U.S. Department of the Interior

U.S. Geological Survey

The Continuous Slope-Area Method for Computing Event 

Hydrographs

Scientific Investigations Report 2010-5241
Cover. Babocomari River in southern Arizona, looking downstream during a summer flow event 

(photograph by J.T. Cordova).
The Continuous Slope-Area Method for 

Computing Event Hydrographs

By Christopher F. Smith, Jeffrey T. Cordova, and Stephen M. Wiele

Scientific Investigations Report 2010–5241

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

This report and any updates to it are available online at:

http://pubs.usgs.gov/sir/2010/5241/

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Telephone: 1-888-ASK-USGS

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only and does not imply endorsement by the U.S. Government.

Although this report is in the public domain, it may contain copyrighted materials that 

are noted in the text. Permission to reproduce those items must be secured from 

the individual copyright owners.

Library of Congress Cataloging-in-Publication Data

Suggested citation:

Smith, C.F., Cordova, J.T., and Wiele, S.M., 2010, The continuous slope-area method for computing event hydrographs: 

U.S. Geological Survey Scientific Investigations Report 2010-5241, 37 p.
iii

Contents

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

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

Purpose and Scope .......................................................................................................................................1

Discharge Measurements Using the Slope-Area Method .....................................................................2

The Slope-Area Computation Program.............................................................................................2

Sensitivity of Indirect Discharge Computations to Slope ..............................................................2

The Continuous Slope-Area Method..........................................................................................................3

Site Selection.........................................................................................................................................3

Evaluation of Pressure-Transducer Data and Calculated Hydrographs .....................................4

Comparison of Pressure-Transducer Peaks to Crest-Stage Gage Peaks.................4

Stage-Discharge Relations ...............................................................................................4

Hysteresis in the Stage-Discharge Relations ................................................................4

Evaluation of Channel Geometry......................................................................................5

The Effect of Unsteadiness on Discharge Computation Accuracy............................5

Study Site on the Babocomari River...........................................................................................................5

Description of Channel Conditions along the Slope-Area Reach and Roughness Coefficient 

Selection...................................................................................................................................9

Application of the Continuous Slope-Area Method on the Babocomari River .................................11

Installation of Pressure Transducers ..............................................................................................11

Collection and Reduction of Pressure-Transducer Data .............................................................12

Calculation of Hydrographs Using the Continuous Slope-Area Method...................................13

Batch-Processing Discharge Computations..................................................................................13

Development of Stage-Discharge Relations .................................................................................14

Major Flows on the Babocomari River 2002–2006 ........................................................................14

Flow of October 9, 2003.............................................................................................................14

Channel Geometry ............................................................................................................14

Evaluation of the High-Water Marks .............................................................................16

Conventional Slope-Area Computation and Analysis.................................................17

Evaluation of the Pressure-Transducer Data...............................................................18

Continuous Slope-Area Discharge Computations and Analysis ..............................18

Rating Development ........................................................................................................18

Summary of the October 2003 Event..............................................................................19

The Flow Event of July 27, 2006 ...............................................................................................19

Changes in Channel Shape .............................................................................................19

Evaluation of the High-Water Marks .............................................................................20

Slope-Area Computation and Analysis of High-Water Marks .................................20

Slope-Area Computation of Peak Discharge using PT Data and Analysis of PT 

Data .......................................................................................................................22

Evaluation of the Pressure-Transducer Data...............................................................23

Development of Stage-Discharge Relation..................................................................24

Transfer of the CSA Stage-Discharge Relation to the Babocomari River near Tombstone 

Streamflow-Gaging Station .................................................................................................24

Conclusions...................................................................................................................................................26

References Cited..........................................................................................................................................30
iv

Figures

1. Error in discharge calculated with equation 2, caused by errors in measured 

reach drop. The sample calculation shown is for a true drop in the reach 

of 0.5 ft............................................................................................................................................3

2. Percent error in the St. Venant momentum equation as a result of neglecting the 

unsteady term as a function of change in velocity for three reach slopes.......................6

3. Velocity and du/dQ as function of discharge for a trapezoidal channel with a bed 

width of 50 ft, slope of 0.001, and a Manning’s n of 0.035. The bank width 

was specified as two times the depth .....................................................................................6

4. Hydrograph computed with the Continuous Slope-Area method and the normalized 

unsteady term from the momentum equation (du/dt)/(gS) during the July 27, 

2006, event on the Babocomari River.......................................................................................7

5. Histogram of the absolute value of the normalized unsteady term in equation 4 for

the Babocomari River hydrograph shown in figure 4............................................................7

6. Map showing the study area on the Babocomari River........................................................8

7. View looking downstream from cross section 1. Note the dense grass where trees 

are sparse.....................................................................................................................................9

8. View looking upstream from cross section 4. Ash trees grow along the low-flow 

channel..........................................................................................................................................9

9. Views from cross section 1 looking upstream (left), downstream (center), and 

downstream (right)....................................................................................................................10

10 Views from cross section 2 looking upstream (left), downstream (center), 

and downstream (right)..............................................................................................................10

11. Views from cross section 3 looking upstream (left), downstream (center), 

and downstream (right)..............................................................................................................10

12. Views from cross section 4 looking upstream (left), downstream (center), 

and downstream (right)..............................................................................................................11

13. Installation of the crest-stage gage (left). The pressure transducer is clamped to 

the bottom of the crest-stage gage board (center and right)............................................11

14. Plan view of the cross sections and eight pressure transducers in the Babocomari 

River continuous-slope-area reach .......................................................................................12

15. Pressure-transducer-pin elevations (dry with no flow)......................................................13

16. Peak streamflows recorded on the Babocomari River during the study period, 

2002–2006....................................................................................................................................14

17. Stage hydrographs from the October 9, 2003, flow event on the Babocomari River.....15

18. Channel surveys in cross section 1 before and after the October 9, 2003, event. 

The blue dashed line shows the water-surface elevation at the peak 

discharge....................................................................................................................................16

19. Channel surveys in cross section 2 before and after the October 9, 2003, event. 

The blue dashed line shows the water-surface elevation at the peak 

discharge....................................................................................................................................16

20. Channel surveys in cross section 3 before and after the October 9, 2003, event. 

The blue dashed line shows the water-surface elevation at the peak 

discharge....................................................................................................................................17

21. Channel surveys in cross section 4 before and after the October 9, 2003, event. 

The blue dashed line shows the water-surface elevation at the peak 

discharge....................................................................................................................................17

22. Average left- and right-bank pressure-transducer-stage hydrographs during 

 the October 9, 2003, event ........................................................................................................18
v

23. Discharge values computed with the average pressure-transducer and crest-

 stage gage data for the October 9, 2003, event ....................................................................19

24. Stage-discharge relation determined with discharges computed from the 

 averaged pressure-transducer data and crest-stage gage data for the 

 October 9, 2003, event...............................................................................................................20

25. July 27, 2006, stage hydrographs for six pressure transducers. Right-bank 

 pressure transducers are indicated by R in the legend label; left-bank 

 pressure transducers are indicated by L in the legend label; the number 

 in the legend label corresponds to the cross-section number..........................................21

26. Right-bank pressure transducer in cross section 1 (PTR1) after the July 27, 2006, 

 flow event....................................................................................................................................22

27. View looking upstream from cross section 3 on the right bank after the July 27, 

 2006, event. The floodway is mostly clear of obstacles .....................................................22

28. Channel surveys in cross section 1 before and after the July 27, 2006, event. 

 The blue line shows the water-surface elevation at the peak discharge. At the 

 peak discharge, the difference in cross-section areas is 2 percent ................................22

29. Channel surveys in cross section 2 before and after the July 27, 2006, event. 

 The blue line shows the water-surface elevation at the peak discharge. At the 

 peak discharge, the difference in cross-section areas is 8 percent ................................23

30. Channel surveys in cross section 3 before and after the July 27, 2006, event. 

 The blue line shows the water-surface elevation at the peak discharge. 

 At the peak discharge, the difference in cross-section areas is 0.5 percent .................23

31. Channel surveys in cross section 4 before and after the July 27, 2006, event. The 

 blue line shows the water-surface elevation at the peak discharge. At the 

 peak discharge, the difference in cross-section areas is 4 percent ................................24

32. Debris pile near left bank in cross section 3 after the July 27, 2006, event .....................26

33. Stage hydrographs of the four pressure transducers that were used to compute

 discharge for the July 27, 2006, event ....................................................................................27

34. Stage values from the left-bank pressure transducer in cross section 1 and the

 corresponding discharge computed with stage data in X1-X4 during the 

 July 27, 2006, event are shown as dots. All stage and discharges shown 

 occurred prior to the rotation of the pressure transducers. The solid line 

 is a cubic polynomial fitted to the stage-discharge relation..............................................28

35. Reach below the Babocamari River near the Tombstone stream gage was heavily

 vegetated prior to the July 27, 2006, event (left). Much of that vegetation was gone

 after the event (right). The rock in the right foreground of the left 

 photograph is the same as the rock occupying the right lower quadrant 

 of the right photograph .............................................................................................................29

36. Stage hydrographs from the Babocomari River near Tombstone gage and the left

 bank pressure transducer in cross section 1 (PTL1) during the July 27, 2006, event

 Stages from the two sites were adjusted to coincide on the rising limb .........................29

37. Stage-discharge relations before and after the July 27, 2006, event. The blue line

 represents conditions prior to the peak and included the effects of the dense

 vegetation. The red curve represents the condition after vegetation was 

 scoured........................................................................................................................................30
vi

Tables

1. Elevation difference between crest-stage and pressure-transducer datums (dry)......13

2. Peak stages recorded by the crest-stage gages and by the pressure transducers 

 during the October 9, 2003, event...........................................................................................15

3. Peak discharge for cross sections 1–4, based on average of left- and right- stage 

 data from the pressure transducers and crest-stage gage from October 9, 2003,

 event............................................................................................................................................18

4. Water-surface elevations from surveyed high-water marks and pressure 

 transducers from the July 27, 2006, event ............................................................................25

5. Peak discharge computed using surveyed left-bank high-water marks for the 

 July 27, 2006, event...................................................................................................................25

6. Peak discharges computed using surveyed right-bank high-water marks for the 

 July 27, 2006, event...................................................................................................................25

7. Peak discharge computed with the left-bank pressure transducers for the 

 July 27, 2006, event...................................................................................................................25

8. Peak discharge computed with the right-bank pressure transducers for the 

 July 27, 2006, event...................................................................................................................26

Appendices 

1. Stage data and computed discharge for five runoff events in the Babocomari 

 River ............................................................................................................................................31

2. Input files to the SAC program used in the continuous slope-area calculations of 

 discharge for five events on the Babocomari River............................................................35
vii

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

°F=(1.8×°C)+32

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

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the insert datum name (and abbreviation) here 

for instance, 

“North American Vertical Datum of 1988 (NAVD 88).”

Horizontal coordinate information is referenced to the insert datum name (and abbreviation) 

here for instance, 

“North American Datum of 1983 (NAD 83).”

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

Conversion Factors

Inch/Pound

foot

(ft)

0.3048

0.3048

meter (m)

meter (m)

Multiply By

Length

To obtain

foot per second (fts/s)

Flow rate
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Abstract

The continuous slope-area (CSA) method expands 

the slope-area method of computing peak discharge to 

a complete flow event. Continuously recording pressure 

transducers installed at three or more cross sections provide 

water-surface slopes and stage during an event that can be 

used with cross-section surveys and estimates of channel 

roughness to compute a continuous discharge hydrograph. 

The CSA method has been made feasible by the availability 

of low-cost recording pressure transducers that provide a 

continuous record of stage. The CSA method was implemented on the Babocomari River in Arizona in 2002 to 

monitor streamflow in the channel reach by installing eight 

pressure transducers in four cross sections within the reach. 

Continuous discharge hydrographs were constructed from 

five streamflow events during 2002–2006. Results from this 

study indicate that the CSA method can be used to obtain 

continuous hydrographs and rating curves can be generated 

from streamflow events. 

Introduction

The U.S. Geological Survey (USGS) operates about 

7,500 stream gages throughout the Nation. The rating 

curves that relate stage to discharge at these gaging stations 

are formulated from periodic measurements of discharge 

at known stages. Stages are recorded at regular intervals, 

typically 15 min, and the discharge is computed from stage 

using the stage-discharge rating curve. A well-defined rating 

curve typically requires many discharge measurements at a 

range of discharges. Obtaining discharge measurements over 

a wide range of stage is not always possible as a result of 

remoteness of the streamflow-gaging stations, inaccessibility 

due to flooding, flashy events, or limited resources. 

If a direct measurement of discharge is not obtained at 

a high flow, the USGS routinely uses slope-area method to 

estimate discharge (Dalrymple and Benson, 1967). A slopearea measurement is a discharge calculated using measured 

cross sections, estimations of channel roughness, and a 

water-surface slope derived from field evidence, such as 

debris lines. The Manning equation, in which the slope is the 

energy slope, is used to calculate discharge.

The use of a water-surface slope derived from field 

evidence to calculate the discharge in slope-area measurements has two potential drawbacks. First, the high-water 

marks used to infer the water-surface slope may not be well 

defined and may not accurately represent the water-surface 

slope in the main part of the flow. Debris lines are subject to 

wave action, downslope creep, and diffusion by rainfall and 

gravity that produce inaccuracies or an apparent irregularity 

in the water-surface slope. Smaller peaks following a large 

event can add to the difficulty in identifying the relevant 

high-water marks. Bank roughness can generate real variability in the water-surface slope that poorly represents the 

slope near the center of the channel. The resulting scatter in 

the water surface that is used in the slope-area calculations 

can be a source of error. Second, the use of high-water marks 

allows only for the calculation of the peak discharge. The 

event hydrograph cannot be estimated from peak discharge 

calculations.

This report presents an extension of the slope-area 

method for obtaining peak discharges to a method for recording continuous time series stage at multiple cross sections, 

development of stage discharge relationships, and computation of discharge hydrographs for the slope-area reach. The 

method requires some foresight—slope-area reaches must 

be identified and instrumented prior to events—and, because 

the method depends on estimates of channel roughness and 

reaches with desirable properties for slope-area measurements may not be available, it cannot consistently achieve 

the level of accuracy characteristic of standard USGS stream 

gages with rating curves that are well defined by many direct 

discharge measurements. The method can produce more 

complete discharge records than would otherwise be possible, where the resources are not available to install and 

maintain stream gages or the required measurements are not 

possible due to logistical obstacles.

Purpose and Scope

The CSA method for computing hydrographs has been 

under development by the USGS Arizona Water Science 

Center Data Program since the summer of 2002. This report 

The Continuous Slope-Area Method for Computing Event 

Hydrographs 

By Christopher F. Smith, Jeffrey T. Cordova, Stephen M. Wiele
2 The Continuous Slope-Area Method for Computing Event Hydrographs

describes the installation of crest-stage gages (CSG) with continuously recording pressure transducers (PT), data acquisition and analysis, and computed results from the Babocomari 

River continuous slope-area reach that was operated over a 

5-yr period from 2002 to 2006, as well as the basics of the 

method and its implementation. Additional sections cover 

implementation of the method in the Babocomari River. Five 

significant flows occurred during the study period and the CSA 

method was used to determine a hydrograph for each of them; 

the application of the CSA method to two of these events is 

described in this report, and the stage data, computed discharges, and channel shape and roughness for all five events 

are available in appendices 1 and 2. Although the study lasted 

5 years, the southeastern Arizona climate combined with 

drought conditions during the study period limited the total 

time of recorded flow to only about 9 hours. Thus, this report 

should be considered an initial application of the method and 

not a comprehensive techniques and methods manual. Other 

applications are ongoing (for example, Stewart and others, 

2008) and will aid in refining field methods and the analysis of 

stage records.

Discharge Measurements Using the 

Slope-Area Method

A slope-area discharge measurement uses channel 

surveys, estimates of water-surface slopes, and estimates 

of channel roughness to calculate peak discharge. Benson 

and Dalrymple (1967) and Dalrymple and Benson (1967) 

explain the practical and theoretical components of slope-area 

discharge measurements. Channel geometry of the reach is 

important in producing accurate slope-area computations of 

discharge. Large changes in the shape of the channel along a 

reach, for example, should be avoided due to uncertainties in 

energy losses. Ideally, cross sections selected in the slope-area 

reach will be uniform and have nearly the same shape and area 

for a given discharge. In addition, the reach should be long 

enough and the fall large enough that errors associated with 

interpretations in the high-water profile are small. In reality, 

some compromises between logistical considerations and 

desirable channel properties are typically required. The length 

of the indirect reach is often limited by the geometry of the 

channel and the practical difficulties of surveying long reaches 

of a river channel, and a uniform channel may be difficult or 

impossible to find. 

The Slope-Area Computation Program

The Slope-Area Computation (SAC) Program (Fulford, 

1994) has greatly improved the ease of the computation. 

Input files to SAC supply all required information and the 

program automates the indirect peak discharge calculation. 

SAC output includes discharges computed for all cross-section 

combinations and warnings for reach length, drop, and other 

parameters that affect or help evaluate the accuracy of the 

result. 

Sensitivity of Indirect Discharge Computations 

to Slope

The calculation of accurate discharges using the slopearea method depends on the accuracy of the water-surface 

elevations, and thus the reach slope, supplied in the input to 

SAC. Unlike step-backwater calculations, in which the watersurface elevation is specified as a boundary condition at the 

downstream end (for subcritical flow) and the upstream water 

surface profile is calculated, the slope-area method for computing discharge imposes a water-surface slope (modified by 

streamwise changes in velocity head) on the calculation that 

is used to directly calculate discharge. The sensitivity of the 

calculated discharge to errors in the reach water-surface drop 

can be determined by finding the ratio of discharges calculated 

using the true water-surface slope and the water-surface slope 

estimated from surveys of reach length and apparent drop in 

the water surface. The Manning equation is used to compute 

discharge,

(1)

where Q is the discharge, n is the Manning roughness coefficient, A is the cross-section area, R is the hydraulic radius, 

and S is the water-surface slope. Equation 1 is used with 

metric units; with Imperial units, the 1/n is replaced by 1.49/n. 

Representing the surveyed water-surface drop in the reach 

used to calculate the discharge as the true drop plus an error, 

the ratio of the true and calculated discharges can be represented by,

 

 Q

Q

e

d

c

t

c

t

 















 1

1 2

,

/

 

 

(2)

 

where Qc is the discharge calculated with the measured water 

surface drop, Qt is the true discharge, ec is the error in the 

measured drop in the reach used to calculate Qc, and dt is the 

true drop in the reach. Note that reach length is not represented 

in equation 2. Small differences in the cross-sectional area 

and hydraulic radius related to differences in water-surface 

drops are neglected in equation 2. An example application of 

equation 2 over a range of errors in reach drop (fig. 1) shows 

that an error in reach drop of a few tenths of a foot can lead to 

a calculated discharge that is off by about 25 percent. Equation 1 shows that the discharge is linearly related to crosssectional area and roughness but is related to the square root of 

the slope, thus indicating greater sensitivity to channel shape 

and roughness than slope. Channel shape is well defined by 

surveys if the channel does not change significantly during a 

flow event, however, and roughness is generally well defined 

by published methods for estimating roughness or verified 

roughness in similar channels.

Q

n  AR S , 1 2 3/ / 1 2
The Continuous Slope-Area Method 3

The Continuous Slope-Area Method

The CSA method expands the slope-area method of 

computing peak discharge to a complete flow event. Continuously recording pressure transducers (PTs) installed at 

three or more cross sections provide water-surface slopes 

and stage during an event that can be used along with 

cross-section surveys and estimates of channel roughness to 

compute a continuous-discharge hydrograph. The method, 

as demonstrated by the applications described in this report, 

can also reveal complexities during significant flows that are 

not evident from peak-flow estimates derived from post-flow 

evidence. 

The CSA method has been made feasible by the availability of low-cost recording PTs that provide a continuous 

record of stage at each cross section. In addition to the applications described in this report, such devices have been used 

at crest-stage gages to record continuous stage in ephemeral 

streams (Waltemeyer, 2005). Crest-stage gages were used in 

this experiment to incorporate standard USGS equipment and 

methods. 

Site Selection

Information about the channel required for the slope-area 

method is also required for application of the CSA method. A 

minimum of variability between cross sections and a sufficient 

drop in the channel are desirable properties. Channel roughness may be estimated using published methods or derived 

from direct measurements of discharge and water-surface 

slope. A detailed guide to the slope-area method of discharge 

is presented by Dalrymple and Benson (1967).

Dalrymple and Benson (1967) indicate that the selection 

of cross-section locations should be determined by breaks in 

slope of the water surface profile determined from surveys of 

debris lines. This method of determining cross-section locations can be difficult to apply where debris lines are poorly 

defined and is not possible prior to a flow, as would typically 

be the case for an initial CSA application. Consequently, cross 

sections for a CSA reach can be located initially, depending on 

resources available, based on a visual assessment or survey of 

the reach to identify changes in bed slope or channel width. If 

sufficient resources are available, a step-backwater model of 

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

R

A

TIO

OF C

ALC

ULA

TED

Q

T

O

T

R

UE Q-1

ERROR IN REACH DROP, IN FEET

Figure 1. Error in discharge calculated with equation 2, caused by errors in measured reach 

drop. The sample calculation shown is for a true drop in the reach of 0.5 ft.
4 The Continuous Slope-Area Method for Computing Event Hydrographs

the reach would provide an estimated water surface profile that 

could be used in accordance with the criteria of Dalrymple and 

Benson (1967) for cross-section location. After a significant 

flow has occurred in the reach, cross-section location could be 

adjusted according to the methods of Dalrymple and Benson 

(1967) if debris lines are adequate. 

Evaluation of Pressure-Transducer Data and 

Calculated Hydrographs

The calculation of discharge using the slope-area method, 

on which the CSA method is based, could be accomplished 

with only two PTs at two cross sections, but at least three cross 

sections are considered minimum for obtaining reasonably 

accurate results. The redundancy of multiple cross sections, 

and possibly more than one PT per cross section, can be an 

important aid in interpreting stage data and choosing the best 

sequence of cross sections and stage hydrographs for the discharge calculation and can be critical if instruments malfunction. Including more cross sections in the discharge calculation 

also increases confidence in the computed discharges.

Irregularities in the calculated-discharge hydrographs 

can be a result of errors in the PT data, changes in the channel 

during the flow event, or accurate PT readings that are affected 

by local conditions such as debris piles, wave action, or isolation from the main flow. The errors in the stage data can come 

from PT errors, such as time drift and loss of calibration, or 

CSG errors that can occur from burial or plugging by sediment 

or from accumulation of local debris. Loss of calibration can 

be detected by comparing the PT readings with high-water 

marks on the bank, if clear marks are available, or peak stage 

was recorded by the CSG. A PT water-surface elevation higher 

than the high-water marks may indicate a problem with the PT. 

Changes in the channel during runoff events can include scour, 

fill, and changes in vegetation along the slope-area reach. 

Scour may occur at one cross section while fill conditions 

may affect another cross section during the same flow event. 

Channel roughness can be modified during floods, if vegetation is bent over or scoured out or if debris collects on trees. 

All of these conditions need to be identified during the channel 

survey after the runoff event and considered when evaluating 

the accuracy of the computed discharge. 

Comparison of Pressure-Transducer Peaks to Crest-Stage 

Gage Peaks

If reliable CSG peak stages or other indicators of maximum stage are available, as in the Babocomari River study 

reach, they can be compared to the peak stages indicated 

by the PTs. Differences between the two do not necessarily 

indicate error in the PT stage, however. The PTs, for example, 

may miss the peak stage even if they are recording at 5-min 

intervals.

If the CSG peak stages are recorded in enough cross sections, a slope-area calculation can be made to determine the 

event-peak discharge. Water-surface elevations from CSGs at 

cross-section locations is not as comprehensive as a continuous water surface derived from surveyed debris lines, as is 

typically used in a conventional slope-area measurement, but 

CSGs, which are constructed and widely used by the USGS 

to obtain accurate records of peak stage, may provide more 

accurate water-surface elevations at cross sections than those 

inferred from debris lines. The computation can be used to 

help identify the most favorable cross-section combination for 

the CSA calculations, and the event peak computed with CSG 

data can also be compared with the peak discharge calculated 

with the CSA method to test the accuracy of the CSA method. 

Because the 5-min recording interval used in the stage recorders may miss the instantaneous peak stage during a flashy 

event, the CSA peak stage could be less than the event peak. 

The CSA peak stage can equal the CSG peak stage, but the 

CSA peak stage should never exceed the CSG peak, unless the 

CSG is overtopped. 

Stage-Discharge Relations

Stage-discharge plots derived from the CSA hydrograph 

are an effective tool for examining PT performance. The computed discharge is sensitive to the measured fall in the reach. 

If one or more PTs do not function properly, the computed discharge as a function of stage will be erratic, and a tight relation 

will not be possible. A tight fit does not assure the accuracy of 

the stage-discharge relation, but it is an important indicator of 

the quality of the stage data. If the channel was stable and the 

instruments performed normally during an event, plots of the 

calculated discharges against the corresponding stages from 

each of the pressure transducers should form a tight, consistent 

plot. If the plot is widely scattered, it likely indicates faulty 

data or channel instability. A tight plot for medium and high 

discharge may be accompanied by considerable scatter at low 

discharges, especially in sand-bedded channels. In this case, 

the lower discharges may be affected by small-scale channel 

features that are not significant at higher discharges. 

Hysteresis in the Stage-Discharge Relations

The CSA method can be used to make indirect measurements during the rise and fall of the event hydrograph. The 

data may be used to evaluate differences in hydraulic conditions on the rising and falling limbs of a hydrograph which 

can cause a loop in the stage-discharge rating curve commonly 

referred to as hysteresis. Hysteresis in rating curves can be 

caused by an increase or decrease in the steady-discharge 

water-surface slope related to the passing of a discharge 

wave. On the rising limb, the water-surface slope is increased 

and lowers the stage at a given discharge with respect to the 

steady-discharge water-surface slope. The opposite occurs on 

the falling limb of the hydrograph. The magnitude of the hysteresis can be estimated by scaling the terms in the momentum 

equation using reasonable values for wave speed (which can 

be estimated from dQ/dA), the rate at which the stage rises or 

falls, and the steady-discharge water-surface slope (for example, Wiele and Smith, 1996). Changes in roughness or shape 
Study Site on the Babocomari River 5

during an event can also cause a loop in the rating curve. In 

ephemeral channels or channels with low base flow, such as 

the Babocomari River, vegetation commonly grows within 

the channel between significant flow events. Channel roughness can be reduced significantly during a large discharge, if 

vegetation is uprooted and washed downstream or if flexible 

vegetation, such as grass, is bent over. Conversely, uprooted 

vegetation can form dams that cause significant backwater 

effects. Scour or deposition can also contribute to changes in 

the stage-discharge relation during an event.

Apparent hysteresis can potentially be caused by instrument error or weaknesses in its installation. If the PT position 

is not firmly fixed, the reference elevation used in the conversion of pressure to stage can change, introducing error into the 

stage.

Evaluation of Channel Geometry

Changes in channel shape can be determined by comparing cross sections that were surveyed before and after the flow 

event. After each event, the cross sections should be evaluated to determine if they should be resurveyed. Many small 

and medium events produce little or no change to the channel 

and will not require the channel to be resurveyed. High flows, 

however, can significantly modify the channel, making new 

surveys necessary. Accuracy of computed peak or continuous discharges can be degraded if significant channel change 

occurred. 

The Effect of Unsteadiness on Discharge Computation 

Accuracy

The slope-area computation used for indirect discharge 

measurements and the CSA method is based on an assumption 

of steady flow. For indirect measurements, this is not an issue 

because the change in velocity over time is zero at the peak 

discharge. For computing continuous hydrographs, as in the CSA 

method, the change in velocity over time is nonzero except at the 

peak. The significance of neglecting the unsteadiness of the flow 

can be estimated by considering the relative magnitudes of the 

terms in the one-dimensional St. Venant equation for momentum,

∂

∂



∂

∂



∂

∂ − 



 



 

u

t

u

u

x

g

e

x

S u*

Rh

2

0,

 

(3)

where x is the streamwise dimension, g is gravity, de/dx is the 

additional water-surface slope due to a varying flow field, S is the 

steady-flow water-surface slope, u* is the shear velocity, and Rh is 

the hydraulic radius. Dividing equation 3 by the driving term, gS, 

normalizes the equation and reduces the driving term to unity,

 (4)

Taking gravity as a constant, the first term in equation 4 

indicates that the significance of the error, induced by using 

steady-flow equations to model unsteady flow in the CSA 

method, is a function of the change of velocity over time and 

the reach slope. Reaches with steeper slopes are less sensitive to changes in velocity over time than reaches with lower 

slopes (fig. 2). In the flows on the Babocomari River discussed 

below, the discharge, and consequently velocity, changes 

rapidly, but the slope of the reach was about 0.01, which tends 

to reduce the significance of the unsteadiness on discharge 

calculations.

Sample calculations with a hypothetical trapezoidal channel (slope = 0.001, bed width = 50 ft, Manning’s n = 0.035, 

bank width = two times the depth) illustrate that the velocity 

and du/dQ tend to change most rapidly with respect to discharge 

at lower discharges (fig. 3). At the medium and high discharges 

at which the CSA method is most effective, the relatively muted 

response of velocity to changes in discharge tends to favor the 

use of steady-flow equations, but this can be offset by a rapid 

rise in discharge. During the largest flow on the Babocomari 

River on July 27, 2006, the normalized unsteady term in equation 4 was not significant (figs. 4, 5), indicating that the accuracy of the computed hydrograph was not significantly affected 

by the use of steady-flow equations.

Study Site on the Babocomari River

A reach of the Babocomari River was chosen for the 

initial application and testing of the CSA method (fig. 6). The 

Babocomari River is a tributary to the San Pedro River in 

southeastern Arizona, and the study reach and access to it are 

on Bureau of Land Management land. The elevation of the 

study reach is 3,980 ft and the drainage area is about 307 mi2. 

The stream is typically perennial with a base flow during the 

winter of about 1 ft3/s. Peak flows usually occur during the 

summer months as a result of local convective storms. The 

streamflow record of the Babocomari River has been used for 

groundwater studies of the San Pedro basin and the effects of 

groundwater development on the San Pedro River, a free flowing river that provides vital habitat in an area undergoing rapid 

population increases and urban development. 

There are two permanent streamflow-gaging stations 

along the Babocomari River. The USGS stream gage Upper 

Babocomari River near Huachuca City, AZ (identification 

number 09471380) measures the runoff from the Huachuca 

and Mustang Mountains (fig. 6). The USGS stream gage Babocomari River near Tombstone, AZ (09471400) was installed 

for the primary purpose of measuring base flow from a perennial section of the river where groundwater is discharged to 

the surface (Pool and Coes, 1999). This section of the river is 

not accessible for medium to high flow measurements. 

Starting in the summer of 2002, a CSA reach was 

selected and monitored on the Babocomari River. The slopearea reach is approximately 0.25 mi downstream from the 

Babocomari River stream gage (09471400) near Tombstone, 

AZ. The study site conforms more closely to the criteria established by Dalrymple and Benson (1967) than other reaches in 

1 1 0,

2

gs

u

t

u

gs

u

x

e x

s

u

gR sh

∂

∂

+

∂

∂

+

∂ ∂

− + = /
6 The Continuous Slope-Area Method for Computing Event Hydrographs

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5

PER

CEN

T ER

R

O

R

CHANGE IN VELOCITY OVER AN HOUR, IN METERS PER SECOND

0.01

0.001

0.0001

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1,000 C

H

A

N

GE IN

VELO

CITY

WIT

H

RES

PEC

T

T

O

DIS

C

H

A

R

GE, IN (FEET

PER

SEC

O

N

D)/(C

U

BIC FEET

PER

SEC

O

N

D)

VELO

CITY, IN FEET

PER

SEC

O

N

D

DISCHARGE, IN CUBIC FEET PER SECOND

velocity

du/dQ

Figure 3. Velocity and du/dQ as function of discharge for a trapezoidal channel with a bed width of 50 ft, 

slope of 0.001, and a Manning’s n of 0.035. The bank width was specified as two times the depth.

Figure 2. Percent error in the St. Venant momentum equation as a result of neglecting the unsteady term as a function 

of change in velocity for three reach slopes.
Study Site on the Babocomari River 7

Figure 4. Hydrograph computed with the Continuous Slope-Area method and the normalized unsteady term from the momentum 

equation (du/dt)/(gS) during the July 27, 2006, event on the Babocomari River.

0

10

20

30

40

50

60

70

80

90

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 More

N

U

M

BER

OF O

C

C

U

REN

CES

(du/dt)/(gS)

Figure 5. Histogram of the absolute value of the normalized unsteady term in 

equation 4 for the Babocomari River hydrograph shown in figure 4.

- 0.05

- 0.04 - 0.03 -

- 0.02

0.01

0.01

0.02

0.03

0.04

0.05

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0 5 10 15

(du/dt)/(gS)

DISC

H

A

R

GE, IN

C

U

BIC FEET

PER SEC

O

N

D

TIME, IN HOURS

Discharge (du/dt)/gS

0
8 The Continuous Slope-Area Method for Computing Event Hydrographs

HUACHUCA MOUNTAINS

Sierra Vista

Tombstone

(09471400)

(09471380)

(09471550)

MULE MOUNTAINS

HUACHUCA MOUNTAINS

(

(

#

#

#

Babocomari River

110°30'0"W 110°15'0"W 110°0'0"W

0 5 10 Miles

River

80

80

82

90

90

90

82

92

San Pedro

31°30'

31°45'

110°15' 110°

Tucson

UNITED STATES

MEXICO

Gila 

River

ARIZONA

MUSTANG MOUNTAINS

# STREAMFLOW-GAGING STATION—

U.S. Geological Survey

10 Kilometers

WHETSTONE MOUNTAINS

DRAGOON MOUNTAINS

MULE MOUNTAINS

Base from U.S. Geological Survey 

digital elevation model data,

1:250,000, 1982

Universal Transverse Mercator

Projection, Zone 12, 

Datum: NAD 27

CONTINUOUS SLOPE-AREA GAGE—

U.S. Geological Survey

#

#

Figure 6. Map showing the study area on the Babocomari River.
Study Site on the Babocomari River 9

Figure 7. View looking downstream from cross section 1. Note the 

dense grass where trees are sparse.

Figure 8. View looking upstream from cross section 4. Ash trees 

grow along the low-flow channel.

the area. At this downstream location, the flow is confined to 

one main channel. A tributary that flows intermittently enters 

the river between the gage and the CSA reach.

Description of Channel Conditions along the 

Slope-Area Reach and Roughness Coefficient 

Selection

The slope-area reach was selected because it was straight 

and uniform. The reach is about 300 ft long with about a 2.7-ft 

fall in water-surface elevation over the range of observed flows. 

The reach is straight and uniform for about 50 ft above the 

upstream cross section and 50 ft below the downstream cross 

section. The total length of the reach was limited by a tributary 

confluence just upstream of the reach and by an expanding 

channel downstream of the reach. The cross sections were 

spaced approximately 100 ft apart.

The grass upstream and downstream of cross section 

1 (the upstream extent of the study reach) was dense and 

consistently about 2 ft tall (fig. 7). The grass throughout the 

rest of the reach during the study period was sparse on the left 

bank and dense on the right bank. The density of grass in the 

reach is related to the density of trees growing in the reach; 

areas of dense grass are areas of sparse trees. The exposure, 

absence, or burial of grass in the reach was used to determine 

if scour or fill occurred during a high-flow event. 

The trees in the slope-area reach consist of ash, willow, 

mesquite, and walnut. The ash and willow are the predominant types of trees growing in the slope-area reach. The 

younger ash trees (6–14 inches in diameter) line the low-flow 

channel and form a ribbon of trees that create barriers on the 

left bank of the channel and often collect debris (fig. 8).

 The willows are not as numerous as the ash trees but 

tend to be 14 to 20 inches in diameter. There were a few small 

willows in the low-flow portion of the channel. The mesquite 

form dense mesquite bosques in the overbank flow areas. A 

few walnut trees, 10 to 14 inches in diameter, grew on the left 

bank between cross sections 1 and 2. 

A small tributary with a drainage area of less than 0.5 mi2

flows into the channel between the gage and the slope-area 

reach. A PT gage was installed to determine whether inflow 

from the tributary occurred during main-stem events. The flow 

from this tributary was not significant during the five events 

that occurred during the study period and was neglected in the 

discharge calculations.

The flow through all four cross sections during the study 

period was contained by steep and well-defined embankments. The vegetation in cross section 1 (X1), the most 

upstream cross section, consists mostly of grass and small 

trees (fig. 9). At low flow, the water is contained in a narrow 

3-ft-wide channel. The majority of the section is covered with 

thick grass. 

Cross section 2 (X2) is 110 ft downstream of X1 and has 

a more incised section of flow where the water is ponded at 

low flow. The vegetation at X2 consists of grass and sapling 

trees with some mesquite trees higher on the banks (fig. 10).

Cross section 3 (X3), 79 ft downstream from X2, also 

has an incised section of channel and has vegetation types 

similar to X2 (fig. 11). A row of ash trees, located on the lowflow section of the left bank starting in X3, extends downstream through cross section 4 (X4). 
10 The Continuous Slope-Area Method for Computing Event Hydrographs

Cross section 4 (X4), 111 ft downstream of X3, does not 

have an incised channel but has a wider and shallower section 

of flow. The main section of flow consists of small cobbles 

and gravels (fig. 12). At low flow, riffles form at this cross 

section.

A Manning’s roughness coefficient was selected based 

on the type and density of the vegetation in the slope-area 

reach. Grass is the predominant natural condition that affects 

the Manning’s roughness coefficient for medium and low 

flows. For these conditions, a Manning’s roughness coefficient of 0.035 was selected for all four cross sections, based 

on values from reference tables and previous publications 

(Aldridge and Garrett, 1973; Thomsen and Hjalmarson, 1991; 

Phillips and Tadayon, 2006). For high flows, the trees along 

the bank increase the Manning’s roughness coefficient to 

0.040, which is also based on reference tables and previous 

publications (Aldridge and Garrett, 1973; Thomsen and Hjalmarson, 1991; Phillips and Tadayon, 2006). 

Figure 11. Views from cross section 3 looking upstream (left), downstream (center), and downstream (right).

Figure 9. Views from cross section 1 looking upstream (left), downstream (center), and downstream (right).

Figure 10. Views from cross section 2 looking upstream (left), downstream (center), and downstream (right).
Application of the Continuous Slope-Area Method on the Babocomari River 11

Application of the Continuous SlopeArea Method on the Babocomari River

Installation of Pressure Transducers

The initial installation of PTs for the continuous slopearea application consisted of a modification of the existing 

crest-stage gage (CSG) design. The CSGs were made of a 

4-ft length of 2-in galvanized pipe with a perforated cap on 

the bottom (fig. 13). The galvanized pipe contains a narrow 

wooden stick and granulated cork on the bottom cap. During a streamflow event, the cork rises to the peak elevation of 

streamflow and remains on the wooden stick after the stage 

recedes, leaving a mark where the crest occurred. PTs were 

secured to the bottom of the crest-stage gage sticks with hose 

clamps.

Eight PTs were installed at four cross sections in the 

overbank area on both sides of the channel (fig. 14). One additional PT gage was installed in a tributary located about 100 ft 

upstream from the first cross section to document any inflows 

between the permanent USGS gage and the CSA reach. Each 

PT installed in the reach is identified by its location in the 

reach. For example, PTL2 (pressure transducer 2, left bank) 

is installed on the left bank and along cross section 2, while 

PTR2 (pressure transducer 2, right bank) is installed on the 

right bank. Figure 15 shows the elevations of the CSG pins 

(used as an elevation reference) on the left and right banks. 

The streamwise elevation differences between CSG pins on 

either bank are shown in table 1. On each bank the elevation 

difference between the farthest upstream and downstream 

CSG pins is greater than 2 ft. The minimum elevation difference between each CSG pin on the left bank was 0.47 ft, and 

the minimum on the right bank was 0.07 ft. The CSG pins 

on the left bank were installed along the overbank area of the 

channel and are at a higher elevation than the CSG pins on 

the right bank. The CSG pins on the right bank were installed 

closer to the active channel. The fall in the reach and between 

the CSG pins should be uniform, for example the CSG pin in 

PTR3 should have been installed at an elevation 0.5 ft lower 

than the pin in PTR2.

The miniTROLL PTs with a sensor range of 0–30 PSI 

manufactured by In-Situ Inc. were used for this study. The PTs 

Figure 12. Views from cross section 4 looking upstream (left), downstream (center), and downstream (right).

Figure 13. Installation of the crest-stage gage (left). The pressure transducer is clamped to the bottom of the crest-stage gage board 

(center and right).
12 The Continuous Slope-Area Method for Computing Event Hydrographs

were programmed to record at 5-min intervals regardless of 

whether the channel was flowing. In the absence of equipment 

malfunction, the PT’s internal data recorders were capable 

of measuring and recording pressure at this rate for approximately 6 months. The PTs used for this application measured 

absolute pressure because they are not vented to the atmosphere. Consequently, in addition to measuring the depth of 

water above the PT, atmospheric pressure was also measured. 

To remove the effects of atmospheric pressure, a PT measuring 

the barometric pressure was placed in the gage house, which is 

located about 0.25 mile upstream from the slope-area reach. 

Collection and Reduction of PressureTransducer Data

The stage data were downloaded from the PTs after 

significant flows. In addition, the cross sections and CSG pin 

elevations were resurveyed to document any scour or fill in the 

channel and to ensure the CSG pins had not moved. During 

each site visit, the CSGs were inspected for high-water marks. 

The bottom CSG cap was also removed and inspected to 

ensure the PT was in connection with the river and not clogged 

with sediment and debris. After each site visit, fresh cork 

was added to the CSGs. If high-water marks were present, 

they were measured and documented. In addition, any other 

indications of streamflow were noted, such as debris on the 

base of the CSG and the condition of the vegetation. The PTs 

were synchronized with atomic clocks to prevent time drift. If 

time drift was detected, it was documented and the transducer 

data were corrected. It is imperative that clocks in the PTs 

are synchronized so that they record water-surface elevations 

simultaneously during an event. 

Each downloaded data set from the PTs was corrected for 

barometric effects, PT elevation, and CSG pin elevation. The 

CSG peak was corrected to gage datum by adding the highwater marks from the crest-stage gage to the CSG pin elevation to determine the final peak elevation. After these corrections were applied, both peaks (PT and CSG) were compared 

for quality control because the PT-recorded peak should not be 

higher than the CSG high-water mark. 

X1

X2

X3

X4

0 25 METERS

PTR1

PTL1

PTL2

PTR2

PTR3

PTL3

PTL4

PTR4

573480 573510 573540 573570 573600

3507400

3507420

3507440

3507460

3507480

Babocomari River

0 40 FEET

573450

EASTING, IN METERS

NORTHING, IN METERS

Left Bank

Right Bank

PRESSURE TRANSDUCER LOCATION

Figure 14. Plan view of the cross sections and eight pressure transducers in the Babocomari River continuous-slope-area reach.
Application of the Continuous Slope-Area Method on the Babocomari River 13

Calculation of Hydrographs Using the 

Continuous Slope-Area Method

After the necessary corrections were applied to the PT data 

sets, stage hydrographs were produced from the left- and rightbank pressure-transducer data. The water-surface profiles can 

be evaluated for comparison with the guidelines recommended 

by Dalrymple and Benson (1967). The water-surface profiles 

can show insufficient fall between cross sections, which reduces 

the accuracy and consistency of the results. A similar practice 

is followed with conventional indirect methods, where highwater marks and cross sections can be removed from the final 

calculation to improve the quality of discharge computations. 

Following the initial evaluation of the stage data, discharges are 

computed with the SAC program. 

Batch-Processing Discharge Computations

The calculation of the continuous discharge is accomplished by applying the SAC program to each step in the 

Figure 15. Pressure-transducer-pin elevations (dry with no flow).

Table 1. Elevation difference between crest-stage and pressure-transducer datums (dry)

Reach Right-bank elevation 

 difference (ft)

Left-bank elevation 

difference (ft)

X1-X2

X2-X3

X3-X4

X1-X3

X2-X4

X1-X4

0.52

0.07

1.59

0.59

1.66

2.18

0.92

0.69

0.47

1.61

1.16

2.08

43.00

43.50

44.00

44.50

45.00

45.50

46.00

46.50

47.00

47.50

48.00

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Right bank CSA pin elevation

Left bank CSA pin elevation

ELEVATION ABOVE ARBITRARY DATUM, IN FEET

PTL1

PTR1

PTL2

PTR2

PTL3

PTR3

PTL4

PTR4

Cross Section 1 Cross Section 2 Cross Section 3 Cross Section 4

STATION, IN FEET DOWNSTREAM OF CROSS SECTION 1
14 The Continuous Slope-Area Method for Computing Event Hydrographs

stage-time series. This procedure was automated with a utility 

program (CSA2SAC) developed for this project that reads in 

the channel parameters used in the SAC program and the stage 

data, generates the SAC input files for each time step, runs the 

SAC program for each time step, reads the SAC output files, 

and finally generates a separate file containing the computed 

hydrograph.

Development of Stage-Discharge Relations 

A stage-discharge relation can be created from the 

stage data collected by any of the PTs and the discharge data 

computed by the SAC program. The development of stagedischarge relations is generally best achieved by using the 

discharges computed using more than two cross sections. The 

multi-section reach computation averages reach conditions, 

producing a more consistent discharge. 

Major Flows on the Babocomari River 2002–2006

During the five-year study period, Arizona experienced 

one of the driest periods ever recorded, so medium- and 

high-flow events were less frequent than normal (Phillips and 

Thomas, 2005). Five events that inundated the CSG and PT 

gages occurred during the study period and, as a result, were 

sufficiently large for the application of the CSA method (table 

2; fig. 16). The events between 2002 and 2005 were moderate flows of similar magnitude. The width of flow for these 

events was about 80 ft. During flow in 2006, which was the 

largest during the study, the width of flow exceeded 150 ft 

and depths were over 12 ft. The following sections describe 

one of the four moderate events (October, 2003) and the high 

flow in 2006 to illustrate the CSA application under field conditions. Stage data, computed discharges, and channel shape 

and roughness for all five events are recorded in appendices 1 

and 2.

Flow of October 9, 2003

A moderate event occurred on October 9, 2003, that was 

caused by a late-season monsoon. The streamflow event lasted 

about 1 hr, and the water-surface elevations were high enough 

to submerge all eight PTs for 20 min. The recorded stage 

hydrographs from each of the PTs are shown in figure 17. 

Channel Geometry

The channel geometry surveyed before and after the 

October 9, 2003, flow event indicates little channel change 

during the event (figs. 18–21). 

2002 2003 2004 2005 2006 2007

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

750 cfs

August 3, 2002 500 cfs

July 25, 2003

600 cfs

October 9, 2003

900 cfs

August 14, 2005

9,600 cfs

July 27, 2006

ANNUAL PEAK STREAMFLOW, IN CUBIC FEET PER SECOND

CALENDAR YEAR

Figure 16. Peak streamflows recorded on the Babocomari River during the study period, 2002–2006.
Application of the Continuous Slope-Area Method on the Babocomari River 15

44.00

44.50

45.00

45.50

46.00

46.50

47.00

47.50

48.00

19:30 19:45 20:00 20:15

ELEV

A

TIO

N

A

B

O

VE ARBITRARY

D

A

T

U

M, IN FEET

OCTOBER 9, 2003

PTR1 PTR2 PTR3 PTR4

PTL1 PTL2 PTL3 PTL4

Figure 17. Stage hydrographs from the October 9, 2003, flow event on the Babocomari River.

Table 2. Peak stages recorded by the crest-stage gages and by the pressure transducers 

during the October 9, 2003, event.

Pressure transducer (PT)

(R, right; L, left) 

Crest-stage gage height

(feet)

Peak (ft) and time

recorded by the PT 

PTR1 47.33 47.30 at 19:55

PTL1 47.54 47.49 at 19:55

PTR2 47.17 47.00 at 19:55

PTL2 47.22 47.10 at 19:50

PTR3 46.53 46.38 at 19:50

PTL3 46.71 46.63 at 19:55

PTR4 46.33 46.34 at 19:55
16 The Continuous Slope-Area Method for Computing Event Hydrographs

Evaluation of the High-Water Marks

Crest-stage gage heights representing the crest of the 

peak were present on all eight of the crest-stage gages following the flow event. The crest-stage gage heights and the 

PT-recorded peak values and times associated are shown in 

table 2. On the left bank, the crest-stage gage heights were 

higher than the recorded PT peak values; on the right bank, 

the recorded PT peak values were within 0.01 ft or less than 

the crest-stage gage heights, with the exception of PTR4 that 

Figure 19. Channel surveys in cross section 2 before and after the October 9, 2003, event. The blue dashed line 

shows the water-surface elevation at the peak discharge.

Figure 18. Channel surveys in cross section 1 before and after the October 9, 2003, event. The blue dashed line 

shows the water-surface elevation at the peak discharge.

40

41

42

43

44

45

46

47

48

49

50

20 40 60 80 100 120 ELEV

ATIO

N

A

B

O

VE A

R

BIT

R

A

R

Y

D

AT

U

M, INFEET

DISTANCE, IN FEET

Cross section1

Before Event

After Event

Event Peak

40

41

42

43

44

45

46

47

48

49

50

0 20 40 60 80 100 120 ELEV

ATIO

N

A

B

O

VE A

R

BIT

R

A

R

Y

D

AT

U

M, INFEET

DISTANCE, IN FEET

Cross section2

Before Event

After Event

Event Peak
Application of the Continuous Slope-Area Method on the Babocomari River 17

recorded the same water-surface elevation as PTR3. Six of 

the eight PTs recorded the peak water surface at 19:55, while 

two PTs recorded the peak at 19:50. The difference between 

these peak times could be attributed to splashing or wave 

action. 

Conventional Slope-Area Computation and Analysis

A slope-area calculation using the corrected CSG elevations at four cross sections was performed. A Manning’s n

value of 0.035 was judged appropriate for each of these four 

Figure 20. Channel surveys in cross section 3 before and after the October 9, 2003, event. The blue dashed line 

shows the water-surface elevation at the peak discharge.

Figure 21. Channel surveys in cross section 4 before and after the October 9, 2003, event. The blue dashed line 

shows the water-surface elevation at the peak discharge.

40

41

42

43

44

45

46

47

48

49

50

0 20 40 60 80 100 120 ELEV

ATIO

N

A

B

O

VE A

R

BIT

R

A

R

Y

D

AT

U

M, INFEET

DISTANCE, IN FEET

Cross section3

Before Peak

After Peak

Event Peak

40

41

42

43

44

45

46

47

48

49

50

0 20 40 60 80 100 120 140 ELEV

ATIO

N

A

B

O

VE A

R

BIT

R

A

R

Y

D

AT

U

M, INFEET

DISTANCE, IN FEET

Cross section4

Before Event

After Event

Event Peak
18 The Continuous Slope-Area Method for Computing Event Hydrographs

Table 3. Peak discharge for cross sections 1–4, based on average of left and right stage data from 

the pressure transducers and crest-stage gage from the October 9, 2003, event.

cross sections based on channels with similar conditions in 

southeastern Arizona (Aldridge and Garrett, 1973; Phillips 

and Tadayon, 2006). The computed discharge, using the 

average of the left and right crest-stage gage heights, was 

626 ft3/s (table 3). 

Evaluation of the Pressure-Transducer Data

The left and right averaged PT-stage values used for the 

CSA computation are shown in figure 22. The average of the 

left- and right-bank water surfaces results in a hydrograph 

that represents the water surfaces during the flow event. The 

four hydrographs contain water-surface elevations recorded 

nine times during the 40-minute event.

Continuous Slope-Area Discharge Computations and 

Analysis

The discharge values computed from the average peak 

left and right CSG heights and the recorded PT-gage heights 

are shown in table 3. The CSA-computed discharge values 

ranged from 340 to 591 ft3/s during the streamflow event. The 

computed peak discharge using the CSG heights (626 ft3/s) 

was 35 ft3/s greater than the computed peak discharge from the 

PTs (fig. 23). 

Rating Development 

A stage-discharge relation was developed showing 

the relation between the discharge computed with the CSA 

44.00

44.50

45.00

45.50

46.00

46.50

47.00

47.50

48.00

19:30 19:45 20:00 20:15

ELEV

A

TION

ABOVE ARBITRARY DA

TUM, IN FEET

OCTOBER 9, 2003

X1

X2

X3

X4

Figure 22. Average left- and right-bank pressure-transducer-stage hydrographs during the 

October 9, 2003, event.

Peak discharge computed from the creststage gage heights (ft3

/s)

Peak discharge computed from the PT

recorded elevations (ft3/s)

626 591 
Application of the Continuous Slope-Area Method on the Babocomari River 19

method and stage from PTR1 (fig. 24). Stage values from 

PTR1 were selected over the stage values from the other PTs, 

because PTR1 stage values produced the closest fit in the 

stage-discharge relation. The single discharge value calculated 

from the CSG heights was also included in the plot and is 

consistent with the CSA results. 

Summary of the October 2003 Event

The third flow event of the study period occurred on October 

9, 2003, and all eight of the PTs were submerged and recorded 

stage during part of the 1-hr event. Crest-stage gage heights were 

also obtained from eight of the CSGs. Slope-area calculations 

were performed to determine the peak streamflow using both data 

from the PTs and the CSG heights. The computed peak discharge 

value from the CSG heights was about 6 percent higher than the 

peak discharge value calculated from the peak PT values. 

The Flow Event of July 27, 2006

The July 27, 2006, event produced the peak of record, 

9,600 ft3/s, which had an annual exceedance probability of 

4 percent. This peak was nearly 10 times greater than any of 

the previous peaks during the study. Six out of the eight PTs 

collected data for this event (fig. 25); two PTs (PTR2, PTL4) 

did not work due to lost battery power. All four cross sections 

were used in the analysis. 

Five of the six PTs that worked for this flow event were 

rotated about their base shortly after the peak. The pipes supporting PTR1, PTL2, PTR3, PTL3, and PTR4 were all rotated 

about 45o (fig. 26) in the downstream direction; only PTL1 

remained upright. The five PTs continued to record throughout the event, but only data obtained prior to their displacement were used in the analysis. A sudden shift of about 0.3 ft 

in stage at each PT indicated the time at which the PTs were 

displaced. 

Changes in Channel Shape

The only measureable change to the reach during the study 

period was caused by the July 27, 2006, flood. Two trees were 

uprooted and deposited near the PTs in X1 and X2 but appeared to have minimal effect on the cross-sectional areas of 

X1 and X2. Vegetation debris accumulated near X3, and sand 

and gravel were deposited near X4. The changes are generally 

minor, and their effects on channel hydraulics over the course 

of the event were neglected in the discharge calculations (fig. 

27). The channel changes, however small, introduce additional 

uncertainty in the computed hydrograph and illustrate another 

0

100

200

300

400

500

600

700

19:30 19:45 20:00 20:15

DISCHARGE, IN CUBIC FEET PER SECOND

OCTOBER 9, 2003

X1-X4 PTR1

Slope Area Calculation

from CSG

Figure 23. Discharge values computed with the average pressure-transducer and crest-stage gage data 

for the October 9, 2003, event.
20 The Continuous Slope-Area Method for Computing Event Hydrographs

46.00

46.25

46.50

46.75

47.00

47.25

47.50

47.75

48.00

0 100 200 300 400 500 600 700

WATERS

U

RFA

CE ELEV

A

TIO

N

A

T PT

R1

DISCHARGE, IN CUBIC FEET PER SECOND

X1-X4 PTR1

Slope Area

Calculation from

CSG

Figure 24. Stage-discharge relation determined with discharges computed from the averaged pressuretransducer data and crest-stage gage data for the October 9, 2003, event.

source of potential error that is present in any kind of hydraulic 

reconstruction of a significant flow, whether it is step-backwater 

modeling, multi-dimensional hydraulic modeling, peak-flow 

indirect measurements, standard stream gaging, or CSA applications. The precise timing of the changes to channel shape 

is unknown but likely occurred near the peak discharge. Gravel 

deposited near the right bank in X1 caused a 2 percent decrease 

in the peak-flow cross-sectional area (fig. 28). Scour in the thalweg and the left side of the channel caused an 8 percent increase 

in cross-sectional area in X2 (fig. 29). In X3, a 0.5 percent increase occurred as a result of scour in the center of the channel 

(fig. 30). There was a 4 percent decrease in cross-sectional area 

in X4, caused by deposition of sand and gravel in the center of 

the channel (fig. 31).

Evaluation of the High-Water Marks

High-water marks from the CSGs were not present, because the CSGs were overtopped. Instead, surveyed 

high-water marks were used in the slope-area computation, 

although high-water marks were not preserved on the large 

rocks that dominate the left bank at X1 and X2. The large 

rocks were present on the left bank 50 ft upstream of X1 and 

extended continuously downstream through X2. The surveyed 

high-water marks combined with the peak stage values from 

the PTs are shown in table 4. The peak recorded from PTL3 

of 56.95 ft was greater than the high-water mark of 55.79 ft 

surveyed in X3 on the left bank. This may have been caused 

by debris that accumulated in the center of the channel, which 

caused an elevated water surface next to PTL3, but did not 

extend far enough along the bank to elevate the left-bank highwater mark or to affect PTL2. 

Slope-Area Computation and Analysis of High-Water 

Marks

A slope-area calculation of the peak discharge using the 

surveyed high-water marks at the four cross sections was performed. A Manning’s n of 0.040 was selected, which is greater 

than the value of 0.035 used in previous flow events. The n 

value was increased to account for debris that was collected 

on trees and bushes in the slope-area reach, and the fallen trees 

that collected deposits of sand and gravel. 

The fall between cross sections X3-X4 on the left bank 

was 0.60 ft, and a discharge of 12,044 ft3/s was computed (table 

5). On the right bank, the subreach X1-X2 had an inverse slope 
Application of the Continuous Slope-Area Method on the Babocomari River 21

46

48

50

52

54

56

58

0:00:00 4:48:00 9:36:00 14:24:00 19:12:00

ELEV

A

TIO

N, IN FEET

TIME, IN HOURS:MINUTES

PTR1

PTL1

PTL2

PTR3

PTL3

PTR4

Figure 25. July 27, 2006, stage hydrographs for six pressure transducers. Right-bank pressure transducers are 

indicated by R in the legend label; left-bank pressure transducers are indicated by L in the legend label; the 

number in the legend label corresponds to the cross-section number.
22 The Continuous Slope-Area Method for Computing Event Hydrographs

Figure 28. Channel surveys in cross section 1 before and after the July 27, 2006, event. The blue line shows the water-surface elevation 

at the peak discharge. At the peak discharge, the difference in cross-section areas is 2 percent.

and, therefore, that combination of cross sections could not be 

used to compute discharge. The discharges computed with rightbank elevations ranged from 7,818 ft3

/s to 12,409 ft3/s (table 

6). The most consistent results came from the multiple crosssection reaches X1-X3, X2-X4, and X1-X4.

Slope-Area Computation of Peak Discharge using PT Data 

and Analysis of PT Data

The peak discharge was computed using the slope-area 

method and peak PT elevations from the left (table 7) and 

right (table 8) banks. The results of the left-bank slope-area 

computation of discharge showed that only one subreach, 

X1-X2, could be used in the analysis as a result of the debris 

pile downstream. The fall between X1-X2 was 0.33 ft and 

the computed discharge was 8,466 ft3/s. 

The peak stage values from the right bank produced a 

small range in computed discharge of 9,138 ft3/s to 10,589 ft3/s 

(table 8). The discharge computed using stage values from 

the right bank (X1-X4) of 9,621 ft3/s was considered the 

discharge most likely to be accurate from the slope-area 

computations, because it uses the longest reach and incorporates more channel data than the other cross-section 

combinations. 

Figure 26. Right-bank pressure transducer in cross section 1 

(PTR1) after the July 27, 2006, flow event.

Figure 27. View looking upstream from cross section 3 on the right 

bank after the July 27, 2006, event. The floodway is mostly clear of 

obstacles.

40

42

44

46

48

50

52

54

56

58

60

0 20 40 60 80 100 120 140

ELE

V

A

TIO

N, IN FE

E

T

Before

After

Event

peak

DISTANCE, IN FEET
Application of the Continuous Slope-Area Method on the Babocomari River 23

38

40

42

44

46

48

50

52

54

56

58

60

0 20 40 60 80 100 120 140 160

ELEV

A

TIO

N, IN FEET

DISTANCE, IN FEET

Before

After

Event peak

Figure 29. Channel surveys in cross section 2 before and after the July 27, 2006, event. The 

blue line shows the water-surface elevation at the peak discharge. At the peak discharge, the 

difference in cross-section areas is 8 percent.

Figure 30. Channel surveys in cross section 3 before and after the July 27, 2006, event. The blue line 

shows the water-surface elevation at the peak discharge. At the peak discharge, the difference in 

cross-section areas is 0.5 percent.

Evaluation of the Pressure-Transducer Data

Data from the six working PTs were evaluated to determine the optimum combination for discharge computations. 

PTL3 was not used because of the elevated stage effects from 

the accumulated debris (fig. 32). The remaining five PTs were 

PTR1, PTR3, and PTR4 from the right bank and PTL1 and 

PTL2 from the left bank. Because the right bank high-water 

marks and pressure-transducer peaks produced a narrower 

range of discharges in computing the slope-area discharges, 

the right bank PTs were used along with PTL2, which was the 

only sensor available for X2, for the final discharge computation. PTL1 was not used in the computation of discharge, but, 

because it was the only PT not displaced during the event, it 

was used for the stage record in developing the event-rating 

curve and the event-discharge hydrograph. 

40

42

44

46

48

50

52

54

56

58

0 20 40 60 80 100 120 140 160

ELE

V

A

TIO

N, IN FE

E

T

DISTANCE, IN FEET

Before

After

Event peak
24 The Continuous Slope-Area Method for Computing Event Hydrographs

Figure 31. Channel surveys in cross section 4 before and after the July 27, 2006, event. The blue line shows the 

water-surface elevation at the peak discharge. At the peak discharge, the difference in cross-section areas is 4 

percent.

Stage hydrographs from PTR1, PTL2, PTR3, and PTR4 

(fig. 33) were selected to compute discharge. The CSGs 

attached to these PTs were rotated to about a 45o angle from 

vertical just after the flow peak and, consequently, discharge 

values were not computed after the peak. The event-rating 

curve was developed from discharge values computed 

using stage values that were recorded prior to the PTs being 

displaced. 

Development of Stage-Discharge Relation

The stage-discharge relation was developed from stage 

values from PTL1 and discharge values computed with stage 

values recorded before the PTs were knocked over (fig. 34). 

A log function fit to the stage-discharge points has a R2 of 

0.9957, indicating that the stage-discharge relation fits the 

data closely with little scatter.

Transfer of the CSA Stage-Discharge Relation 

to the Babocomari River near Tombstone 

Streamflow-Gaging Station

The July 27, 2006, flood removed most of the 

large trees that were growing in the channel reach 

above and below the Babocomari River near Tombstone 

streamflow-gaging station, about 0.25 mi above the CSA site 

(fig. 8). The large trees in the channel bottom were the controls for the medium to high flows near the gage (fig. 35). 

This is a common condition at many USGS streamgages 

in Arizona. Periods of low or no flow allow dense vegetation growth in the channel that can significantly modify the 

channel hydraulic properties.

During the July flood, nearly all of the vegetation in the 

channel near the gage was removed near the flood peak and 

during the recession. In contrast, the same flood only caused 

minor changes in the downstream CSA reach. The stagedischarge relation for the Babocomari River near Tombstone 

gage depends on the condition of vegetation in the channel 

and was altered by the removal of vegetation during the 

July 27, 2006, flood. Consequently, a new stage-discharge 

relation was developed for the gage. The stage-discharge 

relation will return to its pre-flood form as the vegetations 

grow back in the channel. 

The stage hydrograph from the Babocamari River near 

Tombstone gage was compared with the stage hydrograph 

from PTL1 (fig. 36). The two hydrographs matched until 

just after the peak, when the gage hydrograph diverges from 

the PTL1 hydrograph, most likely as a result of the scouring of vegetation from the gage reach. On the recession, the 

gage hydrograph drops more than the PTL1 hydrograph by 

as much as 3 ft. 

40

42

44

46

48

50

52

54

56

0 20 40 60 80 100 120 140 160

ELEV

A

TIO

N, IN FEET

DISTANCE, IN FEET

Before

After

Event peak
Application of the Continuous Slope-Area Method on the Babocomari River 25

Pressure transducer High-water mark found 

near PT (ft)

Peak recorded by the 

PT (ft)

PTR1 56.57 56.06

PTL1 N/A 55.60

PTR2 56.71 N/A

PTL2 N/A 55.27

PTR3 55.30 55.08

PTL3 55.79 56.95

PTR4 55.06 54.47

PTL4 55.19 N/A

Table 4. Water-surface elevations from surveyed high-water marks and pressure 

transducers from the July 27, 2006, event.

Reach Fall (ft) Discharge (ft3

/s) 

X3-X4 0.60 12,044

Reach Fall (ft) Discharge (ft3

/s) 

X1-X2 -0.14 NA

X2-X3 1.41 12,409

X3-X4 0.24 7,818

X1-X3 1.27 10,791

X2-X4 1.65 11,230

X1-X4 1.51 10,089

Table 5. Peak discharge computed using surveyed left-bank high-water marks for the July 

27, 2006, event.

Table 6. Peak discharges computed using surveyed right-bank high-water marks for the July 

27, 2006, event.

Table 7. Peak discharge computed with the left-bank pressure transducers for the July 27, 

2006, event.

Reach Fall (ft) Discharge (ft3

/s)

X1-X2 0.33 8,466
26 The Continuous Slope-Area Method for Computing Event Hydrographs

Reach Fall (ft) Discharge (ft 3

/s) 

X1-X3 0.98 9,138

X3-X4 0.61 10,589

X1-X4 1.59 9,621

Table 8. Peak discharge computed with the right-bank pressure transducers for the July 27, 

2006, event.

Figure 32. Debris pile near left bank in cross section 3 after the July 27, 2006, event.

Stage-discharge relations were developed for the gaging station for conditions before and following the vegetation 

scour using the stage values from the gaging station with 

corresponding discharge values that were computed using the 

CSA method (fig. 37). Travel time between the two locations 

was small and neglected in developing the rating curves. 

Conclusions

The CSA method uses continuously recording pressure transducers to extend slope-area methods for computing 

peak discharge to entire event hydrographs. The method was 

initially implemented on the Babocomari River in Arizona in 

2002. The pressure transducers provide records of stage that 

are input to the slope-area SAC program (Fulford, 1994) with 

cross-section and roughness information to compute discharge 

hydrographs. The CSA method can produce the event-peak 

stage and discharge, continuous-discharge hydrographs for 

an event, and a stage-discharge relation for the site. The SAC 

program provides considerable flexibility in computing discharge, including the specification of a stage-dependent n. 

Discharges calculated with the CSA method are subject 

to the same error sources as indirect measurements. Surveying errors are typically small, and significant survey errors 

are usually evident if standard surveying practice is followed. 

Accuracy of the roughness parameter depends on available 

information and the judgment of the user, as with any indirect 
Conclusions 27

47

48

49

50

51

52

53

54

55

56

57

58

0:00:00 4:48:00 9:36:00 14:24:00 19:12:00

S

TA

GE, IN FEET

TIME, IN HOURS:MINUTES

Stage hydrograph PTR1

Stage hydrograph PTL2

Stage hydrograph PTR3

Stage hydrograph PTR4

Figure 33. Stage hydrographs of the four pressure transducers that were used to compute discharge for the July 27, 

2006, event.
28 The Continuous Slope-Area Method for Computing Event Hydrographs

R2 = 0.9957

47

48

49

50

51

52

53

54

55

56

100 1,000 10,000

S

TA

GE, IN FEET

DISCHARGE, IN CUBIC FEET PER SECOND

Figure 34. Stage values from the left-bank pressure transducer in cross section 1 and 

the corresponding discharge computed with stage data in X1-X4 during the July 27, 

2006, event are shown as dots. All stage and discharges shown occurred prior to the 

rotation of the pressure transducers. The solid line is a cubic polynomial fitted to the 

stage-discharge relation.

measurement. The CSA method adds more information 

regarding a flow event but requires a corresponding amount 

of data evaluation, especially if the flow was sufficient to 

rearrange the channel or damage instruments. The continuous 

record of stage at multiple locations offers the opportunity to 

decipher the short history of a flow event in a way that is not 

possible with a slope-area method but at the cost of sorting 

through a larger volume of information.

In the study on the Babocomari River, comparisons to 

slope-area computations were made by using the high-water 

marks recorded by the CSGs or high-water marks surveyed 

in the CSA cross sections. The computed discharge was then 

compared to a discharge computed using the peak values 

recorded by the CSA PTs. Only two events are discussed 

in detail in this report, but similar applications were completed for all the flow events that produced good results. On 

occasion, PTs or high-water marks were affected by local 

conditions, such as debris piles, that degrade the accuracy 

of computed discharges. The data were not used where this 

occurred.

Ongoing experiments in CSA applications are refining 

optimum installation designs of the pressure transducers. The 

main consideration when installing a PT is stability of the 

base. The CSG design by Rantz (1982) is excellent at collecting the crest elevations. These types of gages are installed in 

areas out of the main area of flow that have slower velocities. To collect streamflow data at lower discharges, the PTs 

need to be installed nearer the deeper parts of the channel in 

the main areas of flow. The design of the PT installation in 

the Babocomari River performed well for the medium-flow 

ranges, as in the first four flow events. At discharges closer to 

the peak discharge of 9,600 ft3/s, the bases of the CSG gages 
Conclusions 29

Figure 35. Reach below the Babocomari River near the Tombstone stream gage was heavily vegetated prior to the July 27, 2006, event 

(left). Much of that vegetation was gone after the event (right). The rock in the right foreground of the left photograph is the same as the 

rock occupying the right lower quadrant of the right photograph.

0

2

4

6

8

10

12

14

16

0:00 2:24 4:48 7:12 9:36 12:00 14:24 16:48 19:12

S

TA

GE, IN FEET

TIME, IN HOURS:MINUTES

PTL1

Gage

Figure 36. Stage hydrographs from the Babocomari River near Tombstone gage and the left-bank pressure 

transducer in cross section 1 (PTL1) during the July 27, 2006, event. Stages from the two sites were adjusted to 

coincide on the rising limb.
30 The Continuous Slope-Area Method for Computing Event Hydrographs

were scoured out, causing the CSA gage to rotate. Future 

installations of CSA gages should utilize shorter pipes that will 

collect less debris, and pipes should be angled at 45o to allow 

them to better shed debris. This design will survive large flows 

but will lose the ability to record the crest elevation of a flood 

on the CSGs.

References Cited

Aldridge, B.N., and Garrett, J.M., 1973, Roughness coefficients for stream channels in Arizona: U.S. Geological 

Survey Open-File Report 73-3, 87 p. 

Benson, M.A., and Dalrymple, T., 1967, General field and 

office procedures for indirect discharge measurements: U.S. 

Geological Survey Techniques of Water-Resources Investigations, book 3, chap. A1, 12 p. (http://pubs.er.usgs.gov/

usgspubs/twri/twri03A1).

Dalrymple, T., and Benson, M.A., 1967, Measurement of 

peak discharge by the slope-area method: U.S. Geological 

Survey Techniques of Water-Resources Investigations, book 

3, chap. A2, 12 p. (http://pubs.usgs.gov/twri/twri3-a2/pdf/

twri_3-A2_a.pdf).

Fulford, J. M., 1994, User’s guide to SAC, a computer program for computing discharge by slope-area method: U.S. 

Geological Survey Open File Report 94-360, 31 p. 

Phillips, J.V., and Thomas, B.E., 2005, Hydrologic conditions 

in Arizona during 1999–2004— A historical perspective: 

U.S. Geological Survey Fact Sheet 2005-3081, 4 p.

Phillips, J.V., and Tadayon, S., 2006, Selection of Manning’s 

roughness coefficient for natural and constructed vegetated 

and non-vegetated channels, and vegetation maintenance 

plan guidelines for vegetated channels in central Arizona: 

U.S. Geological Survey Scientific Investigations Report 

2006-5108, 41 p.

Pool, D.R., and Coes, A.L.,1999, Hydrogeologic investigations of the Sierra Vista subwatershed of the upper San Pedro 

Basin, Cochise County, southeast Arizona: U.S. Geological 

Survey Water-Resources Investigations Report 99-4197, 41 p. 

Rantz, S.E., 1982, Measurement and computation of 

streamflow,Volume 1— Measurement of stage and discharge: 

U.S. Geological Water-Supply Paper 2175, 284 p.

Stewart, A. M., Callegary, J.B., Smith, C.F., Wiele, S.M., Cordova, J.T., Fritzinger, R.A., and Gupta, H.V., 2008, Use of the 

Continuous Slope-Area Method to Estimate Runoff Through 

Ephemeral Stream Channels in SE Arizona, Eos Trans. AGU 

89(53), Fall Meet. Suppl., Abstract H11E-0823.

Thomsen, B.W., and Hjalmarson, H.W., 1991, Estimated Manning’s roughness coefficient for stream channels and flood 

plains in Maricopa County, Arizona: Phoenix, Flood Control 

District of Maricopa County report, 126 p.

Waltemeyer, S.D., 2005, Automated crest-stage gage application in ephemeral streams in New Mexico: U.S. Geological 

Survey Fact Sheet 2005-3136, 4 p.

Wiele, S.M. and Smith, J.D., 1996, A reach-averaged model of 

diurnal discharge wave propagation down the Colorado River 

through the Grand Canyon: Water Resources Research, v. 32, 

no. 5, p. 1375–1386.

STAGE (FT)

DISCHARGE, IN CUBIC FEET PER SECOND

1 10 100 1,000 10,000

STAGE, IN FEET

Figure 37. Stage-discharge relations before and after the July 27, 2006, event. The blue line 

represents conditions prior to the peak and included the effects of the dense vegetation. 

The red curve represents the condition after vegetation was scoured.
Appendix 1 31

Appendix 1. Stage data and computed discharge for five runoff events in the 

Babocomari River.

Right Bank

Stage, in feet Date and 

time

PTR1 PTR2 PTR3 PTR4

8/3/02 12:50 46.37 46.19 45.63 45.43

8/3/02 12:55 46.41 46.20 45.73 45.56

8/3/02 13:00 46.47 46.35 45.84 45.64

8/3/02 13:05 46.72 46.61 46.10 45.90

8/3/02 13:10 46.78 46.72 46.18 45.98

8/3/02 13:15 46.86 46.88 46.29 46.10

8/3/02 13:20 47.09 47.00 46.47 46.28

8/3/02 13:25 47.14 47.16 46.51 46.30

8/3/02 13:30 47.16 47.11 46.53 46.21

8/3/02 13:35 47.07 47.04 46.49 46.23

8/3/02 13:40 46.87 46.79 46.29 46.02

8/3/02 13:45 46.74 46.63 45.98 45.78

8/3/02 13:50 46.62 46.39 45.77 45.56

8/3/02 13:55 46.53 46.29 45.65 45.39

August 3, 2002 runoff event on the Babocomari River

Left Bank

Stage, in feet Date 

and time PTL1 PTL2 PTL3 PTL4

8/3/02 12:50 NA 46.46 45.77 45.31

8/3/02 12:55 NA 46.46 45.79 45.41

8/3/02 13:00 NA 46.46 45.94 45.52

8/3/02 13:05 NA 46.70 46.16 45.78

8/3/02 13:10 NA 46.81 46.24 45.86

8/3/02 13:15 NA 46.98 46.38 45.97

8/3/02 13:20 NA 47.16 46.55 46.15

8/3/02 13:25 NA 47.21 46.63 46.19

8/3/02 13:30 NA 47.28 46.71 46.21

8/3/02 13:35 NA 47.16 46.64 46.17

8/3/02 13:40 NA 46.93 46.44 45.97

8/3/02 13:45 NA 46.70 46.22 45.66

8/3/02 13:50 NA 46.47 45.97 45.45

8/3/02 13:55 NA 46.41 45.84 45.33

Note: PTL1 was not inundated

Date and Average stage, in feet

time X1 X2 X3 X4

8/3/02 12:50 46.32 45.70 45.37

8/3/02 12:55 46.33 45.76 45.48

8/3/02 13:00 46.41 45.89 45.58

8/3/02 13:05 46.65 46.13 45.84

8/3/02 13:10 46.77 46.21 45.92

8/3/02 13:15 46.93 46.33 46.04

8/3/02 13:20 47.08 46.51 46.22

8/3/02 13:25 47.19 46.57 46.24

8/3/02 13:30 47.20 46.62 46.21

8/3/02 13:35 47.10 46.56 46.20

8/3/02 13:40 46.86 46.37 45.99

8/3/02 13:45 46.67 46.10 45.72

8/3/02 13:50 46.43 45.87 45.51

8/3/02 13:55 46.35 45.74 45.36

Computed discharge, ft3/s

431

428

458

528

566

620

675

724

750

702

620

551

471

447
32 The Continuous Slope-Area Method for Computing Event Hydrographs

July 25, 2003 runoff event on the Babocomari River

Right bank

Stage, in feet

Date 

and 

time PTR1 PTR3 PTR5 PTR7

7/25/03 19:10 46.25 45.73 45.57 44.17

7/25/03 19:15 46.92 46.76 46.09 45.80

7/25/03 19:20 47.03 46.78 46.06 46.12

7/25/03 19:25 46.867 46.67 46.001 45.97

7/25/03 19:30 46.674 46.432 45.887 45.683

7/25/03 19:35 46.425 46.119 45.573 45.239

Average stage, in feet Date and 

time X1 X2 X3 X4

7/25/03 19:10 46.80 46.07 45.65 44.71

7/25/03 19:15 47.13 46.76 46.10 45.73

7/25/03 19:20 47.19 46.80 46.20 46.07

7/25/03 19:25 47.11 46.69 46.11 45.92

7/25/03 19:30 47.01 46.48 45.96 45.65

7/25/03 19:35 46.89 46.27 45.66 45.26

Computed discharge, ft3/s

430

527

508

491

468

429

October 9, 2003 runoff event on the Babocomari River

Right bank

Stage, in feet

Date 

and 

time PTR1 PTR2 PTR3 PTR4

10/9/03 19:35 46.231 45.657 45.578 44.244

10/9/03 19:40 46.817 46.506 46.136 45.599

10/9/03 19:45 47.03 46.781 46.349 46.118

10/9/03 19:50 47.254 46.907 46.386 46.3

10/9/03 19:55 47.297 46.995 46.384 46.338

10/9/03 20:00 47.2 46.975 46.296 46.172

10/9/03 20:05 47.019 46.693 45.995 45.885

10/9/03 20:10 46.766 46.475 45.893 45.481

10/9/03 20:15 46.471 46.172 45.655 45.08

Left bank

Stage, in feet

Date 

and 

time PTL 2 PTL 4 PTL 6 CSA8

10/9/03 19:35 47.339 46.405 45.727 45.271

10/9/03 19:40 47.337 46.549 46.073 45.544

10/9/03 19:45 47.339 46.883 46.424 46.062

10/9/03 19:50 47.452 47.145 46.636 46.227

10/9/03 19:55 47.493 47.103 46.627 46.239

10/9/03 20:00 47.369 47.039 46.539 46.122

10/9/03 20:05 47.34 46.788 46.333 45.804

10/9/03 20:10 47.34 46.442 46.072 45.398

10/9/03 20:15 47.34 46.405 45.822 45.284

Average stage, in feet Computed discharge, ft3 Date and /s time X1 X2 X3 X4

10/9/03 19:35 46.231 46.031 45.6525 44.7575 340

10/9/03 19:40 46.817 46.5275 46.1045 45.5715 459

10/9/03 19:45 47.1845 46.832 46.3865 46.09 529

10/9/03 19:50 47.353 47.026 46.511 46.2635 580

10/9/03 19:55 47.395 47.049 46.5055 46.2885 591

10/9/03 20:00 47.2845 47.007 46.4175 46.147 567

10/9/03 20:05 47.1795 46.7405 46.164 45.8445 530

10/9/03 20:10 46.766 46.4585 45.9825 45.4395 444

10/9/03 20:15 46.471 46.2885 45.7385 45.182 374

Left bank

Stage, in feet

Date 

and 

time PTL 2 PTL 4 PTL 6 PTL 8

7/25/03 19:10 47.346 46.412 45.74 45.255

7/25/03 19:15 47.345 46.766 46.107 45.646

7/25/03 19:20 47.343 46.822 46.333 46.017

7/25/03 19:25 47.347 46.713 46.219 45.872

7/25/03 19:30 47.349 46.522 46.027 45.619

7/25/03 19:35 47.352 46.415 45.746 45.289
Appendix 1 33

August 15, 2005 runoff event on the Babocomari River

Left bank

Stage, recorded in feet Computed discharge, ft3 Minutes /s PTL1 PTR2 PTL3

0 47.375 47.035 46.332 607

5 47.55 47.159 46.486 664

10 47.499 47.138 46.431 650

15 47.441 47.075 46.381 627

20 47.365 47.013 46.321 602

25 47.569 47.271 46.548 678

30 47.723 47.343 46.685 728

35 47.785 47.465 46.861 746

40 47.818 47.524 46.945 748

45 47.834 47.51 46.891 764

50 47.839 47.471 46.912 759

55 47.824 47.474 46.878 756

60 47.812 47.411 46.85 749

65 47.765 47.409 46.835 737

70 47.728 47.372 46.8 720

75 47.66 47.341 46.752 695

80 47.609 47.228 46.689 668

85 47.567 47.15 46.623 653

90 47.492 47.046 46.52 623

95 47.45 46.916 46.46 600

100 47.406 46.826 46.422 580

105 47.39 46.739 46.351 572

110 47.56 47.242 46.611 662

115 47.856 47.684 46.877 801

120 48.06 47.912 47.064 897

125 48.137 47.988 47.205 918

130 48.133 48.008 47.237 909

135 48.134 48.014 47.278 900

140 48.093 47.969 47.25 879

145 48.025 47.955 47.187 857

150 47.958 47.808 47.105 823

155 47.856 47.661 47.021 770

160 47.846 47.534 46.895 772

165 47.747 47.549 46.823 749

170 47.697 47.415 46.736 723

175 47.629 47.303 46.671 690

180 47.575 47.226 46.608 667

185 47.516 47.174 46.526 648

190 47.459 47.045 46.512 613

195 47.406 46.899 46.488 578
34 The Continuous Slope-Area Method for Computing Event Hydrographs

July 27, 2006 runoff event on the Babocomari River

Stage, recorded in feet Time PTR1 PTL2 PTR3 PTR4

2:15:00 46.726 46.479 45.633 44.333

2:20:00 47.664 47.486 46.888 46.356

2:25:00 48.164 48.12 47.122 47.202

2:30:00 48.398 48.252 47.298 47.334

2:35:00 48.399 48.346 47.138 47.258

2:40:00 48.459 48.373 47.264 47.379

2:45:00 48.675 48.497 47.575 47.381

2:50:00 49.023 48.806 47.623 47.478

2:55:00 49.352 49.146 47.954 47.824

3:00:00 49.507 49.307 48.203 47.969

3:05:00 49.663 49.393 48.181 48.132

3:10:00 49.619 49.305 48.208 48.157

3:15:00 49.465 49.165 48.287 48.162

3:20:00 49.301 49.021 48.134 48.128

3:25:00 49.208 48.927 48.249 47.867

3:30:00 49.109 48.853 48.002 47.887

3:35:00 49.078 48.775 48.033 47.8

3:40:00 48.976 48.724 48.013 47.819

3:45:00 48.944 48.647 47.958 47.652

3:50:00 48.963 48.535 47.899 47.664

3:55:00 48.77 48.404 47.912 47.787

4:00:00 48.59 48.21 47.953 47.641

4:05:00 48.516 48.056 47.767 47.559

4:10:00 48.308 47.881 47.478 47.314

4:15:00 48.141 47.75 47.372 47.204

4:20:00 48.161 47.711 47.273 47.027

4:25:00 48.163 47.746 47.21 47.114

4:30:00 48.235 47.847 47.343 47.181

4:35:00 48.386 47.997 47.355 47.274

4:40:00 48.584 48.166 47.536 47.296

4:45:00 48.899 48.392 47.73 47.431

4:50:00 49.156 48.626 47.767 47.558

4:55:00 49.363 48.778 47.803 47.89

5:00:00 49.56 48.966 48.123 47.816

5:05:00 49.692 49.073 48.169 48.088

5:10:00 49.749 49.142 48.215 48.257

5:15:00 49.715 49.212 48.464 48.121

5:20:00 49.749 49.233 48.375 47.991

5:25:00 49.771 49.222 48.376 47.787

5:30:00 49.64 49.21 48.308 48.249

5:35:00 49.785 49.225 48.293 48.06

5:40:00 50.072 49.403 48.409 48.058

5:45:00 50.611 49.775 49.138 48.498

5:50:00 51.245 50.732 49.866 48.834

5:55:00 51.755 51.082 50.172 49.742

6:00:00 52.724 52.546 51.135 49.933

6:05:00 53.509 53.121 51.53 50.889

6:10:00 53.678 53.581 52.752 52.018

6:15:00 54.986 53.877 53.522 52.261

6:25:00 56.055 55.055 54.226 53.507

Discharge, in cfs

CSA Discharge 

383

645

706

807

806

821

981

1,139

1,311

1,427

1,455

1,423

1,352

1,216

1,281

1,155

1,171

1,103

1,121

1,103

949

891

839

768

700

739

712

753

806

925

1,088

1,196

1,218

1,435

1,445

1,443

1,558

1,585

1,641

1,423

1,557

1,743

2,224

2,988

3,302

4,749

5,546

6,020

8,481

10,097
Appendix 2 35

Appendix 2. Input files to the SAC program used in the continuous slope-area 

calculations of discharge for five events on the Babocomari river. These files are 

templates. The stages are replaced when computing the hydrograph with stages 

from the CSA pressure transducers. Documentation of the SAC program can be found 

in Fulford (1994).

T1 Babocomari River CSA reach

T2 08/03/2002 event

XS X4 0.0

GR 0.0,48.1 11.8,47.1 18.8,46.0 23.3,45.2 30.3,43.9 37.6,41.6

GR 38.0,41.4 40.8,41.4 43.8,41.1 45.4,41.0 47.0,41.0 47.8,41.7

GR 48.9,42.2 55.3,42.6 58.6,43.0 64.0,44.2 71.8,46.3 78.8,47.2

GR 84.2,47.8 92.5,48.7

N 0.035 

HP X4 46.12

XS X3 111

GR 0.0,48.1 3.8,47.4 12.4,46.5 18.8,45.7 30.9,43.7 35.5,43.2

GR 37.5,42.2 37.9,41.5 43.8,41.3 44.5,42.6 48.7,43.7 53.9,44.6

GR 59.6,45.3 62.1,45.4 67.4,47.2 75.5,48.4 79.7,49.9

N 0.035

HP X3 46.06

XS X2 190

GR 0.0,49.4 6.6,48.1 10.4,47.5 15.1,47.1 21.1,46.1 30.1,45.5

GR 33.9,44.8 36.2,43.6 37.2,41.4 47.5,41.8 48.2,42.7 51.5,44.1

GR 55.2,44.7 59.7,45.5 66.9,46.5 70.7,47.2 74.9,48.1 86.2,51.6

GR 92.1,52.5

N 0.035 

HP X2 46.78

XS X1 300

GR 0,56.6 6.3,52 8.1,49.6 15.8,48.4 22.1,48 23.5,47.4 30.7,46.6

GR 35.9,45.6 39.7,45.3 43.1,44.8 49.2,44.2 54.4,44 55.8,42.6 58.1,42.8

GR 58.8,44 61.6,44.4 64.5,45.3 67.2,45.6 70.5,45.8 75,46.8 81.2,47.9

GR 84,48.4 96.9,52.8 100.5,54.4

N 0.035

HP X1 47.03

T1 Babocamari River CSA reach

T2 07/25/2003 event

XS X4 0.0

GR 0.0,48.1 11.8,47.1 18.8,46.0 23.3,45.2 30.3,43.9 37.6,41.6

GR 38.0,41.4 40.8,41.4 43.8,41.1 45.4,41.0 47.0,41.0 47.8,41.7

GR 48.9,42.2 55.3,42.6 58.6,43.0 64.0,44.2 71.8,46.3 78.8,47.2

GR 84.2,47.8 92.5,48.7

N 0.035 

HP X4 46.12

XS X3 111

GR 0.0,48.1 3.8,47.4 12.4,46.5 18.8,45.7 30.9,43.7 35.5,43.2

GR 37.5,42.2 37.9,41.5 43.8,41.3 44.5,42.6 48.7,43.7 53.9,44.6

GR 59.6,45.3 62.1,45.4 67.4,47.2 75.5,48.4 79.7,49.9

N 0.035

HP X3 46.06

XS X2 190

GR 0.0,49.4 6.6,48.1 10.4,47.5 15.1,47.1 21.1,46.1 30.1,45.5

GR 33.9,44.8 36.2,43.6 37.2,41.4 47.5,41.8 48.2,42.7 51.5,44.1

GR 55.2,44.7 59.7,45.5 66.9,46.5 70.7,47.2 74.9,48.1 86.2,51.6

GR 92.1,52.5

N 0.035 

HP X2 46.78

XS X1 300

GR 0,56.6 6.3,52 8.1,49.6 15.8,48.4 22.1,48 23.5,47.4 30.7,46.6

GR 35.9,45.6 39.7,45.3 43.1,44.8 49.2,44.2 54.4,44 55.8,42.6 58.1,42.8

GR 58.8,44 61.6,44.4 64.5,45.3 67.2,45.6 70.5,45.8 75,46.8 81.2,47.9

GR 84,48.4 96.9,52.8 100.5,54.4

N 0.035

HP X1 47.03
36 The Continuous Slope-Area Method for Computing Event Hydrographs

T1 Babocamari River CSA reach

T2 10/09/2003 event

XS X4 0.0

GR 0.0,48.1 11.8,47.1 18.8,46.0 23.3,45.2 30.3,43.9 37.6,41.6

GR 38.0,41.4 40.8,41.4 43.8,41.1 45.4,41.0 47.0,41.0 47.8,41.7

GR 48.9,42.2 55.3,42.6 58.6,43.0 64.0,44.2 71.8,46.3 78.8,47.2

GR 84.2,47.8 92.5,48.7

N 0.035 

HP X4 46.09

XS X3 111

GR 0.0,48.1 3.8,47.4 12.4,46.5 18.8,45.7 30.9,43.7 35.5,43.2

GR 37.5,42.2 37.9,41.5 43.8,41.3 44.5,42.6 48.7,43.7 53.9,44.6

GR 59.6,45.3 62.1,45.4 67.4,47.2 75.5,48.4 79.7,49.9

N 0.035

HP X3 46.39

XS X2 190

GR 0.0,49.4 6.6,48.1 10.4,47.5 15.1,47.1 21.1,46.1 30.1,45.5

GR 33.9,44.8 36.2,43.6 37.2,41.4 47.5,41.8 48.2,42.7 51.5,44.1

GR 55.2,44.7 59.7,45.5 66.9,46.5 70.7,47.2 74.9,48.1 86.2,51.6

GR 92.1,52.5

N 0.035 

HP X2 46.83

XS X1 300

GR 0,56.6 6.3,52 8.1,49.6 15.8,48.4 22.1,48 23.5,47.4 30.7,46.6

GR 35.9,45.6 39.7,45.3 43.1,44.8 49.2,44.2 54.4,44 55.8,42.6 58.1,42.8

GR 58.8,44 61.6,44.4 64.5,45.3 67.2,45.6 70.5,45.8 75,46.8 81.2,47.9

GR 84,48.4 96.9,52.8 100.5,54.4

N 0.035

HP X1 47.18

T1 Babocamari River CSA reach

T2 8/15/2005 event

XS X4 0.0

GR 006.00,055.19 014.00,049.78 041.80,047.10 048.80,046.00

GR 053.30,045.20 060.30,043.90 067.60,041.60 068.00,041.40

GR 070.80,041.40 073.80,041.10 075.40,041.00 077.00,041.00

GR 077.80,041.70 078.90,042.20 085.30,042.60 088.60,043.00

GR 094.00,044.20 101.80,046.30 108.80,047.20 114.20,047.80

GR 122.50,048.70 124.00,048.99 130.00,050.33 136.00,055.06

N 0.035

HP X4 44.333

XS X3 115

GR 003.00,055.79 019.80,048.30 031.50,046.60 035.70,046.30 

GR 038.70,045.80 042.20,045.20 047.20,044.50 050.50,043.90

GR 053.30,043.50 055.30,043.70 056.20,043.10 059.50,041.00

GR 061.10,040.90 063.10,041.00 064.50,041.70 065.40,043.00

GR 066.80,043.60 070.90,043.90 074.50,044.60 075.80,044.50

GR 077.10,044.70 078.40,045.00 081.90,045.40 083.10,046.10

GR 086.60,046.80 091.00,047.60 101.00,050.28 106.10,050.80

GR 120.00,052.69 138.00,055.30

N 0.035

HP X3 45.633

XS X2 188

GR 001.70,055.50 003.00,054.83 006.00,053.06 012.60,050.62

GR 017.20,049.42 022.00,048.97 028.50,048.16 043.50,045.77 

GR 044.00,046.35 052.00,045.57 056.50,043.97 056.50,041.47 

GR 066.00,041.77 070.00,042.07 070.50,043.07 077.00,045.17 

GR 077.50,045.58 085.00,046.27 095.00,048.09 098.00,048.82 

GR 098.00,048.82 101.00,049.75 107.70,052.00 115.80,053.37

GR 126.40,054.23 136.20,055.41 139.00,056.71

N 0.035

HP X2 46.479

XS X1 301

GR 004.00,058.65 019.00,050.48 027.60,049.00 031.10,048.00

GR 034.30,047.70 036.00,047.90 037.50,047.50 038.90,047.30

GR 041.40,046.80 042.20,046.80 044.80,046.50 049.90,045.70

GR 055.00,045.27 057.30,044.80 061.90,044.60 067.90,044.10

GR 068.40,042.80 069.60,042.70 070.10,043.10 070.70,042.80

GR 071.00,042.60 071.40,042.70 071.80,043.80 074.80,044.50

GR 078.20,045.40 079.50,045.50 082.00,045.60 082.90,045.50

GR 084.30,045.80 088.00,046.70 091.70,047.20 098.70,048.60

GR 099.00,048.80 107.00,052.16 116.00,054.82 128.00,056.57

N 0.035

HP X1 46.726
Appendix 2 37

T1 Babocomari River CSA reach

T2 7/27/2006 event

XS X4 0.0

GR 006.00,055.19 014.00,049.78 041.80,047.10 048.80,046.00

GR 053.30,045.20 060.30,043.90 067.60,041.60 068.00,041.40

GR 070.80,041.40 073.80,041.10 075.40,041.00 077.00,041.00

GR 077.80,041.70 078.90,042.20 085.30,042.60 088.60,043.00

GR 094.00,044.20 101.80,046.30 108.80,047.20 114.20,047.80

GR 122.50,048.70 124.00,048.99 130.00,050.33 136.00,055.06

N 0.040

HP X4 44.333

XS X3 115

GR 003.00,055.79 019.80,048.30 031.50,046.60 035.70,046.30 

GR 038.70,045.80 042.20,045.20 047.20,044.50 050.50,043.90

GR 053.30,043.50 055.30,043.70 056.20,043.10 059.50,041.00

GR 061.10,040.90 063.10,041.00 064.50,041.70 065.40,043.00

GR 066.80,043.60 070.90,043.90 074.50,044.60 075.80,044.50

GR 077.10,044.70 078.40,045.00 081.90,045.40 083.10,046.10

GR 086.60,046.80 091.00,047.60 101.00,050.28 106.10,050.80

GR 120.00,052.69 138.00,055.30

N 0.040

HP X3 45.633

XS X2 188

GR 001.70,055.50 003.00,054.83 006.00,053.06 012.60,050.62

GR 017.20,049.42 022.00,048.97 028.50,048.16 043.50,045.77 

GR 044.00,046.35 052.00,045.57 056.50,043.97 056.50,041.47 

GR 066.00,041.77 070.00,042.07 070.50,043.07 077.00,045.17 

GR 077.50,045.58 085.00,046.27 095.00,048.09 098.00,048.82 

GR 098.00,048.82 101.00,049.75 107.70,052.00 115.80,053.37

GR 126.40,054.23 136.20,055.41 139.00,056.71

N 0.040

HP X2 46.479

XS X1 301

GR 004.00,058.65 019.00,050.48 027.60,049.00 031.10,048.00

GR 034.30,047.70 036.00,047.90 037.50,047.50 038.90,047.30

GR 041.40,046.80 042.20,046.80 044.80,046.50 049.90,045.70

GR 055.00,045.27 057.30,044.80 061.90,044.60 067.90,044.10

GR 068.40,042.80 069.60,042.70 070.10,043.10 070.70,042.80

GR 071.00,042.60 071.40,042.70 071.80,043.80 074.80,044.50

GR 078.20,045.40 079.50,045.50 082.00,045.60 082.90,045.50

GR 084.30,045.80 088.00,046.70 091.70,047.20 098.70,048.60

GR 099.00,048.80 107.00,052.16 116.00,054.82 128.00,056.57

N 0.040

HP X1 46.726
38 The Continuous Slope-Area Method for Computing Event Hydrographs

This page intentionally left blank
Produced in the Western Region, Menlo Park, California

Manuscript approved for publication, August 9, 2010

Layout and design by Stephen L. Scott
Smith, others—The Continuous Slope-Area Method for Computing Event Hydrographs—Scientific Investigations Report 2010-5241