discharge relation, similar to the historical one 

shown in figure 5. When the gaging station was operated as a 

streamgage from 1940 to 1975, this relation was maintained 

and updated on a near-monthly basis, but when the streamgage 

was converted to a water-level gaging station, these updates 

ended, thus, the reliability of this historical relation is uncertain. Within the study area, major tributaries to the Ohio River 

include Licking River and the Little Miami River; minor 

tributaries include Twelvemile Creek, Big Indian Creek, Little 

Indian Creek, and Fourmile Creek. 

The GCWW provides about 136 Mgal/d of water to the 

Cincinnati Metropolitan Area and to nearby communities in 

northern Kentucky. Intakes on the Ohio River and wells within 

the Great Miami Aquifer are used for public-water supply. 
Monongahela River

Allegheny River

Ohio River Mississippi River

Cario, Ill.

Study area

Watershed

Pittsburgh

Cincinnati

Locks and dams

Base map from the Ohio River Basin Consortium for Research and Education (http://www.ent.ohiou.edu/~orbcre/basin/)

 Watershed Major river Lock and dam

75o W

0 50 100 200 MILES

40o N45o N

75o W

90o W

90o W

EXPLANATION

Figure 1. The Ohio River Basin, excluding the Tennessee River, in northeastern United States. 
4 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Twelvemile Creek

38o 50'

39o 00'

39o 10'

84o 30' 84o 20' 84o 10'

Ohio River

Ohio River

Little Miami

Big Indian Creek

RM 445

RM 450

RM 455

RM 

460

RM 465

RM 470

RM 475

RM 435

RM 440

Licking River

Mill Creek

EXPLANATION

River mile 450 and identifier

U.S. Geological Survey 

water-Level gaging station (03255000)

Site of water-level measurement

Site 1009

Site 1008

Site 1007

Site 1006

Site 

1005

Neville,

Ohio

California,

Ohio

New Richmond,

Ohio

Clemontville,

Ohio

Moscow,

Ohio

Tenmile Creek Fourmile

Creek

RM

450

Figure 2. Study area of the Ohio River from Meldahl Dam to Cincinnati, Ohio. 
Summary of Hydrologic, Bathymetric, and Hydraulic Data Used in Models 5

1/1/00 7/1/00 1/1/01 7/1/01 1/1/02 7/1/02 1/1/03 7/1/03 1/1/04 7/1/04 1/1/05 7/1/05 1/1/06

20

30

40

50

60

D

AILY

MEAN 

G

A

GE 

HEIGHT

S, IN FEET

The project pool elevation for Markland Dam of 455 feet on the Ohio River Datum is equivalent

to a gage height of 26.12 feet at U.S. Geological Survey water-level gaging station 03255000.

Figure 3. Daily mean gage heights on the Ohio River at Cincinnati, Ohio, at the U.S. Geological Survey water-level gaging station 

03255000, January 2000–06. 

Figure 4. Average monthly flow on the Ohio River at Cincinnati, Ohio, at the U.S. Geological Survey streamgaging station 

03255000, 1940–75. 

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

0

50,000

100,000

150,000

200,000

250,000

A

VER

AGE FLOW, IN

CUBIC FEE

T PER

SECOND
6 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

0 200,000 400,000 600,000 800,000 1,000,000 1,200,000

450

460

470

480

490

500

510

520

WATER-SURFACE ELEVATION AT CINCINNATI, OHIO, 

U.S. GEOLOGICAL SURVEY STREAMFLOW-GAGING 

STATION 03255000, IN FEET ABOVE NORTH AMERICAN 

VERTICAL DATUM OF 1988

DISCHARGE, IN CUBIC FEET PER SECOND

Figure 5. Historical stage-discharge relation at the U.S. Geological Survey streamgaging station at Cincinnati, Ohio, 

03255000. 

Meldahl Dam is at the upstream limit of the study area. 

At Meldahl Dam, two parallel locks on the north (Ohio) side 

of the river facilitate navigation by raising and lowering vessels about 30 ft across the dam (fig. 6). The main lock is 110 ft 

wide and 1,200 ft long; the shoreward auxiliary lock is 110 ft 

wide and 600 ft long. Under normal operating conditions when 

there is a 30-ft difference between water levels on the downstream and upstream sides of the dam, each time the main 

lock is operated, an equivalent downstream flow of 1,100 ft3/s 

for 1 hour results; similarly, use of the smaller auxiliary lock 

results in 550 ft3/s for 1 hour. These releases and accompanying surges in the flows were not accounted for in modeling 

activities described in this report. 

Water levels upstream from Meldahl Dam are controlled 

by the operation of 12 tainter gates south of the locks. A tainter 

gate is a segment of a cylinder mounted on radial arms that 

rotates on trunnions anchored to the piers that separate the 

gates. At Meldahl Dam, each 100-ft-wide gate is separated 

by piers that are about 15 ft wide. The radial arms are 64 ft 

long, and the trunnions are set at an elevation of 487 ft above 

the Ohio River Datum (ORD). When closed, the gates rest on 

the weir crest that underlies the gate; the weir crests have an 

elevation of 450 ft above the ORD. The tainter gates are numbered consecutively from gate 1 near the locks on the Ohio 

side of the river to gate 12 on the Kentucky side. 

The tainter gates are operated by a fixed schedule to 

improve the reaeration of the river (appendix 1). The positions 

of all tainter gates can be inferred from the reported total gate 

opening. For example, a total gate opening of 2 ft implies that 

gates 1 and 4 are raised 1 ft above the weir crest. Each of the 

gates can be raised a maximum of 30 ft; a gate opening of 

360 ft implies that all gates are fully open. A gate opening of 

999 implies that all gates as well as the locks are fully open. 

About 50 percent of the time (fig. 7), a gate opening of 30 ft is 

needed to maintain the normal pool elevation of 485 ft ORD 

upstream from Meldahl Dam. 
Summary of Hydrologic, Bathymetric, and Hydraulic Data Used in Models 7

U.S. Army Corps of Engineers (USACE) 

tailwater gage

USACE 

headwater gage

Right bank

Left bank

Flow

direction

Locks

Figure 6. Meldahl Dam on the Ohio River near Neville, Ohio. (Photograph by U.S. Army Corps of Engineers (http://www.lrh.usace.

army.mil/_storage/Photos/1951.jpg, accessed March 2, 2006). Used with permission.) 

Figure 7. Histogram 

of hourly gate openings 

at Meldahl Dam near 

Neville, Ohio, 2000–05. 

(Gate-openings 

analysis based on data 

provided by Stanley 

Wisbith, U.S. Army 

Corps of Engineers, 

written commun., 

March 2006). 

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

INDICATED GATE OPENING, IN FEET

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

RELATIVE FRE

QUENCY

999
8 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

In the absence of streamflow records derived from up 

to date ratings based on systematic flow measurements, flow 

through Meldahl Dam was computed based on the gate rating 

or the tailwater rating. The USACE commonly computes flow 

across Meldahl Dam from the gate rating (fig. 8) (Stanley 

Wisbith, U.S. Army Corps of Engineers, written commun., 

March 2006). The gate rating does not, however, account for 

water passing through the locks. Because of their emphasis 

on high-flow conditions, the Ohio River Forecast Center 

(OHRFC) bases their estimates of flow exclusively on the tailwater rating, using the downstream pool elevation measured 

at the USACE water-level gaging station named Ohio River at 

Meldahl Dam near Neville, Ohio1. 

Gate and tailwater ratings have not been updated in 

more than 30 years. Some systematic differences between 

these rated flows occur during high- and low-flow conditions 

(fig. 9). Discrepancies between rated flows may be attributable 

to degradation in the accuracy of the tailwater rating as a result 

of variable backwater conditions from the Markland Dam during low flow. The discrepancies between rated flows result in 

differences between estimated flow-exceedance characteristics 

(fig. 10), which were computed by use of hourly values from 

November 1, 2000 to October 31, 2005. This recent period of 

record was selected because it contained few periods of missing record and it was considered adequate to provide a context 

for flow conditions during the ADCP surveys and dye injection 

studies. Exceedance probabilities indicate the likelihood that 

hourly flows will exceed a specified magnitude. For example, 

a flow of 100,000 ft3/s will be exceeded about 40 percent of 

the time at Meldahl Dam; 60 percent of the time, flows will be 

less than 2100,000 ft3/s.

Flows were measured with ADCP for model calibration. 

ADCP units emit acoustic signals into the water and receive 

returning echoes from suspended particles and the river 

bottom at a rate of about once per second. Processing these 

signal pairs provides a basis for determining flow velocity and 

water depth. By temporally discretizing the returning signal, 

an ensemble of water velocities was computed at 0.82-ft 

intervals throughout the water column at that point (physical 

limitations prevent the measurement of velocities near the 

surface and near the channel bottom). Flows were determined 

from about 600 ensembles per transect, which were obtained 

from an ADCP unit tethered to a boat that traversed the river 

at about 2 ft/s. Each acoustic signal is coordinated with the 

measurement of position by a global positioning system (GPS) 

receiver to provide the ensemble location. Because of the 

random velocity variations introduced by the pitch, roll, and 

yaw of the ADCP unit during data collection, the small vertical (upward or downward) velocity component of flow could 

1

 For more information on the development or maintenance of the ratings 

at Meldahl Dam, contact the Huntington District of the U.S. Army Corps of 

Engineers or the Ohio River Valley Forecast Center. 

2

 For more information on the development and maintenance of the gate 

and tailwater ratings should contact the Huntington District of the U.S. Army 

Corps of Engineers, or the Ohio River Forecast Center, respectively. 

not be determined effectively from the ADCP data. Therefore, 

only the variations in horizontal velocity components with 

flow depth were investigated in this study. 

Flows measured during the ADCP surveys were compared with rated flows computed from gate openings (fig. 11) 

(the gate rating is thought to be less sensitive than the tailwater rating to variable backwater conditions during low-flow 

periods). Comparison indicates there may be a systematic difference between the measured and rated flows, although this 

apparent discrepancy diminishes at higher flow rates. A regression equation (fig. 11) provides a basis for adjusting gaterated flows less than 140,000 ft3

/s to more closely correspond 

to flows measured at single-transect ADCP measurements 

obtained during this study. The regression equation is thought 

to have utility for adjusting boundary inflows at Meldahl Dam 

to avoid bias in this model calibration. Because the adjustment 

does not account for the attenuation of flows between the dam 

and the measurement location, uncertainty in the adjusted 

flows remains high. 

Single-transect ADCP measurements were used primarily 

to measure local velocity patterns throughout the study area, 

rather than to measure flows at individual cross sections. To 

compute flows, USGS guidelines for ADCP measurements 

(U.S. Geological Survey, 2005) require at least four transects 

at a cross section. Application of these guidelines to measurements of velocity patterns in this report, however, would have 

limited the density of information needed to describe flow 

patterns. Therefore, single-transect data were used to estimate 

flow for the regression analysis, but the utility of the regression equations for use outside this model calibration effort is 

uncertain. 

Bathymetry and Acoustic Doppler Current 

Profiler Surveys

Koltun and others (2006) collected bathymetry data 

at about 800-ft intervals throughout the study area from 

October 2004 to March 2006 with a boat-mounted NaviSound 

210 single-beam echosounder. Horizontal coordinates of the 

depth measurements were determined with differentially 

corrected GPS measurements and were referenced to the Ohio 

State Plane Coordinate System (Ohio South) in feet. Depth 

measurements were converted to streambed elevations by 

use of periodic water levels that were referenced to a system 

of elevation reference marks established by survey-grade 

GPS units along the study reach. Water levels, thus depths, 

for locations other than those colocated with the reference 

marks were determined by assuming a constant water-surface 

slope between reference marks. These unpublished waterlevel measurements obtained during bathymetry surveys 

were quality assured and adjusted by staff from USGS 

Office of Surface Water (Robert R. Mason, USGS National 

Center, written commun., 2007) and listed in appendix 2. 
Summary of Hydrologic, Bathymetric, and Hydraulic Data Used in Models 9

0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 1,400,000

RATED FLOW, IN CUBIC FEET PER SECOND

0

10

20

30

40

50

60

70

80

90

100

TAILW

ATE

R LE

VEL AT

T

HE U.S. ARMY CORPS OF ENGINEERS

G

AGE DOWN

S

T

REAM FROM MELDAHL

D

AM,

IN FEET ABOVE GAGE DATUM

0

40

80

120

160

200

240

280

320

360

TO

T

AL GATE OPENING, IN FEET

Tailwater rating based on gage height (left axis)

Gate rating based on total gate opening (right axis).

Note: Gate rating not defined above 300,000 cubic 

feet per second

Figure 9. Relation 

between hourly flows 

on the Ohio River at 

Meldahl Dam near 

Neville, Ohio, estimated 

from the tailwater 

and the gate-opening 

ratings maintained by 

the U.S. Army Corps of 

Engineers Huntington 

District. 

Figure 8. Gate and tailwater ratings at Meldahl Dam on the Ohio River near Neville, Ohio. (Gate and tailwater ratings based on data 

provided by Stanley Wisbith, U.S. Army Corps of Engineers, written commun., March 2006). 

0

0

50,000

50,000

100,000

100,000

150,000

150,000

200,000

200,000

250,000

250,000

300,000

300,000

RATED FLOW BASED ON GATE OPENINGS, 

IN CUBIC FEET PER SECOND

RATED FLOW BASED ON TAILWATER ELEVATIONS, 

IN CUBIC FEET PER SECOND

Hourly values

Line of agreement
10 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000

FLOW, IN CUBIC FEET PER SECOND

0.0

0.2

0.4

0.6

0.8

1.0

EXCEEDA

NCE

PROBABILITY

Tailwater rating

Meldahl gate rating

Flow range from Oct. 4-8, 2004

Flow range from Aug. 1-5, 2005

Flow range from Nov. 2-5, 2005

Flow range from Mar. 20-23, 2006

20,000

20,000

40,000

40,000

60,000

60,000

80,000

80,000

100,000

100,000

GATE-OPENING RATED FLOW, IN CUBIC FEET PER SECOND

ACOUSTIC DOPPLER CURRENT PROFILER 

MEASURED FLOW, IN CUBIC FEET PER SECOND

Measured-rated pairs (n=159)

Line of agreement 

Regression line: QADCP = -8,578.8 + 1.0612 QGateRate

for QGateRate < 140,000 cubic feet per second, 

otherwise QADCP = QGateRate

ˆ

Figure 10. Flow-exceedance characteristics on the Ohio River at Meldahl Dam near Neville, Ohio, estimated by gate and tailwater 

ratings maintained by the U.S. Army Corps of Engineers Huntington District. 

Figure 11. Relation 

between measured flows 

and flows estimated from 

the gate rating on the 

Ohio River at Meldahl 

Dam near Neville, Ohio, 

2004–06. 
Modeling Approach 11

Elevations are referenced to the North American Vertical 

Datum of 1988 (NAVD 88)3 in feet. 

Koltun and others (2006) also used ADCPs in a systematic survey of stream velocities and flows at about 2,200-ft 

intervals throughout the study reach during three periods of 

data collection. The upper reach, from RM 437 to 447, was 

surveyed October 25–November 4, 2005; the middle reach, 

from RM 447 to 464, was surveyed October 5–7, 2004; 

and the lower reach, from RM 464 to 470, was surveyed 

March 21–23, 2006. Additional ADCP transects were measured August 2–4, 2005, to support the dye-injection studies 

discussed in the following section. Water-level data measured 

during the bathymetry surveys are mostly from October 2005. 

Dye-Injection Studies

Koltun and others (2006) conducted two dye-injection 

studies on the Ohio River in August 2005. The studies used 

two injection sites on opposite sides of the river within two 

overlapping stream reaches to provide dye concentration 

data needed to estimate transport parameters associated with 

transverse mixing characteristics. Rhodamine WT dye, a red 

dye that fluoresces when exposed to light, was used as a tracer 

because it (1) is nontoxic, (2) is fairly conservative (slowly 

decaying), (3) fluoresces at a magnitude proportional to its 

concentration, and (4) is measurable at low concentrations 

(parts per trillion) (Smart and Laidlaw, 1977). The 20-percent 

aqueous solution of rhodamine WT dye used in the dye-injection studies had a specific gravity of about 1.15 at 20°C and an 

active-ingredient concentration of 230,000 mg/L that disperses 

well in water. As such, rhodamine WT dye is thought to characterize the dispersion of other similar conservative, dissolved 

constituents in water. In both studies, dye was injected at a 

nominal rate of 200 mL/min (767 mg/s of active ingredient), 

starting about 24 hours preceding and throughout the concentration measurements. 

Dye concentrations and flows were measured in cross 

sections downstream from the points of injection, generally spaced 1 to 2 mi apart. Multiple transverses were made 

at some cross sections to measure dye concentrations. In 

particular, multiple transverses were used to sample dye 

concentrations with depth until vertically well-mixed conditions were established. For injections at mid-depth locations, 

tracers are thought to become vertically well mixed within 

a distance of about 50 times the depth of water (Rutherford, 

1994). In the dye-injection studies, dye was injected about 0.5 

to 1 ft below the water surface, where average flow depths are 

less than 25 ft. ADCP measurements of flow were measured 

during the first traverse at each cross section. Transects where 

3

 The velocity, bathymetry, and dye-concentration data can be downloaded 

as electronic documents from links in USGS Open-File Report 2006–1159 by 

Koltun and others, 2006, titled Velocity, bathymetry, and transverse mixing 

characteristics of the Ohio River upstream from Cincinnati, Ohio, October 

2004–March 2006, http://pubs.usgs.gov/of/2006/1159/, accessed November 

2007). 

dye concentrations and flows were measured are shown on 

figure 12. 

Depth-averaged flow-velocity magnitudes, derived from 

ADCP measurements obtained by Koltun and others (2006), 

had similar distributions at all dye-measurement transects 

(fig. 13), indicating slow and uniform velocities within the 

gently meandering dye-injection reaches. Of the measured 

depth-averaged velocities, 95 percent ranged from 0.26 to 

1.3 ft/s, August 2–4, 2005. 

On August 2, 2005, dye was injected about 1,180 ft 

downstream from the mouth of Twelvemile Creek, about 

125 ft east of the Kentucky shoreline at cross section OH 4 

(fig. 12). The flow direction in this reach is northerly; the 

injection point on the west side of the river is on the left as one 

faces downstream. This injection site and reach, referred to as 

the Twelvemile Creek (TMC) in this report, and as the “Downstream Dye Study” in the report by Koltun and others (2006), 

was near RM 451.7, with an injection point near N38o58’23” 

and W84o18’05.” In this report, the TMC injection reach 

refers to the Ohio River between transects OH 4 and OH 16, 

approximately RM 451.7 to 463.9 (fig. 2). Vertically wellmixed concentrations were measured at cross section OH 10, 

about 6 mi downstream from the point of injection. Koltun and 

others (2006) considered all dye concentrations downstream 

from OH 10 also to be vertically mixed. 

On August 4, 2005, dye was injected about 400 ft downstream from the mouth of Big Indian Creek, about 60 ft west 

of the Ohio shoreline at cross section OH 0 (fig. 12). This 

injection site and reach, referred to as Big Indian Creek (BIC) 

in this report, and as the “Upstream Dye Study” by Koltun and 

others (2006), was near RM 445.2 (fig. 2), with an injection 

point near N38°53’38” and W84°14’05,” which is near the 

right bank. The BIC injection reach refers to the Ohio River 

between transects OH 0 and OH 9, from RM 445.1 to 456.8. 

Vertically well-mixed concentrations were measured at OH 3, 

about 5.5 mi downstream from the point of injection; concentrations also were considered vertically mixed downstream 

from that point. 

Modeling Approach

A generalized 2D hydrodynamic code was applied to 

simulate the time-varying depth-averaged velocities and 

water levels within the study reach, based on water levels and 

inflows specified at the boundaries of the model area. Surveys 

of river bathymetry and channel geometry depicted on navigational charts were used to describe the model area. Hydraulic 

parameters describing channel friction losses and dispersion 

characteristics were systematically varied to improve the 

match between measured flow velocities and depths, flows, 

and water levels with simulated values for five scenarios. 
12 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Meldahl Dam

Big Indian Creek 

Injection Site

Twelvemile Creek 

Injection Site

Figure 12. Location of transects related to dye-tracer studies (Koltun and others, 2006, fig. 6). 
Modeling Approach 13

OH 1

OH 2

OH 3

OH 4

OH 5

OH 6

OH 7

OH 8

OH 9

OH10

OH11

OH12

OH13

OH14

OH15

OH16

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

VELOCITY MAGNITUDE, IN FEET PER SECOND

TRANSECTS ASSOCIATED WITH DYE CONCENTRATION MEASUREMENTS

EXPLANATION

Median

Lower

quartile

Upper

quartile

Upper

hinge

Lower

hinge

Outliers

Figure 13. Distribution of depth-averaged flow-velocity magnitudes at dye-measurement transects on the Ohio River, 

August 2–4, 2005 (data from Koltun and others, 2006). 

Simulated flow velocities and water levels provided input to a 

2D water-quality transport model to describe the hydrodynamics during the two dye-injection studies (Koltun and others, 

2006). Calibration involved estimating water-quality parameters that describe turbulent mixing and dye-decay characteristics by matching measured and simulated dye concentrations. 

The estimated hydraulic parameter that describes dispersion 

commonly is used to estimate the water-quality parameter that 

describes turbulent mixing. These two parameters, estimated 

from the flow and transport models that use different types of 

data, are compared. 

Dye-Mixing and Transport Rates

Dye concentrations, sampled at a rate of about once 

in 10 seconds, were obtained along the same transect as 

ADCP velocity ensembles, sampled at a rate of about once 

per second. Although the USGS does not ordinarily use 

single-transect ADCP measurements to compute flow, these 

measurements were considered the best information available for determining the magnitude and distribution of flow 

associated with dye-concentration measurements in this study. 

Therefore, cumulative flows at points of dye concentration 

measurements were determined from ADCP data. The cumulative flows were used to compute incremental flows for each 

dye-concentration sample, as shown for flows and dye-concentrations measured on the Ohio River near OH 15 on August 2, 

2005, from 13:44 to 13:54 EST (fig. 14). 

The flow-weighted mean concentration commonly is 

defined as C Q c dq

Q

= ⋅ ∫ 1 0 , where c is the continuous variation in concentration with flow (Q) across the channel. In this 

report,the flow-weighted mean concentration was approximated as 

C Q c i q i = i m 1 ∑ ( )⋅∆ ( ), where the individual dye-concentration measurements along a transect are indicated by cm(i)

and the corresponding incremental flows centered at points of 

dye-concentration measurement are indicated by ∆q i( ).
14 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

1,418,500 1,419,000 1,419,500 1,420,000

395,000

395,500

396,000

396,500 1,000

cubic

feet per

second

Dye concentration

0.5 micrograms

per liter 

Flow

EXPLANATION 

Note: Flows and concentrations are proportional to referenced

values above.

NORTHING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

EASTING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

0 100 200 500 FEET

Figure 14. Flows and dye concentrations at OH 15 on the Ohio River from the Twelvemile Creek dye-injection study, near California, 

Ohio, August 2, 2005, 1344–1354 Eastern Standard Time. 

Similarly, the dye-transport rate was computed as M C= ⋅Q  .

The percent mixing, which is the degree to which a dispersant is mixed in any cross section of the river, is 

defined as P Q

c

C dq m

Q

= − − ∫ 1 1

2 1 0

 and approximated as 

  P Q

c i

C

q i m

m

i

= −1 1 ∑ − ⋅∆ 2 1 ( ) ( ). In general, mean dye concentrations and transport rates decreased with distance downstream 

from the point of injection, and percent mixing increased 

(table 1). 

Hydrodynamic Simulation

In this report, the hydrodynamic code refers to the generalized RMA2 hydrodynamic FORTRAN (Formula Translation) code; the hydrodynamic model refers to the set of input 

files describing the geometry, bathymetry, hydraulic characteristics, and boundary conditions of the Ohio River between 

Meldahl Dam and Cincinnati, Ohio. The code and model 

are used together to simulate depth-averaged velocities and 

water levels for flows and water levels specified at the model 

boundaries. 
Modeling Approach 15

RMA2 Hydrodynamic Code

RMA2 is a generalized computer code for 2D hydrodynamic simulation of surface-water bodies. The code facilitates 

the computation of horizontal flow-velocity components and 

water levels for subcritical, free-surface flow. RMA2 implements a finite-element solution of the Reynolds form of the 

Navier-Stokes equations for turbulent flows. Donnell and 

others (2005) provide detailed documentation of the governing equations, their solution by the finite-element method, 

and recommended uses and limitations of the RMA2 code. 

RMA2 is under continual development by the USACE at the 

Waterways Experiment Station, Coastal Hydraulics Laboratory, in Vicksburg, Miss. RMA2 version 4.56, last modified 

on April 5, 2006, was used in this report. A brief overview of 

those modeling aspects needed to help understand the simulation and calibration process is provided. 

The Reynolds form of the Navier-Stokes equations governing 2D flow that were used consist of a momentum (equation 1) and continuity (equation 2) are 

h u

t

hu u

x

hv u

y

h E u

x

E u

y

gh a

x

h

x

∂

∂

+

∂

∂

+

∂

∂ − ∂

∂

+

∂

∂





 





+

∂

∂

+

∂

∂









2

2

2

2





 + ⋅ ⋅

( ) ( ) + =

∂

∂

+

∂

∂

+

∂

∂ − ∂

g u n

h

u v

h v

t

hu v

x

hv v

y

h E

2

1 6 2

2 2

1

2

2

1 486

0

.



v

x

E v

y

gh a

x

h

x

g v n

h

u

∂

+

∂

∂





 





+

∂

∂

+

∂

∂





 



 + ⋅ ⋅

( )

+

2

2

2

2

1 6 2

2

1.486

v

2

1

2 ( ) = 0

(1)

∂

∂

+

∂

∂

+

∂

∂





 



 +

∂

∂

+

∂

∂ = h

t

h u

x

v

y

u

h

x

v

h

y

0 (2)

where

h is water depth,

u,v are velocities in the Cartesian directions,

x,y,t are Cartesian coordinates and time,

 is the density of water,

E is the isotropic eddy-viscosity coefficient, 

g is gravitational acceleration,

a is the elevation of the channel bottom,

n is Manning’s channel roughness value, and

1.486 is the conversion from metric to English units 

of measurement. 

Table 1. Computed mean dye concentrations, percent mixing, and transport rates at selected Ohio River transects, August 2–4, 2005. 

(Data from Koltun and others, 2006) 

Transect 

identifier

Distance 

downstream 

from injection 

point, in miles

Dyemeasurement 

start time,

Eastern 

Standard Time

Measured flow, 

in cubic feet 

per second

Flow-weighted mean 

dye concentration, 

C,

 in micrograms 

per liter

Computed 

dye-transport 

rates, M, 

in milligrams 

per second

Percent 

mixing, 

Pm



Simulated 

travel 

time, 

in days

Twelvemile Creek injection, August 2, 2005

OH 10 5.99 10:13 28,200 0.875 700 28.0 0.656

OH 11 7.01 11:01 28,300 .683 549 34.3 .746

OH 12 8.02 11:05 27,900 1.02 803 40.8 .844

OH 13 9.07 11:27 30,300 1.20 1,040 41.7 .948

OH 14 10.1 11:36 28,600 .837 678 70.3 1.058

OH 15 11.2 13:44 32,400 .529 487 89.0 1.167

1

OH 16a 12.0 12:49 28,600 .507 412 90.7 1.250

1

OH 16b 12.0 13:07 27,600 .471 386 90.5 1.250

Big Indian Creek injection, August 4, 2005

OH 3 5.49 9:49 21,200 1.20 653 66.0 0.458

OH 4 6.49 10:09 21,000 1.15 546 72.3 .563

OH 5 7.45 12:39 21,100 1.21 669 77.3 .656

OH 6 8.45 12:50 20,500 .921 535 81.2 .771

OH 7 9.52 13:35 20,100 .897 576 93.0 .865

OH 8 10.5 13:25 18,800 .666 383 92.8 .960

1

OH 9a 11.5 14:08 20,800 .401 256 87.4 1.063

1

OH 9b 11.5 14:08 21,800 .432 299 87.7 1.063

1

Transects labeled with an “a” or “b” suffix were collected at the same location but at different times or by different boat crews.
16 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Equations 1 and 2 are solved by the finite-element 

method, using the Galerkin method of weighted residuals 

(Donnell and others, 2005). Integration in space is performed 

by Gaussian integration; derivatives in time are evaluated by a 

nonlinear finite-difference approximation. The solution is fully 

implicit, and the set of simultaneous equations is solved by 

Newton-Raphson iteration (Donnell and others, 2005). 

To numerically solve the partial differential-flow equations, the channel is discretized into a finite-element mesh, 

which provides a flexible means to represent an irregularly 

shaped waterway. Quadrilateral and triangular elements 

formed by nodes at the vertices and midsides of the connecting 

arcs compose the mesh. Eight nodes are defined per quadrilateral element; six nodes are defined per triangular element. 

Contiguous elements forming branches or subreaches of the 

waterway are grouped into material zones to facilitate characterization of the waterway. Channel-roughness coefficients and 

eddy-viscosity characteristics are assigned to material zones. 

Hydrodynamic simulations compute water levels and 

flow velocities at interior nodes from boundary conditions 

specified at exterior (boundary) nodes, the hydraulic characteristics of the waterway, and the flow equations. Boundary conditions include flow (discharge across one or more elements) 

and water level. Quadratic interpolation is used to determine 

water levels and velocities within the elemental areas, based 

on nodal values. Greater densities of nodes provide improved 

spatial resolution of velocity fields but also require additional 

computational resources. 

Velocity distributions are largely determined by the 

advection component described by hydrodynamic simulation. 

Water velocities may decrease in shallow areas because of 

aquatic vegetation that effectively increases channel roughness; adjacent points may have similar velocities, based on 

the effectiveness of turbulent exchange in mixing the water. 

Neither channel roughness nor turbulent exchange (which is 

the fluid momentum transfer resulting from chaotic motions 

of fluid particles) (Donnell and others, 2005) can be measured 

directly in the field; they are inferred from measurements of 

flow, water level, and velocity. 

In RMA2, the eddy-viscosity coefficient represents the 

effects of molecular viscosity and turbulence on turbulence 

exchange in which the turbulence component normally 

dominates. In general, turbulence exchanges depend on the 

momentum of the flow, spatial gradients of the velocity, and 

the scale of the flow phenomenon, as described by the length 

of the element in the direction of flow. For consistency with 

the physical system, eddy-viscosity coefficients in the mesh 

should increase with element size and flow velocity. Higher 

eddy viscosities are associated with greater uniformity of 

velocity distributions across a channel segment. 

Although eddy viscosities may be assigned directly to 

elements in material zones, greater consistency and flexibility 

is obtained within RMA2 by assigning eddy viscosities to elements on the basis of the Peclet formula (Donnell and others, 

2005) in which the Peclet number is inversely related to the 

eddy viscosity as 

E u dx

PRMA

= ⋅ ⋅

2

(3)

where

E is the eddy viscosity assigned to an element, 

 is the water density, determined as a function 

of water temperature, 

u is the average elemental velocity, 

dx is the length of the element in the streamwise 

direction, and 

PRMA2 is the dimensionless Peclet number, which is 

generally recommended to be between 15 

and 40 (Donnell and others, 2005). 

Greater Cincinnati Hydrodynamic Model of the 

Ohio River

The geometry (shoreline) of the Ohio River was based 

on Ohio River Navigation Charts 115–122, published by 

U.S. Army Corps of Engineers (2000). The charts were available as map images in Adobe Systems Incorporated’s Portable 

Document Format (PDF). The PDF files were converted to the 

Joint Photographic experts Group (JPG) graphic format for 

import into Surface Water Modeling System (SMS) (Environmental Modeling Research Laboratory, 2006). Within 

SMS, the JPG files were georeferenced to scale and rotate the 

images. Selected latitude and longitude tic marks shown on the 

chart images were converted to Ohio South (3402) State Plane 

Coordinate System of 1983 with Corpscon (U.S. Army Corps 

of Engineers, 2005) for spatial reference. 

The bathymetry of the Ohio River within the model area 

was based on surveys from 2004 to 2006 by Koltun and others 

(2006)4. Bathymetry data were measured at an average transect spacing of about 800 ft by a boat-mounted single-beam 

echosounder. To compute streambed elevations, depth information obtained from the echosounder were postprocessed 

and subtracted from the water surface that was determined 

from GPS survey techniques or derived from the assumption 

of constant water-surface slope between surveyed locations. 

The bathymetry data were written to text files formatted as a 

series of space-delimited x-, y-, and z-coordinates. Geographic 

coordinates for bathymetry data in this report are referenced 

to the North American Datum of 1983 (NAD 83), Ohio State 

Plane (Ohio South) coordinates, U.S. Survey Feet. Streambed 

elevations are reported in feet relative to the North American 

Vertical Datum of 1988 (NAVD 88). Bathymetry data can 

be downloaded from the Internet at http://oh.water.usgs.gov/

ORreport/data/bathymetry.zip (accessed December 2006). 

4

 Bathymetry data can be downloaded from the Internet at http://pubs.usgs.

gov/of/2006/1159 through a link in the table of contents titled “Retrieval of 

Data” in U.S. Geological Survey Open-File Report 2006–1159 by Koltun and 

others (2006). 
Modeling Approach 17

The surveyed bathymetry data were supplemented with 

nearshore elevations shown on the Ohio River Navigation 

Charts (U.S. Army Corps of Engineers, 2008). Charts are 

referenced to the Ohio River vertical datum (U.S. Army Corps 

of Engineers, 2005b). Between Meldahl Dam and the Cincinnati water-level gaging station, the USACE communication 

directs users to subtract an average of 0.73 ft from the Ohio 

River Vertical Datum to obtain the “1929 General Adjustment,” which is interpreted as the National Geodetic Vertical 

Datum of 1929 (NGVD 29). In the model area, elevations 

referenced to NAVD 88 can be obtained by subtracting 0.65 ft 

from elevations referenced to NGVD 29. 

SMS software (Environmental Modeling Research 

Laboratory, 2006) was used to develop the finite-element mesh 

and to help interpolate the bathymetry between measured 

transects. In SMS, a map coverage was created that subdivided 

the study area into 52 polygons defined by 319 arcs. Four arcs 

typically were used to outline a polygon. Arcs are defined by 

vertices that initially were located by digitizing straight-line 

segments that outlined the channel geometry in subreaches 

about 1-mi long. When the channel geometry was defined, the 

vertices were redistributed uniformly along the arcs at about 

100-ft intervals. Subsequently, the patch-meshing technique 

was assigned to each polygon. This meshing technique defines 

elements and nodes throughout the polygon by constructing a 

partial bicubic Coon’s patch. This patch is based on the outlining vertex locations when the map coverage is converted to a 

finite-element mesh (Environmental Modeling and Research 

Laboratory, 2006). A material zone was assigned to each 

polygon; material zones share common channel-roughness and 

eddy-viscosity characteristics. To allow for possible systematic 

differences in effective channel roughness between areas of 

deep and shallow flow, the model contains two material zones. 

The deep zone corresponds to mid-channel areas shown in 

white on the navigational charts; the shallow zone corresponds 

to near-bank areas shown in purple. 

Finite-Element Mesh

The finite-element mesh developed for the hydrodynamic 

study of the Ohio River area (a section of which is shown 

in fig. 15) includes 29,392 quadrilateral and 359 triangular 

elements defined by 92,622 nodes. Corner nodes are at the 

vertices of the elements, and midside nodes are midway along 

an arc that connects adjacent corner nodes. Each element is 

about 100 ft on a side, and there is little variability in areas 

among elements. The entire mesh spans about 10.5 mi2. Within 

the finite-element mesh, nodestrings were defined to connect 

nodes that span the width of a river or a tributary. Nodestrings 

were used to specify flow and water-level boundary conditions 

and to specify transects where flow would be computed. 

Elements

Nodes

Nodestring 

defining flow

boundary

Nodestring

defining

continuity

check line

1,418,000 1,419,000 1,420,000 1,421,000 1,422,000

399,000

398,000

397,000

EASTING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

NORTHING, IN OHIO SOUTH 1983 STATE PLANE 

COORDINATE SYSTEM FEET

0 200 400 1,000 FEET

Figure 15. Image of the finite-element mesh near the confluence of Little Miami River and the Ohio River. 
18 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Individual nodes within the mesh were repositioned as 

needed to satisfy mesh quality-assurance criteria that increase 

the accuracy and reduce numerical instability of finite-element 

computations. These criteria include a minimum interior angle 

of 10 degrees for triangular elements (20 degrees for a quadrilateral element), no concave quadrilaterals, and an elementarea change restriction that prevents elements from being 

50 percent larger or smaller than adjacent elements. 

Bathymetry data from measurement at transects and nearshore elevations from topographic maps were interpolated to 

model nodes in a two-step process. In the first step, a curvilinear grid was superimposed over the model area that followed 

the curvature of the centerline of the river. The grid was composed of rectangular cells, which had a length of 70 ft in the 

streamwise direction and 20 ft in the cross-stream direction. 

The template method (McDonald, Bennett, and Nelson, in 

press) was used to interpolate river elevations across the grid. 

A template consists of a moveable cluster of cells 

centered at the point of estimation, which for the Ohio River 

analysis was 4 cells long in the streamwise direction and 

1-cell wide in the cross-stream direction. For each cell, the 

area spanned by the template was used to search adjacent grid 

cells for bathymetry data. The basic idea of this method is that 

riverine topography tends to vary more in the cross-stream 

(transverse) direction than it does in the streamwise (longitudinal) direction (McDonald, Bennett, and Nelson, in press). 

At each grid cell, an estimate of the channel bottom is 

computed as the inverse distance-weighted average of data 

spanned by the template. If no points were detected in the 

initial search, the template was doubled in size, preserving the 

specified ratio of length to width, and searched again until one 

or more points were found. Up to 3 template expansions were 

possible. In this analysis, the weighting exponent was one, 

which is equivalent to simple averaging of bathymetry values. 

In the second step, a triangular irregular network (TIN) 

was formed from the bathymetry values in the curvilinear grid. 

This grid was overlain on the finite element mesh and linear 

interpolation was used to estimate the elevation of all model 

nodes. 

Boundary-Condition Scenarios

Boundary conditions were defined for five scenarios that 

correspond to the periods of the data collection. The scenarios, 

shown with associated data, are identified as Oct2004 (fig. 16), 

Aug2005 (fig. 17), Oct2005, (fig. 18), Nov2005 (fig. 19), and 

Mar2006 (fig. 20) to correspond to the month and year of 

data collection. One scenario (Oct2005) is associated with the 

water-level measurements (table 2, fig. 21) obtained during the 

2004–06 bathymetry surveys. 

Figure 16. Water 

levels and flows 

in the Ohio River 

model area, 

October 4–8, 2004, 

scenario (Oct2004). 

10/4/04 0:00 10/5/04 0:00 10/6/04 0:00 10/7/04 0:00 10/8/04 0:00

MONTH/DAY/YEAR HR:MN, IN EASTERN STANDARD TIME

454

456

458

460

455

457

459

W

ATER LEVEL, IN FEET ABO

VE NORTH 

AMERICAN VERTICAL DATUM OF 1988

30,000

40,000

50,000

60,000

70,000

80,000

90,000

FLOW, IN CUBIC FEET PER SECOND

EXPLANATION

Meldahl water level

Meldahl rated flow

Meldahl adjusted flow

Acoustic Doppler curremt profiler flow

Cincinnati water-level gaging station
Modeling Approach 19

8/1/05 0:00 8/2/05 0:00 8/3/05 0:00 8/4/05 0:00 8/5/05 0:00

MONTH/DAY/YEAR HR:MN, IN EASTERN STANDARD TIME

454.5

455.0

455.5

456.0

454.8

455.3

455.8

W

ATER LEVEL, IN FEET ABO

VE NORTH 

AMERICAN VERTICAL DATUM OF 1988

16,000

20,000

24,000

28,000

32,000

36,000

FLOW, IN CUBIC FEET PER SECOND

EXPLANATION

Meldahl water level

Meldahl rated flow

Meldahl adjusted flow

Acoustic Doppler curremt profiler flow

Cincinnati water-level gaging station

10/21/05 10/22/05 10/23/05 10/24/05 10/25/05 10/26/05 10/27/05 10/28/05 10/29/05

MONTH/DAY/YEAR

454

455

456

457

458

459

460

461

462

W

ATER LEVEL, IN FEET ABO

VE NORTH 

AMERICAN VERTICAL DATUM OF 1988

0

20,000

40,000

60,000

80,000

100,000

FLOW, IN CUBIC FEET PER SECOND

EXPLANATION

Meldahl water level

Meldahl rated flow

Meldahl adjusted flow

Cincinnati water-level gaging station

Figure 17. Water 

levels and flows 

on the Ohio River, 

August 1–5, 

2005, scenario 

(Aug2005). 

Figure 18. Water 

levels and flows 

on the Ohio River, 

October 21–29, 

2005, scenario 

(Oct2005). 
20 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

11/2/05 0:00 11/3/05 0:00 11/4/05 0:00 11/5/05 0:00

MONTH/DAY/YEAR HR:MN, IN EASTERN STANDARD TIME

454.0

455.0

456.0

457.0

458.0

454.5

455.5

456.5

457.5

W

ATER LEVEL, IN FEET ABO

VE NORTH 

AMERICAN VERTICAL DATUM OF 1988

30,000

35,000

40,000

45,000

50,000

FLOW, IN CUBIC FEET PER SECOND

EXPLANATION

Meldahl water level

Meldahl rated flow

Meldahl adjusted flow

Acoustic Doppler curremt profiler flow

Cincinnati water-level gaging station

3/20/06 0:00 3/21/06 0:00 3/22/06 0:00 3/23/06 0:00

MONTH/DAY/YEAR HR:MN, IN EASTERN STANDARD TIME

456.0

460.0

464.0

468.0

454.0

458.0

462.0

466.0

W

ATER LEVEL, IN FEET ABO

VE NORTH 

AMERICAN VERTICAL DATUM OF 1988

60,000

80,000

100,000

120,000

140,000

FLOW, IN CUBIC FEET PER SECOND

EXPLANATION

Meldahl water level

Meldahl rated flow

Meldahl adjusted flow

Acoustic Doppler curremt profiler flow

Cincinnati water-level gaging station

Figure 20. Water 

levels and flows 

on the Ohio River, 

March 20–23, 

2006, scenario 

(Mar2006). 

Figure 19. Water 

levels and flows 

on the Ohio River, 

November 2–5, 

2005, scenario 

(Nov2005). 
Modeling Approach 21

Table 2. Sites of water-level measurements during bathymetry surveys. 

River mile Site 

reference

Site 

description

Nearest 

RMA2 model 

node

Latitude/ 

longitude

Northing/easting 

(Ohio South 

1983 State Plane 

Coordinate 

System Feet)

436.1 Meldahl Dam Ohio River downstream from 

Meldahl Dam

1 38°47’50”

84°10’00”

294,747

1,493,506

438.7 1009 Ohio River at Neville, Ohio 6,359 38°48’25”

84°12’43”

298,529

1,480,670

442.7 1008 Ohio River at Boat Ramp at 

Moscow, Ohio

16,013 38°51’22”

84°14’00”

316,548

1,474,920

446.9 1007 Ohio River at Bubbers Restaurant 

near Clermontville, Ohio

27,959 38°54’57”

84°15’05”

338,395

1,470,200

449.4 1006 Ohio River at Skippers Boat Ramp 

near New Richmond, Ohio

35,604 38°56’44”

84°16’46”

349,374

1,462,433

462.5 1005 Ohio River at the Boat Ramp at 

California, Ohio

73,875 39°03’52”

84°25’54”

393,571

1,420,083

470.6 Cincinnati water-level 

gaging station

Ohio River at Cincinnati, Ohio 

(03255000)

92,573 39°05’40”

84°30’38”

404,966

1,397,923

Table 3. Drainage areas of the Ohio River and selected tributaries. 

Stream name 

and location

Drainage 

area 

(mi2)

Ohio 

river mile 

(RM)

Basin location Drainage 

area ratio

Flow 

adjustment 

ratio

Ohio River at Meldahl Dam 70,808 436.5 Ohio and Kentucky 1.00000 1.0000

Big Indian Creek at mouth 40.0 445.1 Ohio .00056 .00059

Twelvemile Creek at mouth 46.0 451.5 Kentucky .00065 .00067

Fourmile Creek at mouth 16.4 461.3 Kentucky .00023 .00024

Little Miami River at mouth 1,757 463.6 Ohio .02481 .02573

Licking River at mouth 3,707 470.3 Kentucky .05235 .05429

Subtotal 76,374 -- -- 1.07861 11.08152

Ohio River at Cincinnati, Ohio 76,580 471.5 Ohio and Kentucky 1.08152 --

The flow-exceedance characteristics during these ADCPrelated scenarios varied from 0.87 to 0.16 (fig. 10). Transient 

simulations were used to track time-varying water levels 

and flows within these scenarios with boundary conditions 

specifications at 4-hour intervals. The downstream boundary for the simulations was time-varying water levels at the 

Cincinnati water-level gaging station. The upstream boundary 

was time-varying flows at Meldahl Dam, which were based 

on the adjusted gate-rated flows. Flow boundaries for selected 

tributaries were computed to account for inflows between Meldahl Dam and the Cincinnati water-level gaging station. Flow 

boundary specifications at tributaries were generally based on 

simple drainage-area ratio adjustments of flow computed at 

Meldahl Dam (table 3). 
22 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

10/5/04 12:00 10/6/04 0:00 10/6/04 12:00 10/7/04 0:00 10/7/04 12:00 10/8/04 0:00

MONTH/DAY/YEAR HR:MN, IN EASTERN STANDARD TIME

454.5

455.0

455.5

456.0

456.5

457.0

457.5

458.0

454.0

455.0

456.0

457.0

458.0

459.0

460.0

W

A

TER LEVEL, I

N FEE

T

ABO

VE NORTH AMERICAN VERTICAL DATUM OF 1988

10/23/05 10/25/05 10/27/05 10/29/05 10/31/05 11/2/05 11/4/05 11/6/05

456.0

457.0

458.0

459.0

460.0

461.0

462.0

3/21/06 12:00 3/22/06 0:00 3/22/06 12:00 3/23/06 0:00 3/23/06 12:00 3/24/06 0:00

SITE

Meldahl Dam

1009

1008

1007

1006

1005

Cincinnati water-level gaging station

Figure 21. Water-level measurements during the 2004–06 bathymetry surveys. 
Modeling Approach 23

Water-Quality Simulations

Water-quality simulations were developed to approximate 

the distribution of dye concentrations measured during two 

dye-injection studies. Water-quality simulations were based on 

a water-quality transport code that used the flow velocities and 

depths simulated by the RMA2 hydrodynamic model of the 

Ohio River. A dispersion parameter in the transport model was 

adjusted to improve the match between measured and simulated dye concentrations. 

RMA4 Water-Quality Transport Code

The generalized water-quality transport code RMA4 

WES (version 4.5), referred to in this report as RMA4 (Letter 

and others, 2005), was used as a basis for dye-concentration 

simulations on the Ohio River. RMA4 is designed to simulate 

depth-averaged advection-diffusion processes in surface-water 

bodies where flow paths can be approximated by longitudinally integrating their local depth-averaged horizontal-velocity 

components. The model is applicable to vertically mixed, 

conservative constituents that are dissolved or neutrally buoyant in water. Non-conservative substances may be described 

if their mass loss can be approximated by a first-order decay 

process. The model has been used to identify potential critical 

areas for the spread of pollutants (Letter and others, 2005). 

RMA4 is a finite-element water-quality transport code 

that simulates 2D (depth-average) equations of transport and 

mixing, having the form 

h c

t u c

x v c

y

D

x

c

x

D

y

c

y

kc ∂ x y

∂

+

∂

∂

+

∂

∂ − ∂

∂

∂

∂





 



 − ∂

∂

∂

∂





 



 − + 





  

 = 0 (4)

where

h is water depth,

c is dye concentration, 

t is time,

u,v are velocity in the x (easting) and y (northing) 

directions,

Dx, Dy are turbulent mixing coefficients, which were 

assumed to be anisotropic such that 

Dx = Dy = 5D, k is first order decay coefficient for dye 

concentrations, and 

 specifies the loading rate of dye of 767 mg/s 

for both injections sites. 

5

 According to Fischer and others (1979), “Turbulence causes longitudinal 

mixing presumable at about the same rate as transverse mixing because there 

is an equal lack of boundaries to inhibit motion. ... Rates of turbulent longitudinal mixing have not been measured by dye spreading experiments, because 

of the difficulty in separating the effects of longitudinal turbulent fluctuations 

from the results of the shear flow.” 

The terms in the transport and mixing equation describe 

local storage, easting and northing advection, easting and 

northing dispersion, local sources of dye, and exponential 

decay, respectively. Like RMA2, the transport equation is 

solved by the finite-element method, using Galerkin weighted 

residuals (Letter and others, 2005). 

In equation 4, the turbulent-mixing coefficients were 

dynamically assigned on the basis of local simulated velocity 

and element size as 

D u dx

PRMA

= ⋅

4

(5)

where

D is the turbulent-mixing coefficient,

u is the average elemental velocity, 

dx is the element length computed in the 

direction of flow, and 

PRMA4 is the RMA4 Peclet number. 

RMA4 always is run in transient (dynamic) mode, 

regardless of whether the RMA2 hydrodynamic results are 

steady state or transient. If the RMA2 solution is steady state, 

the hydrodynamics are reapplied at every time step in RMA4. 

For transient RMA2 simulations, the starting and stopping 

time for RMA4 can be specified within the duration of the 

RMA2 run. Letter and others (2005) provide detailed instructions for coding the Timing Control (TC) card in the RMA4 

run-control file needed to specify the starting time within the 

RMA2 simulation, the time step, and the total number of time 

steps in the simulation, the Boundary Loading (BL) card to 

constituent loadings at elements, and the Boundary Concentration (BC) card to specify constituent concentrations at the 

model boundaries. 

Greater Cincinnati Water-Quality Transport 

Model of the Ohio River

The Greater Cincinnati water-quality transport model 

uses simulated velocities and water level data from the 

hydrodynamic model as a basis for transport simulations. The 

finite-element mesh for transport simulations described in this 

section has been refined from the hydrodynamic version. The 

refinements were implemented to provide a greater density 

of velocity and flow-depth information near the dye-injection 

sites at TMC and BIC and to accommodate minor inflows 

from Fourmile and Tenmile creeks, small tributaries to the 

Ohio River near RM 461.4 and 455.0, respectively (fig. 2). 

The refinements facilitated estimation of transport parameters associated with turbulent mixing, which were derived 

from the analysis of dye-concentration data from the two 

dye-injection studies. Once estimated, the transport parameters 

were used with the hydrodynamic mesh for transport simulations. The transport model also contains a decay coefficient 

that is constituent specific and describes the loss of the constituent with time. 
24 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Mesh Refinement

In this report, dye-loading rates were specified at selected 

elements to simulate the discharge of dye from injections 

at TMC and BIC. So that the dye-injection elements more 

closely matched the size of the injection points, the finiteelement mesh was refined in the vicinity of the dye-injection 

sites. Within SMS, refinement implies that an element is 

subdivided into four equally sized (sub) elements, with a corresponding increase in nodes. 

A nested, two-stage refinement was applied to elements 

that surround each dye-injection site (fig. 22). In the first stage, 

a rectangular array of elements (about eight elements long in 

the direction of flow and four elements wide) outward from 

the edge of the channel, was refined. After the initial refinement, unrefined elements along the perimeter of the array 

were split into two or three elements to avoid excessive area 

changes between refined and unrefined elements. A second 

refinement of a subset of the previously refined array was 

applied similarly. General procedures for mesh refinement are 

documented within SMS (Environmental Modeling Research 

Laboratory, 2006). 

In addition to mesh refinements near the injection sites, 

elements and a flow-boundary nodestring were added to represent flow from Fourmile and Tenmile Creeks at the confluence 

with the Ohio River. The refined mesh comprises 30,398 elements and 94,343 nodes. To maintain numerical efficiency, the 

nodes and elements were renumbered. Thus between the two 

hydrodynamic model versions, nodestrings identifying sets 

of boundary nodes and geometry-continuity check lines may 

refer to the same nodes but may have different node numbers. 

Although mesh refinement can improve the horizontal 

resolution of water-quality transport simulations, the vertical 

resolution is fixed as the depth-averaged concentration. At 

both sites, dye was injected about 0.5 to 1 ft below the water 

surface. Based on transects downstream from the injection 

points in which dye was measured at multiple depths, Koltun 

and others (2006) indicate that dye concentrations were vertically mixed 5 mi downstream from the injection points. 

Boundary-Condition Scenarios

Two scenarios were used to represent the two dye-injection studies. In each scenario, a loading rate of 767 mg/s was 

specified at the element corresponding to the dye-injection 

site, and zero was assigned to constituent concentrations at all 

flow boundaries. Hydrodynamic boundaries and parameters 

were consistent with those that were specified in the Aug2005 

hydrodynamic scenario. In contrast to 4-hr hydrodynamicsimulation time steps, however, water-quality transport was 

simulated at 1-hr time steps to accommodate rapid temporal 

and spatial changes in concentrations downstream from the 

points of injection. Transport rates expressed in milligrams per 

second result in simulated concentrations in milligrams per 

cubic meter or micrograms per liter, which is consistent with 

measured dye-concentration units (Koltun and others, 2006). 

In the refined mesh, element 16642 was selected to 

represent the TMC dye-injection site, and element 23087 

represents the BIC injection site. The area of these elements 

is about 282 ft2, which is a closer approximation to a point 

injection than the average element area of about 10,000 ft2. As 

the distance from the point of injection to the area of interest 

increases, the impact of refining the injection element on simulated concentrations near the target area diminishes. In this 

report, dye transects where vertical mixing had occurred about 

5.5 mi or more downstream from the point of injection were 

selected for use in calibrating the transport model. 

Simulations with the water-quality model may be done in 

all English or all metric units. The hydrodynamic model was 

developed in English units so that the more familiar system of 

units in the United States could be used to specify the geometry, bathymetry, and boundary conditions of the system. Dye 

concentrations, however, were measured in metric units of 

micrograms per liter. To provide consistency between units of 

measured and simulated dye concentrations, scaling factors 

were applied to the hydrodynamic model to convert the English units to metric units. 

Within the water-quality model, unit conversion is 

accomplished by changing three input-card images in the runcontrol file of the water-quality model, which by default has 

the extension trn. The SI Card, for the International System of 

units, is coded as “SI 1” to identify the card type and specify a 

value of 1 (true) for the variable METRIC; this indicates that 

metric units are expected as input and used for output. The 

GS Card, for converting the river geometry and bathymetry 

data, is coded as “GS 0.3048 0.3048” to identify the card type 

and specify values for the variables XSCALE and YSCALE, 

respectively, which provide the feet-to-meter conversion. 

The HS Card, for hydrodynamic conversion, is coded as “HS 

0.3048 0.3048 0.3048” to identify the card type and specify a 

scaling factor for variable USCALE, applied to the simulated 

easting velocity components; the variable VSCALE, applied to 

the simulated northing velocity components; and the variable 

WSCALE, applied to the simulated depths of flow. Letter and 

others (2005) provide detailed instructions on coding RMA4. 

Parameter Estimation and Model Calibration

Inverse modeling techniques were used in this report to 

estimate RMA2 and RMA4 parameters that have physical significance for describing flow and dispersion but, unlike geometry and bathymetry, cannot be measured directly. Parameters 

had to be inferred from measurements of other attributes by 

comparing simulated with measured values. A nonlinearregression technique embedded within UCODE_2005 (Poeter 

and others, 2005) was used with measurements of water level, 

flow, water depth, water velocity, and dye concentrations to 

estimate RMA2 parameters associated with channel roughness 

and eddy viscosity and RMA4 Peclet numbers associated with 

turbulent mixing and decay rate. Parameters in RMA2 were 

estimated independently of parameters in RMA4. 
Modeling Approach 25

Twelvemile Creek

Injection point

358,000

361,000

1,456,000 1,458,000

Big Indian Creek

Injection point

330,000

332,000

1,473,000 1,475,000

Base chart from 

U.S. Army Corps

of Engineers, 2002.

North American

Datum of 1983

State Plane 

Projection, Ohio

South, in feet

EASTING, IN OHIO SOUTH STATE PLANE COORDINATE SYSTEM FEET

NORTHING, IN OHIO SOUTH STATE PLANE COORDINATE SYSTEM FEET

0 250 500 1,000 FEET

Figure 22. Refined mesh areas that surround dye-injection sites near Twelvemile Creek and Big Indian Creek on the 

Ohio River. 
26 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Nonlinear Regression

Nonlinear regression provides a generally applicable 

method for calibrating models in which simulated values 

vary nonlinearly with model parameters (Hill, 1998). In this 

study, the objective was to minimize the sum of the weightedsquared differences between measured and simulated values as 

S b y y b i

N

i i i ( ) = − [ ] ( ) ∑ = 

1

2  (6)

where 

S b( ) is the sum of weighted-squared differences 

between measured and simulated values,

b is a vector of model parameters of length p, 

N is the number of measurements, 

yi is the i

th measurement, 

y b i( ) is the i

th simulated value, which is a function 

of the underlying model and associated 

parameters, and

i is the weight for the i

th measurement. 

The difference y y b [ ] i i −  ( ) is referred to as a residual; 

the difference i i i y y b 1 2 [ ] −  ( ) is a weighted residual. Measurement weights  provide a mechanism for expressing 

the uncertainty of individual measurements and for including 

measurements in different scales (for example, flow, in cubic 

feet per second and water level, in feet) within the same objective function. In this report, the weight matrix Ω was approximated as a diagonal matrix with elements ii , which does not 

account for correlations among measurement errors. 

Initial values of model parameters b 0 were assigned 

physically plausible values. After the first model simulation 

was completed with the initial (reference) parameter vector, each parameter was, in turn, varied by a small amount 

(perturbed) and the model was rerun. The collection of p+1

simulations was used to compute a forward approximation 

of the sensitivity matrix X N p × , which describes the sensitivity of each simulated value for which there is a matching 

observation to each parameter. The i,jth element in the forward 

sensitivity matrix is computed as

∆

∆

∆

∆

   y

b

y b b y b

b b b

i

j

i j i

j

= ( ) + − ( )

( ) + − ( ) (7)

where 

∆bj is the change in j

th parameter estimate, and

∆bj is a zero vector of length p except for the j

th

element, which contains ∆bj . 

To facilitate the comparison of sensitivities among 

parameters and measurements in different scales, a dimensionless scaled sensitivity is calculated as 

ss y

b

b ij

i

j

= j ii











 ⋅ ∆

∆

 1 2

The composite scaled sensitivity css provides a measure 

of the total sensitivity of the estimated parameters to the measured data. Parameters associated with higher css values are 

more sensitive to the data. Values of css are independent of the 

measured values and the model fit. Hill (1998) calculates css

for each parameter as css s j s N ij b i

N

= ( ) ∑ =

2

1 . 

When the sensitivity matrix is computed, based on the 

initial parameter estimates and perturbation results, all parameter estimates are updated simultaneously using an iterative 

process of the modified Gauss-Newton optimization method 

(Hill, 1998) as 

d C C X X C I m

C X y y b

b

r r

T

r

T

r r p p r

T

r

T

r

r

r

r

= ⋅( ⋅ ⋅ ⋅ ⋅ + ⋅ )

⋅ ⋅ ⋅ − ( )

×

−

Ω

Ω

1

( )

+1 = ⋅ r r + r d b 

(8)

where

d r is the computed change in the parameter 

vector for the rth regression iteration, 

Xr is the sensitivity matrix evaluated with 

parameter estimates b r ,

Ω is a diagonal weight matrix with nonzero 

elements ii ,

Cr is a p dimensional diagonal scaling matrix 

with elements c X r jj r X T

r jj ( ) = ⋅ ( ) Ω⋅

I p p × is an identity matrix, and 

mr is the Marquardt parameter, which improves 

regression performance for ill-posed 

problems (Hill, 1998), 

br+1 is the updated parameter vector, and

r is a damping parameter between 0 and 1 that 

is used to reduce parameter oscillations. 

Values in the updated parameter vector can be modified 

because of parameter constraints before use as the reference 

parameter vector for the calculation of revised model simulations and perturbation analyses. Regression iterations continue 

until convergence is achieved and changes in the objective 

function are less than the specified amount and parameters 

are stable, or the maximum number of regression iterations is 

exceeded or other difficulties are encountered. 
Modeling Approach 27

For regressions that converge, several overall statistical 

measures of fit are computed. In particular, the estimated error 

variance is computed as 

s S b N p f

2 = − ( ) ( ) (9)

where

S bf ( ) is the weighted sum of squared residuals 

computed with the final estimate of the 

parameter vector.

This variance, together with the final estimate of the sensitivity matrix, is used to compute the symmetrical covariance 

matrix of the parameter vector as V bf s X f X T

f ( ) = ⋅ ( ) ⋅ − 2 1

Ω .

The standard error of the regression is the square root of 

the estimated error variance. The diagonal elements are 

the variances of the individual parameters sbj

2 , and the off 

diagonal elements are covariances between parameter pairs. 

An (1-α)-level linear confidence interval is computed for 

each parameter as b t s j N p bj ± ⋅ − −,1  2 , where t is the Student-t

statistic with N-p degrees of freedom. Finally, the parametercorrelation matrix is computed from covariance elements 

of cov ( ) ij = V bf ij and the correlation between the i

th and jth

parameter corij = ij ii jj cov cov ⋅ cov . Parameter correlations 

can vary in the interval [-1, 1]. Parameter correlations with an 

absolute value greater than 0.85 indicate that some degradation in parameter estimates may have occurred because of the 

ambiguity of the effects caused by two model parameters on 

simulated results. 

UCODE Analyses

UCODE provides for parameter estimation, using nonlinear regression by controlling the execution of the regression analysis, defining the magnitudes and uncertainties of 

measured data, providing instructions for extracting simulated 

values from model output files and, in some cases, deriving simulated values that better correspond with points of 

measured data. Commonly, derived values were spatially or 

temporally interpolated from simulated values to improve the 

match to locations of measured data. 

Parameters in the hydrodynamic model were estimated 

before parameters in the water-quality transport model were. 

Hydrodynamic model parameters for channel roughness or 

resistance to flow were targeted at determining whether there 

were significant differences in average roughness characteristics between zones of flow depth. The eddy-viscosity parameter, estimated from the dimensionless RMA2 Peclet number, 

was used to characterize the variability of velocities across the 

river. In general, higher RMA2 Peclet numbers are associated with lower eddy viscosities and more local variability in 

velocities; lower Peclet numbers are associated with higher 

eddy viscosities and more uniform local velocities. In RMA2, 

hydrodynamic simulations can become numerically unstable if 

Peclet numbers are too high. 

Results of hydrodynamic model calibration are passed 

to the water-quality transport model in the form of simulated velocities and depths of flow. In addition, the (RMA2) 

Peclet number estimated in the hydrodynamic-model calibration PRMA2 provides an initial estimate of the (RMA4) Peclet 

number in the water-quality transport model PRMA4, which was 

updated on the basis of dye-concentration data. Eddy viscosities, E in lb-s/ft, derived from the PRMA2 have different units 

than turbulent mixing coefficients (D in ft2/s) derived from the 

PRMA4. This sequential calibration strategy provided an opportunity to test the possibility that PRMA2 = PRMA4, which would 

imply that dye-concentration data may not be needed for 

estimating turbulent mixing characteristics in the water-quality 

model; thus, dye injection-studies might not be needed. 

Hydrodynamic-Model-Calibration Strategy

Five transient-flow scenarios were used to estimate 

hydrodynamic-model parameters in equation 1. Two parameters were used to describe possible systematic differences 

in channel resistance to flow among shallow and deep zones. 

On navigational charts (fig. 15), shallow zones of the river are 

shown with a blue tint; deep zones are shown in white. Each 

element was assigned to the shallow or deep zone. One additional parameter in equation 4, referred to as the RMA2 Peclet 

number, is used to assign eddy-viscosity values as a function 

of flow velocities and element sizes. 

The Greater Cincinnati hydrodynamic model simulates 

flow depths y b d ( ) and easting y b VelE ( ) and northing y b VelN ( )

velocity components at nodes, monitored water levels y b H ( ) ,

and flows y b Q ( ) for comparison with measured values. The 

following text describes how corresponding measurements 

yd , yVelE , yVelN , yH , and yQ were computed and how 

weighting factors ω were assigned to individual measured 

values and measurement types to represent their corresponding 

precisions. 

During the five scenarios used in model calibration, 

water depths and flow velocities were measured at each ADCP 

ensemble throughout numerous transects across the Ohio 

River (Koltun and others, 2006). Although few ensembles 

were colocated with nodes for direct comparison, numerous 

nodes were located near one or more ensembles. In this report, 

a node N was considered estimable if one or more ensembles 

E were within 50 ft of a model node. If a node was determined 

to be estimable, the closest of up to 10 ensembles was used to 

compute an inverse, distance-weighted average and standard 

deviation for the flow depth and velocity components at that 

node. Water depths and flow velocities computed by the transformation of measured values described in the following text 

are referred to as measured water depths and flow velocities. 
28 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Inverse distance weighting factors i j ( ) were computed 

for each of the i n = ≤10 closest ensembles to the j

th node as 

 i j N j E i N j E i Easting Easting Northing Easti ( )

' = 1 ( ( ) ( − ) ) + ( ( ) ( − ) 2

ng

N j

i

i j N j

i j

i j

)

( )

'

( )

'

( )

( )

( )

2

10

Α

Α

=

=

≤

∑

 

(10)

where 

N j Easting ( ) and N j Northing ( ) indicate the easting and northing 

coordinates for the j

th node, 

respectively, with 

 E i Easting ( ) and E i Northing ( ) defined similarly for the i

th ADCP 

ensemble. 

When the weighting factors were computed, the estimate of 

depth at the j

th node was computed as y y d j i j d E i

i n

( ) = ⋅ ( ) ( ( ))

=

∑

Similar computations were used to determine the easting 

yVelE( )j and northing yVelN ( )j velocity components at the j

th

node. The standard deviation of the inverse, distance-weighted 

averages of flow depths was computed at estimable nodes as 

( )

( ( )) ( )

d j ( )

d E i d j

i

n

i j

i

n y y

n = ( − ) − ⋅ = =

∑ ∑

2

1

2

1 1

(11)

Measurement weights for depths were computed as a function 

of measurement uncertainty and the number of depth measurements, as 

(12)

where

 NumMeaSet is the number of depth measurements. 

For depth and velocity data, the number of measurements 

in the set is the number of estimable nodes. Adjusting measurement weights for the number of measurements in the set 

prevented the parameter-estimation analysis from being too 

heavily weighted by any particular type of measurement. 

Similar computations were used to compute measurement 

weights for easting and northing velocity components VelE( )j

and VelN ( )j . Linear interpolation was used to temporally 

adjust simulated depths and velocities to match measured 

values near nodes. 

During the five scenarios, water-level data yH were 

obtained at 4-hour intervals from tailwater measurements at 

Meldahl Dam and from miscellaneous water-level obtained 

during the October 2005 bathymetry survey. A standard deviation of 0.15 ft was specified (Robert R. Mason, Jr., USGS 

Office of Surface Water, written commun., 2008) as the uncertainty of the water-level data. 

Flow data yQ were based on single-transect ADCP flow 

measurements during the five scenarios. Although the accuracy of single-transect measurements is uncertain, they were 

considered to be of fair to poor quality with an uncertainty of 

about 10 percent. Within UCODE_2005, this was expressed as 

a coefficient of variation of 0.10; the corresponding measurement weights were computed as 

 Q i i = ⋅ 1 0 ( 10 Q N⋅ umMeaSet) 2 ( . ) , 

where

Qi is the measured flow. 

Simulated flows were linearly interpolated with time for comparison with measured flows. The number of measurements 

of each type used in the estimation of the RMA2 parameters 

varied from 116 to 7,174 (table 4). 

Water-Quality-Transport Model-Calibration Strategy

Two water-quality-transport scenarios were used with 

UCODE_2005 to estimate turbulent-mixing coefficients in 

equation 6. Turbulent mixing coefficients are assigned as a 

function of the RMA4 Peclet number parameter, simulated 

flow velocities, and element sizes (equation 7). The two 

scenarios are based on the TMC and BIC dye-injection studies 

and provide a basis for independently estimating RMA4 Peclet 

numbers in the two overlapping study reaches. Consistent 

parameter estimates for the studies would support the use of 

a single RMA4 Peclet number to represent dispersion and 

mixing throughout the study area. The RMA4 Peclet number 

initially was set to the RMA2 Peclet number. 

Table 4. Number of measurements used in the estimation of RMA2 parameters for the 

hydrodynamic model of the Ohio River near Cincinnati, Ohio, by scenario, 2004–06. 

[ADCP, acoustic Doppler current profiler]

Scenario 

(Month and year 

of ADCP survey)

Number of observations used in the parameter-estimation analysis, 

by measurement type

Water levels Flows Water depths Easting and northing 

velocities

Oct2004 16 59 1,742 3,484

Aug2005 17 23 729 1,458

Oct2005 61 0 0 0

Nov2005 10 26 791 1,582

Mar2006 12 14 324 650

Total 116 122 3,586 7,174
Greater Cincinnati Hydrodynamic Model of the Ohio River 29

In addition to the RMA4 Peclet numbers, the transport 

model contains a decay coefficient to describe the loss of nonconservative constituents with time. Decay coefficients were 

estimated independently for the two scenarios on the basis 

of simulated traveltimes and measured dye-transport rates at 

measured transects. In contrast, the decay coefficients describing any dye losses within the study area were considered constituent specific and sensitive to environmental conditions. As 

such, estimated decay coefficients may have limited transfer 

value to other investigations. 

In comparison to ADCP ensembles, dye-concentration 

measurements are relatively sparse. Typically, 50 to 90 concentration measurements were obtained in one dye transect. 

Therefore, the strategy for matching measured and simulated 

values differed from that used with depths and velocities in the 

hydrodynamic model. Rather than inverse, distance-weighted 

averages of measured values as approximations to simulate 

values at nodes, a quadratic interpolation scheme was used to 

compute a simulated value at a point within an element where 

a concentration measurement was made. The details of the 

procedure are discussed in the following text. 

The element J containing the kth measured dye concentration (ck ) and all its associated nodes, indexed by j, was 

identified for each measured concentration. The point of the 

dye-concentration measurement was considered the local 

origin, and the easting and northing of the dye-measurement 

location was subtracted from those in the surrounding nodes to 

form localized easting and northing coordinate pairs x y   j j , for 

all nodes defining element J. 

For quadrilateral elements, the interpolating function was 

of the form 

 

      

 

c x y b x y x y

x y

j j j j j

j j

( , ) = + j j ⋅ + ⋅ + ⋅ + ⋅

+ ⋅ ⋅ +

    



0 1 2 3

2

4

2

5   6

2

7

2 ⋅ ⋅ x y   + ⋅ x y   ⋅ j j j j

 (13)

where 

cj is the simulated concentration at the j

th node, 

given the parameter vector b, and 

 are values estimated for the interpolating 

function. 

From this equation, the design matrix corresponding to a quadrilateral element was 

 Z x y x y x y x y x y Quad =  ⋅ ⋅ ⋅   ×  18 1

2 2 2 2 

          (14)

The 8 by 8 Psi matrix Ψ8 8× was computed as

Ψ8 8

1

×

−

= ⋅ 

  Z Z Quad Quad ⋅ ZQuad

' ' , which is only a function of the unit vector 18 1× and localized easting x and 

northings y of the static node coordinates and not a particular set of simulated concentrations. Typically, the Ψ

matrix together with a vector of simulated dye concentrations 



c would be used to compute a full beta vector 

β8 1× × = ⋅ Ψ8 8 8 1× c ˆ , which provides a means to estimate 

simulated values of concentrations anywhere in the element 

as ( ) , y x =  y x y xy x y xy  

⋅ × 1 2 2

8 1 . In 

this analysis, however, the only simulated point of interest in 

the element is at the kth measured dye concentration for which 

x y   k k = = 0. This restriction provides a basis to precompute 

the top row of the Psi matrix Ψ1 1, :8 , which together with 

the simulated concentrations in the surrounding j

th element 



c∀ ∈j J , provides a basis for quadratic interpolation as 

, , : c x y c k j ( = = 0 0 j ) = [ ] 1 ⋅ ⋅ Ψ1 18 . This computed concentration is unbiased as Ψ1

1 8

1 ,

:

. j

j

= =

∑ For triangular elements, the

quadratic interpolation function is

 

     

  

c x y b x y x

y x y

j j j j j

j j

j

j

( , ) = + ⋅ + ⋅ + ⋅

+ ⋅ + ⋅ ⋅

   

 

0 1 2 3

2

4

2

5

(15)

The corresponding design and Psi matrices for triangular 

elements are defined similarly to those of the quadrilateral 

elements. The standard deviations of the measured dye concentrations were computed as σˆ . . c k k = ⋅ 0 1 c + 0 05, and the 

corresponding measurement weights ck were computed as 

1 2 / σˆ . ck

Greater Cincinnati Hydrodynamic 

Model of the Ohio River

When the geometry and bathymetry of the Ohio River 

study reach were described and boundary conditions for the 

five calibration scenarios were specified, hydraulic parameters 

describing channel resistance to flow and eddy viscosity were 

estimated by minimizing the differences between measured 

and simulated depths of flow, heads, flows, and velocities. The 

following discussion characterizes the results of the parameterestimation analysis and the correspondence between simulated 

and measured values. 

Parameter Estimation

Estimation for the hydrodynamic-model parameters of 

effective channel roughness for shallow and deep zones and 

the Peclet number converged at a weighted sum of squared 

residuals S(b) equal to 47.329. The estimated effective Manning’s “n” value for the shallow zone (0.02751) was about 

17.3 percent higher than that for the deep zone (0.02345) 

(table 5). Parameter estimates were consistent with the range 

of Manning’s “n” values associated with materials expected on 

the Ohio River (Barnes, 1967). The estimated RMA2 Peclet 

number of 38.3 was within the recommended range of 15–40 

(Donnell and others, 2005). 
30 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Absolute values of correlation among parameter pairs 

exceeding 0.85 can create ambiguity among parameter estimates and degrade the interpretability of parameter estimates 

(Poeter and others, 2005). The maximum correlation between 

parameters was 0.5565 between Manning’s “n” for the deep 

zone and the RMA2 Peclet number. The minimum correlation between parameters was -0.6120 between Manning’s 

“n” values in the deep and shallow zones. Thus, parameter 

correlation is not expected to degrade parameter estimates. As 

indicated by the scaled sensitivity values (table 5), Manning’s 

“n” parameters were more sensitive to the data than the Peclet 

parameter. 

Simulation

The relation between measured and simulated flow 

depths, heads, flows, and velocities is shown by scenario 

in table 6. Across all scenarios, the average coefficient of 

determination (r2) was greater than or equal to 0.90 for all 

measurement types. Also, the interval computed about the 

bias, plus or minus twice the standard deviation of residuals, 

included zero for all measurement types and scenarios, except 

for the Mar2006 flows. This bias may have been smaller if 

the time step for the hydrodynamic simulations would have 

been smaller to better account for rapidly changing boundary 

conditions. Figures 23 through 28 show the relation between 

computed and simulated values for all scenarios. These results 

indicate that point measurements of flow depths, heads, flows, 

and velocities generally are consistent with corresponding 

simulated values. 

Greater Cincinnati Water-QualityTransport Model of the Ohio River

Application of the RMA4 transport model to the Ohio 

River study area requires estimation of dye-decay and RMA4 

Peclet number (turbulent-mixing) parameters. Comparison 

between measured and simulated dye concentrations demonstrates the effectiveness of the water-quality transport model. 

In the following section, model-parameter estimates are presented and discussed, and comparisons between measured and 

simulated dye concentrations are provided. 

Parameter Estimation

Parameters in the water-quality transport model were 

estimated independently for each dye study. Independent estimation of parameters provided a means to assess their consistency and reproducibility for different injection sites. Initially, 

least squares estimates of dye-decay parameters were determined from computed dye-transport rates and simulated travel 

times. Subsequently, an attempt was made to simultaneously 

estimate dye-decay and RMA4 Peclet numbers describing 

turbulent-mixing by use of UCODE with transport simulations 

and measured dye concentrations. 

Table 5. Parameter estimates for the two-dimensional hydrodynamic and transport models of the Ohio River near Cincinnati, Ohio. 

Parameter 

statistic

Manning’s “n” Peclet 

number

RMA2

Twelvemile 

Creek 

RMA4 

Peclet 

number

Big Indian Creek

Deep zone Shallow zone

RMA4 

Peclet 

number

Decay 

coefficient

Upper 95 percent confidence limit 0.02361 0.02806 46.13 190.5 38.26 0.342

Expected value .02345 .02751 38.33 173.3 37.19 .323

Lower 95 percent confidence limit .02329 .02697 30.52 157.6 36.15 .342

Standard deviation .0000835 .0002763 3.984 185.08 .305 .0000993

Coefficient of variation .003559 .0104 .1040 .4910 .00821 .000307

Composite scaled sensitivity .2587 .07918 .00728 4.002 3.969 1.968

1

RMA4 Peclet numbers were determined under a log10 transformation. The standard deviation shown was applied to log10 estimates of the Peclet numbers 

and transformed back to arithmetic space by power transformation. 
Greater Cincinnati Hydrodynamic Model of the Ohio River 31

Table 6. Summary statistics describing the match between simulated and computed flow depths, heads, flows, and velocities 

for the hydrodynamic model of the Ohio River near Cincinnati, Ohio, October 2004–March 2006. 

Parameter Scenario Count Coefficient of 

determination

Residuals

Bias Standard 

deviation

Flow depth Oct2004 1,742 0.9204 -0.3626 2.006

Aug2005 729 .9342 -.0385 1.850

Nov2005 791 .9283 .0344 1.575

Mar2006 324 .9499 .3155 1.841

All 3,586 .9353 -.1479 1.885

Head Oct2004 16 .8516 -.0431 .2298

Aug2005 17 .7659 -.0520 .1025

Oct2005 61 .9882 .0879 .2281

Nov2005 10 .5568 .2293 .1714

Mar2006 12 .9961 .0708 .2281

All 116 .9004 .0598 .1980

Flow Oct2004 59 .928 -1,880 1,623

Aug2005 23 .910 475 1,508

Nov2005 26 1.000 1,709 1,393

Mar2006 14 .990 -2,607 581

All 122 .988 -755.0 1,467

Easting velocity Oct2004 1,742 .8996 .0162 .1888

Aug2005 729 .8851 -.0120 .1195

Nov2005 791 .9523 -.0566 .1228

Mar2006 325 .9109 .1158 .2334

Total 3,587 .9093 .0034 .1747

Northing velocity Oct2004 1,742 .9041 -.0031 .1609

Aug2005 729 .8022 .0103 .1165

Nov2005 791 .8374 .1122 .1922

Mar2006 325 .9746 .0109 .2771

Total 3,587 .9401 .0263 .1804

1

Flows showed little variability during the period.
32 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

0

20

40

60

0

20

40

60

SIMUL

ATED FLOW

D

E

P

TH, IN FEET

0 20 40 60

COMPUTED FLOW DEPTH, IN FEET

0 20 40 60

SCENARIO: Oct2004 SCENARIO: Aug2005

SCENARIO: Nov2005 SCENARIO: Mar2006

Line of agreement Line of agreement

Line of agreement Line of agreement

Figure 23. Relation between computed and simulated flow depths on the Ohio River near Cincinnati, Ohio, October 2004–

March 2006. 
Greater Cincinnati Hydrodynamic Model of the Ohio River 33

454 456 458 460 462 464

MEASURED WATER LEVEL, IN FEET ABOVE

NORTH AMERICAN VERTICAL DATUM OF 1988

454

456

458

460

462

464

SIMULATED W

ATER LEVEL, IN FEE

T

A

B

OVE

NORTH AMERICAN VERTICAL DATUM OF 1988

EXPLANATION

October 2004

August 2005

November 2005

March 2006

Line of agreement

454 456 458 460 462 464

MEASURED WATER LEVEL, IN FEET ABOVE

NORTH AMERICAN VERTICAL DATUM OF 1988

454

456

458

460

462

464

SIMULATED W

ATER LEVEL, IN FEE

T

A

B

OVE

NORTH AMERICAN VERTICAL DATUM OF 1988

EXPLANATION

Line of agreement

Meldahl Dam

1009

1008

1007

1006

1005

Figure 25. Relation between 

miscellaneous measurements and 

simulated water levels at miscellaneous 

sites measured during bathymetry 

surveys. 

Figure 24. Relation between 

systematically measured and simulated 

water levels on the Ohio River 

downstream from Meldahl Dam near 

Neville, Ohio, October 2004–March 2006. 
34 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

20,000 40,000 60,000 80,000 100,000

MEASURED FLOW, IN CUBIC FEET PER SECOND

20,000

40,000

60,000

80,000

100,000

SIMULATED FLOW, IN CUBIC FEE

T PER

S

ECOND

EXPLANATION

October 2004

August 2005

November 2005

March 2006

Line of agreement

Figure 26. Relation between measured and simulated flows on the Ohio River near Cincinnati, Ohio, 

October 2004–March 2006. 

Dye-Decay Parameters

Rhodamine WT dye is a conservative constituent, 

although some losses can occur as a result of degradation 

associated with sunlight and sorption on particles in water. 

Dye-transport rates were determined at several transects 

downstream from the dye-injection points to assess possible 

losses. Resulting transport rates showed variability within both 

injection reaches (table 1). In the TMC dye-injection study, 

the computed transport rates exceeded the injection rate at two 

transects. Sources of variability in transport rates are uncertain 

but may include unsteadiness of flow, transport measurements 

occurring before steady-state concentrations were established, 

and dye- and flow-measurement uncertainties. Measurement 

uncertainties, for example, were evident in near-simultaneous 

measurements of transport rates by two boat crews at OH 9a 

and OH 9b that differed by about 15 percent (table 1). 

Constituent losses may be accounted for by the exponential decay equation 

M t t M t e o o

k t to ( ) ( ) [ )] − = ⋅ − ⋅ 1 ( ) − (16)

where

M(t) is the transport rate at time t, and 

k1 is the estimated decay parameter, with units of 

day-1. 

In this report, the product of the flow-weighted mean concentration and measured flow at a transect downstream from 

the point of injection was used to estimate the transport rate 

M(t). 

The traveltimes from the TMC dye-injection site to 

dye-measurement transects were estimated with SMS droguetracking capabilities. In particular, a hypothetical massless 

particle was placed in the simulated transient-flow field for 

the Aug2005 scenario near the TMC dye-injection point. The 

drogue was tracked at 0.5-hour intervals during an interval 

corresponding approximately to the dye-injection period, 

August 1, 2005, at 12:00 EST to August 2, 2005, at 13:00 EST. 

The traveltime to individual transects was estimated by 

interpolating between drogue positions at 0.5-hour intervals. 

Measurements of dye-transport rates at transects OH 16 (a and 

b) were not used to estimate the decay coefficient because concentrations may not have reached near-steady-state concentrations before dye concentrations were measured. The relatively 

low transport rates computed at transects OH 15 and OH 16 

may be partially explained by dye measurements being made 

before concentrations reached their near-steady-state values. 
Greater Cincinnati Water-Quality-Transport Model of the Ohio River 35

-3

-2

-1

0

1

-3

-2

-1

0

1

SIMULAT

E

D EAS

TIN

G

VELOCITY, IN FEET PER SECOND

-3 -2 -1 0 1

COMPUTED EASTING VELOCITY, IN FEET PER SECOND

-3 -2 -1 0 1

SCENARIO: Oct2004 SCENARIO: Aug2005

SCENARIO: Nov2005 SCENARIO: Mar2006

Line of agreement Line of agreement

Line of agreement Line of agreement

Figure 27. Relation between computed and simulated easting velocities on the Ohio River near Cincinnati, Ohio, October 2004–

March 2006. 
36 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

-3

-2

-1

0

1

2

3

4

-3

-2

-1

0

1

2

3

4

SIMULA

T

E

D NORTHING VELOCI

TY, IN FEET PE

R

S

ECOND

-3 -2 -1 0 1 2 3 4

COMPUTED NORTHING VELOCITY, IN FEET PER SECOND

-3 -2 -1 0 1 2 3 4

SCENARIO: Oct2004 SCENARIO: Aug2005

SCENARIO: Nov2005 SCENARIO: Mar2006

Line of agreement Line of agreement

Line of agreement Line of agreement

Figure 28. Relation between computed and simulated northing velocities on the Ohio River near Cincinnati, Ohio, 

October 2004–March 2006. 
Greater Cincinnati Water-Quality-Transport Model of the Ohio River 37

Drogue tracking also was used to estimate traveltimes 

along the BIC dye-injection-flow path. Again, with simulations from the Aug2005 scenario, drogue tracking was 

approximately constrained to the injection interval that was 

initiated on August 3, 2005, at 1300 EST and continued 

through August 4, 2005, at 1400 EST at 0.5-hour intervals. 

Based on this traveltime analysis, concentrations at transect 

OH 9 may have been measured before near-steady-state concentrations developed and were not used in the estimation of 

the decay coefficient for the BIC reach. Again, the relatively 

low transport rates computed at transects OH 8 and OH 9 may 

be related to insufficient traveltimes. 

Measured transport rates were generally lower within the 

BIC dye-injection reach than those in the TMC injection reach 

for the same traveltimes, even though loading rates were the 

same for the two injection studies. Part of these differences 

may be associated with the greater magnitude of the estimated 

decay coefficient for the BIC injection reach. Transport rates 

used to estimate these parameters, however, were highly variable (fig. 29). 

RMA4 Peclet Numbers

In RMA4, Peclet numbers are used to dynamically 

compute turbulent-mixing parameters. To assess the reproducibility of the transverse-mixing characterization provided by 

the two dye-injection studies, Peclet numbers were allowed to 

vary between the TMC and the BIC dye-injection sites. Higher 

RMA4 Peclet numbers are associated with lower turbulent 

mixing, which causes slower rates of simulated transverse and 

longitudinal mixing with distance downstream from the point 

of injection. 

An initial attempt to simultaneously estimate dye-decay 

and RMA4 Peclet number parameters for the TMC dyeinjection study was not successful. In particular, the dye-decay 

parameter estimate tended to 1, indicating a complete loss of 

dye. Subsequently, the least-squares estimate of the dye-decay 

parameter (0.218) was used with UCODE to estimate the 

RMA4 Peclet number within the TMC dye-injection reach. 

UCODE results converged to an RMA4 Peclet number of 173 

(table 5), which is not consistent with the recommended (or 

physically plausible) range of 15 to 40, or with the estimated 

RMA2 Peclet number of 38.3. Thus, the utility of the parameter estimate, and corresponding simulated concentrations, 

are considered highly uncertain. The sum of squares weighted 

residuals, S(b), was 13,775, based on 607 dye concentration 

measurements. The standard error of the parameter regression 

is 4.77. 

In contrast, estimates of the dye-decay and RMA4 Peclet 

number parameters for the BIC reach converged simultaneously in UCODE to 0.323 and 37.2, respectively (table 5). The 

correlation between the two parameter estimates was -0.152, 

indicating that the pair of estimates is not degraded because 

of correlation. The final value of S(b) was equal to 1,044, 

based on 571 concentration measurements; this corresponds 

to a standard error of the regression of 1.35. The composite 

scaled sensitivities for the RMA4 Peclet number and the decay 

coefficient was 3.97 and 1.97, respectively, indicating sensitivity to the measured BIC concentrations. The decay coefficient 

estimated by use of UCODE is considered to supersede the 

estimate based on measured dye transport rates (fig. 30). The 

RMA4 parameter estimate is consistent with the expected 

parameter range and does not differ significantly from the 

RMA2 Peclet number. The discrepancy between the final 

estimates of RMA4 Peclet numbers at the two dye-injection 

sites makes application of the water-quality model to spills at 

new locations problematic because the RMA4 Peclet number 

cannot be consistently estimated. 

Simulation

On August 2, 2005, measured dye concentrations within 

the TMC dye-injection reach were initially higher near the 

left bank, which is consistent with the side of the river where 

dye was injected in the TMC study. Maximum concentrations 

of about 8 μg/L were measured near the left bank at transect 

OH 10, which was about 6 mi downstream from the site of 

injection, and the first transect where dye concentrations were 

considered to be vertically mixed. Generally, these maximum 

concentrations attenuated with distance downstream, although 

this attenuation was not uniform with distance. In particular, 

maximum concentrations near the left bank decreased about 

1 μg/L per mile along the four transects from OH 10 to OH 13 

(fig. 30). Measured and simulated dye concentrations were 

generally consistent in these transects. From OH 13 to OH 14, 

however, maximum measured concentrations along the left 

bank decreased about 2.5 μg/L per mile, and a second concentration mode appeared mid channel. At transect OH 14, 

maximum dye concentrations in the mid-channel mode were 

greater than concentrations near the left bank. From transect 

OH 14 to OH 15, the measured mid-channel concentration 

mode appears to have continued its translation to the right 

bank, while maximum measured concentrations near the left 

bank again decreased at a rate of about 1 μg/L per mile downstream. Simulated concentrations do not indicate the presence 

or translation of a mid-channel model of elevated concentrations near OH 14 or OH 15. At OH 15, maximum concentrations were near the right bank, and these concentrations 

increased about 0.5 μg/L between samples collected starting 

at 12:56 PM and those samples collected starting 48 minutes 

later. Average concentrations elsewhere in transect OH 15 

appeared unchanged during the two periods of measurements. 

Measured dye concentrations at transect OH 16 were approximately uniformly distributed, except near the right bank where 

average concentrations were about 0.5 μg/L lower than average. These concentrations may have been lowered by inflows 

of dye-free water from Little Miami River, which discharges 

into the Ohio River on the right bank between transects OH 15 

and OH 16. Simulated dye concentrations at transects OH 15 

and OH 16 exceeded 1.5 μg/L near the left bank and were near 

zero near the right bank. 
38 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

0.4 0.6 0.8 1.0 1.2 1.4

SIMULATED TRAVEL TIME, IN DAYS

200

400

600

800

1,000

1,200

DY

E TRANSPORT R

ATE, 

IN

MILLIG

R

A

M

S

PER

S

E

C

O

N

D

OH10

OH11

OH12

OH13

OH14

OH15

OH16a OH16b

OH 3

OH 4

OH 5

OH 6

OH 7

OH 8

OH 9a

OH 9b

EXPLANATION

TMC, Twelvemile Creek; BIC, Big Indian Creek

Transport rate M at time t, in days, M(t)

 MLS is the transport rate based on the least-squares estimate of the decay parameter

 MUCODE is the transport rate based on the UCODE estimate of the decay parameter

TMC: Computed transport from measured concentrations and flows

TMC: MLS(t) = 767 exp(-0.2181 t)

BIC: Computed transport from measured concentrations and flows

BIC: MLS(t) = 767 exp(-0.4544 t)

BIC: MUCODE(t) = 767 exp(-0.3230 t)

Figure 29. Dye-decay characteristics inferred from dye-injection sites near Twelvemile and 

Big Indian Creeks on the Ohio River upstream from Cincinnati, Ohio, August 2005. 
Greater Cincinnati Water-Quality-Transport Model of the Ohio River 39

0 200 400 600 800 1000 1200 1400 1600 1800

DISTANCE FROM LEFT EDGE OF WATER, IN FEET

0.0

2.0

4.0

6.0

8.0

0.0

2.0

4.0

6.0

8.0

0.0

2.0

4.0

6.0

0.0

1.0

2.0

3.0

4.0

5.0

DYE CO

NCENTRATION, IN MICROGR

A

MS PER LI

TER

0.0

1.0

2.0

3.0

4.0

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

Transect: OH11

Distance: 7.01 miles

Period: 11:01 - 11:15 EST

Transect: OH10

Distance: 5.99 miles

Period: 10:13 - 10:25 EST

Transect: OH12

Distance: 8.02 miles

Period: 11:05 - 11:15 EST

Transect: OH13

Distance: 9.07 miles

Period: 11:27 - 11:40 EST

Transect: OH14

Distance: 10.1 miles

Period: 11:36 - 11:46 EST

Transect: OH15

Distance: 11.2 miles

Period: 12:56 - 13:07 EST

Period: 13:44 - 13:54 EST

Period: 12:49 - 12:57 EST

Period: 13:00 - 13:07 EST

Period: 13:43 - 13:49 EST

Transect: OH16

Distance: 12.0 miles

Dye concentration

Time period Measured

12:49-12:57 EST

13:00-13:07 EST

13:43-13:49 EST

Simulated

EXPLANATION

Note: In all plots, dye measurements are shown as distinct symbols 

and simulated dye concentrations are shown as lines. Colors group 

simulated and measured data sets. Distances are referenced in 

miles downstream from the point of injection. 

Figure 30. Measured and simulated dye concentrations at vertically mixed transects within the Twelvemile 

Creek injection reach of the Ohio River near Cincinnati, Ohio, August 2, 2005. 
40 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

The inability to simulate the measured bimodal distribution of dye concentrations is an inherent limitation of a 2D 

transport model under any parameterization. The bimodal 

distribution of concentrations is thought to be associated with 

transport phenomena that are not sufficiently described by a 

2D flow model. Investigation of 3D flow and transport characteristics within the TMC injection reach would provide a more 

comprehensive theoretical framework for simulation, and 

additional flow and concentration data from transects OH 4–

OH 9 would support additional parameter estimation. 

On the August 4, 2005, dye-injection study of the BIC 

reach, maximum measured dye concentrations were on the 

right side of the river, which is consistent with the location of 

the dye injection site. Transect OH 3, which is about 5.5 mi 

downstream from the BIC injection site, was the first transect 

where dye concentrations were considered vertically mixed. 

Maximum measured concentrations at OH 3 were about 

2.6 μg/L (fig. 31), in contrast to maximum measured concentrations of about 8 μg/L at transect OH 10 during the TMC 

injection study. The lower maximum initial concentrations 

during the BIC study occurred despite a 19 percent decrease 

in flow from August 2–4, 2005, and a BIC injection site that 

was less than half the distance to the shoreline (60 ft) as the 

distance from the TMC injection site to the shoreline (125 ft). 

(Dye injection rates were the same for both injection studies.) Thus, dye concentrations during the TMC injection study 

might be considered initially under dispersed with respect to 

concentrations measured during the BIC injection study. 

Maximum measured dye concentrations decreased with 

distance downstream at a rate of less than 0.5 μg/L per mile 

during the BIC injection study, which is a rate less than half 

the corresponding rate measured during the TMC injection 

study. The lower initial concentrations during the BIC study 

combined with the lower rate of decrease resulted in similar 

maximum concentrations of about 0.6 μg/L at the terminal 

transects of both injection studies, which were both about 

12.0-mi downstream from their corresponding injection sites. 

In contrast to bimodal distribution of dye concentrations 

that developed during the TMC injection study, the distribution of dye concentrations during the BIC injection study was 

unimodal, although asymmetric, with maximum concentrations consistently on the right side of the river. Concentrations 

at the right bank, however, were commonly lower than maximum concentrations. This near-shore affect was attributed 

to inflows of dye-free water from local tributaries, including 

Tenmile Creek. 

Given the quantitative and qualitative differences 

between the distributions of dye concentrations measured 

during the two injection studies, differences between transport 

model parameters were inevitable. Dye concentrations simulated for the BIC injection study generally tracked the attenuation of measured dye concentrations with distance downstream 

from the point of injection. (fig. 31). 

Despite the general consistency between measured and 

simulated dye concentrations in the BIC injection reach, 

some anomalies occurred. For example, measured dye 

concentrations near the left bank at transect OH 7 were higher 

than left-bank dye concentrations at all upstream transects; 

which did not follow the general pattern of dye concentrations decreasing with downstream distance. In particular, at 

upstream transect OH 6, near RM 8.5, left-bank dye concentrations were about 0.3 μg/L; downstream at OH 7, near 

RM 9.5, concentrations increased to about 0.7 μg/L but then 

decreased to 0.25 μg/L at OH 8, near RM 10.5. This discrepancy in measured dye concentrations may be attributable to 

transients in flow that were not measured or accounted for in 

hydrodynamic time steps used for all scenarios. 

In addition, simulated dye concentrations generally 

tracked measured concentrations at transects OH 8 and OH 9, 

although measured dye concentrations near the right bank 

were markedly lower than simulated values. In this area, 

unmeasured inflows to the Ohio River from creeks on the Ohio 

side of the river may have diluted local dye concentrations. 

The fluctuations of flows near the mouths of ungaged tributaries to the Ohio River are difficult to quantify; these effects 

were not included in the hydrodynamic or transport models. 

The slight discontinuity in the simulated concentrations at 

transect OH 8, about 1,600 ft from the left edge of water, is 

attributed to simulations that transitioned at 13:30 EST from 

conditions at 13:00 EST to the right of this point to conditions 

at 14:00 EST to the left of this point. The transition indicates 

that simulated concentrations were still increasing with time 

when this transect was measured. 

Dye concentrations and flows were measured almost 

simultaneously at OH 9 by two boat crews that were following 

slightly different paths across the transect (Koltun and others, 

2006). The slight discrepancy between simulated flows for the 

two dye transects is the result of interpolating simulated concentrations at the same time step to different boat paths used to 

measure the dye. 

The relation between percent mixing and distance 

downstream from the dye-injection point differed substantially 

between the TMC and BIC dye-injection studies (fig. 32). For 

the most upstream transects in the vertically mixed reaches, 

the computed mixing within the TMC reach was 28 percent 

at a point 6.0 mi downstream from the injection point. In contrast, the computed mixing within the BIC reach was 66 percent at a point 5.5 mi downstream from the injection point. 

At points greater than 11.5 mi downstream from the injection, 

however, both reaches showed mixing greater than 87 percent. 

Thus, the rate of mixing in the TMC reach increased about 

2.5 times faster with downstream distance than mixing in 

the BIC reach, based on linear approximations to the relation 

between percent mixing and distance from the injection point. 

Extrapolation of either linear relation upstream through the 

unmixed reaches is unsatisfactory because neither relation 

has an intercept near zero-percent mixing. The differences 

between the rates of mixing during the TMC and BIC injection studies indicate sensitivity to the location of dye injection. 

This sensitivity may indicate that transverse flow components, 

not described by the 2D hydrodynamic model, affect transverse mixing characteristics in the study reach. 
Greater Cincinnati Water-Quality-Transport Model of the Ohio River 41

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

DISTANCE FROM LEFT EDGE OF WATER, IN FEET

0.0

1.0

2.0

3.0

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

DYE CO

NCENTRATION, IN MICROGR

A

MS PER LI

TER

0.0

0.5

1.0

1.5

0.0

0.5

1.0

0.0

0.5

1.0

Transect: OH 3

Distance: 5.49 miles

Transect: OH 4

Distance: 6.49 miles

Transect: OH 5

Distance: 7.45 miles

Transect: OH 6

Distance: 8.45 miles

Transect: OH 7

Distance: 9.52 miles

Period: 13:35 - 13:47 EST

Period: 13:25 - 13:39 EST

Transect: OH 8

Distance: 10.5 miles

Transect: OH 9

Distance: 11.5 miles

Period: 14:08 - 14:19 EST

Period: 14:08 - 14:20 EST

Period: 12:50 - 13:01 EST

Period: 10:09 - 10:19 EST

Period: 12:39 - 12:54 EST

Period: 09:49 - 09:59 EST

Dye concentration

Time period Measured

14:08-14:19 EST

14:08-14:20 EST

Simulated

EXPLANATION

Note: In all plots, dye measurements are shown as distinct symbols 

and simulated dye concentrations are shown as lines. Colors group 

simulated and measured data sets. Distances are referenced in 

miles downstream from the point of injection. 

Figure 31. Measured and simulated dye concentrations at vertically mixed transects within the Big Indian 

Creek dye-injection reach of the Ohio River near Cincinnati, Ohio, August 4, 2005. 
42 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

0 2 4 6 8 10 12 14

DISTANCE DOWNSTREAM FROM INJECTION, IN MILES

0

20

40

60

80

100

PE

R

CENT MIXING

OF DYE

OH10 OH11

OH12

OH13

OH14

OH15

OH16a

OH16b

OH03

OH04

OH05

OH06

OH07

OH08

OH09a

OH09b

EXPLANATION

Twelvemile Creek computed

Twelvemile Creek fitted

Big Indian Creek computed

Big Indian Creek fitted

Hydrodynamic Model Limitations and 

Impacts on Water-Quality-Transport 

Simulations

RMA2 and RMA4 are based on the assumption that 

vertically averaged velocities are adequate to describe the 

variations of flow velocities with depth. The 2D hydrodynamic 

model developed in this report closely matches local depthaveraged velocities, flows, depths, and water levels along the 

modeled reach of the Ohio River. The 2D water-quality-transport model effectively integrates these local depth-averaged 

velocities longitudinally to define flow paths for transport 

simulations. Where vertical profiles of velocity deviate systematically from depth-averaged velocities, however, integration of velocities can result in a cumulative departure between 

simulated and actual flow paths with increasing longitudinal 

distances. This discussion uses ADCP velocity data collected 

on the Ohio River to illustrate how departures from 2D model 

assumptions may impact the accuracy of water-quality transport simulations. 

Two-dimensional hydrodynamic-model simulations 

describe horizontal variations in depth-averaged velocities. In 

reaches that curve toward the left in the downstream direction, 

however, maximum velocities tend to be closer to the right 

bank (fig. 33). In straight reaches, maximum velocities tend 

to be near the center of the channel (fig. 34). In reaches that 

curve toward the right, maximum simulated velocities tend to 

be closer to the left bank (fig. 35). The general horizontal pattern of simulated velocities is consistent with depth-averaged 

ADCP velocity data; these data are computed by averaging 

horizontal velocities in 0.25-m bins that are available throughout the water column from individual ADCP ensembles. 

Figure 32. Relation between distance downstream from dye-injection points near 

Twelvemile Creek and Big Indian Creek and percent mixing on the Ohio River near 

Cincinnati, Ohio, August 2–4, 2005. 
Hydrodynamic Model Limitations and Impacts on Water-Quality-Transport Simulations 43

1,472,000 1,474,000 1,476,000

EASTING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

NORTHING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

330,000

332,000

333,000

331,000

0 min

10 min

20 min

30 min

40 min

50 min

Big Indian Creek

0 500 1,000 1,500 FEET

EXPLANATION

Simulated velocities at nodes (lengths show distances 

traveled downstream in 1 minute)

Depth-averaged velocities at acoustic Doppler current profiler 

ensemble locations on OR 64 (lengths show distances traveled in 1 minute)

Simulated flow path. Distances between markers represent the 

distance that the depth-averaged flow moved in 5 minutes.

Isopleths of simulated travel time from reference line at 0 minutes.

Base map by U.S. Army 

Corps of Engineers, 2002

OR64

Figure 33. Variation in depth-averaged velocities, November 3, 2005, near acoustic Doppler current profiler transect OR 64 in a 

reach of the Ohio River near Cincinnati, Ohio, that curves to the left. 
44 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

1,473,000 1,474,000 1,475,000 1,476,000 1,477,000

EASTING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

NORTHING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

320,000

321,000

322,000

323,000

0 min

10 min

20 min

30 min

40 min

Base map by U.S. Army 

Corps of Engineers, 2002

Little Indian Creek

OR69

0 250 500 1,000 FEET

EXPLANATION

Simulated velocities at nodes (lengths show distances 

traveled downstream in 1 minute)

Depth-averaged velocities at acoustic Doppler current profiler 

ensemble locations on OR 69 (lengths show distances traveled in 1 minute)

Simulated flow path. Distances between markers represent the 

distance that the depth-averaged flow moved in 5 minutes.

Isopleths of simulated travel time from reference line at 0 minutes.

Figure 34. Variation in depth-averaged velocities, November 3, 2005, near acoustic Doppler current profiler transect OR 69 in 

straight reach of the Ohio River near Cincinnati, Ohio. 
Hydrodynamic Model Limitations and Impacts on Water-Quality-Transport Simulations 45

I-275

OR20

0 250 500 1,000 FEET

EXPLANATION

Simulated velocities at nodes (lengths show distances 

traveled downstream in 1 minute)

Depth-averaged velocities at acoustic Doppler current profiler 

ensemble locations on OR 20 (lengths show distances traveled in 1 minute)

Simulated flow path. Distances between markers represent the 

distance that the depth-averaged flow moved in 5 minutes.

Isopleths of simulated travel time from reference line at 0 minutes.

1,418,000 1,419,000 1,420,000 1,421,000 1,422,000

EASTING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

NORTHING, IN OHIO SOUTH 1983 STATE PLANE COORDINATE SYSTEM FEET

390,000

391,000

392,000

393,000

0 min

10 min

20 min

30 min

Base map by U.S. Army 

Corps of Engineers, 2002

Figure 35. Variation in depth-averaged velocities, October 7, 2004, near acoustic Doppler current profiler transect OR 20 in a 

reach of the Ohio River near Cincinnati, Ohio, that curves to the right. 
46 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

As an alternative to depth-averaged velocities, horizontally averaged velocities also can be computed by depth 

intervals from ADCP velocity data. These horizontally averaged velocities provide insight into the 3D variations in flow 

velocities. In the following paragraphs, variations in horizontal 

water speeds and directions with depth are discussed. 

The average velocity magnitude (speed) was computed 

for each 0.25-m bin interval from 24 adjacent ensembles near 

the deepest part of the channel at OR 20 from data obtained 

during the ADCP survey, October 7, 2004 (Koltun and others, 

2006). Because of the effects of vertical shear, the average 

speed varies approximately linearly with the depth below the 

water surface across the range of depths where velocity data 

were available (fig. 36). In particular, the average water speed 

increases about 59 percent from 1.16 ft/s in the lowest bin of 

the ensemble set at 43.1 ft below the water surface to 1.85 ft/s 

at 2.89 ft below the water surface. 

Longitudinal mixing is determined by the vertical shear 

velocity and the longitudinal turbulent diffusive components. 

In contrast, transverse mixing is determined primarily by 

transverse turbulent mixing, except where significant transverse velocity shear occurs from secondary circulation. Within 

the study reach, secondary circulation patterns are thought to 

be restricted primarily to areas immediately downstream from 

Meldahl Dam; these may form as a result of the asymmetric release of flows across the gates and locks. According to 

Fischer and others (1979), rates of turbulent longitudinal mixing have not been measured by dye experiments because of 

the difficulty in separating the effects of longitudinal turbulent 

fluctuations from the results of shear flow. Presumably, turbulence causes longitudinal mixing at about the same rate as 

transverse turbulent mixing because there is an equal lack of 

boundaries to inhibit motion (Fischer and others, 1979); this is 

consistent with the assumption of an isotropic eddy-viscosity 

coefficient used in this report (equation 2). 

Unlike transverse velocity shear in areas of secondary 

circulation, vertical shear velocity is integrated with depth 

(eliminated) in these 2D hydrodynamic and transport models. 

Thus, although an isotropic eddy-viscosity coefficient may 

be appropriate for describing the turbulent dispersion component, longitudinal mixing may be underestimated because the 

effect of vertical shear is not reflected in the simulations. Thus, 

concentrations simulated downstream from slug releases—for 

example, short-duration spills—may be overestimated because 

the longitudinal mixing associated with vertical shear is not 

taken into account. Use of a constant dye-injection rate and 

delaying dye sampling until near-steady-state concentrations 

developed at each transect facilitated data collection; however, 

the design made it difficult to quantify longitudinal mixing 

characteristics. 

ADCP survey data also were used to investigate the 

variation of flow direction with depth through channel reaches 

with different curvatures (fig. 37). The ADCP data were subdivided into four quartiles corresponding to the cumulative flow 

from the left bank. At transect OR 64, which curves to the left, 

velocity azimuths in all flow quartiles tend to increase with 

depth. Given this general tendency, velocity azimuths span 

the largest range (about 19 degrees) with depth in the fourth 

quartile of flow Q75–100, near the right bank. At transect OR 69, 

which has little curvature, velocity azimuths tend to have little 

relation to depth of flow. At transect OR 20, which curves 

to the right, azimuths tend to decrease with flow depth; this 

trend spans the largest range (about 14 degrees) with depth 

in the first quartile of flow Q0–25, near the left bank. Thus, 

transverse-flow components in the vicinity of channel bends 

may significantly affect the transverse mixing of constituents; 

the significance of this effect may vary with the depth of the 

constituent in the water column. 

1.0 1.2 1.4 1.6 1.8 2.0

VELOCITY MAGNITUDE, IN FEET PER SECOND

50

40

30

20

10

0

DEPTH BELOW THE WA

TER SURFACE, IN FEET

Average water depth at ensemble set.

Ensemble average velocity

Regression line

Flow direction

Figure 36. Variation of speed of flow with depth below 

the water surface at OR 20, Ohio River near Cincinnati, 

Ohio, October 7, 2004. 
Hydrodynamic Model Limitations and Impacts on Water-Quality-Transport Simulations 47

16

12

8

4

0

16

12

8

4

0

50

40

30

20

10

0

16

12

8

4

0

20

16

12

8

4

0

50

40

30

20

10

0

20

16

12

8

4

0

DEPT

H BELOW 

W

A

TER S

U

RFA

CE, IN FEET

324 328 332 336 340

20

16

12

8

4

0

20

16

12

8

4

0

40

30

20

10

0

2 4 6 8 10

AZIMUTH OF FLOW, FROM ZERO DEGREES NORTH

20

16

12

8

4

0

335 340 345 350 355 360

25

20

15

10

5

0

OR64 (left-curving channel)

November 3, 2005

OR69 (straight channel)

November 3, 2005

OR20 (right-curving channel)

October 7, 2004

Q0-25

Q25-50

Q50-75

Q75-100

Figure 37. Relation between flow depth and flow-velocity azimuth from selected acoustic Doppler current profiler surveyed 

cross sections on the Ohio River near Cincinnati, Ohio, 2004–05. 
48 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

The 2D flow and transport model applied in this report do 

not account for transverse-flow components. Transverse-flow 

components, however, may be associated with an anomalous 

distribution of dye from the TMC dye injection and the associated estimate of RMA4 Peclet number that is far outside the 

recommended range for this parameter. The inconsistency 

between measured velocity variations with depth and 2D 

model assumptions of depth-averaged flow impose restrictions 

on the application or interpretation of simulation results. 

The lack of consistency between turbulent-mixing 

characteristics in the TMC and BIC reaches leaves significant 

uncertainty as to the appropriate turbulent-mixing characteristics for other reaches in the study area. Simulations of flows 

with RMA2 and concentration distributions with RMA4 (using 

the RMA4 Peclet number of 37.3 determined from the BIC 

dye-injection study), however, may be helpful for emergency 

planning of responses to contaminant spills. Areas likely to 

be affected by actual contaminant spills, however, would be 

identified more reliably from real-time flow measurements and 

water-quality sampling. Finally, implementation of a 3D flow 

and transport model within the Cincinnati reach of the Ohio 

River may reduce the uncertainty of simulated concentrations. The ADCP velocity and dye-concentration data such as 

that used in this model development, plus improved streamflow information as might be obtained from an operational 

streamgage may provide a basis for 3D model implementation 

and calibration. 

Summary and Conclusions

Beginning in 2005, two-dimensional hydrodynamic and 

water-quality models were developed for a 34-mi reach of the 

Ohio River from Cincinnati, Ohio, upstream to Meldahl Dam, 

near Neville, Ohio. The models were developed on the basis of 

bathymetry, flow information, water-levels, and dye concentration measurements made by Koltun and others (2006). The 

study was done in cooperation with the Greater Cincinnati 

Water Works (GCWW) and the American Water Works Association Research Foundation (AwwaRF) to better understand 

flow and transport in the Ohio River. 

Channel boundaries were digitized from georeferenced 

images of navigational charts of the Ohio River. Bathymetry 

of the channel was based on surveys from 2004-06 conducted 

by the U.S. Geological Survey. Based on these data, a finiteelement mesh was developed to discretize the study reach, 

which is needed to facilitate the solution of hydrodynamic and 

transport equations. The mesh comprises 29,751 elements, 

averaging 100 ft on a side, defined at their vertices and midside edges by 92,622 nodes. Groups of contiguous elements 

define three material zones. Hydrodynamic and transport 

simulations compute water levels, velocities, and constituent concentrations at nodes; quadratic interpolation is used to 

estimate corresponding quantities within the interior of the 

elements. 

Five scenarios representing transient flow conditions 

were used to calibrate the hydrodynamic model. Boundary 

conditions described time-varying flow and water-surface 

elevations at the model limits. In this report, Ohio River flows 

at the upstream model boundary were specified on the basis of 

the gate rating at Meldahl Dam, developed by the U.S. Army 

Corps of Engineers, and modified on the basis of flow measurements made in conjunction with this study. Flows near 

the mouths of Big Indian Creek, Twelvemile Creek, Little 

Miami River, and Licking River on the Ohio River also were 

specified as a proportion of the flows at Meldahl Dam. Watersurface elevations were specified on the basis of water levels 

recorded at the USGS water-level gaging station on the Ohio 

River at Cincinnati, Ohio. 

The hydrodynamic model was based on the generalized 

finite-element hydrodynamic code RMA2 to simulate depthaveraged velocities and flow depths. The hydrodynamic model 

contains parameters that characterize the channel’s resistance 

to flow and eddy viscosity, which controls the local variability 

of velocities that affect turbulent exchange and mixing. Unlike 

channel geometry, parameters cannot be measured directly 

but must be inferred from other measurements. In this report, 

measurements of flow, velocity, and water depth obtained 

during USGS ADCP surveys, measurements of tailwater 

elevation at Meldahl Dam, and miscellaneous measurements 

of water-surface elevation were used to estimate parameters in 

the hydrodynamic model. The parameter-estimation process, 

based on a nonlinear regression technique embedded within 

UCODE_2005, produced estimates for the hydrodynamic 

parameters that were considered physically plausible. Also, 

simulation results were consistent with measured flows, water 

levels, flow depths, and depth-averaged velocities. 

The generalized water-quality code RMA4, using hydrodynamics simulated with RMA2, was used to simulate the 

transport of vertically mixed dye, which is a water-soluble 

constituent having a density similar to water. Two water-quality scenarios, representing two USGS dye-injection studies on 

Twelvemile Creek (TMC) and Big Indian Creek (BIC), were 

used to estimate dye-loss rates and turbulent-mixing characteristics for the two overlapping reaches. The two studies used 

the same dye-injection rates and were conducted two days 

apart under similar flow conditions. The transverse distribution of dye concentration was measured in several transects 

downstream from the injection sites. Minor dye losses within 

the injection reaches were described with an exponential decay 

formula; coefficients were estimated on the basis of simulated 

travel times and computed dye-transport rates at transects 

downstream from the points of injection. Both dye-injection 

studies showed more than 87-percent mixing of dye concentrations along transects more than 11.5 mi downstream from 

the point of injection. The rates of turbulent mixing and the 

ability to match simulated and measured dye concentrations, 

however, differed widely between the two reaches. 
References Cited 49

In the TMC injection study, maximum dye concentrations 

exceeded 7.5 μg/L in the upstream transects, starting at about 

6 mi downstream from the injection site, and were less than 

0.8 μg/L in some downstream transects. To simulate the measured distribution of dye concentrations in the more-upstream 

transects, a RMA4 Peclet number of 173 was estimated, which 

is far outside the recommended range from 15 to 40 and is 

considered implausible. This parameter estimate, however, 

resulted in simulations that underestimated the attenuation in 

the downstream transects and resulted in less-uniform concentrations than were measured. In the BIC dye-injection reach, 

the attenuation of maximum dye concentrations from 2.5 μg/L

at OH 3 (the first measured transect about 5.5 mi downstream 

from the injection) to 0.6 μg/L at OH 9 (the last measured 

transect about 11.5 mi downstream from the injection) were 

approximated by a RMA4 Peclet number of 37.2, which is 

within the recommended range from 15 to 40. 

The 2D models used in this report assume that depthaveraged velocities are adequate to describe flow and transport 

within the study reach. This assumption was investigated by 

examining the variation of horizontal velocity components 

with depth from ADCP measurements. Comparisons indicate 

that in the vicinity of channel bends, variations in velocity 

directions with depth are not well approximated by depthaveraged values. Departures from model assumptions associated with flow and transport are thought to be associated with 

the anomalous parameter estimate obtained for the RMA4 

Peclet number at the TMC dye-injection reach. Although the 

estimated RMA4 Peclet number of 37.2 for the BIC injection reach is within the recommended range and produces a 

consistent match with measured concentrations in downstream 

transects, the model application may be restricted to emergency planning. In particular, the lack of consistency between 

turbulent-mixing characteristics in the TMC and BIC reaches 

leaves significant uncertainty as to the appropriate turbulentmixing characteristics for other reaches in the study area. 

Application of 3D flow and transport models using the existing ADCP and dye-concentration data may help address some 

of this ambiguity. The dye-injection studies provided critical 

information needed to calibrate and assess the validity of the 

transport model. Although the RMA2 Peclet number and the 

RMA4 Peclet number for the BIC dye-injection study were 

similar, ADCP velocity data, as applied in this study, could not 

be substituted for dye-concentration data. 

Acknowledgments

This study was done in cooperation with the Greater 

Cincinnati Water Works (GCWW) and the AWWA Research 

Foundation (AwwaRF). Mr. Ramesh Kashinkunti, Supervising Engineer with GCWW, and Dr. Kenan Ozekin, Senior 

Account Manager with AwwaRF, provided technical assistance and coordination. Dr. Richard W. Gullick, Environmental Engineering & Technology, Inc.; Dr. Eugene J. LeBoeuf, 

Vanderbilt University; Dr. Morton W. Reed, Columbus Water 

Works; and Mr. Ed Roehl, Advanced Data Mining International, served on AwwaRF’s Project Advisory Committee and 

provided technical review and oversight. Mr. Stan Wisbith, 

U.S. Army Corps of Engineers, Great Lakes and Ohio River 

Division, provided data on flows, water levels, operations, and 

conditions that were critical in modeling the river. Mr. Michael 

Griffin, USGS Kentucky Water Science Center, provided 

unpublished water-level data obtained during the bathymetry 

surveys. Graphical and editorial assistance was provided by 

Ms. Sharon Baltusis and Ms. Patricia Long of the U.S. Geological Survey. Mr. Chad Wagner, U.S. Geological Survey, 

also provided technical review. Mr. Robert R. Mason, Jr. and 

staff at the USGS Office of Surface Water, quality assured 

miscellaneous water-level data obtained by the USGS Kentucky Water Science Center during the bathymetry surveys. 

References Cited

Barnes, H.H., Jr., 1967, Roughness characteristics of natural 

channels: U.S. Geological Survey Water-Supply Paper 

1849, 213 p.

Donnell, B.P., Letter, J.V., Jr., McAnally, W.H., and others, 

2005, Users guide to RMA2 WES Version 4.5: Vicksburg, Miss., U.S. Army, Engineer Research and Development Center, Waterways Experiment Station, Coastal and 

Hydraulics Laboratory, 277 p. 

Environmental Modeling Research Laboratory, 2006, SMS 

Surface-Water Modeling System Reference Manual, Version 9: Provo, Utah, Environmental Modeling Systems, 

Inc., 342 p. 

Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, Jörg, and 

Brooks, N.H., 1979, Mixing in inland and coastal waters: 

New York, Academic Press, 483 p. 

Hill, M.C., 1998, Methods and guidelines for effective model 

calibration; with application to UCODE, a computer 

code for universal inverse modeling, and MODFLOWP, 

a computer code for inverse modeling with MODFLOW: 

U.S. Geological Survey Water-Resources Investigations 

Report 98–4005, 90 p., accessed December 1, 2007, at 

http://pubs.er.usgs.gov/usgspubs/tm/tm6A11/. 

Koltun, G.F., Ostheimer, C.J., and Griffin, M.S., 2006, Velocity, bathymetry, and transverse mixing characteristics of the 

Ohio River upstream from Cincinnati, Ohio, October 2004–

March 2006: U.S. Geological Survey Open-File Report 

2006–1159, accessed December 3, 2007, at http://pubs.usgs.

gov/of/2006/1159/. 
50 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio 

Letter, J.V., Donnell, B.P., and others, 2005, Users guide to 

RMA4 WES Version 4.5: Vicksburg, Miss., U.S. Army, 

Engineer Research and Development Center, Waterways 

Experiment Station, Coastal and Hydraulics Laboratory, 

173 p. 

McDonald, R.R., Nelson, J.M., and Bennett, J.P., in press, 

Multi-dimensional surface-water modeling system user’s 

guide: U.S. Geological Survey Techniques and Methods, 

6–B2, 136 p.

Ohio River Valley Water Sanitation Commission, 2006, Ohio 

River Facts, accessed December 3, 2007, at http://www.

orsanco.org/rivinfo/facts.asp

Poeter, E.P., Hill, M.C., Banta, E.R., Mehl, Steffen, and Christensen, Steen, 2005, UCODE_2005 and six other computer 

codes for universal sensitivity analysis, calibration, and 

uncertainty evaluation: U.S. Geological Survey Techniques and Methods 6–A11, 283 p., accessed December 3, 

2007, at http://www.mines.edu/igwmc/freeware/ucode/

UCODE_2005_Manual_USGS-TM6-A11.pdf

Rutherford, J.C., 1994, River mixing: New York, John Wiley 

& Sons, 347 p.

Smart, P.L., and Laidlaw, I.M.S., 1977, An evaluation of 

some fluorescent dyes for water tracing: Water Resources 

Research, v. 13, no. 1, p. 15–33. 

U.S. Army Corps of Engineers, 2005a, Coordinate Conversion Program Corpscon (v. 6.0.1): Alexandria, Va., Engineer 

Research and Development Center, Topographic Engineering Center, accessed December 1, 2006, at http://crunch.tec.

army.mil/software/corpscon/corpscon.html

U.S. Army Corps of Engineers, 2005b, Difference between 

“1929 General Adjustment” and “Ohio River” datum 

planes: Louisville, Ky., Louisville District, accessed 

December 1, 2007, at http://www.lrl.usace.army.mil/optm/

article.asp?id=231

U.S. Army Corps of Engineers, 2008, Ohio River and Green 

River Navigation Charts: Louisville, Ky., U.S. Army Corps 

of Engineers, Louisville District, accessed December 12, 

2008, at http://www.lrl.usace.army.mil/optm/article.

asp?id=145&MyCategory=41

U.S. Geological Survey, 2005, Policy and guidance for 

archiving electronic discharge measurement data: U.S. Geological Survey Office of Surface Water Technical Memorandum No. 2005.08, September 26, 2005 5 p., accessed 

June 23, 2009, at http://hydroacoustics.usgs.gov/memos/

OSW2005-08.pdf
Appendixes 1 and 2 
52 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio

Appendix 1. Regimen of the gate-opening sequence for individual gates as a function of total gate opening at Meldahl Dam, near 

Neville, Ohio. —Continued

[Feet of gate opening for individual gates, which are numbered sequentially starting from 1 at the northern-most gate next to the main lock and ending at 12 at 

the gate closest to Kentucky shoreline. Gate opening data were provided by Stanley Wisbith, U.S. Army Corps of Engineers, written commun., March 2006]

Total 

gate 

opening, 

in feet

Gate 1 Gate 2 Gate 3 Gate 4 Gate 5 Gate 6 Gate 7 Gate 8 Gate 9 Gate 10 Gate 11 Gate 12

1 0 0 0 0 0 0 0 0 0 0 0 1

2 0 0 0 1 0 0 0 0 0 0 0 1

3 0 0 0 2 0 0 0 0 0 0 0 1

4 0 0 0 2 0 0 0 0 1 0 0 1

5 0 0 0 2 0 0 0 0 2 0 0 1

6 0 0 0 2 0 0 0 0 3 0 0 1

7 0 0 0 3 0 0 0 0 3 0 0 1

8 0 0 0 3 0 0 0 0 3 1 0 1

9 0 0 0 3 0 0 0 0 3 2 0 1

10 0 0 0 3 0 0 0 0 3 3 0 1

11 0 0 1 3 0 0 0 0 3 3 0 1

12 0 0 2 3 0 0 0 0 3 3 0 1

13 0 0 3 3 0 0 0 0 3 3 0 1

14 0 0 3 3 0 1 0 0 3 3 0 1

15 0 0 3 3 0 2 0 0 3 3 0 1

16 0 0 3 3 0 3 0 0 3 3 0 1

17 0 0 3 3 0 3 1 0 3 3 0 1

18 0 0 3 3 0 3 2 0 3 3 0 1

20 0 0 3 3 1 3 3 0 3 3 0 1

22 0 0 3 3 3 3 3 0 3 3 0 1

24 0 0 3 3 3 3 3 2 3 3 0 1

26 0 1 3 3 3 3 3 3 3 3 0 1

28 0 3 3 3 3 3 3 3 3 3 0 1

30 0 3 3 3 3 3 3 3 3 3 2 1

32 1 3 3 3 3 3 3 3 3 3 3 1

34 3 3 3 3 3 3 3 3 3 3 3 1

36 3 3 3 3 3 3 3 3 3 3 3 3

36 3 3 3 3 3 3 3 3 3 3 3 3

38 3 3 3 3 3 4 4 3 3 3 3 3

40 3 3 3 3 4 4 4 4 3 3 3 3

42 3 3 3 4 4 4 4 4 4 3 3 3

44 3 3 4 4 4 4 4 4 4 4 3 3

46 3 4 4 4 4 4 4 4 4 4 4 3

48 4 4 4 4 4 4 4 4 4 4 4 4

50 4 4 4 4 4 5 5 4 4 4 4 4

52 4 4 4 4 5 5 5 5 4 4 4 4

54 4 4 4 5 5 5 5 5 5 4 4 4

56 4 4 5 5 5 5 5 5 5 5 4 4

58 4 5 5 5 5 5 5 5 5 5 5 4
Appendix 1 53

Appendix 1. Regimen of the gate-opening sequence for individual gates as a function of total gate opening at Meldahl Dam, near 

Neville, Ohio. —Continued

[Feet of gate opening for individual gates, which are numbered sequentially starting from 1 at the northern-most gate next to the main lock and ending at 12 at 

the gate closest to Kentucky shoreline. Gate opening data were provided by Stanley Wisbith, U.S. Army Corps of Engineers, written commun., March 2006]

Total 

gate 

opening, 

in feet

Gate 1 Gate 2 Gate 3 Gate 4 Gate 5 Gate 6 Gate 7 Gate 8 Gate 9 Gate 10 Gate 11 Gate 12

60 5 5 5 5 5 5 5 5 5 5 5 5

62 5 5 5 5 5 6 6 5 5 5 5 5

64 5 5 5 5 6 6 6 6 5 5 5 5

66 5 5 5 6 6 6 6 6 6 5 5 5

68 5 5 6 6 6 6 6 6 6 6 5 5

70 5 6 6 6 6 6 6 6 6 6 6 5

72 6 6 6 6 6 6 6 6 6 6 6 6

76 6 6 6 6 6 8 8 6 6 6 6 6

80 6 6 6 6 8 8 8 8 6 6 6 6

84 6 6 6 8 8 8 8 8 8 6 6 6

88 6 6 8 8 8 8 8 8 8 8 6 6

92 6 8 8 8 8 8 8 8 8 8 8 6

96 8 8 8 8 8 8 8 8 8 8 8 8

100 8 8 8 8 8 10 10 8 8 8 8 8

104 8 8 8 8 10 10 10 10 8 8 8 8

108 8 8 8 10 10 10 10 10 10 8 8 8

112 8 8 10 10 10 10 10 10 10 10 8 8

116 8 10 10 10 10 10 10 10 10 10 10 8

120 10 10 10 10 10 10 10 10 10 10 10 10

124 10 10 10 10 10 12 12 10 10 10 10 10

128 10 10 10 10 12 12 12 12 10 10 10 10

132 10 10 10 12 12 12 12 12 12 10 10 10

136 10 10 12 12 12 12 12 12 12 12 10 10

144 12 12 12 12 12 12 12 12 12 12 12 12

148 12 12 12 12 12 14 14 12 12 12 12 12

152 12 12 12 12 14 14 14 14 12 12 12 12

156 12 12 12 14 14 14 14 14 14 12 12 12

160 12 12 14 14 14 14 14 14 14 14 12 12

168 14 14 14 14 14 14 14 14 14 14 14 14

172 14 14 14 14 14 16 16 14 14 14 14 14

176 14 14 14 14 16 16 16 16 14 14 14 14

180 14 14 14 16 16 16 16 16 16 14 14 14

184 14 14 16 16 16 16 16 16 16 16 14 14

192 16 16 16 16 16 16 16 16 16 16 16 16

196 16 16 16 16 16 18 18 16 16 16 16 16

200 16 16 16 16 18 18 18 18 16 16 16 16

204 16 16 16 18 18 18 18 18 18 16 16 16

208 16 16 18 18 18 18 18 18 18 18 16 16

216 18 18 18 18 18 18 18 18 18 18 18 18
54 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio

Appendix 1. Regimen of the gate-opening sequence for individual gates as a function of total gate opening at Meldahl Dam, near 

Neville, Ohio. —Continued

[Feet of gate opening for individual gates, which are numbered sequentially starting from 1 at the northern-most gate next to the main lock and ending at 12 at 

the gate closest to Kentucky shoreline. Gate opening data were provided by Stanley Wisbith, U.S. Army Corps of Engineers, written commun., March 2006]

Total 

gate 

opening, 

in feet

Gate 1 Gate 2 Gate 3 Gate 4 Gate 5 Gate 6 Gate 7 Gate 8 Gate 9 Gate 10 Gate 11 Gate 12

220 18 18 18 18 18 20 20 18 18 18 18 18

224 18 18 18 18 20 20 20 20 18 18 18 18

228 18 18 18 20 20 20 20 20 20 18 18 18

232 18 18 20 20 20 20 20 20 20 20 18 18

240 20 20 20 20 20 20 20 20 20 20 20 20

244 20 20 20 20 20 22 22 20 20 20 20 20

248 20 20 20 20 22 22 22 22 20 20 20 20

252 20 20 20 22 22 22 22 22 22 20 20 20

256 20 20 22 22 22 22 22 22 22 22 20 20

264 22 22 22 22 22 22 22 22 22 22 22 22

268 22 22 22 22 22 24 24 22 22 22 22 22

272 22 22 22 22 24 24 24 24 22 22 22 22

276 22 22 22 24 24 24 24 24 24 22 22 22

280 22 22 24 24 24 24 24 24 24 24 22 22

288 24 24 24 24 24 24 24 24 24 24 24 24

292 24 24 24 24 24 26 26 24 24 24 24 24

296 24 24 24 24 26 26 26 26 24 24 24 24

300 24 24 24 26 26 26 26 26 26 24 24 24

304 24 24 26 26 26 26 26 26 26 26 24 24

312 26 26 26 26 26 26 26 26 26 26 26 26

316 26 26 26 26 26 28 28 26 26 26 26 26

320 26 26 26 26 28 28 28 28 26 26 26 26

324 26 26 26 28 28 28 28 28 28 26 26 26

328 26 26 28 28 28 28 28 28 28 28 26 26

336 28 28 28 28 28 28 28 28 28 28 28 28

340 28 28 28 28 28 30 30 28 28 28 28 28

344 28 28 28 28 30 30 30 30 28 28 28 28

348 28 28 28 30 30 30 30 30 30 28 28 28

352 28 28 30 30 30 30 30 30 30 30 28 28

360 30 30 30 30 30 30 30 30 30 30 30 30
Appendix 2 55

Appendix 2. Miscellaneous water-level measurements on the Ohio River between Cincinnati and Meldahl Dam obtained during 

2004–06 bathymetry surveys. —Continued

[NAVD 88, North American Vertical Datum of 1988; Michael Griffin, USGS Kentucky Water Science Center, obtained the miscellaneous water-level measurements listed in this appendix. Robert Mason, Jr. and staff from the USGS Office of Surface Water, revised and quality assured these data in 2008]

Date and time 

(Eastern Standard)

River 

mile Site reference

Water-surface 

elevation 

(NAVD 88)

Site description

10/5/04 13:00 471.0 Cincinnati water-level gaging station 454.94 Ohio River at Cincinnati, Ohio (03255000)

10/5/04 13:40 462.5 1005 455.30 Ohio River at the boat ramp at California, Ohio

10/5/04 13:00 436.0 Meldahl Dam 457.37 Ohio River downstream from Meldahl Dam

10/5/04 19:00 471.0 Cincinnati water-level gaging station 455.10 Ohio River at Cincinnati, Ohio (03255000)

10/5/04 19:00 462.5 1005 455.41 Ohio River at the boat ramp at California, Ohio

10/5/04 12:00 436.0 Meldahl Dam 457.35 Ohio River downstream from Meldahl Dam

10/6/04 09:00 471.0 Cincinnati water-level gaging station 455.18 Ohio River at Cincinnati, Ohio (03255000)

10/6/04 09:00 462.5 1005 455.38 Ohio River at the boat ramp at California, Ohio

10/6/04 09:00 436.0 Meldahl Dam 456.87 Ohio River downstream from Meldahl Dam

10/6/04 18:00 471.0 Cincinnati water-level gaging station 454.68 Ohio River at Cincinnati, Ohio (03255000)

10/6/04 18:30 462.5 1005 454.82 Ohio River at the boat ramp at California, Ohio

10/6/04 18:30 436.0 Meldahl Dam 456.34 Ohio River downstream from Meldahl Dam

10/7/04 09:00 471.0 Cincinnati water-level gaging station 455.08 Ohio River at Cincinnati, Ohio (03255000)

10/7/04 09:00 462.5 1005 455.37 Ohio River at the boat ramp at California, Ohio

10/7/04 09:20 436.0 Meldahl Dam 457.64 Ohio River downstream from Meldahl Dam

10/7/04 19:00 471.0 Cincinnati water-level gaging station 455.48 Ohio River at Cincinnati, Ohio (03255000)

10/7/04 19:00 462.5 1005 455.81 Ohio River at the boat ramp at California, Ohio

10/7/04 19:00 436.0 Meldahl Dam 457.89 Ohio River downstream from Meldahl Dam

10/27/05 08:30 471.0 Cincinnati water-level gaging station 456.07 Ohio River at Cincinnati, Ohio (03255000)

10/27/05 08:30 449.4 1006 458.03 Ohio River at Skippers Boat Ramp near 

New Richmond, Ohio

10/27/05 08:45 446.9 1007 458.51 Ohio River at Bubblers Restaurant near 

Clermontville, Ohio

10/27/05 09:40 442.6 1008 459.06 Ohio River at boat ramp at Moscow, Ohio

10/27/05 09:15 438.7 1009 459.25 Ohio River at Neville, Ohio

10/27/05 08:30 436.0 Meldahl Dam 459.72 Ohio River downstream from Meldahl Dam

10/28/05 09:00 471.0 Cincinnati water-level gaging station 455.86 Ohio River at Cincinnati, Ohio (03255000)

10/28/05 09:00 449.4 1006 458.12 Ohio River at Skippers Boat Ramp near 

New Richmond, Ohio

10/28/05 09:30 446.9 1007 458.59 Ohio River at Bubblers Restaurant near 

Clermontville, Ohio

10/28/05 09:00 442.6 1008 459.14 Ohio River at boat ramp at Moscow, Ohio

10/28/05 09:00 436.0 1009 459.72 Ohio River at Neville, Ohio

11/3/05 10:00 471.0 Cincinnati water-level gaging station 454.84 Ohio River at Cincinnati, Ohio (03255000)

11/3/05 09:40 449.4 1006 455.54 Ohio River at Skippers Boat Ramp near 

New Richmond, Ohio
56 Initial Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River near Cincinnati, Ohio

Appendix 2. Miscellaneous water-level measurements on the Ohio River between Cincinnati and Meldahl Dam obtained during 

2004–06 bathymetry surveys. —Continued

[NAVD 88, North American Vertical Datum of 1988; Michael Griffin, USGS Kentucky Water Science Center, obtained the miscellaneous water-level measurements listed in this appendix. Robert Mason, Jr. and staff from the USGS Office of Surface Water, revised and quality assured these data in 2008]

Date and time 

(Eastern Standard)

River 

mile Site reference

Water-surface 

elevation 

(NAVD 88)

Site description

11/3/05 09:30 446.9 1007 455.77 Ohio River at Bubblers Restaurant near 

Clermontville, Ohio

11/3/05 09:05 442.6 1008 456.02 Ohio River at boat ramp at Moscow, Ohio

11/3/05 09:00 438.7 1009 456.00 Ohio River at Neville, Ohio

11/3/05 11:20 436.0 Meldahl Dam 456.32 Ohio River downstream from Meldahl Dam

11/4/05 09:15 471.0 Cincinnati water-level gaging station 455.14 Ohio River at Cincinnati, Ohio (03255000)

11/4/05 07:50 449.4 1006 455.96 Ohio River at Skippers Boat Ramp near 

New Richmond, Ohio

11/4/05 08:10 446.9 1007 456.15 Ohio River at Bubblers Restaurant near 

Clermontville, Ohio

11/4/05 08:30 442.6 1008 456.41 Ohio River at boat ramp at Moscow, Ohio

11/4/05 08:50 438.7 1009 456.36 Ohio River at Neville, Ohio

11/4/05 09:15 436.0 Meldahl Dam 456.92 Ohio River downstream from Meldahl Dam

3/21/06 19:50 471.0 Cincinnati water-level gaging station 457.29 Ohio River at Cincinnati, Ohio (03255000)

3/21/06 19:00 462.5 1005 458.35 Ohio River at the boat ramp at California, Ohio

3/22/06 14:45 471.0 Cincinnati water-level gaging station 456.58 Ohio River at Cincinnati, Ohio (03255000)

3/22/06 14:15 462.5 1005 457.46 Ohio River at the boat ramp at California, Ohio

3/22/06 22:15 471.0 Cincinnati water-level gaging station 455.38 Ohio River at Cincinnati, Ohio (03255000)

3/22/06 23:30 462.5 1005 457.65 Ohio River at the boat ramp at California, Ohio

3/23/06 14:30 471.0 Cincinnati water-level gaging station 456.42 Ohio River at Cincinnati, Ohio (03255000)

3/23/06 14:30 462.5 1005 457.20 Ohio River at the boat ramp at California, Ohio

3/23/06 21:15 471.0 Cincinnati water-level gaging station 456.41 Ohio River at Cincinnati, Ohio (03255000)

3/23/06 21:10 462.5 1005 457.20 Ohio River at the boat ramp at California, Ohio

David J. Holtschlag—Investigation of Multidimensional Flow and Transverse Mixing Characteristics, Ohio River, Cincinnati, Ohio—Scientific Investigations Report 2009–5107

Printed on recycled paper