U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2013–1082

Prepared in cooperation with the University of Wisconsin–Madison Discovery Farms program 

and the University of Wisconsin– Platteville Pioneer Farm program

Implications of Flume Slope on Discharge Estimates from 

0.762-meter H Flumes Used in Edge-of-Field Monitoring
Cover images: 

Upper left: U.S. Geological Survey employee testing 0.762-meter H flume at the Colorado State University Hydraulics 

Laboratory, Fort Collins, Colorado.

Upper right: Edge-of-field monitoring station showing installed 0.762-meter H flume with wingwall and gaging station.

Lower left: Edge-of-field monitoring station showing use of 0.762-meter H flume to measure snowmelt runoff.

Lower right: Edge-of-field monitoring station showing use of 0.762-meter H flume to capture rainfall runoff.
Implications of Flume Slope on Discharge 

Estimates from 0.762-meter H Flumes 

Used in Edge-of-Field Monitoring 

By Matthew J. Komiskey, Todd D. Stuntebeck, Amanda L. Cox, and 

Dennis R. Frame

Prepared in cooperation with the University of Wisconsin–Madison Discovery 

Farms program and the University of Wisconsin–Platteville Pioneer Farm program

Open-File Report 2013–1082

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Komiskey, M.J., Stuntebeck, T.D., Cox, A.L., and Frame, D.R, 2013, Implications of flume slope on discharge estimates 

from 0.762-meter H flumes used in edge-of-field monitoring: U.S. Geological Survey Open-File Report 2013–1082, 

11 p. 
iii

Contents

Acknowledgments........................................................................................................................................iv

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

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

Purpose and Scope .......................................................................................................................................2

Methods...........................................................................................................................................................2

Factors Influencing the Discharge Accuracy of H Flumes............................................................3

Types of Corrections.............................................................................................................................3

Hydraulic Setting for Initial Case Study ............................................................................................3

Hydraulic Setting for Refined Correction Case Study ....................................................................4

Results and Discussion.................................................................................................................................7

Initial Case Study ..................................................................................................................................7

Refined Correction Case Study ..........................................................................................................8

Scaling of Corrections to Other H-Flumes Sizes .............................................................................9

Impacts on Estimated Annual Runoff Volume..................................................................................9

Conclusion.....................................................................................................................................................11

References Cited..........................................................................................................................................11

Figures

1. Graph showing measured flume slopes at University of Wisconsin–Platteville 

Pioneer Farm, Platteville, Wisconsin, water years 2002–9....................................................4

2. Photograph showing H-flume test installation at Colorado State University 

Hydraulics Laboratory, Fort Collins, Colorado..........................................................................5

3. Plan view of 0.762-meter H flume showing measurement points for slope 

computation and proper head measurement location...........................................................7

4. Graph showing the relation between flume slope and the discharge bias for 

each tested flow and slope condition. Discharge bias is the percentage error 

between the apparent discharge (Qa) and the Qa at 0 percent flume slope .......................9

Tables

1. Case study test results for initial flume-slope correction......................................................4

2. Case study test results for refined flume-slope correction...................................................6

3. Computed annual discharge comparison for different correction methods....................10
iv

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Area

acre 0.4047 hectare (ha)

acre 0.004047 square kilometer (km2

)

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in)

millimeter (mm) 0.03937 inch (in)

meter (m) 3.281 foot (ft) 

meter (m) 1.094 yard (yd) 

Volume

cubic meter (m3

) 264.2 gallon (gal) 

cubic meter (m3

) 0.0002642 million gallons (Mgal) 

Flow rate

liter per second (L/s) 15.85 gallon per minute (gal/min) 

Acknowledgments

The authors would like to thank Randy Mentz and Justin Daugherty of the University of 

Wisconsin– Platteville Pioneer Farm program and Eric Cooley, Aaron Wunderlin, Tim Radatz, and 

John Frame of the University of Wisconsin–Madison Discovery Farms program for field support 

in the edge-of-field studies and the staff at the Colorado State University Hydraulics Laboratory, 

Fort Collins, Colorado, for support during the flume-slope tests. Thanks also are extended to 

David Owens and Frank Younger of the U.S. Geological Survey for their technical assistance.
Implications of Flume Slope on Discharge Estimates from 

0.762-meter H Flumes Used in Edge-of-Field Monitoring

By Matthew J. Komiskey,1 Todd D. Stuntebeck,1 Amanda L. Cox,2 and Dennis R. Frame3

Abstract

The effects of longitudinal slope on the estimation of discharge in a 0.762-meter (m) (depth at flume entrance) H flume 

were tested under controlled conditions with slopes from −8 to 

+8 percent and discharges from 1.2 to 323 liters per second. 

Compared to the stage-discharge rating for a longitudinal 

flume slope of zero, computed discharges were negatively 

biased (maximum −31 percent) when the flume was sloped 

downward from the front (entrance) to the back (exit), and 

positively biased (maximum 44 percent) when the flume was 

sloped upward. Biases increased with greater flume slopes and 

with lower discharges. A linear empirical relation was developed to compute a corrected reference stage for a 0.762-m 

H flume using measured stage and flume slope. The reference 

stage was then used to determine a corrected discharge from 

the stage-discharge rating. A dimensionally homogeneous correction equation also was developed, which could theoretically 

be used for all standard H-flume sizes. Use of the corrected 

discharge computation method for a sloped H flume was determined to have errors ranging from −2.2 to 4.6 percent compared to the H-flume measured discharge at a level position. 

These results emphasize the importance of the measurement 

of and the correction for flume slope during an edge-of-field 

study if the most accurate discharge estimates are desired.

Introduction

Monitoring surface runoff from agricultural fields is a 

critical component to understanding the impacts of agriculture 

on the environment. Evaluating data from fields representing 

different on-farm practices and management styles can help to 

determine how each affects runoff-water quantity and quality. 

There is a need to document and quantify the environmental 

benefits realized by the various management efforts and to 

identify and promote the most successful, cost-effective techniques (Bishop and others, 2005).

In order to accurately quantify the impact of on-farm 

management strategies, a comprehensive method to measure 

runoff and to obtain representative water-quality samples must 

be established. Harmel and others (2006a) provided practical 

guidance for monitoring discharge and collecting water-quality data at the field and small-watershed scale and described 

the use of pre-calibrated control structures to estimate runoff 

volumes. Also noted was the inherent uncertainty introduced 

into measurement of water-quantity and -quality data that is 

often overlooked in many study designs (Harmel and others, 

2006b). These uncertainties included laboratory analysis and 

data-collection techniques, which could potentially influence 

the interpretation of study results.

Use of pre-calibrated control structures to estimate runoff 

from fields or small watersheds has been well documented 

(Kilpatrick and Schneider, 1983; Thornton and others, 1998; 

McDowell and others, 2001; Udawatta and others, 2002). 

When used properly, these control structures offer advantages 

over open-channel (stream) methods. Unlike streams, development of a stage-discharge relation is typically not necessary. 

This is especially helpful at locations where manual measurement of discharge during flashy runoff events is problematic. 

Since the stage-discharge relation is known from the beginning of a study, discharge-based sampling methods can be 

employed. In a stream, channel features that control the stagedischarge relation can often change over time; this is not the 

case for a pre-calibrated control structure. 

Pre-calibrated structures do have limitations, particularly 

owing to constraints in discharge ranges for which they are 

calibrated with respect to their physical size, drainage area, 

and topography of the watershed in which they are utilized. 

To accurately estimate discharge, these structures typically 

require open-flow conditions (no interference of flow within 

the structure) and stability with respect to the flow (the 

structure is level and in line with the flow) (Brakensiek and 

others, 1979). Each of these conditions can be compromised 

by environmental conditions (freeze/thaw processes, saturated 

soils, etc.) and by measurement errors that can introduce error 

into the estimation of discharge. 1

U.S. Geological Survey, Middleton, Wisconsin.

2

Colorado State University-Hydraulics Laboratory, Fort Collins, Colorado.

3

University of Wisconsin-Madison Discovery Farms program, Pigeon Falls, 

Wisconsin.
2 Implications of Flume Slope on Discharge Estimates from 0.762-meter H Flumes Used in Edge-of-Field Monitoring

H flumes offer advantages over other pre-calibrated control structures in that their design allows for relatively accurate 

estimation of both low and high flow. In addition, they are 

capable of passing runoff that contains a heavy sediment load 

and are capable of shedding floating debris (Hudson, 1993). 

The stage-discharge relation developed for H flumes assumes 

that they are installed level, both side to side and front to back, 

that water entering the flume is at subcritical velocity and 

nonturbulent, and that water exiting the flume is unimpeded 

(not operating in a submerged condition) (Grant and Dawson, 

2001).

At the edge-of-field setting, the standardized stagedischarge relationship for the H flumes is used as the discharge 

rating, assuming the flume is level. An H flume should be level 

from side to side and from front to back, with the bottom of 

the flume at the same elevation as the inlet. Compromises to 

this ideal configuration owing to installation characteristics or 

support and substrate instability from episodic environmental 

conditions such as frost heave or soil saturation can compromise the standardized stage-discharge relation. In addition, due 

to the infrequency in the timing of flow and short duration of 

runoff events, check measurements of discharge to confirm or 

develop a new rating is difficult and calibrating each H flume 

is cost prohibitive. 

While several tests have been done on a variety of flume 

types and sizes regarding the effect of slope and submergence 

on discharge determination, the majority of work seems to 

have been conducted on Parshall flumes. Abt and others 

(1995) reviewed literature results evaluating the effects of 

settlement and submergence on Parshall flumes and developed 

a comprehensive method to correct the discharge. Limited 

published work is available on correcting for submergence of 

an H flume (Brakensiek and others, 1979; Gwinn, 1984; Bos, 

1989), and no studies were found that evaluate the effect of 

flume slope (FS) on discharge estimates.

Purpose and Scope

This report summarizes the corrections used to compute 

discharge from the standard stage-discharge relationship for an 

H flume in situations where calibration or verification of the 

H flume rating is not possible and the H flume level may vary. 

The primary objectives of this study were to determine 

how the standard stage-discharge relation for a 0.762-m (depth 

at flume entrance) H flume is affected by longitudinal slope 

and to develop a simplified correction method. A secondary 

objective was to determine the implications of using postcorrected discharge data on annual discharge estimates using 

real datasets.

Methods

Many of the techniques described in this report were 

developed by the U.S. Geological Survey (USGS) for use in 

cooperative projects with the Discovery Farms and Pioneer 

Farm programs (http://www.uwdiscoveryfarms.org/, http://

www.uwplatt.edu/pioneerfarm/, accessed April 9, 2012). These 

programs are tasked with monitoring agricultural runoff from 

a variety of geographic locations and farm-management styles. 

This report highlights specific data and situations that occurred 

at Pioneer Farm, but is representative of typical conditions that 

were encountered for both programs.

Pioneer Farm is a mixed-livestock farm owned by the 

University of Wisconsin–Platteville, located in northwest 

Lafayette County, Wisconsin. The 30-year annual average 

precipitation for Pioneer Farm is 916.9 millimeters (mm), and 

the farm receives 1,041.4 mm of snow/sleet/ice per year, on 

average (Midwestern Regional Climate Center, 2011). Soils 

on the farm are classified as Tama silt loam (U.S. Department 

of Agriculture, 2009), a fine, silty-clay loam with moderately 

high permeability. Soil- and water-conservation practices 

on the monitored fields include conservation tillage, grassed 

waterways, conservation-crop rotation, strip-cropping, and terraces. Twelve edge-of-field monitoring stations were installed 

at Pioneer Farm at various times, beginning in March 2002, 

to measure surface-runoff volumes and to collect samples of 

runoff from grassed waterways that drain small agricultural 

basins ranging in size from 2.6 to 74.7 acres, with slopes ranging from 2 to 7 percent. H flumes were used to monitor flow 

from these edge-of-field locations. Surface runoff is monitored 

year-round in all weather conditions. Station locations were 

chosen to be representative of typical runoff amounts and 

quality of sediment and nutrients from a farm in a corn-alfalfa 

rotation with conservation tillage in southwest Wisconsin. The 

measured discharges from six of the sites are used as examples 

in this report.

The procedure for the installation and maintenance of 

H flumes on the Pioneer Farm is described by Stuntebeck 

and others (2008). The installation was designed to have low 

impact on agricultural activities by minimizing soil disturbance and limiting the equipment needed for construction. In 

any of the installation techniques described, there have been 

situations where the H flume level was compromised from 

environmental conditions, primarily frost heave and ice formations under the flume supports. Currently, level bubbles have 

been installed on the H flumes to track flume levels during site 

visits and flume level is measured when changes in the bubble 

level are recorded.
Methods 3

Factors Influencing the Discharge Accuracy of 

H Flumes

The accuracy of discharge estimated from H flumes is 

dependent upon a number of factors, not the least of which is 

proper construction. The dimensions of the flume must adhere 

to standardized dimensions, and the construction material 

must be strong and rigid enough to prevent deformation during 

periods of high flow.

Proper installation of the H flume also is crucial for 

accurate discharge estimation. Care must be taken to ensure 

that the flume is level from front to back and from side to side. 

In the edge-of-field setting, however, this requirement can 

be challenging to maintain. Changing environmental conditions and site characteristics can affect the level of the flume; 

thus, affecting the accuracy of discharge estimates. FS can be 

compromised for a variety of reasons including frost heave 

during frozen-ground periods, sinking or failure of the flume 

supports, and flexing of the wing wall. 

Proper entrance and exit conditions are another important 

aspect of accurate discharge estimation. Water should enter 

the flume at subcritical velocity and under nonturbulent flow 

conditions, while water exiting the flume should be unimpeded 

(unsubmerged) (Grant and Dawson, 2001). Submergence 

issues can be especially problematic in landscapes with low 

slope, as vegetation or ice downstream from the flume can 

impede flow and cause backwater.

Differences between the recorded stage and the actual 

stage also affect discharge accuracy. A continuous record of 

discharge often is desired, and various types of stage-measurement sensors are available; however, instrument error, calibration error, and ice or snow in the flume can cause the continuous stage readings to be inaccurate. If the stage readings are 

inaccurate, the resultant discharge will be inaccurate as well.

Finally, the location of stage measurement can affect 

discharge accuracy. There is a drawdown curve in flumes 

(a decrease in water-surface elevation as water accelerates 

toward the exit), which makes the stage measurement location 

important. For H flumes, the proper measurement location is 

at a distance of 1.05 times the flume depth, upstream from the 

tip of the flume exit (Grant and Dawson, 2001). In a 0.762-m 

H flume, this distance is 0.80 m.

Types of Corrections

There were two basic types of corrections applied to the 

stage and discharge data collected as part of the Pioneer Farm 

monitoring program. The first type was a datum correction 

applied to the stage record to compensate for measurement 

error. Frequent staff-gage readings were obtained during 

runoff events and compared to the concurrent stage reported 

by the continuous-measurement sensor. The staff gage readings were assumed to be the “true” depth of flow in the flume. 

Datum corrections were applied when the differences between 

the staff gage and the sensor reading exceeded 0.003 m. For 

example, if the stage output by the sensor was 0.031 m and the 

staff gage reading in the flume was 0.046 m, a datum correction of +0.015 m was applied to the sensor record. During 

water years4 (WY) 2002–9, several datum corrections were 

applied among the sites at Pioneer Farm, ranging from −0.015 

to 0.079 m. Corrections were the result of ice/sediment in the 

flume, sensor malfunction, and sensor drift.

The second type of correction was a rating shift, which 

was applied for periods when the flume rating was compromised or biased. This primarily occurred when the flume was 

not installed level or the slope of the flume changed during 

the monitoring period. Rating shifts were applied similarly 

to datum corrections and were either constant or variable 

depending upon site conditions. For example, if the flume was 

installed with a slight drop in elevation from the entrance to 

the exit, a rating shift was applied to increase the discharge 

per unit stage from the standard rating. Freeze/thaw processes 

had a tendency to change the FS at some sites. To track these 

changes, the flumes were surveyed several times a year to 

monitor the slope. Small bubble levels were attached to the 

outside of the flume to enable periodic visual checks during site visits. Rating shifts were applied when survey data 

indicated changes in the FS by more than 0.003 m. Shifts were 

sometimes related to high-flow periods when the weight of 

water pressed down the flume supports. In these cases, rating 

shifts were either prorated from the event start to the peak 

or were applied after a series of events. Freezing and thawing conditions were sometimes problematic. Flume supports 

occasionally sank after the ground thawed (causing the flume 

exit to tilt downward), while the flume sometimes was thrust 

upward because of ice formation beneath the flume or when 

frost heaved the flume supports. Measured FS at Pioneer Farm 

ranged from 7 to −5 percent (fig. 1) during WY 2002–9.

Hydraulic Setting for Initial Case Study

The USGS initially conducted an independent test on the 

effect of changes in longitudinal slope on discharge estimation 

for a 0.762-m H flume at a local lake. Portable pumps were 

used to supply water at rates ranging from 1.24 to 7.27 liters 

per second (L/s). Four different FS, ranging from 1.7 to 

−0.7 percent, were evaluated (table 1). Negative slopes indicated that the flume exit was below the entrance.

4

Water year is the 12-month period October 1, for any given year through 

September 30, of the following year. The water year is designated by the calendar year in which it ends and which includes 9 of the 12 months. Thus, the 

year ending September 30, 2002 is called the “2002” water year.
4 Implications of Flume Slope on Discharge Estimates from 0.762-meter H Flumes Used in Edge-of-Field Monitoring

-6

-4

-2

0

2

4

6

8

Pioneer Farm, water years 2002–9 

Slope, in percent Positive flume slope Negative flume slope 

Sites

1 2 3 4 5 6 7 8 9 10 11 2b

Maximum: 7 percent, site 4, flume frost heave

Minimum: 5 percent, site 7, flume support failed

Median: -0.05 percent

EXPLANATION

Figure 1. Measured flume slopes at University of Wisconsin—Platteville Pioneer Farm, Platteville, Wisconsin, 

water years 2002–9.

Figure 1. Measured flume slopes at University of Wisconsin–Platteville Pioneer Farm, Platteville, Wisconsin, water 

years 2002–9.

Table 1. Case study test results for initial flume-slope correction.

Measured 

discharge (Qm), 

in liters per 

second

Flume stage (Ha ),

in meters

Apparent 

discharge (Qa), 

in liters per 

second

Flume slope (FS), 

in percent

Corrected reference 

stage (Hr), 

in meters

Final 

discharge (Qf),

in liters per 

second

1.97 0.043 1.50 0.7 0.048 1.87

1.97 .059 2.68 1.7 .047 1.75

1.97 .035 1.07 −1.5 .047 1.79

3.90 .065 3.11 −.6 .069 3.55

7.27 .093 6.10 −.6 .098 6.72

1.24 .030 .80 −.6 .034 1.04

The flume and an approach area were installed on an elevated dock. FS was adjustable and runoff water was captured 

from the flume exit in a calibrated container. Free-flow conditions prevailed for all test measurements. FS was calculated 

using survey data of multiple fixed points within the flume. 

Once the desired FS was determined, the portable pumps were 

activated to achieve a constant discharge. The factory installed 

staff gage was used to determine stage (read to the nearest 

0.3 mm), and discharge was evaluated by determining the time 

it took to fill the calibrated container as water exited the flume. 

Several evaluations of stage and discharge were done at each 

of the four slopes, with one value reported for each of the six 

trials.

Hydraulic Setting for Refined Correction Case 

Study

A more robust evaluation of the impacts of FS on the 

standardized H-flume stage-discharge rating was conducted at 

the Colorado State University (CSU) Hydraulics Laboratory. 

In this setting, a larger range of discharges could be tested. 

A 0.762-m H flume was installed in a 2.44 m wide, 60.96 m 

long, and 1.22 m deep recirculating flume. Water was supplied 

by a 125-horsepower pump, and discharge was measured in 

the supply line using an orifice plate accurate to ±2.5 percent. 

The maximum discharge capacity of the recirculating flume 

was 1,557.4 L/s, and the bed slope could be adjusted from 

horizontal to approximately 2 percent. For this study, the slope 

of the recirculating flume was positioned at 0.53 percent.
Methods 5

The flume was installed level in the lateral direction 

within the recirculating flume using transition wing walls 

that were fit and sealed to the flume entrance. An adjustable 

bracket was placed at the exit section of the flume to allow 

adjustment of the longitudinal slope (fig. 2). Seven discrete FS, ranging from −8 to +8 percent, were tested at four 

discharges corresponding to approximately 20, 40, 60, and 

80 percent of the maximum flume depth (at 23, 68, 166, and 

323 L/s, respectively) using the standard rating. Free-flow 

conditions prevailed for all test measurements. Seven evaluations of stage and slope were done at each of 4 discharges, for 

a total 28 trials.

Discharges measured by the orifice plate in the recirculating flume (Qm ) were adjusted to reach each target discharge. 

Staff-gage readings (Ha ) recorded to the nearest 0.3 mm were 

used to determine the apparent discharge (Qa ), based on the 

standard 0.762-m H-flume rating equation. FS was calculated 

using survey data of multiple fixed points within the flume and 

on the exterior flume structure. Survey data were recorded to 

the nearest 0.3 mm using an auto level. Fixed locations on the 

H-flume exterior framework were used as survey reference 

points to compute FS during higher discharges when water 

velocity in the flume made it difficult to accurately position the 

survey rod. FS was negative when the flume exit was lower 

than the flume entrance.

The test procedures were consistent for each set of discharge/slope evaluations. Flow in the recirculating flume was 

increased until the target discharge was reached and the flume 

was then surveyed and adjusted to the desired slope (table 2). 

The stage was allowed to stabilize (verified with continuous 

readings from a non-submersible pressure transducer) prior 

to recording Ha. Once all slopes were evaluated for a given 

discharge, the flow was increased to the next desired discharge 

and the process was repeated.

Figure 2. H-flume test installation at Colorado State University Hydraulics Laboratory, Fort Collins, Colorado.
6 Implications of Flume Slope on Discharge Estimates from 0.762-meter H Flumes Used in Edge-of-Field Monitoring

Table 2. Case study test results for refined flume-slope correction.

[Unknown accuracy of measured discharges at 20 percent of flume depth not reported]

Flume slope 

(FS), 

in percent

Flume stage 

(Ha ), 

in meters

Measured 

discharge 

(Qm ), 

in liters per 

second

Apparent 

discharge 

(Qa ), 

in liters per 

second

Difference between 

Qa and Qa at 0 percent 

flume slope position at 

each trial, in percent

Corrected 

reference 

stage (Hr ), 

in meters

Final 

discharge 

(Qf), 

in liters per 

second

Difference between 

Qf and Qf at 0 percent 

flume slope position at 

each trial, in percent

40 percent flume depth

0 0.313 68.0 1

72.3 

(6.4 percent)

0.0 0.313 72.3 0.0

−1 .310 68.0 70.5 −2.5 .316 73.9 2.3

−2 .304 68.0 67.8 −6.2 .317 74.4 2.9

−3 .293 68.0 63.0 −12.9 .314 72.6 .5

−8 .264 68.0 49.8 −31.1 .317 74.4 2.9

4 .345 68.0 89.5 23.8 .318 74.9 3.6

8 .370 68.0 104.2 44.2 .316 73.6 1.9

60 percent flume depth

0 0.470 165.9 1

178.1 

(7.3 percent)

0.0 0.470 178.1 0.0

−1 .461 165.9 170.2 −4.5 .467 175.8 −1.3

−2 .454 165.9 165.1 −7.3 .468 176.3 −1.0

−3 .445 165.9 157.7 −11.5 .465 174.2 −2.2

−8 .416 165.9 135.5 −23.9 .470 177.8 −.2

4 .495 165.9 200.2 12.4 .468 176.3 −1.0

7 .518 165.9 222.9 25.1 .471 179.5 .8

80 percent flume depth

0 0.625 322.8 1

345.5 

(7.5 percent)

0.0 0.625 345.5 0.0

−1 .619 322.8 337.3 −2.4 .626 346.3 .2

−2 .613 322.8 329.6 −4.6 .627 347.2 .5

−3 .608 322.8 301.0 −12.9 .628 348.3 .8

−8 .584 322.8 293.6 −15.0 .638 361.3 4.6

4 .647 322.8 374.6 8.4 .620 338.4 −2.0

7 .667 322.8 401.8 16.3 .620 338.4 −2.0

1

Percent difference between flume discharge (Qm ) and standard rating (apparent) discharge (Qa ).
Results and Discussion 7

Results and Discussion

Initial Case Study

The range in discharges tested was relatively small for 

a 0.762-m H flume (approximately 0.22 to 1.3 percent of 

maximum capacity), owing to the capacity limitations of the 

portable pumps. Nonetheless, a linear relation was observed 

between FS and the change in observed stage from the stage 

observed at a level position.

Data from this evaluation show that the differences 

between the apparent and actual discharge are a function of 

FS (table 1). Apparent discharges (Qa ) were negatively biased 

(underestimating measured discharge) when the flume was 

sloped downward from entrance to exit, and positively biased 

(overestimating measured discharge) when the flume was 

sloped upward. 

The case study indicated that a direct rating shift applied 

to the measured stage, as a function of the FS, provided accurate discharges. FS was determined by

FS

EP MP MP MP

=

− −  −



 



 























100 2

0 80

1

2 1

. (1)

where

FS = the flume slope, in percent; 

MP1 = elevation of interior survey point next to the 

staff gage in the flume, in meters; 

MP2 = elevation of interior survey point opposite 

the staff gage or stage-measurement 

location, in meters; 

EP = elevation of interior survey point at the exit 

of the H flume, in meters (fig. 3); and

0.80 = distance from exit of the 0.762-meter 

H flume to the head measurement section, 

in meters; use 2.625 if using a 2.5-foot 

H flume and measurements are in feet. 

For example, if the elevation of MP1 was 0.3050 m; the 

elevation of MP2 was 0.3110 m (indicating that MP2 is higher 

in elevation than MP1); and the EP was 0.2990 m, the resulting FS would be −1.13 percent slope. Typically, the stage in 

the flume is referenced to a staff gage on one side of the flume 

wall. This equation accounts for FS in both the lateral and longitudinal direction if the stage-measurement sensor is adjusted 

to match the staff gage. 

Figure 3. Plan view of 0.762-meter H flume showing measurement points for slope computation and proper head 

measurement location.

MP2 MP1

EP

0.762-meter H Flume (2.5 feet)

(plan view)

Head measurement

section

Staff gage

1.05 x D

EXPLANATION

MP2 - elevation of interior survey point opposite the

staff gage or stage-measurement location, in meters 

MP1 - elevation of interior survey point next the 

staff gage in the flume, in meters 

EP - elevation of interior survey point at the exit of

the H flume, in meters 

Figure 3. Plan view of 0.762-meter H flume showing measurement points for slope computation and proper head 

measurement location.
8 Implications of Flume Slope on Discharge Estimates from 0.762-meter H Flumes Used in Edge-of-Field Monitoring

This observed relation between FS and the rating shift 

yielded the following initial equation:

H H FS r a = − 0.008 (2)

where

Hr = corrected reference stage, in meters, the 

stage at which discharge is computed using 

the standard rating table for a 0.762-meter 

H flume;

Ha = measured flume stage, in meters; 

FS = flume slope, in percent; and

0.008 = constant to convert flume slope to a 

decimal, in meters; use 0.02625 if using 

a 2.5-foot H flume, where Hr and Ha

measurements are in feet. 

Flumes with negative slopes (MP1>EP) necessitate a 

positive correction to the Ha measurement. For example, the 

corrected reference stage (Hr) for a flume with −0.009 m drop 

in elevation (−1.13 percent slope in a 0.762-m H flume) at a 

stage (Ha ) of 0.0610 m would be 0.0700 m. 

Use of equation 2 yielded discharge errors from 5 to 

16 percent, with larger errors computed at the lower discharges. The discharge error was up to 46 percent with no correction. Computed discharge errors from small changes in discharge at the low flow can yield large percentage differences.

Refined Correction Case Study

The capacity of the CSU flume allowed for a more 

thorough comparison of the accuracy of the tested 0.762-m 

H flume to the standard rating for a range of discharges. The 

equivalent discharge at 20 percent depth was not used for any 

analyses because accuracy of the measured discharge through 

the CSU recirculating flume was unknown and variable at 

such a low rate. Differences between measured discharge (Qm) 

and apparent discharge (Qa ) for a level flume (0.0 percent 

longitudinal slope) revealed that the flume overestimated discharge by approximately 7 percent at discharges equivalent to 

40, 60, and 80 percent of flume capacity (table 2). 

This finding stresses the importance of calibrating flumes 

prior to use if highly accurate discharge data are desired. 

However, limited availability of testing facilities and the costs 

to perform these calibrations typically result in use of the 

standard stage-discharge rating. Development of a new stagedischarge rating using manual discharge measurements can 

be difficult because runoff from fields can be short-lived and 

runoff rates can change rapidly. At the least, verification of the 

flume dimensions seems prudent.

Because the flume did not match the standard rating, FS

test data were evaluated using the apparent discharge (Qa ) 

from the level flume position as the actual discharge. Results 

are therefore independent of the measured discharge. 

Similar to the initial test, biases between the apparent and 

actual discharge were a function of the FS. In addition, these 

biases increased with increasing slope and with lower depth of 

flow in the flume (fig. 4). 

Several approaches were evaluated using the stage, 

discharge, and slope data to determine a correction method or 

equation. By applying a best-fit linear regression through the 

data, a new equation—referred to as a refined correction—was 

defined as

H H FS r a = − 0.006716 (3)

where

0.006716 = multiplier, in meters; use 0.022034 if using 

a 2.5-foot H flume, where Hr and Ha

measurements are in feet.

Discharges computed using equation 3 had biases ranging 

from 0.2 to 4.6 percent compared to the errors up to 44.2 percent with no stage correction. Effectively, the corrected stage 

(Hr) corresponds to the theoretical stage value, in meters, for 

a given discharge and rating equation for a horizontal FS. For 

flumes that have negative slopes (EP<MP1), a positive correction would be applied, which would result in a corrected stage 

value greater than the measured stage within the flume. Using 

equation 3, a flume with a slope of −1.13 percent and a measured stage of 0.0610 m, would have a corrected stage (Hr

) of 

0.0686 m. A discharge value of 3.47 L/s would be computed 

using this corrected reference stage value.

More rigorous evaluations of the data were reviewed 

to determine if a multi-linear regression could be used to 

improve upon the refined linear correction. Regression equations for stage correction (Hr

) that were a function of both FS

and measured Ha were evaluated. Including the measured Ha

as a predictor for the stage correction did not produce lower 

average percent errors than equation 3, which uses only FS.

When evaluating the new slope correcting method to 

compensate for change in FS and flow depth, it was apparent that despite some variability in the measurements, the 

computed Qa values were less than 4.6 percent of the horizontal H-flume measured discharges. Reported accuracies of 

pre-calibrated flow-control structures such as H flumes are 

approximately ±5–8 percent (Harmel, 2006b). Therefore, it 

was determined that the stage-correction method was a reasonable predictor for discharge correction and could be easily 

measured and applied.

When developing runoff-monitoring designs with the 

use of H flumes, the size of the flume in relation to the depth 

of water anticipated should be considered. As depicted in 

figure 4, it is apparent that the effect of FS is greater at lower 

depths of flow and subsequent discharge. Though not evaluated in this report, it is suspected that H flumes with larger exit 

openings (HL flumes, for example) would be more sensitive to 

discharge bias owing to FS and depth of flow.
Results and Discussion 9

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

Discharge bias

Flume slope

Figure 4. The relation between flume slope and the discharge bias for each tested flow and slope condition. Discharge bias is the 

percentage error between the apparent discharge (Qa) and the Qa at 0 percent flume slope.

68 liters per second

166 liters per second

323 liters per second

Measured discharge

EXPLANATION

Figure 4. The relation between flume slope and the discharge bias for each tested flow and slope condition. Discharge bias is the 

percentage error between the apparent discharge (Qa

) and the Qa at 0 percent flume slope.

Scaling of Corrections to Other H-Flumes Sizes

The size of the H-flume flow-control opening is a function of the convergence angle and sidewall top slope (Grant 

and Dawson, 2001). H flumes of varying sizes maintain the 

same geometric scaling ratios in all directions; therefore, a 

new refined slope correction equation applicable to H flumes 

of varying sizes was produced and tested based on the principles of Froude scaling. A form of the correction equation 

that used dimensionless variable groupings was obtained by 

dividing both sides of equation 3 by the flume depth (D) of 

0.762 m. Equation 4 provides a dimensionally homogeneous 

correction equation, which theoretically could be used for all 

standard H-flume sizes:

H H r a = + ( . −0 0088136 FS * ) D (4)

where

D = flume depth, in meters. 

This equation would not necessarily be valid for variants 

of the H flume (HS and HL) owing to differences in geometry.

Impacts on Estimated Annual Runoff Volume

The accuracy of discharge data among different sites 

could be highly variable because differences between the 

apparent and rated discharge in H flumes were determined 

to be a function of the direction of FS (positive or negative 

slopes), the degree of slope, and the depth of flow. Some sites 

may experience more problems (FS shifts or inaccurate stage 

measurements) than others. Diligence in frequently recording 

these changes and correctly applying shift corrections when 

necessary would be important as well. The range of discharges 

in proportion to the flume size also can affect accuracy (small 

biases for small discharges equal large percentage differences). 

For these reasons, discharge accuracy from project to project or from site to site should not be assumed for sites using 

H flumes.

To estimate the impact of correcting for FS among sites, a 

comparison was made between annual runoff volumes for sites 

at Pioneer Farm with and without rating corrections applied. 

The sites included those that had large slope changes owing 

to frost heave or flume-support failure (sites 1 and 2) and sites 

that maintained a relatively consistent FS (sites 3, 4, and 5). 
10 Implications of Flume Slope on Discharge Estimates from 0.762-meter H Flumes Used in Edge-of-Field Monitoring

Annual runoff volumes computed without corrections 

ranged from 29 percent lower than to 27 percent higher than 

the volumes computed with the refined equation (equation 3; 

table 3). Percentage differences were related not only to the 

magnitude of observed FS, but to the annual runoff volume 

as well (small differences for small volumes equaled large 

percentage differences). 

Though these differences may not seem excessive, it 

is important to recognize that any discharge bias will carry 

through to the water-quality load computations and may cause 

problems with data interpretation for certain studies. This 

would be especially problematic if, for example, detected 

statistical trends were the result of changing discharges caused 

by uncorrected, changing FS instead of actual changes caused 

by management activities on the landscape.

Table 3 also shows differences between runoff volumes 

computed using the initial slope correction method (equation 2) and the refined slope correction method (equation 3). 

Annual runoff volumes computed using the initial equation 

ranged from 4 percent lower than to 6 percent higher than the 

volumes computed with the refined equation. These results 

indicate that, in general, the initial equation provided a relatively accurate method of correcting discharge for FS.

Table 3. Computed annual discharge comparison for different correction methods.

Water year

Annual discharge, in cubic meters Observed flume slopes

No 

correction

Initial 

correction

Refined 

correction

Minimum, 

in percent

Maximum, 

in percent

Site 1

2003 3,364 3,364 3,364 0.0 0.0

2004 7,676 8,919 8,688 0 4.8

2005 14,886 14,886 14,886 0 0

2006 5,927 5,933 5,933 0 0

2007 13,579 10,262 10,683 −4.2 .2

Site 2

2004 4,132 4,740 4,578 1.0 1.0

2005 8,418 9,943 9,681 1.0 1.0

2006 1,510 1,824 1,748 1.0 1.0

2007 4,308 4,975 4,863 .8 1.9

2008 6,563 7,500 7,354 .3 3.8

Site 3

2004 1,691 2,024 1,967 1.1 1.1

2005 2,105 2,550 2,472 1.1 1.1

2006 30 45 43 1.1 1.1

2007 2,858 2,987 2,967 .2 .5

2008 3,280 3,320 3,312 .1 .6

Site 4

2007 2,034 1,843 1,872 −1.3 1.1

2008 2,430 2,391 2,392 −1.3 2.0

Site 5

2007 1,027 1,045 1,038 0.1 1.1

2008 2,037 1,917 1,934 −.5 .5
References Cited 11

Conclusion

This report describes the corrections used to compute 

discharge from the standard stage-discharge relationship for 

a 0.762-meter (depth at flume entrance) H flume, as well as 

highlights study results and determination of a simplified correction method for longitudinal flume slope changes. In addition to these discharge computation corrections, the implications of using the post-corrected discharge data on the annual 

discharge measurements were described.

Correcting for discharge biases introduced by flume slope 

can improve the accuracy of water datasets used by environmental managers, policymakers, and producers. The results 

from this study showed that the application of an empirical 

equation to correct for flume slope predicted discharge from 

−2.2 to 4.6 percent of the H-flume measured discharge at a 

horizontal position. Literature estimates for H-flume discharge 

error are reported to be ±5–8 percent for properly leveled 

flumes. In addition, annual runoff volumes computed without 

correction ranged from 29 percent lower to 27 percent higher 

than volumes when corrections were applied. 

During the 10 years of edge-of-field monitoring and 

use of H flumes for the Pioneer Farm and Discovery Farms 

programs, the use and corrections relating to flume slope 

have improved overall accuracy of discharges from H flumes. 

Increases in accuracy from application of corrections not only 

improve the ability to properly evaluate the environmental 

benefits of a particular management practice, but also allow 

for cross-sharing of information from project to project, region 

to region, and State to State.

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Publishing support provided by the U.S. Geological Survey 

Science Publishing Network, 

Columbus Publishing Service Center

For more information concerning the research in this report, 

contact the 

Director, Wisconsin Water Science Center

U.S. Geological Survey

8505 Research Way

Middleton, WI 53562

http://wi.water.usgs.gov/
Komiskey and others—Implications of Flume Slope on Discharge Estimates from 0.762-meter H Flumes Used in Edge-of-Field Monitoring—Open-File Report 2013–1082