APPLICATI-ON OF THE U.S. GEOLOGICAL SURVEY 

RAINFALL-RUNOFF SIMULATION MODEL TO 

IMPROVE FLOOD-FREQUENCY ESTIMATES 

ON SMALL TENNESSEE STREAMS 

by Herman C. Wibben 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations 76-120 

Prepared in cooperation with 

Tennessee Department of Transportation 

Bureau of Planning and Programming 

and 

U.S. Department of Transportation 

Federal Highway Administration 

1976 
BIBLIOGRAPHIC DATA 1. Report No. 2. 

SHEET 

4. Title and Subtitle 

3. Recipient’s Accession No. 

APPLICATION OF THE U.S. GEOLOGICAL SURVEY RAINFALL-RUNOFF 

SIMULATION MODEL TO IMPROVE FLOOD-FREQUENCY ESTIMATES ON SMALL 

TENNESSEE STREAMS. 

5. Report Date 

1976 

6. 

7. Author(s) 

H. C. Wibben 

9. Performing Organization Name and Address 

U. S. Geological Survey, Water Resources Division 

A-413 Federal Building - U. S. Courthouse 

Nashville, Tennessee 37203 

8. Performing Organization Rept. 

NoUSGS/WRI-76-120 

10. Project/Task/Work Unit No! 

11. Contract/Grant No. 

12. Sponsoring Organization Name and Address 

U. S. Geological Survey, Water Resources Division 

A-413 Federal Building - U. S. Courthouse 

Nashville, Tennessee 37203 

13. Type of Report & Period 

Covered 

Final 

14. 

15. Supplementary Notes Prepared in cooperation with Tennessee Depart ent of Transportation, 

Bureau of Planning and Programming, and U. S. Department of Transportation, Federal 

Highway Administration. 

16* AbstractsThe U. S. Geological Survey rainfall-runoff simulation model was used in 

conjunction with National Weather Service climatological data to improve flood-frequency estimates for 52 small drainage basins in Tennessee. The basins range in size from 

0.17 to 64 square miles (0.44 to 166 square kilometers) and are distributed throughout 

the State. Model parameters were determined by calibration with observed data from 

each site. Average error of peak discharge simulation was about 36 percent. Techniques 

used in screening data for calibration as well as those used to optimize parameter 

values are discussed. A scheme developed to assess the relative accuracy of the 

frequency curves based on observed and simulated data indicated that the simulated dat2 

are equivalent to nine years of observed data in defining 2-year floods, and fifteen ; 

years in defining loo-year floods. Discharges corresponding to the best estimate of 

flows for selected recurrence intervals are tabulated for each modeled basin. 

17. Key Words and Document Analysis. 17a. Descriptors 

Peak discharge*, Small watersheds*, Model studies*, Surface runoff, Floods. 

7b. Identifiers/Open-Ended Terms 

Rainfall-runoff models, Model parameters, Flood peaks. 

17~. COSATI Field/Group 

18. Availability Statement 

No restriction on distribution 

l=ORM NTIS-SS ,RE”. 10-73, ENDORSED BY ANSI AND UNESCO. 

19. sReecputt)y Class (This 

UN20. Security Class (This 

Page 

UNCLASSIFIED 

THIS FORM MAY BE REPRODUCED 

21. ‘No. of Pages 

58 

22. Price 

USCOMM-DC ?22.5-P74 

t ;’ I 
APPLICATION OF THE U.S. GEOLOGICAL SURVEY 

RAINFALL-RUNOFF SIMULATION MODEL TO 

IMPROVE FLOOD-FREQUENCY ESTIMATES 

ON SMALL TENNESSEE STREAMS 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations 76-120 

Prepared in cooperation with 

Tennessee Department of Transportation 

Bureau of Planning and Programming 

and 

U.S. Department of Transportation 

Federal Highway Administration 
UNITED STATES DEPARTMZWI' OF THE INTERIOR 

Thomas S. Kleppe, Secretary 

GEOLOGICAL SURVEY 

V, E. IVIcKelvey, Director 

For additional information write to: 

U.S. Geological Survey 

Room A-413 U.S. Courthouse 

Nashville, Tennessee 37203 
CONTENTS 

Abstract. . , . , , , e o o l l e . . l a l l 

Introduction, ................ 

Use of metric units. ........... 

Data collection ............... 

Description of the model. .......... 

Model calibrations. ............. 

Selection of data for calibration. .... 

Calibration results, ........... 

Notable calibration techniques . . , . a . 

Separation of base flow ........ 

Non-linearity ............. 

Seasonal bias ............. 

Effective impervious area . , . , . , . 

Peak discharge simulations. ......... 

Simulation results ............ 

Weighting observed and simulated frequency 

curves .................. 

Evaluation of modeling. ........... 

Summary ......... . ......... 

Selected references ............. 

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Glossary. . . , . . , . . . . . . . . . . . . . . . 

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27 

30 

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52 

- III - 
ILLUSTRATIONS 

Page 

Figure l,-- Schematic outline of the model, showing 

components, parameters, and variables. . 7 

2 .--Map showing locations of modeled stations. 11 

3-12 .--Graphs showing: 

3. --Hydrograph for which base-flow separation 

can be made accurately , , . . . . . . . 25 

4 .--Hydrograph for which base-flow separation 

is complex and potentially inaccurate. . 26 

5. --Hydrograph typical of those on which model 

routing parameters should be based . . . 28 

6 .--Hydrograph typical of those that should 

not be used to determine model routing 

parameters . . . . . . . . . . . . . . . 29 

7 .--Results of volumetric optimization using 

both summer and winter storms. . . . . . 31 

P ,.--Results of volumetric optimization summer 

storm only. . . . . . . . . . . . . . . 32 

9 .--Results of volumetric optimization using 

winter storms only . . . . . . . . . . . 33 

10 .--Results of volumetric optimization using 

measured impervious area . . . . . . . . 34 

11 .--Results of volumetric optimization using 

reduced value for impervious area. . . . 35 

12 .--Frequency curves based on observed and 

simulated data . . -. . . . . . . . . . . 37 

- IV - 
TABLES 

Page 

Table 1 .--Stations used to calibrate the U.S. Geological Survey rainfall-runoff model. , . 12 

2 .--Summary of calibrated model parameters. . . 20 

3 .--Summary of simulated t-year discharges 

formodeledbasins.. ,,,....... 38 

4 .--Summary of observed, composite, and weighted 

t-year discharges for modeled basins. . . 46 

-v- 
APPLICATION OF THE U.S. GEOLOGICAL SURVEY 

RAINFALL-RUNOFF SIMULATION MODEL TO 

IMPROVE FLOOD-FREQUENCY ESTIMATES 

ON SMALL TENNESSEE STREAMS 

By Herman C. Wibben 

ABSTRACT 

The U.S. Geological Survey rainfall-runoff simulation 

model was used in conjunction with National Weather Service 

climatological data to improve flood-frequency estimates 

for 52 small drainage basins in Tennessee. The basins range 

in size from 0.17 to 64 square miles (0.44 to 166 square 

kilometers) and are distributed throughout the State, Model 

parameters were determined by calibration with observed data 

from each site. Average error in peak discharge simulation 

was about 36 percent. Techniques used in screening data for 

calibration as well as those used to optimize parameter 

values are discussed. A scheme developed to assess the relative accuracy of the frequency curves based on observed and 

simulated data indicated that the simulated data are equivalent to 9 years of observed data in defining 2-year floods 

and 15 years in defining loo-year floods. Discharges corresponding to the best estimate of flows for selected recurrence intervals are tabulated for each modeled basin. 

INTRODUCTION 

Proper design of drainage structures relies on sound 

evaluation of the magnitude and frequency of floods. In the past, data on which this evaluation was made, was collected 

only on the larger streams, Most of the flood data currently available on streams smaller than 50 mi2 (129.5 km2) 

have record lengths less than 20 years. 

The U.S. Geological Survey, in cooperation with the Tennessee Department of Transportation, began a study of 

flood-frequency characteristics of small rural watersheds in 

Tennessee during 1953. This project was the first major undertaking to eliminate the near void of small stream flood 

data. Crest-stage gages were initially installed at 87 sites 

-l- 
ra 

7 

ing in size from 0.034 mi2 (0.088 km2) to 201 mi2 (520 

km These gages provide a record of the annual peak stages. 

The ipproach used for analysis was to compute the annual peak 

discharges from stage-discharge ratings and subsequently to 

develop station flood frequency curves from these observed 

discharges. These curves can then be used in a regional 

analysis of flood-frequency characteristics. One drawback 

to this approach is the lag between the time data collection 

begins and the time at which events with a high recurrence 

interval can be reliably defined. 

During 1963, an awareness of the shorta e of small 

basin streamflow data was intensified by the f arge number of 

drainage structures being built under the interstate highway 

system. Since reliability of flood frequency characteristics 

derived from observed floods is dependent upon length of 

record, a lengthy data collection period would be necessary 

before data from new sites would produce reliable results 

using conventional techniques. This resultant time lag was 

greater than designers were willing to accept. Because of 

the urgency, the use of rainfall-runoff models was considered 

as a way to reduce the data collection period by extending 

the data base in time through the use of long-term climatological information. 

A second cooperative program was initiated by the 

Geological Survey and the Tennessee Department of Transportation in 1965 to expand the small streams data network, 

This program was designed to provide concurrent rainfall and 

discharge data as input to the Geological Survey rainfallrunoff model developed by Dawdy, Lichty, and Bergmann (1972). 

The purpose of this report is to present flood-frequency 

information on small streams in Tennessee resulting from application of the Geological Survey rainfall-runoff model. The 

feasibility of using the model to extend flood records in 

time is demonstrated, and general observations made during 

application of the model are documented for the benefit of 

future model users. Observed, simulated, and weighted discharges for selected recurrence intervals and calibrated 

model parameters are listed for each modeled basin. A discussion is included of techniques used to screen input data, 

to operate the model, and to assess the accuracy of the 

simulated data. Output from this study was combined with 

other streamflow data in a report prepared by Randolph and 

Gamble (1976) to define flood-frequency characteristics of 

Tennessee streams. 

-2- 
This report was prepared under the cooperative highway 

research program with the Tennessee Department of Transportation, Bureau of Planning and the U.S. Department of Transportation, Federal Highway Administration. The contents of this 

report reflect the views of the author. The Geological Survey is responsible for the facts and the accuracy of the data 

presented herein. The contents do not necessarily reflect 

the official views or policies of the Federal Highway Adminis-- 

tration. Insofar as the Federal Highway Administration is 

concerned, this report does not constitute a standard, 

specification, or regulation. 

Daily precipitation and evaporation data and 5-minute 

incremental storm rainfall data for historic periods were obtained from the National Oceanic and Atmospheric Administration at Asheville, North Carolina. Streamflow and rainfall 

data collected at fourteen gaging stations under a cooperative program with the Metropolitan Government of NashvilleDavidson County were included in the analysis. I 

R, W. Lichty, research hydrologist with the U.S. Geological Survey provided advice and assistance during the study. 

Use of Metric Units of Measurement 

The analysis and compilations in this report were made 

with English units of measurements. The equivalent metric 

units are given in the text and illustrations where appropriate. English units only are shown in tables where, because 

of space limitations, the dual system of English and metric 

units would not be practicable. To convert English units to 

metric units, the following conversion factors should be usedr 

Multiply English units kx To obtain metric units 

inches (in) 

feet (ft) 

25.4 millimeters (mm) 

meters (m) 

miles (mi) 0.305 

square miles (mi2) 

1.61 kilometers (km) 

feet per mile (ft$mi> 2.59 square kilometers (km2> 

0.189 meters per kilometer 

h/W cubic feet er 

second (ft 3 /s) 0.0283 cubic meters er 

second (m3/s P 

DATA COLLECTION 

Forty-nine gaging stations were established in clusters 

within the six physiographic provinces of the State. Sites 

were selected to represent the range of basin characteristics 

encountered in the field. The gages were to be operated for 

-3- 
up to 10 years to collect sufficient data to calibrate the 

model. Stage-rainfall (circular-chart graphic) -recorders 

were initially installed at 35 sites and analog digital recorders (paper-tape digital-punch) were installed at the 

other 14 sites. At most sites, the intakes were installed 

such that, only storm flows were recorded in order to obtain 

a more reliable record of stream stage by reducing maintenance problems. Stage and rainfall data were collected concurrently at these sites. 

The SR recorders proved to be less desirable than the 

ADR recorders even though they were considerably cheaper. 

Since both the stage pen and the rainfall pen of the SR recorders mark on the same chart to insure proper timing, all 

stations equipped with SR recorders had to have their stage 

wells and precipitation collectors mounted adjacent to each 

other, As a result of this constraint, compromises frequently had to be made in locating the stage well in order 

to provide adequate exposure for the rain gage. SR recorders 

were also less reliable than the ADR recorders. Although 

the'chart drives operated satisfactorily, various problems 

with the recording pens and the float wheels resulted in considerable lost record. In addition, conversion of the storm 

data to a machine readable form was expensive and tedious. 

SR recorders were gradually replaced with ADR recorders as 

time and funds permitted. 

At sites instrumented with ADR recorders more flexibility in locating the gages were permitted. The precipitation and stage recorders could be installed at separate locations when required. This distance was usually held to 100 

ft (30.5 m) or less to insure reliability of the recorders 

since they were both activated with the same timer. Reliability and accuracy of these installations was better than that 

of the SR installations, and the data were recorded in a 

machine readable form. All ADR recorders were operated at 

a punch frequency of five minutes. 

Most of the gages were placed in clusters such that 

increasingly larger segments of the basin were gaged, The 

decision to locate the sites in clusters has been a source 

of some controversy. One positive aspect of the cluster concept lies in providing a means to screen precipitation data 

for the model calibrations. 

in nature. 

Uniform rainfall rarely occurs 

Since the assumption that rainfall input is uniformly distributed throughout the basin is built into. the 

Geological Survey rainfall-runoff model, it is helpful to 

know how closely this assumption is being met. With the 

gages located within a mile or so of each other, storm rainfall could be checked for uniformity. Storm rainfall could 

also be transferred to a nearby gage when one of them failed 

to function and the other gages indicated uniform rainfall. 

Another consideration for clustering the gages was to provide 

-4- 
data for future stream-systems modeling. The clusters would 

allow for following a storm through a basin with discharge 

hydrographs available at each site to check theoretical 

routing techniques. The negative aspect of the cluster concept is the potential for extremely high inter-station correlation values since truly independent events are not being 

sampled by gaging increasingly larger segments of a basin. 

Daily rainfall data from the closest ADR station were 

normally used for gage sites equipped with SR recorders since 

the daily values were not available from the circular charts. 

Daily rainfall from the closest National Weather Service reporting gage was used when record from a nearby gage was not 

available. 

Daily pan evaporation data from the National Weather 

Service station at Center Hill Dam were used for all calibrations. This station was the only one that had been operated 

year-round for a long period of time. The record length of 

25 years was significant in that the data would later be used 

to generate harmonic average evaporation data for those 

periods during which actual data were not available. 

Long-term precipitation data used to simulate series 

of peak discharges were obtained from the National Weather 

Service. Rainfall stations and the periods for which data 

were used are listed below. 

National Weather Service Station Period 

Memphis, TN 18984971 

Nashville, TN 18984970 

Chattanooga, TN 1901-1971 

Knoxville, TN 18984971 

Criteria for selecting storm events from the rainfall stations were based on an analysis of daily rainfall. A maximum 

of five storms per water year having a 2 day sum equal to or 

greater than 1 inch and a 1 day maximum ranking in the top five 

for the year were selected as the events likely to have caused 

the annual peak discharge. Five minute incremental rainfall 

for those events at Memphis, Nashville, and Knoxville were 

digitized by the National Weather Service from original charts, 

Comparable data at Chattanooga were processed by personnel in 

the Georgia District of the Geological Survey. 

DESCRIPTION OF THE MODEL 

The U.S. Geological Survey rainfall-runoff model is a 

parametric simulation model based on bulk-parameter approximations to the physical laws governing infiltration, soil 

moisture accretion and depletion, and surface streamflow. It 

was developed by Dawdy, Lichty, and Bergmann (1972) for use 

-5- 
with point rainfall data and daily potential evapotranspiration data to predict flood volumes and peak rates of runoff 

for small drainage basins. 

The model deals with three components of the hydrologic 

cycle-antecedent moisture, infiltration, and surface flow 

routing. A schematic outline of the model is shown in figure 1. 

Brief descriptions of the model parameters are listed below. 

Parameter 

identifier 

code Units Application 

PSP--------------Inches-------------Represents the combined 

effects of soil moisture 

I contents and suction at 

the wetting front for soil 

moisture at field capacity. 

RGF---------------------------------Ratio of PSP for &oil moisture at wilting point to 

that at field capacity. 

KSAT --------Inches per hour---------The minimum saturated value of hydraulic conductivity used to determine 

infiltration soil rates. 

BlYSM-------------Inches -------------Soil moisture-storage 

volume at field capacity. 

EVC ---------------------------------Coefficient to convert pan 

evaporation to potential 

evapotranspiration values. 

DRN ---------Inches per hour--------- A constant drainage rate for 

redistribution of soil mcisture. 

RR ---------------------------------- Proportion of daily rainfall 

that infiltrates the soil. 

KSW ---------------Hours -------------Time characteristic for 

linear reservoir storage. 

TC ----------------Minutes -----------Time base of the triangular 

translation hydrograph. 

TP ----------------minutes -----------Time to peak of triangular 

translation hydrograph. 

-6- 
ANTECEDENT-MOISTURE INFILTRATION ROUTING 

ACCOUNTING COMPONENT COMPONENT COMPONENT 

Saturated-unsaturated Philip infiltration Modified Clark 

soil mositure regimes equation instantaneous unit 

hydrograph 

g= tl + P (m-m ) 

i 

oParameter Variable D 

Parmeter Variable ATl--A 

EVC 

Parameter 

BMS PSP BMS KSW 

RR SMS KSAT SMS TC 

BMSM RGF TP 

DRN 

INPUT DATA 

Daily rainfall Unit rainfall 

Daily pan evaportion BMS 

Initial condition SMS 

Rainfall excess 

OUTPUT DATA 

BMS 

SMS 

Rainfall excess Discharge 

Figure l.--Schematic outline of the model, showing components, 

parameters, and variables. 

The antecedent - moisture component is designed to determine the initial infiltration rate for a storm. The four 

parameters included within this component are EVC, RR, BlMSlK, 

and DRN. Input are daily rainfall and daily pan evaporation, 

and output is BMS (amount of base-moisture storage) and SW 

(infiltrated surface-moisture storage). BMS represents a 

uniform antecedent-moisture content of the active soil column, 

and its range of values should simulate the moisture range 

from wilting-point conditions to field capacity. SMS represents 

the moisture content of the surface layer that forms during 

-7- 
infiltration. Evaporation data is used as an index to seasonal variability of transpiration as well as evaporation, 

The infiltration component uses the Philip (1954) equation, which is believed to be a somewhat better approximation 

to the differential equation for saturated flow than the classical Horton (1940) exponential-decay-infiltration equation. 

Input are storm rainfall, BMS, and SMS, Parameters consist 

of PSP, RGF, and KSAT. This component determines the amount 

of storm rainfall that infiltrates the soil and produces rainfall excess as output. 

The third component, surface-runoff.routing, is based on 

a modification of the Clark (1945) form of the instantaneous 

unit hydrograph. Input is the rainfall excess computed in 

the infiltration component, and output is the storm-runoff 

hydrograph. Three parameters, KSW, TC, and TP, are utilized 

within this component. It consists of a two-step procedure. 

First, the precipitation excess is converted into a triangular translation hydrograph representing the effects of varying travel times in the basin. In the second step, successive flow rates of the translation hydrograph are attenuated 

by routing through linear storage using a storage constant 

of KSW. 

Output from one component is input to the next resulting 

in many interactions among the parameters. This interaction 

is particularly active in the antecedent-moisture-accounting 

and infiltration components, which constitute the loss functions of the model. Often adjustments of one parameter can 

be compensated for by adjustments in one or more other parameters. Over the same error range, many sets of parameter 

values may fit a given set of data equally well. Even 

though the model parameters are chosen so as to be analogous 

to the physical parameters in a basin, the degree of similarity in the optimum set of derived parameter values may mask 

the relation of the values to their supposed prototype. 

Thus, the conceptual physical equivalence of the model may be 

lost in the fitting process. 

Calibration of the model for a basin involves trial and 

error adjustment of parameter values in order to improve the 

comparison between observed input and simulated output, The 

comparison is made by testing for the minimum value of an objective function, which is based on the sum of the squared 

deviations of the logarithms of peak flows, direct runoff 

volumes, or some combination of both. Starting values of 

parameters must be computed or estimated, and maximum and 

minimum parameter limits must be set. The observed rainfall 

and evaporation data serve as input and are used to generate 

a streamflow sequence that is compared with the observed 

streamflow record. Three separate phases of the calibrations 

optimize on three different objective functions. During 

-8- 
phase one direct runoff volumes are used in the objective 

function, and parameters pertaining to the first two components of the model are varied, In phase two, the routing 

phase, peak flows are used in the objective function, and the 

hydrograph shape parameters are optimized. The peak flows 

are multiplied by the ratio of observed volumes to simulated 

volumes so that errors introduced by rainfall data and errors 

in the moisture-accounting and infiltration parameters are 

minimized. In phase three , peak flows are again used in the 

objective function while the parameters affecting the moistureaccounting and infiltration components are varied, 

The current version of the model has been adapted for use 

on urban basins. Percent impervious cover is input to the 

model. It uses a simplified approach in handling impervious 

area. The impervious area is assumed to be uniformly distributed throughout the basin and is assumed to be capable of 

storing 0.05 in (1.27 mm) of preci 

tion in excess of 0.05 in (1.27 mm P 

itation. All precipitais assumed to be direct 

runoff. Because the Survey model simulates only direct runoff, all other flow components are lumped together under the 

category of base flow. The term base flow is used rather 

loosely in this context, Two optional methods for separation of base flow from total runoff are available within the 

model for calibration use. The choice of options can be 

changed from storm to storm within a given calibration. 

The *'B" option requires estimation of a constant value 

of base flow for the duration of each hydrograph. Base flow 

is deducted from each discharge in order to estimate the 

volume of direct runoff and the magnitude of the peak discharge for each storm. This simple technique is adequate for 

base flow separation at most basins and requires little effort by the user prior to calibration since the direct runoff 

volume is computed within the model, 

The "A" option permits much more flexibility in separating 

base flow. An estimate of the direct runoff volume and the 

peak discharge are input to the model instead of base flow, 

Any reasonable method for estimating base flow is then permissible. The estimated base flow must be sketched on the hydrograph plot. Direct runoff can be determined by planimetering the area between the discharge hydrograph and the base 

flow line. Peak discharge is computed as the maximum ordinate 

between the curves. 

MODEL CALIBRATIONS 

All data used in the model calibrations were stored on a 

computer accessible magnetic disk to .facilitate retrieval of 

the massive quantities involved. Calibrations were made on the 

Geological Survey computer system. System memory requirements 

-9- 
for operation of the model vary with the quantity and 

definition frequency of the storm data. Individual calibrations required as much as 500,000 bytes of storage. 

Initial calibrations at all sites were made using the "B" 

version of the model. Selection of a starting and ending 

time for each storm event was required. In general, base 

flows selected were close to the average of the estimated 

base flow at the beginning and ending of the storm event. 

Departures from this average were based on hydrograph shape 

and ground-water recession slope. Starting times for the 

storms usually coincided with the beginning of storm rainfall. Ending times were normally based on a study of the recessions from select storm events to estimate how long direct 

runoff continued after rainfall ceased. 

Starting model parameters were estimated on the basis of 

geology, soil type and hydrograph shape. Constraints were 

imposed on the range within which parameters were allowed to 

vary during calibration in an attempt to hold the values 

close to their range of occurrence in the basins. During the 

first calibration phase, parameters affecting antecedent 

moisture accounting and infiltration were optimized to achieve 

the best simulation of the observed runoff volumes. The optimization routine was not extensively used for the second phase. 

In general, KSW was picked from hydrograph plots of select 

storms. TP/TC was fixed at 0.5 after scanning results of 

initial calibrations since most of these calibrations had 

optimized TP/TC close to that value, This assumption is sup 

ported by the Tennessee data as well as O'Kelly*s (1955) 

conclusions, from a study of drainage basins in Ireland, that 

the smoothing effect of storage on the translation hydrograph 

was so great that the latter could be replaced by an isosceles 

triangle without loss of accuracy. TC was hand fitted on the 

basis of the relative timing of the observed and simulated 

hydrbgraphs of select storms or optimized within a narrow 

range. Optimization of parameters during the third phase was 

used only on the final calibration. 

Selection of Data for Model Calibration 

Data from 38 of the project stations,and 14 of the Nashville urban stations were used with the U.S. Geological Survey 

rainfall-runoff model. These stations are listed in table 1, 

and the map in figure 2 shows their area1 distribution. 

Eleven of the project gages were not used for model calibration due to various problems including questionable stagedischarge ratings, inadequate data from storms of sufficient 

magnitude to reliably separate direct runoff from total flow, 

or gross deviations of the observed hydrographs from assumptions intrinsic to linear unit hydrograph theory. All hydrographs used were defined at 5-minute intervals. 

-lO- 
. 

N 

-11. 
Station 

Number 

Table 1 .--Stations used to calibrate the U.S. 

Drainage 

area 

Stream and Location (mi*) 

03313600 West Fork Drakes Creek tributary near Fountain 0.95 1.55 

Head, Tenn. 

03313620 

03418900 

03420360 

03420380 

03420400 

03427830 

03427840 

03430400 

03430600 

03430700 

03431000 

03431080 

03431120 

West Prong Caney Fork Creek near Oak Grove, Tenn. 

Raccoon Creek near Old Winesap, Tenn. 

Mud Creek tributary No. 2 near Summitville, Tenn. 

Mud Creek tributary near Summitville, Tenn. 

Mud Creek near Summitville, Tenn. 

Short Creek tributary near Christiana, Tenn. 

Short Creek near Christiana, Tenn. 

Mill Creek at Nolensville, Term." 

Mill Creek at Hobson Pike, near Antioch, Term.* 

Indian Creek at Pettus Road, at Nashville, Term.* 

Mill Creek near Antioch, Term.* 

Sims Branch at Elm Hill Pike, near Donelson, Term.* 

West Fork Browns Crzek at General Bates Drive, at 

Nashville, Tenn. 

3.03 3.12 

1.52 1.88 

2.28 2.46 

1.03 1.39 

7.30 4.05 

.17 0.56 

3.54 4.58 

12.0 4.34 

43.0 10.71 

3.86 2.51 

64.0- 17.0 

3.92 3.03 

3.30 3.35 

03431240 East Fork Browns Creek at Bairi Ward Printing 1.58 2.36 

03431340 

03431520 

03431580 

03431600 

Company at Nashville, Tenn. 

Browns Creek at Factory Street, at Nashville, Term." 

Claylick Creek at Lickton, Term." 

Ewing Creek at Knight Road, near Bordeaux, Term.* 

Whites Creek at Tucker Road, near Bordeaux, Term.* 

13.2 6.51 

4.13 3.01 

13.3 4.50 

'51.6 11.13 

B Continuous record 

m Flood hydrograph-rainfall record 

I-1 Crest-stage record 

* Data collected under cooperative program with Metropolitan Government of 

-12- 
Geological Survey rainfall-runoff model. 

Impervious Basin lag Period and type of record 

(ftymi) 

area time St 2 s 2 0 m Station 

(percent) (hrs) s s s s 

G z l-l t-l Number 

73.92 0 1.08 

52.80 0 1.23 

182.27 0 3.58 

35.38 0 2.24 

46.46 0 3.10 

30.62 0 5.15 

100.32 0 0.54 

73.92 0 1.54 

30.58 3.0 1.68 

16.11 3.0 4.16 

45.92 3.0 1.58 

11.40 4.2 5.39 

57.80 22.4 1.08 

77.05 22.3 0.92 

65.59 37.3 1.08 

42.60 31.5 1.92 

69.26 8.2 1.54 

46.70 14.2 2.00 

21.49 8.0 3.48 

c 

03313600 

03313620 

03418900 

03420360 

03420380 

03420400 

03427830 

03427840 

03430400 

03430600 

03430700 

03431000 

03431080 

03431120 

03431240 

03431340 

03431520 

03431580 

03431600 

Nashville-Davidson County. 

-13- 
Table 1 .--Stations used to calibrate the U.S. Geological 

Station 

Number Stream and Location 

Drainage 

area L 

hi21 bi 1 

03431630 Richland Creek at Lynnwood Blvd., at Belle Meade, 2.21 1.96 

03431650 Vaughns Gap Bra%ch at Percy Warner Blvd., at Belle 2.66 2.38 

Meade, Tenn. 

03431700 Richland Creek at Charlotte Avenue, at Nashville, 24.3 7.90 

03435020 

03435030 

03435600 

Term." J 

Red River near New Deal, Tenn. 

Red River near Portland, Tenn. 

Sulphur Fork Red River tributary near White House, 

9.32 4.00 

15.1 6.70 

3.50 3.52 

Tenn. 

03461200 Cosby Creek above Cosby, Tenn. 10.2 4.40 

03469110 Ramsey Creek near Pittman Center, Tenn. 2.18 3.05 

03486225 Powder Branch near Johnson City, Tenn. 4.88 3.87 ' 

03519610 Baker Creek tributary near Binfield, Tenn. 2.10 2.22 

03519630 Griffitts Branch near Greenback, Tenn. 1.46 1.19 

03519640 Baker Creek near Greenback, Tenn. 16.0 8.79 

03519650 Little Baker Creek near Greenback, Tenn. 3.65 4.07 

03535140 South Fork Beaver Creek at Harbison, Tenn. 1.23 1.72 

03535160 Beaver Creek near Halls Crossroads, Tenn. 14.1 6.78 

03535180 Willow Fork near Halls Crossroads, Tenn. 3.23 4.58 

03538900 Self Creek near Big Lick, Tenn. 3.80 3.67 

03539100 Byrd Creek near Crossville, Tenn. 1.10 1.66 

03541100 Bitter Creek near Camp Austin, Tenn. 5.53 4.05 

Term." 

m Continuous record 

m Flood hydrograph-rainfall record 

11 Crest-stage record 

* Data collected under cooperative program with Metropolitan Government of 

-14- 
Survey rainfall-runoff model.--Continued. 

Impervious Basin lag 

(ftymi) 

Period and type of record 

area time 5: z z 2 0 m Station 

(percent) (h-1 2 2 s 

m G : rl l-l l-i Number 

119.00 

83.26 14.9 0.65 

32.97 21.3 2.42 

46.46 

27.98 

51.74 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1.92 

3.11 

1.07 

484.85 

649.44 

124.83 

63.36 

100.32 

17.42 

29.57 

52.80 

15.84 

58.08 

45.41 

40.13 

190.08 

3.88 

6.55 

1.13 

1.65 

1.41 

6.71 

2.25 

1.54 

5.03 

3.08 

6.25 

3.12 

1.89 

11.7 1.33 

c 

03431630 

03431650 

03431700 

03435020 

03435030 

03435600 

03461200 

03469110 

03486225 

03519610 

03519630 

03519640 

03519650 

03535140 

03535160 

03535180 

03538900 

03539100 

03541100 

Nashville-Davidson County. 

-15- 
Table 1. --Stations used to calibrate the U.S. Geological 

Station 

Number Stream and Location 

Drainage 

area L 

2 hi 1 hi 1 

03541200 Forked Creek near Oakdale, Tenn. 2.44 

03597300 Wartrace Creek above Bell Buckle, Tenn. 4.99 

03597400 Wartrace Creek near Bell Buckle, Tenn. 9.59 

03597450 Kelly Creek tributary near Bell Buckle, Tenn. 0.73 

03597500 Wartrace Creek at Bell Buckle, Tenn. 16.3 

03597550 Muse Branch near Bell Buckle, Tenn. 1.86 

03604070 Coon Creek tributary near Hohenwald, Tenn. 0.51 

03604080 Hugh Hollow Branch near Hohenwald, Tenn. 1.52 

03604090 Coon Creek above Chop Hollow near Hohenwald, Tenn. 6.02 

03604100 Coon Creek near Hohenwald, Tenn. 10.1 

07028930 Turkey Creek at Medina, Tenn. 4.75 

07028935 Turkey Creek tributary near Medina, Tenn. 1.08 

07028940 Turkey Creek near Medina, Tenn. 7.87 

07028950 Turkey Creek near Fairview, Tenn. 13.3 

3.03 

4.20 

6.08 

1.70 

8.30 

4.02 

0.87 

2.16 

3.14 

5.23 

3.50 

1.80 

4.56 

6.78 

m Continuous record 

m Flood hydrograph-rainfall record 

.I] Crest-stage record -16- 
Survey rainfall-runoff model.--Continued. 

Tmpervious Basin lag Period and type'of record 

§ area time 5: 2 z 2 E m Station 

(ft/mi> (percent) (hrs) 2 2 2 2 2 & Number v-l 

237.60 0 2.58 

49.63 0 1.79 

31.68 0 2.42 

132.00 0 0.83 

25.71 0 3.33 

58.08 0 1.71 

200.48 0 1.76 

105.60 0 1.33 

73.92 0 1.50 

49.63 0 2.32 

34.32 0 1.70 

52.80 0 1.12 

26.93 0 2.10 

18.48 0 2.86 

I 03541200 1 

I 03597300 

03597400 

03‘5975~0 

03604070 

03604080 

03604090 

03604100 

07028930 

07028935 

07028940 

07028950 

-17- 
Records were initially scanned for completeness and for 

the magnitude of the stage peaks recorded, This information was 

listed and was later used to select storms for processing. 

General criteria for selecting storm events for model calibration involved several factors that, due to wide variat?ons in available data, were applied subjectively. A range 

of storm types and antecedent conditions was sought to be 

sure that data to which the different parameters were sensitive were included in the sample. A balance of data was desired that would represent short-duration, high-intensity 

storms and long-duration, low-intensity storms, dry and wet 

antecedent conditions, large and small peaks, as well as winter and summer storms. Another criterion in selecting storm 

events was that a reasonable separation of direct runoff from 

total flow could be made since the model calibrates only on 

direct runoff. Rainfall distribution over the basin was 

checked for uniformity, particularly on thunderstorm events 

which are usually very localized. Events having rainfall 

variations of more than 50 percent were eliminated. Deviations from the above criteria were permitted at some stations 

because of conflicts within the criteria, for example, the 

inability to separate base flow for extremely small storms at 

some stations precluded their use. 

Calibration Results 

Final values of the model parameters for the modeled 

basins are shown in table 2. Average error of simulated 

peak discharges was 36 percent, and no bias was evident from 

the results of the final calibrations. Accuracy of simulated 

peaks was better for larger peaks than for smaller peaks. 

This trend is assumed to be the result of an effectively simpler model simulating the larger peaks. Saturated soil conditions exist during most of the large storm events. Under 

these conditions, most of the parameters within the antecedentmoisture-accounting component and several of those within the 

infiltration component have a negligible effect upon losses. 

These parameters are effectively ignored within the model, and 

any error introduced by them would be negligible, These very 

parameters are the ones that should have major impact in simulating the smaller events, particularly with dry antecedent 

conditions. Calibration results from basins larger than about 

15 mi2 (38.8 km2) were noticeably poorer than those from 

smaller basins. The sources of the increased error were in 

simulation of precipitation excess, and its cause apparently 

lies in the rainfall variation over these larger basins. 

As previously mentioned, parameters affecting the loss 

components of the model were constrained during initial 

-18- 
calibration with the range of reasonable occurence in the 

field. With only few exceptions, final parameter values are 

within those limits. The constraints were applied to prevent 

unreasonable parameter distortion from parameter interaction. 

Although several of the parameters resulted in variations consistent with their physical occurrence, it seems improbable 

that parameter values for ungaged basins can be predicted 

with accuracy. KSAT is a good example of the effects of pap 

ameter interaction. Basins having thin, tight soils generally 

produced smaller values of KSAT than did basins having thicker 

more permeable soils, This trend was consistent with expectations. Variation in KSAT between adjacent basins, however, 

was frequently over 100 percent, even though physical characteristics of the basins appear to be similar. 

Because hydrograph shape parameters were either computed 

from selected hydrographs or severely constrained during 

optimization, very little of the parameter interaction so 

prevalent in the loss parameters was present in the routing 

parameters. Phase 2 error values were generally in the range 

of 15 to 20 percent, with some as low as 10 percent. With 

KSW and TC determined as mentioned previously and TP/TC 

assumed equal to 0.5, basin lag time can be computed from 

these parameters. A rigorous analysis of the model routing, 

O'Kelly (19551, shows that the time from the centroid of 

precipitation excess to the centroid of direct runoff is 

equal to one-half the base of the isosceles triangle translation hydrograph plus the linear storage constant. In terms 

of the model parameters, this relation reduces to 

TL = KSW + l/2 TC, 

where TL is basin lag time in hours. Units of both KSW and 

TC are in hours. Lag times for the calibrated basins are 

included in table 1. 

-19- 
Table 2. .Smry of calibrated 

Station PSP" KSAT* DRN* RGF* BMSti EVC* 

number (in.) (in./hr) (in.) 

RR* 

03313600 

03313620 

03418900 

03420360 

03420380 

03420400 

03427830 

03427840 

03430400 

03430600 

03430700 

03431000 

03431080 

03431120 

03431240 

03431340 

03431520 

03431580 

03431600 

03431630 

03431650 

03431700 

03435020 

03435030 

03435600 

03461200 

03469110 

03486225 

03519610 

03519630 

03519640 

03519650 

03535140 

03535160 

03535180 

03538900 

03539100 

03541100 

035412OQ 

3.210 0.085 0.551 18.300 5.100 0.945 0.868 

8.710 0.109 0.123 14.900 1.490 0.839 0.922 

3.070 0.103 0.367 10.200 2.350 0.621 0.980 

5.060 0.081 0.338 13.500 6.860 0.829 0.880 

1.560 0.034 0.338 15.100 5.060 0.960 0.979 

2.610 0.058 0.339 10.300 1.930 0.850 0.990 

5.770 0.072 0.412 19.900 3.110 0.801 0.810 

1.450 0.034 0.250 12.000 0.917 0.850 0.900 

1.260 0.029 0.124 14.900 3.980 0.829 0.911 

2.520 0.061 0.260 10.000 1.580 0.590 0.910 

2.230 0.087 0.462 4.720 2.520 0.811 0.899 

1.260 0.078 0.400 6.900 3.460 0.900 0.900 

5.850 0.112 0.131 15.500 1.580 0.791 0.980 

2.020 0.087 0.634 6.990 1.050 0.845 0.759 

7.990 0.123 0.152 24.700 7.880 0.829 0.979 

8.940 0.082 0.526 15.300 8.990 0.829 0.980 

5.820 0.077 0.532 12.300 6.580 0.747 0.911 

1.940 0.043 0.437 8.390 2.660 0.829 0.870 

3.250 0.062 0.242 4.400 4.730 0.622 0.203 

2.520 0.075 0.913 20.800 5.000 0.822 0.928 

7.770 0.128 0.123 9.740 3.460 0.720 0.980 

2.690 0.090 ci.345 19.900 3.940 0.845 0.878 

3.030 0.073 0.566 15.600 3.080 0.850 0.900 

2.990 0.085 0.430 9.320 1.500 0.850 0.900 

6.710 0.094 0.823 17.600 4.760 0.890 0.983 

2.880 0.080 0.222 26.800 1.120 0.980 0.888 

3.750 0.095 0.968 10.400 1.800 0.760 0.979 

6.900 0.168 0.490 27.200 6.150 0.727 0.880 

7.880 0.137 0.367 13.700 3.070 0.990 0.894 

7.100 0.232 0.488 7.310 3.120 0.924 0.900 

7.220 0.164 0.385 4.270 2.680 0.824 0.830 

4.060 0.092 0.325 4.670 3.610 1.040 0.830 

6.440 0.119 0.490 10.300 1.420 0.924 0.810 

4.260 0.076 0.462 lo.-600 5.740 0.968 0.948 

3.460 0.057 0.152 13.200 3.180 0.750 0.994 

5.120 0.080 0.496 10.100 6.410 0.966 0.966 

2.830 0.086 0.607 8.680 6.150 0.941 0.903 

5.000 0.163 0.259 12.800 5.520 0.830 0.911 

4.010 0.100 0.488 8.940 2.850 0.770 0.974 

5.360 0.122 0.336 7.770 3.600 0.770 0.938 

*See p. 6 for definitions of parameters 

-2o- 
model parameters 

Effective 

KS? * 

(hrs) (5,) 

TP/TC? impervious Remarks Station 

area (percent) number 

0.670 50 

0.400 100 

2.000 190 

1.200 125 

1.600 180 

2.860 275 

0.250 35 

0.500 125 

0.640 125 

1.860 275 

0.830 90 

2.710 323 

0.420 80 

0.300 75 

0.830 30 

0.830 130 

0.750 95 

0.750 150 

1.150 280 

0.750 70 

0.310 40 

0.833 190 

0.750 140 

1.400 205 

0.650 50 

2.300 190 

5.300 150 

0.550 70 

0.900 90 

0.830 70 

4.670 245 

4.670 245 

1.500 90 

1.000 65 

3,200 220 

1.750 160 

4.170 250 

1.570 186 

1.170 87 

1,.500 130 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

i:; 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

5” 

0 

10 

5 

0 

5 

0 

5 

2 

5 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

-21- 

Summer storms 

Winter storms 

03313600 

eO3313620 

03418900 

03420360 

03420380 

03420400 

03427830 

03427840 

03430400 

03430600 

03430700 

03431QOO 

03431080 

03431120 

03431240 

03431340 

03431520 

03431580 

03431600 

03431630 

03431650 

03431700 

03435020 

03435030 

03435600 

03461200 

03469110 

03486225 

03519610 

03519630 

03519640 

03519650 

03535140 

03535160 

03535180 

03538900 

03539100 

03541100 

03541200 
Table 2. Summary of calibrated model 

Station PsP* KSAT* DRI@ RGFk BMSfi EVc* RR* 

number (in. 1 (in./hr) (in.) 

03597300 

03597400 

03597450 

03597500 

03597550 

03604070 

0360408Q 

03604090 

03604100 

07028930 

07028935 

07028940 

07028950 

*See p. 6 for definitions of parameters. 

2.510 0.092 0.990 11.100 3.170 0.980 0.608 

1.430 0.052 0.506 9.090 2.520 0.945 0.900 

1.940 0.029 0.419 8.630 2.580 0.850 0.900 

5.670 0.180 0.320 11.700 1.420 0.924 0.608 

2.020 0.091 0.320 16.200 4.200 0.850 0.900 

2.900 0.027 0.320 6.640 2.490 0.850 0.900 

4.260 0.104 0.228 14.200 1.970 0.860 0.966 

2.960 0.030 0.698 10.000 1.700 0.828 0.920 

7.350 0.145 0.779 23.800 3.820 0.946 0.945 

6.490 0.138 0.077 25.600 5.930 0.840 0.858 

9.560 0.243 0.365 34.200 8.050 0.964 0.850 

6.910 0.170 0.308 20.700 5.360 0.461 0.850 

8.150 0.151 0.755 18.000 5.760 1.000 0.576 

8.030 0.048 0.409 19.000 4.860 0.850 0.792 

2.110 0.061 0.958 17.900 5.360 0.905 0.900 

1.580 0.030 0.338 29.300 6.520 0.850 0.900 

1.640 0.033 0.175 20.300 4.720 0.821 0.900 

1.840 0.043 0.230 6.350 2.290 1.020 0.810 

-22- 
parameters. --Continued. 

Effective 

KS@ 

(hrs) (2:) 

TP/TC* impervious Remarks Station 

area (percent) number 

0.920 90 0.5 0 

0.920 120 0.5 0 

0.920 180 0.5 0 

0.500 40 0.5 0 

0.500 40 0.5 0 

1.250 250 0.5 0 

1.000 85 0.5 0 

1.000 85 0.5 0 

1.100 80 0.5 ‘0 

0.920 50 0.5 0 

0.670 100 0.5 0 

0.670 100 0.5 0 

1.100 120 0.5 0 

1.030 185 0.5 0 

0.750 115 0.5 0 

0.420 85 0.5 0 

0.980 135 0.5 0 

1.200 200 0.5 0 

Summer storms 

Winter storms 

Summer storms 

Winter storms 

Summer storms 

Winter storms 

Summer storms 

Winter storms 

Summer storms 

Winter storms 

03597300 

03597400 

03597450 

03597500 

03597550 

03604070 

03604080 

03604090 

03604100 

07028930 

07028935 

07028940 

07028950 

-23- 
Notable Calibration Techniques 

Most of the basins calibrated involved a straightforward 

application of the model. Data adequately fit within limits 

of model assumptions, and general calibration guidelines, as 

previously discussed, were sufficient to optimize the parameters. Situations arose, however, for which special techniques had to be established. Some of these situations involved judgment in interpreting the data so that model assumptions were not grossly violated. Others appear to be due to 

overstressing the model in handling particular circumstances. 

The following discussion points out the notable structures 

and deqcribes how they were dealt with. 

Separation of Base Flow 

For most basins modeled, flow decreased rapidly after 

peaking and returned to a flow rate quite small in relation 

to the peak. Separating direct runoff from total runoff was 

fairly simple for this type of hydrograph. Figure 3 is a 

hydrograph from station 07028930 and is a good example of this 

type of response.. Unsophisticated techniques for separating 

base flow produced acceptable estimates of direct runoff. 

This was mainly due to the base flow comprising a small part 

of the total flow, Errors in base flow estimates caused only 

minor errors in direct runoff estimates. 

Figure 4, however , presents a hydrograph typical of those 

that require careful judgment for base flow separation, This 

hydrograph, from station 03541100, is one for which base flow 

separation is complex and potentially inaccurate. Flow components are indistinct and difficult to separate. The flow 

rate is high in relation to the peak flow long after the time 

direct runoff should have ceased. Direct runoff comprises a 

relatively small portion of total storm runoff, creating a 

situation in which appreciable errors in base flow estimates 

would cause appreciable errors in estimates of direct runoff. 

Therefore, when working with hydrographs of this type, some 

judgment must be made as to whether direct runoff can be 

reasonably estimated. 

this respect. 

Each hydrograph must be evaluated in 

Those for which direct runoff estimates cannot 

reasonably be made cannot be used for calibration. 

Most hydrographs that had to be eliminated from the study 

because of problems with base flow separation were from small 

-24- 
STATION NUMBER: 07028930 - 

STORM DATE: JUNE 11, 1973 

1.1 

15 16 17 18 19 20 21 22 23 24 i 

TIME, IN HOURS 

Figure 3. --Hydrograph for which base-flow 

separation can be made accurately. 

-25. 
STATION NUMBER 03541100 - 

STORM DATE: MARCH 21, 1974 

I I I .I I I I I I 

12 3 4 5 6 7 8 9 10 

TIME, IN HOURS 

11 

Figure 4. --Hydrograph for which base-flow 

separation is complex and 

potentially inaccurate. 

-26. 
storms in which secondary flow components dominate total 

flow, Hydrographs displaying this dominating secondary flow 

component appeared most frequently from stations in the 

eastern one-third of Tennessee. Impact upon model results 

due to systematic elimination of storms has not been evaluated, however, it seems reasonable to expect poorer results 

in simulation of the smaller events. The "A" option of the 

model was used extensively for base flow separation on the 

marginally usable hydrographs. 

Non-Linearity 

A second situation for which special calibration techniques had to be devised was one of apparent non-linearity 

of hydrographs from a number of East Tennessee basins. The 

adjective "apparent" is purposely used to describe this 

situation because it was most prevalent at basins that exhibited the dominating secondary flow components mentioned in 

the preceding section. It is possible that true basin lag 

time is partially masked on small storms from these basins 

and that actual non-linearity does not exist. However, based 

on the best estimate of the direct runoff hydrographs, variable hydrograph time and shape characteristics were indicated, 

and as such the basins do not fit with the definition of linearity as summarized by Dooge (1973). Unit hydrograph theory 

assumes a linear system in which basin lag time should be independent of both the intensity and duration of rainfall. 

The hydrographs in figure 5 and figure 6 are typical of 

the variation encountered. The larger, higher-intensity 

storms tend to produce more consistent and steeper hydrograph recession slopes and shorter lag times than do the 

smaller, lower-intensity storms. 

scheme, however, 

The Survey model routing 

utilizes unit hydrograph theory which assumes 

basin response time to be a constant, Therefore, judgment 

must be made on each station as to the extent of deviation 

of the hydrographs from linearity. If the deviation is minor, 

model routing parameters can be determined from typical hydrographs or optimized by the model. If the deviation is 

considerable, only two choices can be made. One choice would 

be to eliminate the station from the analysis. The other 

would be to pick routing parameters from larger storms in 

cases where these storms indicate more consistent lag times. 

This second choice was generally used in handling the problem 

stations during the study. The storms used for selecting the 

model routing parameters typically had rainfall of short duration, with respect to basin lag time, that ended abruptly, 

and had peak flows within the range of the annual peaks. The resultant routing parameters should produce more representative annual peaks than if the smaller storms had been given 

-27- 
2 0.20- 

6 

g 0.40- 

Z 0.60- 

. 

: 0.80- 

“z 

a l.OOw 

1.20- 

Y, 

0, 0 25 

t; 

s 

5 

STATION NUMBER: 03486225 ’ --lo 2 

STORM DATE: APRIL 26, 1973 z 

m 

,-20 2 

“z 

2 

--30 

1000- 

4 

E 

w v) 

at 

2 looii 

w y. 

ii 

J 

1 .o, I I I I I I I I I 

15 16 17 18 19 20 21 22 23 24 25 

TIME., IN HOURS 

Figure 5. --Hydrograph typical of those on which 

model routing parameters should be determined. 
v) 

u.l 

5 

0 

z 0.20 

z 0.40 m 

i 

a 

2 

3 

1000 

100 

10 

1.0 / I I I I I I I I I I 

23456789 10 11 12 

TIME, IN HOURS 

STATION NUMBER: 03486225 

STORM DATE: DEC. 15, 1972 

- 

Figure 6. --Hydrograph typical of those that should 

not be used to determine model routing parameters. 
weight. This technique for determining routing parameters 

would have a tendency to sacrifice simulation accuracy of 

the smaller storms in order to better reproduce the larger 

ones. 

Potentially the most serious problem in modeling basins 

that deviate from linearity, is not having sufficient data to 

define the basin response of the larger storms. If the data 

were collected in a short period or during an unusually dry 

period such that few, if any, large storms are available for 

analysis, resultant routing parameters could be grossly over 

estimated. The peak discharge from most of the large storms 

would then be underestimated during simulation. 

Seasonal Bias 

A tendency for seasonal bias was indicated in simulating 

direct runoff volumes for some of the basins. It was relatively insignificant on most basins, however it was extensive 

on six of them. Calibrations for several of the six problem 

basins produced phase one errors in excess of 50 percent. 

The majority of the direct runoff volumes of events occurring 

from about mid-April through October were overestimated, and 

most of those during the rest of the year were underestimated. 

The basins for which seasonal bias resulted varied considerably in physical characteristics. Forest cover ranged 

from 3.7 to 95.9 percent and main channel slope ranged from 

17.4 to 132 ft/mi (3.28 to 2Lc.g m/km). Soil cover ranged 

from a thin layer of tight clay overlying limestone to a 

thicker, more permeable clay overlying deep overburden. Consequenty, it was not possible to generalize the type of basin 

from which seasonal bias could be expected and restructure the 

model to minimize this bias. 

As an example of this bias, phase one results from station 03597300, are presented in figure 7. 

was 43 percent. 

The fitting error 

Eight of the summer-storm direct runoff volumes were overestimated and one was underestimated. The direct runoff volumes of fourteen winter storms were underestimated and three were overestimated, Figures 8 and 9 are the 

phase one results from separate calibrations of the summer and 

winter storms respectively, with events occurring between 

April 15 and October 31 being designated summer storms and 

those occurring between November 1 and April 14 being designated winter storms. Phase one fitting error was 27.5 and 

19.9 percent for the summer and winter calibrations respectivelY* Bias within each storm group was eliminated, and the resultant parameters should produce more reliable simulated 

runoff within their respective periods of the year. 

-3o- 
SIMULATED RUNOFF, 

IN MILLIMETERS 

Station 03597300 

OWinter Storms 

‘A Summer Storms 

0.1 

SIMULATED 

I.0 

RUNOFF, IN 

IO 

INCHES 

Figure 7. --Results of volumetric optimization 

using both summer and winter storms. 

The net effect of differences between the sets of parameters from the six stations having significant seasonal bias 

was that the loss functions of the model were increased significantly by the summer parameters as compared with the 

winter parameters. KSAT was the parameter that consistently 

changed the most. The ratio of summer KSAT to winter KSAT 

ranged from 1.43 to 3.47 for these stations. Whether a seasonal variation of KSAT of this magnitude is realistic or not 

is difficult to assess. Other factors, such as extremes in 

antecedent moisture and vegetal cover, undoubtedly have an 

impact upon summer storm losses being greater than those for 

winter storms. In addition, summer rainfall is normally the 

result of thunderstorm activity and as such is generally of 

-3l- 
SIMULATED RUNOFF, 

IN MILLIMETERS 

1.0 IO 100 I I I I 

Station 03597300 

0 Winter Storms 

A Summer Storms 

- 

-100 

0.01 0.1 I.0 IO 

SIMULATED RUNOFF, IN INCHES 

. Figure 8. --Results of volumetric optimization 

using summer storms only. 

short duration and high intensity. Winter rainfall, however, 

is most frequently of longer duration and lower intensity-as 

the result of major frontal storms. The impact of these variations may be masked within and show up as a factor affecting 

KSAT. 

Effective Impervious Area 

Studies of other urban areas have indicated that not all 

the man-made impervious cover was effective in producing additional runoff. Essentially the same situation was indicated 

by data in the vicinity of Nashville. For all the urban basins calibrated, small storm direct runoff volumes were grossly 

-32- 
SIMULATED RUNOFF, 

IN MILLIMETERS 

I 

Station 03597300 

OWinter Storms 

A Summer Storms 

0.01 0.1 1.0 IO 

SIMULATED RUNOFF, IN INCHES 

Figure 9.-- Results of volumetric optimization 

using winter storms only. 

overestimated when the measured percent of impervious area 

was given as input to the model. The phase one results from 

station 03431086 shown in figure 10 are typical. 

In attempting to achieve a better fit of the smaller 

storm runoff volumes, the larger storm runoff volumes were 

frequently underestimated. In addition to this bias, several 

model parameters, mainly PSP, EAT, and RGF, were forced outside a reasonable range of occurrence during optimization. 

The net effect of the unusual parameter values was to drastically reduce runoff from the pervious areas to compensate for 

the increased runoff from the impervious areas. 

Data from the Nashville area do not support runoff volumes 

-33- 
SIMULATED RUNOFF, 

,IN MILLIMETERS 

1.0 IO 100 

USED MEASURED IMPERVIOUS 

PSP= 7.727 PSP= 7.727 

RGF = 28.05 RGF = 28.05 RR 100 

KSAT= 0.301 BMSM = 1.148 

DRN = 0.22 1 EVC=0.951 

Station 03431080 

0.01 0.1 1.0 IO 

SIMULATED RUNOFF, IN INCHES 

Figure 10. --Results of volumetric optimization 

using measured impervious area. 

as large as those produced by the model. It seemed evident 

that either the impervious surfaces were storing more than 

0.05 in (1.27 mm) of precipitation or portions of the flow 

from the impervious surfaces were subsequently infiltrated 

while being routed over pervious areas enroute to the stream 

channels. 

Selection of final parameters was based on the assumption 

that only part of the impervious area was effective in increasing runoff. This approach was similar to that used by 

Durbin (1974) in his study of the Upper Santa Ana Valley in 

California. During subsequent calibrations, the percent impervious area was successively reduced until small runoff 
events were satisfactorily reproduced. As a result of applying this technique, basins having less than 5 percent manmade impervious area were calibrated with no effective impervious area, The average effective impervious area of the 

other urban basins was 22 percent of the measured impervious 

area. The values of effective impervious area for individual 

basins were fairly close to those given by Durbin's curve 

relating the effective impervious area in drainage basins to 

the area affected by urban development. Figure 11 shows the 

phase 1 results from station 03431080 using a reduced value 

of impervious area. 

SIMULATED RUNOFF, 

IN MILLIMETERS 

I.,0 IO 100 I I 

I I I 

USED EFFECTIVE IMPERVIOUS AREA = 5 PER CEN’ 

KSP = 5.854 RGF = 15.49 RR =0.980 

KSAT= 0.112 BMSM = 1.578 

DRN=0.131 EVC=0.79 1 / 

. Station 03431080 

/ 

0 

0.1 I.0 IO 

SIMULATED RUNOFF, IN INCHES 

Figure 11. --Results of volumetric optimization 

using reduced value of impervious area. 

-35 
PEAK DISCHARGE SIMULATIONS 

Model parameters, drainage area, and percent of effective 

impervious area of each calibrated basin along with the Center 

Hill Dam pan evaporation data were used successively with 

each of the long-term precipitation stations to develop four 

series of peak discharges for each basin. The highest simulated peak for each water year was used to compute four logPearson type III discharge-frequency curves for each of the 

calibrated gage sites. 

Annual peak discharge determination was handled a little 

differently at stations for which seasonal calibrations were 

made. Two series of peak discharges were simulated; one 

using summer parameters and one using winter parameters. For 

each water year the highest discharge from the winter and summer periods was chosen as the annual peak. 

Simulation Results 

The simulated frequency curves produced estimates of tyear discharges for individual stations that varied with the 

long-term rainfall data used. A t-year discharge is that discharge corresponding to a specific recurrence interval. Because of the variation, a techniquje was needed to form a composite curve from the four simulated curves. Table 3 presents 

the simulated discharges from the four long-term rainfall 

records for the Z-, 5-, lo-, 25-, 50-, and loo-year recurrence 

intervals for each model basin. Figure 12 shows the simulated 

curves for station 03597500 along with the frequency curve 

based on 22 years of observed annual peaks. 

The simulated data were analyzed by two methods to determine relative trends. The first method tested the four series 

of annual peaks in pairs for identical distributions via the 

Cramer-von-Mises-Two-Sample test as described by Conover 

097% Test results indicated that Memphis, Nashville, and 

Chatanooga rainfall data would produce simulated flood series 

from the same distribution but that Knoxville data would not. 

The second analysis was essentially an overview of the 

four sets of frequency curves and indicated that identical 

distributions as determined from the above test do not necessarily produce comparable discharge-frequency curves. In 

general, Memphis and Knoxville data produced comparable 100- 

year flood estimates. Nashville and Chattanooga data also 

produced comparable loo-year flood estimates, however, they 

were usually lower than those based on Memphis and Knoxville 

data. At the 2-year flood level, Memphis data consistently 

produced the highest values, and Knoxville data produced the 

-36- 
100.000 - I I I I IllI I I I I 

STATION 03597500 

9 9 52 0 s 

52 

0 

---@--Observed discharge data 

v 

z --&--Memphis precipitation data 

1000 z 

~Nashviile precipitation data 

ce LY w 2 2 p. 

---@-Chattanooga precipitation data v) 

z UJ ---El-Q- Knoxville precipitation data z 

u, lv 2 

ij 10.000 v 

U z 

E 5 

., 

z 

z 

. 

2 G 

5 100 2 

m 

zz : 

5 

1000 I I I IIIII I I I I 

2 3 a 5 6 78910 20 30 40 50 100 

RECURRENCE INTERVAL. IN YEARS 

Figure 12. --Frequency curves based on observed and 

simulated data. 

lowest ones. Nashville and Chattanooga data resulted in cornparable 2-year flood estimates within the discharge range established by Memphis and Knoxville data. 

The average spread between highest and lowest values 

among the sets of loo-year discharge estimates was 28 percent 

of the lowest values. The maximum was 64 percent, and the 

minimum was 7 percent. At the 2-year recurrence interval, 

average difference in extremes was 79 percent. Elimination 

of the t-year estimate based on the most distant rainfall 

record reduced the scatter considerably, Average spread of 

extremes decreased to 19 percent for the loo-year values and 

decreased to 47 percent for the 2-year values. 

As a result of the above comparisons, a method for developing composite curves was selected that utilized frequency 

-37- 
Table 3 .--Summary of simulated flood frequency values for modeled basins. 

Drainage Long-term Simulation results 

Station area 

tmi*> 

rainfall Q50 Qloo Skew 

number station (Z3/s, $t3/s) $ot3,s) (1iZ3,,) (ft3ls) (ft3/s) coefficient 

03313600 0.95 

03313620 3.03 

03418900 1.52 

03420360 2.28 

03420380 1.03 

03420400 7.30 

03427830 0.17 

03427840 3.54 

03430400 12.0 

03430600 43.0 

03430700 

03431000 

3.86 

64.0 

Memphis 260 416 528 677 792 912 -0.127 

Nashville 213 371 477 606 697 784 -0.603 

Chattanooga 256 401 493 604 682 755 -0.499 

Knoxville 148 286 404 583 739 914 -0.001 

Memphis 480 884 1200 1640 1990 2370 -0.218 

Nashville 356 692 936 1250 1480 1700 -0.599 

Chattanooga 458 822 1090 1440 1710 1990 -0.366 

Knoxville 259 520 760 1150 1510 1930 -0.165 

Memphis 237 357 442 552 638 725 -0.053 

Nashville 212 328 394 464 508 545 -0.871 

Chattanooga 203 306 384 496 589 691 0.339 

Knoxville 160 267 353 478 585 703 0.191 

Memphis 389 631 804 1030 1200 1380 -0.212 

Nashville 302 530 685 878 1020 1150 -0.556 

Chattanooga 371 578 713 876 991 1100 -0.451 

Knoxville 221 422 594 856 1090 1350 0.045 

Memphis 252 354 426 522 598 677 0.221 

Nashville 229 327 387 459 508 555 -0.412 

Chattanooga 229 315 375 452 512 574 0.151 

Knoxville 184 278 352 459 549 648 0.401 

Memphis 1060 1540 1870 2300 2630 2970 0.029 

Nashville 932 1380 1630 1910 2090 2250 -0.733 

Chattanooga 894 1280 1560 1950 2260 2590 0.282 

Knoxville 752 1150 1460 1890 2250 2630 0.243 

Memphis 68 115 148 192 226 259 -0.311 

Nashville 54 101 132 170 196 221 -0.694 

Chattanooga 66 109 138 173 199 223 -0.486 

Knoxville 36 71 101 145 183 226 -0.064 

Memphis 1510 2050 2440 2970 3400 3860 0.449 

Nashville 1370 1970 2350 2800 3120 3420 -0.374 

Chattanooga 1390 1940 2330 2850 3260 3690 0.251 

Knoxville 1170 1800 2260 2900 3420 3970 0.121 

Memphis 4890 6680 7930 9600 10900 12300 0.274 

Nashville 4500 6390 7590 9040 10100 11100 -0.289 

Chattanooga 4530 6290 7550 9260 10600 12000 0.322 

Knoxville 3830 5800 7270 9300 11000 12700 0.195 

Memphis 7950 11400 13800 16900 19400 21600 0.074 

Nashville 7060 10300 12200 14300 15700 16900 -0.682 

Chattanooga 6640 9470 11600 14600 17200 19900 0.479 

Knoxville 5660 8660 11000 14500 17500 20900 0.446 

Memphis 1360 1910 2290 2780 3170 3560 0.106 

Nashville 1220 1840 2220 2680 3000 3290 -0.478 

Chattanooga 1240 1800 2210 2760 3200 3670 0.222 

Knoxville 1000 1620 2100 2760 3300 3880 0.058 

Memphis 10500 14900 18000 22200 25500 28900 0.147 

Nashville 9310 13400 15900 18800 20800 22700 -0.475 

Chattanooga 8860 12500 15100 18600 21300 24100 0.203 

Knoxville 7560 11200 14100 18100 21400 25000 0.361 

-38- 
Table 3 .--Summary of simulated flood frequency values for modeled basins.--Continued 

Drainage Long-term Simulation results 

Station area rainfall 

number hi21 

Q5 Q5 

(ft /s) (ft3/s) (ft Q14 1s) 

425 Q50 

station Qloq Skew 

(ft3/s) (ft3/s) (ft /s)coefficient 

03431080 

03431120 

03431240 

03431340 

03431520 

03431580 

03431600 

03431630 

03431650 

03431700 

03435020 

03435030 

3.92 

3.30 

1.58 

13.2 

4.13 

13.3 

51.6 

2.21 

2.66 

24.3 

9.32 

15.1 

Memphis 958 1550 1990 

Nashville 766 1330 1710 

Chattanooga 935 1500 1880 

Knoxville 566 1040 1450 

2570 3040 

2180 2520 

2360 2710 

2100 2690 

3410 3910 

3410 3870 

3360 3830 

3410 4040 

3520 -0.104 

2840 -0.540 

3060 -0.355 

3380 0.248 

Memphis 1600 2290 2780 

Nashville 1420 2220 2750 

Chattanooga 1550 2260 2750 

Knoxville 1210 2010 2610 

4420 0.099 

4330 -0.411 

4300 -0.095 

4690 -0.162 

Memphis 307 508 659 868 1030 1210 -0.058 

Nashville 232 408 550 738 934 1130 0.048 

Chattanooga 294 500 659 885 1070 1270 -0.012 

Knoxville 175 311 430 619 792 995 0.385 

Memphis 2060 3500 4580 6030 7180 8380 -0.179 

Nashville 1560 2900 3950 5430 6620 7880 -0.223 

Chattanooga 1970 3290 4250 5550 6570 7610 -0.187 

Knoxville 1150 2200 3130 4580 5880 7390 0.149 

Memphis 954 1530 1920 2410 2770 3120 -0.377 

Nashville 771 1370 1790 2330 2720 3110 -0.495 

Chattanooga 915 1450 1830 2310 2680 3050 -0.234 

Knoxville 540 1000 1410 2040 2600 3250 0.179 

Memphis 4560 6310 7560 9230 10600 11900 0.282 

Nashville 4160 6010 7190 8610 9630 10600 -0.315 

Chattanooga 4110 5780 7010 8700 10100 11500 0.366 

Knoxville 3480 5330 6730 8690 10300 12000 0.222 

Memphis 10300 15100 18700 23700 27800 32100 0.323 

Nashville 8880 13800 16800 20300 22800 25000 -0.583 

Chattanooga 8750 12800 15900 20100 23500 27100 0.270 

Knoxville 7310 11800 15400 20400 24600 29200 0.161 

Memphis 641 974 1210 

Nashville 569 923 1150 

Chattanooga 644 971 1190 

Knoxville 416 726 980 

1970 -0.119 

1740 -0.653 

1850 -0.296 

2060 0.151 

Memphis 903 1490 1890 

Nashville 743 1380 1850 

Chattanooga 879 1460 1870 

Knoxville 497 961 1370 

1510 1740 

1400 1580 

1460 1650 

1360 1690 

2390 2770 

2460 2910 

2410 2820 

2010 2580 

3130 -0.400 

3360 -0.493 

3240 -0.288 

3250 0.128 

Memphis 4570 7140 8990 11500 13400 15400 -0.050 

Nashville 3890 6230 7690 9410 10600 11700 -0.629 

Chattanooga 4320 6540 8010 9840 11200 12500 -0.288 

Knoxville 3000 5110 6800 9250 11300 13600 0.105 

Memphis 2110 3310 4160 5280 6160 7050 -0.115 

Nashville 1890 3050 3730 4470 4940 5360 -0.836 

Chattanooga 1990 3030 3770 4750 5510 6290 -0.036 

Knoxville 1430 2480 3280 4390 5290 6250 -0.117 

Memphis 

Nashville 

Chattanooga 

Knoxville 

2710 4070 

2330 3640 

2350 3480 

1840 3080 

-39- 

5060 6390 7440 8540 0.081 

4420 5280 5840 6330 -0.760 

4280 5350 6190 7060 0.051 

4050 5460 6630 7910 0.098 
Table 3 .--Summary of simulated flood frequency values for modeled basins.--Continued. 

Drainage Long-term Simulation results 

Station area rainfall 

number .2 Q5 425 Q50 

(ml 1 station (ft3/s) (ft3/s) (ft3/s) (ft3/s) (ft3/s) (ft /s) coefSEent 42 Qlo Qlog 

03435600 

03461200 

03469110 

03486225 

03519610 

03519630 

03519640 

03519650 

03535140 

03535160 

03535180 

03538900 

3.50 

10.2 

2.18 

4.88 

2.10 

1.46 

16.0 

3.65 

1.23 

14.1 

3.23 

3.80 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

669 1190 

528 1020 

684 1210 

334 695 

1080 1740 

874 1590 

980 1580 

729 1300 

175 '271 

150 240 

150 231 

112 193 

561 1160 

409 929 

560 1200 

243 565 

214 419 

161 327 

198 378 

109 222 

148 283 

119 242 

137 264 

74 167 

1230 1890 

1030 1650 

1060 1600 

813 1310 

421 732 

319 605 

375 644 

242 471 

301 465 

250 416 

292 436 

179 331 

1910 2790 

1710 2520 

1640 2400 

1360 2080 

452 729 

361 608 

425 645 

266 496 

386 593 

323 508 

347 507 

250 421 

-4o1580 2120 2540 2980 -0.253 

1360 1790 2090 2370 -0.700 

1580 2040 2370 2700 -0.514 

1040 1630 2190 2890 0.257 

2190 2780 3210 3640 -0.316 

2050 2570 2920 3230 -0.843 

1970 2450 2790 3120 -0.484 

1730 2330 2820 3330 -0.189 

340 432 504 578 -0.046 

292 346 379 407 -0.944 

291 374 442 513 0.126 

260 359 444 541 0.194 

1660 2400 3010 3690 -0.241 

1360 1990 2490 3020 -0.477 

1740 2540 3200 3910 -0.326 

903 1520 2160 2990 0.306 

589 842 1060 1290 -0.129 

455 627 759 892 -0.520 

524 738 918 1110 -0.123 

323 483 628 794 0.031 

396 563 705 864 -0.058 

337 465 563 662 -0.521 

369 524 655 799 -0.100 

260 424 585 787 0.222 

2370 3046 3570 4130 0.095 

2000 2390 2630 2840 -0.873 

2000 2540 2970 3430 0.147 

1680 2190 2600 3030 -0.014 

964 1280 1530 1800 -0.204 

809 1070 1260 1440 -0.591 

847 1130 1350 1590 -0.127 

672 983 1260 1580 0.067 

577 722 830 939 -0.217 

526 661 756 847 -0.538 

526 636 713 786 -0.410 

462 663 841 1040 0.140 

3390 4160 4750 5340 -0.065 

2970 3440 3740 3990 -0.843 

2960 3720 4330 4970 0.218 

2630 3440 4120 4880 0.382 

930 1200 1410 1620 -0.146 

774 977 1120 1260 -0.527 

781 938 1050 1150 -0.564 

688 979 1230 1510 0.050 

739 930 1080 1230 -0.095 

623 758 850 935 -0.602 

607 726 809 888 -0.417 

553 740 893 1060 0.011 
Table 3 .--Summary of simulated flood frequency values for modeled basins.--Continued,. 

Station 

number 

Drainage Long-term Simulation results 

area rainfall 

bi2> 

Q2 Q5 QUI 425 Q50 Qloo Skew 

station (ft3/s> (.ft3/s> (ft3/s> (ft3/s> (ft3/s) (ft3/s) coefficient 

03539100 1.10 

03541100 5.53 

03541200 2.44 

03597300 4.99 

03597400 9.59 

03597450 0.73 

03597500 16.3 

03597550 1.86 

03604070 0.51 

03604080 1.52 

03604090 6.02 

03604100 10.1 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

.Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Chattanooga 

Knoxville 

102 180 

77 142 

93 161 

54 107 

1180 1820 

1050 1710 

1090 1680 

746 1330 

351 574 

295 507 

321 514 

209 388 

1370 1990 

1200 1810 

1250 1750 

944 1500 

3020 4170 

2790 3980 

2720 3790 

2360 3520 

233 362 

125 244 

246 372 

120 202 

4130 5760 

3780 5360 

3600 5010 

3150 4640 

482 701 

438 664 

476 671 

327 507 

38 81 

29 63 

38 79 

18 40 

191 374 

128 265 

176 345 

88 194 

627 1290 

356 845 

605 1130 

286 538 

1250 2200 

872 1740 

1080 1880 

624 1180 

-41- 

238 316 378 442 -0.274 

188 247 291 333 -0.545 

209 271 318 364 -0.407 

155 232 303 385 0.128 

2260 2830 3260 3690 -0.201 

2100 2540 2820 3060 -0.838 

2100 2670 3120 3590 -0.021 

1820 2540 3150 3840 0.084 

729 927 1070 1220 -0.336 

645 808 920 1020 -0.677 

650 829 966 1110 -0.190 

541 778 987 1230 0.138 

2430 3040 3530 4040 0.230 

2180 2610 2890 3160 -0.596 

2090 2540 2880 3230 0.094 

1920 2520 3020 3560 0.171 

5020 6180 7120 8120 0.422 

4730 5640 6290 6920 -0.281 

4580 5650 6520 7440 0.387 

4400 5630 6650 7750 0.306 

447 554 631 706 -0.367 

328 434 509 581 -0.672 

440 508 549 582 -0.983 

267 362 442 530 0.126 

6940 8570 9880 11300 0.381 

6350 7540 8370 9160 -0.344 

6040 7470 8610 9830 0.409 

5790 7430 8810 10300 0.436 

854 1050 1210 1370 0.022 

802 963 1070 1170 -0.566 

792 934 1030 1130 -0.367 

643 831 984 1150 0.128 

118 177 230 289 -0.077 

90 128 156 185 -0.574 

112 158 193 230 -0.490 

63 105 147 202 0.299 

523 739 917 1110 -0.215 

373 522 638 758 -0.477 

476 655 795 938 -0.407 

293 459 615 801 0.076 

1760 2330 2730 3090 -0.806 

1300 2010 2650 3360 -0.244 

1530 2070 2510 2980 -0.249 

765 1130 1470 1880 0.363 

2900 3810 4500 5200 -0.363 

2400 3270 3920 4580 -0.541 

2400 3020 3440 3820 -0.707 

1640 2340 2950 3630 0.021 
Table 3.-- Summary of simulated flood frequency values for modeled basins.--Continued. 

Station 

number 

Drainage Long-term Simulation results 

are 9 rainfall Qloo Skew 

(mi > station (s/S) Q:t3,s) Yf!3/s) Yf5K3,s) Q5pt3/s) (ft3/s) coefficient 

07028930 4.75 Memphis 1310 1970 2430 3060 3550 4060 0.034 

Nashville 1160 1820 2220 2680 2990 3270 -0.665 

Chattanooga 1280 1870 2240 2700 3020 3330 -0.326 

Knoxville 870 1510 2020 2780 3430 4140 0.107 

07028935 1.08 Memphis 491 691 827 1000 1130 

Nashville 444 664 806 978 1100 

Chattanooga 478 675 814 996 1140 

Knoxville 360 581 752 997 1200 

07028940 7.87 Memphis 2450 3430 4120 5020 5720 

Nashville 2240 3220 3830 4540 5030 

Chattanooga 2280 3160 3790 4620 5270 

Knoxville 1800 2770 3520 4610 5530 

07028950 13.3 Memphis 3640 5070 6120 7560 8730 9980 0.409 

Nashville 3290 4740 5660 6790 7610 8390 -0.279 

Chattanooga 3190 4480 5410 6700 7740 8850 0.366 

Knoxville 2750 4130 5180 6700 7970 9360 0.383 

1270 0.017 

1220 -0.372 

1290 0.141 

1420 0.147 

6440 0.138 

5490 -0.449 

5950 0.227 

6540 0.347 

curves produced by data from the three closest rain gages. 

The t-year discharges were weighted on the inverse ratios of 

the distances from the rainfall stations to the discharge 

site. Use of this weighting scheme recognizes the potential 

rainfall variation with geographical location and as such 

assigns more weight to discharges based on the closer rain 

gages. 

Weighting Observed and Simulated Frequency Curves 

Log-Pearson type III curves were computed from observed 

data in accordance with current Water Resources Council recommendations (1976) for all stations having seven or more annual peaks. Each of these gaging stations then had two estimates of its flood-frequency characteristics, one on the basis 

of observed annual peaks and one on the basis of a composite 

of simulated annual peaks. In order to objectively proportion the two estimates rather than averaging them, some measure of their relative accuracy at various recurrent intervals was needed. The technique selected (R. W. Lichty, oral 

commun., 1976) was to weight the pairs of t-year discharges 

on the inverse ratios of their relative error. The scheme 

used to compute the relative error is analogous to a variance 

analysis except that the expected value of mean square error 

was used as an indicator of error instead of regression variance. The method is outlined below: 

-42- 
1. The measure of error between the observed and 

simulated discharges was computed for each 

recurrence interval using 

E= 

C(lOg Qobs - log Qsim)2 

= vts+vm 

n 

in which 

E= mean square error, in log units, 

Q 3 

obs = observed t-year station discharge, in ft /s, 

Q 3 

sim = simulated t-year station discharge, in ft /s, 

n = number of stations, 

%s = average error associated with the observed discharge, in log units, 

'm = average error associated with the simulated discharge, in log units, 

rors'@ 

was assumed to result mainly from time-sampling ernce the average record length was only about 10 years. 

It is referred to as the average time-sampling variance. 

2. From log-Pearson type III statistics of observed 

station data, the time sampling variance was estimated for each station for selected recurrence intervals using a modification to the equation developed by Hardison (1971) as followsr 

V ts = 

(R)2(Iy)2 

N 

where V ts = station time-sampling variance, in 

log units, 

R = factor relating standard error of a tyear event to I, and N, 

Iv = standard deviation of logarithms of 

annual events, in log units, 

N = number of annual peaks. 

-43- 
The average time-sampling variance was computed from 

the station values. 

3. vrn was computed as the difference between E and 'iJts 

for each recurrence interval. 

4. The simulated data error for each recurrence interval cannot be estimated for individual stations 

since it encompasses a multitude of sources, such 

as model errors and long-term rainfall data errors, 

whose impact cannot be evaluated. For this analysis, the assumption was made that the simulated 

data error for individual stations (V,) closely 

approximates the average (V,). Using this assumption the discharges can be weighted by the inverse 

ratio of Vt,/V, such that 

Q weighted = 

(Vt. X Qsim) + cVm x Qobs) 

'ts + 'rn 

Although the above technique is arbitrary, it does remove 

subjectivity from the process of combining the pairs of 

curves. It assigns less weight to Qobs values as the standard 

deviation of the observed data increases and more weight as 

the standard deviation decreases. It assigns less weight to 

Qobs values from short records than it does long ones. The 

weighting technique also gives more weight to Qobs ValUeS 

at lower recurrence intervals than it does at higher ones. 

These trends are consistent with those normally associated 

with the relative accuracy of discharge-frequency curves. 

, 

Average record length of the observed data is about 10 

years. The average weight given to simulated discharges at 

the loo-year recurrence interval was 1.5 times the average 

weight given to the observed discharges. At the Z-year recurrence interval the average weight assigned to the simulated 

data was 0.9 times that of the observed data. Use of these 

weighting factors implies that the effective record length of 

the composite simulated data is 15 years for loo-year floods 

and 9 years for 2-year floods. Accuracy of the weighted discharges in terms of equivalent years of record should be 

greater than either the length of the observed data or the 

effective length of the composite simulated data, but is 

probably less than their total. It should be noted that the 

accuracy estimates are relative to the particular period of 

data collection and, as such, are not absolute values. 

Discharges for selected recurrence intervals from 

-44- 
frequency curves developed on the basis of observed data, 

composite simulated data, and the above weighting technique 

are presented in table 4, where applicable. Observed frequency curves were not computed for stations that did not 

have sufficient data to adequately define them. The composite simulated data are the only date available at these 

stations, and, consequently, only the discharges based on 

the simulated data are listed. The weighted discharges 

should be used as the best estimate of t-year floods at 

stations for which they are available. 

EVALUATION OF MODELING 

Application of the Geological Survey rainfall-runoff 

model has added greatly to the quantity of information available for definition of flood frequency characteristics of 

small Tennessee streams, In a flood-frequency study for 

Tennessee by Randolph and Gamble (1976), the model d basins 

co prised 42 percent of the basins less than 50 mi 3 km ) s q9.5 

and 56 percent of those less than 20 mi* (51.8 km > 

that were used. No bias due to modeling was detected in the 

study. The t-year discharges from modeled stations did exhibit less variance than those from stations with observed 

discharges only. This trend is undoubtedly due, in part, to 

the long-term precipitation data being common to all simulations. Also, the various weighting techniques would tend to 

filter out extremes and as such would be a factor in reducing 

variance. 

Although the average record length of observed annual 

peaks was about 10 years, the average length of flood hydrograph collection was less than 10 years as shown in table 1. 

Stations 03418900 and 03486225 had only 3 years of record 

when the model was calibrated for them, The particular period 

during which these two gages were operated provided a sufficient quantity and variety of storms for calibration. Modeling experience with the Tennessee stations indicates that a 3- 

year-data-collection period is probably close to the minimum 

record length needed to adequately sample storm types. Maxi-r 

mum length of data collection required will vary from station 

to station and will vary with the particular period of data 

collection, but a period of about 7 years should suffice. 

Approximately one-fourth of the project gages were continued in some capacity, mainly as crest-stage stations, to 

provide further evaluation of the simulated data. These gages 

will be operated until 20 to 25 annual peaks are available to 

define their flood frequency estimates. An updated comparison 

of the simulated and observed frequency is planned to be made 

at that time. 

-45- 
Table 4 .--Summary of observed, composite and weighted T-year discharge for modeled basins. 

Drainage Type of 

Station area frequency 

(mi2> 42 Q5 Qlo 425 Q50 Qloo Skew 

number curve (ft3/s) (ft3/s) (ft3/s) (ft3/s) (ft3/s) (ft3/s) coefficient 

03313600 0.95 

03313620 3.03 

03418900 1.52 

03420360 2.28 

03420380 1.03 

03420400 7.30 

03427830 0.17 

03427840 3.54 

03430400 12.0 

03430600 43.0 

03430700 3.86 

03431000 64.0 

03431080 3-92 

03431120 3.30 

03431240 1.58 

03431340 13.2 

Observed 155 368 571 905 

Composite 211 364 469 602 

Weighted 194 365 495 672 

Composite 356 686 933 1260 

Composite 190 297 376 482 

Observed 312 593 831 1190 

Composite 311 526 677 873 

Weighted 311 554 735 982 

Observed 246 '407 530 702 

Composite 220 313 376 457 

Weighted 234 361 448 563 

Observed 1150 2540 3830 5960 

Composite 882 1300 1570 1920 

Weighted 954 1600 2050 2680 

Observed 65 104 133 173 

Composite 55 98 129 167 

Weighted 61 101 131 130 

Observed 1570 2590 3350 4420 

Composite 1340 1940 2330 2830 

Weighted 1460 2250 2780 3470 

Observed 3700 5280 6330 7670 

Composite 4460 6340 7560 9080 

Weighted 3880 5550 6680 8120 

Observed 4210 6150 7470 9160 

Composite 6970 10200 12100 14300 

Weighted 4930 7290 8910 10900 

Observed 612 893 1080 1320 

Composite 1210 1820 2210 2690 

Weighted 790 1190 1480 1850 

Observed 6330 9830 12300 15600 

Composite 9250 13300 15800 18800 

Weighted 6890 10600 13100 16400 

Observed 620 1230 1760 2540 

Composite 766 1320 1710 2180 

Weighted 698 1280 1730 2310 

Observed 864 1500 

Composite 1420 2220 

Weighted 1100 1830 

1990 2680 

2750 3400 

Observed 231 323 

Composite 233 409 

Weighted 231 343 

Observed 1980 2650 

Composite 1570 2900 

Weighted 1910 2700 

2360 3060 

383 459 

551 759 

426 546 

3070 3600 

3940 5410 

3250 4030 

1210 1580 

701 798 

818 972 

1520 1780 

568 660 

1500 1850 

1020 1170 

1180 1390 

843 993 

518 581 

655 751 

7930 10300 

2180 2450 

3230 3850 

205 239 

195 222 

200 230 

5290 6210 

3200 3580 

4030 4590 

8660 9650 

10200 11300 

9150 10200 

10400 11700 

15900 17300 

12300 13700 

1510 1690 

3020 3350 

2100 2350 

18100 20700 

20800 22800 

18800 21300 

3220 3970 

2520 2850 

2770 3250 

3240 3840 

3880 4340 

3580 4110 

514 569 

935 1130 

637 737 

3970 4340 

6600 7860 

4600 5200 

-0.110 

0.010 

0.010 

0.010 

-0.010 

-0.010 

-0.100 

-0.100 

-0.100 

-0.100 

-0.100 

-0.100 

-0.100 

-0.100 

-46- 
Table 4 .--Summary of observed, composite and weighted T-year discharge for modeled basins.--Continued. 

Drainage Type of 

Station area 

hi21 

frequency Q2 Q5 number Qlo C25 Q50 QIOO Skew 

curve (ft3/s) (ft3/s) (ft3/sj (ft3/s) (ft3/s) (ft3/s) coefficient 

03431520 4.13 

03431580 13.3 

03431600 51.6 

03431630 2.21 

03431650 2.66 

03431700 24.3 

03435020 9.32 

03435030 15.1 

03435600 3.50 

03461200 10.2 

03469110 2.18 

03486225 4.88 

03519610 2.10 

03519630 1.46 

03519640 16.0 

Observed 838 1510 2040 2810 3430 4110 

Composite 768 1350 1770 2310 2710 3110 

Weighted 806 1430 1900 2530 3020 3540 

Observed 2920 3950 4610 5410 6000 6580 

Composite 4120 5960 7150 8620 9700 10800 

Weighted 3130 4350 5170 6200 6920 7660 

Observed 5310 791p 9700 12000 13800 15500 

Composite 8810 13600 I.6700 20300 22900 25300 

Weighted 6300 9630 12000 15000 17200 19200 

Observed 414 661 840 1080 1270 1460 

Composite 566 916 1140 1400 1600 1770 

Weighted 474 768 977 1240 1430 1620 

Observed 537 801 982 1220 1390 1570 

Composite 739 1360 1820 2420 2880 3340 

Weighted 594 970 1260 1660 1940 2240 

Observed 2720 4290 5420 6920 8090 9300 

Composite 3870 6190 7670 9420 10600 11800 

Weighted 3110 4970 6310 8000 9180 10400 

Observed 2200 3580 4590 5960 7040 8170 

Composite 1850 2970 3680 4500 5070 5610 

Weighted 2030 3270 4100 5120 5900 6660 

Observed 2520 3900 4870 6140 7120 8130 

Composite 2270 3540 4350 5310 6000 6650 

Weighted 2430 3760 4650 5760 6600 7440 

Observed 639 1110 1460 1960 2360 2780 

Composite 527 1010 1360 1800 2130 2460 

Weighted 583 1060 1400 1860 2220 2580 

Observed 816 1170 1420 1760 2020 2290 

Composite 805 1400 1830 2390 2830 3260 

Weighted 814 1220 1510 1920 2240 2560 

Observed 132 245 341 491 624 776 

Composite 125 207 270 360 436 518 

Weighted 128 223 297 404 497 600 

Composite 366 819 1230 1900 2520 3250 

Observed 

Composite 

Weighted 

214 483 743 1180 1600 2110 

119 240 346 512 659 826 

152 314 453 671 872 1100 

Observed 149 291 415 610 783 982 

Composite 85 184 279 438 592 780 

Weighted 115 228 330 496 654 844 

Observed 775 1550 2240 3330 4320 5460 

Composite 864 1380 1750 2260 2660 3080 

Weighted 824 1450 1930 2600 3180 3800 

-0.100 

-0.100 

-0.100 

-0.100 

-0.100 

-0.100 

-0.110 

-0.110 

-0.120 

0.150 

0.150 

0.080 

0.080 

0.080 

-47- 
Table 4 .--Summary of observed, composite and weighted T-year discharge for modeled basins.--Continued. 

Drainage Type of 

Station are 1 frequency 

(E3/s) yft3/s) Fft31s) yt3/s) (ft3/s) (ft /S) coefficient 

Qso Qlog Skew 

number bi > curve 

03519650 

03535140 

03535160 

03535180 

03538900 

03539100 

03541100 

03541200 

03597300 

03597400 

03597450 

03597500 

03597550 

03604070 

03604080 

03604090 

3.65 

1.23 

14.1 

3.23 

3.80 

1.10 

5.53 

2.44 

4.99 

9.59 

0.73 

16.3 

1.86 

0.51 

1.52 

6.02 

Observed 286 697 1120 1870 2610 3530 0.080 

Composite 267 506 707 1010 1270 1570 

Weighted 273 557 803 1190 1530 1940 

Composite 204 357 479 658 811 981 

Observed 981 1560 1990 2600 3100 3630 

Composite 1440 2170 2710 3480 4120 4800 

Weighted 1180 1860 2370 3100 3700 4320 

Observed 230 484 719 1100 1460 1880 

Composite 298 529 710 973 1190 1440 

Weighted 271 514 713 1010 1260 1550 

0.100 

0.100 

Observed 385 755 1080 1570 2010 2510 

Composite 306 476 591 738 849 961 

Weighted 338 578 750 983 1180 1390 

Observed 122 232 325 466 590 729 

Composite 74 136 183 250 306 364 

Weighted 96 176 236 324 400 482 

Observed 1210 2480 3620 5450 7110 9040 

Composite 883 1480 1940 2570 3090 3650 

Weighted 1010 1840 2480 3400 4210 5100 

Observed 414 733 992 1370 1700 2050 

Composite 250 437 584 795 971 1160 

Weighted 335 576 758 1020 1250 1490 

0.030 

0.030 

0.050 

0.050 

Observed 1490 2920 4140 6000 7640 9480 

Composite 1170 1740 2110 2570 2910 3240 

Weighted 1310 2200 2840 3690 4410 5170 

Observed 2310 3880 5100 6820 8220 9740 

Composite 2700 3840 4620 5640 6420 7220 

Weighted 2510 3860 4820 6090 7090 8140 

Observed 395 467 509 559 594 627 

Composite 160 275 351 444 509 573 

Weighted 378 451 493 546 584 620 

Observed 4080 5880 7110 8710 9920 11200 

Composite 3620 5140 6170 7500 8520 9560 

Weighted 4020 5760 6940 8470 9630 10900 

0.000 

0.000 

0.000 

0.000 

Observed 501 718 866 1060 1200 1350 0.000 

Composite 430 638 771 931 1040 1160 

Weighted 482 694 834 1010 1140 1280 

Observed 

Composite 

Weighted 

56 121 180 27= 356 450 -0.100 

34 72 103 148 184 223 

42 88 126 182 230 283 

Composite 155 312 436 609 746 889 

Observed 822 1670 2410 3530 4500 

Composite 484 1030 1470 2110 2640 

Weighted 619 1270 1790 2550 3210 

5590 -0.100 

3200 

3910 
Table 4.--Summary of observed, composite and weighted T-year discharge for modeled basins.--Continued. 

Drainage Type of 

Station area frequency 

(mi2) 

425 Qso 9100 Skew 

number curve cf9:3/4 ik3/,) :s/,) (ft3/s) (ft3/s) (ft3/s) coefficient 

03604100 

07028930 

07028935 

07028940 

07028950 

10.1 

4.75 

1.08 

7.87 

13.3 

Observed 1080 2010 2770 3870 4790 5800 -0.100 

Composite 1020 1900 2530 3350 3960 4560 

Weighted 1050 1950 2620 3530 4240 4970 

Observed 1660 2370 2830 3390 3800 4200 -0.220 

Composite 1260 1900 2330 2860 3260 3660 

Weighted 1550 2230 2670 3200 3610 4010 

Observed 486 905 1230 1690 2070 2460 -0.220 

Composite 473 679 818 993 1120 1260 

Weighted 479 779 989 1250 1480 1710 

Observed 2760 3460 3870 4340 4660 4970 -0.220 

Composite 2350 3310 3960 4790 5410 6040 

Weighted 2700 3440 3880 4420 4790 5160 

Observed 3190 4550 5440 6540 7340 8120 -0.200 

Composite 3440 4850 5840 7160 8180 9260 

Weighted 3274 4650 5590 6800 7680 8590 

Using a rainfall-runoff model with 3 to 7 years of data 

instead of using conventional techniques which require 20 to 

25 years of data is advantageous if there is an urgent need 

for flood information, The Geological Survey rainfall-runoff 

model seems to fulfill the validity requirements of such a 

model. No bias was detected when residuals of the regression 

equations for the stations studied in this report were compared with residuals of the previously mentioned flood-frequency study in Tennessee. 

SUMMARY 

Data from 52 small drainage basins in Tennessee were used 

to calibrate the U.S. Geological Survey rainfall runoff model. 

Average error of peak discharge simulation on the final calibrations was about 36 percent, however peak simulation was 

generally more accurate for larger peaks than for the smaller 

ones. The calibrated model parameters were used with longterm precipitation data from Memphis, Nashville, Chattanooga 

and Knoxville to simulate four discharge-frequency curves for 

each modeled basin. Composite simulated frequency curves 

were computed on the basis of a distance weighting of the 

simulated curves from the three closest stations having longterm precipitation data. Discharge-frequency curves were 

also computed from observed annual peaks for stations that 

had sufficient data. For those stations, t-year discharges 

\ from the composite simulated curves and the observed curves 

were weighted on the basis of their relative accuracy to make 

up the best estimate of the flood characteristics that can 

currently be made, 

-49- 
Average record length at the modeled basins was 10 years. 

Results of this study indicate that accuracy of the simulated 

data is equivalent to 9 years of data at the 2-year recurrence interval and 15 years at the loo-year recurrence interval. The effective record length of the weighted frequency 

curves should be greater than either the observed data period 

or the effective length of the simulated data but probably 

less than their total. It should be noted that the accuracy 

estimate is relative to the particular peripd during which 

the data was collected, and, as such, is not an absolute value. 

The mo eled basins comprise 42 percent of the basins less 

than 50 mi !i!. 

mi2 (51.8 km h 129.5 km2) and 56 percent of those less than 20 ) that are currently available for definition of 

flood-frequency characteristics of Tennessee streams. These 

basins were analyzed along with other basins having observed 

data only in a recent flood-frequency study for Tennessee. No 

bias due to modeling was detected. 

Regionalization of model parameters does not appear to be 

promising at this time. Although general trends of several 

parameters were consistent with expectations, actual values 

were significantly affected by parameter interaction. This 

interaction was expected since, within some error range, 

many sets of parameter values may fit a given set of data 

equally well. These sets of parameters should produce comparable simulated annual peaks. 

This report illustrates that rainfall-runoff modeling can 

be an effective way to extend observed data in time. Quality 

of the simulated data is dependent upon how closely the observed data fit within the assumptions inherent to the hydrologic components of the model. Consequently, model users 

should be familiar with these components and should exercise 

careful judgment in selecting input data. The Survey model 

performed acceptably over a wide range of conditions when the 

above guidelines were followed. 

-5o- 
SELECTED REFERENCES 

Clark, C. 0.. 1945, Storage and the unit hydrograph! Am. 

Sot, Civil Engineers Trans., v. 110, p. 1419-1488. 

Conover, W. J., 1971, Practical nonparametric statistics8 

New York, John Wiley, p, 314-316, 

Dawdy, D. RI, Lichty, R. W., and Bergmann, J, M., 19'72, 

A rainfall-runoff simulation model for estimation of 

flood peaks for small drainage basins8 U.S. Geol. 

Survey Prof. Paper 506-B, 28 p. 

Dooge, J. C, I., 1973, Linear theory of hydrologic systems: 

U.S. Dept. Agriculture, Agr. Res. Service, Tech. Bull. 

1468, p. 202. 

Durbin, T. J., 1974, Digital simulation of the effects of 

urbanization on runoff in the upper Santa Ana Valley, 

California: U.S. Geol. Survey Water Resources Inv, 

41-73, 44 pa 

Hardison, C, H., 1971, Prediction error of regression estimates of streamflow characteristics at unnaged sites; 

U.S. Geol. Survey Prof. Paper 750-C, pm 22&236. 

Horton, R. E., 1940, Approach toward a physical interpretation of infiltration capacity: Soil Sci. Sot. Am. 

Proc., vm 5, p. 399-417. 

O'Kelly, J. I., 1955, The employment of unit-hydrograph to 

determine the flows of Irish arterial drainage channels; 

Proc. Inst. Civil Engineers, Y. 4, pt. 3, p* 365-412. 

Philip, J. R., 1954, An infiltration equation with physical 

significance: Soil Sci. Sot. Am. Proc., V. 77, pm 153- 

157. 

Randolph, W. J., and Gamble, C, R., 1976, Technique for estimating magnitude and frequency of floods in Tennessee; 

Tenn, Dept. of Transportation (In Press). 

U.S. Water Resources Council, 1976, Guidelines for determing 

flood flow frequency; U.S. Water Resources Bull. 17, 

196 PO 

-51- 
GLOSSARY 

antecedent moisture. --moisture stored within a drainage 

basin before a storm. 

baseflow.-- in context of the usage in this report baseflow 

is all runoff except direct runoff; sustained flow. 

continuous-record gaging station .--site on a stream where 

stage discharge data are obtained continuously over a 

period of time. 

crest-stage martial-record gaging station.--site on a stream 

where only flood peak data are collected systematically 

over a period of years. 

direct runoff,-- that runoff that enters stream channels 

promptly after rainfall, 

dual-digital gaging station .--site on a stream equipped with 

two recorders to measure the stage and concurrent rainfall associated with a flood event. 

flood-freauency curve .--graphic relationship between recurrence interval and flood-magnitude. 

harmonic averape evaporation data,--simulated evaporation 

values, used during periods of no actual evaporation 

data, based on a curve fitted through actual data. 

instantaneous unit hydropraph.--a hydrograph with direct runoff eaual to one inch from a storm uniformly distributed 

over the drainage basin and occurring within a unit 

time of zero. 

lag time.-- the time interval between the centroid of rainfall excess and the centroid of direct runoff. 

linear storage.--that characteristic of storm hydragraphs 

having storage conceptualized as being within a 

fictitious reservoir in which the storage is directly 

proportional to outflow. 

mean square error.--8 measure of error between the observed 

discharges and the simulated discharges that is equal 

to the iurn of the squared deviations-divided by the 

number of discharge values tested. 

-52. 
GLOSSARY--Continued 

multiple regression ,--statistical technique for defining the 

relationship between a dependent variable and two or 

more independent variables. 

physiogranhic provinces .--areas within the State of Tennessee 

where soils and drainage patterns have been developed 

on geologically similar materials. 

recurrence interval .--average interval of time, in years* 

within which the given flood event is expected to be 

exceeded once, The reciprocal of the recurrence interval is the probability of occurrence during any one 

year. (A SO-year flood, Q OI has a 2 percent chance 

of being exceeded in any g d ven year). Recurrence 

intervals imply no regularity of occurrence; a 500 

year flood event might be exceeded in consecutive 

years, or it might not be exceeded in a period many 

times 50 years in length, 

regional analysis, regionalization.--a method of combining 

records within a region which reduces the sampling 

error, bases the results on a uniform period of 

experience, and produces flood-frequency relations 

generally applicable within the region. 

standard deviation .--a measure of the dispersion or precision 

of a series of statistical values such as precipitation, streamflow, etc. It is the square root of the 

mean of the sum of the squares of the deviations from 

the arithmetic mean. 

standard error of estimate .--range of error such that the 

value estimated by the regression equation is within 

this range at about two out of three sites and is 

within twice the range at about 19 out of 20 sites. 

skew coefficient,--one of the measures of the distortion of 

the data from a normal distribution about the mean, 

water year. --the l&month period from October 1 through 

September 30, designated by the calendar year in which 

it ends. 

-53-