EVALUATING CHANNEL-FORMING DISCHARGES: A STUDY OF LARGE RIVERS IN OHIO

Transcription

1 EVALUATING CHANNEL-FORMING DISCHARGES: A STUDY OF LARGE RIVERS IN OHIO G. E. Powell, D. Mecklenburg, A. Ward ABSTRACT. Measured data were used to evaluate whether bankfull discharges were related to effective discharges for large rivers in Ohio. The frequency and sediment transport associated with these channel-forming discharges was also examined. Rural watersheds in the Midwest region of the U.S. are dominated by agricultural land uses that incorporate subsurface drainage improvements. Bankfull discharges were determined by measuring fluvial features at each USGS gage and then relating these features to the rating curve and historic daily discharge data for each gage. Effective discharges were determined by using suspended sediment data obtained at the gages, the Wolman-Miller method for calculating geomorphic work, and bin sizes based on stage intervals to group sediment and discharge data. There was good agreement between the effective discharge and bankfull discharge estimates. Bankfull and effective discharges were primarily related to flows that transported the middle 5% of the total sediment load. Recurrence intervals of the bankfull and effective discharges ranged from.3 to 1.4 years. These recurrence intervals are more frequent than generally reported in the literature. The duration of daily discharges that equaled or exceeded the channel-forming discharge ranged from 1 to 24 days annually, with mean values of 9 and 11 days for the bankfull discharge and effective discharge, respectively. Common methods for determining the recurrence interval are inadequate for frequent channel-forming discharges, and better insight is obtained by determining the number of days on which these flows are exceeded annually. Keywords. Effective and bankfull discharge, Recurrence interval, Sediment transport. Since the classic work of Wolman and Miller (196), there have been numerous studies of bankfull discharge and effective discharge concepts. Bankfull discharge is identified by collecting and analyzing channel dimension data (Andrews, 198; Nolan et al, 1987; Rosgen, 1994; Johnson and Heil, 1996). Effective discharge involves the collection and analysis of flow rate data and sediment (bedload and/or suspended) data (Andrews, 198; Nash, 1994; Andrews and Nankervis, 1995; Orndorff and Whiting, 1999; Whiting et al., 1999; Biedenharn et al; 2; Emmett and Wolman, 21; Simon et al., 24). Leopold (1994) proposed that bankfull discharge is equal to effective discharge. By equating these channel-forming discharges, Leopold associated the measured geomorphic features with the calculated sediment transport. However, potential design errors and confusion can result when these terms are used synonymously without considering their individual definitions and site-specific conditions. In this study, we use the definitions of bankfull and effective discharge proposed by Wolman and Miller (196): bankfull Article was submitted for review in March 25; approved for publication by the Soil & Water Division of ASABE in December 25. The authors are G. Erick Powell, ASABE Student Member, Doctoral Research Associate, Department of Food, Agricultural, and Biological Engineering, The Ohio State University, Columbus, Ohio; Dan Mecklenburg, Ecological Engineer, Ohio Department of Natural Resources, Columbus, Ohio; and Andy Ward, ASABE Member Engineer, Professor, Department of Food, Agricultural, and Biological Engineering, The Ohio State University, Columbus, Ohio. Corresponding author: G. Erick Powell, Department of Food, Agricultural, and Biological Engineering, The Ohio State University, 59 Woody Hayes Dr., Columbus, OH 4321; phone: ; powell.354@osu.edu. discharge is the stream flow that fills the main channel and begins to spill onto the active floodplain; effective discharge is the discharge that transports the most sediment over time. Channel-forming discharge is used as a general term to designate both bankfull and effective discharge. To date, most published studies of bankfull or effective discharges have been based on natural streams and rivers in the western U.S. These watersheds usually have steeper gradients and less human modification to the landscape than the larger rural watersheds in the Midwest region of the U.S. Midwestern watersheds are dominated by agricultural land uses that incorporate subsurface drainage improvements. These subsurface systems discharge into headwater channels that are either constructed channels (ditches) or modified streams. Throughout the Midwest, most natural headwater channels have been deepened and straightened to facilitate the flow of water from agricultural subsurface drainage outlets and to maximize conveyance capacity. Constructed channels typically undergo routine maintenance and often lack a sinuous pattern and the two-stage relationship, between a main (bankfull) channel and a floodplain, that is often found in gravel-bed streams. Most of the headwater systems in this study are dominated by over-deep and over-wide incised channels that rarely exhibit out-of-bank flows onto a broad floodplain. Johnson and Heil (1996) questioned the use of geomorphic bankfull concepts on unstable channels like agricultural ditches. However, recent studies have shown that these disturbed headwater systems exhibit geomorphic features, such as a main channel system with a series of bars and benches (Jayakaran et al., 25; Landwehr and Rhoads, 23; Kuhnle et al., 1999). While significant research detailing geomorphology concepts is abundant, attempts to apply these concepts to Transactions of the ASABE Vol. 49(1): American Society of Agricultural and Biological Engineers ISSN

2 engineering design have emerged only recently. In many stream systems, the channel geometry and dynamic equilibrium are associated with the supply and transport of sediment. However, lack of sufficient data and the complexities associated with sediment scour, transport, and deposition processes have led to widespread application of simplified bankfull concepts. This oversimplification is most often observed when engineering designs estimate channel-forming discharges by calculating them based on hydrology concepts and a 1 to 2 year recurrence interval flow. This article details the suitability of using channel-forming discharge concepts in engineering applications in the Midwest. OBJECTIVES Measured data for ten large river systems in Ohio were used to address the following objectives: (1) evaluate whether bankfull discharges are related to effective discharges for large rivers in Ohio, and (2) examine the frequency and sediment relationships between bankfull and effective discharges. Both objectives provide critical clarification on relating channel-forming discharges to engineering sustainable stream designs in the Midwest. Quantifying channel-forming discharges is important in stream designs, particularly in Midwest headwater streams. Headwater streams in the Midwest are typically modified without the use of available sediment transport data. System designs based on recurrence intervals may therefore be inappropriate and unstable. REVIEW OF PREVIOUS STUDIES The importance of understanding and quantifying channel-forming discharges is illustrated by two recent studies. Shields et al. (23) present an important and useful discussion on the application of channel-forming discharges in channel designs. They discuss the design usage of channel-forming discharges based on effective, bankfull, or specific return interval discharges. They also discuss the difficulties of quantifying channel-forming discharges and problems associated with designs based on bankfull discharges. Shields et al. (23) define bankfull discharge as the maximum discharge that the channel can convey without overflow onto the floodplain, which is slightly different from the Wolman and Miller (196) definition. Palmer et al. (25) identify five criteria for ecologically successful river restoration designs. They do not specifically discuss channel-forming discharges; however, the focus of their approach is to establish self-sustaining systems. One of the criteria that they identify is to develop a guiding image of dynamic state. This criterion emphasizes the range and average of key stream variables, including geomorphology, hydrology, chemistry, physical habitat, and biology. Another criterion is to increase the system resilience, or the ability to maintain equilibrium despite changes. Both criteria emphasize the need for a consistent effective discharge even though system changes occur; adequate floodplain is necessary to dissipate large energy flows and allow future system adjustments. The Wolman-Miller model (fig. 1) is the most common approach used to calculate effective discharge (Andrews and Nankervis, 1995). The sediment transport rate (fig. 1, curve A) is determined by fitting a power regression function to the sediment and discharge data. Low discharges are ineffective in transporting sediment; conversely, extremely large discharge events transport large sediment quantities. Flow data are grouped into bins of similar discharge values. Event frequency (fig. 1, curve B) plots the discharge events in terms of how often the flows of each bin occur. When the bin-discharge event frequency is multiplied by the corresponding sediment transport rate, a measure of the total sediment carried over time is obtained, expressed as sediment tons (fig. 1, curve C). This curve, often referred to as the geomorphic work (Wolman and Miller, 196; Ward and Trimble, 24), peaks at the effective discharge value. Several studies, including his own research, prompted Leopold (1994) to equate bankfull discharge and effective discharge. For example, Andrews (198) evaluated 15 reaches at USGS gauging stations in the Yampa River Basin in Colorado and Wyoming. He concluded that the bankfull and effective discharges were nearly equal at all gauging stations. Andrews and Nankervis (1995) reported an almost perfect one-to-one correlation between bankfull and effective dis Figure 1. Wolman-Miller model for the Maumee River at Waterville illustrating its components, including geomorphic work and effective discharge (1 cms = 35.3 cfs; 1 Mg = 1.1 ton) (Ward and Trimble, 24). 36 TRANSACTIONS OF THE ASABE

3 charge for 17 reaches (with a well-defined channel and floodplain) along mountain streams in Colorado in the vicinity of a USGS gage. Emmett and Wolman (21) reported that the ratio of effective discharge to bankfull discharge ranged from.98 to 1.31 for five snowmelt-dominated mountain streams in the northern Rocky Mountains. Whiting et al. (1999) found that the effective discharge averaged.8 of the bankfull discharge for 23 headwater streams in central and northern Idaho. Many studies use recurrence intervals to describe the frequency of channel-forming discharge. While these studies report recurrence interval values ranging from 1 year to more than 5 years (Nash, 1994; Whiting et al., 1999; Emmett and Wolman, 21; Petit and Pauquet, 1997; Simon et al., 24), the most common published value is 1.5 to 2 years. Simon et al. (24) concluded that for 17 ecosystems throughout the U.S., the recurrence interval varied from ecosystem to ecosystem and ranged from 1.1 to 1.7 years; the discharge associated with the 1.5-year recurrence interval appeared to be a reasonably good estimate of the recurrence interval for the effective discharge. No ecosystems in Ohio were studied, but the central Corn Belt plains, to the west of Ohio, had the lowest reported recurrence interval of 1.1 years for the effective discharge and a value of.6 for the ratio of bankfull to effective discharge. A few studies have reported channel-forming discharge recurrence interval values that are less than one year. In a recent geomorphic study of Illinois streams, Crowder and Knapp (25) reported low recurrence intervals of close to one year and often less than one year. Jurmu and Andrle (1997) also reported very frequent recurrence intervals in wetland streams that are dominated by sand and silt bed material. Kuhnle et al. (1999) reported recurrence interval values of.69 to 1. years for locations in the incised Goodwin Creek, Mississippi, experimental watershed. Channel-forming discharge frequencies are sometimes described by flow duration instead of recurrence intervals (Emmett, 1975; Andrews, 198; Andrews and Nankervis, 1995). Flow duration, or the annual frequency of exceedance, is defined as the estimated times per year that the specified flow occurs or is exceeded. For example, Andrews (198) reported effective discharge flow duration values of 1.5 to 11 days annually, with corresponding recurrence intervals of 3.26 and 1.18 years, respectively. These duration values are similar to values of 6 to 11 days per year that were published by Wolman and Miller (196). Bankfull and effective discharge have also been characterized by the total sediment percentage transported by the channel-forming discharges (Andrews, 198; Nolan et al. 1987; Andrews and Nankervis, 1995; Sichingabula, 1999). Nolan et al. (1987) reported that discharges, which transported 5% to 9% of the sediment load, had recurrence intervals of.27 to 16.1 years. Andrew and Nankervis (1995) and Sichingabula (1999) independently described discharges that transported 5% to 8% of the sediment load to have flow durations of 11 to 8 days annually. EXPERIMENTAL APPROACH SITE DESCRIPTION The analysis presented in this article was conducted on ten low-gradient rivers in Ohio (fig. 2, primary sites); USGS gauging stations are located at each site, and USGS discharge and sediment data were used for this analysis. Characteristics of each watershed are summarized in table 1. The drainage areas for the study sites range from 74.9 to 19,223 km 2, and stream orders range from 2 to 6. All sites have an average channel slope equal to or less than.1% and drain either to Lake Erie or to the Ohio River. The north-central and northwestern Ohio watersheds are located in the lake plain Figure 2. USGS gage study sites throughout Ohio. USGS gage numbers are listed for each labeled primary and secondary site. Vol. 49(1):

4 Site No. (in fig. 2) Gage Name (USGS Gage) 1 North Fork Massie (32415) 2 Loramie River (326195) 3 Portage River (41955) 4 Stillwater River (3265) 5 Upper Great Miami (3275) 6 Grand River (42121) 7 Sandusky River (4198) 8 Scioto River (32345) 9 Maumee River (41935) 1 Muskingum River (315) Drainage Area (km 2 ) Table 1. Characteristics of the study watersheds and river systems. Channel Slope (%) Aquatic Ecoregion North Central Tillplain North Central Tillplain Stream Order Land Use (%) Agric. Forest Urban Years of Sediment (Range) ( ) ( ) Great Lakes ( ) North Central Tillplain North Central Tillplain Erie Drift Plain N.C. Tillplain, Great Lakes North Central Tillplain ( ) ( ) ( ) ( ) ( ) Great Lakes ( ) Western Allegheny Plateau ( ) Years of Discharge (Range) 14 ( ) 39 ( ) 75 ( ) 87 ( ) 89 ( ) 29 ( ) 8 ( ) 73 (193-23) 16 ( ) 82 ( ) region of Ohio that includes the Great Black Swamp (portions of the Maumee and Portage River watersheds) that was traditionally a wetland with low gradients. The other watersheds are located in flat to rolling glacial till regions. Most of the watersheds are dominated by corn and soybean cropping systems. Flows on the Loramie, Scioto, and Muskingum Rivers are modified by one or more flood control structures. MEASURING AND CALCULATING BANKFULL PROPERTIES At each gage location, bankfull discharge was determined by identifying and measuring the stage of a bankfull fluvial feature, computing the channel cross-sectional area associated with the measured stage, and then calculating the discharge conveyed by the cross-sectional area. Bankfull stage information at two of the gages (North Fork and Grand) was measured by the USGS as part of a study to develop regional curves for Ohio; we performed all the remaining measurements and observations associated with the bankfull features included in this study. Many of the rivers were entrenched, so the dominant bankfull feature was typically a narrow floodplain or bench located below the top of the bank. These features exhibited a combination of changes in the bank material, slope, particle size distribution, and vegetation. Each bank was examined for a few hundred meters both up and downstream of each USGS gage location. Using the gage as a point of reference, the bankfull stage was measured at the most prominent observed bankfull feature using a laser level, a telescoping leveling rod, and a laser receiver. The time was recorded and used to obtain the water stage elevation (at the time of measurement) from the real-time USGS gage. Determination of the cross-sectional area and bankfull discharge was based on published USGS measurements at the gage, a USGS gage rating curve, and our measurement of the bankfull stage. CALCULATING THE EFFECTIVE DISCHARGE The effective discharge at each gage was determined based on USGS daily measurements of sediment and discharge. A spreadsheet tool was used to develop a Wolman-Miller model of the geomorphic work (Mecklenburg and Ward, 24; Ward and Mecklenburg, 25). Calculating effective discharge values using the Wolman- Miller model requires that bins are comprised of discharges that represent similar flows. Determining bin sizes and grouping discharge ranges based on similar flows is difficult and has been approached differently in several published studies. The U.S. Army Corps of Engineers publications recommend that discharge should be divided into equal discharge bin intervals (Biendenharn et al., 2). Biendenharn et al. (2) provided strategic details on accommodating outliers when the flow data is divided into equal flow bins. Sichingabula (1999) suggested grouping discharges using an event-based approach to provide better estimation of similar discharge bins. Using components of these approaches, we created a unique spreadsheet tool, which incorporates an alternative bin-sizing procedure that groups discharges based on equal stage intervals. This equal stage approach creates bin sizes that group similar discharges regardless of the discharge event and allows larger infrequent flows to be grouped together (fig. 3). The spreadsheet tool allows users to quickly evaluate the results of selecting a different bin size by changing the stage interval. The discharge range of each bin was determined using the USGS rating curve for each gage site. A stage interval was set, and all discharges from the rating curve that fell within the first stage interval were grouped by the spreadsheet tool into the first bin. The next bin incorporated all the discharges for the next stage interval, and this process was repeated until all discharges were considered. For example, if we defined the stage interval to be.3 m, then bin 1 would contain all the flows associated with stage readings from to.3 m, bin 2 would contain all flows associated with stage readings from.3 to.6 m, etc. (fig. 3). 38 TRANSACTIONS OF THE ASABE

5 5 4 Equal stage intervals Stage (m) 3 2 Corresponding discharge ranges associated with stage intervals Figure 3. The USGS rating curve for the Maumee River at Waterville divided into equal stage intervals and corresponding discharge ranges. With the discharge data divided into bins of similar flows, the sediment load data were examined to determine the best representation of sediment transport by discharge. Figure 4 illustrates the USGS-measured suspended sediment versus measured discharge data for the Maumee River. Most sediment analysis presented in the literature fit a single regression line (fig. 4, dashed line). In this analysis, the sediment and discharge data were divided into three groups that were each fitted with a separate regression equation. Simon et al. (24) discussed the difficulty of using a single regression trendline to represent the sediment transport function. The technique of multiple regression equations provides a more accurate functional representation of the sediment transport data during the most influential discharges. Because data in the low discharge range had little influence on the effective discharge calculation, the regression equation through low discharge values was eliminated and the middle sediment transport function was extended to create estimates for low discharge conditions. The discharge breakpoints for each range were selected based on visual breaks in the slope of the discharge versus sediment scatter-plot (Simon et al., 24). The visually selected breakpoints were then evaluated to provide the best correlation between the measured and predicted sediment transport load. The high and middle discharge regression functions were used to develop the Wolman-Miller model (fig. 1). The sediment transport function (fig. 4) was evaluated by calculating the measured sediment for each bin size and comparing the calculated results to the predicted sediment using the sediment transport function. The average number of daily occurrences per year for each bin is shown in figure 5. The mean bin discharge values are plotted in figure 5 with the average occurrence values. A regression line is fitted to the data, with the exclusion of extreme large-discharge and drought low-discharge events at the tails, to provide the most accurate regression fit possible around the flows that determine the effective discharge. Figure 4. Daily sediment discharge data for the Maumee River at Waterville. The dashed regression line is fitted to the entire data set. The middle and high data sections are shown with their respective regression lines and corresponding breakpoints. Vol. 49(1):

6 1 Days from data 1 Days calculated Number of Days (avg. per year) Figure 5. Discharge-frequency relationship for the Maumee River at Waterville. The regression line excludes outliers to better represent the frequency of the dominant discharge range. The spreadsheet tool utilizes four different methods to calculate the effective discharge and geomorphic work: Work 1 is the result obtained by multiplying the mean bin values for the measured sediment and discharge data. Work 2 is similar to Work 1 except that the sediment functions, rather than the measured sediment values, are used to calculate the sediment load associated with each discharge value in each bin. Most USGS gage stations throughout the U.S. have more extensive daily discharge than sediment discharge data. Therefore, to obtain Work 3 and Work 4, the sediment function is applied to the complete record of daily discharge values. These applied functions provide estimates for effective discharge over a longer period of time. Work 3 is the result of multiplying the mean sediment value in each bin with the mean discharge value of each bin. Work 4 differs from Work 3 by using the regression equations for sediment transport (fig. 4) and frequency (fig. 5) of the entire discharge period of record. Work 4 results in a plotted function that demonstrates a continuous relationship between discharge and sediment transport over time. The effective discharge values reported in this study are the geomorphic work values from Work 1, which is most similar to the method typically reported in the literature. Work 4 results are also reported to provide comparison between traditional values and the regression functions we have developed. For each study location, the initial stage interval evaluated to define the discharge and sediment bins was set to.6 m. The stage interval was incrementally increased by about.3 m (.1 ft) until a distinct effective discharge peak was produced. As the stage interval approached.37 m, all study sites yielded a good Wolman-Miller model relationship. The stage intervals were then increased further in.3 m increments until no effective discharge peak could be identified or until the bin sizes were greater than a 1 m stage interval. For each stage interval where there was a distinct estimate of the effective discharge, the value was recorded. The mean and range of all the estimates for a gage were then obtained for Work 1 and Work 4 (table 3). DISCHARGE VERSUS RECURRENCE INTERVAL RELATIONSHIPS Common statistical techniques used for predicting the recurrence interval of channel-forming discharges based on an annual peak series apply to occurrence intervals greater than one year and are best suited for extreme flow events. To better ascertain the frequency of bankfull and effective discharge events, we investigated three different frequency methods: (1) annual series log-pearson type III frequency analysis, (2) annual peak series simple log regression analysis, and (3) time duration analysis. Discharge recurrence intervals using method 1 (annual series log-pearson type III frequency analysis) were determined by using the NRCS Log-Pearson Frequency Analysis Spreadsheet, Version 2. (Yochum, 23). The NRCS spreadsheet was developed to compute and plot recurrence intervals based on the log-pearson type III distribution, as outlined in Bulletin 17B from the U.S. Water Resources Council (Rallison, 1982). Variance, standard deviation, and skewness of the annual peak discharge data were determined and used with statistical K-values to produce discharge estimates for specific return periods. Use of the K-values from Bulletin 17B is equivalent to a one-sided t-value that predicts outliers at the 1% level of significance. The K-values are based on a normal distribution for detection of single outliers. The K-value is multiplied by the standard deviation and is added or subtracted to the mean to predict a high or low outlier threshold. Method 1 is consistent with most recurrence interval approaches reported in the literature. Results from method 1 for each gage were fitted with a log regression equation to provide estimates of recurrence intervals. Method 2 (annual peak series simple log regression analysis) eliminates the use of the log-pearson type III statistical K-values. Annual peak discharge data were sorted, ranked, and plotted using the Weibull method (Ward and Trimble, 24). The data typically yield a linear relationship for the less frequent (RI > 2 years) values and produce an elbow tailing down towards zero for the more frequent events (RI < 2 years). As in method 1, a log regression equation was fitted to the data to best represent the discharge 4 TRANSACTIONS OF THE ASABE

7 Table 2. Bankfull discharge (cms) results. Bankfull Discharge Gage Value Range Stage 2 (a) 59 cms Work 1: Median discharge of.6 m stage increment North Fork [a] Loramie Portage Stillwater Upper Great Miami Grand [a] Sandusky Scioto Maumee Muskingum [a] USGS measured bankfull. Sediment (Mg/year) Work 4 and recurrence intervals. The regression equation was used to estimate discharge recurrence intervals for bankfull and effective discharge flows. Method 3 (time duration analysis) utilizes the USGS daily discharge data collected at each study site. Daily discharges were sorted in descending order and then ranked and divided by the total number of days to yield a percentage of time that the specific flow was met or exceeded (Emmett, 1975). The duration was plotted against the ratio of daily discharge and divided by either the bankfull discharge or the effective discharge. A discharge ratio of one identifies the flow that corresponds to the channel-forming discharge. The flow duration value that corresponds to the discharge ratio of one estimates the percentage of time that flow is met or exceeded (fig. 9). ANALYSIS At each gage site, methods 1 and 2 were used to estimate flows for the.6,.8, 1., 1.5, and 2 year recurrence interval discharges. The discharge versus recurrence interval relationship was used to determine the recurrence intervals of the effective discharge and bankfull discharge. Method 3 was used to calculate the number of days annually that the channel-forming discharge was equaled or exceeded. The bankfull discharge results were compared to the effective discharge results. To provide further insight into bankfull and effective discharges and to facilitate comparison of these results with results reported in the literature, we calculated sediment transport discharge thresholds at each gage. The breakpoints used in the sediment function (fig. 4) were adjusted to determine the specific discharges that transported 1%, 25%, 5%, 75%, and 9% of the total sediment load. These Table 3. Effective discharge (cms) results. Work 1 Work 4 Gage Mean Range Mean Range North Fork Loramie Portage Stillwater Upper Great Miami Grand Sandusky Scioto Maumee Muskingum Sediment (Mg/year) Sediment (Mg/year) cms (b) 77 cms 82 cms Work 1: Median discharge of.37 m stage increment Work (c) 57 cms 1 cms Work 1: Median sischarge of 1. m stage increment Work Figure 6. Maumee River effective discharge results for various stage increments. Vol. 49(1):

8 Sediment (Mg/year) Sediment (Mg/year) Sediment (Mg/year) (a) 14 cms 65 cms (b) 9 cms 8 cms Work 1: Median discharge of.6 m stage increments Work 4 Work 1: Median discharge of.37 m stage increments Work (c) 6 cms Work 1: Median discharge of 1. m stage increments Work Figure 7. Upper Great Miami River effective discharge results for various stage increments. discharges were then compared to the bankfull and effective discharges. RESULTS OBJECTIVE 1 A summary of the bankfull discharge results for our study sites are presented in table 2. Discharge results less than 1 cms were rounded to the nearest 5 cms, and results greater than 1 cms were limited to two significant figures. Calculation of the bankfull discharge is dependent on the variability in the fluvial features at each gage; for our study, this variability ranged from a few tenths of a meter to almost one meter (table 2). The Sandusky River gage had the most variable and poorly defined bankfull features, while the Portage River had a broad and active floodplain. The North Fork and the Grand bankfull stage measurements were provided by the USGS and did not include information on the variability of the stage measurements. Results of the effective discharge calculation for each study site were dependent on the quality and quantity of the data. The results in table 3, figure 6 (Maumee River), and figure 7 (Upper Great Miami River) demonstrate that the channel-forming discharge for each site may be a range of values. Each figure displays Work 1 and Work 4 for the three stage intervals that were examined to generate the effective discharge range. The geomorphic work model of the Maumee River (figs. 6a to 6c) shows distinct effective discharge estimates across the entire range of bin sizes. However, at the tails of the geomorphic work curve (stage increments of.6 and 1. m in figs. 6a and 6c), there was poor agreement between the estimates for the two geomorphic work approaches. The Upper Great Miami River (figs. 7a and 7c) demonstrated scatter in the Work 1 estimate for the stage increment of.6 m, and no estimate for the stage increment of 1. m. Close agreement between the Work 1 and Work 4 results for each gage suggest that discharge relationships may have changed little over the entire recording period. Ratios of the effective discharge, divided by the bankfull discharge, are presented in table 4. The averages of the effective to bankfull discharge ratios for both Work 1 and Work 4 are 1.. The North Fork and the Grand sites had the largest deviation from the average, with ratio values of 2.5 and.4, respectively. Due to the similarity between the values calculated for Work 1 and Work 4 (tables 3 and 4), all remaining results are presented for Work 1 only. Table 4. Ratios of effective discharge results (Work 1 and Work 4) divided by bankfull discharge. Effective/Bankfull Ratio Work 1 Work 4 Gage Mean Range Mean Range North Fork Loramie Portage Stillwater Upper Great Miami Grand Sandusky Scioto Maumee Muskingum TRANSACTIONS OF THE ASABE

9 Gage Regression Method R 2 Table 5. Results of annual peak series recurrence interval discharge method: fit and discharge estimates for the study sites..6-year RI.8-year RI 1-year RI 1.5-year RI 2-year RI 5-year RI North Fork 1 (log-pearson type III) (simple log regression) Loramie 1 (log-pearson type III) (simple log regression) Portage 1 (log-pearson type III) (simple log regression) Stillwater 1 (log-pearson type III) (simple log regression) Upper Great Miami 1 (log-pearson type III) (simple log regression) Grand 1 (log-pearson type III) (simple log regression) Sandusky 1 (log-pearson type III) (simple log regression) Scioto 1 (log-pearson type III) (simple log regression) Maumee 1 (log-pearson type III) (simple log regression) Muskingum 1 (log-pearson type III) (simple log regression) OBJECTIVE 2 The recurrence interval results for method 1 (log-pearson type III) and method 2 (simple log regression) are summarized in table 5. Regression lines relating discharge to recurrence interval are highly correlated for both methods (R 2 =.75 to.99), but do not predict identical results. Regression methods that were fitted to an annual series to estimate recurrence intervals of less than one year sometimes generated negative discharges. These negative values are reported as zero in table 5. Method 2 (fig. 8) produced conservative (higher) recurrence interval values for frequent flows because the annual peak series simple log regression is heavily influenced by abundant discharge values with recurrence intervals of less than a few years. Recurrence intervals based on the log-pearson type III results were lower (more frequent) than the simple log regression results that are reported. Effective discharge and bankfull discharge recurrence interval estimates for all the gages are presented in table 6. The annual number of days that flows equaled or exceeded the bankfull or effective discharge is also reported in table 6. The duration of daily discharges that equaled or exceeded the channel-forming discharge ranged from 1 to 24 days annually, with mean values of about 11 and 9 days annually for the effective and bankfull discharge, respectively. Figure 9 illustrates the plotted duration for the Maumee River (fig. 9a) and the Grand River (fig. 9b). The Maumee River had close agreement between the two channel-forming discharges, while the Grand River showed the poorest correlation between the bankfull and effective discharge durations. The relative discharges associated with sediment transport thresholds (1%, 25%, 5%, 75%, or 9%) are presented in table 7. Each discharge associated with a sediment 1 Mean Daily 1 Partial Duration Series Log Regression R 2 =.98 Annual Peak Series Log Pearson III Regression R 2 =.97 Annual Peak Series Simple Log Regression R 2 =.92 Bankfull Discharge = 84 cms Effective Discharge = 76 cms Recurrence Interval (years) Figure 8. Maumee River recurrence interval analysis comparing three common approaches for solving recurrence interval. Maumee River bankfull and effective discharges are represented by horizontal lines. Vol. 49(1):

10 Table 6. Frequency results of channel-forming discharges. Bankfull Discharge RI Gage (years) % Duration Effective Discharge days/ RI year (years) % Duration days/ year North Fork Loramie Portage Stillwater Upper Great Miami Grand Sandusky Scioto Maumee Muskingum Table 7. Discharge ratios (discharge divided by the bankfull discharge) associated with certain sediment transport percentages. A ratio of 1. indicates that the discharge associated with a certain sediment transport percentage is equal to the bankfull discharge. Total Sediment Load Gage 1% 25% 5% 75% 9% North Fork Loramie Portage Stillwater Upper Great Miami Grand Sandusky Scioto Maumee Muskingum Ratio of Discharge to Bankfull/Effective Discharge (a) Bankfull Discharge Effective Discharge Ratio of Discharge to Bankfull/Effective Discharge (b) Bankfull Discharge Effective Discharge.1.1% 1.% 1.% 1.% Duration, in Percentage of Time.1.1% 1.% 1.% 1.% Duration, in Percentage of Time Figure 9. Ratio of daily discharge to channel-forming discharge plotted against duration in percentage of time for: (a) Maumee River, and (b) Grand River. transport threshold was divided by the bankfull discharge to obtain a relative discharge ratio. The results show that about 5% of the sediment load is transported by discharges ranging on average from.3 to 2.6 times the bankfull discharge (the 25% to 75% sediment load range in table 7). For all rivers studied, flows that were less than the mean annual discharge transported less than 1% of the sediment load. DISCUSSION Our results showed good agreement (average ratio of 1.) between bankfull and effective discharge. Directly comparing geomorphic results between our study and published studies is difficult because of differences in methodology and site characteristics. Despite these differences, our results appear consistent with other cited studies that discuss the relationship between bankfull and effective discharge (Andrews, 198; Leopold, 1994; Andrews and Nankervis, 1995; Whiting et al., 1999; Emmett and Wolman, 21). Effective discharges are commonly used in engineering design to maintain similar sediment transport in natural and engineered systems. Determining the effective discharge can be difficult without detailed sediment and discharge data; insufficient data require making calculated estimates of sediment transport. By equating bankfull and effective discharge, measurements of fluvial formed features within a channel system, and subsequent bankfull discharge calculations, can be used to approximate the effective discharge. The results suggest that measured bankfull features are likely the result of sediment carried by the effective discharge. The effective discharge range was dependent on the bin size increment and the placement of the breakpoints selected to develop the discharge and sediment transport function. Once the breakpoints were selected, the functional work relationship (Work 4) was less sensitive to changes of the effective discharge peak when bin sizing was changed than was the measured work relationship (Work 1). Effective discharges Work 4 and Work 1 resulted in similar estimates for the discharge range that carries the most sediment over time. These effective discharge approaches used different discharge data sets with the measured sediment data. Work 4 utilized a more extensive and continuous discharge record, but it did not significantly alter the effective discharge estimate. This evidence suggests that the effective 44 TRANSACTIONS OF THE ASABE

11 discharge has not significantly changed over the daily discharge time span despite the changes in land use. The stability of the effective discharge could be attributed to the high watershed percentage of agricultural land use; increased sediment loads and discharge events from urbanization occur on a small percentage of the studied watersheds. Unlike previous studies that cite recurrence intervals ranging between 1 and 2 years, many of the rivers in our study had channel-forming discharges that occurred more frequently than a 1-year return period. Shields et al. (23) recommend that channel-forming discharges with a recurrence interval less than one year or greater than three years be questioned. Our bankfull and effective discharge frequency results are contrary to their recommendations. This is significant because simply applying recurrence intervals of 1.5 to 2 years to many streams in Ohio, and other locations in the Midwest region of the U.S., can result in designing oversized, incised channels. When possible, geomorphic measurements for design applications should be obtained at the location of interest and on channel systems that are in equilibrium (Ward and Trimble, 24). A weight of evidence, or diagnostic, approach should then be used to determine the design parameters of interest (Montgomery and MacDonald, 22). These parameters should then be evaluated. The spreadsheet tool used in this study (Mecklenburg and Ward, 24) was useful for determining the effective discharge and a variety of other geomorphic data. The recurrence interval (annual peak series using simple log regression, or log-pearson type III regression) is often used to provide more detail on how often specific discharge events occur (Leopold et al., 1964; Andrews, 198; Petit and Pauquet, 1997; Whiting et al., 1999; Emmett and Wolman, 21; Simon et al., 24). However, many studies report difficulty in relating the recurrence interval, based on an annual series, to the actual frequency of these discharges (Andrews, 198; Simon et al., 24). Based on the simple log regression of the annual peak series, the bankfull and effective discharges of our study rivers had a recurrence interval range of.3 to 1.4 years. Using the conventional annual series regression analysis (method 2) approach has two drawbacks: first, the annual series cannot be used to determine recurrence intervals that are less than one year without fitting a regression equation to the data; second, an annual series of peak flows does not take into account that a number of channel-forming discharges may occur annually. Calculating the flow duration in percentage of time provides more detail concerning the actual average percentage that a specific flow is reached or exceeded, and this appears to be a useful approach for reporting the frequency of channelforming discharges. The duration results for the channelforming discharge when these flows were equaled or exceeded were 1 to 24 days annually. A regression analysis was performed to determine whether the durations and recurrence intervals in table 7 were related statistically. Using an exponential function, we calculated three separate R 2 values: (1) an average of all sites of the bankfull discharge recurrence interval versus the duration (R 2 =.7), (2) an average of all sites of the effective discharge recurrence interval versus the duration (R 2 =.49), and (3) an average of all sites of the channel-forming discharge recurrence interval versus the duration (R 2 =.59). The lower relationship (R 2 =.49) for the effective discharge results may be the consequence of a lack of recent sediment data at the gage sites and the mathematical manipulations that estimate effective discharge. Several additional approaches were considered for analyzing frequency. The partial duration series of daily discharge was initially examined as a method to provide a more accurate representation of the recurrence interval than the annual peak series. Figure 8 compares the annual peak series to the partial duration series. Although the partial duration series results were an order of magnitude lower than the more conservative annual peak series results, the annual peak series values were reported to provide the highest comparability with other published studies. In a recent study of low-gradient rivers in Illinois, Crowder and Knapp (25) discussed watersheds that have similar land uses and slope characteristics to our Ohio study sites. Crowder and Knapp reported that the effective discharge was often similar to or less than the mean annual discharge. The mean annual discharge is the average flow over the entire year, and it usually results in a low flow value in Midwest watersheds. These effective discharge results compiled by Crowder and Knapp contradict the foundation of the Wolman-Miller model, which identifies low flows as flows that are ineffective at transporting sediment and building banks. Crowder and Knapp also reported that the effective discharge was exceeded 6 to 194 days annually. Although this is a much larger range than we found for most of our study sites, in an analysis on the St. Joseph River near Newville, Indiana (fig. 2), we found that bankfull discharge occurred on an average of 4 to 8 days annually (Ward et al., 24). We concur with the finding of Crowder and Knapp that the recurrence interval of the effective discharge is more frequent than commonly cited in the literature, often less one year. Our study indicates that the recurrence interval of channel-forming discharges is.3 to 1.4 years. In addition, we have made measurements and calculations at several other secondary locations in Ohio that validate our results. In small channelized headwater systems, we have found that the recurrence interval of bankfull discharges is very small, often a fraction of a year (Ward et al., 24; Jayakaran et al., 25). The Cuyahoga River at Independence is located southwest of the Grand River (fig. 2) and has similar characteristics to the Grand River. The effective discharge had a recurrence interval of.4 years and an annual flow duration of 17 days. The bankfull discharge at Paint Creek at Greenville (fig. 2) was associated with a 1-year recurrence interval and 8 days duration. All USGS gage locations in Ohio, where there were at least 3 years of sediment data, were analyzed to determine the frequency of the calculated effective discharge. These effective discharge estimates (not shown) all fell within the frequency range of our results and confirm that effective discharges occur more frequently in the Midwest than previously reported. CONCLUSIONS AND RECOMMENDATIONS For the ten rivers studied, we found good agreement between the effective discharge and bankfull discharge, with an average ratio of 1. between these channel-forming discharges. The bankfull and effective discharges were primarily related to the transport of the middle 5% of the total sediment load. The recurrence interval of the channelforming discharge ranged from.3 to 1.4 years, as deter- Vol. 49(1):

12 mined by an annual peaks series simple log regression. However, obtaining reliable estimates of recurrence intervals that are less than one year are questionable if the analysis is based on annual peaks series data. The duration results for channel-forming discharge range from.4% to 6.6% and are equivalent to 1 to 24 days per year. The duration results provide a clear representation of discharge frequency compared to the more ambiguous recurrence interval values. We recommend using duration in percentage of time when reporting frequent discharge occurrences. Our study supports a number of previous studies that demonstrate that the effective discharge and bankfull discharge are similar. Unlike many previous studies, however, our results suggest that channel-forming discharges in Ohio occur more frequently than is commonly recognized and used in design. Bankfull and effective discharges cannot be calculated by using a generic recurrence interval or sediment transport percentage. We recommend using a weight of evidence, or diagnostic, approach for determining a design discharge. REFERENCES Andrews, E. D Effective and bankfull discharges of streams in the Yampa River basin, Colorado and Wyoming. J. Hydrology 46(3-4): Andrews, E. D., and J. M. Nankervis Effective discharge and the design of channel maintenance flows for gravel-bed rivers. Natural and anthropogenic influences in fluvial geomorphology. Geophysical Monograph 89: Washington, D.C.: American Geophysical Union. Biedenharn, D. S., R. R. Copeland, C. R. Thorne, P. J. Soar, R. D. Hey, and C. C. Watson. 2. Effective Discharge Calculation: A Practical Guide. ERDC/CHL TR--15. Vicksburg, Miss.: U.S. Army Corps of Engineers, Coastal and Hydraulics Laboratory. Crowder, D. W., and H. V. Knapp. 25. Effective discharge recurrence intervals of Illinois streams. Geomorphology 64(3-4): Emmett, W. W The channels and waters of the Upper Salmon River area Idaho. USGS Professional Paper 87-A. Denver, Colo.: USGS Federal Center. Emmett, W. W., and M. G. Wolman. 21. Effective discharge and gravel-bed rivers. Earth Surface Processes and Landforms 26(13): Jayakaran, A., D. Mecklenburg, A. Ward, and L. Brown. 25. The formation of fluvial benches in headwater channels in the midwestern region of the USA. International J. Agric. Eng. 14(4): (in press). Johnson, P. A., and T. M. Heil Uncertainty in estimating bankfull conditions. Water Resources Bulletin 32(6): Jurmu, M. C., and R. Andrle Morphology of a wetland stream. Environmental Mgmt. 21(6): Kuhnle, R., S. A. Simon, and R. Binger Dominant discharge of the incised channels of Goodwin Creek. In Proc. ASCE Water Resources Engineering Conference. Reston, Va.: ASCE. Landwehr, K., and B. L. Rhoads. 23. Depositional response of a headwater stream to channelization, east central Illinois, USA. River Res. and Applications 19(1): Leopold, L. B A View of the River. Cambridge, Mass: Harvard University Press. Leopold, L. B., M. G. Wolman, and J. P. Miller Fluvial Processes in Geomorphology. San Francisco, Cal.: W. H. Freeman. Mecklenburg, D., and A. Ward. 24. STREAM modules: Spreadsheet tools for river evaluation, assessment, and monitoring. In Proc. ASAE Specialty Conference Self-Sustaining Solutions For Streams, Watersheds, and Wetlands, St. Joseph, Mich.: ASAE. Montgomery, D. R., and L. H. MacDonald. 22. Diagnostic approach to stream channel assessment and monitoring. JAWRA 38(1): Nash, D. B Effective sediment-transporting discharge from magnitude frequency analysis. J. Geology 12(1): Nolan, K. M., T. E. Lisle, and H. M. Kelsey Bankfull discharge and sediment transport in northwestern California. In Proc. International Symposium: Erosion and Sedimentation in the Pacific Rim, IAHS Publication 165. Wallingford, U.K.: International Association of Hydrological Sciences. Orndorff, R. L., and P. J. Whiting Computing effective discharge with S-Plus. Computers and Geosciences 25(5): Palmer, M. A., E. S. Bernhrdt, J. D. Allan, P. S. Lake, G. Alexander, S. Brooks, J. Carr, S. Clayton, C. N. Dahm, J. Follstad Shah, D. L. Galat, S. G. Loss, P. Goodwin, D. D. Hart, B. Hassett, R. Jenkinson, G. M. Kondolf, R. Lave, J. L. Meyer, T. K. O Donnell, L. Pagano, and E. Sudduth. 25. Standards for ecologically successful river restoration. J. Applied Ecology 42(2): Petit, F., and A. Pauquet Bankfull discharge recurrence interval in gravel-bed rivers. Earth Surface Processes and Landforms 22(7): Rallison, R. E Guidelines for determining flood flow frequency. Bulletin 17B of the Hydrology Subcommittee. Reston, Va.: Department of the Interior, U.S. Interagency Advisory Committee on Water Data. Rosgen, D A classification of natural rivers. Catena 22(3): Shields, F. D., R. R. Copeland, P. C. Klingeman, M. W. Doyle, and A. Simon. 23. Design for stream restoration. J. Hydraulic Eng. 129(8): Sichingabula, H. M Magnitude-frequency characteristics of effective discharge for suspended sediment transport, Fraser River, British Columbia, Canada. Hydrological Processes 13(9): Simon A, W. Dickerson, and A. Heins. 24. Suspended-sediment transport rates at the 1.5-year recurrence interval for ecoregions of the United States: Transport conditions at the bankfull and effective discharge? Geomorphology 58: Ward, A. D., and D. E. Mecklenburg. 25. Design discharge procedures in the STREAM spreadsheet tools. In Proc. World Water and Environmental Resources Congress: Impacts of Global Climate Change. Reston, Va.: ASCE Environmental and Water Resources Institute. Ward, A. D., and S. W. Trimble. 24. Environmental Hydrology. 2nd ed. Boca Raton, Fla.: Lewis Publishers. Ward, A. D., D. Mecklenburg, G. E. Powell, L. C. Brown, and A. C. Jayakaran. 24. Designing two-stage agricultural drainage ditches. In Proc. 8th International Drainage Symposium, St. Joseph, Mich.: ASAE. Whiting, P. J., J. F. Stamm, D. B. Moog, and R. L. Orndorff Sediment-transporting flows in headwater streams. GSA Bulletin 111(3): Wolman, M. G., and J. P. Miller Magnitude and frequency of forces in geomorphic processes. J. Geology 68(1): Yochum, S. 23. NRCS log-pearson frequency analysis spreadsheet, Version 2.. Available from the author: steven.yochum@co.usda.gov. 46 TRANSACTIONS OF THE ASABE