THE USE OF THREE-PARAMETER RATING TABLE LOOKUP 

PROGRAMS, RDRAT AND PARM3, IN HYDRAULIC FLOW 

MODELS

By Curtis L. Sanders, Jr.

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations Report 95-4090

Columbia, South Carolina 

1995
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director

For additional information write to:

District Chief 

U.S. Geological Survey 

Stephenson Center- Suite 129 

720 Gracern Road 

Columbia, SC 29210-7651

Copies of this report can be purchased from:

U.S. Geological Survey

Earth Science Information Center

Open-File Reports Section

Box 25286, Mail Stop 517

Denver Federal Center

Denver, CO 80225
CONTENTS

Page

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

Introduction ................................................................. 1

Functional specifications ....................................................... 2

Three-parameter ratings........................................................ 4

Input data................................................................... 7

Software description ......................................................... 10

Summary .................................................................. 12

References cited............................................................. 13

Appendix - Input data set ..................................................... 15

ILLUSTRATIONS

Figure 1. Graph showing three-parameter rating with types of curves

and input data points ............................................... 5

2. Graph showing three-parameter rating with input data points ................. 14

CONVERSION FACTORS AND ABBREVIATIONS

Multiply By To obtain 

foot (ft) 0.3048 meter

r\

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

cubic foot per second (ft3/s) 0.0283 cubic meter per second

THE USE OF THREE-PARAMETER RATING TABLE LOOKUP 

PROGRAMS, RDRAT AND PARM3, IN HYDRAULIC

FLOW MODELS

By Curtis L. Sanders, Jr.

ABSTRACT

Subroutines RDRAT and PARM3 enable computer programs such as the 

BRANCH open-channel unsteady-flow model to route flows through or over 

combinations of critical-flow sections, culverts, bridges, road-overflow sections, 

fixed spillways, and(or) dams. The subroutines also obstruct upstream flow to 

simulate operation of flapper-type tide gates. A multiplier can be applied by date 

and time to simulate varying numbers of tide gates being open or alternative 

construction scenarios for multiple culverts. The subroutines use three-parameter 

(headwater, tailwater, and discharge) rating table lookup methods. These tables 

may be manually prepared using other programs that do step-backwater 

computations or compute flow through bridges and culverts or over dams. The 

subroutine, therefore, precludes the necessity of incorporating considerable 

hydraulic computational code into the client program, and provides complete 

flexibility for users of the model for routing flow through almost any affixed 

structure or combination of structures. The subroutines are written in Fortran 77 

language, and have minimal exchange of information with the BRANCH model or 

other possible client programs. The report documents the interpolation 

methodology, data input requirements, and software.

INTRODUCTION

Subroutines RDRAT and PARM3 enable "client" computer programs such as the U.S. 

Geological Survey (USGS) branch-network one-dimensional (BRANCH model) unsteady flow 

model (Schaffranek and others, 1981) to route flows through subreaches of natural streams or 

structures, where flow can alternate between super- and sub-critical flow regimes. The 

subroutines also route flows through or over complex combinations of culverts, bridges, road 

overflow sections, fixed spillways, and (or) dams. In addition, the subroutines account for the 

operation of flapper-type tide gates, which obstruct upstream flow and a multiplier can be applied 

to computed discharges based on date and time. The multiplier can be used to simulate varying 

numbers of operational flapper gates or alternative construction scenarios for multiple culverts.
Flows are routed within the client program for all structures by use of three-parameter 

(headwater, tailwater, and discharge) rating table lookup methods. Input for the subroutines is 

prepared external to the BRANCH Model by the user, using output from hydraulic programs such 

as the Water Surface Profile Computations (WSPRO) program (Shearman, 1990) or the culvertflow computation program A526 (H.F. Matthai, H.E. Stull, and Jacob Davidian, U.S. Geological 

Survey, written commun., undated). Complex hydraulic data entry and computations, therefore, 

do not have to be incorporated into the client program, and the user has total flexibility, except for 

coding conventions, as to how the ratings are constructed. A knowledge of hydraulics and the 

interpolation methods is necessary, however, to construct the ratings. Several three-parameter 

ratings can be added together graphically to create a single rating where several structure types 

exist at a single location. The subroutines presented in this report also do simpler two-parameter 

(headwater and discharge) rating table lookups.

Inclusion of these subroutines in the BRANCH Model allow routing of hydrographs from 

non-uniform sub-basins through stream reaches where the storage-basin outflow ratings are in 

backwater or where flow can go upstream into large storage areas. In addition, these subroutines 

can be used by the National Water Information System (NWIS) to compute flow through culverts 

using recorded headwater and tailwater stages. The NWIS is the USGS computerized 

computation and storage system for its national treasury of water data. The subroutines also can 

be modified to do interpolations for three-parameter relations used to compute entrance-loss 

coefficients for indirect computations of flows through culverts and bridges.

This report documents the three-parameter rating table interpolation method, data input, and 

the required software. Subroutine RDRAT reads the necessary input data, and subroutine PARM3 

computes the discharge for the client program based on rating numbers, headwater elevations, and 

tailwater elevations. Subroutine RDRAT also can apply a multiplier based on date and time, and 

prevents negative flows for simulations of flapper-type tide gates.

FUNCTIONAL SPECIFICATIONS

Subroutines were designed to minimize the interaction with the client program (BRANCH 

model) by using data encapsulation in a manner similar to that suggested by Delong and others 

(1992). Subroutine RDRAT reads all necessary data using only the name of the American 

Standard Code for Information Interchange (ASCII) file holding the rating table and a Fortran 77 

(F77) unit number as provided to subroutine RDRAT by the client program. Subroutine PARM3 

does all the computations. The client program provides subroutine PARM3 with date and time, 

the rating numbers, and headwater and tailwater elevation. The PARM3 subroutine returns the 

discharge and error flags to the client program. The client program does not have to share large 

common blocks of information with either subroutine, because most of the necessary data are 

read by the subroutines from the ASCII file.
Computational specifications are:

1. Interpolations can be arithmetic or logarithmic with log offset.

2. Two-parameter (headwater and discharge) interpolations can be done for:

a. Critical-flow sections

b. Highway embankments

c. Fixed spillways at dams

3. Three-parameter (headwater, tailwater, and discharge) interpolations can be done for 

flow at:

a. cross sections where flows can change back and forth from supercritical to

subcritical,

b. cross sections where flows are affected by variable backwater, 

c. culverts, 

d. bridges, and 

e. electric turbines.

4. Interpolations can be done for any combinations of flows in (2) and (3) above by 

graphical or numerical combinations of these ratings into one rating. For example, 

assume that separate tailwater ratings for a tailwater elevation of 8.0 ft are available for 

two bridges. Assume that at a headwater elevation of 8.5 ft, the flow through the 

bridges are 1,000 and 1,500 ft3/s, as determined from the ratings. Then, for a headwater 

of 8.5 ft and a tailwater of 8.0 ft the total flow would be 2,500 ft3/s. The process can be 

repeated for all the tailwater ratings for the two bridges. The process is easier if done 

graphically:

a. Plot the tailwater ratings as a series of smooth curves on arithmetic paper with 

headwater elevation on the vertical axis and discharge on the horizontal axis.

b. Project a horizontal line at selected headwater increments, and use a pair of dividers 

to cumulate flows through all structures along this horizontal line for each tailwater 

curve. Use a plotting symbol to represent the cumulated flow for the flows 

associated with the tailwater curve.

c. Draw a smooth line through the plotting symbols, and read off the cumulated flows at 

increments small enough for straight-line interpolation to be sufficiently accurate.

5. Different ratings for positive and negative flow can be used.

6. Flapper-type tide gates can be simulated by preventing negative flow when negative falls 

exceed a specified amount.

7. A multiplier can be applied to discharge based on beginning date and time to simulate 

varying numbers of active tide gates or varying numbers of structures for testing of 

alternative multiple-culvert construction scenarios.
THREE-PARAMETER RATINGS

The complex rating in figure 1 is shown to demonstrate all the interpolation methods used by 

the subroutines. The coding and theory for a simple three-parameter rating without changes in flow 

type is simpler. The three-parameter rating shown in figure 1 is for a 100-ft long, 3-ft diameter 

concrete-pipe culvert with zero slope. Data for the rating were computed by USGS program A526 

(H.F. Matthai, H.E. Stull, and Jacob Davidian, U.S. Geological Survey, written commun., 

undated). Bodhaine (1969) gives a detailed description of culvert hydraulics and flow types. A 

rating from step-backwater program WSPRO (Shearman, 1990) is not shown, but would be similar 

to the rating below the horizontal line where (HW-Z)/D=1.2 in figure 1, for a cross-section that 

undergoes subcritical and supercritical flow. In the equation above, HW is the headwater 

elevation, Z is the elevation of the upstream invert of the culvert, and D is the maximum vertical 

opening of the culvert in feet. Headwater elevation is shown on the ordinate, and discharge is 

shown on the abscissa (fig. 1) for designated tailwater curves. Enough points and tailwater curves 

must be obtained by the user for straight-line arithmetic or logarithmic interpolation to be valid.

Types 1, 2, and 3 flow are open-pipe culvert flow. Critical flow exists at the entrance for 

type 1 flow and at the outlet for type 2 flow. Tranquil flow exists throughout the culvert for type 3 

flow. In type 4 flow, the whole culvert is submerged. In flow types 5 and 6, high-head flow exists 

at the entrance of the culvert and the outlet of the culvert is not submerged. The culvert flows full 

for type 6 flow, but not for type 5 flow (Bodhaine, 1969).

The limiting-flow curve shown in figure 1 is the limiting headwater-discharge rating for a 

critical-flow section in a natural stream or for types 1, 2, 5, or 6 culvert flow. The tailwater curves 

may or may not be tangential to the limiting-flow curve (points 4 and 6 in figure 1), but they do 

intersect it at fairly uniform intervals.

For culverts, there is an indeterminate transitional zone for flow types between headwater 

elevations corresponding to (HW-Z)/D=1.2 and 1.5 (fig. 1). Flow in this zone can be alternating 

between high-head parallel construction flow (types 5 or 6) and open-pipe flow (types 1, 2, or 3). 

Usually, straight lines are constructed between the computations for headwater elevations where 

(HW-Z)/D=1.2 and 1.5 (points 10 and 12 and points 11 and 12 in figure 1).

The method of interpolation, where the rating is defined only by the tailwater curves, is to 

interpolate a tailwater curve from the input tailwater curves, as shown by the dashed line through 

points 1 and 2 (fig. 1), and to lookup the discharge from this curve using the input headwater. It is 

important to remember that when coding input data for this type of rating, sufficient upper and 

lower bounds of input-tailwater curves need to be provided. Interpolation is done in the vertical 

and only from tailwater curves. It is incorrect to interpolate a tailwater curve in this zone using a 

tailwater curve and a limiting-headwater discharge-rating curve. Tailwater curves, therefore, 

must be coded bounding the zones where the tailwater curve is to be interpolated. For example, 

points 1 and 2 (fig. 1) are interpolated in the vertical from data points on the 2.5 and 3.0 ft 

tailwater curves.
LU 

LLJ 

U_

? 5

Z

o

h-

£ 4

LLJ

CC 

LLJ i 3

Q

LLJ

I

CULVERT DESCRIPTION 

3-ft concrete pipe 

100-ft long 

Zero slope

(HW-Z)/D=1.5

NOTE:

Below this elevation, 

the rating is similar to a 

step-backwater rating with 

sub-critical and critical flow.

LIMITING HEADWATER-DISCHARGE CURVE

HEADWATER-TAIL WATER-DISCHARGE CURVE, 

DRAWN THROUGH RATING DATA POINTS

INTERPOLATED HEADWATER-TAIL WATERDISCHARGE CURVE

SELECTED DATA POINT AND REFERENCE NUMBER

10 20 30 40 50

DISCHARGE, IN CUBIC FEET PER SECOND

60 70

Figure 1 .-Three-parameter rating with types of curves and input data points.
Interpolation within triangles defined by points 4-5-6, 9-10-11, and 10-11-12 (fig. 1), do not 

qualify for the interpolation method described above. The dashed line or tailwater curve between 

points 2 and 3 is defined by interpolating point 2 from points 4 and 5 and by interpolating point 3 

from points 4 and 6.

The dashed line between points 7 and 8 is determined by interpolating point 7 from points 

9 and 10 and by interpolating point 8 from points 10 and 11. The dashed line between points 8 and 

12 is determined by interpolating point 8 from points 10 and 11 as before, and using point 12 

directly. Point 12 is the point where the culvert type 5 or 6 flow intersects the line where 

(HW-Z)/D=1.5. Points 4, 6, 10, 11, and 12 are at intersections of graphically extended rating lines 

with other rating lines or lines marking a change of flow type. The user must select rating points 

with a full understanding of the above linear-logarithmic-interpolation schemes.

For the special case of type 4 culvert flow (submerged culvert flow), discharge is computed 

directly by:

Q = K(HW-TW)0 5 , (1)

where

Q is the discharge, in cubic feet per second,

HW is the headwater elevation, in feet,

K is a constant, in feet 2l5 per second, and

TW is the tailwater elevation, in feet.

The constant K, is determined by the equation:

K = CAo

1 +

29 C2 n 2 L' (2)

where

A0 is the area of the culvert, in square feet,

C is the entrance coefficient,

g is the constant acceleration of gravity, 32.2 feet per second squared,

L is the length of culvert, in feet,

n is the Manning's roughness coefficient for the culvert, and

R0 is the hydraulic radius of the culvert, in feet.

Equations 1 and 2 are applicable when HW and TW are greater than or equal to the sum of the 

largest vertical dimension of the culvert and the elevation of the upstream invert, in feet.
INPUT DATA

Input data for ratings can be extracted from graphs such as figures 1 and 2 (fig. 2 at end of 

report). The data may be entered into an ASCII file, as presented in the appendix of this report, 

for input to program RDRAT.

A graph such as figure 1 is essential for the coding of input data for complex culvert ratings 

and three-parameter ratings that include a limiting-flow curve. In general, the limiting-flow curve 

should be constructed first. For culverts, construct a straight line between the limiting-flow curve 

points at (HW-Z)/D = 1.2 and 1.5. Next, construct the tailwater curves, and smooth them with the 

limiting-flow curve [below (HW-Z)/D = 1.2, for culvert ratings]. Terminate tailwater 

curves at (HW-Z)/D = 1.2 for culvert ratings, and draw straight lines from these points to the 

limiting-flow curve at (HW-Z)/D =1.5.

The record types of the dataset are identified by the first two columns of each record by "TA," 

"Tl-4," and "TD" as described below. Subroutine RDRAT searches any flat file for their record 

types; therefore, the records are either in a master control file with other data used by the client 

program or in its own separate file. The remaining data in columns 2 to 80 are entered in list 

format, and are separated by blanks. The maximum number of ratings on the "TA" record, rating 

points for each of the TI-4 records, and dates coded on the TD record are 5, 100 and 50, 

respectively. These limits can be easily changed, however, as described in the "software 

description" section of this report.

Input data needed by the subroutine are: 

"TA" Record:

Column 1-2, Code "TA" for record type.

Column 3-80, Code the following, separated by blanks:

Rating number:

Should be sequential, starting with the number 1. 

Rating type:

0 = arithmetic interpolation

1 = logarithmic interpolation

Logarithmic stage offset, in feet; code 0.0 if not applicable 

Number of parameters in rating:

2 = headwater-discharge rating

3 = headwater-tailwater-discharge rating

Culvert type 4 "K" factor (eq. 1) for positive flow; code 0.0 if not applicable
Culvert type 4 "K" factor for negative flow; code 0.0 if not applicable.

Tailwater elevation, in feet, above which culvert type 4 submerged flow exists; code 

999999.0, if not applicable.

Tailwater elevation, in feet, below which only the limiting headwater discharge 

rating will be used; code -999999.0, if not applicable.

Headwater elevation, in feet, above which only the limiting headwater-discharge 

rating will be used; code -999999.0 if not applicable. This is also point 12 in 

figure 1, where culvert type 5 or 6 flow intercepts the (HW-Z)/D=1.5 line.

Fall, in feet, across tide gates, at which water is to be prevented from flowing 

upstream through the gates. This will normally be set to 0.0 or a small negative 

number. Code 0.0 if tide gates are not present.

Datum correction 1 to be ADDED to the input headwaters and tailwater elevations 

before application to rating.

"Tl" Record:

Columns 1-2, Code "Tl" for record type; this record describes a rating point located 

only on the limiting headwater-discharge curve as indicated in figure 2.

Columns 3-80, Code the following, separated by blanks:

Discharge, in cubic feet per second, and headwater elevation, in feet.

Note: It is not necessary to code a value for tailwater elevation.

"T2" Record:

Columns 1-2, Code "T2" for record type; this record type describes a rating point 

common to the limiting headwater-discharge rating curve and to a headwatertailwater-discharge rating curve as identified in figure 2.

Columns 3-80, Code the following, separated by blanks:

Discharge, in cubic feet per second, 

Headwater elevation, in feet, and 

Tailwater elevation, in feet.

1 The datum correction can be used to adjust output from program A526, which does not allow 

negative elevations, to experimentally raise or lower structures, or to use one rating for several structures at 

different datums.
"T3" Record:

Columns 1-2, Code "T3" for record type; this record type describes a rating point 

located only on a headwater-tailwater-discharge rating curve as identified in 

figure 2.

Columns 3-80, Code the following, separated by commas:

Discharge, in cubic feet per second,

Headwater elevation, in feet, and

Tailwater elevation, in feet - for parallel construction with "T2" record.

T4" Record:

Columns 1-2, Code "T4" for record type; this record type describes a rating point 

located on a headwater-tailwater-discharge rating curve and also at the 

^l .2 line, such as is identified in figure 2.

Note: The (HW-Z)/D=1 .2 line need not be horizontal as shown in figure 1 ; it can 

be a series of segments as described by the "T4" record. This is usable if there is a 

skewed upper boundary for three-parameter rating lookup, such as for turbine 

ratings.

Column 3-80, Code the following, separated by blanks:

Discharge, in cubic feet per second,

Headwater elevation, in feet, and

Tailwater elevation, in feet - for parellel construction with "T2" record.

"TD" Record:

Columns 1-2, Code "TD" for record type; if this record type exists, the multiplier 

defined below will be applied to the computed discharge if the date and time below 

are equalled or exceeded. This can be used to simulate varying numbers of tide 

gates open at specified times or to simulate the effects of varying the numbers of 

structures at a site.

Columns 4-9, YYMMDD, date to begin multiplier, where YY is the year, MM is the 

month, and DD is the day of the month.

Columns 11-14, HHMM, time to begin multiplier, where HH is the hour and MM is the 

minute.

Columns 15-24, Multiplier to be applied to computed discharge. The multiplier is not 

prorated between adjacent date-times.
Outputs from culvert program A526 and step-backwater program WSPRO are generally 

sorted by discharge, tailwater, and headwater, as is required for input to this subroutine. However, 

output from these programs should not be input blindly to this subroutine, without a hydraulic 

analysis of plots of the three-parameter ratings. For example, points 4, 6, 9, 10, 11, and 12 (fig. 1) 

are not automatically output by these two programs. These points had to be determined from the 

graphic plot for coding on the "T2" and "T4" records.

Points shown on figure 2 are a guide for coding the "Tl-4" records as described above and 

tabulated in the appendix of this report, based on the interpolation schemes. Enough points and 

tailwater curves are coded to maintain accuracy of straight-line interpolation. The rating points 

should be vertically aligned as shown in figure 2. A vertical string of points also should be created 

from the tailwater curves and limiting headwater discharge curve for "T2" and "T4" records as 

shown in figure 2. In general, as shown in the appendix, the "Tl-4" records are all sorted by 

discharge, tailwater elevation, and headwater elevation. For a simple two-parameter headwaterdischarge rating, the "T2-4" records are not needed.

SOFTWARE DESCRIPTION

The client program calls only the RDRAT and PARM3 subroutines described below. 

Subroutine RDRAT reads the rating-input data, and subroutine PARM3 does the interpolation 

using the rating data and other data provided by the client program. Ratings are identified by a 

rating number and are fully described by the "TA," "Tl-4," and "TD" records. The client program 

needs only the rating number to access all respective rating data on these records. A rating from a 

master file of ratings also can be used by reference to the rating number in several calls without 

repetitive coding of the rating. Both subroutines are written in F77 programming language. The 

number of ratings, rating points, and dates allowed by the subroutines on the "TA," "TI-4," and 

"TD" records can be modified by changing the "parameter" declaration of the subroutine variable 

"NORATS," "RTPTS," and "NORTDT," respectively, in the subroutine-source code before 

compilation.

Subroutine RDRAT reads into common blocks the data necessary for the PARM3 rating 

table lookup subroutine, and the data are kept in memory for subsequent access by the PARM3 

subroutine. Arguments for the RDRAT subroutine are:

1. Name of the file holding the rating data (input, 48 character maximum). The subroutine 

assumes the file to be closed, opens it, reads the data, and closes the file. This can be a 

file separate from control files used by the client program, or the TA, TI-4, and TD 

records can be part of the control files. The program searches the file for records having 

"TA," "Tl-4," or "TD" coded in the first two columns.

10
2. Unit number to be assigned to the file (input, integer).

3. Fatal warning flag (output, integer). If this flag is not zero, an error occurred in reading 

the data, and the client program should issue warning messages and discontinue 

computations. Fatal warning flags are:

1 = error in opening file

2 = error in reading file

3 = error in closing file

4 = error due to attempt to take the logarithm of a number less than or equal to zero.

Subroutine PARM3 tests all the conditions for interpolation and does the interpolation. It 

also checks to see if the multiplier described above exists, applies it if it exists, and checks the date 

to see when it is to be changed. It also tests for negative flow, changes ratings, if the rating for 

negative flow is not the same as for positive flow, and prevents negative flow if tide gates are 

present. Arguments for subroutine PARM3 are:

1. Year, month, day, hour, and minute of the values being computed (input, integer), for use 

in applying multiplication factors to the computed discharge.

2. Positive and negative flow-rating numbers (input, integer).

3. Headwater and tailwater elevations (input, real).

4. Discharge (output, real).

5. A warning error flag (not used).

6. A fatal error flag (output, integer). If this flag is not zero, a fatal error occurred, and the 

client program should issue a warning message and discontinue all computations. Fatal 

warning flags are:

4 = error because of an attempt to take the logarithm of a number less than or equal 

to zero

5 = error because more dates were input than allowed by program dimension 

statement

6 = error because a rating table was exceeded

7 = error because the program was unable to arrive at a discharge solution, 

probably because of a programming error from not identifying all solution 

cases

8 = error because more rating points were input than allowed by limits defined by 

the program dimension statement

9 = error because more ratings were input than allowed by limits defined by the 

program dimension statement

10 = error because of an attempt to divide by zero in interpolation equations because 

two consecutive rating-input (not output) values were equal.

11
Subroutine PARM2 does a simple arithmetic rating-table lookup for subroutine PARM3. 

Logarithmic conversions are already made prior to its being called.

Subroutine INTERP does simple interpolation for subroutine PARM2.

Subroutine LOGX applies logarithmic offsets and takes logarithms of headwater, tail water, 

and discharge.

SUMMARY

Subroutines RDRAT and PARM3 were developed to route flows through or over 

constrictions of natural channels (such as bridges or dams) and through multiple flapper-type tide 

gates using three-parameter (headwater elevation, tailwater elevation, and discharge) rating-table 

lookup methods. The subroutines also use two-parameter (headwater elevation and discharge) 

rating-table lookup methods and can interpolate both arithmetically and logarithmically. Different 

ratings for positive and negative flows can be used, and a multiplier can be applied to discharge 

based on beginning date and time to simulate varying numbers of tide gates or varying numbers of 

structures for the testing of multiple-culvert construction scenarios.

The two- and three-parameters rating tables are prepared external to the client program (the 

U.S. Geological Survey BRANCH one-dimensional unsteady flow model, in particular) by using 

any valid hydraulic method or program. Therefore, the subroutines can be used for almost any 

fixed structure and relieve the calling program from having to accommodate a huge variety of 

hydraulic computational methods. The theory of two- and three-parameter rating-table lookup 

methodology, interpolation methods used, data input, and software are described.

12
REFERENCES CITED

Bodhaine, G.L., 1969, Measurement of peak discharge at culverts by indirect methods: U.S. 

Geological Survey Techniques of Water-Resources Investigations, book 3, chap. A3, 60 p.

Delong, L.L., Thompson, D.B., and Fulford, J.M., 1992, Data encapsulation using Fortran 77 

modules: Fortran Forum 11/(3), p. 11-19.

Schaffranek, R.W., Baltzer, R.A., and Goldberg, D.E., 1981, A model for simulation of flow in 

singular and interconnected channels: U.S. Geological Survey Techniques of WaterResources Investigations, book 7, chap. 3, 110 p.

Shearman, J.O., 1990, User's manual for WSPRO - a computer model for water surface profile 

computations: U.S. Department of Transportation, Federal Highway Administration, 

Publication No. FHWA-IP-89-027, 177 p.

13
CULVERT DESCRIPTION 

3-ft concrete pipe 

100-ft long 

Zero slope

TRANSITION 

ZONE

NOTE:

Use tailwater = 3.6 ft 

for this point

NOTE:

Determine the T2 and T3 

points from graph

Tl DATA POINT 

T2 DATA POINT 

T3 DATA POINT 

T4 DATA POINT

LIMITING HEADWATERDISCHARGE RATING

20 30 40 50 60 

DISCHARGE, IN CUBIC FEET PER SECOND

Figure 2.--Three-parameter rating with input data points.

14
APPENDIX

Input data set

15
Appendix Input data set

TA

Tl

T3

T3

T3

T3

T3

Tl

T3

T3

T3

T3

T3

T2

T3

T3

T3

T3

Tl

T3

T3

T3

T3

Tl

T3

T3

T3

T3

T2

T3

T3

1

2.0

2.0

2.0

2.0

2.0

2.0

4.0

4.0

4.0

4.0

4.0

4.0

6.0

6.0

6.0

6.0

6.0

8.0

8.0

8.0

8.0

8.0

10.0

10.0

10.0

10.0

10.0

14.0

14.0

14.0

0

1.79

2.03

2.51

3.00

3.50

3.90

2.06

2.12

2.53

3.02

3.51

3.91

2.26

2.57

3.03

3.52

3.92

2.45

2.63

3.06

3.54

3.93

2.62

2.70

3.09

3.56

3.95

2.91

3.18

3.62

0.0

0.0

2.0

2.5

3.0

3.5

3.9

0.0

2.0

2.5

3.0

3.5

3.9

2.0

2.5

3.0

3.5

3.9

0.0

2.5

3.0

3.5

3.9

0.0

2.5

3.0

3.5

3.9

2.5

3.0

3.5

3 38.28 20.0

lilitll

4.0 2.0 5.5 -999999. 0.0

16
T3

Tl

T3 

T3

T3

Tl

T3

T3

T3

T2

T3

T3

Tl

T3

T3

Tl

T3

T3

Tl

T3

T4

T2

Tl

T4

Tl

Tl

Tl

Tl

Tl

TD

TD

TD

14.0

18.0

18.0 

i s n

18.0

22.0

22.0

22.0

22.0

24.0

24.0

24.0

26.0

26.0

26.0

30.0

30.0

30.0

34.0

34.0

34.0

38.0

39.2

39.2

53.6

56.0

60.0

65.0

70.0

911001

911005

911005

4.01

3.17

3.31

3

fC\

4.08

3 42

3.47

3.80

4.17

3.55

3.86

4.20

3.66

3.92

4.29

3.91

4.07

4.43

4.16

4.26

4.60

4.49

4.60

4.60

5.50

5.67

5.95

6.34

6.76

0100

0400

1000

3.9

0.0

3.0

3.5

3.9

0.0

3.0

3.5

3.9

3.0

3.5

3.9

0.0

3.5

3.9

0.0

3.5

3.9

0.0

3.5

3.9

3.5

0.0

3.6

0.0

0.0

0.0

0.0

0.0

1.0

2.0

0.0

17