EFFECTS OF URBANIZATION ON FLOOD CHARACTERISTICS 

IN NASHVILLE-DAVIDSON COUNTY, TENNESSEE 

by Herman C. Wibben 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations 76-1.21 

Prepared in cooperation with the 

Metropolitan Government of Nashville 

and Davidson County, Tennessee 

1976 
~IBLl3CRAPHIC DATA , 1. Report No. 

iHEET I 

;3. 

I 

13. Reclplent’s Accesston No. 

I 

I. Title and Subtitle 1 5. Report Date 

EFFECTS OF URBANIZATION ON FLOOD CHARACTERISTICS 

IN NASHVILLE-DAVIDSON COUNTY, TENNESSEE 

r. Author(s) 

H. C. Wibben 

1. Performing Organization Name and Address 

U.S. Geological Survey, Water Resources Division 

A-413 Federal Building - U.S. Courthouse 

Nashville, Tennessee 37203 

1976 

6. 

8. Performing Organization Reptl 

N"USGS/WRI-76-121 

10. Project/Task/Work Unit No.’ 

11. Contract/Grant No. 

2. 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 

14. 

15. Supplementary Notes 

Prepared in cooperation with the Metropolitan Government of 

Nashville and Davidson County, Tennessee 

16. Abstracts Streamflow data from 14 basins in Davidson County were extended in time by 

use of a digital model of the hydrologic system. The basins ranged in size from 1.58 

to 64.0 square miles (4.09 to 165.8 square kilometers) and ranged in extent of manmade impervious cover from 3 to 37 percent. The flood-frequency characteristics were 

defined by weighting frequency curves based on simulated discharges with those based on' 

observed discharges. The average record length of the three raingages used in simulation was 72 years, and the average record length of observed discharges was 11 years. 

Discharges corresponding to 2-, 5-, lO-, 25-, 50-, loo-year floods from the modeled basins were compared with discharges from regional equations for estimating peak : 

discharge rates from rural basins. Basin lag times of the urban basins were compared 

with those of nearby rural basins. The analyses indicated that in a fully-developed 

residential area, the flood peaks and the basin lag times will not be significantly 

different from those expected from an undeveloped area. Data were not sufficient to 

determine if 'an increase in flood peaks would occur from extremely small basins with 

extremely intensive development. 

17. Key Words and Document Analysis. 170. Descriptors 

Urbanization*, rainfall-runoff relationship, peak discharge 

17b. Identifiers/Open-Ended Terms 

Rainfall-runoff models, model parameters, regional regression analysis 

17~. COSATI Field/Group 

18. Availability Statement 

No restriction on distribution 

19. Security Class (This 21. -No. of Pages 

Report) 

UNC-D 38 

20. Security Class (This 22. Price 
EFFECTS OF URBANIZATION ON FLOOD CHARACTERISTICS 

IN NASHVILLE-DAVIDSON COUNTY, TENNESSEE 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigation 76-121 

Prepared in cooperation with the 

Metropolitan Government of Nashville 

and Davidson County, Tennessee 
UNITED STATES DEPARTMENT OF THE INTERIOR 

Thomas S, Kleppe, Secretary 

GEOLOGICAL SURVEY 

V. E. McKelvey, Director 

For additional information write to: 

U,S. Geological Survey 

Room A-413 U.S. Courthouse 

Nashville, Tennessee 37203 
CONTENTS 

Page 

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

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

Purpose and scope of the urban study . . . . . . . 

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

Background of project ................ 

Peak-flow simulations ................ 

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

Calibration results. ............... 

Flood-frequency determination. .......... 

General effects of urbanization ........... 

Index of development ............... 

Local effects of urbanization ............ 

Analysis of lag time ............... 

Comparison of wak discharges with regional 

estimates ................... 

Impact on storm volumes. ............. 

Determination of flood frequency. .......... 

Limitations. ................... 

Summary and conclusions ............... 

References cited .................. 

2 

3 

3 

4 

4 

10 

13 

16 

16 

17 

17 

20 

20 

28 

30 

31 

32 

- III - 
ILLUSTRATIONS 

Page 

Figure l.-- Location of Metropolitan NashvilleDavidson County and the numbered gaging 

stations selected for modeling. . . . . . 

2 .--Schematic outline of the model, showing 

components, parameters, and variables . . 

3-12. --Graphs showing: 

3 .--Results of calibration of storm volumes 

using measured impervious area. . . . . . 

4 .--Results of calibration of storm volumes 

using reduced value of impervious area. . 

5.-- Relation between lag time and basin lengthslope ratio for Nashville-area rural and 

urban basins. . . . . . . . . . . . . . . 

6 ,--Water-surface profile of 50-year flood 

along Sugartree Creek . . . . . . . . . . 

7 .--Relation between discharges from regional 

regression equation and those from 

Nashville-area streams of 2-year 

recurrence interval . . . . . . . . . . . 

8 .--Relation between discharges from regional 

regression equation and those from 

Nashville-area streams of fi-year 

recurrence interval , . . . . . . . . . . 

9 .--Relation between discharges from regional 

regression equation and those from 

Nashville-area streams of lo-year 

recurrence interval . . . . . . . . . . . 

10 .--Relation between discharges from regional 

regression equation and those from 

Nashville-area streams of 250year 

recurrence interval . . . . . . . . . . . 

- IV - 

5 

7 

12 

14 

19 

21 

22 

23 

24 

25 
Figure 11 .--Relation between discharges from regional 

Page 

regression equation and those from 

Nashville-area streams of SO-year 

recurrence interval . . , . . . . . . . . 26 

12 .--Relation between discharges from regional 

regression equation and those from 

Nashville-area streams of loo-year 

recurrence interval . . . . . . . . , . , 27 

TABLES 

Table 1 ,--Stations in the Nashville area used to calibrate the U. S, Geological Survey 

rainfall-runoff model . , . . . . . . . . . 6 

2 .--Summary of calibrated model parameters. . . . 11 

3. --Summary of t-year discharges for modeled 

basins, . . . . , . . . . . . . . * . . . . 25 

4 .--Rural gaging stations surrounding Davidson 

County for which lag times have been 

computed. . . . , . . . , . . . . l . , . . I8 
EFFECTS OF URBANIZATION ON FLOOD CHARACTERISTICS 

IN NASHVILLE-DAVIDSON COUNTY, TENNESSEE 

BY 

Herman C, Wibben 

ABSTRACT 

Streamflow data from 14 basin8 in Davidson County 

were extended in time by use of a digital model of the hydrologic system. The basin8 ranged in size from 1.58 to 

64.0 square miles (4.09 to 165.8 square kilometers) and 

ranged in extent of man-made impervious cover from 3 to 37 

percent. The flood-frequency characteristic8 were defined 

by weighting frequency curves based on simulated discharges 

with those based on observed discharges. The average record 

length of the three rain-gage8 used in simulation was 72 

years, and the average record length of observed discharge8 

was 11 years. 

Discharge8 corresponding to 2-, 5-, lo-, 25-, 50.. 

and loo-year floods from the modeled basin8 were compared 

with discharges from regional equations for estimating peak 

discharge rates from rural basins. Lag times between rainfall and runoff in the urban basins were compared with those 

of nearby rural basins. The analyses indicated that in a 

fully-developed residential area* the flood peaks and the 

basin lag times will not be significantly different from 

those expected from an undeveloped area. Data were not sufficient to determine if an increase in flood peaks would 

occur from extremely small basins with extremely intensive 

development. 

INTRODUCTION 

As urban development take8 place in a previously rural 

basin, substantial changes in flood Characteristics of the 

basin often occur. The effect of the changes, in general, 

is to increase the magnitude and frequency of flooding. The 

impact of this increased flooding can be minimized if it is 

-l- 
considered in the planning and design of buildings and 

drainage structures. Adequate design is not possible if 

the magnitude of change in flooding is not known. 

Most urban areas lack sufficient streamflow information to determine the effects of urbanization upon the flood 

characteristics of its streams. Design techniques currently 

used in urban areas consist largely of using empirical equations developed decades ago, Variables within these equations are normally selected from curves or tables based on 

small quantities of, data from various locations. The curves 

or tables may not be at all representative of the locale, in 

which they are being used since they reflect average values. 

Recent studies have shown that the effect of urbanization 

can vary greatly from area to area, 

A study in Houston, Texas by Johnson and Sayre (1973) 

indicated that changing a rural basin into an urban basin 

having 35 percent impervious area would increase the magnitude of the 2-year flood about nine times and the magnitude 

of the fiO-year flood about five times. A similar study in 

Dallas, Texas by Dempster (1974) indicated considerably different results. The Dallas study indicated that a fully developed residential urban basin would increase the flood 

peak at the 2-year recurrence interval by about 1.4 times 

and at the 50-year recurrence interval by about 1.2 times 

the discharge from the same basin under rural conditions. 

Anderson (1970), in a study of Fairfax County, Virginia, 

found increases in flood peaks due to urbanization that were 

about halfway between those from the Houston and Dallas 

studies. The results of the above Studie8 point out the 

extent of the potential error that can result from transferring output from the study of one urban area to another 

without having local data to verify such a transfer. 

Purpose and Scope of the Urban Study 

The purpose of this report is to assess the effects of 

urbanization upon magnitude and frequency of floods in 

Nashville-Davidson County, Tennessee. Data from urban basins 

are compared with data from rural basins in and around 

Davidson County to quantify the increase in flooding. The 

discussion and presentation of results provide information 

needed,to design drainage systems and facilitate optimum 

land-use planning. 

The author acknowledges the assistance of Mr. Glenn 

Bowles, Environmental Planner, Metropolitan Government of 

Nashville-Davidson County Planning Commission in computing 

-2- 
the area1 extent of man-made impervious cover in the study 

basins. Daily precipitation data, s-minute incremental 

storm data, and evaporation data for historical periods 

were obtained from the National Oceanic and Atmospheric 

Administration at Asheville, North Carolina. 

Use of Metric Units of Measurement 

The analysis and compilations in this report were 

made with English units of measurement. 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 

units and metric units would not be practicable. To convert 

English units to metric units, the following conversion factors should be used: 

Multiply English units lx To obtain metric units 

inches (in) 

feet (ft) 

miles (mi) 

square miles (mi2) 

feet per mile 

(ft;/mi) 

cubic feet per 

second (ftj/s) 

25.4 

0.305 

1.619 

2.59 

0.189 

0.0283 

millimeters (mm) 

meters (m) 

kilometers (km) 

square kilometers (km2) 

er kilometer 

cubic mete 

second (m 3 /g?' 

BACKGROUND OF PROJECT 

The U,S, Geological Survey, in cooperation with the 

Metropolitan Government of Nashville-Davidson County, began 

a program aimed at meeting future needs for information on 

the flood hydrology in Davidson County in July 1963. This 

program entailed delineating extent and frequency of flooding 

likely to be experienced in the areas covered by 88 flood 

inundation maps. Water-surface profile information used to 

delineate the flood boundaries are presented in a report by 

Conn and Boyd (1975). The project also included collection 

of streamflow and rainfall data in four tributary basins in 

the county. 

In 1974 a second cooperative program oetween the Geological Survey and the letropolitan Government of NashvilleDavidson County was initiated to provide planners a means for 

assessing the impact of basin developmentalternatives upon 

-3- 0 
flooding. Data available for analysis consisted mainly of 

the data from the earlier cooperative program. Length of 

record at the gaging stations averaged only about 11 years, 

In addition, the data were collected during an unusually 

dry period. Because of these two factors, time-sampling 

bias of the observed data resulted in the potential for 

Introducing considerable error in any flood-frequency analysis based directly on the observed data. Data from 14 of 

the stations fulfilled requirements of input to the U, S. 

Geological Survey rainfall-runoff model, Consequently, the 

approach used in this second program to minimize the timesampling bias of the Nashville data base was to calibrate 

the Geological Survey rainfall-runoff model with observed 

data from the 14 stations and subsequently, to simulate a 

series of annual peaks on the basis of long-term climatological data. The average length of record simulated was 72 

zI?i;de 

Determination of flood-frequency characteristics 

utilizing the simulated data. 

Figure 1 shows the locations of the gaging stations 

which have data available for model use. Some physical 

characteristics of the modeled basins along with their 

respective record periods are presented in table 1. 

PEAK-FLOW SIMULATIONS 

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, soilmoisture accretion and depletion, and surface streamflow. 

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

use 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 2. Brief descriptions of the model parameters are 

listed below. 

-4- 
03431520 

. 1 

i /' 

i ,.' i- 

\ 

\ 

\ 

\ 

\ 

\ 

\ .-- 

)-.--. ‘+-- -m--_--m --- -0- - 

j’ 

‘,&-/--,;; 3 

j’ 

TENNESSEE /’ 

----m-.--.---J 

INDEX MAP 

__-- -0-L 

SCALE 

0 ! p 3 4 5 Miles 

0 I 2 3 4 5 6 7Kilometers 

Figure l.-- Location of Metropolitan Nashville-Davidson County 

and the numbered gaging stations selected for 

modeling. 

-5- 
-6- 
ANTECEDENT-MOISTURE INFILTRATION ROUTING 

ACCOUNTING COMPONENT COMPONENT COMPONENT 

Saturated-unsaturated Philip infiltration Modified Clark 

soil mositure regimes equation instantaneous unit 

hydrograph 

g = (Z + p (ym ) 

II 

-A7 

Parameter Variable 

D 

Parmeter Variable LA 

Parameter 

EVC 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 2. --Schematic outline of the model, showing components, 

parameters, and variables. 
Parameter 

identifier 

code 

Units Application 

PSP-------------Inches----------Represents the combined effects of soil moisture content and suction at the 

wetting front for soil moisture at field capacity. 

RGF ----------------------------- Ratio of PSP for soil 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. 

BMSM------------Inches---------- Soil moisture-storage volume at 

field capacity. 

EvC-----------------------------Coefficient to convert pm 

evaporation to potential evapotranspiration values. 

D~------------I Inches per hour-A constant drainage rate for 

redistribution of soil moistire. 

RR ---------------"-I------"----" 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--------------linutes---------Time to peak of triangular 

translation hydragraph. 

The antecedent-moisture component determines the initial 

infiltration rate for a storm. Input to this component are 

daily rainfall and daily evaporation, and output is the amount 

of base-moisture storage (BMS) and infiltrated surfacemoisture storage (SW), 
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 

equatfon, Input are storm rainfall, BMS, and SMS, This 

component computes the amount of storm rainfall that infiltrates the soil and determines rainfall excess as output. 

The third component, surface-runoff routing, is based 

on a modification of the Clark (1945) form of the instantaneous unit hydragraph. Input is the rainfall excess 

computed in the infiltration component, and output is the 

storm-runoff hydrograph. First, the precipitation excess is 

converted into a triangular translation hydragraph representing the effects of varying travel times in the basin 

smoothed by storage. In the second step, successive flow 

rates of the translation hydrograph are attenuated by 

routing through linear storage, 

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, storm 

rolcn8es, or some combiarition of botlr. Starting values of 

parameters must be caaputed 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 

calibration optimize on three different objective functions. 

During 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 hydragraph shape parameters are optimized. Volumes 

routed are the observed direct runoff volumes so that errors 

introducted by rainfall data are eliminated. In phase three 

peak flows are again used in the objective function while 

the parameters affecting the moisture-accounting 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. 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 precipitation. All precipitation in excess of 0.05 in (1.27 mm) that falls on the 

impervious area is assumed to be direct runoff. 

-9- 
Final model parameters for the calibrated basins are 

shown in table 2. The model calibrations are described in 

more detail in an earlier report (Wibben, 1976). Average 

error of peak discharge simulation was 38 percent and no 

simulation bias was evident from the results of the final 

calibrations. Accuracy of simulated peaks was better for 

large peaks than for smaller ones. This trend is assumed to 

be the result of an effectively simpler model simulating the 

larger peaks. Saturated soil conditions exist during many 

of the larger storms. Under these conditions, most of the 

parameters within the antecedent-moisture-accounting component and several of those within the infiltration component 

have a negligible effect upon losses. These parameters are 

effectively ignored by the model and as such, any error introduced by them would be negligible. On the other hand, 

these very parameters are the ones that should have major 

impact in simulating the smaller events, Calibration results from the basins larger than 15 mi2 (38.8 km2) were 

noticeably poorer than those from smaller basins. The 

source of the increased error seems to be in simulation of 

precipitation excess, and its cause lies in the rainfall 

variation over these larger basins. 

Parameters affecting the loss components of the model 

were constrained during calibration within the range of 

reasonable occurrence in the field. With only a few exceptions, final parameter values are within those limits. The 

constraints were applied to prevent unreasonable parameter 

distortion from interaction during calibration. 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 parameter 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 basin were nearly the same. 

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 errors were generally in the 

range of 15 to 20 percent, with some as low as 10 percent, 
-ll- 
In studies of urban areas from other parts of the 

U.S. ( data frequently 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. At all the urban basins calibrated, smalLstorm direct runoff volumes were overestimated when the measured impervious area was used as input 

to the model, The phase one results from station 03431080 

shown in figure 3 are typical, 

SIMULATED RUNOFF, 

IN MILLIMETERS 

\ 

USED MEASURED IMPERVIOUS AREA=22 PER/CiNi 

1 PSP= 7.727 RGF = 28.05 RR = 0.980 

KSAT= 0.301 BMSM =I.148 

DRN = 0.221 EVC =0.951 / 

Station 0343 1080 

0.01 0.1 1.0 10 

SIMULATED RUNOFF, IN INCHES 

Figure 3.-- Results of calibration of storm volumes 

using measured impervious area. 

-12- 
When a better fit of the smaller storm volumes was 

achieved through parameter optimization larger storm 

volumes frequently were underestimated, In addition to 

this bias, several model parameters, mainly PSP, KSAT, and 

RGF, were forced outside a reasonable range of occurrence 

during optimization. The net effect of the unusual parameter 

values was to reduce runoff from the pervious areas to compensate for the increased runoff from the impervious areas. 

Evidently the im 

P 

ervious 

0.05 in (1.27 mm 

surfaces were storing more than 

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. 

The approach used in selected final parameters was 

based on the assumption that only part of the impervious 

area was effective in increasin 

similar to that used by Durbin 'i 

runoff. 

1974) 

This approach was 

in his study of the 

Upper Santa Ana Valley in California. During subsequent 

calibrations, the percent impervious area was suacessively 

reduced until the model would reproduce small runoff events, 

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 and are included in table 2. 

Figure 4 shows the phase one results from station 03431080 

using a reduced value of impervious area. 

Flood-Frequency Determination 

Log-Pearson type III discharge-frequency curves were 

computed from observed annual peaks in accordance with Water 

Resources Council (1976) recommendations for each of the 

fourteen gaging stations, Log-Pearson type III dischargefrequency curves were also computed from annual peaks simulated by the Geological Survey rainfall-runoff model using 

the calibrated parameters, long-term rainfall data from 

Nashville, Chattanooga, and Knoxville, and evaporation data 

from Center Hill Dam. The average record length of the 

precipitation data was 72 years. The three simulated frequency curves for each gaging station were combined into a 

composite simulated frequency curve by prorating them inversely with the distances from the long-term rain gages to 

the streamflow site, The observed frequency curves and the 

composite simulated frequency curves were then combined 

using a weighting technique based on their relative accuracy 

-13- 
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=O.79 1 

. Station 03431080 

J 

0 

0.01 0.1 I.0 IO 

SIMULATED RUNOFF, IN INCHES 

Figure 4. --Results of calibration of storm volumes 

using reduced value of impervious area. 

-14. 
Table 3 .--Summary of t-year discharges for modeled basins. 

Station 

number 

Drainage 

area 

(Tlii2) Q2 (ft3/s> 

Q5 Qlo 

(f t3/s) (ft3/s) 

425 

(f t3/s> 

Q50 

(ft3/s) 

QlOO 

(f t3/s) 

03430400 12.0 3880 5550 6680 8120 9150 10200 

03430600 43.0 4930 7290 8910 10900 12300 13700 

03430700 3.86 790 1190 1480 1850 2100 2350 

03431000 64.0 6890 10600 13100 16400 18800 21300 

03431080 3.92 698 1280 1730 2310 2770 3250 

03431120 3.30 1100 1830 2360 3060 3580 4110 

03431240 1.58 231 343 426 546 637 737 

03431340 13.2 1910 2700 3250 4030 4600 5200 

03431520 4.13 806 1430 1900 2530 3020 3540 

03431580 13.3 3130 4350 5170 6200 6920 7660 

03431600 51.6 6300 9630 12000 15000 17200 19200 

03431630 2.21 474 768 977 1240 1430 1620 

03431650 2.66 594 970 1260 1660 1940 2240 

03431700 24.3 3110 4970 6310 8000 9180 10400 

at select recurrence intervals. The measure of relative 

accuracy used is described in more detail by Wibben (1976). 

It is analgous to a variance analysis except that the expected value of mean square error was used as an indicator 

of error rather than regression variance. 

Discharges resulting from application of the weighting 

technique are presented in table 3 for select recurrence 

intervals. They represent the best estimate available of 

the flood-frequency characteristics of the modeled basins, 

-15- 
GENERAL EFFECTS OF URBANIZATION 

Previous studies of the hydrology of urban streams 

have indicated that hydrographs, and consequently flood 

peaks, are affected two ways by the urban development, One 

is that quantities of storm flow are generally increased because of reduced infiltration at those parts of basins 

covered by impervious surfaces. The other is that improvements to drainage systems normally increase their hydraulic 

efficiency such that storm flows leave the basins in a 

shorter period of time, thus increasing the peak discharges. 

A commonly used measure of a basin's hydraulic efficiency 

is basin lag time which is defined as the average time interval between the centroid of rainfall excess and the centroid of resultant runoff. Decreases in basin lag time can 

result from improvements to the overland flow system, such 

as storm sewers and drainage ditches, as well as improvements to the channel flow system that would increase the 

conveyance of the channels. 

Index of Development 

To compare flood characteristics of basins having 

various degrees of development, some index of development 

was needed. The area1 extent of man-made impervious cover 

was chosen as that index. Impervious cover was felt to be 

a reasonable indicator of potential increased runoff. 

Studies by Putnam (1972) and Johnson and Sayre (1973) indicated that impervious cover should also be a reasonable indicator of the hydraulic improvements in a basin. Insufficient information was available to accurately determine the 

extent of storm sewering and to subsequently relate it to 

impervious area. 

The percent impervious area within each basin was determined by: (1) Delineating areas of similar development 

on 1:48,000 scale maps as determined from Metropolitan 

Government of Nashville-Davidson County Planning Commission 

property maps1 recent aerial photographs, and visual in*- 

spectations; (2) Selecting representative parcels from each 

of the development types and measuring the extent of impervious cover; (3) Plankmetering the areas of similar development types within each basin and multiplying the areas by 

their respective percenta e of impervious cover8 and (4) 

Summing the results of (3 7 and dividing by the basin drainage 

area. 

-3.G 
The values of impervious area (table 1) reflect conditions as of mid-1974. No previous computations of impervious 

area or any other index of urbanization have been made. consequently, a slight bias toward overestimating impervious 

area at the time of data collection may be present, Planning 

Commission officials (G, R, Bowles, oral commun., 1974) indicated that the bias would generally be less than 2 percent. 

Average percent of impervious area used by the Planning 

Commission for various land-use types, which are similar to 

those used in other urban areas, are as follows: 

Land-use type Impervious area 

(percent) 

Low-density residential 

Medium-density residential 

High-density residential, 

Apartments, Warehousing, 

Wholesaling 

Manufacturing and Storage 

Commercial, Retail arterial 

Commercial retail concentrations 

i; 

50 

60 

LOCAL EFFECTS OF URBANIZATION 

Analysis of Lag Time 

Lag times were computed for the Nashville-area stations, 

as well as 15 rural gaging stations (Wibben, 1976) from the 

model routing parameters. The rural stations are listed in 

table 4 along with some physical basin characteristics. 

O'Kelly (1955) showed that lag time, the time from the centroid of precipitation excess to the centroid of direct runoff, is equal to one-half the time base of the isosceles 

triangle translation hydrograph plus the linear storage constant. In terms of model parameters, this relation is 

TL = KSW = l/2 TC, (1) 

where TL is basin lag time in hours and the units of both 

KSW and TC are in hours, The computed lag times for the 

Nashville-area stations and the nearby rural stations are 

given, respectively, in table 1 and table 4. 

-17. 
Table 4.0- Rural gaging stations surrounding 

Davidson County for which lag times 

have been determined 

Station 

Number 

Drainage 

are 9 bi 1 (ft?mi) 

Basin lag 

time 

(hrs) 

03313600 0.95 1.55 73.9 1.1 

03313620 3.03 3.12 52.8 1.2 

03427830 0.17 0.56 100.3 0.5 

03427840 3.54 4.58 73.9 1.5 

03435020 9.32 4.00 46.5 lb9 

03435030 15.1 6.70 28.0 3.1 

03435600 3.50 3.52 51.7 l.,l 

03597300 4.99 4.20 49.6 1.8 

03597400 9.59 6.08 31.7 2.4 

03597450 0.73 1.70 132.0 0.8 

03597500 16.3 8.30 25.7 3*3 

03597550 1.86 4.02 58.1 1.7 

03604080 1.52 2.16 105.6 1*3 

03604090 6.02 3.14 73.9 1.5 

03604100 10.1 5.23 49.6 2,3 

-18. 
The data points and the regression equation are plotted 

on figure 5. The standard error of equation 2 was 21.2 

LEWWSLOPE RATIO, L/K(L IN KILOMETERS, S IN METERS PER KILOMETER) 

l,o 1Q I I I 111 1 I 1 .O $1 

I 1 I I ltBasins having less 

Basins having more 

1. 

0. 

A multiple regression analysis using basin lag time and 

basin characteristics for the combined data for urban and 

rural basins resulted in the following equation for lag time: 

TL = 2.25 (L/ S)"*52 (2) 

where 

TL is the basin lag time in hours, 

L is the length of principal stream in miles, 

S is the difference in principal stream elevation, 

in feet per mile, at points 10 and 85 percent of 

the stream length, in miles, 

than 5'percent ikpervioks area 

I 1 I I II I I 

0.01 0.1 1.0 

LENGTH-SLOPE RATIO, L/c(L IN MILES, S IN FEET PER MILE) 

Figure 5.-- Relation between lag time and basin length-slope ratio 

for Nashville-area rural and urban basins. 

-19- 

t 111 

10 
percent. Percent of impervious area dropped out of the regression model at the 5 percent level of significance. 

Pigure 5 indicates that lag times for basins having more 

than 5 percent impervious area are not significantly less 

than those for rural basins. 

The lack of difference in lag times is attributed 

partly to the efficiency of the natural channels in Davidson 

County. Current development practices increase channel conveyance very little. Major changes, such as lining, widening, 

or deepening channels, are rare except for localized reaches 

where channel improvements are made to replace conveyance 

lost to flood-plain encroachment. Extensive storm sewering 

to help relieve local drainage problems is not-provided 

throughout most basins. In addition, the large number of 

stream crossingsby roads has a tendency to increase channel 

storage which could actually increase lag times. This 

tendency is illustrated by the Sugartree Creek SO-year flood 

profile (Corm and Boyd, 1975) presented in figure 6. The 

elevated profile at Woodmont Lane and Estes Road reflect 

additional storage at these road crossings. Equation 2 

should provide reasonable estimates of lag time for basins 

within Davidson County whose basin characteristics are within 

the range of those used in the regression model and whose 

drainage systems have not been significantly altered. 

Comparison of Peak Discharpes with Regional Estimates 

Peak discharges were computed for each of the modeled 

basins using regression equations (Randolph and Gemble, 1976) 

for estimating discharges for selected recurrence intervals 

from ungaged rural basins. The computed discharges for the 

29 50, lo-, 250, 500, and loo-year recurrence intervals 

are plotted respectively, in figures 7 through 12, against 

the station discharges from table 3. Percent of im;;c;;s 

area is shown as a third variable on the figures. 

the plots show that t-year floods from the urban streams are 

not signifiaantly larger than those expected from rural 

basins. 

Impact 6n Storm Volumes 

As mentioned previously, urbanization generally increases flood peaks by a combination of increasing storm 

runoff and increasing hydraulic efficiency. Studies of figures 7 through 12 indicate that flood peaks have not been 

significantly increased due to urbanization. In addition, the data indicate that little or no change in basin lag 

times have occurred due to urbanization. Therefore, it 

-2o- 
DISTANCE DISTANCE ALONG SUGARTREE SUGARTREE CREEK, IN HUNDREDS HUNDREDS OF METERS 

13 I3 14 14 IS 16 I6 17 I7 I8 18 19 20 21 

SIOC Slot 1 I 

,dSS 

SOS 454 

SO YEAR FLOOD v) 

453 E 

- - - STREAMBED 

so0 s 

. 

/ 

.I44 

470_ sto! 1 4 

6 7 

DISTiNCE ALONG SUZARTREE CREEK, IN THOUSANDS OF FEET 

Figure 6.-- Water-surface profile of 50-year flood along 

Sugartree Creek. 

-21- 
OISCHARGE FROM STATION DATA, 

IN CUBIC METERS PER SECOND 

DISCHARGE FROM STATION DATA, 

IN CUBIC FEET PER SECOND 

Figure 7. --Relation between discharges from regional regression 

equation and those from Nashville-area streams of 

2-year recurrence interval. 

-22- 
DISCHARGE FROM STATION DATA, 

IN CUBIC METERS PER SECOND 

I / 

5: 

E 

100 

100 1000 lop00 I00,000 

DISCHARGE FROM STATION DATA, 

IN CUBIC FEET PER SECOND 

Figure 8.-- Relatibn between discharges from regional regression 

equation and those from Nashville-area streams of 

5-year recurrence interval. 

-23- 
DISCHARGE FROM STATION DATA, 

IN CUBIC METERS PER SECOND 

l00,000 

IO loo 1000 

” 

i5 

5 

2 

I0,000 

100 

1000 

-.I0 

I”” 

100 1000 lop00 I00,000 

DISCHARGE FROM STATION DATA, 

IN CUBIC FEET PER SECOND 

Figure 9.-- Relation between discharges from regional regression 

equation and those from Nashville-area streams of 

lo-year recurrence interval. 

-24- 
DISCHARGE FROM STATION DATA, 

IN CUBIC METERS PER SECOND 

03,000 

IO loo 1000 

I 

5 

s 

2 

100 700 1000 lop00 I I00,000 

DISCHARGE FROM STATION DATA, 

IN CUBIC FEET PER SECOND 

Figure lO.-- Relation between discharges from regional regression 

equation and those from Nashville-area streams of 

25year recurrence interval. 

-25- 
DISCHARGE FROM STATION DATA, 

IN CUBIC METERS PER SECOND 

I0,000 

100 

1000 

IO 

Inn 

100 1000 IO/300 I00,000 

DISCHARGE FROM STATION DATA, 

IN CUBIC FEET PER SECOND 

Figure 11. --Relation between discharges from regional regression 

equation and those from Nashville-area streams of 

50-year recurrence interval. 

-26- 
DISCHARGE FROM STATION DATA, 

IN CUBIC METERS PER SECOND 

DISCHARGE FROM STATION DATA, 

IN CUBIC FEET PER SECOND 

Figure12 .--Relation between discharges from regional regression 

equation and those from Nashville-area streams of 

loo-year recurrence interval. 

-27- 
follows that within limits of urbanization reflected by 

the data, storm runoff volumes are not significantly increased. 

The lack of impact on storm volumes is apparently due 

to the shallow soil cover and low permeability over most of 

Davidson County. The landscape is composed of loamy and 

clayey soils, the depth of which ranges from less than 1 

foot to about 4 feet, and rock outcrops are numerous. 

DETERMINATION OF FLOOD FREQUENCY 

T 

64.0 mi 9 e urban basins studied range in size from 1.58 to 

(4.09 to 165.8 k$) and in average impervious area 

from 3 to 37 percent. The regional equations developed by 

Randolph and Gamble (1976) that are applicable to the 

Nashville area are listed below: 

standard error 

of estimate 

(percent) 

Q2 = 319 (A)0733 

Q5 = 512 (A)‘725 

~~0’ 651 (A)s723 

425~836 (A)*720 

Qso=977 (A)‘72o 

Qioo=1125 (A)*719 

30 

31 

32 

34 

equivalent 

years of 

record 

3 ( 3) 

4 (4) 

6 (5) 

8 (6) 

8 (7) 

9 (8) 

where 

Qt is that discharge, in ft3/s, likely to be exceeded 

at an average interval of t years. 

A is the contributing drainage area in mi2, 

Flood frequency at gaged sites can be determined by a 

combined use of the regression equations and the gaging-station 

frequency curve. The recommended procedure (U.S. Water 

Resources Council, 1976) is to compute the discharge for the 

desired recurrence interval as a weighted average of the station value and the regression value. 

-2% 
The weighted average is based on length of record of 

the station data and equivalent years of record for the 

regression value as indicated above. For modeled stations, 

the average length of record (Ng) used in this study was 25 

years for all flood levels. TheAequation, 

1% Q*(w) = 

log Qt(g)(Ng) + log Q%(r) (NU) 

Ng + Nu 

is used to compute the weighted average, where 

Qt(w) = the weighted station discharge for 

recurrence interval t, 

Qt w z the station discharge from the gaging 

station frequency curve for recurrence 

interval t, 

Qt(r) E the regression discharge for recurrence 

interval t, 

Ng = the number of years of gage record used to 

compute Qt(g)e and 

NU = the equivalent years of record for at(r) 

indicated above. 

The weighted values can be used directly for design purposes 

at gage sites, 

When the site for which flood magnitudes are desired 

is located between two gages on the same stream, compute the 

regionally weighted discharge for the desired recurrence 

interval for each gage and estimate the discharge at the site 

by interpolation on the basis of contributing drainage area. 

Interpolation may be done by plotting discharge versus 

drainage area on logarithmic paper for the two gaged sites, 

connecting the two parts with a straight line, and then 

entering the relation with the value of drainage area at the 

site where information is desired. If the drainage area at 

the downstream gage is more than three times that at the upstream gage, use of one of the following procedures is 

recommended, 

Flood discharges at sites which are relatively near a 

gaging station on the same stream can be calculated by a 

combined use of the regression equations and the nearby station data. The station value can be transferred upstream 

-29- 
or downstream by the equation, 

and a weighted value ean be calculated by the equation, 

where 

Q(w) = the weighted station discharge, Qttw), transferred upstream or downstream to the ungaged 

site, 

Q",(,) = the final weighted discharge at the ungaged 

site for recurrence interval t, 

Qt(r) = the discharge at the ungaged site from the 

regression equation for recurrence interval t, 

Au = the drainage area at the ungaged site 

Ag = the drainage area at the gaged site 

AA = the absolute difference between Au and Ag, and 

b- the regression coefficient (exponent) of drainage 

area for recurrence interval t. 

When the drainage area at the desired site differs by more 

than 50 percent from that at the gaged site, the regional 

estimate of Q, should be used. 

Limitations 

Equations 3 through 8 should provide reliable estimates 

of t-year floods for rural basins in Davidson County and for 

urban basins that are within the size and development range 

of the gaged urban basins. They are not applicable for small 

basins that are highly developed or basins that have undergone extensive drainage system improvements. Us of the e ua- tions for urban basins draining less than 1.5 mi B (3.88 km8 

or for basins containing more than 50 percent impervious area 

is not recommended. 

-3o- 
SUMMARY AND CONCLUSIONS 

The U. S, Geological Survey rainfall-runoff simulation 

model was applied to 14 gaged basins in Davidson County to 

reduce the time-sampling bias of the obs 1 rved data. The basins ranged in size from 1.58 to 64.0 mi (4.09 to 165.8 km*) 

and in development from 3 to 37 percent impervious area. 

Calibrated model parameters were used with long-term climatological data to simulate annual peak discharges and to derive 

discharge-frequency curves for the basins. Six selected 

recurrence-interval (t-year) floods, based on observed and 

simulated data, were weighted to provide eetimates of the 

flood-frequency characteristics of the 14 stations. 

The t-year floods from the gaged urban basins in 

Davidson County are not significantly larger than those from 

rural basins. Lag times between rainfall and runoff in the 

urban basins showed little or no decrease as compared to 

those of rural basins. Consequently, regional equations for 

estimating peak runoff from rural basins should be reliable 

estimators of t-year floods from urban basins in Davidson 

County within the size and development range of the gaged 

urban basins. 

Data are needed from smaller basins, with more intense 

development than was sampled, to determine whether the results of this report would be applicable to them. 

-31. 
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in northern Virginia: U, S, Geol. Survey Water-Supply 

Paper 2001-C. 22 p* 

Clark, C, 0.. 1945, Storage and the unit hydrographi Am. 

Sou. civil Bngfneer8 Trans., ve .llO, pa 141%14880 

Corm, L. G,, and Boyd, E. B., 1975, Flood information for 

selected streams in Nashville-Davidson County, 

Tennessee: U, S, Geol. openfile rept., 81 p* 

Dawdy, D. R,, Lichty, R. W., and Bergmann, J, #I., 1972, 

A rainfall-runoff simulation model for estimation of 

flood peaks for small drainage basins: U, S. Geol. 

Survey Prof. Paper 506-B. 28 pm 

Dempster, G. R., 1974, Effects of urbanization on floods in 

the Dallas, Texas, metropolitan area: U, S, Geol. 

Survey Water Resources Inv. 60-73, 51 pa 

Durbin, T. J., 1974, Digital simulation of the effect8 of 

urbanization on runoff in the upper Santa Ana Valley, 

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41-73, 44 pm 

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

v* 5. p. 399-417. 

Johnson, S. L., and Sayre, D. M., 1973, Effects of urbanieation on floods in the Houston, Texas metropolitan area1 

U. S, Geol. Survey Water Resources Inv, 3-73, 50 pm 

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

determine the flows of Irish arterial drainage channels8 

Proc. Inst. Civil Engineers, v, 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. 

Putnam, A. L., 1972, Effect of urban development on floods 

in the Piedmont Province of North Carolina, U, S. Geol. 

Survey open-file rept,, 87 p. 

-32- 
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 determining flood flow frequency: U, S. Water Resources 

Bull. 17, 196 p. 

Wibben, H, C., 1976, Application of the U, S. Geological 

Survey rainfall-runoff simulation model to improve floodfrequency estimates on small Tennessee streams. U, Se 

U. S. Geol. Survey Water Resources Inv. 76-120, 51 PO 

-330