Graphical Calculation of First-Flush Flow Rates for Storm-Water Quality Control

Transcription

1 Graphical Calculation of First-Flush Flow Rates for Storm-Water Quality Control David C. Froehlich, Ph.D., P.E., D.WRE, M.ASCE 1 Abstract: Regulations for mitigating nonpoint source pollution from small catchments often include requirements for treating a first-flush depth of runoff, either by storing the storm water until it can be treated and released, or by passing it through a filtering device. In either case, the structural measure used to improve water quality needs to be designed or selected to accommodate a flow rate that corresponds to the first-flush runoff depth. An uncomplicated graphical procedure for calculating first-flush design flow rates is presented that is based on standard National Resource Conservation Service rainfall runoff computation methods in which excess precipitation obtained by applying the runoff curve-number approach to 24-h design storm storms is transformed to runoff using triangular unit hydrographs. The solution is made dimensionless by grouping parameters, and, as a result, can be condensed into a single graph tharovides highly accurate flow rate estimates. DOI: / ASCE :1 68 CE Database subject headings: Computation; Flow rates; Stormwater management; Water quality; Quality control. Introduction 1 Consulting Engineer, 303 Frenchmans Bluff Dr., Cary, NC dcfroehlich@aol.com Note. Discussion open until July 1, Separate discussions must be submitted for individual papers. The manuscript for this paper was submitted for review and possible publication on September 9, 2007; approved on June 24, This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 135, No. 1, February 1, ASCE, ISSN /2009/ /$ In early stages of storm runoff from small catchments, pollutants that have accumulated on land surfaces since the previous rainfall, particularly on impervious areas such as roofs and pavements, can be washed quickly into nearby receiving waters. Because storm-water flows typically rise more quickly than they fall, and because pollutant concentrations have been shown to rise and fall faster than the flow in which they are transported, comparatively large concentrations of contaminants often occur at the onset of runoff Vanderborght and Wollast 1990; Spangberg and Niemczynowicz Known as the first flush, or first foul flush, large pollutant loads from initial wash-off have been confirmed by experimental studies, particularly in catchments where large expanses of land are covered by impervious surfaces and drainage is carried off by underground conduits Barrett et al Unlike contaminants from industrial and sewage treatment plants, pollutants in storm runoff have many nonspecific, or nonpoint, sources, both human-made, and naturally occurring Hager For this reason, regulations intended to mitigate nonpoint source pollution from developing areas or highways often include requirements for storing an initial volume of runoff until contaminants can be removed, or until the stored water infiltrates into soils Atlanta Regional Commission 2001; California Department of Transportation 2007; Division of Water Quality 2007; Urban Drainage and Flood Control District However, regulatory requirements for storm-water control vary throughout the United States. For example, the State of South Carolina South Carolina Code of Regulations 2005 requires that water quality ponds having a permanenool store temporarily the first 1/2 in. of runoff from storms having a 10-year average recurrence interval, releasing it over at least a 24-h period. Additionally, when permanent pools are noart of a design, the first full inch of runoff from the drainage area needs to be treated to remove pollutants. Further, the regulations require that National Resource Conservation Service NRCS rainfall runoff calculation procedures be used to design storm-water quality control structures. If the initial or first-flush runoff is held in a storage area not connected directly to the main drainage channel that is, if runoff is held in an off-stream storage area, a control device needs to be built that will divert stream flows into the holding area until the desired volume is captured Kuo and Zhu 1989; Guo Pollutants, mostly floating debris and suspended solids, can also be removed from the initial runoff volume by passing the flows through a filtering device of some kind. In either case i.e., either off-stream storage or pass-through treatment, the structural measure provided for water quality control needs to be designed or selected to accommodate a specific runoff flow rate. Diversion structures or pass-through treatment devices are normally sized based on calculated hydrographs in which flow rates increase until the peak rate of runoff is reached, after which the runoff rates decrease Lenhart 2004; Ogintz If the firstflush runoff volume is filled before the peak rate is reached, then the volume will correspond to a unique flow rate that can be used to design control structures. On the other hand, if the maximum runoff rate occurs before the first-flush volume is filled, diversions or filtering devices need to be sized based on the peak discharge from the catchment. Ahlfeld and Minihane 2004 develop a probabilistic method to find first-flush design discharges in which the rational method is used to relate flow and precipitation intensity. However, most often a straightforward approach is taken by summing the accumulated runoff obtained from a computed hydrograph to establish the time and the discharge at which the required runoff volume is reached Adams Although the calculations can be made easily for a specific catchment using well-written computer codes, an even less complicated graphical procedure is presented here 68 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009

2 for determining first-flush flow rates. The approach is based on conventional NRCS hydrologic calculations in which excess precipitation obtained by applying the runoff curve-number method to standard 24-h design storm rainfall is transformed to runoff by means of triangular unit hydrographs. The procedure is carried out using dimensionless parameters that reduce the number of variables involved in the computation. Consequently, the entire series of calculations can be condensed into a single graph that applies to any small catchment within a geographical region having similar rainfall-frequency characteristics. First-Flush Effect The initial cleansing or flush of contaminants from urban catchments was recognized at the beginning of the 20th Century by Metcalf and Eddy 1914, p. 204 who describe the process as follows: There is a general impression that it is wise to provide in intercepting sewers for a small quantity of storm water, expressed often as being sufficient for the first flushings of street surfaces and sewers. This impression is based upon the assumption that there are accumulations of sewage sludge in the sewers and quantities of filth on the streets which will be immediately flushed into the intercepting sewers with the first runoff due to rain. Recent investigations find that first-flush effects can vary considerably depending on catchment conditions and constituent characteristics. For example, from a study of nine watersheds in Korea, Lee and Bang 2000 conclude thaeak pollutant concentrations preceded peak flow rates where drainage areas were less than 100 ha 250 ac and impervious percentages were more than 80%, and that combined sewer systems enhance the first-flush effect. On the other hand, Hudak and Banks 2006 find that for mosollutants from four small, mixed land use watersheds in north-central Texas, the composite concentrations exceeded the first-flush concentrations, although differences were significant only for fecal coliforms. Lack of high initial concentrations of some constituents may be due to their low solubility, as noted by Hvitved-Jacobsen and Yousef In general, however, studies show that contaminant concentrations, most notably particulate matter, are indeed greater during initial storm runoff periods Chang et al Taebi and Droste 2004 find that a weak first flush exists for total solids, total suspended solids TSS, and chemical oxygen demand COD in runoff collected from a mixed residential and commercial urban catchment in a semi arid region of Iran. From storm-water runoff collected at three highway sites in Los Angeles, Han et al. 2006a, b find thaollutant concentrations in early runoff were from 1.9 to 7.4 times higher than the mean concentrations. Strong first flush was observed for COD and other organic pollutants, with 40% of the pollutant mass being discharged in the first 20% of the runoff volume, whereas weak first flush was observed for ionic pollutants, such as nitrate and nitrite. Irish and others 1996 find that most of the constituents in highway runoff are attached to fine-grained sediments that tend to accumulate within one meter of roadway curbs during dry periods, and, as a result, are easily washed into sewers at the start of a storm. Use of retention/detention basins to capture first-flush pollutants has been effective in most cases, particularly for solids England A study of urban runoff in Sydney, Australia by Birch et al. 2006, for example, shows that retention/detention basins successfully remove significant amounts of TSS, Kjeldahl nitrogen, and total nitrogen, but that mean removal efficiencies are low for fecal coliform, and are negative for total nitrous oxide and total phosphorus. The amount of contaminants in total annual runoff that are removed by treating the first flush varies depending on the effectiveness of the treatmenractice and on the rainfall characteristics of the geographical region. Because comparatively small, frequently occurring storms account for the majority of rainfall events that generate storm-water runoff, the same storms also account for the largesortion of annual pollutant loadings. For this reason, by processing all runoff from frequently occurring small storms, along with a portion of the runoff from larger events, it is possible to reduce substantially harmful water quality impacts Guo and Urbonas 1996, The quantity of initial runoff that needs to be treated, often called the water quality volume, is usually defined as a depth of rainfall excess draining from the catchment area, and is denoted here by Q f. Regulations either specify Q f directly or require that Q f equal the total runoff from a storm having a specified rainfall depth. In humid areas of the United States, approximately 90% of the average annual runoff will be treated when water quality volumes equal the runoff produced by rainfall of about 25 mm 1 in.. Smaller water quality volumes are needed in regions that are more arid to obtain the same degree of pollutant removal. From a study of storm runoff in Austin, Texas, Chang et al find that a 25 mm water-quality treatment depth will exceed the goal of 90% annual runoff treatment goal in undeveloped watersheds, but will fall short of the desired level in highly impervious catchments. Calculations needed to evaluate Q f and to design or size water quality control structures are usually based on specified water quality design storms. Regulations sometimes require that the storms and the hydrologic procedures used to transform excess rainfall into runoff be chosen from standard methods, frequently those developed by the NRCS. Uncomplicated graphical methods for determining peak rates of runoff and water quality control structure design flows using these procedures are now described. NRCS Rainfall Runoff Relations Catchmeneak flow rates are affected significantly by the duration of design storms and the distribution of rainfall within them. Design of storm-water runoff controls is based widely on storms having durations of either 24-h or the time of concentration i.e., the time needed for runoff to flow from the hydraulically most remote point in a catchment to the outlet. Seeking a rational basis for using either of the two durations, Levy and McCuen 1999 show that for a humid climate in the eastern United States the storm duration producing the annual maximum discharge is slightly longer than 24 h, even for watershed areas as small as 5km 2 2mi 2, and that the duration increases only slightly with watershed area. They also find that the most appropriate design storms have peak rainfall intensities positioned near their centers, a conclusion also drawn by Packman and Kidd 1980 based on the analysis of rainfall-runoff data from the United Kingdom. For these reasons, hydrologic computations are carried here out using standard rainfall distributions having durations of 24 h developed by the NRCS formerly known as the Soil Conservation Service or SCS, along with other NRCS rainfall-runoff calculation techniques SCS JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009 / 69

3 Fig. 2. Schematic diagram of NRCS rainfall-runoff relation between rainfall depth P, total runoff depth Q, initial abstraction I a, and actual rainfall retention F Q = P I a 2 P I a + S 1 Fig. 1. Cumulative normalized rainfall for standard NRCS 24-h design storms Rainfall Distributions Standard rainfall patterns for storms of 24-h duration called Types 1, 1A, 2, and 3 storms have been prepared by the NRCS for four different geographic regions of the United States. The synthetic design storms are based on National Weather Service rainfall maps SCS 1983, 1986; Chow et al. 1988, pp ; McCuen 1989, pp ; Ponce 1989, pp , and are presented as ratios of cumulative rainfall depth to total rainfall depth as functions of time. The rainfall patterns are intended for use in catchments with areas of 250 km mi 2 or less, and they are considered applicable to storms of any average recurrence interval. NRCS Type 1 24-h storms are characteristic of the Pacific coast maritime climate with wet winters and dry summers common in southern California, Alaska, and Hawaii. Type 1A storms are representative of low-intensity rainfall associated with frontal storms west of the Cascade and Sierra Nevada mountain ranges in northern California, Oregon, and Washington. Type 3 storms characterize coastal areas along the Atlantic and Gulf of Mexico where tropical storms are responsible for large 24-h rainfalls. Type 2 storms typify high intensity thunderstorms and apply elsewhere. Ratios of accumulated rainfall to total rainfall are plotted against time for each of the four NRCS 24-h design storms in Fig. 1. Rainfall Excess The NRCS procedure for estimating rainfall excess accounts for total storm rainfall P by dividing it into three components: direct runoff Q, actual rainfall retention during a storm F, and the initial abstraction I a SCS 1986; McCuen 1989; Ponce 1989; Mishra and Singh The physical unit of each of these quantities is precipitation volume per unit area, or precipitation depth, commonly given as inches in the United States. The conceptual relation between P, Q, F, and I a is shown schematically in Fig. 2, and is given by where S = potential maximum retention. Empirical studies show that initial abstractions are related to retention as I a =k a S, where k a 0.2=dimensionless coefficient. Potential maximum retention is calculated as S = k s 10 1,000 CN 2 where k s =retention depth units conversion factor 1.0 for S in inches, 25.4 for S in millimeters, and CN=runoff curve number=an index ranging from 0 to 100 that represents the combined effect of soil type, land use, and land cover vegetation types, degree of imperviousness, and agricultural treatments. Runoff Hydrographs Unit hydrograph methods are based on the idea introduced by Sherman 1932 that a linear relation exists between excess rainfall and the time distribution of runoff from a catchment. When a unit depth of excess rainfall distributed uniformly across a catchment at a constant rate within a specified time is considered, the resulting time distribution of runoff forms the unit hydrograph that corresponds to that duration of rainfall excess. Linearity of the rainfall runoff relation implies that the outflow from the catchment caused by a storm producing a different amount of excess rainfall is just the unit hydrograph ordinates multiplied by the effective rainfall depth. A dimensionless curvilinear unit hydrograph developed by the NRCS, which is based on a large number of unit hydrographs from basins that varied in size and geographic location, has 3/8 of the total runoff volume in the rising side, and is approximated closely by a triangle Snider 2001; McCuen 1989, pp Consequently, for the triangular approximation, k r =t r / =5/3, where =time-to-peak=time between the beginning of runoff from a short high-intensity storm and the corresponding peak rate of runoff from the catchment, and t r =recession time=time from peak flow rate to the end of direct runoff, as shown in Fig. 3. The ratio k r might vary depending on watershed topography, amount of impervious land cover, and the extent to which natural stream channels have been replaced by storm sewers. However, the following analysis is based on k r =5/3, which is the average value 70 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009

4 +0.6t c =, from which we find that D=2/15t c, and =2/3t c. The dimensionless representation of the NRCS triangular unit hydrograph 3 is then given by q = t q p for t 1 1 k r t 1 for 1 t 1+k r 0 for t 1+k r where t=time since the start of runoff. 4 Dimensionless Runoff Calculations Fig. 3. Dimensionless NRCS triangular unit hydrograph with k r =t r /t c =5/3 found by the NRCS. Peak discharge from a catchment of area A given by the triangular unit hydrograph for an effective rainfall depth Q is then found as q p = k q AQ 2 1+k r 3 where k q =units conversion factor that depends on the units of q p, A, Q, and k q for q p in cubic meters per second and cubic feet per second for various combinations of possible units of A, Q, and is given in Table 1. From evaluation of hydrographs from a large number of watersheds, the optimal rainfall duration of the unit hydrograph D = /5 Kent 2001; McCuen 1989, pp The point of inflection on the recession side of the curvilinear hydrograph is found to be 1.7 times the time-to-peak. With time-of-concentration t c of the catchment taken as the length of time from the end of excess rainfall to the inflection point, and the average lag time i.e., the time from the centroid of excess rainfall to the time-topeak found to be t lag =0.6t c, which gives t c +D=1.7 and D/2 Table 1. Values of the Peak Discharge Units Conversion Factor k q for Various Combinations of Related Parameter Units Units Units of the following parameters conversion q p A Q t c factor k q m 3 /s km 2 mm h km 2 mm min km 2 cm h km 2 cm min ha mm h ha mm min ha cm h ha cm min ft 3 /s mi 2 in. h mi 2 in. min 38,720 ac in. h ac in. min 60.5 Making use of the NRCS rainfall-runoff procedures, which include the 24-h storm distribution, the runoff curve-number method to calculate the rainfall excess, and the triangular unit hydrograph to transform excess rainfall into runoff rates, outflow from a catchment is given by the following functional relation: q = f t,t c,a,s,k a,p 24,t d,storm Type,k r 5 where S=function of CN given by Eq. 2 ; P 24 =24-h rainfall depth; t d =storm duration; and StormType=NRCS standard 24-h design storm type 1, 1A, 2, or 3. By creating a set of dimensionless parameters, the number of variables in Eq. 5 can be reduced, and the task of calculating runoff can be made less complicated. Using appropriate combinations of t c, P 24, and A to normalize the remaining variables, the following dimensionless functional relation results: qt c P 24 A = f t S,,k a, t d,storm Type,k t c P 24 t c r 6 For specified values of k a, k r, and a particular 24-h rainfall distribution, Eq. 6 is reduced to where q * = f t *,S *,t d * q * = qt c P 24 A, t * = t, S t * = S, t d c P * = t d t c Because storm duration t d =24 h is constant in our analysis, t c can replace t d*, which gives q * = f t *,S *,t c Making use of dimensionless NRCS rainfall-runoff procedures, graphical solutions for peak discharge rates q p and flow rates needed to design water quality control structures, called the firstflush flow rate and denoted here as q f, can be developed as functions of the dimensionless independenarameters as will be shown. Normalized Peak Flow Rate If only peak discharge q p is needed to size water quality control structures, as it might be if the first-flush volume equals runoff from a storm having a specified rainfall depth, the time distribution of runoff is not involved and the functional relation for the normalized peak rate of runoff is given by 7 9 JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009 / 71

5 q p * = q pt c P 24 A. 11 Because q p* depends on only two variables, the relation can be graphed easily, thereby providing a rapid and uncomplicated means of finding the peak rate or runoff from small catchments. Graphical solutions for k r =5/3, k a =0.2, and the NRCS Type 2 rainfall distribution created by generating dimensionless runoff hydrographs for various combinations of S * ranging from 0 to 3 by increments of 0.01 and t c 5, 10, 15, 20, 30, 45, and 60 min and plotting q p* as a function of S * for each of the times-ofconcentration are shown in Fig. 4. The curves are based on highly accurate numerical runoff solutions. Accuracy of graphical estimates of q p depend only on the precision of interpolated values. The graph for normalized peak flow rate given in Fig. 4 has been divided into three sections for successive ranges of S *, with the ordinate scale changing in each to provide more accurate estimates of q p* as the t c curves converge. With values of A, t c, CN, and P 24 having been obtained for a catchment, the peak outflow rate q p is found as follows: Step 1. Calculate S=k s 1000/CN 10 ; Step 2. Calculate S * =S/ P 24 ; Step 3. Obtain q p* from Fig. 4 from the appropriate t c curve interpolation between adjacent curves might be needed ; Step 4. Calculate the units conversion factor k q or obtain it from Table 1 based on the units of A, t c, and P 24 and the desired units of q p ; and Step 5. Calculate q p =k q P 24 A/t c q p*. Graphical solutions for q p* similar to the one in Fig. 4 need to be used for other NRCS storm types, and for coefficients k a and k r that differ from the standard values. Normalized First-Flush Flow Rate The functional relation for q f is the same as for q p, except for the addition the specified first-flush runoff depth Q f, and can be written in dimensionless form as q f * = f S *,t c,q f * 12 where Fig. 4. Graphical solution for normalized peak runoff rate q p* as a function of normalized maximum storage depth S * and time-ofconcentration t c for NRCS Type 2 design storms where q p * = f S *,t c 10 q f * = q ft c P 24 A, Qf * = Q f 13 P 24 are the normalized first-flush flow rate and first-flush runoff depth, respectively. Graphical representations of Eq. 12 providing q f* as a function of S * and t c can be prepared for specified values of Q f and P 24. If the peak rate of runoff occurs before the specified first-flush depth Q f is reached, q f is set equal to q p because water quality control structures will need to be designed for the maximum discharge. However, this condition is likely to take place only when the catchment runoff curve number is comparatively small, signifying a highly pervious drainage basin. For example, two regions having homogenous rainfall characteristics have been defined in Greenville County, S.C., where the initial 1 in. of runoff from a 10-year, 24-h NRCS Type 2 design storm needs to be treated South Carolina Code of Regulations The 10-year, 24-h rainfall depth in the northern part of the county is 6.1 in. 155 mm, and in the southern section it is 5.4 in. 137 mm. Graphical relations for q f* in northern Greenville County are shown in Fig. 5 for Q f =1.0 in. 25 mm The ordinate scale for S * ranges from 0 to 0.6 in Fig. 5 because first-flush runoff volumes beyond S* =0.6 are all reached following the discharge peak. A similar graph has been developed for southern Greenville County where the 10-year, 24-h rainfall depth is less. With known values of A, t c, CN, and P 24, the first-flush flow rate q f is found as follows: Step 1. Calculate S=k s 1000/CN 10 ; Step 2. Calculate S * =S/ P 24 ; Step 3. Obtain q f * from Fig. 5 from the appropriate t c curve interpolation between adjacent curves might be needed ; Step. 4 Calculate the units conversion factor k q or obtain it from Table 1 based on the given units of A, t c, and P 24 and the desired units of q f ; and Step 5. Calculate q f =k q P 24 A/t c q f *. 72 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009

6 Fig. 5. Graphical solution for normalized first-flush flow rate q f* as a function of normalized maximum storage depth S * and time-ofconcentration t c for NRCS Type 2 design storms in the northern part of Greenville County where Q f =1.0 in mm and the 10-year P 24 =6.1 in. 155 mm Curves in Fig. 5 have been smoothed slightly. Nonetheless, solutions for q f found from the graph are highly accurate, depending largely on the precision of interpolated values, which will be high enough for design of water quality control structures. Example Application Fig. 7. Runoff hydrograph from the NRCS Type 2 design storm with P 24 = mm that shows the first-flush flow rate q f =16.9 ft 3 /s m 3 /s at time t f =11:54:40, and the peak discharge q p =27.5 ft 3 /s m 3 /s An example is presented for a small catchment in northern Greenville County, S.C. where the first full inch of runoff Q f =1.0 in. =25.4 mm from an NRCS 10-year, 24-h design storm needs to be treated. The watershed has a drainage area A=6 ac 2.43 ha, a time-of-concentration t c =20 min, a runoff curve number CN =85, and a 10-year, 24-h rainfall depth P 24 =6.1 in. 155 mm. The first-flush flow rate q f ft 3 /s is to be found along with the peak discharge from the catchment. Rainfall runoff calculations carried out using the NRCS curve number procedure along with the triangular unit hydrograph provide the cumulative runoff depth for the storm given in Fig. 6, which shows that the specified first-flush depth Q f =1.0 in mm is reached at time t f =11:54:40 hh:mm:ss. Catchment outflow q f =16.9 ft 3 /s m 3 /s at time t f as shown in the runoff hydrograph in Fig. 7, in which the computed peak discharge q p =27.5 ft 3 /s m 3 /s is also noted. Although the calculations were made quickly by computer, q f is found even more simply using the graph provided in Fig. 5 as follows: Step 1. With k s =1.0, the potential maximum retention depth S = k s = = 1.76 in. CN 85 Step 2. S * =S/ P 24 =1.76/6.1=0.289; Step 3. From Fig. 5, q f * =0.153; Step 4. From Table 1, k q =60.5 for the given units of A ac, t c min, and P 24 in., and q p ft 3 /s ; and Step 5. Then q f =k q P 24 A/t c q f * = / =16.9 ft 3 /s. The graphical solution for q f is shown in Fig. 8. Peak discharge from the 10-year storm is found just as easily and with * high accuracy using the graphical solution for q p as shown in Fig. 9. We have used a 10-year average recurrence interval rainfall depth of 6.1 in. 155 mm to develop the graph used in this example because that is the South Carolina regulatory requirement. Fig. 6. Cumulative runoff depth from the NRCS Type 2 design storm with P 24 = mm that shows the specified first-flush runoff depth Q f =1.0 in mm attained at time t f =11:54:40 hh:mm:ss Fig. 8. Graphical solution for q f* JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009 / 73

7 also varies geographically and by average recurrence interval, a specific water-quality treatment runoff depth which, in South Carolina, varies depending on the type of control and also geographically, coastal counties having more stringent requirements, and a specific NRCS triangular hydrograph which depends on the characteristics of a watershed, although nearly always the standard hydrograph is used. Despite the limitations, the same idea presented here can be used with other design rainfalls of fixed duration, not just NRCS 24-h storms, and for other unit hydrographs, not just the standard NRCS triangular hydrograph. Notation Fig. 9. Graphical solution for q p* However, similar graphical relations can be developed for any 24-h rainfall depth, the average recurrence interval of the rainfall amount is not relevant. Consequently, the same idea can be used for other regulatory requirements in other regions of the country. Summary and Conclusions If first-flush runoff is held in a storage area not connected directly to the main drainage channel i.e., if runoff is held in an offstream storage area, a control device needs to be built to divert streamflow until the desired volume is captured. Contaminants, mostly floating debris and suspended solids, may also be removed from the initial runoff by passing the storm water through a treatment device of some kind. In either case, the structural measure provided for water quality control needs to be designed or selected to accommodate a specific flow rate. An uncomplicated graphical procedure for calculating firstflush design flow rates is presented that is based on standard NRCS rainfall runoff computation methods in which excess precipitation obtained by applying the runoff curve-number approached to 24-h design storm storms is transformed to runoff using triangular unit hydrographs. The solution is carried out using dimensionless parameters, which reduces the number of variables involved in the calculations. As a consequence, the entire procedure is condensed into a single graph that gives the discharge q f needed to design or size water quality control structures for a specified first-flush depth Q f, where rainfall frequency characteristics are constant. An example is presented to show how first-flush flow rates can be found for a small catchment where the first full inch of runoff Q f =1.0 in mm from an NRCS 10-year, 24-h design storm is to be treated. Although graphs have to be prepared for each combination of Q f and P 24 that occur, once completed, flow rates needed to design or size water quality control structures can be calculated accurately and without difficulty. The graphical procedure developed here for obtaining firstflush flow rates is limited to comparatively small catchments where storm-water runoff can be estimated accurately by standard NRCS rainfall runoff calculations. However, the main shortcoming of the procedure is that there is no universal graph that can be used for all locations for all types of storms. A particular graph is based on a specific NRCS 24-h duration rainfall pattern which varies by geographic region, a specific 24-h rainfall depth which The following symbols are used in this paper: A catchment area; CN runoff curve number; D unit hydrograph rainfall duration; F actual rainfall retention during a storm volume per unit area or depth ; I a initial abstract depth volume per unit area or depth ; k a I a /S=initial abstraction depth ratio; k q flow rate units conversion factor; k r t r / =ratio of triangular unit hydrograph recession time to time-to-peak; k s retention depth unit conversion factor; P total rainfall or potential maximum runoff volume per unit area or depth ; P h storm rainfall depth; Q direct storm runoff volume per unit area or depth ; Q f water-quality capture volume per unit area or depth ; q flow rate volume per unit time ; q f water-quality capture depth flow rate i.e., the calculated flow rate at which the water-quality capture depth is reached at the catchment outlet volume per unit time ; q p peak runoff flow rate from a catchment; S potential maximum retention at the start of a storm; t c catchment time-of-concentration; t d storm duration; t f time at which first-flush runoff depth is reached; t lag catchment lag time; unit hydrograph time-to-peak; and t r unit hydrograph recession time. Subscripts * normalized or dimensionless parameter. References Adams, T. R Storm water facility design: Calculating the first flush. Pollut. Eng., 30 13, Ahlfeld, D. P., and Minihane, M Storm flow from first-flush precipitation in stormwater design. J. Irrig. Drain. Eng., 130 4, Atlanta Regional Commission Georgia stormwater management manual Vol. 2: Technical handbook, Atlanta. Barrett, M. E., Irish, L. B., Jr., Malina, J. F., Jr., and Charbeneau, R. J Characterization of highway runoff in Austin, Texas area. J. Environ. Eng., 124 2, / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / JANUARY/FEBRUARY 2009

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