U.S. Department of the Interior

U.S. Geological Survey

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 9

Computer Programs for Describing the 

Recession of Ground-Water Discharge and 

for Estimating Mean Ground-Water 

Recharge and Discharge from Streamflow 

Records—Update

A Contribution of the 

Regional Aquifer-System Analysis Program

8-4148
U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 9

Computer Programs for Describing the 

Recession of Ground-Water Discharge and 

for Estimating Mean Ground-Water 

Recharge and Discharge from Streamflow 

Records—Update

A Contribution of the 

Regional Aquifer-System Analysis Program

8-4148

By A.T. Rutledge

Reston, Virginia

1998

(Supercedes Water-Resources Investigations Report 93-4121)
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Thomas Casadevall, Acting Director

For additional information write to: Copies of this report can be purchased

from:

U.S. Geological Survey

Information Services

Box 25286

Federal Center

Denver, CO 80225

The use of firm, trade, and brand names in this report is for identification purposes 

only and does not constitute endorsement by the U.S. Geological Survey.

Ground Water Specialist

Northeastern Region

U.S. Geological Survey

433 National Center

Reston, VA 20192
PREFACE

Preface III

This report is an update on the programs that were first documented by Rutledge (1993). Most of the differences between the old and new programs are 

improvements in program output and messages to prevent the incorrect use of the 

programs. The basic mathematical procedures executed by the programs are 

unchanged.

The computer programs and related files will be available for downloading 

over the Internet from a USGS software repository. The public anonymous FTP 

site is on a Water Resources Division server (ftprvares.er.usgs.gov or 

130.11.51.209) in the /pub/arutledg/sf.programs directory.

Contents V

CONTENTS

 Page

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

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

 Applicability of methods........................................................................................................... 2

 Overview of programs and files................................................................................................ 3

 Compiling, loading, and executing programs ........................................................................... 4

 Preparation of data files ............................................................................................................ 4

 Catalogue file STATION.............................................................................................. 6

 Creating daily-values files ........................................................................................... 6

 Screening daily-values files......................................................................................... 9

Computer programs for describing the recession of ground-water discharge....................................... 9 

Mathematical basis .................................................................................................................... 9

 Program RECESS ..................................................................................................................... 11

 The algorithm............................................................................................................... 12

 Program execution ....................................................................................................... 12

 Output files .................................................................................................................. 15

 Program CURV ......................................................................................................................... 17

Computer program for estimating mean ground-water recharge .......................................................... 17

 Theory and method development.............................................................................................. 19

 Program RORA......................................................................................................................... 21

 The algorithm............................................................................................................... 21

 Program execution ....................................................................................................... 24

 Output files .................................................................................................................. 25

 Comparison of results of manual and computerized methods .................................................. 27

 Sensitivity to variations in recession index............................................................................... 29

 Sensitivity to variations in the requirement of antecedent recession ....................................... 31

Computer program for estimating mean ground-water discharge......................................................... 33

 Method development................................................................................................................. 33

 Program PART .......................................................................................................................... 34

 The algorithm............................................................................................................... 34

 Program execution ....................................................................................................... 34

 Output files .................................................................................................................. 36

 Comparison of results of manual and computerized methods .................................................. 38

Comparison of estimates of recharge and discharge ............................................................................. 39

Summary................................................................................................................................................ 40

References cited..................................................................................................................................... 41
VI Contents

FIGURES

Page

1. Diagram showing recommended order of procedures for preparing data 

files and executing the programs documented in this report .................................................. 5

2. Diagram showing example of daily-values z-file constructed by 

program TRANS..................................................................................................................... 7

3-11. Graphs showing:

3. Schematic representation of the method used to determine the master recession 

curve: (A) selected recession segments, (B) recession index (K) and best-fit line, 

and (C) the master recession curve, obtained from coefficients of function in B .................. 12

4. Example of graphical output generated on the computer monitor by program 

RECESS for the purpose of user selection of a near-linear recession segment 

for analysis.............................................................................................................................. 13

5. Example of graphical representation of the master recession curve that 

can be generated from program output files: (A) plot showing each individual 

recession segment with time adjusted so that the segments fall on the master 

recession curve, and (B) plot showing the exact mathematical equation that is 

the master recession curve .................................................................................................... 18

6. Procedure for use of the recession-curve displacement method to estimate 

ground-water recharge in response to a recharge event ........................................................ 20

7. Schematic of hydrograph and flow diagram showing the procedures executed

for each peak in the recession-curve displacement method .................................................. 22

8. Example hydrograph of streamflow graphically showing decisions and 

calculations performed by program RORA ........................................................................... 26

9. Relation between annual recharge estimated by program RORA and by the 

manual method for each year analyzed for each station......................................................... 28

10. Change in the estimate of recharge from program RORA that results from 

changing the recession index to 0.5 times and 1.5 times its default value ............................. 30

11. The change in the number of peaks detected and the change in the estimate 

of recharge from program RORA that results from increasing the requirement

of antecedent recession to values that are 1 day and 2 days larger than default..................... 32

12. Flow diagram showing the procedure of streamflow partitioning.......................................... 35

13. Hydrographs showing the results of streamflow partitioning................................................. 37

14. Relation between the mean ground-water recharge estimated by program 

RORA and the mean ground-water discharge estimated by program PART.......................... 39
Contents VII

TABLES

1. Streamflow-gaging stations used for comparisons between results 

of program RORA and results of the manual application of the 

recession-curve displacement method .................................................................................... 27

2. Published results of base-flow record estimation and results from

 program PART ...................................................................................................................... 38

CONVERSION FACTORS

 Multiply by To obtain 

inch (in.) 2.54 centimeter

foot (ft) 0.3048 meter

foot squared per day (ft2

/d) 0.09290 meter squared per day

inch per year (in/yr) 2.54 centimeter per year

cubic foot (ft3) 0.02832 cubic meter

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

cubic foot per second per 0.01093 cubic meter per second

 square mile (ft3/s)mi2 per square kilometer 

1

Computer Programs for Describing the 

Recession of Ground-Water Discharge and 

For Estimating Mean Ground-Water Recharge 

and Discharge from Streamflow 

Records—Update

By A.T. Rutledge

Abstract

The computer programs included in this report can be used to develop a mathematical 

expression for recession of ground-water discharge and estimate mean ground-water recharge 

and discharge. The programs are intended for analysis of the daily streamflow record of a basin 

where one can reasonably assume that all, or nearly all, ground water discharges to the stream 

except for that which is lost to riparian evapotranspiration, and where regulation and diversion 

of flow can be considered to be negligible. The program RECESS determines the master recession curve of streamflow recession during times when all flow can be considered to be groundwater discharge and when the profile of the ground-water-head distribution is nearly stable. The 

method uses a repetitive interactive procedure for selecting several periods of continuous recession, and it allows for nonlinearity in the relation between time and the logarithm of flow. The 

program RORA uses the recession-curve displacement method to estimate the recharge for each 

peak in the streamflow record. The method is based on the change in the total potential groundwater discharge that is caused by an event. Program RORA is applied to a long period of record 

to obtain an estimate of the mean rate of ground-water recharge. The program PART uses 

streamflow partitioning to estimate a daily record of base flow under the streamflow record. The 

method designates base flow to be equal to streamflow on days that fit a requirement of antecedent recession, linearly interpolates base flow for other days, and is applied to a long period of 

record to obtain an estimate of the mean rate of ground-water discharge. The results of programs 

RORA and PART correlate well with each other and compare reasonably with results of the corresponding manual method.
2 Computer Programs for Describing the Recession of Ground-Water Discharge

INTRODUCTION

This report documents computer programs that read data files of daily mean streamflow and then 

perform the following procedures:

1. Develop a mathematical expression that describes streamflow recession during times when all flow can 

be considered to be ground-water discharge,

2. Estimate mean ground-water recharge by use of the recession-curve displacement method, and

3. Estimate mean ground-water discharge by use of a method of base-flow record estimation.

Past work, theory, and mathematical basis for each of the procedures are described, the steps 

required to execute the programs are itemized, and the output files are explained. Where appropriate, the 

report includes comparisons between the results of the programs and results of corresponding manual 

methods.

The programs are written in Fortran-77 and do not depend on separate software (such as statistical 

or graphical software). The programs were designed for analysis of records of daily mean streamflow 

because this is the common mode by which streamflow data are stored by the U.S. Geological Survey 

(USGS). The USGS collects and stores records of daily streamflow for several thousand gaging stations 

in the United States. The programs are intended primarily for use by the worker who has access to a USGS 

data base, but some guidelines are included to allow for the transfer and analysis of data from other 

sources.

The computer programs were developed as part the USGS Regional Aquifer System Analysis 

(RASA) of the area that includes the Appalachian Valley and Ridge, Piedmont, and Blue Ridge physiographic provinces (Appalachian-Piedmont RASA, or AP-RASA) (Swain and others, 1991). Although the 

programs were developed for application in the AP-RASA project, they are documented here because of 

the potential application in other settings. This report is an update on the programs, which were first documented by Rutledge (1993). Most of the differences between the old and new programs are improvements in program output and messages to prevent the incorrect use of the programs. The basic 

mathematical procedures executed by the programs are unchanged. 

Applicability of Methods

The methods described in this report are intended for the analysis of the ground-water-flow system 

of a basin for which a streamflow-gaging station at the downstream end can be considered the only point 

of outflow. For most applications, it should be reasonable to assume that all or nearly all ground water in 

the basin discharges to the stream, except for that which is lost by evapotranspiration. The area of contribution in the ground-water system is equal to the surface-drainage area for the purpose of expressing flow 

in units of specific discharge (for example, inches per year). Regulation and diversion of flow should be 

negligible.

It is preferable, but not required, that the record of daily mean streamflow is at least several years in 

duration. Results are most useful if the programs are executed to give long-term (at least yearly) results. 

Interbasin comparisons should be made only when the programs are executed for a uniform time period 

because of climatic variations. The programs work on the basis of the calendar year. In the application of 

the methods for estimating recharge or discharge, it is preferable that the record is complete for each year 

in the period of analysis (365 or 366 daily values per calendar year). 
Introduction 3

The procedure for defining the recession of ground-water discharge selects several individual periods of continuous streamflow recession (periods during which each pair of subsequent daily values must 

meet the condition that the first value exceeds or is equal to the second). Periods of reduced precipitation 

must be long enough that the profile of the ground-water head distribution is nearly stable and groundwater discharge will plot with characteristic linearity or near-linearity on the graph of the logarithm of 

flow as a function of time. This condition may not be met for ground-water-flow systems of very low 

diffusivity (transmissivity divided by storage coefficient).

The procedure for defining streamflow recession allows for the possibility of nonlinearity in the 

relation between the logarithm of ground-water discharge and time when the profile of the ground-water 

head distribution is nearly stable. Nonlinearity can result from variation in saturated thickness, geologic 

heterogeneities, and attrition of ground water to leakage or evapotranspiration.

The methods for estimation of recharge or discharge are intended for the analysis of flow systems 

that are driven by areally diffuse recharge events that can be considered to be roughly concurrent with 

peaks in streamflow. The stream is the sink (discharge boundary) of the ground-water-flow system. 

Results of these methods may not be reliable for flow systems dominated by leakage to or from regionalflow systems, snowmelt runoff, recharge from losing streams, or ground-water withdrawals. The methods for estimating recharge or discharge should be used only if the drainage area is larger than 1 square 

mile, so that the requirement of antecedent recession will exceed the time increment of the data (1 day). 

The upper limit of drainage area may depend on the degree of nonuniformity of weather systems. Linsley 

and others (1982) suggest that the unit-hydrograph concept should not be applied for basins that are larger 

than 2,000 square miles and that the upper limit may be much smaller where convective rainfall predominates. The upper limit for the unit-hydrograph concept may also apply to the methods described here for 

estimating recharge and discharge. The author recommends that 500 square miles be used as an upper 

limit for selection of streamflow-gaging stations for data analysis.

In addition to the above, the user should assess the validity of the mathematics described in following sections to the study area. For example, the procedure for defining streamflow recession uses the 

assumption that the recession index is linearly related to the logarithm of flow, and the methods for estimating ground-water recharge and discharge use an empirical equation to estimate the number of days 

after a peak in streamflow when most flow can be considered ground-water discharge. Output of the programs allow for some degree of adjustment for variation between the real problem and the default mathematics of the programs. 

Overview of Programs and Files

This report describes three programs--RECESS, RORA, and PART.

RECESS This program determines the master recession curve (MRC) of streamflow recession during 

times when all flow can be considered to be ground-water discharge and when the profile of 

the ground-water head distribution is nearly stable. The program uses a repetitive 

interactive procedure for selecting several periods of continuous recession, determines a 

best-fit equation for the rate of recession as a function of the logarithm of flow, then uses 

the coefficients of this equation to derive the MRC, which is an equation of time as a 

function of the logarithm of flow. The program thus allows for the possibility of 

nonlinearity in the relation between time and the logarithm of flow.
4 Computer Programs for Describing the Recession of Ground-Water Discharge

RORA This program uses the recession-curve-displacement method to estimate the recharge for 

each peak in the streamflow record. The method, also called the Rorabaugh Method 

(Rorabaugh, 1964; Daniel, 1976), is based on the measurement of the change in the total 

potential ground-water discharge as estimated at critical time after the peak by extrapolation 

from the pre-peak and the post-peak recession periods. The method is applied to a long 

period of record and gives an estimate of the mean rate of ground-water recharge.

PART This program uses streamflow partitioning to estimate a daily record of base flow under the 

streamflow record. The program scans the record for days that fit a requirement of 

antecedent recession, designates base flow to be equal to streamflow on these days, then 

linearly interpolates the daily record of base flow for days that do not fit the requirement of 

antecedent recession. The program is applied to a long period of record to give an estimate 

of the mean rate of ground-water discharge.

Other support programs included are TRANS, which translates data into a format that can be read 

by the programs above; and CURV, which reads an output file from program RECESS, then creates a simple file that can be used as input to separate graphical software from which an MRC can be drawn. Other 

files that are included with this documentation include STATION, which is a data file that consists of properties of the gaging stations of interest, and OUTREC.SUM, OUTRORA.SUM, and OUTPART.SUM, 

which are headings for output files of programs RECESS, RORA, and PART, respectively. Other output 

files are automatically created when the programs are executed. Read files are included in the computer 

directory that give example input and output for the computer programs, using streamflow data files that 

are also included in the directory.

Compiling, Loading, and Executing Programs

All five programs, which are provided in the form of Fortran source code, should be compiled and 

loaded at one time before execution. The keyboard should be kept in lower case when working with these 

programs. Although file names in this publication are in upper case letters, the actual file names are in 

lower case if the computer operating system is case sensitive.

One way to compile and load on a Data General AViiON Workstation, is to enter the command

ghf77 program.f -o program.b

This creates an executable file "program.b" from the original fortran file "program.f."

The programs should be executed later, according to the steps recommended in following sections. 

One way to execute the program is to enter program.b on the Data General AViiON Workstation.

Preparation of Data Files

Before the programs RECESS, RORA, or PART can be executed, steps must be taken to prepare 

required data files. After these procedures (illustrated as steps 1-3 in fig. 1) are completed, any one of 

RECESS, RORA, or PART can be executed. The user might execute RECESS before RORA to obtain 

the median recession index, which program RORA can read from file OUTREC.SUM.
Introduction 5

 Step 2 can be executed before step 1. In addition,

1. The second step can be performed by retrieval from a USGS data

base. If the user obtains data from another source, then steps 2 

and 3 could be superseded by customized methods. These methods

should result in daily values z-files as described in figure 2.

2. It is recommended (but not required) that RECESS be executed before

RORA so that RORA can obtain the median recession index from a 

file that is filled by RECESS (file OUTREC.SUM). Otherwise, the user

will be required to enter the median recession index interactively during

execution of RORA.

Figure 1. Recommended order of procedures for preparing data files and executing the programs documented in this report.

Add one line to file STATION for each streamflow station

Obtain daily-values files of streamflow in “2 and 3 card”

format for each station1

Prepare daily-values z-file using program TRANS for each station1

Program RECESS Program RORA Program PART

Program CURV

Step 1

Step 2

Step 3

2

2
6 Computer Programs for Describing the Recession of Ground-Water Discharge

Catalogue File STATION

The user should add a one-line entry to file STATION for each streamflow-gaging station of interest. 

Each line of file STATION gives the following information for a station: 

(1) latitude in degrees, minutes, and seconds (columns 1-6), 

(2) longitude in degrees, minutes, and seconds (columns 7-13), 

(3) an optional two-digit sequential number (usually left blank, columns 14-15), 

(4) the USGS eight-digit gaging-station number (columns 16-23), 

(5) the drainage area, in square miles (columns 24-31), 

(6) the name of the daily-values z-file (columns 34-49), and 

(7) an abbreviated station name (columns 53-80). 

The user can observe this format list for all new entries: A6, A7, A2, A8, 1F8.2, 2X, A16, 3X, A29. 

Alternatively, entries in the version of STATION that is included with this report can be used as guides to 

the correct format. The only items that are required are the drainage area and the name of the daily-values 

z-file (the latter should be a short, unique name for the stream preceded by the letter "z"). The USGS eightdigit number may also be required depending on options selected in the execution of the program TRANS. 

Other items could be left blank, but it is recommended that they are filled in for the purpose of clarity. The 

line in STATION that corresponds to a given station can be automatically written to the daily-values z-file 

when program TRANS is executed. Although the entry of data to STATION is illustrated as step 1 in figure 1, data could be entered after step 2. It is nonetheless recommended that step 3 be executed after step 

1 so that program TRANS will read data from STATION.

Creating Daily-Values Files

Programs RECESS, RORA, and PART read data from a daily-values z-file (fig. 2). If the user has 

access to a USGS data base, the z-files are created in two steps: (1) obtaining a daily-values file from the 

data base in the "2 and 3-card" format, and (2) translating the data from this file to a z-file using program 

TRANS. Each of these steps, illustrated as steps 2 and 3 in figure 1 and described below, can be executed 

for several streamflow stations at one time.

A data file of daily mean streamflow can be obtained from a USGS data base by use of ADAPS. The 

menu options to "retrieve/write ADAPS data" followed by "retrieve/write daily-values data" are selected. 

Calendar years are selected ("years beginning January"). The time period of the retrieval should begin 

after 1890 and must not exceed 120 years in duration because of dimension limitations of the programs 

documented here. For the "station" option, the 8-digit USGS station number is entered, and the variable 

selected is "discharge in cfs." The user must enter a file name for the resulting data file that will be in "2 

and 3-card" format. The file name, which should be 14 characters or less, must be identical to the file name 

listed in file STATION, without the "z" at the beginning (the z-file will be created with program TRANS). 

The user should enter the option for "DV card output," and the statistic code should be 3 (which represents 

the mean value). When the prompt is "final data only?," the user should push the “enter” key.
Introduction 7

LAT--LONG..... .STA.#... DR.AREA.. FILENAME......................STA.NAME.............

 3739570795422 02018000 329.00 zcraug CRAIG CR AT PARR

 

THIS FILE NAME:zcraig

THIS FIRST “2 CARD” IN THE ORIGINAL ADAPS FILE:

 2 02018000 00060000003 ENT

-999=before period of record, -99=missing data, -9999=nonexistnet date: ADAPS retrieval=1993 

MAXIMUM ON RECORD:

 21000.00

MINIMUN ON RECORD:

 25.00 

Figure 2. Example of daily-values z-file constructed by program TRANS. (The record for this station is actually complete from April 1, 

1925, to the date of this publication. The above illustrates the entire z-file that would result if the last day of record were December 31, 

1926.)

1925 1 2 3 4 5 6 7 8 9 10 11 12

1 -999.00 -999.00 -999.00 150.00 900.00 75.00 78.00 40.00 42.00 46.00 85.00 82.00

2 999.00 -999.00 -999.00 150.00 708.00 68.00 68.00 42.00 47.00 51.00 82.00 78.00

3 -999.00 -999.00 -999.00 140.00 557.00 64.00 59.00 43.00 45.00 56.00 83.00 92.00

4 999.00 -999.00 -999.00 140.00 472.00 62.00 58.00 42.00 43.00 60.00 86.00 88.00

5 999.00 -999.00 -999.00 132.00 419.00 64.00 59.00 43.00 39.00 59.00 85.00 92.00

6 999.00 -999.00 -999.00 129.00 344.00 67.00 59.00 46.00 39.00 52.00 85.00 98.00

7 999.00 -999.00 -999.00 103.00 282.00 75.00 71.00 49.00 40.00 48.00 85.00 118.00

8 999.00 -999.00 -999.00 99.00 260.00 72.00 57.00 48.00 38.00 47.00 88.00 116.00

9 999.00 -999.00 -999.00 96.00 234.00 77.00 72.00 46.00 38.00 48.00 94.00 111.00

10 999.00 -999.00 -999.00 92.00 247.00 78.00 72.00 43.00 38.00 46.00 125.00 107.00

11 999.00 -999.00 -999.00 107.00 252.00 67.00 59.00 42.00 36.00 46.00 135.00 103.00

12 999.00 -999.00 -999.00 125.00 472.00 58.00 55.00 45.00 38.00 46.00 164.00 103.00

13 999.00 -999.00 -999.00 116.00 557.00 57.00 51.00 51.00 60.00 49.00 1290.00 101.00

14 999.00 -999.00 -999.00 109.00 500.00 57.00 46.00 47.00 78.00 55.00 616.00 96.00

15 -999.00 -999.00 -999.00 101.00 419.00 56.00 51.00 49.00 62.00 82.00 368.00 92.00

16 -999.00 -999.00 -999.00 90.00 368.00 60.00 51.00 42.00 58.00 143.00 264.00 99.00

17 -999.00 -999.00 -999.00 85.00 301.00 67.00 56.00 41.00 50.00 107.00 207.00 99.00

18 -999.00 -999.00 -999.00 101.00 269.00 75.00 62.00 39.00 54.00 82.00 167.00 101.00

19 -999.00 -999.00 -999.00 107.00 239.00 74.00 56.00 43.00 55.00 72.00 146.00 98.00

20 -999.00 -999.00 -999.00 98.00 214.00 68.00 51.00 47.00 57.00 69.00 129.00 92.00

21 -999.00 -999.00 -999.00 90.00 188.00 59.00 77.00 47.00 49.00 64.00 125.00 96.00

22 -999.00 -999.00 -999.00 111.00 171.00 56.00 49.00 46.00 49.00 63.00 111.00 103.00

23 -999.00 -999.00 -999.00 226.00 154.00 55.00 55.00 46.00 49.00 63.00 103.00 111.00

24 -999.00 -999.00 -999.00 305.00 140.00 60.00 49.00 42.00 49.00 67.00 96.00 137.00

25 -999.00 -999.00 -999.00 247.00 129.00 80.00 49.00 39.00 47.00 85.00 92.00 140.00

26 -999.00 -999.00 -999.00 214.00 120.00 80.00 52.00 38.00 48.00 143.00 88.00 149.00

27 -999.00 -999.00 -999.00 247.00 107.00 92.00 47.00 38.00 46.00 191.00 94.00 122.00

28 -999.00 -999.00 -999.00 247.00 101.00 88.00 46.00 39.00 38.00 129.00 96.00 114.00

29 -999.00 -9999.00 -999.00 1180.00 94.00 146.00 43.00 38.00 44.00 103.00 88.00 120.00

30 -999.00 -9999.00 -999.00 1040.00 86.00 109.00 42.00 38.00 44.00 90.00 83.00 114.00

31 -999.00 -9999.00 -999.00 -9999.00 78.00 -9999.00 42.00 39.00 -9999.00 85.00 -9999.00 103.00

1926 1 2 3 4 5 6 7 8 9 10 11 12

1 99.00 1650.00 586.00 900.00 181.00 90.00 48.00 116.00 64.00 52.00 96.00 319.00

2 99.00 1200.00 586.00 677.00 171.00 85.00 47.00 88.00 62.00 56.00 108.00 310.00

3 98.00 900.00 586.00 586.00 164.00 82.00 47.00 72.00 63.00 82.00 85.00 273.00

4 107.00 803.00 500.00 500.00 157.00 78.00 55.00 62.00 62.00 68.00 79.00 255.00

5 120.00 771.00 472.00 446.00 149.00 80.00 58.00 58.00 58.00 65.00 76.00 238.00

6 135.00 708.00 419.00 394.00 140.00 86.00 116.00 67.00 60.00 59.00 73.00 229.00

7 151.00 616.00 472.00 344.00 135.00 88.00 103.00 103.00 62.00 54.00 73.00 205.00

8 164.00 586.00 1040.00 344.00 132.00 92.00 78.00 67.00 67.00 52.00 72.00 189.00

9 291.00 586.00 803.00 368.00 129.00 72.00 67.00 72.00 63.00 51.00 79.00 201.00

10 177.00 557.00 646.00 419.00 132.00 69.00 59.00 54.00 59.00 50.00 121.00 301.00

11 140.00 472.00 557.00 394.00 132.00 64.00 55.00 49.00 55.00 50.00 213.00 557.00

12 135.00 368.00 528.00 740.00 129.00 62.00 56.00 44.00 50.00 48.00 168.00 472.00

13 107.00 446.00 472.00 1040.00 135.00 62.00 57.00 51.00 48.00 54.00 143.00 646.00

14 107.00 835.00 446.00 1200.00 137.00 60.00 57.00 45.00 48.00 60.00 129.00 835.00

15 103.00 2890.00 394.00 1040.00 132.00 59.00 57.00 44.00 48.00 70.00 186.00 646.00

16 94.00 1380.00 394.00 835.00 160.00 57.00 55.00 54.00 48.00 69.00 5310.00 528.00

17 96.00 900.00 394.00 708.00 239.00 55.00 52.00 63.00 47.00 66.00 1650.00 446.00

18 1120.00 740.00 394.00 586.00 239.00 55.00 48.00 57.00 46.00 63.00 970.00 394.00

19 4970.00 708.00 446.00 500.00 199.00 55.00 46.00 50.00 46.00 60.00 835.00 310.00

20 1950.00 708.00 528.00 419.00 177.00 62.00 45.00 264.00 45.00 63.00 646.00 287.00

21 1040.00 646.00 557.00 368.00 157.00 59.00 44.00 301.00 46.00 65.00 500.00 319.00

22 970.00 557.00 500.00 344.00 146.00 64.00 42.00 191.00 46.00 72.00 394.00 2640.00

23 803.00 500.00 472.00 319.00 132.00 67.00 40.00 129.00 46.00 68.00 319.00 2060.00

24 646.00 419.00 446.00 301.00 122.00 63.00 52.00 118.00 46.00 73.00 273.00 1200.00

25 528.00 500.00 394.00 278.00 116.00 58.00 51.00 129.00 46.00 205.00 238.00 1290.00

26 419.00 1380.00 394.00 252.00 107.00 57.00 57.00 154.00 47.00 296.00 229.00 9090.00

27 394.00 900.00 446.00 230.00 107.00 55.00 85.00 151.00 45.00 197.00 319.00 3020.00

28 319.00 708.00 394.00 214.00 103.00 52.00 62.00 120.00 45.00 148.00 394.00 1560.00

29 273.00 -9999.00 368.00 207.00 103.00 50.00 62.00 96.00 46.00 121.00 368.00 2520.00

30 230.00 -9999.00 344.00 191.00 98.00 48.00 96.00 77.00 51.00 103.00 344.00 1560.00

31 305.00 -9999.00 528.00 -9999.00 92.00 -9999.00 214.00 69.00 -9999.00 99.00 -9999.00 1120.00

9999
8 Computer Programs for Describing the Recession of Ground-Water Discharge

Program TRANS is executed to translate data from the data file that is in "2 and 3-card" format to a 

daily-values z-file. When executed, TRANS will prompt the user to enter the date of the retrieval, which 

will be written to the top of every z-file to be created. The program then initiates a repetitive process of 

reading a file in the "2 and 3-card" format and creating a corresponding z-file, then moving on to the next 

"2- and 3-card" file. The user is given the choice of controlling this process by manually entering the name 

of each file to read, or letting the program automatically read every daily-values file that is listed in STATION. If the manual option is picked, the user is prompted for the name of each daily-values file, and 

should enter the same name as given during the retrieval. The name of the resulting z-file will be identical 

to this with the exception of the letter "z," which will be placed at the beginning. If the automatic option 

is picked, the program will read each line in STATION and (for each) will read the file in the directory that 

has the same name as the file name without the z at the beginning, then will create a new z-file which will 

have a name that is identical to the z-file name in STATION. The automatic procedure will terminate when 

a blank line is reached in STATION. In the automatic procedure, program TRANS writes the single-line 

entry for the station of interest to the top of the z-file, for identification purposes. The reading of STATION 

is optional for each file when the manual procedure is used. Program TRANS writes other information 

near the top of the z-file, such as the first "2 card" from the original daily-values file obtained from the 

USGS data base. This information could serve as a verification check that the correct data retrieval was 

made. Program TRANS determines the maximum and the minimum streamflow for the station, then 

writes this information near the top of the z-file (fig. 2). The range of streamflow is used by program 

RECESS for determining the limits of simple graphics that can be produced during execution.

If the user obtains a daily record of streamflow from a source other than USGS data files, it may be 

necessary to construct z-files by customized methods. The z-file must be in a particular format so that it 

can be read by programs RECESS, RORA, and PART. For construction of these z-files, the user can 

observe the format illustrated in figure 2 and the statements in program TRANS that write to unit 10. The 

following guidelines also could be useful:

1. The reading program will skip all lines until it reads the line with the word MAXIMUM (beginning at 

the third space). After this, the program reads the maximum on the next line, skips the next line, reads 

the minimum, and begins a repetitive procedure of reading data for each year of record. For simplicity, a customized z-file could begin with the line with the word MAXIMUM.

2. Each line that indicates a year is read with the format I4.

3. If the year is 9999, the program stops reading. Therefore, the number 9999 should be written at the bottom of the z-file.

4. Each line that indicates a year is followed by 31 lines that are written with the format I4,12(1F9.2,1A1). 

The F9.2, which is for the daily streamflow, can be alternatively written F9.1 or F9.0. The 1A1 is 

reserved for a character that can indicate whether the streamflow that precedes it is an estimate 

(because this field has not been used as of the time of this publication, the user could use it for any 

purpose). 

5. Each of the 31 lines that follows a year consists of the day of the month (first number on the left) 

followed by the daily streamflow on that day of January, then February, and so on, ending with 

December.

6. Nonexistent dates (such as February 31) are indicated with a streamflow of -9999. Missing data on real 

dates are indicated with a streamflow of -999 for days that precede the period of record or with 

streamflow of -99 for days that occur within gaps in record.
Computer Programs for Describing the Recession of Ground-Water Discharge 9

Screening Daily-Values Files

The original versions of these programs (Rutledge, 1993) included an auxiliary program STREAM. 

The purpose of this program was to allow the user to determine the completeness of the streamflow 

record, using a tabulation of the number of daily values of streamflow for each calendar year on a given 

z-file. This was needed because the original versions of programs RORA and PART should only be executed for periods of complete calendar years of record (365 or 366 values per year). The program 

STREAM allowed the user to determine when periods of complete record exist prior to executing RORA 

or PART. Because the present versions of RORA and PART will generate a tabulation showing the completeness of the streamflow record, the program STREAM is not included here. It is also worthy of note 

that the present versions of RORA and PART allow greater flexibility for application if there is missing 

record at the beginning or end of the period of interest. 

COMPUTER PROGRAMS FOR DESCRIBING THE RECESSION OF 

GROUND-WATER DISCHARGE

The mathematical description of the recession of ground-water discharge can be useful for estimating aquifer diffusivity and for discerning qualitative similarities or dissimilarities between ground-waterflow systems of various basins. There may also be applications in the comparison of ground-water-supply potential of various basins and the estimation of the rate of loss of ground water to evapotranspiration 

or the rate of leakage to regional ground-water-flow systems.

 Mathematical Basis

For the purpose of this report, the master recession curve (MRC) represents the recession of streamflow during times when all flow is from ground-water discharge, when no ground-water recharge is 

occurring, and when the profile of the ground-water head distribution is nearly stable. The MRC is usually assembled from numerous intervals of continuous recession; thus, it illustrates the recession that 

would occur given a period without direct surface runoff that is greater than any such time period in the 

original data. The matching strip method has been used for assembly of the MRC (Snyder, 1939; Toebes 

and Strang, 1964; Nathan and McMahon, 1990). The MRC is often constructed from non-summer data, 

so that the result will not be affected by evapotranspiration.

Although the linear model of streamflow recession (on the graph that shows flow on a logarithmic 

scale as a function of time on a linear scale) may be applicable (Barnes, 1939; Ineson and Downing, 

1964; Rorabaugh, 1964; Bevans, 1986), many factors can cause nonlinearity, most of which cause continuous variation in recession slope as streamflow recedes. Physical and mathematical models have 

shown that the presence of the moving free surface (water table) can cause nonlinearity of streamflow 

recession for a stream fed by an unconfined aquifer (Ibrahim and Brutsaert, 1965; Hornberger and others, 

1970), and this nonlinearity can be enhanced by variable head at the ground-water-outflow boundary 

(Werner and Sundquist, 1951; Singh, 1969; Singh and Stall, 1971). Nonlinearity can result from the gain 

or loss of ground water because of leakage or evapotranspiration (Singh, 1969; Daniel, 1976) or from 

geologic heterogeneities in the basin (Horton, 1933; Riggs, 1964; Ineson and Downing, 1964; Trainer and 

Watkins, 1974, 1975; Petras, 1986). Anderson and Burt (1980) suggest that curvature can result from 

"combined changes in the slope and size of the saturated wedge." Wood and others (1972) developed 

nonlinear MRC’s for several streams in eastern Pennsylvania, and Nutbrown and Downing (1976) indi-
10 Computer Programs for Describing the Recession of Ground-Water Discharge

cate that nonlinearity can be common for even the simplest of ground-water systems in England. The 

methods described here allow for the possibility that the MRC can be nonlinear.

For the purpose of constructing the MRC, it is assumed that the nonlinearity of the MRC is slight 

compared with the nonlinearity of streamflow recession during times when surface (direct) runoff is significant or when the profile of the ground-water head distribution has not yet become nearly stable. Therefore, it is possible to extract segments of continuous recession from the record and select "near-linear" 

parts of each segment that are indicative of the MRC. As a mathematical convenience, it is assumed that 

the recession index, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of flow (LogQ). Because the actual relation may be more complex for a given stream, the user has 

the opportunity to test the validity of this assumption.

The method described here includes the selection of several individual segments of continuous 

recession only--periods during which each pair of subsequent daily values must meet the condition that 

the first value exceeds or is equal to the second. The resulting tendency to avoid time periods during which 

some recharge might be occurring is different from the approach taken in use of many manual methods; 

that is, simply connecting the minimums or roughing-in a straight line over a part of the hydrograph that 

shows a period of general downward trend. These manual methods can be crude because they are based 

on the tacit assumption of no recharge during the period. Conversely, the method of selecting only segments of continuous recession can be disadvantageous because it requires periods of reduced precipitation 

that are of sufficient duration that the recession of ground-water discharge can obtain the characteristic linearity or near-linearity that will develop when the profile of the ground-water head distribution is nearly 

stable. As mentioned previously, this condition may not be met for ground-water-flow systems of very 

low diffusivity (transmissivity divided by storage coefficient). Analysis of such systems may require other 

methods of estimation.

 The computerized method described in this report involves the automatic location of a period of 

continuous recession, the display of the recession period for user evaluation, and the manual selection of 

the part of the recession period that is representative of the MRC. The recession period is displayed as 

streamflow as a function of the number of days since the last peak. In most cases, the data at the beginning 

of the recession period should not be used because a significant part of the streamflow is surface runoff or 

interflow. The duration of time after a peak in streamflow during which the components of streamflow 

due to surface runoff and interflow are significant can be estimated from the following empirical relation 

(Linsley and others, 1982:

(1)

where

 N is number of days after the peak, and

 A is drainage area in square miles.

The presence of surface runoff or interflow at the beginning of the recession period is usually evident 

from an upward departure (on the graph of the logarithm of flow as a function of time) for the first few 

days of the period, relative to the general trend of data later in the recession period. 

 After surface runoff has ceased, there may still be an upward departure (on the graph of the logarithm of flow as a function of time) relative to the linear extrapolation of data from later in the recession 

period. This can happen because the profile of the ground-water head distribution, soon after the recharge 

N A0.2 =
Computer Programs for Describing the Recession of Ground-Water Discharge 11

event, has not yet obtained a nearly stable shape. An estimate of the amount of time after a recharge event 

(or peak) during which nonlinearity may result from this effect can be obtained from Rorabaugh (1964), 

who expressed ground-water discharge to a stream as an infinite series function of time after the recharge 

event; he found, however, that the function can be approximated after "critical time" by an equation that 

expresses the logarithm of ground-water discharge as a linear function of time. Critical time is expressed 

by the following equation (Rorabaugh, 1964):

(2)

where 

 Tc is critical time (T), 

 a is the average distance from the stream to the hydrologic divide (L), 

 S is the storage coefficient, and 

 TR is transmissivity (L2/T).

A formulation that gives critical time as a function of the streamflow recession rate can be obtained 

by combining equation 2 with the following equation from Rorabaugh and Simons (1966):

(3)

where K is the recession index (T), which is the time required for ground-water discharge to decline 

through one log cycle after critical time. By solving for (a2)S/TR, and substituting into equation 2, Tc can be expressed as:

 (4)

The strict conclusion from the preceding analysis--that no recession data should be used until a 

period of time after the peak that is approximately one-fifth of the recession index--is not valid for all 

recession periods. The computer program displays the streamflow on each day since the last peak, where 

the last peak is operationally defined as the last day on which the daily streamflow exceeded streamflow 

of both the day that precedes it and the day that follows it. If this peak was caused by a minor precipitation event resulting in negligible recharge, then the period of nonlinearity may be much shorter than critical time. Equation 4 can be used as an estimate of the duration of time during which instability in shape 

of the ground-water profile might cause nonlinearity for large recharge events. Equation 4 is approximate 

because Rorabaugh’s model is based on an aquifer in which permeability, storage coefficient, and aquifer 

thickness do not vary in space or time. 

Program RECESS

Program RECESS uses a combination of interactive and automatic procedures to calculate the 

mathematical expression for the MRC for a streamflow-gaging station. Because of the reliance on user 

decisions for the selection of recession segments, allowances should be made to ensure consistency in 

program execution, especially if the program is used to compare recession properties of various stations. 

In such situations it is advisable that only one user works with the program. Some experimentation with 

the program may be useful prior to doing the analysis. 

Tc 0.2 a2 ( )S

TR = ----------------------

K 0.933 a2 ( )S

TR = ----------------------------

Tc 0.2144 K = ×
12 Computer Programs for Describing the Recession of Ground-Water Discharge

The Algorithm

The basic steps for determining the MRC are illustrated in figure 3. First, the program locates periods of streamflow recession and allows the user to select nearly-linear segments (fig. 3A). Then, for each 

segment, the program determines the best linear equation for time as a function of LogQ (logarithm of 

flow), and extracts from this equation a coefficient that is the recession index (K) of the segment (data 

points, fig. 3B). The program then determines the best linear equation for K as a function of LogQ, which 

is the line in Figure 3B. Coefficients of this equation are used to obtain the MRC (fig. 3C), which is a 

second-order polynomial expression for time as a function of LogQ. These steps are described in greater 

detail below.

Program Execution

Before program execution, one line must exist in file STATION and one daily-values z-file must be 

prepared for each gaging station of interest. File OUTREC.SUM, which is an output file for program 

RECESS, must also exist (see “Overview of Programs and Files”).

When the program is executed, it asks for the number of days to be displayed on the computer monitor when recession periods are displayed (default = 30). To maximize this without loss of the display of 

program menu options, the user enters the number of lines that the monitor displays minus five. Next, 

when the program asks for the file of interest, the user enters the name of the original data file that was 

obtained from the data base (the file name without the "z" in the beginning). The program actually reads 

the z-file. The program displays a monthly (and yearly) tabulation of the completeness of the streamflow 

record and finds the single-line entry in file STATION that represents the station of interest, so that the 

drainage area and other variables are known. When the program requests the time period of interest, the 

user enters the beginning and the ending calendar years as four-digit integers. It is advisable, but not 

required for this program, that the user selects a period of continuous record for analysis. Next, the program requests the months of interest. The user enters the number of months, then integers to represent 

each month. For example, if the months of interest are January, February, and December, then the user 

enters the number 3, then the numbers 1, 2, and 12. The program will detect only recession periods that 

begin in the months specified. A single letter is entered to designate the season, such as "w" for winter.

The next entry is the minimum number of days required for detection of a recession period. The 

number entered may depend on the desired degree of restrictiveness in selection, which may in turn 

A B C

MRC

LOG OF STREAMFLOW

TIME AFTER LAST PEAK

 IN STREAMFLOW

RECESSION INDEX (K) TIME

Figure 3. Schematic representation of the method used to determine the master recession curve: (A) selected recession segments, (B) recession index (K) (time per log cycle of streamflow recession)

and best-fit line, and (C) the master recession curve, obtained from coefficients of function in B. 
Computer Programs for Describing the Recession of Ground-Water Discharge 13

depend on the duration of record that is available for analysis. If the number selected is too large, then 

few recession periods will be found, and the result will be poor definition of the MRC. If the number is 

too small, then too many recession periods will be detected, and the user may be required to skip the analysis of many. For the analysis of streamflow-gaging stations in the APRASA project, the number entered 

is generally 10 to 20. Records for most of these stations are 15 to 40 years in duration. 

The program then starts a procedure of searching through the period of interest from the start to the 

end, detecting periods of recession, allowing the user to select a near-linear segment to be included in analysis, and proceeding to the next period of recession. With each new period of recession, the program displays the data in graphic (fig. 4) or tabular form and gives the user various options for the course of action, 

as itemized below. The only options that will cause the program to proceed to the next period of recession 

are "r" and "a." The number of periods skipped depends on the desired number of periods to analyze. As 

a rough guideline, a satisfactory execution of program RECESS might include 20 to 30 periods of recession. 

For most periods of recession, option "c" should be entered before option "r." The repetitive procedure of 

searching through the record for periods of recession will be terminated if (1) the end of record is reached, 

(2) the maximum number of recession periods (50) has been reached, or (3) the user enters option "q."

| LOG Q = 1.00 3.20 |

| 1 1959 10 25 * |

| 2 1959 10 26 * |

| 3 1959 10 27 * |

| 4 1959 10 28 * |

| 5 1959 10 29 * |

| 6 1959 10 30 * |

| 7 1959 10 31 * |

| 8 1959 11 1 * |

| 9 1959 11 2 * |

| 10 1959 11 3 * |

| 11 1959 11 4 * |

| 12 1959 11 5 * |

| 13 1959 11 6 * |

| 14 1959 11 7 * |

| 15 1959 11 8 * |

| 16 1959 11 9 * |

| 17 1959 11 10 * |

| 18 1959 11 11 * |

| 19 1959 11 12 * |

| 20 1959 11 13 * |

| 21 1959 11 14 * |

| 22 1959 11 15 * |

| 23 1959 11 16 * |

| 24 1959 11 17 * |

| 25 1959 11 18 * |

| 26 1959 11 19 * |

| 27 1959 11 20 * |

| 28 1959 11 21 * |

| 29 1959 11 22 * |

| 30 1959 11 23 * |

Figure 4. Example of graphical output generated on the computer monitor by program RECESS for the purpose of user 

selection of a near-linear recession segment for analysis. (This graphic, produced by option g in the program, shows 

recession data for North Fork Shenandoah River at Cootes Store, Virginia. Each line except the first shows days since the last

peak, year, month, and day of month, followed by a graphical representation of streamflow on logarithmic scale, the range of 

which is indicated on the first line.)
14 Computer Programs for Describing the Recession of Ground-Water Discharge

 Options are the following:

g Generates a graphical representation of the data, where time is in the vertical (proceeding 

downward) and the logarithm of flow is in the horizontal. The first day shown is the first day after 

the peak, and each subsequent day is represented by one line of data. Figure 4 shows an example of 

graphical display produced by option g.

g2 Same as g except that the user can specify the starting day and the time interval between subsequent 

lines

e Changes the extremes for the graphical representation of the data to values that the user will enter 

(the minimum and the maximum logarithm of flow).

o Changes the extremes for the graphical representation of the data back to the default values (the 

logarithms of the minimum and maximum streamflow as read near the top of the daily-values z-file).

t Generates a tabular display of the data, where time proceeds in the vertical. The data displayed for 

each day include streamflow, the logarithm of streamflow, and the daily change in the logarithm of 

streamflow (log of present day’s flow minus log of previous day’s flow). The first day shown is the 

first day after the peak, and each subsequent day is represented by one line of data.

t2 Same as t except the user can specify the starting day.

a Skips the present period of recession and advances to the next period. This option is chosen if the 

user decides that the present period of recession does not favorably represent the MRC (for example, 

if the period of recession is too short or if there are variations in flow that are caused by other 

processes). This option may also be used simply to reduce the number of selected recession 

segments.

c Allows the user to select the time limits of the nearly linear segment of recession that is to be used 

(the first and the last days will be entered). As an example, this option could be used to select the 

range of day 16 to day 29 for the recession data shown in figure 4.

b Allows the user to negate the time limits that were entered after option c (this can be used if the user 

mistakenly entered a shorter time period than desired).

r Instructs the program to analyze the recession segment that has been selected--determines the bestfit linear equation of time as a function of LogQ, then extracts from this equation a coefficient that is 

the recession index of this segment (equivalent to differentiation of the equation), stores this 

recession index with the mean LogQ for the segment (this data pair, represented by a point in figure 

3B, is used later to estimate the MRC), and then proceed to the next period of recession (or to the 

end of the period of record if no more suitable periods of recession exist).

q Terminates the repetitive procedure of searching for periods of recession.

 The display options enhance the user’s ability to select recession segments that most accurately 

represent the MRC. The graphical display options (g or g2) can be used to find, on a recession period, the 

time at which near-linearity is reached. The option “e” can be used to expand the LogQ scale on these 

graphics, allowing the user to see more easily when near-linearity is reached. For example, if the default 

values for the minimum and maximum values of LogQ are 1 and 4, yet most recession data fall in the range 

of 1.5 to 3, the user can change the extremes to 1.5 and 3. The options of tabular display (t and t2) can be 

used in deciding the limits of the segment to use. For example, the column that shows the daily change in 
Computer Programs for Describing the Recession of Ground-Water Discharge 15

LogQ can be scanned from top to bottom. The condition of near-linearity may be evident when there is 

no longer a trend in these numbers with time. A trend would cause a gradual increase (or decrease) in 

the daily change from top to bottom. When observing the data in the graphical or tabular mode, the user 

should be aware that rounding of the original data will cause an apparent “stepping” in the relation 

between LogQ and time. Some tendency of stepping in the data will also be caused by the simple graphical procedure that is executed by options “g” and “g2” -- for example, the stepping evident for the nearlinear recession segment from day 16 to day 29 in figure 4. The selected recession segment should be 

long enough to define a recession slope, but short enough to be considered linear or nearly linear. 

After recession segments are selected, the program generates a list that shows for each segment, the 

mean of the LogQ, the recession index (K), and a simple graphical representation of K. Because this listing is generated in order of decreasing value of the mean of LogQ, it gives the user a rough idea of the 

relation between K and LogQ. The user has the option of eliminating outliers--values of K that depart 

significantly from the general trend. Particular types of departures that may be evident are those caused 

by prolonged periods of slight precipitation or by slight regulation of flow when flow is small. The elimination of outliers depends on the strategy of the individual program user.

Because the next procedure executed by the program is determination of the best linear equation 

for K as a function of LogQ, the user can, at this point, assess the validity of the assumed linear relation. 

The user should be aware that the graphic generated simply shows K for each ordered value of LogQ--

apparent curvature in this simple graphic can be caused by a nonuniform sampling of LogQ. Linearity 

could be tested by manually transposing some of the data pairs to a graph. A rigorous test of linearity 

between K and LogQ could be done with separate computer graphical or statistical software. The testing 

of linearity can be done after program execution because this listing is also produced in one of the output 

files (the x-file). Because subsequent calculations are based upon linearity, nonlinearity may require that 

the user exercise caution in interpretation of results, or it may require other methods for obtaining the best 

MRC. For example, discontinuities in the relation between K and LogQ might require manual estimation 

of the MRC (Trainer and Watkins, 1974, 1975). Other methods may nonetheless use the x-file.

Next, the program determines the best-fit linear equation for K as a function of LogQ (fig. 3B) by 

using only the recession segments that have not been eliminated. The program then uses the coefficients 

of this equation to derive the following polynomial expression of time as a function of LogQ:

 (5)

where 

T is time (T), and 

A, B, and C are coefficients.

This equation, which is the MRC (fig. 3C), is the result of integration of the best-fit linear equation for 

K as a function of LogQ. It is unique because at time=0, LogQ is the maximum value of the LogQ 

from all selected recession segments. The coefficients are written to file OUTREC.SUM and to the xfile.

Output Files

Results of program RECESS are written to three output files, described as follows:

T A LogQ2 = ( ) + + B LogQ ( ) C
16 Computer Programs for Describing the Recession of Ground-Water Discharge

OUTREC.SUM Each time RECESS is executed, one new line is written to the bottom of 

OUTREC.SUM. This line gives a summary of results of the session: name 

of daily-values file; single-letter designation of the season; time period of 

analysis; number of recession segments used; the minimum, median, and 

maximum recession indexes of the segments used; the minimum and 

maximum LogQ of all segments used; and the three coefficients of the 

MRC (eq. 5). Program CURV reads file OUTREC.SUM for the purpose of 

generating an x-y file for producing a graph of the MRC by use of separate 

graphics software. Program RORA will read file OUTREC.SUM to obtain 

the median value of the recession index for wintertime recession data 

(season = "w").

 X-file A new x-file gives details about one execution of RECESS. The x-file is 

assigned a name equal to the name of the original daily-values file that is 

obtained from the USGS data base, except two letters have been added to 

the beginning of the name. The first is the letter "x" and the second is the 

letter that designates the season. Included in the x-file is detailed 

information about each recession segment that was initially selected--date of 

the peak and designation of the starting and ending of the recession segment 

(days after the peak). Also included is a listing of each data pair of LogQ 

and K for each recession segment and a graphical representation of K for 

each segment. This listing is shown twice: once before and once after the 

user eliminates segments not wanted. The x-file also shows the best-fit 

linear equation for K as a function of LogQ and the resulting second-order 

polynomial that is the MRC (simple graphics of both equations also are 

shown). Because of the name of the x-file, if RECESS is executed twice 

for the same streamflow-gaging station and season, the first x-file will be 

overwritten. 

Y-file A new y-file gives detailed information about the time and flow for each 

day of each selected recession segment. The y-file is assigned a name equal 

to the name of the original daily-values file that is obtained from the USGS 

data base, except two letters have been added to the beginning of the name. 

The first is the letter "y" and the second is the letter that designates the 

season. The y-file can be used to generate a graph of each recession 

segment. One such graph could be the flow as a function of the time since 

the last peak. Another could be the flow as a function of time, where the 

time has been adjusted so that all recession segments are drawn on the same 

MRC. The variables for each day of each recession segment are the 

adjusted time, the flow, the logarithm of flow, and the unadjusted time (days 

since the last peak). In figure 5A, which is generated from a y-file, flow is 

plotted as a function of the adjusted time. Figure 5A represents an analysis 

that is deliberately simplified for illustration purposes--a rigorous analysis 

would include a larger number of recession segments. As with the x-file, if 

RECESS is executed twice for the same streamflow-gaging station and 

season, the first y-file will be overwritten. The y-file is used to illustrate 

one MRC showing each recession segment that is selected in program 

RECESS. Program CURV (described below) is used to illustrate the exact 

solution of the equations for several MRC’s on the same graph, without 

showing each recession segment.
Computer Program for Estimating Mean Ground-Water Recharge 17

Program CURV

Program CURV, which is provided here as an auxiliary program to RECESS, provides a way of displaying the MRC (eq. 5) for more than one stream on the same graph. It may also be used to display more 

than one MRC for the same stream, each representing different seasons. The flow can be drawn in units 

of specific discharge, normalizing for drainage area (the units used are cubic feet per second per square 

mile). Program CURV produces a simple output that can be read by separate graphical software. 

For execution, there should be one line in file STATION for each streamflow-gaging station of 

interest, and there should be one line in file OUTREC.SUM that represents each combination of station 

and season of interest. For example, if two MRC’s, representing the summer and the winter for one station are to be illustrated, then program RECESS must be executed for each season such that file OUTREC.SUM includes two lines for this station--one would specify "w" for winter, and the other would 

specify "s" for summer.

When executed, program CURV asks for the daily-values file name of interest. The user enters the 

name of the original data file that was obtained from the data base (the file name without the "z" in the 

beginning). Next, the program asks for the single-letter designation of the season of interest. The program then reads files STATION and OUTREC.SUM. After the appropriate lines in these files have been 

read, the program asks if there is another station of interest, and the process repeats. If the user wants an 

MRC for the same station as before but for a different season, the same daily-values file name should be 

entered, followed by the single-letter designation for the different season. 

For each combination of station and season requested, the program determines 50 evenly-spaced 

values of LogQ--from the maximum of the LogQ to the minimum of the LogQ for all recession segments 

selected in the execution of RECESS (these limits are read from OUTREC.SUM). Then, for each LogQ, 

the time (T) is calculated according to equation 5 (by use of the appropriate coefficients in OUTREC.SUM). Each pair of LogQ and time thus results in one data point for plotting the MRC. 

For each requested combination of station and season, the program writes 50 lines to its output file 

OUTCURV. Each line gives (1) time in days, (2) logarithm of flow, in cubic feet per second, (3) logarithm of flow, in cubic feet per second per square mile, (4) flow, in cubic feet per second, and (5) flow, in 

cubic feet per second per square mile. Some editing may be necessary before file OUTCURV is used as 

input to the graphical software that the user might have; for example, removal of header information at 

the top of the file. File OUTCURV was used to generate figure 5B, which results from the same recession 

data illustrated in figure 5A.

COMPUTER PROGRAM FOR ESTIMATING MEAN GROUND-WATER 

RECHARGE

The recession-curve-displacement method is a theoretically based procedure for estimating total 

recharge from streamflow records. The method should be used only if the conditions described in "Applicability of Methods" are met. When a long time period is considered, the total recharge should exceed 

the ground-water discharge (base flow) by an amount equal to riparian evapotranspiration. 
18 Computer Programs for Describing the Recession of Ground-Water Discharge

Figure 5. Example of graphical representation of the master recession curve that can be generated from program output files: 

 (A) plot showing each individual recession segment (in this case, five were selected) with time adjusted so that the segments fall on 

the master recession curve (this plot is generated from the y-file produced by program RECESS); and (B) plot showing the exact 

mathematical equation that is the master recession curve (this plot is generated from the 50 x-y data points listed in the output file 

OUTCURV that is generated by program CURV, and results from the same recession segments that are used in A). (Results here, 

which are for Johns Creek at New Castle, VA., represent an application that is deliberately simplified for illustration purposes. 

A rigorous analysis of recession would include a larger number of recession segments). 

A

B

300

100

50

10

300

100

50

10

0 20 40 60 80

FLOW, IN CUBIC FEET PER SECOND

TIME, IN DAYS
Computer Program for Estimating Mean Ground-Water Recharge 19

 Theory and Method Development

The recession-curve displacement method is based on the upward shift in the streamflow recession curve that occurs as a result of a recharge event. A recharge event will increase the total potential 

ground-water discharge, V, which is the total volume of water that will drain from the system if 

allowed to do so for infinite time without further recharge. Meyboom (1961) expressed V in the following expression, which is based upon a linear relation between the logarithm of ground-water discharge and time:

 (6)

where

 V is total potential ground-water discharge (L3), and

 Q is ground-water discharge at initial time (L3/T).

The formulations of Glover (1964) and Rorabaugh (1964) show that the total potential groundwater discharge to the stream at critical time (eqs. 2 and 4) after a peak in streamflow is equal to 

approximately one-half of the total volume of water that recharged the ground-water system during 

the peak. This finding, combined with the principle of superposition, is the basis for the method--

total recharge is thus calculated by use of the following equation:

 (7)

where

 R is total volume of recharge due to the event (L3),

 Q1 is ground-water discharge at critical time as extrapolated from the pre-event 

streamflow recession (L3/T), and 

 Q2 is ground-water discharge at critical time as extrapolated from the post-event 

streamflow recession (L3/T).

The recession-curve-displacement method consists of the following steps, most of which are 

shown in figure 6 (Bevans, 1986): (1) determination of the recession index (K) from the hydrograph 

during prolonged periods of negligible recharge, (2) calculation of critical time (Tc) from equation 4, 

(3) use of critical time to determine the time on the hydrograph to which streamflow recessions will 

be extrapolated, (4) determination of the hypothetical ground-water discharge to the stream at critical 

time by extrapolation of the pre-event recession curve, (5) determination of the hypothetical groundwater discharge to the stream at critical time by extrapolation of the post-event recession curve, and 

(6) application of equation 7. Steps 1 and 2 need only be executed once for a given streamflow gaging 

station--other steps are executed once for each peak. In practice, the user identifies the position of 

the post-event recession curve soon after surface runoff ceases so that the effects of riparian evapotranspiration are minimized; thus, the result is an estimate of total ground-water recharge. The recession-curve-displacement method, often referred to as the "Rorabaugh Method" (Rorabaugh, 1964; 

Daniel, 1976), has been applied manually by several investigators (Wilder and Simmons, 1978; 

Daniel and Sharpless, 1983; Evaldi and Lewis, 1983; Bevans, 1986; Gerhart and Lazorchick, 1988; 

Faye and Mayer, 1990; Hoos, 1990)

V Q K×

2.3026 = -----------------

R 2 Q2 Q1 ( ) – K

2.3026 = -----------------------------------
20 Computer Programs for Describing the Recession of Ground-Water Discharge

. 

1.0

10,000

1,000

100

10

1 10 20 31

Recharge event of interest

 (Q2)

6.86 d

Tc

(Q1)

DAILY MEAN STREAMFLOW, IN CUBIC FEET PER SECOND

 MARCH 1974

EXPLANATION

DAILY STREAMFLOW

EXTRAPOLATED GROUND-WATER DISCHARGE

PROCEDURE

1. Compute recession index, K (32d/ log cycle)

2. Compute critical time, Tc (0.2144xK, or 6.86 d)

3. Locate time that is 6.86 days after peak

4. Extrapolate pre-event recession to Q1 (5 ft3⁄s)

5. Extrapolate post-event recession to Q2 (23 ft3⁄s)

6. Compute total recharge,

Figure 6. Procedure for use of the recession-curve displacement method to estimate ground-water 

recharge in response to a recharge event. (Modified from Bevans, 1986, fig. 5.)

2x 18ft3

s

------     x32d

2.3026 ------------------------------------- x

86400s

1d ----------------- 4.32x107

ft

3 =

23ft3

S

------

5ft3

S

------
Computer Program for Estimating Mean Ground-Water Recharge 21

Program RORA

Program RORA executes the recession-curve-displacement method to estimate ground-water 

recharge for each peak in streamflow using a set of procedures that includes the identification of periods 

of ground-water-flow recession, the identification of peaks, and the extrapolation of data from the periods 

of recession to critical time after peaks. 

The Algorithm

The first procedure executed by program RORA locates days in the streamflow record that fit an 

antecedent recession requirement (eq. 1, rounded to the next larger integer). Then the program identifies 

periods of ground-water-flow recession, which can consist of one or more days that each fit this requirement. The program then defines a peak as the largest streamflow between two consecutive periods of 

ground-water-flow recession, and considers that peak to be a recharge event. The total recharge is calculated for each peak by use of procedures diagrammed in figure 7.

A crucial aspect of the method is the extrapolation (in time) of ground-water discharge from periods 

of ground-water-flow recession to points in time that are outside of these periods of recession. Before critical time, this equation is used:

 (8)

where 

 dQ is the difference between the ground-water discharge and the ground-water discharge 

that would have occurred at the same time in the absence of the recharge event (L3

/T),

 C is a constant, the value of which is dependent on the magnitude of the recharge event 

(L3/T0.5), and 

 dT is the time since the recharge event (T).

Equation 8, a simplified version of Rorabaugh’s (1964) equation 4, quantifies the margin of flow 

resulting from the recharge event that is superimposed on the flow that would have occurred in the absence 

of the event. Equation 8 is used to extrapolate the margin of flow at critical time by solving for C for each 

day of a period of ground-water-flow recession that occurs before critical time, obtaining the average, and 

substituting this C and critical time back into the equation. 

After critical time, linear extrapolation is used: 

 (9)

where 

 Q is ground-water discharge extrapolated to a time after critical time(L3/T),

 Qo is ground-water discharge extrapolated to critical time after the peak, as derived from 

equation 8 and superposition (L3/T), and 

 dT is the time period from critical time to the day of interest (T).

Equation 9 is mathematically the same as the graphical method of drawing a straight line through a 

known ground-water discharge at critical time and reading on this line the extrapolated ground-water discharge at a time after the critical time (the graph being ground-water discharge on a logarithmic scale as a 

function of time on a linear scale, and the inclination of the line being equal to K). One value for the recession index is used in calculations for an entire streamflow record. This is either the median recession index 

from the execution of program RECESS, or is a user-specified value.

dQ C

dT = -----------

Q Qo 10( ) –dT K⁄ = ×
22 Computer Programs for Describing the Recession of Ground-Water Discharge

Figure 7. Schematic of hydrograph (above) and flow diagram (right) showing the procedures executed for each peak in the 

recession-curve displacement method.

PEAK I-1

PEAK I

PEAK I + 1

RECESSION RATE = K

QC (I)

QB (I)

TBC (I)

TP (I)

Tc

dQc

TA (I)

QA (I) dT

dQ

1 DAY

N

 TIME 

STREAMFLOW (LOGARITHMIC SCALE)
Computer Program for Estimating Mean Ground-Water Recharge 23

 Explanation

N Result of equation 1 rounded to next larger integer.

K Recession index (days per log cycle of recession after critical time).

Tc Critical time.

I Peak counter -- The above calculations pertain to the “present peak,” which is peak I.

TP(I) The time of occurrence of peak I.

C(I) A value (for peak I) that is calculated in the equation for the difference between the flow during a period of 

 ground-water flow recession and the ground-water flow that would have occurred in the absence of the peak, up to

 the critical time after the peak.

(I) The average value of C (I) for all days in the period of ground-water flow recession following peak I.

QA(I), TA(I) The flow and time at critical time after the last peak (I-1) that would have occurred in the absence of all peaks

 subsequent to the last peak; one exception is that if I=1, then QA(I) and TA(I) are the flow and time on the last day

 of the recession period before the first peak.

QB(I), TBC(I) The flow and time at critical time after the present peak (I) that would have occurred in the absence of present peak

 and all subsequent peaks.

QC(I), TBC(I) The flow and time at critical time after the present peak (I) that would have occurred in the absence of all peaks

 subsequent to the present peak.

dT Time increment between the peak and a day during the ground-water flow recession period after the peak.

dQ Difference between the measured flow during the period of ground-water flow recession after peak I and the flow that

 would have occurred in the absence of peak I.

dQc Difference between the hypothetical ground-water discharge at critical time after peak I as extrapolated from the

 ground-water flow recession period after the peak and the hypothetical ground-water discharge at critical time after 

 peak I as extrapolated from the ground-water flow recession period that precedes the peak.

On the hydrograph, the flow on a day during the period of ground-water flow recession that follows peak I.

Figure 7. --Continued.

C

Calculate QC (I) = QB (I) + dQc

Recharge = 2 x dQc x K / 2.3026 Repeat for

next peak

Using the average value of C (I), calculate dQc for this event at critical time: dQc = (I) / C Tc

For each day of the period of ground-water-flow recession that follows the peak (days that fit a requirement of 

antecedent recession), calculate C (I) from the equation C (I) = dQx , where dT is the time since the day

of peak I, and dQ is the difference between the ground-water discharge on the day in question and the “baseline”

ground-water discharge that would have occurred on this day if peak I had not occurred. The baseline groundwater discharge is determined by use of one of these methods:

1. If the day of recession is after TA(I), obtain baseline flow by log-linear extrapolation from TA(I) and QA(I).

2. If the day of recession is before TA(I), obtain baseline flow by linear extrapolation from TA(I-1) and

(QA(I-1), then add a margin of flow that is equal to C(I-1) / , where dT is the time increment from 

peak I-1 to the day of recession being considered.

dT

dT

Obtain QB(I) and TBC(I): TBC(I)=TP(I) + Tc, and QB(I) is calculated from linear extrapolation 

in semilog space from QA(I) and TA(I). This extrapolation uses a line with inclination equal to K.

If this is the first peak, then QA(I) and TA(I) are the flow and

time of the last day of the recession period before the first peak. 

If this is any peak after the first, then 

QA(I)=QC (I-1) and TA(I)=TBC (I-1)
24 Computer Programs for Describing the Recession of Ground-Water Discharge

Program Execution

Before the program is executed, one line of data must exist in file STATION and one daily-values 

z-file must be prepared for each gaging station of interest. The program RORA should be used to analyze 

periods of continuous record only. File OUTROR.SUM, which is an output file for the program, must 

also exist (see "Overview of Programs and Files").

Before program RORA is executed, it is advisable, but not required, for program RECESS to be 

executed for each gaging station of interest so that RORA can read the median recession index from file 

OUTREC.SUM. Program RECESS can be executed expediently for this purpose only: the user can 

select a small number of recession segments (5 to 10 for example) that represent a range of different conditions. From file OUTREC.SUM, program RORA uses the median recession index only. Such an expedient use of program RECESS can be sufficient for obtaining the median recession index, but may not 

adequately define the MRC. Program RORA will search file OUTREC.SUM for the first line that 

includes the station name of interest and a "w" designating the season. Execution of RECESS for winter 

data exclusively is not required but it is advisable that the results represent recession during periods of 

small riparian evapotranspiration. The user has the option to enter the recession index using the computer 

keyboard during execution of RORA. It will be shown that the result of program RORA is only slightly 

sensitive to variation in the recession index.

When the program is executed, it will ask for the name of the daily-values file of interest. The user 

should enter the name of the original data file that was obtained from the data base (the file name without 

the "z" at the beginning). The program actually reads the z-file. When the program requests the time 

period of interest, the user should enter the beginning and the ending calendar years as four-digit integers. 

It is preferable that this is a period of complete record. Unlike the original version of RORA (Rutledge, 

1993), this version can be used to make calculations if there is missing record at the beginning or the end 

of the period specified. In this circumstance, no results will be written to the summary output file OUTRORA.SUM, but some results will appear on other output files. If there is a gap in record within the 

period specified, the program will not make any calculations. If the streamflow record includes zeros, the 

program will substitute the value of 0.01 cubic feet per second so that extrapolation on the log scale is 

possible. The program user is given the opportunity to substitute some other value. 

The program will find the single-line entry in file STATION that represents the station of interest to 

obtain the drainage area. The program obtains the recession index from file OUTREC.SUM (or directly 

from the user). From the recession index, the program calculates the critical time (eq. 4), which becomes 

the maximum time after each peak at which the position of the ground-water recession curve is measured. 

The last day used for a given period of ground-water-flow recession may actually occur before critical 

time if there is another period of increasing streamflow (fig. 7). 

The program uses the result of equation 1, rounded to the next larger integer, to determine the 

default antecedent recession requirement. In effect, this is the minimum time after each peak at which the 

position of the ground-water recession curve is measured. The user is given the option of modifying this 

value for testing purposes, and should under most conditions consider the default value to be required for 

yielding the best estimate of recharge. The requirement of antecedent recession can be changed to a value 

that exceeds its default value, by 1, 2, or 3 days. This might reduce errors due to residual surface runoff, 

but may also introduce other errors because increasing the requirement of antecedent recession will 

decrease the number of peaks that are detected by the program. The number of peaks detected is written 

to the computer monitor when calculations are completed and is also written to file OUTRORA.SUM.
Computer Program for Estimating Mean Ground-Water Recharge 25

Output Files

Results of program RORA are written to four output files:

OUTRORA.SUM One new line is written to the bottom of file OUTRORA.SUM each time 

the program is executed, giving a summary of the results. Included are the 

name of the daily-values file, the gaging-station number, the drainage area 

of the station, the time period analyzed, the requirement of antecedent 

recession, the number of peaks detected, the recession index, and the mean 

recharge rate.

OUTRORA.QRT File OUTRORA.QRT gives a tabulation of total recharge for each quarteryear. This file also gives a tabulation of total recharge for each calendar 

year.

OUTRORA.MON File OUTRORA.MON gives a tabulation of total recharge for each month. 

This file also gives a tabulation of total recharge for each calendar year.

OUTRORA.PEK File OUTRORA.PEK gives details about calculations of recharge for each 

peak. One line is written to OUTRORA.PEK for each peak, giving most 

of the variables defined in figure 7. Time is reported in days since the 

beginning of the analysis, and flow is reported in cubic feet per second. 

Recharge is reported in inches. Variables not defined in figure 7 include 

TS, TE, and QP, which are the time of the beginning and the ending of the 

period of ground-water flow recession after the peak, and the streamflow 

for the day of the peak, respectively.

All of these files, except OUTRORA.SUM, are overwritten completely each time the program is 

executed.

Results from the program RORA are most reliable when reported at a large time scale; such as a 

year or more. It is recommended that for most applications, the output files that should be used are OUTRORA.SUM and OUTRORA.QRT. Results on the basis of a multiple-month period may be reliable in 

some circumstances. This would include, for example, the quarter-year totals that are reported in file 

OUTRORA.QRT. The file OUTRORA.MON is provided so that the program user might report results 

for other multiple-month periods, such as winter (December-February). File OUTRORA.PEK might be 

used to generate a graphical representation of calculations that are made for each recharge event (fig. 8). 

The user should exercise caution in presenting and interpreting results at such a small time scale because 

of complex sets of recharge events: that is, multiple events that occur within such a short period of time 

that the period of ground-water-flow recession (fig. 7) cannot be adequately measured between events. 

The resulting errors tend to compensate for each other when a longer time period is used. For example, 

the first peak of a pair of closely-spaced peaks may be assigned a recharge that is anomalously large, but 

the second may be assigned a recharge that is anomalously small. Riparian evapotranspiration, which is 

the loss of water to the atmosphere from ground water and from the channel, may also affect the accuracy 

of the method when it is applied at a small time scale because of the change in slope of the ground-waterdischarge recession (Daniel, 1976). Because calculations for each recharge event require streamflow data 

before and after the event, there can be errors near the beginning and the end of the period of interest. 

These errors can include nondetection of a recharge event. In some applications the program might be 

executed for a period that begins prior to the period of interest and ends after the period of interest, then 

results for the period of interest can be extracted from files OUTRORA.QRT and OUTRORA.MON.
26 Computer Programs for Describing the Recession of Ground-Water Discharge

EXPLANATION

Indicates that this day meets the requirement of antecedent recession--this day is thus considered to be during 

a period of ground-water-flow recession. A period of ground-water-flow recession can be one isolated day that 

meets the requirement, or it can be multiple days that all meet the requirement.

Indicates a day that is considered a peak in streamflow--the largest streamflow between two subsequent 

periods of ground-water-flow recession. The number identifies the peak for cross-reference with items 

explained below.

Top of bar indicates, for the peak identified below the bar, the flow at critical time after the peak that would 

have occurred in the absence of all peaks subsequent to the peak (Q2 in equation 7).

Bottom of bar indicates, for the peak identified below the bar, the flow at critical time after the peak that would 

have occurred in the absence of the peak and all subsequent peaks (Q1 in equation 7).

Figure 8. Example hydrograph of streamflow graphically showing decisions and calculations performed by 

program RORA, (streamflow-gaging station is Indian Creek near Laboratory, N.C.).

5

5
Computer Program for Estimating Mean Ground-Water Recharge 27

Comparison of Results of Manual and Computerized Methods

Results from program RORA were tested by comparing them with results from a corresponding manual 

method. For purposes of this investigation, results from Daniel (1990) were used for the comparison (Rutledge and 

Daniel, 1994). Daniel’s evaluation of an automated base-flow-record estimation method resulted in an extensive 

data set giving results of manual application of the recession-curve-displacement method for 16 streamflow-gaging 

stations in the eastern United States. For the purpose of this investigation, one station was eliminated from analysis 

because its small drainage area results in a requirement of antecedent recession (eq. 1) that is less than 1 day. 

Although some of the stations have drainage areas that exceed the limits suggested earlier (see "Applicability of 

Methods"), they were used because the purpose here is to simply compare annual recharge values calculated by 

RORA with values calculated by Daniel’s manual method. For the 15 streamflow-gaging stations used, a period of 

10 consecutive years is used, except for 1 station where 16 years is used (table 1). 

Table 1. Streamflow gaging stations used for comparisons between results of program RORA and 

results of the manual application of the recession-curve displacement method

Station

sequence 

number

U.S. 

Geological 

Survey 

station 

number Station name

Drainage 

area

(square

miles)

Recession 

index (days 

per log cycle)

Time 

period 

analyzed 

(water 

years)

 1 01452500 Monocacy Creek at Bethlehem, Pa. 0044.5 37.4 1965-74

 2 01459500 Tohickon Creek near Pipersville, Pa. 00 97.4 28.3 1960-69

 3 01465500 Neshaminy Creek near Langhorne, Pa. 0210.0 46.0 1935-44

 4 01555000 Penns Creek at Penns Creek, Pa. 0301.0 39.0 1934-43

 5 02080500 Roanoke River at Roanoke Rapids, N.C. 8,384.0 49.0 1940-49

 6 02083500 Tar River at Tarboro, N.C. 2,183.0 45.0 1978-87

 7 02089500 Neuse River at Kinston, N.C. 2,692.0 41.0 1978-87

 8 02093800 Reedy Fork near Oak Ridge, N.C. 0020.5 65.0 1971-80

 9 02096700 Big Alamance Creek near Elon College, N.C. 0116.0 45.0 1971-80

10 02099000 East Fork Deep River near High Point, N.C. 0014.8 43.0 1971-80

11 02126000 Rocky River near Norwood, N.C. 1,372.0 35.0 1979-88

12 02339500 Chattahoochee River at West Point, Ga. 3,550.0 59.0 1940-55

13 03453500 French Broad River at Marshall, N.C. 1,332.0 49.0 1958-67

14 03538225 Poplar Creek near Oak Ridge, Tenn. 0082.5 32.0 1975-84

15 03565300 South Chestuee Creek near Benton, Tenn. 0031.8 45.8 1969-78
28 Computer Programs for Describing the Recession of Ground-Water Discharge

For this comparison test, 156 estimates of annual recharge from the manual method are paired with 

the corresponding results of program RORA. For the execution of RORA, the recession indexes were set 

equal to the value used in the manual method (table 1), and the requirement of antecedent recession was 

maintained at its default value (see "Execution of Program"). For consistency with the results from the 

manual method, output files from RORA were processed to yield annual recharge on the basis of the water 

year.

Results of the manual and computerized methods are in reasonable agreement (fig. 9). The results 

of the comparison test can be expressed quantitatively by introducing a variable P that represents the percentage of difference between the two methods:

 (10)

where

 P is the percentage by which the computerized method exceeds that of the

 manual method,

 Ra is the annual recharge estimated by the computerized method (L), and

 Rm is the annual recharge estimated by the manual method for the same year (L).

Figure 9. Relation between annual recharge estimated by program RORA and by the manual method for each 

year analyzed for each station. (See table 1.)

P 100 Ra Rm × ( ) –

Rm = --------------------------------------------

30

20

10

0 20 10 30

0

ANNUAL RECHARGE BY MANUAL METHOD, IN INCHES

 ANNUAL RECHARGE BY AUTOMATED

 METHOD, IN INCHES

35

5 15 25 35

5

15

25
Computer Program for Estimating Mean Ground-Water Recharge 29

The distribution of P for the 156 samples is summarized below:

 Percentile P

90th 20.9

75th 12.3

50th 4.5

25th -3.9

10th -10.8

Sensitivity to Variations in Recession Index

Whether the recession-curve-displacement method is executed by manual or computerized 

techniques, it is preceded by the assignment of a value to the recession index. It is therefore reasonable 

to test the sensitivity of the result (the estimate of recharge) to the variation in the recession index. For 

this purpose, sensitivity testing is shown here for results obtained in the AP-RASA study. This test 

consists of the 89 streamflow-gaging stations in this study that have complete record for the period 

1961-1990. Recharge estimates for these stations (Rutledge and Mesko, 1996, table 3) were used as a 

baseline. These estimates were obtained using the program RORA and specifying the recession index 

to be as listed in table 2 of the same report. The recession index originally used is the median recession 

index for each station that was obtained using the program RECESS. Considerable variation in the 

recession index was observed, but most recession-segment slopes occurred within a range of values 

that spans from 0.75 times to 1.25 times the median. The sensitivity test shown here (figure 10) was 

performed by changing the recession index for each station to a value that is 0.5 times and then 1.5 

times the recession index originally used. This test shows that if the recession index is decreased by 50 

percent the estimate of recharge will increase by generally 4-8 percent. This test also shows that if the 

recession index is increased by 50 percent the estimate of recharge will decrease by generally 2-4 

percent. A similar sensitivity test shown in the report that documents the original version of RORA 

also shows minor sensitivity to variation in the recession index, using the 15 stations described in the 

earlier section on comparison with manual results (Rutledge, 1993, figure 10).
30 Computer Programs for Describing the Recession of Ground-Water Discharge

1.2

1.1

1.0

0.9

0.8

NEW ESTIMATE OF RECHARGE DIVIDED

BY DEFAULT ESTIMATE OF RECHARGE

A B

EXPLANATION

Percentile -- Percentage of

values equal to or less

than indicated values

90th

75th

50th (Median)

25th

10th

Figure 10. Change in the estimate of recharge from program RORA that results from changing the 

recession index to (A) 0.5 times the default value and (B) 1.5 times the default value. (Source: all 

streamflow stations in the AP-RASA project with complete records for 1961-1990: Rutledge and 

Mesko, 1996, table 3. Sample size =89. The default recession index for each station is tabulated on 

table 3 of that report. All recharge estimates are the mean for the time period 1961 to 1990.)
Computer Program for Estimating Mean Ground-Water Recharge 31

Sensitivity to Variations in the Requirement of Antecedent Recession

As explained earlier, RORA uses the result of equation 1, rounded to the next larger integer, to 

determine the default antecedent recession requirement. Because the program user is given the option to 

modify this variable, a test is illustrated here to show the sensitivity of the result (the estimate of recharge) 

to variation in the requirement of recession. This test also uses the streamflow stations in the AP-RASA 

project which have complete record for the period 1961-1990 (Rutledge and Mesko, 1996). Results on 

table 3 of that report were obtained using RORA and the default value of the requirement of antecedent 

recession. This sensitivity test shows that if the requirement of antecedent recession is increased by 1 day 

above its default value the number of peaks that are detected will decrease by approximately 20 percent 

and most estimates of recharge decrease by 1-4 percent (figure 11). This test also shows that if the 

requirement of antecedent recession is increased by 2 days above its default value the number of peaks 

that are detected will decrease by approximately 40 percent and most estimates of recharge decrease by 

2-8 percent.

An increase in the requirement of antecedent recession can cause a reduction in errors that are 

caused by direct surface runoff. The test shows, however, that this adjustment can induce other errors 

because there is a reduction in the number of peaks detected. For this reason the program user should 

avoid modification of this variable whenever possible. Some hydrologic settings may require that the 

variable is increased above its default value. For example if the basin is characterized by limited slope, 

then the time period during which the hydrograph is affected by surface runoff may be long. This in turn 

may require a larger requirement of antecedent recession. Whenever possible the change in this variable 

should be limited to a small amount, such as 1 or 2 days. The RORA program should not be used to analyze basins of extremely small relief. A large drainage area also can cause the time period during which 

a hydrograph is affected by surface runoff to be large. The distribution of basin drainage area in the APRASA data set (figures 10 and 11) is: 10th percentile = 30 square miles; 50th percentile = 106 square 

miles; and 90th percentile = 300 square miles. The RORA program should not be used to analyze basins 

that drain areas much larger than 500 square miles.
32 Computer Programs for Describing the Recession of Ground-Water Discharge

0.8

0.7

0.6

0.5

0.9

1.0

0.5

0.6

0.7

0.8

0.9

1.0

DETECTED UNDER DEFAULT CONDITIONS

BY NUMBER OF PEAKS

NEW NUMBER OF PEAKS DETECTED DIVIDED 

NEW ESTIMATE OF RECHARGE DIVIDED

BY DEFAULT ESTIMATE OF RECHARGE

EXPLANATION

Percentile -- Percentage of values equal to or less

than indicated values

90th

75th

50th (Median)

25th

10th

AB A B

Figure 11. The change in the number of peaks detected and the change in the estimate of recharge from program RORA 

that results from increasing the requirement of antecedent recession to values that are (A) 1 day larger than default and (B) 

2 days larger than default. (Source: All streamflow stations in the AP-RASA project with complete records for 1961-

1990: Rutledge and Mesko, 1996, table 3. Sample size = 89. The recession index for each station is tabulated on table 2 of 

that report. All recharge estimates are the mean for the time period 1961 to 1990.)
Computer Program for Estimating Ground-Water Discharge 33

COMPUTER PROGRAM FOR ESTIMATING MEAN GROUND-WATER 

DISCHARGE

The method of base-flow-record estimation is a relatively arbitrary procedure of estimating a continuous record of ground-water discharge, or base flow, under the streamflow hydrograph. If the streamflow record is incremental (such as daily) instead of continuous, estimates of ground-water discharge can 

be made on an incremental basis. The method should, in most cases, be applied over a long period of 

record (a year or more) to obtain an accurate estimate of the mean ground-water discharge. When the 

period of analysis is long enough that the effect on the water balance of changes in storage can be considered negligible, the mean ground-water discharge can be considered the effective recharge. The effective 

recharge should be less than total recharge by an amount equal to riparian evapotranspiration. Base-flowrecord estimation should only be used if the conditions described in "Applicability of Methods" are met.

Method Development

Many different techniques, most of which involve considerable subjectivity in their application, 

have been used to estimate a record of ground-water discharge under the streamflow hydrograph. Horton 

(1933) described a method of shifting a "normal depletion-curve" horizontally across a hydrograph--noting that segments of the hydrograph that coincide with this curve represent periods during which streamflow is equal to ground-water discharge--then estimating ground-water discharge during periods of 

surface runoff by simply connecting the points where the hydrograph departs from the normal depletion 

curve. Barnes (1939) separated surface flow, storm seepage, and base flow by assigning a distinct "depletion factor" to each. Kulandaiswamy and Seetharaman (1969) pointed out that Barnes’ method may not 

be reliable for separating streamflow into three parts but that the hydrograph can be separated into direct 

runoff and base flow. In some applications, investigators have used characteristic curves of ground-water 

discharge in combination with records of precipitation, snowfall, temperature, and ground-water levels 

(Olmsted and Hely, 1962).

In many cases, the method can be described as two steps: (1) locating periods of negligible surface 

runoff and designating that ground-water discharge equals streamflow, and (2) interpolating groundwater discharge between these periods. The decision that surface runoff is negligible can be based on 

antecedent recession. Linsley and others (1982) used the empirical relation of equation 1. For a given 

day, the antecedent recession requirement is met if recession has been continuous for N days or more preceding the day. Other investigators use linearity of recession, on the graph of logarithm of streamflow as 

a function of time, as the indicator that ground-water discharge equals streamflow (Ineson and Downing, 

1964). There are many methods for executing step 2 (Snyder, 1939; Chow, 1964; Pettyjohn and Henning, 

1979; and Nathan and McMahon, 1990): some are based on the assumption that the ground-water-discharge peak is concurrent with the streamflow peak, and others are based on the assumption that the 

recession of ground-water discharge continues after the time when surface runoff begins; that is, the 

response of ground-water discharge is delayed relative to surface runoff. Some methods involve simple 

linear interpolation to estimate ground-water discharge between the start and the end of surface runoff.

Computer techniques have been used for base-flow-record estimation and have allowed for 

increased speed of analysis and repeatability of results. Hewlett and Hibbert (1967) used a computer program for separating "quick flow" from "delayed flow" in streams of the eastern United States. Pettyjohn 

and Henning (1979) and Sloto and Crouse (1996) used a method that involves searching for the minimum 

streamflow along an interval of record that is 2N days in duration and then assigning values of daily base 

flow by three different techniques (N is defined in equation 1). A method developed by the Institute of 

Hydrology (1980) includes searching for the minimum streamflow along 5-day, non-overlapping periods, 

searching the series of minimums for values that are less than 0.9 times the two outer values, and defining 

such values as turning points. The base-flow hydrograph is constructed by connecting all the turning 
34 Computer Programs for Describing the Recession of Ground-Water Discharge

points. This method and a digital filter method used in signal analysis (Lyne and Hollick, 1979) are discussed by Nathan and McMahon (1990). A method called streamflow partitioning (Knisel and Sheridan, 

1983; Shirmohammadi and others, 1984; Shirmohammadi and others, 1987) requires daily records of 

streamflow and precipitation and the designation of a threshold daily precipitation. For a given day, base 

flow equals streamflow if, on that day and all days that precede it by N days or less, precipitation is less 

than the threshold value. Base flow on all other days is estimated by linear interpolation.

Program PART

The method of base-flow-record estimation that is described here is a form of streamflow partitioning that is similar to that of other investigators (Knisel and Sheridan, 1983; Shirmohammadi and others, 

1984; Shirmohammadi and others, 1987) in that (1) daily values of streamflow are used and (2) linear 

interpolation is used to estimate ground-water discharge during periods of surface runoff. It differs in the 

method of designating days when ground-water discharge equals streamflow. Although previous methods 

are based on antecedent precipitation, this method is based on antecedent streamflow recession. 

The Algorithm

A flow diagram of the steps executed by program PART is shown in figure 12. The program fills a 

one-dimensional array of daily mean streamflow data then searches this array for days that fit an antecedent recession requirement. On each of these days, ground-water discharge is designated equal to streamflow as long as it is not followed by a daily decline of more than 0.1 log cycle. It can be inferred from 

Barnes (1939) that a daily decline more than 0.1 log cycle could indicate interflow (stormflow) or surface 

flow. The program searches the array again, determining by linear interpolation the ground-water discharge on the remaining days. For some streamflow records, this interpolation can cause the calculated 

ground-water discharge to exceed streamflow for a few days in the record. The last step of the procedure 

corrects for this.

The entire procedure is executed three times: once considering the requirement of antecedent recession to be the largest integer that is less than the result of equation 1, and once for each of the next two 

larger integers. The program constructs a second-order polynomial expression for ground-water discharge 

as a function of the requirement of antecedent recession, using the three data pairs of ground-water discharge and requirement of recession. Then the program calculates the ground-water discharge for the 

exact result of equation 1 using the polynomial expression.

Program Execution 

Before the program is executed, one line must exist in file STATION and one daily-values z-file must 

be prepared for each gaging station of interest. Program PART should be used to analyze periods of continuous record only. File OUTPART.SUM, which is an output file for the program, also must exist (see 

“Overview of Programs and Files”).

When the program is executed, it will ask for the name of the daily-values file of interest. The user 

should enter the name of the original data file that was obtained from the data base (the file name without 

the "z" at the beginning). The program actually reads the z-file. When the program requests the time 

period of interest, the user should enter the beginning and the ending calendar years as four-digit integers. 

It is preferable that this is a period of complete record. Unlike the original version of PART (Rutledge, 

1993), this version can be used to make calculations if there is missing record at the beginning or the end 

of the period specified. In this circumstance, no results will be written to the summary output file OUTPART.SUM, but some results will appear on other output files. If there is a gap in record within the period 
Computer Program for Estimating Ground-Water Discharge 35

EXPLANATION

The antecedent recession requirement is met for the day in question if, for the part of the 

daily mean streamflow record that includes all days that precede the day in question by N 

days or less, the streamflow on each of these days is greater than or equal to the 

streamflow on the day that follows it. 

The entire procedure is executed for three values of N: one is the next integer smaller then 

the result of equation 1, and the other two are the next two integers that are larger than the 

result of equation 1. Curvilinear interpolation gives the final estimate of base flow that 

corresponds to the precise result of equation 1.

Figure 12. Flow diagram showing the procedure of streamflow partitioning. (Base flow is considered to be groundwater discharge.)

Construct three parallel 1-dimensional arrays:

1. Streamflow

2. Base flow

3. “ALLGW”

Read a data file of daily mean streamflow, and assign values to Streamflow. Assign 

all values of ALLGW=0.

Locate all days that fit the antecedent recession requirement (see EXPLANATION). 

On these days, reassign ALLGW=* and assign Base flow=Streamflow.

 Locate each day when ALLGW=*. If it is followed by a daily decline 

of the log of streamflow exceeding 0.1, then reset ALLGW=0.

 Locate all days when ALLGW=0. For these days, calculate the log of the 

base flow by linear interpolation between (1) the log of base flow of the 

closest preceding day when ALLGW=*, and (2) the log 

of base flow of the closest following day when ALLGW=*. 

Assign a value to base flow accordingly.

Are there any days when the base flow exceeds the streamflow?

If no,

then stop.

 If yes, locate any intervals where the value of ALLGW is 

continuously equal to 0 and where there is at least one day 

when base flow>streamflow. Find the day that exhibits the 

largest “log of base flow minus log of streamflow,” and 

 reassign ALLGW=* on this day.
36 Computer Programs for Describing the Recession of Ground-Water Discharge

specified, the program will not make any calculations. The program will find the single-line entry in file 

STATION that represents the station of interest and obtain the drainage area. The program will then ask 

if the user chooses to execute according to default conditions. If not, the user can change the value for 

the threshold for daily decline in the log of streamflow, which is 0.1 log cycle per day by default. The 

user is given the option of modifying this value for testing only and should consider the default value to 

be required for yielding the most accurate estimate of ground-water discharge. 

The user can then choose to finish the analysis, causing the program to complete all calculations 

and write results to the monitor and to output files (next section). Prior to finishing the analysis, the user 

has the option of writing a daily tabulation of streamflow and base flow to output file OUTPART.DAY. 

When the program completes all calculations, the estimate of base flow for each of the three values 

of the requirement of antecedent recession is displayed to the monitor, along with the final calculation of 

base flow.

Output Files

Results of program PART are written to four output files:

OUTPART.SUM One new line is written to the bottom of file OUTPART.SUM each time 

the program is executed, giving a summary of the results. Included are the 

name of the daily-values file, the gaging-station number, drainage area, the 

time period analyzed, the three values of the requirement of antecedent 

recession, the mean streamflow, the mean base flow (ground-water 

discharge), and the mean base-flow index (ratio of mean base flow to mean 

streamflow).

OUTPART.QRT OUTPART.QRT gives a tabulation of total base flow for each quarteryear. This file also includes a tabulation of total base flow for each 

calendar year.

OUTPART.MON File OUTPART.MON gives a tabulation of total base flow for each month. 

This file also includes a tabulation of total base flow for each calendar 

year.

OUTPART.DAY If the user selects the option of writing daily streamflow and base flow 

prior to program termination, file OUTPART.DAY is created. Daily 

streamflow and base flow is written to each line a file OUTPART.DAY for 

the period specified by the program user. The file can be used to generate 

hydrographs (fig. 13). 

The files OUTPART.QRT and OUTPART.MON are overwritten each time the program is executed. 

File OUTPART.DAY is overwritten when the program is executed and the option is selected to write to 

OUTPART.DAY.

The hydrographs of figure 13 demonstrate why the results of base-flow-record estimation should 

only be applied at a large time scale. Base flow is shown to increase or decrease gradually from the beginning to the end of the period of surface runoff. Results of chemical analysis of stream water during peak 

discharge indicate that the record of base flow may increase and decline during the event in a manner that 

roughly mimics the peak in streamflow (Pinder and Jones, 1969). Analysis of changes in water levels in 

wells near a streamflow gaging station showed that the base flow record may actually decrease during 

the event because of the effects of bank storage (Daniel and others, 1970). Such variation in findings may 

be related to the specific method employed. As is the case for any method of base-flow-record estimation, the user should exercise caution when using the results of program PART at a small (daily) time 

scale, especially during periods of surface-water runoff. The suggested time scale for interpreting and 

reporting results of program PART is at least one year. Nonetheless, results reported on the basis of the 

month or a multiple-month period may be useful in some circumstances. 
Computer Program for Estimating Ground-Water Discharge 37

Figure 13. Hydrograph showing the results of streamflow partitioning. Where the curves coincide, ground-water discharge equals 

streamflow. For both hydrographs, the requirement of antecedent recession is 3 days.

10,000

1,000

100

10

MAY JUNE JULY AUGUST SEPTEMBER OCTOBER

Estimated daily mean

ground-water discharge

Daily mean 

streamflow

 Sewee Creek near Decatur, Tennessee

 (Valley and Ridge physiographic province)

 Drainage area - 117 square miles

DISCHARGE, IN CUBIC FEET PER SECOND 10,000

1,000

100

10

MAY JUNE JULY AUGUST SEPTEMBER OCTOBER

Indian Creek near Laboratory, North Carolina

 (Piedmont physiographic province)

 Drainage area - 69.2 square miles

Daily mean

streamflow

Estimated daily mean

ground-water discharge

1989
38 Computer Programs for Describing the Recession of Ground-Water Discharge

Comparison of Results of Manual and Computerized Methods

Program PART can be tested by comparison with published results of the manual execution of the baseflow-record estimation method. Results obtained (table 2) compare reasonably well. The result of the computerized method departs from that of the manual method by less than 10 percent, for 75 percent of the pairs 

of base-flow estimates.

Table 2. Published results of base-flow record estimation and results from program PART

Program PART uses calendar years only, except for comparison with publication 9, for which the data-input file was customized. 

Publications 1 and 8 used water years. All cited publications used base-flow record estimation for the entire period indicated, 

except publication 10 (in which the long-term mean base flow was estimated as the mean of base flow during a wet year and a dry

year) and publication 2 (in which the long-term mean base flow was estimated as the mean of three separate years: one with 

above normal, one with normal, one with below normal precipitation). In publication 6, the drainage area is 103 square miles,

but 107 square miles was used here

 Publication

 (number, authors, and year)

Result

 from 

publication 1

Result 

from

PART 1

1

 The mean ground-water discharge (base flow) is expressed in two ways: top number is base flow in inches per year; 

bottom number is base-flow index, which is the ratio of mean base flow to mean streamflow, expressed in percent.

 Station Time period

 1. Becher and Root, 1981 Conodoguinet Creek 

near Hogestown, Pa.

1968-74 13.0

66.0

12.9

65.6

Yellow Breeches Creek 

near Camp Hill, Pa.

1968-74 16.8 

80.0

16.9

80.4

 2. Carswell and Lloyd, 1979 Brodhead Creek 

near Minisink Hill, Pa.

1963, 1969, 

and 1973

19.6

66.0

20.8

70.0

 3. Dingman and Meyer, 1954 Rock Creek at

Sherrill Dr., Md.

1933-49 08.5

67..0

08.4

66..0

 4. Dingman and Ferguson, 1956 Little Gunpowder Falls

near Laurel Brook, Md.

1927-49 11.3

66.0

12.3

71.0

 5. Olmsted and Hely, 1962 Brandywine Creek at

Chadds Ford, Pa.

1928-31 11.2

67.8

11.6

70.3

 6. Stewart and others, 1964 Etowah River 

near Dawsonville, Ga.

1956 20.3

75.0

20.6

80.6

 7. Stuart and others, 1967 Swatara Creek 

above Harper Tavern, Pa.

1919-60 11.3

49.0

14.3

62.0

 8. Taylor and others, 1983 Spring Creek 

near Axemann, Pa.

1961-80 12.7

89.0

12.7

89.0

 9. Waller, 1976 Roanoke River 

at Roanoke, Va.

April 1969 to

March 1970

05.2

67..0

05.7

73..0

10. Wood, 1980 West Conewago Creek 

at Manchester, Pa.

1931-76 06.0

38.5

07.4

46.9
Comparison of Estimates of Recharge and Discharge 39

COMPARISON OF ESTIMATES OF RECHARGE AND DISCHARGE

In the preceding sections, results of the computerized methods used to estimate ground-water 

recharge and discharge compared reasonably with the corresponding manual methods. Further validation 

of the computerized methods can be achieved by direct comparison between results of programs PART 

and RORA. For this purpose, the mean rate of ground-water recharge and discharge at 157 streamflowgaging stations was determined for the period 1981-90. All stations are within the APRASA study area. 

Results show a close correlation between recharge and discharge (fig. 14). 

Figure 14. Relation between the mean ground-water recharge estimated by program RORA and the mean ground-water 

discharge estimated by program PART. (Each point represents one of the 157 streamflow stations in the Appalachian Valley 

and Ridge, Blue Ridge, and Piedmont physiographic provinces of the eastern United States, for the period of 1981-90. 

Regulation and diversion of flow at all stations is negligible, and records are classified as “good” in U.S. Geological Survey data 

books.)

 If ground-water withdrawals are negligible, the difference between mean rate of ground-water 

recharge and discharge is riparian evapotranspiration--the loss of water from stream channels and the saturated zone near stream channels to the atmosphere. On the basis of these results, the distribution of riparian evapotranspiration can be described as having a 25th percentile of approximately 1 inch per year and 

a 75th percentile of approximately 2 inches per year. Because the estimate of this variable (riparian evapotranspiration) is calculated as a small margin between two variables that are approximately an order of 

magnitude larger, the error in the estimate is considerable. These estimates of riparian evapotranspiration 

may not be representative of all hydrologic settings. 

LINE OF ZERO RIPARIAN

EVAPOTRANSPIRATION

MEAN GROUND-WATER DISCHARGE

IN INCHES PER YEAR

MEAN GROUND-WATER RECHARGE,

 IN INCHES PER YEAR

50

40

30

20

10

0

0 20 30 40 50 10
40 Computer Programs for Describing the Recession of Ground-Water Discharge

SUMMARY

The computer programs included here develop a mathematical expression for recession of groundwater discharge and estimate mean ground-water recharge and discharge. Because the programs read data 

files of daily mean streamflow, instructions are included for the assembly of data files from USGS records 

or from other sources before program execution. Use of the programs does not require separate computer 

software (other than the software that is required to compile, load, and execute Fortran-77 computer programs), but some output files can be read by separate graphics software for illustrating results.

The programs are intended for analysis of the streamflow record of a basin where one can reasonably 

assume that all, or nearly all ground water discharges to the stream except for what is lost to riparian 

evapotranspiration, and where regulation and diversion of flow can be considered negligible. The methods 

for estimation of recharge or discharge are intended for the analysis of a flow system that is driven by 

areally diffuse recharge events that can be considered roughly concurrent with peaks in streamflow.

 Program RECESS determines the master recession curve (MRC) of streamflow recession during 

times when all flow can be considered to be ground-water discharge and when the profile of the groundwater head distribution is nearly stable. The method uses a repetitive interactive procedure for selecting 

several periods of continuous recession, determines a best-fit equation for the rate of recession as a function of the logarithm of flow, and then uses the coefficients of this equation to derive the MRC, an equation 

of time as a function of the logarithm of flow. The method thus allows for the possibility of nonlinearity 

in the relation between time and the logarithm of flow. Output files generated by RECESS and by an auxiliary program can be read by separate graphics software for illustrating the MRC. 

Program RORA uses the recession-curve-displacement method to estimate the recharge for each 

peak in the streamflow record. The procedure, also called the Rorabaugh Method, is based on the measurement of the change in the total potential ground-water discharge as estimated at critical time after the 

event by extrapolation from the pre-peak and the post-peak recession periods. The method is applied to a 

large period of record and gives an estimate of the mean rate of ground-water recharge. Results of RORA 

compare reasonably well with the results of manual execution of the recession-curve-displacement 

method that were obtained for 15 streamflow-gaging stations in the eastern United States. Sensitivity 

analysis indicates that the results of program RORA are not very sensitive to changes in the recession 

index.

Program PART uses streamflow partitioning to estimate a daily record of ground-water discharge 

under the streamflow record. The program scans the record for days that fit a requirement of antecedent 

recession, designates base flow to be equal to streamflow on these days, then linearly interpolates the daily 

record of base flow for days that do not fit the requirement of antecedent recession. The program is applied 

to a large period of record to give an estimate of the mean rate of ground-water discharge, or effective 

recharge. Results of PART compare reasonably well with published results of the manual execution of 

base-flow-record estimation in the eastern United States. 

A test of the programs for 157 streamflow-gaging stations in the eastern United States shows that 

the result of program RORA (ground-water recharge) correlates well with the result of program PART 

(ground-water discharge). Recharge exceeds discharge by a small margin that can be considered riparian 

evapotranspiration.
References Cited 41

REFERENCES CITED

Anderson, M.G., and Burt, T.P., 1980, Interpretation of recession flow: Journal of Hydrology, v. 46, 

p. 89-101.

Barnes, B.S., 1939, The structure of discharge recession curves: Transactions of American Geophysical 

Union 20, p. 721-725.

Becher, A.E., and Root, S.I., 1981, Groundwater and geology of the Cumberland Valley, Cumberland 

County, Pennsylvania: Pennsylvania Geological Survey, 4th ser., Water Resources Report 50, 95 p.

Bevans, H.E., 1986, Estimating stream-aquifer interactions in coal areas of eastern Kansas by using 

streamflow records, in Subitzky, Seymour, ed., Selected papers in the Hydrologic Sciences: 

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Carswell, L.D., and Lloyd, O.B., 1979, Geology and groundwater resources of Monroe County, 

Pennsylvania: Pennsylvania Geological Survey, 4th Series, Water Resources Report 47, 61 p.

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Daniel, C.C., III, and Sharpless, N.B., 1983, Ground-water supply potential and procedures for well-site 

selection in the upper Cape Fear River Basin, North Carolina: North Carolina Department of Natural 

Resources and Community Development and U.S. Water Resources Council, 73 p.

Daniel, C.C., III, 1990, Comparison of selected hydrograph separation techniques for estimating groundwater recharge from streamflow records [abs.]: Geological Society of America Abstracts with 

Programs, v. 22, no. 4, p. 9.

Daniel, J.F., Cable, L.W., and Wolf, R.J., 1970, Ground water-surface water relation during periods of 

overland flow, in Geological Survey Research 1970: U.S. Geological Survey Professional Paper 700-

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Daniel, J.F., 1976, Estimating groundwater evapotranspiration from streamflow records: Water Resources 

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14, p. 1-139.

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resources of Baltimore and Harford Counties: Maryland Department of Geology, Mines, and Water 

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Evaldi, R.D., and Lewis, J.G., 1983, Base flow and ground water in Upper Sweetwater Valley, Tennessee: 

U.S. Geological Survey Water-Resources Investigations Report 83-4068, 30 p.

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plain of Georgia and adjacent parts of Alabama and South Carolina: U.S. Geological Survey WaterResources Investigations Report 88-4143, 83 p.

Gerhart, J.M. and Lazorchick, G.J., 1988, Evaluation of the ground-water resources of the lower Susquehanna River basin, Pennsylvania and Maryland: U.S. Geological Survey Water-Supply Paper 2284, 

128 p.

Glover, R.E., 1964, Ground-water movement: U.S. Bureau of Reclamation Engineering Monograph 

Series, no. 31, p. 31-34.

Hewlett, J.D. and Hibbert, A.R., 1967, Factors affecting the response of small watersheds to precipitation 

in humid areas, in Sopper, W.E., and Lull, H.W., eds., International Symposium on Forest Hydrology: 

New York, Pergamon, p. 275-290.

Hoos, A.B., 1990, Recharge rates and aquifer hydraulic characteristics for selected drainage basins in middle and east Tennessee: U.S. Geological Survey Water-Resources Investigations Report 90-4015, 34 

p.

Hornberger, G.M., Ebert, Janet, and Remson, Irwin, 1970, Numerical solution of the Boussinesq 

Equation for aquifer-stream interaction: Water Resources Research, v. 6, no. 2, p. 601-608.
42 Computer Programs for Describing the Recession of Ground-Water Discharge

Horton, R.E. 1933, The role of infiltration in the hydrologic cycle: Transactions of American Geophysical 

Union 14, p. 446-460.

Ibrahim, H.A. and Brutsaert, Wilfried, 1965, Inflow hydrographs from large unconfined aquifers: 

American Society of Civil Engineers, Journal of Irrigation and Drainage Division, v. 91, no. IR 2, 

p. 21-38.

Ineson, J. and Downing, R.A., 1964, The ground-water component of river discharge and its relationship 

to hydrogeology: Journal of the Institution of Water Engineers, v. 18, no. 7, p. 519-541.

Institute of Hydrology, 1980, Low flow studies: Wallingford, U.K., Institute of Hydrology, Research 

Report 1 [variously paged].

Knisel, W.G., and Sheridan, J.M., 1983, Procedure for characterizing hydrologic processes in the coastal 

plain of the southeastern United States, in Hydrology on Large Flatlands: UNESCO International Program on Hydrology, Buenos Aires, Argentina, April 1983, Proceedings, v. 1, p. 191-211.

Kulandaiswamy, V.C., and Seetharaman, S., 1969, A note on Barnes’ method of hydrograph separation: 

Journal of Hydrology, v. 9, p. 222-229.

Linsley, R.K., Jr., Kohler, M.A., and Paulhus, J.L.H., 1982, Hydrology for engineers (3d ed.): 

New York, McGraw-Hill, 508 p.

Lyne, V. and Hollick, M., 1979, Stochastic time-variable rainfall-runoff modelling, in Hydrology and 

Water Resources Symposium, Perth, Australia, September 10-12, 1979, Proceedings: Perth, Australia, 

National Committee on Hydrology and Water Resources of the Institution of Engineers, no. 79/10, p. 

89-92.

Meyboom, P., 1961, Estimating ground-water recharge from stream hydrographs: Journal of Geophysical 

Research, v. 66, no. 4, p. 1,203-1,214.

Nathan, R.J., and McMahon, T.A., 1990, Evaluation of automated techniques for base flow and recession 

analysis: Water Resources Research, v. 26, no. 7, p. 1,465-1,473.

Nutbrown, D.A., and Downing, R.A., 1976, Normal-mode analysis of the structure of baseflow-recession 

curves: Journal of Hydrology, v. 30, p. 327-340.

Olmsted, F.H. and Hely, A.G., 1962, Relation between ground water and surface water in Brandywine 

Creek basin Pennsylvania: U.S. Geological Survey Professional Paper 417-A, 21 p.

Pettyjohn, W.A., and Henning, Roger, 1979, Preliminary estimate of ground- water recharge rates, related 

streamflow and water quality in Ohio: Columbus, Ohio, Ohio State University Water Resources Center, Project Completion Report 552, 323 p.

Petras, Ivan, 1986, An approach to the mathematical expression of recession curves: Pretoria, 

South Africa, Hydrologic Research Institute, Water S.A., v. 12, no. 3, p. 145-150.

Pinder, G.F., and Jones, J.F., 1969, Determination of the ground-water component of peak discharge from 

the chemistry of total runoff: Water Resources Research, v. 5, no. 2, p. 438-445.

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