Two types of hysteresis loops have been observed on Goodwin Creek: those with a greater flow depth for a given discharge on the falling limb of the hydrograph (type 1) and those with a greater flow depth for a given discharge on the rising limb of the hydrograph (type 2). Causes of these 2 loop types are investigated in this paper

Bowie, Andrew J

Kuhnle, Roger A

English

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Publications from USDA-ARS / UNL Faculty U.S. Department of Agriculture: Agricultural Research Service, Lincoln, Nebraska 1992 Loop Rating Curves from Goodwin Creek Roger A. Kuhnle USDA National Sedimentation Laboratory Andrew J. Bowie USDA National Sedimentation Laboratory Follow this and additional works at: https://digitalcommons.unl.edu/usdaarsfacpub  Part of the Agricultural Science Commons Kuhnle, Roger A. and Bowie, Andrew J., "Loop Rating Curves from Goodwin Creek" (1992). Publications from USDA-ARS / UNL Faculty. 316. https://digitalcommons.unl.edu/usdaarsfacpub/316 This Article is brought to you for free and open access by the U.S. Department of Agriculture: Agricultural Research Service, Lincoln, Nebraska at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Publications from USDA-ARS / UNL Faculty by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Loop Rating Curves from Goodwin Creek Roger A. Kuhnle and Andrew J. Bowie1 Abstract Two types of hysteresis loops have been observed on Goodwin Creek: those with a greater flow depth for a given discharge on the falling limb of the hydrograph (type 1) and those with a greater flow depth for a given discharge on the rising limb of the hydrograph (type 2). Causes of these 2 loop types are investigated in this paper. Introduction Determining the flow discharge of a stream accurately is essential for hydraulic and hydrological studies. Yet relationships between the depth of flow and flow discharge on streams are not unique. Loop rating curves have been described by many authors (e.g. Carey and Keller, 1957; Colby, 1960; Simons, Richardson, and Haushild, 1962; Combs and Flowers, 1977; Combs, 1991) usually with the depth of flow for a given discharge greater on the falling than on the rising limb of the hydrograph. In this study two types of hysteresis loops were identified for Goodwin Creek and the causes of these loops were investigated. Study Area The study site was at station 2 of the Goodwin Creek Research Watershed in north central Mississippi. The channel has a mean bed slope of 0.003, bed sediment with 050 = 8.3 mm (range 0.1 - 64 mm), and a drainage area of 17.9 km2 • At the site is a concrete supercritical flow flume which was designed to have a unique relationship between flow depth in the flume and flow discharge (Bowie and Sansom, 1986). Depth of flow in the channel was measured using four USGS bubble gages in a 91 m long straight reach of channel 63 m upstream of the flume. The bubble gages were connected to pressure transducers from which data were collected every minute by the remote 1Research Geologist and Research Hydraulic Engineer, respectively, USDA National Sedimentation Laboratory, P.O. Box 1157, Oxford, MS 38655 741 Published in Hydraulic Engineering: Saving a Threatened Resource—In Search of Solutions: Proceedings of the Hydraulic Engineering sessions at Water Forum ’92. Baltimore, Maryland, August 2–6, 1992. Published by American Society of Civil Engineers.742 HYDRAULIC ENGINEERING telemetry system of the watershed. Flow depths from the bubble gages were related to flow discharges calculated from the recorded depth in the supercritical flow flume. Background It is generally agreed that there are two main causes of hysteresis loops in depth discharge relations. These are the dynamics of the flood wave and lags in the formation and destruction of bed forms (or other bed roughness elements) with the changing flow in the channel. The dynamics of the unsteady flow during a runoff event can be shown to result in a loop curve between depth and discharge. For a wide channel in which the vertical components of acceleration in the flow are small the following equation can be written: (1) v av _ gl ~Vt) g ax u (Henderson, 1966) where Q-flow discharge, A-flow area, c-Chezy coefficient, y-flow depth, So-slope of the bed, v-flow velocity, g-acceleration of gravity, x-flow parallel coordinate, and t-time coordinate. For Goodwin Creek the velocity slopes in (1) can be assumed to be small allowing (2) to be written. If the Chezy C is taken to be constant (2) can be divided by its uniform flow equivalent to yield: (3) where Qo is the flow discharge for uniform flow (Henderson, 1966). Q/Qo in (3) represents the effect of the dynamics of the flood wave on the depth-discharge relationship. Only Q/Qo can be calculated unless an independent measure of the roughness is available. The effect of bed roughness changes on depth-discharge relations has been studied by Simons et al. LOOP RATING CURVES 743 (1962) • Simons et al. demonstrated with a series of simulated hydrographs in a laboratory flume that a variety of types of hysteresis loops could be generated. The cause of these loops was attributed to the formation and destruction of bed forms in a sand bedded channel. Simons et al. found that type 1 loops could be generated by keeping the whole hydrograph in the lower flow regime, while type 2 loops could be generated by starting with lower flow regime dunes, increasing the flow to form an upper flow regime plane bed and then forming lower flow regime dunes again as the flow decreases. Hysteresis Loops on Goodwin Creek Flow depth versus flow discharge curves for 47 runoff events with peak discharges greater than 14 m3 S·1 for the period 1985-1989 were plotted and examined. Of the 47 events plotted 43 had identifiable hysteresis loops with 79% being type 1 and the rest type 2. The variation in discharge for a given depth resulting from a given loop 2.5 2.5 A 4/23/85 B 10/23/84 ~.o ~2.0 :x: ~1.5 Ii: 1.5 ... ... 0 0 ~1.0 ~1.0 t+!+t RISING STAGE 0 t+!+t RISING STAGE 0 ..... ~ rAWNG STAGE ..... ~ rAWNG STAGE I&. I&. 0.5 0.5 0.00 0.00 10 203ft 40 10 20 3~ 40 FLOW DISCHARGE m"ls) FLOW DISCHARGE m"ls) 0.40 C E ...... 0.20 TYPE 1 ..: •• l5 .;. .'~ ,. . . :x: • • " •• * Ii: 0.00 • . .... • 0 ~-0.20 TYPE 2 •• ~ -0.4010 20 30 40 50 60 PEAK FLOW DISCHARGE (ma/s) Fig. 1- Examples of type 1 (A), type 2 (B) loops, and (e) MDD versus peak discharge. Negative values refer to type 2 loops. 744 HYDRAULIC ENGINEERING varied by a factor of as much as 1.7. Examples of the 2 loop types and the range of maximum depth differences (MOD) for a given discharge are shown in Figure 1. Causes of the Loops The separation of the dynamic effects from the roughness effects on the depth-discharge relations could not be accomplished explicitly in this study because of the lack of an independent measure of the boundary roughness. Boundary roughnesses on sediment beds with a mixture of sand and gravel are difficult to predict. To approximate the effect of the dynamics of the flow on the depth-discharge relation, equation (3) was used with the collected slope data to calculate the maximum Q ratio ( (QclQo) I (Qf/Qo) = Qr/Qf for a given flow depth, with r -rising stage, f - falling stage) for the 27 runoff events with MOD's greater than 0.05 m. This was compared to the maximum Q ratio measured graphically from digitized plots of the depth-discharge relations. The results of this comparison were varied. In 11 cases a significant portion (mean of the 11 = 62%) of the Q ratio could be explained by the calculated dynamic effects of the flow, while in the rest of the 27 (including all of the type 2 loops) none of the Q ratio could be explained. For the cases when the dynamics of the flow could not explain the observed loops in the depth-discharge relations, the bed roughness was believed to be the cause. Lags in the formation and destruction of bed forms in sand have been shown to cause hysteresis loops similar to the two types identified in this study (simons et al., 1962). However, the type of bed forms that form in a gravel bed channel and the flow strengths at which they form is poorly known. Simons et al. (1962) created a depth-discharge curve very similar to the type 2 curves identified here, however, lower flow regime dunes and upper flow regime plane bed configurations were required to produce it. While the types of the bed forms on the bed of Goodwin Creek during runoff are generally unknown, indirect evidence suggests that upper flow regime conditions are not present. The coarseness of the bed sediment, and maximum Froude numbers at the study site of 0.4, seem to preclude the formation of an upper regime plane bed similar to the ones generated in simons et al. 's (1962) experiments. In several instances large dune-like bed forms have been observed on the bed of Goodwin Creek after large runoff events. Heights and lengths of the bed forms observed were generally about 0.4 0.8 m and 18 22 m, respectively (Fig. 2). Documentation of a type 2 depth-discharge loop after observation of large bed forms on the bed after a runoff event has been elusive, probably because of the high probability that low flows would plane off the bed forms before a flow of sufficient magnitude occurs. Possibly LOOP RATING CURVES 745 the inherited roughness is more subtle than the large dunes that have been observed after large runoff events. ~:.:[:': ::;: ;:,::~: :.:: ~ w 0 20 40 60 80 In DISTANCE (m) Fig. 2. - Flow parallel transect of bed surface taken after 5/9/89 runoff event at Goodwin Creek, station 2. Downstream is to the left, vertical axis is exaggerated by a factor of 4. The mechanism that we believe causes the type 2 loops on Goodwin Creek is the presence of a relatively high bed roughness, inherited from a previous runoff event, on the bed at the beginning of a runoff event. The initial high bed roughness on the rising limb of the hydrograph causes the flow depth to be relatively high for a given discharge. By the time of the peak flow most of the inherited roughness has been destroyed and the falling limb of the hydrograph has lower flow depths than were present on the rising limb. In the cases when the type 1 loops cannot be explained by the dynamics of the flow, a sequence of lags in the formation and destruction of the bed forms (or bed roughness elements) is hypothesized. This sequence would be analogous to the one observed by Simons et al. (1962). Discussion While the above analysis using equation (3) was instructive, it also raises questions about the dynamics of the system operating on Goodwin Creek. Figure 3 is a plot of equation (3) for the 5/9/89 event. The sloping trend of the data in Figure 3 is typical for all of the 26 others. Our expectation was that the trend of these plots 1.2 1.1 0.8 0.7 0.8 t....."""'""= ......... ~"":":~~~~. 0.0 0.5 1.0 1.5 2.Q 2.5 FLOW DEPTH (m) Fig. 3.- Q/Qo versus flow depth for 5/9/89 runoff event. 746 HYDRAULIC ENGINEERING would be horizontal about the line of Q/QO = 1. The slope of the data shown in Figure 3 indicates that the straight reach of channel selected for this study is probably not as simple as desired. Our best hypothesis is that the cross section may be changing over the study reach yielding the observed sloping trend in Figure 3. Conclusions It appears that for Goodwin Creek the causes of the type 1 hysteresis curves are about evenly split between the dynamics of the flood wave and lags in the formation and destruction of bed roughness elements. It is not known what form these roughness elements take. For the type 2 hysteresis curves the dynamics of the flood flow do not appear to explain any of the curves. A relatively high initial bed roughness from a previous runoff event that is progressively destroyed as the flow increases is thought to be the most likely cause of the type 2 curves. More study on bed forms in streams with gravel and sand beds is needed. APPENDIX I.-- References Bowie, A. J. and Sansom, o. W. (1986). "Innovative techniques for collecting hydrologic data", Proceedings of the 4th Federal Interagency Sedimentation Conference, 1-59 - 1-69. Carey, W. C., and Keller, M. D. (1957). "Systematic changes in the beds of alluvial rivers", J. Hydr. Div., ASCE, 83(4), 1331-1 - 1331-24. Colby, B. R. (1960). "Discontinuous rating curves for Pigeon Roost and Cuffawa Creeks in northern Mississippi", u.S. Department of Agriculture, Agricultural Research service, ARB 41-36, 31 p. combs, P. G. and Flowers, D. (1977). "A study of the dynamic rating curve of the Mississippi River", Proceedings Mississippi Water Resources Conference, Mississippi State, MS, 57-75. Combs, P. G. (1991). "Examination of Red River dynamic loop rating curve", Proceedings of the 5th Federal Interagency Sedimentation Conference, 4-24 -4-31. Henderson, F. M. (1966). Open Channel Flow. Macmillan Publishing Company, Inc., New York, NY, 522 p. Simons, D. B., Richardson, E. v., and Haushild, W. L. (1962). "Depth-discharge relations in alluvial channels", J. Hydr. Div., ASCE, 88(5), 57-72. 

Loop Rating Curves from Goodwin Creek

UNL | Libraries

University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Publications from USDA-ARS / UNL Faculty U.S. Department of Agriculture: Agricultural Research Service, Lincoln, Nebraska 
1992 
Loop Rating Curves from Goodwin Creek 
Roger A. Kuhnle 
USDA National Sedimentation Laboratory 
Andrew J. Bowie 
USDA National Sedimentation Laboratory 
Follow this and additional works at: https://digitalcommons.unl.edu/usdaarsfacpub 
 Part of the Agricultural Science Commons 
Kuhnle, Roger A. and Bowie, Andrew J., "Loop Rating Curves from Goodwin Creek" (1992). Publications 
from USDA-ARS / UNL Faculty. 316. 
https://digitalcommons.unl.edu/usdaarsfacpub/316 
This Article is brought to you for free and open access by the U.S. Department of Agriculture: Agricultural Research 
Service, Lincoln, Nebraska at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in 
Publications from USDA-ARS / UNL Faculty by an authorized administrator of DigitalCommons@University of 
Nebraska - Lincoln. 
Loop Rating Curves from Goodwin Creek 
Roger A. Kuhnle and Andrew J. Bowie1 
Abstract 
Two types of hysteresis loops have been observed on 
Goodwin Creek: those with a greater flow depth for a given 
discharge on the falling limb of the hydrograph (type 1) 
and those with a greater flow depth for a given discharge 
on the rising limb of the hydrograph (type 2). Causes of 
these 2 loop types are investigated in this paper. 
Introduction 
Determining the flow discharge of a stream accurately 
is essential for hydraulic and hydrological studies. Yet 
relationships between the depth of flow and flow discharge 
on streams are not unique. Loop rating curves have been 
described by many authors (e.g. Carey and Keller, 1957; 
Colby, 1960; Simons, Richardson, and Haushild, 1962; Combs 
and Flowers, 1977; Combs, 1991) usually with the depth of 
flow for a given discharge greater on the falling than on 
the rising limb of the hydrograph. In this study two 
types of hysteresis loops were identified for Goodwin 
Creek and the causes of these loops were investigated. 
Study Area 
The study site was at station 2 of the Goodwin Creek 
Research Watershed in north central Mississippi. The 
channel has a mean bed slope of 0.003, bed sediment with 
050 = 8.3 mm (range 0.1 - 64 mm), and a drainage area of 
17.9 km2 • At the site is a concrete supercritical flow 
flume which was designed to have a unique relationship 
between flow depth in the flume and flow discharge (Bowie 
and Sansom, 1986). Depth of flow in the channel was 
measured using four USGS bubble gages in a 91 m long 
straight reach of channel 63 m upstream of the flume. The 
bubble gages were connected to pressure transducers from 
which data were collected every minute by the remote 
1Research Geologist and Research Hydraulic Engineer, 
respectively, USDA National Sedimentation Laboratory, 
P.O. Box 1157, Oxford, MS 38655 
741 
Published in Hydraulic Engineering: Saving a Threatened Resource—In Search of Solutions: 
Proceedings of the Hydraulic Engineering sessions at Water Forum ’92. 
Baltimore, Maryland, August 2–6, 1992. Published by American Society of Civil Engineers.
742 HYDRAULIC ENGINEERING 
telemetry system of the watershed. Flow depths from the 
bubble gages were related to flow discharges calculated 
from the recorded depth in the supercritical flow flume. 
Background 
It is generally agreed that there are two main causes 
of hysteresis loops in depth discharge relations. These 
are the dynamics of the flood wave and lags in the 
formation and destruction of bed forms (or other bed 
roughness elements) with the changing flow in the channel. 
The dynamics of the unsteady flow during a runoff 
event can be shown to result in a loop curve between depth 
and discharge. For a wide channel in which the vertical 
components of acceleration in the flow are small the 
following equation can be written: 
(1) 
v av _ gl ~Vt) 
g ax u 
(Henderson, 1966) where Q-flow discharge, A-flow area, c-
Chezy coefficient, y-flow depth, So-slope of the bed, v-
flow velocity, g-acceleration of gravity, x-flow parallel 
coordinate, and t-time coordinate. For Goodwin Creek the 
velocity slopes in (1) can be assumed to be small allowing 
(2) 
to be written. If the Chezy C is taken to be constant (2) 
can be divided by its uniform flow equivalent to yield: 
(3) 
where Qo is the flow discharge for uniform flow (Henderson, 1966). Q/Qo in (3) represents the effect of 
the dynamics of the flood wave on the depth-discharge 
relationship. Only Q/Qo can be calculated unless an independent measure of the roughness is available. 
The effect of bed roughness changes on depth-
discharge relations has been studied by Simons et al. 
LOOP RATING CURVES 743 
(1962) • Simons et al. demonstrated with a series of 
simulated hydrographs in a laboratory flume that a variety 
of types of hysteresis loops could be generated. The 
cause of these loops was attributed to the formation and 
destruction of bed forms in a sand bedded channel. Simons 
et al. found that type 1 loops could be generated by 
keeping the whole hydrograph in the lower flow regime, 
while type 2 loops could be generated by starting with 
lower flow regime dunes, increasing the flow to form an 
upper flow regime plane bed and then forming lower flow 
regime dunes again as the flow decreases. 
Hysteresis Loops on Goodwin Creek 
Flow depth versus flow discharge curves for 47 runoff 
events with peak discharges greater than 14 m3 S·1 for the 
period 1985-1989 were plotted and examined. Of the 47 
events plotted 43 had identifiable hysteresis loops with 
79% being type 1 and the rest type 2. The variation in 
discharge for a given depth resulting from a given loop 
2.5 2.5 
A 4/23/85 B 10/23/84 
~.o ~2.0 
:x: ~1.5 Ii: 1.5 
... ... 
0 0 
~1.0 ~1.0 
t+!+t RISING STAGE 0 t+!+t RISING STAGE 0 
..... ~ rAWNG STAGE ..... ~ rAWNG STAGE I&. I&. 
0.5 0.5 
0.00 0.00 10 203ft 40 10 20 3~ 40 
FLOW DISCHARGE m"ls) FLOW DISCHARGE m"ls) 
0.40 
C 
E 
...... 0.20 TYPE 1 
..: •• 
l5 
.;. .'~ 
,. . . 
:x: 
• • " •• * 
Ii: 0.00 • . .... • 0 
~-0.20 TYPE 2 •• 
~ 
-0.4010 20 30 40 50 60 
PEAK FLOW DISCHARGE (ma/s) 
Fig. 1- Examples of type 1 (A), type 2 (B) loops, and 
(e) MDD versus peak discharge. Negative values 
refer to type 2 loops. 
744 HYDRAULIC ENGINEERING 
varied by a factor of as much as 1.7. Examples of the 2 
loop types and the range of maximum depth differences 
(MOD) for a given discharge are shown in Figure 1. 
Causes of the Loops 
The separation of the dynamic effects from the 
roughness effects on the depth-discharge relations could 
not be accomplished explicitly in this study because of 
the lack of an independent measure of the boundary 
roughness. Boundary roughnesses on sediment beds with a 
mixture of sand and gravel are difficult to predict. To 
approximate the effect of the dynamics of the flow on the 
depth-discharge relation, equation (3) was used with the 
collected slope data to calculate the maximum Q ratio 
( (QclQo) I (Qf/Qo) = Qr/Qf for a given flow depth, with r -
rising stage, f - falling stage) for the 27 runoff events 
with MOD's greater than 0.05 m. This was compared to the 
maximum Q ratio measured graphically from digitized plots 
of the depth-discharge relations. The results of this 
comparison were varied. In 11 cases a significant portion 
(mean of the 11 = 62%) of the Q ratio could be explained 
by the calculated dynamic effects of the flow, while in 
the rest of the 27 (including all of the type 2 loops) 
none of the Q ratio could be explained. 
For the cases when the dynamics of the flow could not 
explain the observed loops in the depth-discharge 
relations, the bed roughness was believed to be the cause. 
Lags in the formation and destruction of bed forms in sand 
have been shown to cause hysteresis loops similar to the 
two types identified in this study (simons et al., 1962). 
However, the type of bed forms that form in a gravel bed 
channel and the flow strengths at which they form is 
poorly known. Simons et al. (1962) created a depth-
discharge curve very similar to the type 2 curves 
identified here, however, lower flow regime dunes and 
upper flow regime plane bed configurations were required 
to produce it. While the types of the bed forms on the 
bed of Goodwin Creek during runoff are generally unknown, 
indirect evidence suggests that upper flow regime 
conditions are not present. The coarseness of the bed 
sediment, and maximum Froude numbers at the study site of 
0.4, seem to preclude the formation of an upper regime 
plane bed similar to the ones generated in simons et 
al. 's (1962) experiments. In several instances large 
dune-like bed forms have been observed on the bed of 
Goodwin Creek after large runoff events. Heights and 
lengths of the bed forms observed were generally about 0.4 
0.8 m and 18 22 m, respectively (Fig. 2). 
Documentation of a type 2 depth-discharge loop after 
observation of large bed forms on the bed after a runoff 
event has been elusive, probably because of the high 
probability that low flows would plane off the bed forms 
before a flow of sufficient magnitude occurs. Possibly 
LOOP RATING CURVES 745 
the inherited roughness is more subtle than the large 
dunes that have been observed after large runoff events. 
~:.:[:': ::;: ;:,::~: :.:: ~ 
w 0 20 40 60 80 
In DISTANCE (m) 
Fig. 2. - Flow parallel transect of bed surface taken after 
5/9/89 runoff event at Goodwin Creek, station 
2. Downstream is to the left, vertical axis is 
exaggerated by a factor of 4. 
The mechanism that we believe causes the type 2 loops on 
Goodwin Creek is the presence of a relatively high bed 
roughness, inherited from a previous runoff event, on the 
bed at the beginning of a runoff event. The initial high 
bed roughness on the rising limb of the hydrograph causes 
the flow depth to be relatively high for a given 
discharge. By the time of the peak flow most of the 
inherited roughness has been destroyed and the falling 
limb of the hydrograph has lower flow depths than were 
present on the rising limb. 
In the cases when the type 1 loops cannot be 
explained by the dynamics of the flow, a sequence of lags 
in the formation and destruction of the bed forms (or bed 
roughness elements) is hypothesized. This sequence would 
be analogous to the one observed by Simons et al. (1962). 
Discussion 
While the above analysis using equation (3) was 
instructive, it also raises questions about the dynamics 
of the system operating on Goodwin Creek. Figure 3 is a 
plot of equation (3) for the 5/9/89 event. The sloping 
trend of the data in Figure 3 is typical for all of the 26 
others. Our expectation was that the trend of these plots 
1.2 
1.1 
0.8 
0.7 
0.8 t....."""'""= ......... ~"":":~~~~. 
0.0 0.5 1.0 1.5 2.Q 2.5 
FLOW DEPTH (m) 
Fig. 3.- Q/Qo versus flow depth for 5/9/89 runoff event. 
746 HYDRAULIC ENGINEERING 
would be horizontal about the line of Q/QO = 1. The slope 
of the data shown in Figure 3 indicates that the straight 
reach of channel selected for this study is probably not 
as simple as desired. Our best hypothesis is that the 
cross section may be changing over the study reach 
yielding the observed sloping trend in Figure 3. 
Conclusions 
It appears that for Goodwin Creek the causes of the 
type 1 hysteresis curves are about evenly split between 
the dynamics of the flood wave and lags in the formation 
and destruction of bed roughness elements. It is not 
known what form these roughness elements take. For the 
type 2 hysteresis curves the dynamics of the flood flow do 
not appear to explain any of the curves. A relatively 
high initial bed roughness from a previous runoff event 
that is progressively destroyed as the flow increases is 
thought to be the most likely cause of the type 2 curves. 
More study on bed forms in streams with gravel and sand 
beds is needed. 
APPENDIX I.-- References 
Bowie, A. J. and Sansom, o. W. (1986). "Innovative 
techniques for collecting hydrologic data", 
Proceedings of the 4th Federal Interagency 
Sedimentation Conference, 1-59 - 1-69. 
Carey, W. C., and Keller, M. D. (1957). "Systematic 
changes in the beds of alluvial rivers", J. Hydr. 
Div., ASCE, 83(4), 1331-1 - 1331-24. 
Colby, B. R. (1960). "Discontinuous rating curves for 
Pigeon Roost and Cuffawa Creeks in northern 
Mississippi", u.S. Department of Agriculture, 
Agricultural Research service, ARB 41-36, 31 p. 
combs, P. G. and Flowers, D. (1977). "A study of the 
dynamic rating curve of the Mississippi River", 
Proceedings Mississippi Water Resources Conference, 
Mississippi State, MS, 57-75. 
Combs, P. G. (1991). "Examination of Red River dynamic 
loop rating curve", Proceedings of the 5th Federal 
Interagency Sedimentation Conference, 4-24 -4-31. 
Henderson, F. M. (1966). Open Channel Flow. Macmillan 
Publishing Company, Inc., New York, NY, 522 p. 
Simons, D. B., Richardson, E. v., and Haushild, W. L. 
(1962). "Depth-discharge relations in alluvial 
channels", J. Hydr. Div., ASCE, 88(5), 57-72. 


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Loop Rating Curves from Goodwin Creek

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