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Publication No. 58 LONGTERM PERFORMANCE OF STORMWATER DETENTION FACILITIES: A COMPARISON OF DESIGN METHODOLOGIES by Gay F.E. Goforth University of Florida Gainesville, FL 326112013 LONGTERM PERFORMANCE OF STORMWATER DETENTION FACILITIES: A COMPARISON OF DESIGN METHODOLOGIES By Gary F. E. Goforth PUBLICATION No. 58 FLORIDA WATER RESOURCES RESEARCH CENTER RESEARCH PROJECT TECHNICAL COMPLETION THESIS ENGINEERING AND INDUSTRIAL EXPERIMENT STATION PROJECT NUMBER 80W31 THESIS SUBMITTED JUNE, 1981 The work upon which this thesis is based was supported in part by funds provided by the Water Research Program, Engineering and Industrial Experiment Station, University of Florida, Gainesville ACK.NOWLEDC.Ei 1'7TS Interaction is free; as such, I owe thanks to many individuals at Black Hall and the Center For Wetlands who have contributed to the completion of this thesis and to my career at the University of Florida. The diversity of professionals in the department has provided a constant challenge to maintain an awareness of the many, yet similar, facets of environmental engineering sciences. A large debt is acknowledged to Bob Dickinson who several times pulled me up when I was close to drowning while SWMMing. Thanks also go to Steve Nix for his help on S/T. The use of the computer resources at the Center For Wetlands, Black Hall and the Northeast Regional Data Center was invaluable. Thanks to Anelia Crawford for the drafted figures. The direction of this thesis is credited to Dr. J. P. Heaney; the stability of the content is credited to Dr. W. C. Huber; the influence of Dr. H. T. Odum is reflected in the holistic approach to the problem assessment and solutions. Their guidance and attention are greatly appreciated. Certainly the greatest debt is owed to my wife, Karen. Her patience, sacrifice, programming and typing ability and overall good spirits in the face of adversity will be forever appreciated. TABLE OF CONTENTS ACKNOWLEDGEMENTS . . LIST OF TABLES . . . LIST OF FIGURES . . LIST OF SYMBOLS . . ABSTRACT . . . INTRODUCTION . . . GENERAL OVERVIEW . . SYSTEM DESCRIPTION . DEFINITION OF CONTROL UNIT CLASSIFICATION OF METHODS . CASE STUDY . . . CATCHMENT CHARACTERIZATION . . . ii . . . v ii . . . x . . . .x i i . 1 . 1 . 3 S 6 . 8 RAINFALLRUNOFF CHARACTERIZATION . Rainfall data. . . . SYNOP. . . . . Runoff Quantity. . . BASIN CHARACTERIZATION . . Flow Conditions. . . Removal. . . . . Theory of Settling. . . Comparison of Flow Conditions . 1 1 . 1 1 . 12 . 12 . 13 . 15 . 23 . 23 . 24 . 24 . 29 METHODOLOGIES . . . . . ANALYTICAL. . . . . EMPIRICAL . . . . . SIMULATION. . . . . STORM ... . . . . SWMM . . . . . Overview . . . . Data Input for Runoff Block . . Data Input for Storage/Treatment Block Constant Discharge Simulation . . Variable Discharge Simulation . . Removal Mechanism.. . ... . OneYear versus 25Year Simulation. . Runoff Block Results. . . Storage/Treatment Block Results . iii . 32 . 32 . 33 . 36 . 36 . 36 . 36 . 38 39 . 45 . 46 ... 147 S 50 . 50 . 52 STATISTICAL TECHNIQUES . . . 70 Event Definition . . . 70 Traditional Design of Flood Control Basins 72 Aggregate Statistical Methods. . .. 74 Data Input. . . . .. 75 Capture Performance Results . . 80 Removal . . . . 83 Analysis Using Simulated Data . 84 COMPARISONS . . . . 87 DISCUSSION . . . . . 91 GENERAL APPLICATION OF METHODOLOGIES . . 93 APPENDIX A Program Listing and Data Input . 97 APPENDIX B BASIN Development and Listing . .103 APPENDIX C Detention Time. . . . 105 REFERENCES . . . . . 112 BIOGRAPHICAL SKETCH . . . . .115 LIST OF TABLES Table 1. Case study catchment characteristics. 12 2. SYNOP results of 24.6 years of Atlanta, Georgia rainfall. 16 3. Relationships between pollutant loads and flow volume (FLOW). 35 4. Comparison( of Runoff Block results using hourly, daily and weekly rainfall input. 38 5. SYNOP results of 24.6 years of simulated runoff data. 41 6. Determination of normalized volume ratios (Vb/Vro). 42 7. Calculation of constant discharge rates (Qc) (Ti = 111. 17 hours; Vro = 18022 cubic feet). 46 8. Comparison of mean runoff event parameters for 1953 with the 24.6year record (minimum interevent time = 4.0 hours). 52 9. Runoff Block 24.6year simulation summary. 51 10. Examples of Storage/Treatment Block summaries. 53 11. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: simulation results. 54 12. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of drawdown height and rate (Vb/Vro=1.61): 1953 simulation results. 65 13. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro = 1.61): 1953 simulation results. 66 14. Computer costs of simulations. 15. Determination of normalized volume ratios. 76 16. Estimates of flow capture efficiency (C) as a function of basin volume and constant discharge rate: statistical results. 80 17. Comparison of simulated runoff mean event statistics with rainfall conversion values. 85 18. Estimates of flow capture efficiency, (C) as a function of basin volume and discharge rate: statistical results with simulated runoff means. 86 19. Estimates of hydraulic volume and detention time of various control units associated with a single rainfall event. 94 LIST OF FIGURES Figure 1. Representation of the hydrologic cycle. 4 2. Discretized subsystems of the hydrologic cycle. 5 3. Processes defining the performance of a control unit. 5 4. Schematic of Case Study catchment area. 7 5. Characterization of the various methodologies. 9 6. Comparison of theoretical and observed distributions of interevent times for Minneapolis/St. Paul airport. 14 7. SYNOP values for mean event volume and duration as a function of minimum interevent time. 17 8. SYNOP values for mean event intensity and interevent time as a function of minimum interevent time. 18 9. A comparison of rainfall and runoff time series depicting the reduction in number of events and the reduction in the event volume. 20 10. Definition of interception and storage for storm events. 21 11. Representation of a time series of runoff flows. 22 12. Development of overflow rate in an ideal settling basin. 25 13. Effluent concentrations for a firstorder removal process in n completely mixed plugs. 28 14. Removal efficiency for a firstorder removal process demonstrating the effect of increased vii turbulence; n=l for quiescent and n=1 for completely mixed. 28 15. Effluent responses to a step input. 30 16. Comparison of real and plug flow reactor volumes for a firstorder reaction. 30 17. Stage relationships as calculated by BASIN; constant and variable' discharge. 40 18. Time series of constant influent pollutant concentration. 44 19. Removal equation used in SWMM S/T Block. 48 20. Comparison of effluent concentrations under ideal plug flow, ideal completely mixed and as calculated with SWMM S/T completely mixed routing; step input of pollutant. 49 21. Solution surface of flow capture efficiency (C) as a function of basin volume and constant discharge rate: 1953 simulation results. 55 22. Solution surface of pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: 1953 simulation results. 56 23. Pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: 1953 and 24.6year simul tion results. 57 24. Pollutant removal efficiency (R) as a function of basin volume under variable discharge conditions: 1953 simulation results. 61 25. Solution surface of pollutant removal efficiency (R) as a function of drawdown height and drawdown rate (Vb/Vro = 1.61): 1953 simulation results. 63 26. Pollutant removal efficiency (R) as a function of drawdown height and constant discharge rate (Vb/Vro. = 1.61): 1953 simulation results. 64 27. Solution surface of pollutant removal efficiency (R) as a function of outlet height viii and outlet diameter (Vb/Vro = 1.61): 1953 simulation results. 67 28. Pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro = 1.61): 1953 simulation results. 68 29. Distribution of the largest sample value from a sample of size n from an exponential distribution. 73 30. Normal probability plot of Kentucky River data. 73 31. Relationship of capture efficiency (C) with normalized basin volume, normalized discharge rate and mean volume coefficient of variation. 79 32. Solution surface of flow capture efficiency (C) as a function of basin volume and constant discharge rate: 1953 statistical results. 81 33. Flow capture efficiency as a function of basin volume and constant discharge rate: 1953 statistical results. 82 34. Comparison of flow capture efficiency. 89 35. Comparison of pollutant removal efficiency. 90 B1. Development of BASIN. 104 CI Various control unit configurations: steadystate conditions. 107 C2 Various control unit configurations: nonsteadystate conditions. 110 LIST OF SYMBOLS USED a,b coefficients of runoff quality power equation ai percentage of flow passing through basin i A crosssectional area of flow c effluent concentration C flow volume capture efficiency cO influent concentration Cro runoff conversion factor CV coefficient of variation dr individual rainfall event duration Dr mean rainfall event duration Dro mean runoff event duration e base of natural logarithm H height of settling zone Hd height at which discharge begins and ends hp height of particle entering settling zone k firstorder reaction coefficient I percent of catchment area that is impervious ir individual rainfall event intensity Ir mean rainfall event intensity Iro mean runoff event intensity kO initial firstorder reaction coefficient ki linear flow coeficient of basin i L length of flow element x n N Qc GcTi/Vro R SA S/T t td Ti v V Vb Vb/Vro Ve Vi vo vp Vr Vro Vs xo turbulence coefficient return period for design storm volumetric flow rate constant discharge rate normalized discharge rate pollutant removal efficiency surface area of settling zone storage/treatment elapsed time detention time of system mean interevent time velocity of flow volume of flow element empty volume of basin normalized basin volume effective volume volume of basin i overflow rate (surface loading rate) particle settling velocity mean rainfall event volume (per unit surface area) mean runoff event volume (per unit surface area) volume of settling zone percentage of particles with vp less than vo Abstract of Thesis Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering LONGTERM PERFORMANCE OF STORMWATER DETENTION FACILITIES: A COMPARISON OF DESIGN METHODOLOGIES by Gary F. E. Goforth June 1981 Chairman: James P. Heaney Major Department: Environmental Engineering Sciences A general overview of empirical, analytical, statistical and simulation techniques for evaluating stormwater detention systems is presented. The benefits and limitations of these methods in designing a control device for water quality improvement are emphasized. A detailed analysis compares continuous simulation utilizing the Environmental Protection Agency's Storm Water Management Model with the statistical techniques advanced by Hydroscience, Inc. The general dynamics of storage and flow xii elements are discussed, emphasizing the importance of detention time in defining a time frame for evaluating systems. Chairman x i i i INTRODUCTION GENERAL OVERVIEW In the urban environment, combined and separate storm sewer overflows contribute the same amount of contaminants to receiving waters as do secondary treatment effluents (Heaney, et al. 1975, C.E.Q. 1978). Presently, simple storage/treatment devices, i.e. one or two component systems such as a stormwater detention basin, provide a costeffective tool for quantity as well as quality control of these storm flows. While the design of these devices has traditionally been based upon a single storm event, the additional information provided by longterm analyses has recently encouraged their adaptation. The engineer or planner concerned with the design of a detention facility for the quality control of stormwater runoff has a variety of solution methodologies available: empirical approaches utilizing average annual values; analytical methods based on solutions to the flow governing equations; simulators amenable to rigorous search techniques; and statistical techniques involving rainfallrunoff parameter distributions. No one method, or coordinated coupling of methods, has been documented as the most costeffective for all applications. This is in part due to the lack of an available longterm data base, but also reflects the lack of comparative studies. This thesis evaluates methodologies available for analyzing the longterm performance of stormwater runoff control devices. A detailed description of these methods is not the intent. The manuals referenced for each provide that service. Rather, the benefits and limitations of these methods in designing a control device for water quality improvement are emphasized. The comparison consists of three criteria: 1. problem assessment, i.e. how does the particular method define the system; 2. ease of application, e.g. data or computer requirements, or cumbersome techniques, and associated costs; and 3. accuracy of results, both absolute and relative to data requirements. Because the longterm performance of detention facilities has not been well documented, there is no available data base to definitively compare the accuracy of the methods. Objectively, this study presents an opportunity to establish relative estimates of the longterm performance of storage/treatment devices designed for stormwater quality control. The optimal design of a control device will depend on problem specific constraints such as discharge quality standards and economic considerations. SYSTEM DESCRIPTION The following definition of a system is presented as a framework to maintain conceptual consistency. A system is any structure, device, scheme, or procedure, real or abstract, that interrelates in a given time reference, an input, cause, or stimulus, of matter, energy or information, and an output, effect, or response, of information, energy, or matter. (Dooge 1973, p. 4) This functional interrelationship of inputs and outputs for a given time reference provides a basis for addressing water quality problems in a spectrum of hydrologic units, from urban stormwater systems to lakes threatened with cultural eutrophication. Before evaluating the performance of a particular system, the hierarchy of systems which influence that performance must be recognized. A classical representation of the hydrologic cycle is presented in Figure 1. Storages and flows of water are the principal elements in the system, although the influences of solar energies, land morphologies and other factors are implicitly included. The system depicted in Figure 1 can be partitioned into discrete subsystems defined by characteristic storage and flows, as shown in Figure 2. These subsystems can be further subdivided into individual components, or control units, whose boundaries similarly reflect the storage and flows emphasized. The basic hydrologic characteristics which define the performance of a control unit, as depicted in Figure 3, are: S__ OCEAN Ground Waler Figure 1. Representation of the hydraulic cycle. leep percolation Figure 2. Discretized subsystems of the hydraulic cycle. Figure 3. Processes defining the performance of a control unit. 1. The source of the mass, the unit's place in the system and its relation to other units; 2. the dynamic storage and flow conditions; and 3. the removal mechanism. DEFINITION OF CONTROL UNIT The following analysis centers on the longterm pollutant removal effectiveness of a hypothetical detention facility. The control unit is a single basin which receives the stormwater runoff from an urban catchment, and discharges to an undescribed receiving water. A schematic of the system is presented in Figure 4. The data source is a 24.6year record of hourly rainfall values obtained from the National Weather Service. The system boundaries of the control unit are drawn at the inlet and outlet. As such, it is not just the rainfall which is the forcing function, but the runoff, a result of the rainfall's interaction with the catchment. The pollutant source is the constituent contaminants of the runoff sand, debris, dust, etc. The removal mechanism responsible for pollutant control is sedimentation, and the removal characteristic is based on the treatment time in the basin. The removal kinetics are defined by the hydraulics within the basin, as determined by basin geometry and the inflow and discharge characteristics. These are the major influences on control efficiency and become the design parameters. RRAINFALL RoRUNOFF ET EVAPOTRANSPIRATION I INFILTRATION W WIDTH OF CATCHMENT L LENGTH OF CATCHMENT DF DETENTION FACILITY D DISCHARGE TO RECEIVING WATER Figure 4. Schematic of Case Study catchment area. CLASSIFICATION OF METHODS Several methodologies are available for estimating the longterm performance of stormwater detention facilities. The approaches are all models of the same complex process, yet differ conceptually and mechanistically. Figure 5 is a schematic depicting the relationship of the various methodologies. For the purpose of this thesis, the following classifications will be used: 1. Analytical approaches utilize some combination of the general mass continuity equation and the advectivedispersion equation to describe the flows, storage, and pollutant removal characteristics of a control unit. 2. Empirical approaches are derived from or guided by experience. Although literally implying the lack of a theoretical background, the expression is used to denote methods which have been developed in scientific and engineering practice. 3. Two types of statistical techniques are widely used (Chow 1964). Frequency analysis methods are based on approximating the value of a random variable with a probability density function, from which frequencies of occurrence may be assigned. Regression and correlation analyses deal with the description of the relationship between two or more variables. R9 EMPIRICAL ANALYTICAL SIMULATION STATISTICAL Figure 5. Characterization of the various methodologies. 10 4. Digital simulation methods were developed to exploit the ability of highspeed computers to manipulate mathematical expressions. The main objective of these methods is to deterministically model the dynamic processes in a physical system. Rarely does a definitive demarcation exist between solution methodologies; there are overlaps and extensions from one to the next. As a model, each method represents simplifications, compromising between ease of application and accuracy. The empirical and statistical approaches provide firstcut approximations based on a small data requirement. The more complicated simulations are generally regarded as more accurate, although they may have extensive data or computational requirements. CASE STUDY CATCHMENT CHARACTERIZATION Usersupplied catchment data are input for most models. The extent of the data collection is dependent on the requirements of the particular method employed. As indicated in Figure 4, there are no streams, lakes or groundwater flows. For simplicity, there was no initial abstraction, areas of depression storage or other consumption of water. The flow routing geometry was kept as simple as possible. Conceptually, the catchment was a sloping plane with no gutter or pipe networks. All the runoff flowed directly to a dummy outlet on the downslope side. The runoff from the entire catchment was routed to the proposed basin, and was subsequently discharged to a local receiving water. The data were based on observed values for a drainage basin in Gainesville, Florida, and are presented in Table 1 (Huber, et al. 1981). In an actual catchment, waste characteristics would be obtained by running column settling tests on runoff samples. Table 1. Case study catchment characteristics. Total area = 24.7 acres Impervious area = 37 percent No depression storage or initial abstraction Average catchment slope = 0.040 ft/ft = 211 ft/mile Maximum infiltration = 2.5 in/hr Minimum infiltration = 0.52 in/hr Evaporation = 0. 1 in/day Population density = 500 people/square mile RAINFALLRUNOFF CHARACTERIZATION Rainfall Data As the storage and flows of water are the principal elements in the catchment system, rainfall is the driving force. Longterm rainfall data are available on several time bases, e.g. continuous gages or discrete hourly, daily, monthly or yearly records. Rainfall data are characterized by volume (depth over the catchment area), average intensity, duration and time between events. The rainfall data source utilized for this study was the National Weather Service (NWS) tape for 24.6 years (June 1948 December 1972) of hourly rainfall at Atlanta, Georgia. The standard NWS format is to record hourly rainfall values in hundredths of an inch on days when there is rain. Days without rain are not recorded on the tape. Hourly data for the first day of each month are recorded regardless of whether it rained or not. SYNOP For methods requiring average event statistics, hourly rainfall data may be analyzed with SYNOP, a computer package developed by Hydroscience, Inc. (1979) to determine synoptic statistics of data time series. Rainfall volumes, intensities, durations and interevent times are the principal parameters evaluated in SYNOP. Available options include complete statistics on an event basis and time basis, e.g. yearly averages. Cumulative conditional probabilities (i.e., given that rain has occurred) and return periods for hourly magnitudes are also calculated, based on the California method of probability plotting. The grouping of hourly data into storm events is based on the minimum number of dry hours between rainfalls, an input variable termed the minimum intervent time. Assuming that the storm events occur as a Poisson process, the time between events is exponentially distributed. The exponential distribution is a special case of the gamma distribution with the coefficient of variation equal to unity. Figure 6 demonstrates the relationship between theoretical and observed results for the cumulative distribution of interevent times. The gamma distribution has been widely applied in hydrology (Haan 1977). To define events, the minimum interevent time is varied to obtain a value close to unity for the coefficient of variation (cv) associated with the interevent time. The SYNOP manual Figure 6. 97 Li > 96 0 95 =,25  94 < 93 2 92 0 9 9o 0 80 50 V= 1.25/ CL, 0 T 0 2 a 56 MULTIPLES F THE MEAN TIME BETWEEN STORMS LECGND; THEONETICAL GAMMA DISTRIBUTION 0 OBSERVED DISTRIBUTION NO TE MINIMUM 6 DRY HOURS BETWEEN STORMS ( :;84HR,V g= 102). Comparison of theoretical and observed distributions ofinterevent times for Minneapolis/St. Paul airport. recommends an initial trial of three hours for the minimum interevent time. SYNOP was run on the entire 24.6year record of Atlanta rainfall to determine the storm statistics. The results of these runs, presented in Table 2 and Figures 7 and 8, give some idea of the sensitivity of the results to the choice of the minimum interevent time. The computer costs averaged $6.25 per run. With eight hours specified as the minimum number of dry hours defining an event, the coefficient of variation for the mean interevent time was 1.004. Values for the means of the parameters were taken from this run, e.g. the mean volume (Vr) of a rainfall event was 0.495 inches. Notice that Vr does not equal the product of Ir and Dr. This is because Vr is the mean of the products of the individual events' intensity (ir) and duration (dr), which is not necessarily equal to the product of the mean intensity (Ir) and the mean duration (Dr), i.e. Vr = mean (irdr) which is not the same as (mean ir)(mean dr) = IrDr. Runoff Quantity The interaction of rainfall and the catchment generates runoff. The quantity of runoff is determined by the influence of infiltration, evaporation, consumption patterns and land use (Eagleson 1970). The watershed system response to these interactions has been evaluated by hydrologists for many years. A comparison of rainfall and runoff time Table 2. SYNOP results of 24.6 years of Atlanta, Georgia rainfall. Minimum # Number Volume cv Duration of dry hours Vr Dr (in) (hr) 3 3215 0.367 1.540 4.642 5 2596 0.454 1.424 6.646 8 2331 0.495 1.384 7.824 12 2134 0.552 1.332 9.817 cv Intensity cv Interevent cv Ir time Ti (in/hr) (hr) 1.126 0.078 1.372 66.73 1.269 1.124 0.077 1.348 82.62 1.067 1.134 0.077 1.356 90.10 1.004 1.143 0.074 1.334 100.55 0.917 0.6 c 0.5 2 J 0 0.4 z LU 0.3 3 6 9 12 1.5 Z 0 1.4 < 1.3 > LL 1,2 1 1.0 L 0 0.9 MINIMUM INTEREVENT TIME, hr 10.0  8.0  7.0  6.0 5.0  H1.5 1. 3 .2 0 1.2 0 L 1.0 LLJ 0 0 3 6 9 12 MINIMUM INTEREVENT TIME, hr Figure 7. SYNOP values for mean event volume and duration as a function of minimum interevent time. 00 MEAN DURATION AA CV I 2 0.079 0. 0.078, C 0.077 U5 0.076 Z LJ I Z 0.075 < 0.074 LI 0 0.073 MINIMUM INTEREVENT 3 6 MINIMUM INTEREVENT TIME, hr 9 12 TIME, hr Figure 8. SYNOP values for mean event intensity and interevent time as a function of minimum interevent time. 3 6 9 12 0 1.4 or 1.3 LLI 0 1.2 1.1 U LL 1.0 LJ 0 0 0.9 1.5 0 1.4 1.3 LL 1.2 F z LL U 1.0 LJ 0 0 0.9 110 100 90 80 70 60 5.0  0 series, presented in Figure 9, depicts two phenomena characteristic of the rainfallrunoff process: 1. a reduction in the number of events due to the capture of low volume storms by the indigenous catchment storage capacity, e.g. depression storage and soil moisture capacity; and, 2. a reduction in the volume of the events due to the catchment storage and flow interception; e.g. infiltration rates. Analyses that deal with single runoff events are not sufficient to characterize these phenomena because the catchment storage and interception capacities are functions of antecedent soil moisture conditions, and are not constant. It becomes necessary to retain as much. information as possible on the time between successive events. The event duration defines the reference time frame for differentiating between storage and interceptor elements. A storage element can detain up to a maximum runoff volume per event, i.e. its detention time is greater than the event duration. An interceptor, on the other hand, can capture up to a maximum flow rate before bypassing Stormwater runoff control devices can also be characterized by storage and interception capacity, as presented in Figure 10. A representation of a time series of runoff flows is presented in Figure 11, a series of flow pulses separated by MAR APR Figure 9. A comparison of rainfall and runoff time series depicting the reduction in number of events and the reduction in the event volume. MAY JUN FEB 2.0 1.0 2.0 1.0 11, h 1 Maximum Minimum storage Sor 0e e  I I 0,0 a) INTERCEPTION b) STORAGE q nv TIME c) INTERCEPTION AND STORAGE TIME Figure 10. Definition of interception and storage for storm events. M7T~ I V. , 0 10 20 30 ' 130 140 150 160 170 TIME, hr Figure 11. Representation of a time series of runoff flows. 4.0 H 2.0l I I /\ I relatively long periods of no flow. The determination of runoff characteristics is a major step in the solution process and is where the methods vary the most. The approaches compared here offer a sharp contrast in the representation of the rainfallrunoff process. The statistical and empirical approaches summarize runoff generation via linear conversion factors applied to rainfall statistics. On the other hand, the simulation technique utilizes some of the most refined concepts in deterministic hydrology. BASIN CHARACTERIZATION Flow conditions The input to the basin is the runoff from the catchment area. The time series of runoff events depicted in Figure 11 suggests two realms of kinetics: rapid, relatively wellmixed during the runoff event, followed by slower (less dispersion, turbulence) kinetics and possibly quiescent conditions during dry weather. Characterizing this time series of discontinuous flows entering the basin is a major obstacle in solution methods. Basin discharge may be either variable, as in the case of gravity drainage, or constant, via a pump or outlet restriction. Negative feedback is inherent in gravity systems, i.e. when the water level is high, the outflow is high, and as such, tends stabilize the flow. It is 24 difficult to deal with this nonlinearity analytically; it is far easier to analyze a constant discharge rate. There has been no evidence to suggest that one is better than the other for pollutant removal. Removal Theory of settling Pollutant removal via settling is the most widely useful operation in water and wastewater treatment (Fair, Geyer and Okun 1968, Liptak 1974). In the design of sedimentation basins, basic assumptions are incorporated: 1. inlet zone the influent is transformed to a uniform vertical distribution of particles. 2. settling zone there is steady, uniform flow and quiescent, discrete and unhindered settling. 3. bottom zone solids which enter the bottom zone are not resuspended. 4. outlet zone solids that do not enter the bottom zone leave in the effluent. These four zones and particle settling paths are shown in Figure 12. The major design parameter is the overflow rate (vo), defined as vo = H/td = (Vs/SA)/(Vs/Q) = Q/SA (1) where H is the depth of the settling zone C L 3, td is the detention time of the settling zone C T 1, Vs is the volume of the settling zone E L3 1, SURFACE AREA = SA PERPENDICULAR TO FLOW CROSS SECTIONAL AREA = A TRAVEL TIME L = L r Q /A LA Q V Q OVERFLOW RATE = Vo = = = t /Q SA Figure 12. Development of overflow rate in an ideal settling basin. Q SA is the surface area of the settling zone C L2 3, and Q is the flow in the settling zone E L3/T J. The settling process is relatively slow, such that it is the removal rates that are important, rather than the equilibrium state (Rich 1974). Under ideal conditions, particles settle at a velocity (vp) governed by Stoke's Law, and are removed if vp is greater than vo. Additional particles are removed which enter the settling zone at a height (hp) less than hp = vp*td (2) The total basin removal is given by R = (1xo) + (1/vo) 5 vp dx (3) where R is the pollutant removal efficiency, and xo is the proportion of particles with vp less than vo. Rarely do detention facilities perform under ideal conditions. Most often, design efficiencies are reduced due to violations of ideal assumptions caused by short circuiting and turbulence, which alter the kinetics from ideal quiescent conditions. Short circuiting is induced through thermal currents, wind action, influent inertia, etc. Resuspension of solids may occur as the flow rate exceeds the scouring velocity. Thomas and McKee derived the 27 effect of longitudinal dispersion in a basin consisting of n completely mixed plugs (Fair, Geyer and Okun, 1968). Figure 13 presents the relative effluent concentrations for an instantaneous injection of dye undergoing a first order decay as it passes through the basin. A completely mixed basin is shown as n=1, while an ideal plug flow basin (n=infinity) would be represented by a spike at t/td of unity. The net effect of altering the flow regime from quiescent to more turbulent conditions is the reduction of the reaction coefficient k (Fair, Geyer and Okun 1968; Rich 1974). Although there is no way to predict before operation the reduction for a particular basin, the phenomena can be represented as in Figure 14, where the reduction of k is given as k/kO = (1c/cO)**n (4) where k is the reaction coefficient, kO is the reaction coefficient under quiescent conditions, c is the effluent concentration, cO is the initial pollutant concentration, and n is the coefficient indicating the degree of turbulence, which increases as the flow regime diverges from ideal conditions. Plug flow conditions are represented by n=0 where k=kO and the pollutant decays according to or, R = 1c/cO = le**(kt). c/cO = e**(kt) (5) Relative time, t/ltd Figure 13. I. o 0 0. 0 o0. 00. 0.  0 0. 0. ^ _ 0C [T ( Figure 14. Effluent concentrations for a firstorder removal process in n completely mixed plugs. 0 8 7 6  5 02 . .. 0 _^ ,^___ 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 45 5.0 RELATIVE TIME, t/td Removal efficiency for a firstorder removal process demonstrating the effect of increased turbulence; n=1 for quiescent and n=1 for completely mixed. Comparison of Flow Conditions Plug flow and completely mixed removal regimes define the extremes of pollutant removal performance. By definition, the hydraulic regime in each plug is complete mixing. Therefore, under static conditions, e.g. a column settling test, there is no difference between the two. The applicability of transferring column settling test results to dynamic conditions was recently reexamined by White (1976). In tank studies, he observed reasonable agreement with column tests, although the results were highly dependent on the waste characteristics. The effect of longitudinal dispersion on plug flow performance has been studied to correlate plug flow and complete mixing under dynamic conditions (Weber 1972). Ideal plug flow is represented as having zero dispersion while complete mixing is assumed to have infinite dispersion. An example of the effect of dispersion is reflected in Figure 15, showing effluent responses to a step input. Weber (1972) presents steadystate solutions that were derived from the general continuity equation fitted to a dispersion model. For a firstorder reaction, the plug flow solution (zero dispersion) is c/cO = e**(ktd) or, R = le**(ktd) (6) For a completely mixed basin, the steadystate solution is or, R = 11/(1+ktd) c/cO = 1/(1+ktd) 1.0 0.8 C. /C 0.6 o 0.4 0.2 1.0 0.8 C /C 0.6 0.4 0.2 INFLUENT EFFLUENT plug flow, 0 intermediate amount of dispersion v x 0. 0025 large amour of dispersion d . d complete mix,  0,2 vxL v L Dx .,small amount of dispersion, 0. 002 0 0.5 1.0 1.5 2.0 B tvx/L Figure 15. Effluent responses to a step input. I c.. (complete mixing) First order ^64 kL/va 200 .... 16 100 50 (Lines of equal volume l. or holding time) 0 (piug flow)  Figure 16. Comparison of real and plug flow reactor volumes for ia firstorder reaction. These two solutions represent the removal efficiency extremes. The lower removal efficiency of complete mixing is a result of the basin concentration being continuously mixed with the influent, yielding a dilution of the influent but a concurrent increase in the basin concentration. In plug flow, the basin effluent more clearly reflects the removal process occurring in the separate plugs. The difference between the steadystate solutions for firstorder reactions is graphically presented in Figure 16, which compares the volume of an ideal plug flow basin to the volume of a basin with dispersion yielding the same removal efficiency (Weber 1972). From Figure 16 it is possible to predict the effect of implementing dispersion reducing mechanisms such as baffles. For example, by reducing the dispersion factor from infinity (completely mixed) to 1.0, the volume necessary to provide 90 percent removal is reduced by a factor of 2. There has been no widely used method for sizing S/T facilities with longterm stormwater quality control as the main objective. Heaney, et al. (1979) presented the mechanics for determining the optimal combination of S/T for steady state conditions, subject to economic constraints. METHODOLOGIES ANALYTICAL Analytical models are developed from a combination of the general mass continuity and advectivedispersion equations. They range in complexity from simple steadystate approximations to more complicated variable flow solutions. The complexity of solution for detailed problems intimidates users and prohibits widespread application. Customarily, a simplification of the system's dynamic processes is necessary to obtain a solution. The analytical approach to stormwater detention facilities has been advanced by Medina (1976). Constant and variable (linear) flow and storage conditions were studied. Conservative and nonconservative pollutant routing were included. Effluent concentrations were derived for "simple" forcing functions. Application of this method requires the runoff flows and pollutants be converted to one of the input functions for which solutions have been derived. The solutions are limited in application due to their complexity and sensitivity to storage and flow conditions, i.e. the need to reduce the complexity of the dynamics to facilitate the analytical solution. The complexity of these solutions precludes their application to stormwater runoff events without the use of detailed simulation. EMPIRICAL A widely used method for characterizing the rainfallrunoff process is the application of a conversion factor to mean rainfall values. Conversion factors are catchment specific and have been correlated to imperviousness, land use, population density and depression storage (Hydroscience, Inc. 1979, Chow 1964). While this method accounts for an average reduction in the volume of storms, it does not correct for the decreased number of events, i.e. it doesn't account for the small volume storms that are retained in the catchment storage. Empirical relationships for runoff water quality have also been developed. Receiving water studies have determined runoff coefficients for with nutrient loadings based on land use (Reckhow 1980). In the urban arena, Smolenyak (1979) determined coefficients of the power equation load = a(flow)**b (8) where load is the pollutant load in the runoff E M 3, flow is the runoff flow C L3/T 3, and a,b are coefficients. Values determined from data in the Urban RainfallRunoff Quality Data Base are presented in Table 3. The practice of water quality control via settling is inherent in most applications of natural waters. Water and wastewater treatment employ several variations of settling basins. Natural hydrologic systems incorporate detention for both the storage of kinetic energy and the deposition of sediment load. As a result of the implementation of reservoirs, siltation studies have contributed to the identification of the relationships between sedimentation and hydraulic parameters. The most popular sediment trap studies are those of Brown, Brune, Churchill and Camp (Ward and Haan 1977). Chen (1976) presents the historical development of theoretical analyses of sediment retention. These methods require the removal assessment of detention facilities based on an annual time frame. As there was no way to reconcile this with the stochastic nature of runoff events, these empirical methods were not investigated further. A recent review by Nix, et al (1980) summarizes the benefits in utilizing detention facilities for stormwater quality improvement. Several combinations of empirical and statistical approaches were suggested for design purposes. TABLE 3. Relationships between Pollutant Loads and Flow Volume (FLOW). Dependent Variable BOD COD NH3N NITN NTOT ORGN TOTN DOP TOP TOTOP TOTP TPHOS' TOTS TSS Sig, Level FTest .28 .76 .44 .80 .57 .88 .74 .83 .46 .27 .66 .91 .69 .56 .99 .99 .99 .99 .99 .99 .99 .99 .99 .90 .99 .99 .99 .99 No. of Events 80 157 20 21 103 40 37 34 119 11 53 8 41 260 Model Load = a(FLOW)b Reg. Coef. a b 34.0 29.8 .215 .119 .0400 .856 .304 .0648 .0104 .0800 .426 .105 279 44.2 1.12 1.08 .72 .80 .71 1.04 1.07 .98 .78 .55 1.5 1.05 1.41 1.10 Source: smoltenyak 1,979 SIMULATION Several models are available for the simulation of the rainfall runoff process and detention pond performance. Simulation is amenable to a trial and error routine, leading to search techniques for determining an acceptable design. STORM The Storage, Treatment and Overflow Model (STORM) of the Corps of Engineers models wetweather flow through separate storage and treatment facilities (U.S.A.C.O.E. 1974). Runoff quantity is generated from an empirical conversion factor applied to rainfall excess. Runoff quality is generated as a function of land use. While flow is routed through the treatment plant, there is no capacity to model the quality improvement provided by detention. SWMM Overview The Storm Water Management Model (SWMM) is one of the most comprehensive and well documented models available for the analysis and design of urban stormwater systems (Huber et al. 1980). SWMM was developed by Metcalf and Eddy, Inc., the University of Florida and Water Resources Engineers, Inc. under a contract for the Environmental Protection Agency. Version I was released in 1971 and has been continually undergoing revision and updating. This study utilized Version III, released in 1980, and also incorporated further refinements. While the model allows for extensive watershed simulation, this study restricted the analysis to a simplified Runoff Block and concentrated on the Storage/Treatment Block. The Runoff Block deterministically models the rainfallrunoff process in a catchment. Physical data such as depression storage, infiltration rates, soil characteristics, catchment area, ground slope, gutter network, evapotranspiration rates and hourly rainfall values are included as the model input. Pollutant buildup and washoff functions are available, as is pollutant generation based on catchment land use. The Runoff Block generates hydrographs and pollutographs as options. Several inherent adjustment factors are available for calibration of the model. The Storage/Treatment (S/T) Block of SWMM models the flow and pollutant routing through a storage and/or treatment device which can be either a detention or nondetention unit. Geometric and hydraulic relationships, e.g. depth to surface area, and evaporation rates, and incoming flows are included as data input for the S/T block. Discharge can be modeled as either constant or variable outflow. The package provides for a variety of removal mechanisms and flow routing options, capable of tracking both stormwater flows and constituent pollutants. Data Input for Runoff Block The Runoff Block accepts hourly rainfall data in the National Weather Service (NWS) format. No gutter or pipe networks were used in the example catchment; all runoff exited the area via a dummy outlet. The impervious area was modeled separately from the pervious area. Runoff generated on either area went directly to the dummy outlet without passing through the other area. Also, there were no areas of depression storage in the modeled catchment. The data input for the Runoff Block consisted of the catchment characteristics presented in Table 1. A complete listing of the data input is given in Appendix A. Currently, continuous SWMM can only be run with hourly rainfall input. As an aside, the hourly rainfall data were transformed into daily and weekly records. SWMM Runoff Block was run on the first 19 months of the Atlanta data and the results are compared in Table 4. Table 4. Comparison of Runoff Block results using hourly, daily, and weekly rainfall input. Rainfall Average Total Infilt. Evap. Runoff Time Step Intensity Rainfall (in) (in) (in) HOURLY HOURLY 81.68 51.72 6.39 28.68 DAILY DAYTOT/Dr 80.53 50.46 8.18 28.00 WEEKLY WEEKTOT/2Dr 81.62 51.73 6.11 28.62 39 Reasonable agreement was obtained, suggesting that if hourly data were not available, continuous SWMM could be run using daily or weekly rainfall data. Data Input for Storage/Treatment Block The basin geometry and hydraulic characteristics required as input data for the S/T block were obtained from a separate computer program, BASIN, written for that purpose. BASIN calculates stage to surface area, stage to volume and stage to discharge relationships for basins given the dimensions, side slope and outlet configuration. Examples are provided in Figure 17. The program development and listing is provided in Appendix B. As a reference, basin volumes (Vb) were normalized to the mean runoff volume per event (Vro), yielding a normalized volume ratio (Vb/Vro). Currently, SWMM does not define storm event statistics, so the SYNOP program was employed. This involved running the Runoff Block with the complete 24.6year (June 1948 December 1972) rainfall record and generating 24.6 years of simulated runoff data. These data were transformed to the format of the NWS rainfall data, which is compatible with the SYNOP input format. As with the rainfall data, the minimum interevent time was varied to obtain the coefficient of variation (cv) for the interevent time close to unity. The results of these runs are presented in Table 5. .i* C 0a 0 0 0 LUI C/) I 2 3 4 5 6 DEPTH, ft 0 1 2 3 4 5 6 DEPTH, ft 30 25 4) 20 2n 20 0 15 W10  ._J 5 0 0 I 2 3 4 5 6 DEPTH, ft UJ D _j 0 > L) 0 0 S I I I I I 0 I 2 3 4 5 6 DEPTH, ft Figure 17. Stage relationships as calculated by BASIN; constant and variable discharge. VOLUME DISCHARGE Table 5. SYNOP results of 24.6 years of simulated runoff data. Minimum # Number Volume CV Duration CV Intensity CV Interevent CV of dry hrs Vro Dro fro Time Ti (in) (hr) (in/hr) (hr) 3 2124 0.180 1.253 4.507 0.964 0.041 1.057 101.35 1.172 4 1998 0.192 1.221 4.980 0.978 0.041 1.058 101.75 1.114 5 1903 0.201 1.196 5.428 0.989 0.041 1.063 113.13 1.070 8 1760 0.217 1.194 6.438 1.030 0.040 1.073 122.32 0.999 12 1646 0.274 1.181 7.448 1.093 0.039 1.052 130.80 0.940 A minimum interevent time of four hours resulted in a cv of 1.000. The mean runoff volume per event (Vro) was determined to be 18022 cubic feet, based on the mean depth of 0.201 inches over 24.7 acres. The number of events was reduced from 2391 rainfall events (Table 2) to 1998 runoff events. Continuity is checked by comparing the product of the mean event volume and the total number of events with the amount of runoff generated by the Runoff Block, (0. 19Z inches/event)(."199 events) = 383,61 inches; from Runoff, 388 inches. Test basin volumes (Vb) were obtained from BASIN to closely approximate volume ratios (Vb/Vro) of 0.5, 1.0, 2.0, 4.0, 10.0. For example, a Vb/Vro ratio of 0.50 implies that the empty basin volume is 50 percent of the mean storm event volume. The basin volumes used are presented in Table 6. Table 6. Determination of normalized volume ratios (Vb/Vro). Basin volume (Vb) Normalized volume (cubic feet) ratio Vb/Vro 7744 0.430 15014 0.833 29064 1.613 74420 4.129 167835 9.313 43 The input data for the Runoff Block are provided in Appendix A. The S/T Block utilized the runoff values generated from the Runoff Block. To save execution time and money, the Runoff Block was run once and the output stored on an interface data disk. The interface data set served as the input to S/T for the subsequent simulations. A constant suspended solids concentration of 100 mg/1l was assigned to the influent. This was chosen as opposed to generating pollutants from the catchment area for four reasons: 1) it avoids concern over how the pollutants are generated 2) it provides a base value (100 mg/1l) for future comparisons; 3) it provides a blockedoff step input as shown in Figure 18; and, 4) a constant influent concentration establishes that the percent of flow bypassed is numerically equal to the percent of the pollutant bypassed. The actual flow condition in a basin is neither plug flow nor completely mixed, but somewhere between, termed "intermediate mixing". The complete mixing option of S/T was chosen for the flow routing regime for its analytical and computational simplicity, resulting in lower simulation costs than the plug flow method. Two options of basin discharge were explored: variable outflow based on hydraulic head above an outlet, and a I I Figure 18. Time series of constant influent pollutant concentration. LL LL :LUL n7 H drawdown scheme which emptied the basin at a constant rate (see Figure 17). The pumping option was run for comparison with the statistical technique, while the variable discharge option was utilized for application to basins with gravity drainage. Constant Discharge Simulation A variable volume, constant outflow unit was simulated by using the pumping option of S/T. As a reference, the constant drawdown rate was normalized as QcTi/Vro where Qc is the drawdown rate in cubic feet per hour, Ti is the mean interevent time in hours, and Vro is the mean runoff volume in cubic feet (Hydroscience, 1979). As Ti and Vro are constants determined from SYNOP, variable values of the ratio reflect different drawdown rates. These rates were calculated to yield ratios of 1, 2, 4, 7, and 10 and are presented in Table 7. It was assumed that drawdown occurs whenever there is water in the basin. The effect of drawdown height (Hd) and drawdown rate on capture and removal efficiencies was analyzed. Table 7. Calculation of constant discharge rates (Oc) (Ti = 111. 17 hours; Vro = 18022 cubic feet). Normalized discharge Drawdown rate (0c) ratio OcTi/Vro (cubic feet/hr) 1 162 2 324 4 648 7 1135 10 1621 Variable Discharge Simulation A variable volume, variable outflow control unit was simulated with the S/T Block by utilizing a power equation for basin discharge based on hydraulic head. This simulates the hydraulics in a basin with gravity drainage. The outlet characteristics were arbitrarily assigned as a six inch circular opening placed one foot above the bottom. Instead of a solution surface, as was provided in the constant discharge simulations, a single removal curve was determined for basin performance versus basin volume. In an analogous manner to the drawdown height and rate combinations, outlet elevation and crosssectional area were recognized as design parameters for basin performance and were analyzed. Evaporation in the S/T unit was arbitrarily assigned a value of 0. 1 inch per day. Removal Mechanism A removal equation was chosen of the form R = Rmax(1e**(kt)) (9) where R is the pollutant removal efficiency, Rmax is the maximum removal efficiency, k is the firstorder rate coefficient E 1/T 3, and t is the treatment time E T 3. Fair, Geyer and Okun (1968) presents general removal curves with k near 1.4 per hour for TSS and 0.50 per hour for BOD, with Rmax of 0.75 and 0.45, respectively. For design purposes, values for Rmax and k would be determined from column settling tests with representative pollutants. Values of 1.0 and 0.6 per hour, respectively, were arbitrarily assigned for these parameters. In the S/T Block, removal is accounted for once per time step, with the length of the time step, one hour, as the treatment time. The removal equation is presented in Figure 19. Because the time step was held constant throughout the simulation there was a constant percent removal (45 percent) of pollutant per time step. A comparison of effluent concentrations for removal governed by this equation in an ideal plug flow basin, an ideal completely mixed basin and the S/T complete mixing regime is presented in Figure 20. As shown, the S/T results lie within the extremes of pollutant removal efficiency provided by ideal plug flow and complete mixing. 1.00 0.9  0.8  0,7 Removal ( t 0.6 0 0 1 f 2 0.5 3 z 5 W 0.451 LL 0.4 O> 0.3  LUJ 0.2  0.1 0.0 0.0   0 1 2. 3 TREATMENT TIME hr Removal equation used in SWMM S/T Block. Figure 19. IDEAL PLUG FLOW 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 SWMM S/T COMPLETELY MIXED IDEAL COMPLETELY MIXED = 10 ft~hr td = 3hr 3 4 5 6 7 8 9 TIME, hr Figure 20. Comparison of effluent concentrations under ideal plug flow, ideal completely mixed and as calculated with SWMM S/T completely mixed routing; step input of pollutant. 0.83 0.72 0.64 0 I 2 SII I I.I... I I I I ~ Oneyear Versus 24.6year Simulation The initial decision to use one year of data as opposed to the full 24.6year history was based on economic considerations; mistakes and debugging were expensive enough without extra data magnifying the costs. The first 12 months of the input record (June 1,1948 May 31,1949) were utilized to get the simulator running. It was realized that if a "typical" runoff year's simulation adequately reproduced longterm basin performance, the costs of the analysis would be reduced by as much as an order of magnitude. A "typical" year, 1953, was chosen on the basis of similar synoptic statistics, as determined by the SYNOP run of the 24.6year runoff data. A comparison of 1953 runoff parameters with those of the 24.6year time series is presented in Table 8. The adequacy of one year's simulation for describing the longterm basin performance was analyzed in a series of simulations; the results are presented below. Runoff Block Results A variety of summary print options are available in the Runoff Block, from detailed hourly results to the total simulation summary, as presented in Table 9. On the hypothetical catchment, 704 inches (60 percent) of the total 1179 inches of rain left via infiltration. A total of 388 inches (33 percent) accumulated as runoff, while 150 inches Table 9. Runoff Block 24.6gear simulation summary. MILLION CUBIC FEET TOTAL PRECIPITATION (RAIN PLUS SNOW) 105.512 TOTAL INFILTRATION 63. 106 TOTAL EVAPORATION 7.846 TOTAL GUTTER/PIPE/SUBCAT FLOW AT INLETS 34.830 TOTAL WATER REMAINING IN GUTTER/PIPES 0.000 TOTAL WATER REMAINING IN SURFACE STORAGE 0.000 $ ERROR IN CONTINUITY, % OF TOTAL PRECIP 0.256 * RUNOFF SIMULATION ENDED NORMALLY * * INCHES OVER TOTAL BASIN 1176.79 703.83 87. 51 388.47 0.00 0.00 Table 8. Comparison of mean runoff event parameters for 1953 with the 24.6year record (minimum interevent time = 4.0 hours). Volume (in) cv Duration (hr) cv Intensity (in/hr) cv Interevent time (hr) cv 24.6year 0. 201 1.222 5.066 0.972 0.043 1. 148 111.71 1.000 1953 0.217 0. 948 6. 190 1. 087 0.044 1. 164 104.83 0.986 (8 percent) were lost to evaporation. Mass continuity was preserved within 0.3 percent over the total 24.6year simulation. Storage/Treatment Block Results The format for the S/T results are similar to the runoff output with more emphasis on quality parameters. Again, as shown in Table 10, the results were presented to facilitate continuity checks. Table 10. Examples of Storage/Treatment Block summaries. DETENTION UNIT CHARACTERISTICS: POLLUTANT ROUTING METHOD : COMPLETELY MIXED RESIDUALS DRAWOFF SCHEME: NEVER DRAWN OFF DEPTHAREASTORAGEFLOW RELATIONSHIPS : DEPTH,FT. 0. 0 0. 50 1. 00 1. 25 1. 50 2. 00 2. 50 3. 00 3. 50 4.00 4. 50 SURFACE AREA,SG.FT. 5000. 0 5304. 0 5616. 0 5775. 0 5936. 0 6264. 0 6600. 0 6944. 0 7296. 0 7656. 0 8024.0 STORACE,CU. FT. 0. 0 2576.0 5306. 0 6729.9 8193. 7 11243. 7 14459.7 17845.7 21405. 7 25143.7 29063.7 * GOVERNED BY PUMPING PUMPED OUTFLOW: DEPTH AT WHICH FIRST PUMPING RATE DEGINS,FT. DEPTH AT WHICH SECOND PUMPING RATE BEGINS,FT. FIRST PUMPING RATE, CFS SECOND PUMPING RATE,CFG DEPTH AT WHICH ALL PUMPING STOPS,FT. UNIT PARAMETER VOLUME (CU. F. )     1 INFLOW,TOTAL INFLOW,NET BYPASS TREATED OUTFLOW RESIDUAL FLOW REMOVED BY DECAY REMAIN.TOT.VOL. EVAPORATION 0.1456E+07 0.1386E+07 0.7027E+05 0. 1364E+07 0. 0 0.5285E+04 0. 1700E+05 CAT KAKA LS. 0. 4547FA04 0.4327E+04 0.0 0.1422E+04 0.0 0.2913E+04 0.3216E01 0.0 0. 0 0. 0 0. 45 0. 45 0. 0 Constant Discharge Simulation Performance results from the constant discharge simulations are presented in Figures 21, 22 and 23, and in Table 11. Table 11. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: simulation results. Normalized Volume Ratio Normalized 0.43 0.83 1.61 4.13 9.31 Discharge ratio 1953 24.6 yr 1953 1953 24.6 yr 1953 1953 25yr 1 C 0.344 0.331 0.476 0.613 0.640 0.852 1.000 0.952 R 0.343 0.322 0.476 0.598 0.638 0.847 0.989 0.941 2 C 0.398 0.552 0.721 0.945 1.000 * R 0.373 0.527 0.690 0.906 0.961 * 4 C 0.468 0.461 0.621 0.804 0.795 0.962 1.000 0.993 R 0.373 0.383 0.532 0.712 0.705 0.864 0.905 0.896 7 C 0.542 0.699 0.839 0.971 1.000 * R 0.365 0.524 0.661 0.792 0.817 * 10 C 0.611 0.608 0.744 0.868 0.876 0.982 1.000 0.999 R 0.342 0.351 0.483 0.603 0.619 0.713 0.728 0.736 * indicates that simulation was not run. The 1953 simulations duplicated the performance results of the 24.6year simulations within five percent over the entire spectrum of basin volumes and discharge rates. Figure 21 presents the solution surface for capture efficiency as a function of drawdown rate and basin volume. 10.0 9.0 6.0 5.0 4.0 3.0 2.0 .70 1.0 0.60 50 0.0 I I I 0 1 2 3 NORMALIZED DI1 Figure 21. Solution surface as a function of discharge rate: CHARGE, QcTi/Vro of flow capture efficiency (C) basin volume and constant 1953 simulation results. 8.0 7.0 6.0 5,0 4.0 3.0 2.0  1.0 0 NbRMALIZED Figure 22., DISCHARGE, QcTi/Vro Solution surface of pollutant removal efficiency (R) as a function of basin volume and constant discharge rate; 1953 simulation results. 0.5  04  0.43 0.3 0.2 1.0 0 .0 Ill1lll[ 0 2 3 4 5 6 7 8 9 10 NORMALIZED DISCHARGE, QcTi/Vro Figure 23. Pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: 1953 and 24.6year simulation results. Isopleths of percent capture were drawn by linear interpolation between calculated values. As expected, flow capture was greater as the drawdown rate increased, due to an increase in the effective volume. Also, as the basin volume increased, the capture efficiency increased due to less bypass. The vertical distance between the isoquants represents the sensitivity of capture performance to basin volume; the smaller the distance, the greater the sensitivity. for drawdown rates greater than 4.0, there appears to be uniform sensitivity to basin volume. The lowest sensitivities occur at the lower drawdown rates (QcTi/Vro less than 2.0). The isoquants converge slightly toward the upper end of the abscissa. The horizontal distance separating the isoquants represents the sensitivity of capture performance to the drawdown rate. The isoquants become parallel to the abscissa above QcTi/Vro of 4.0, implying relative insensitivity to drawdown rate. Sensitivity is increased as the drawdown rate is decreased. Figure 22 presents the solution surface for pollutant removal efficiency as a function of basin volume and drawdown rate. Unlike the solution surface of capture performance, the isoquants in Figure 22 slope upward after an initial negative slope. The result is a solution surface which allows more than one drawdown rate at a specific basin volume to achieve the same removal performance. This demonstrates the performance tradeoff of providing a larger effective volume by emptying the basin quicker versus providing a longer treatment time, although bypassing more flow. Combinations of basin volume and drawdown rate yielding equivalent removal efficiencies are depicted along isoquants. For example, the removal performance obtained by a Vb/Vro of 4. 1 and a QcTi/Vro of 2.0 was the same as a Vb/Vro of 9.3 and a normalized discharge rate of 4.0. The greatest removal occurred in the region of large basin volumes (Vb/Vro > 4.0) and low drawdown rates (QcTi/Vro < 4.0). Figure 23 presents the removal performance in a different manner than in Figure 22. There is no increase in information by presenting the results in this way, although the communication of information is improved. For example, in Figure 23, it is easier than in Figure 22 to see that the sensitivity of removal to drawdown rate increases as the volume ratio increases. Combinations of basin volume and drawdown rates yielding equivalent removal as well as the sensitivity of the removal performance to drawdown rate are demonstrated. For example, the sensitivity of performance to drawdown is represented as the slopes of the curves, and is seen to increase as the volume ratio increases. As the volume ratio increases, the maximum removal efficiency for each volume occurs at decreasing drawdown rates. The 1953 performance curve for a Vb/Vro of 9.3 is depicted as a straight line. This represents a divergence (5 percent at 60 QcTi/Vro = 1.0) from the 24.6year results, possibly due to the lack of a large storm during 1953. All of the curves converge to 4.3 percent removal at QcTi/Vro of 0.0, that is, in the case where there is no outlet. Longterm removal efficiency would undoubtedly be smaller for this case, tending to zero percent. Variable Discharge Simulations The effect of basin volume on capture and removal performance in basins with variable outflow rates was analyzed by running the SWMM S/T Block on five sets of basin geometry and hydraulic characteristics. The results presented in Figure 24 follow an intuitive removal relationship with increased removal as the storage capacity increases. The regions below Vb/Vro of 0.43 and above Vb/Vro of 9.31 were not explored because of the unlikeliness of such a small volume ratio. The resultant removal curve is neither an exponential nor a power equation for the range observed. Only three 24.6year simulations were run due to their low marginal benefit, i.e. the oneyear simulations gave estimates close enough to the 24.6year results to avoid spending the extra money for the longterm simulations. The costs of the runs averaged $0.60 for oneyear and $6.25 for 24.6year simulations. 1.00 0.9 0.8  0.7  0.6  0.5 z 0 00.4 Ld J 5 0.3  w LUl 0.2  0.  Figure 24. 1953 RESULTS A 25YEAR RESULT 25year 1953 Vb/Vro C R C R 0.43 0.903 0.241 0.904 0.251 0.83 0.898 0.529 1.61 0.967 0.643 0.952 0.641 4.13 1.000 0.860 9.31 1.000 0.916 1.000 0.918 J. 1 2 3 4 5 6 7 8 9 10 NORMALIZED VOLUME, Vb/Vro Pollutant removal efficiency (R) as a function of basin volume under variable discharge conditions.: 1953 simulation results. Optimal Basin Design During preparation of the initial performance solution surfaces, it was recognized that the heights at which discharge began and ended would combine with the discharge rate to affect basin performance. Intuitively, increasing the height would decrease the capture efficiency, but due to the completelymixed flow routing regime, the remaining volume would provide dilution of the influent. Combinations of drawdown height (Hd) and rate (Gc) and similarly outlet diameter and invert height, were simulated in an attempt to develop guidelines for the optimal design of detention facilities. A basin with a Vb/Vro of 1.61 was utilized for these simulations. The results from the constant drawdown simulations indicated that a basin with this ratio had the greatest performance sensitivity (26 percent capture and 11 percent removal) over the range of drawdown rates. In the variable discharge runs, a basin with a Vb/Vro of 1.61 yielded results in the knee of the removal curve. It was felt that a basin with this ratio was sensitive enough to reflect the effect of height and discharge combinations on basin performance. The results of the constant drawdown rate simulations are presented in Figures 25 and 26 and Table 12. The solution surface in Figure 25 indicates that maximum performance is achieved by a normalized discharge ratio 3.0 .o z Z: 0 L0 J Ld z 0 C c cc S Figure 25. 2 4 6 8 10 12 14 16 18 20 NORMALIZED DISCHARGE, QcTi/Vro Solution surface of pollutant removal efficiency (R) as a function of drawdown height and drawdown rate (Vb/Vro = 1.61): 1953 simulation results. 0 2 4 6 8 10 12 14 16 18 20 NORMALIZED DISCHARGE, Figure 26& Q cT / Vro Pollutant removal efficiency (R) as a function of drawdown height and constant discharge rate (Vb/Vro = 1.61).: 1953 simulation results. 0.5 0.4 0.3 0.2 1.0 0.0 Table 12. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of drawdown height and rate (Vb/Vro = 1.61): 1953 simulation results. Drawdown Height (ft) Normalized Discharge Ratio 1 C R 2 C R 4 C R 7 C R 10 C R 12 C R 15 C R 18 C R 20 C R * indicates that simulation was not run. of 12.0 with an Hd of one foot Removal efficiencies for basins with complete drawdown (Hd of 0.0) were lower than limited drawdown (Hd greater than 0.0) for all but the lowest rates. The general trend of the isoquants indicates that similar performance can be achieved by a low drawdown 0 0.613 0. 598 0.721 0.690 0.804 0.712 0.839 0.661 0. 868 0.603 0.883 0. 570 0.900 0.520 *i *t 0. 578 0. 578 0.679 0.679 0.756 0.734 0.804 0.752 0.837 0. 761 0.860 0.766 0. 874 0.749 0. 85 0.730 * 0. 517 0. 517 0. 610 0. 610 0. 687 0. 687 0. 749 0. 728 0. 778 0. 738 0. 795 0. 744 0. 831 0. 763 0. 845 0. 758 0. 851 0. 761 4 * * 0. 610 0. 597 0.648 0. 621 0.663 0.636 *f * *f *f *f 0. 717 0. 694 0. 745 0. 713 0. 765 0. 727 0. 776 0. 731 ratio and low height as well as a higher ratio and a corresponding higher drawdown elevation. Figure 26 more clearly presents the removal performance associated with each height. As the height increased, maximum removal occurred at higher drawdown rates. As the drawdown rate increased, removal efficiency increased until a maximum was reached, after which, further increase in drawdown rate yielded decreased removal. The results of the variable outflow simulations are presented in Figures 27 and 28 and Table 13. Table 13. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro=1.61): 1953 simulation results. Outlet Diameter (ft) 0.0 C R 0.25 C R 0. 50 C R 1.00 C R 1. 50 C R 0 0.043 0.043 0.887 0.708 0.976 0.293 1.000 0.018 * Outlet Elevation (ft) 1 2 2. 5 0.043 0.043 0. 043 0.043 0.043 0.043 0.845 0.775 0.721 0.763 0.737 0. 696 0. 952 0.922 0.900 0.641 0.737 0. 753 1.000 1.000 1.000 0.460 0.650 0.705 1.000 * 0.690 * indicates that simulation was not run. 3 0.043 0.043 0.635 0.619 0.876 0.757 0.995 0.747 1.000 0.734 4 0.043 0.043 * 0. 678 0.625 0.951 0.791 1.000 0.798 67 4.0 +63 0.70 0.60 0.75 3.0 75 0.75 4 i^ Z 0.70 , 0 2.0 +74  0.60 0 1.0 64 +29 0 .0 1.. I 1 I I i 0,0' 0,25 0.5 .0 1.5 OUTLET DIAMETER, ft Figure 27. Solution surface of pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro = 1.61): 1953 simulation results. 0,25 0.50 1.00 OUTLET DIAMETER, ft Figure 28. Pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro = 1.61): 1953 simulation results. 1.00 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.I1 0.0  0.0 1.50 69 The capture performance describes intuitive results. As the outlet height increases, the flow captured decreases. As the outlet diameter increases, the capture efficiency increases. The preliminary increase in removal efficiency as the outlet height increases (holding diameter constant) demonstrates the effect of dilution in a completely mixed basin. Capture efficiency decreases, but the remaining volume undergoes continuous pollutant decay, creating a sizeable dilution potential for the influent. For each outlet diameter, a unimodal removal curve was observed as the outlet height increased. This reflected the effect on removal efficiency of decreased capture performance combined with increased dilution. As the outlet diameter increased for a constant outlet elevation, the capture efficiency increased. As observed before, the removal performance peaks and then decreases as the diameter increases, again reflecting the tradeoff of capture and treatment. The maximum removal was observed at an outlet height of 4.0 feet and an outlet diameter of 1.5 feet. Even though the effective volume is small, the rate of discharge was so great that 100 percent of the year's runoff flows were captured. This suggests that a basin with a large outlet, possibly a weir, offers the best capture and removal performance. This is a different case than a basin with no outlet. With no outlet the maximum depth is maintained (minus evaporation etc. losses) and any runoff is immediately bypassed with no treatment. With a large outlet below the maximum depth, the runoff will pass through the basin and receive some degree of treatment by dilution. Extrapolating these results to areas outside the solution surface, the limiting maximum removal configuration would be a drawdown rate as high as the maximum inflow rate, with the discharge height at the top of the basin, i.e. no bypass, but all the runoff would be diluted to some degree as it passed through the basin. These trends suggest that optimal quality control would be provided by a basin that is partially full of water to provide dilution. This conclusion is based on the supposition that pollutant removal follows the exponential removal curve and that there is complete mixing in the basin. The latter assumption is hardly appropriate for sedimentation. The computer costs associated with the simulations are presented in Table 14. STATISTICAL TECHNIQUES Event Definition A preliminary task in statistical analysis is the grouping of raw data into independent events. A commonly used method is the separation of hourly rainfall values by a minimum number of hours with no rain. Serial Table 14. Computer costs of simulations. Procedure Cost * Dollars Runoff Block 24.6year 3.25 Oneyear 0.75 Storage/Treatment Block 24.6year 6.25 Oneyear 0.60 Synop Interface 1.25 24.6year runoff 1.75 * Average costs for low priority execution on the University of Florida system. Normal priority is approximately four times as much. autocorrelation has been used to define this minimum interevent time (Medina 1976). Howard (1976), Hydroscience (1979) and others have suggested that rainfall events occur as a Poisson process, and the time between events is exponentially distributed. The exponential distribution is a special case of the gamma distribution with the coefficient of variation (standard deviation divided by the mean) equal to unity. A cumulative distribution of time between events was presented in Figure 6. The gamma function has been widely applied in hydrology (Haan 1977). Traditional Design of Flood Control Basins The traditional sizing of stormwater detention facilities has been based on the control of a single "design" storm event. These basins are designed to capture the runoff resulting from a storm expected to occur for a given duration on the average once every N years (Haan 1977). Typical values of N range from 150, although incorporation of downstream risk assessment governs the value of N. The typical design storm analysis employs ranking particular storms (e.g. annual maximum 60 minute and 24 hour rainfalls) over a time period and assigning an extreme value probability distribution to the resultant sequence. From this distribution, return periods are assigned to storms of given magnitudes and durations. Figure 29 depicts the relationship between the parent distribution and resulting extreme value distributions. Figure 30 presents a cumulative extreme probability distribution (normal) used to determine the return period of river flood flows. Because this method does not retain information on the time between events, there is a loss of information and the method is said to be inefficient in terms of the data (Haan 1977). One unobtainable parameter whose value is necessary for accurate flow routing is the effective volume, defined as the actual storage volume available at the beginning of a storm, which is a function of antecedent conditions. Some municipalities require that Figure 29. n2 .n,9 y (days) Distribution of the largest sample value from a sample size n from an exponential distribution. 110 . 0 o ioi 0 70 so Z 0 *n Bo ~ RETURN PERIOD ( yrs ) 1.01 1.It 2 5 PERCENT GREATER THAN II ai I6 D0 0 70 ,O 60 40 10 20 I10 50 so oo zoo 10 A I I 0 0 0 iJThiTh~ ~ 1 1' 11, ,, I I 1 7 1 71II I I T Figure 30. Normal probability plot of Kentucky River data. CA Oi 0 I I 1 0o 0 0 0 Do 70 Ao T AU 0 1 tA I t PERCENT LESS THAN HHIIIII I1'11 H H+HHttH V M., IM, 10 i,IlllilliTi11l",IIF,llii, IL4 11I .It ponds be built to contain the runoff from urbanized areas (subdivisions, parking lots, etc. ) resulting from a design storm. The Rational Method, an extension of the design storm concept, is widely used for this purpose. The design storm method is relatively straightforward and does not require computer solution, hence it receives high ratings on ease of application, though as Haan (1977) points out, there is no direct theoretical connection between the solution and the underlying mechanisms governing the storm events. While this method is successfully used for flood control design, no criteria have been established for determining a design storm for quality control. Aggregate Statistical Methods Independently, two groups have developed statistical approaches for designing urban stormwater detention facilities. Howard (1976) presented the theoretical framework for analyzing the interevent times and volumes of combined sewer overflows resulting from various storage/treatment configurations. His derivation was based on approximating intensity, duration and interevent time as independent and exponentially distributed random variables. As part of a study evaluating the longterm performance of stormwater control devices, Di Toro, et al. (1979) derived an analytical expression for the effective volume of a stormwater detention facility available at the beginning of a storm event. Like Howard's method, this technique retains information on the time between events an important parameter for flow routing analyses. The method is based on the SYNOP results for rainfall event statistics: intensity, depth, duration and interevent time; converting them to runoff values; setting up the respective equations for effective volume and solving them. The result is a set of graphs which enable the user to plot the solution surface for percent of flow captured (C) and effective volume (Ve), as a function of the constant drawdown rate (Qc) and the ratio of the empty basin volume (Vb) to the mean runoff volume (Vro). The algorithm requires repetitive application to obtain an optimal basin size for maximum capture efficiency. The method presents a straightforward procedure for a simple catchment, single basin system (Dever, 1980). Data Input The Atlanta rainfall event statistics were obtained from the previous runs of SYNOP. Runoff event parameters were obtained from the rainfall values via a linear conversion factor. The STORM equation was used to determine the volume conversion factor, based on the percent imperviousness for the catchment, Cro = 0.15 + 0.751 (10) where Cro is the runoff conversion factor, and I is the percent of the catchment area that is impervious. With 1=0.37 for the catchment data, Cro=0.4275. The conversions produced a mean runoff volume of 19000 cubic feet based on the mean event depth of 0.212 inches over the catchment area of 24.7 acres. The mean event volume is similar to the value obtained by the SWMM simulation (18022 cubic feet). As mentioned earlier, the conversion method does not account for the reduction in the number of events resulting from catchment capture. This results in a total of 504 inches of runoff for the entire 24.6year record, as compared with the 388 inches obtained by the Runoff Block. Vb/Vro ratios were calculated to correspond to the volumes used in the simulations. The resulting ratios are presented in Table 15. Table 15. Determination of normalized volume ratios. Basin volume Normalized volume ratio (cubic feet) Vb/Vro 7744 0.41 15014 0.79 29064 1.53 92420 3.74 167835 8.83 There was a misrepresentation of the normalized discharge ratio in Di Toro's work. 1. The product QcTi was expressed as the average drawdown between storms. The concept of average drawdown between storms implies that mass continuity be preserved. With no bypass, the average volume entering the basin is equal to the average runoff volume, and represents a limiting value of the average longterm drawdown between storms. The average drawdown would be even less if the average volume entering the basin is less than the average runoff volume, due to bypass. If the product of Qc and Ti were truly the average drawdown between storms, then the ratio (QcTi/Vro) would always be less than or equal to unity; yet relationships are developed for values up to infinity. 2. The product of Oc and Ti would only equal the average drawdown between storms if the time series was complete homogeneous, with mean event volumes occurring at mean interevent intervals. For all other time series: a. the product of Oc and Ti has no relationship to average values; b. the product of Oc and Ti is always greater than the true average drawdown between storms; and, c. the ratio (QcTi/Vro) is not bounded by continuity constraints. This is why values greater than unity are realized. The average drawdown concept developed by Hydroscience, Inc. is a plausible yet erroneous expression. The ratio QcTi/Vro is used in this study merely as a normalized discharge rate. A solution surface of capture performance was prepared as a function of basin volume and pumping rate. The grid was created by using Figure 31 (see arrows) as follows: 1. enter the lower graph at the respective volume ratio (Vb/Vro); 2. move horizontally until intersecting with the normalized discharge curve (QcTi/Vro); 3. move to the upper graph at the effective volume ratio (Ve/Vro), the common side between the graphs; 4. continue up until intersecting the runoff volume coefficient of variation curve (cv); and 5. finally move horizontally and exit at the estimate of capture efficiency (C). This process was repeated for 25 combinations of volume sizes and drawdown rates. NORMALIZED EFFECTIVE VOLUME Ve/Vro 1.0 2.0 3.0 4.0 50 0.4 0.2 0.0 1.0 2.0 3.0 4.0 LU 0.6 CV = 1.38 0.8 CV= 1.22 I I I 1.0 0.5 0.75 1.0 2 510 NORMALIZED DISCHARGE, QcTi/Vro Relationship of capture efficiency (C) with normalized basin volume, normalized discharge rate and mean volume coefficient of variation. 5.0 1 1 0,1 Figure 31 . Capture Performance Results The results are presented in Figures 32 and 33 and Table 16. Table 16. Estimates of flow capture efficiency (C) as a function of basin volume and constant discharge rate: statistical results. Normalized Discharge Ratio Normalized Volume 1 2 4 7 10 Ratio 0.41 0.22 0.23 0.24 0.30 0.30 0.79 0.40 0.47 0.48 0.49 0.49 1.53 0.61 0.68 0.70 0.70 0.71 3.92 0.86 0.90 0.91 0.92 0.92 4.63 0.90 0.93 0.93 0.94 0.94 Isopleths of capture efficiency were drawn which emphasized the apparent insensitivitiy of the performance to varying pumping rates. This relationship exists due to the combined shapes of the upper and lower curves. The capture efficiency is most sensitive to the coefficient of variation and effective volume ratio (Ve/Vro) at the lower end of the Ve/Vro axis. However, at the lower end of the Ve/Vro axis, the effective volume ratio is relatively insensitive to the pumping rate, for the lines converge near a QcTi/Vro of 1.0. Conversely, where the effective volume is most sensitive to the pumping rate, at the upper end of the Vb/Vro axis, the percent capture is least sensitive to effective volume, for 81 10.0 9.0 8.0 7,0 o % 6.0 LU n 5.0 0 492 S4.0  N 4.0 +91 0.90 J nz 3.0 00.80 2.0 +70 0.70 1.0 0.50 +29 0.0o I IIII 0 1 2 3 4 5 6 7 8 9 NORMALIZED DISCHARGE, QcTi/Vro Figure 32. Solution surface of flow capture efficiency (C) as a function of basin volume and constant discharge rate: 1953 statistical results. 0.9 3. .3 0.8 0.7 1.50 0.6 0 Z 0.5 0.77 LL. L 0.4 U  0,40 O_ 0.3 0.2 0.1 0.0 I II! 0 I 2 3 4 5 6 7 8 9 10 NORMALIZED DISCHARGE, QcTi/Vro Figure 33. Flow capture efficiency as a function of basin volume and constant discharge rate: 1953 statistical results. the slopes are the flattest. The greatest overall sensitivity lies in the "middle" region of the graphs. The maximum variation for any given volume was an 11 percent increase from 64 percent to 75 percent for a ratio of 1.6. The largest Vb/Vro ratio available in Figure 31 is 5.0. This limitation precluded a complete comparison with simulation results, where Vb/Vro ratios up to 9.3 were analy zed. Removal A major weakness of using the statistical method for estimating quality control is the inherent assumption of absolute pollutant removal efficiency. In the design of a detention facility for quality control, the determination of a removal efficiency is the primary objective. It was difficult, therefore, to assign a removal expression. It was tempting to use the constant removal value incorporated during each time step in the S/T simulation, however, the two terms are not conceptually equivalent. The statistical method essentially treats the removal mechanism in the basin as a black box in which the constant removal refers to the total captured flow during the complete time history. The simulation employs time steps to route the flow through the basin, and the constant removal term applies only to the volume within the basin during that time step. This implies that for any runoff volume which remains in the basin longer than one time step, the total removal efficiency will be greater than the constant removal term. To make an estimate of removal efficiency would be presupposing the solution in this study. However, an estimate of removal efficiency can be obtained by taking the product of the percent capture and an assigned constant removal percentage. The resulting solution surface will have the same shape as the capture performance presented in Figure 32, but the value of the isoquants will be altered by the removal factor. Analysis Using Simulated Runoff Data For further study, the statistical analysis was repeated on runoff data obtained from the SWMM simulation. The values determined by SYNOP for the data generated from the Runoff Block (see Table 5) of SWMM are compared to the converted values in Table 17. Several differences were noted. The most obvious is that there are 24 percent more events modeled in the statistical method than the simulation. This difference affects the total amount of runoff predicted by the two methods. The simulation yields 308 inches of runoff while the use of a conversion factor yields 504 inches of runoff, or 30 percent more runoff over the 24.6year period. This difference is not apparent from comparison of the estimates of mean runoff volume, where there is only a 5.47 percent difference in the Table 17. Comparison of simulated runoff mean event statistics with rainfall conversion values. Number of events Volume (in) cv Duration (hr) cv Intensity (in/hr) cv Interevent time (hr) cv Minimum interevent time (hr) to yield cv near 1.0 Simulated 1920 0.201 1.222 5.066 0.972 0.043 1. 148 111.71 1.000 4 Conversion 2391 0.212 1.384 7.824 1.134 0.032 1.356 90.10 1.004 8 two methods. This is an interesting point. Because the statistical method deals with basin volumes normalized to the mean event volume, the 30 percent continuity difference between the methods is not reflected in the flow capture solution surface. This implies that satisfying the continuity equation may not be a requisite for a good solution methodology. An important difference is that the minimum interevent time was reduced from 8 hours to 4 hours to obtain a coefficient of variation for interevent time close to unity. At first, this appears to be due to the presence of an effective detention time inherent in the catchment storage, characterized by the attenuation of magnitude and lengthening of duration. The values for the mean duration contradicts this thought, being two hours less than the rainfall mean., This decreased duration may be the result of roundoff error in transferring runoff data into the NWS format for subsequent SYNOP runs. Flows less than 0. 125 cubic feet per second are rounded down to 0.0 inches per hour, based on a catchment area of 24.7 acres. Volume ratios and pumping rates calculated from these new values are identical to those used in SWMM, as the same SYNOP run was the basis for those values. The performance determination was repeated on these new volume ratios and pumping rates. The results are summarized in Table 18. Table 18. Estimates of flow capture efficiency (C) as a function of basin volume and discharge rate: statistical results with simulated runoff means. Normalized Volume Ratio 0.43 0.83 1.61 4.13 5.00 Normalized 1 2 0.28 0.28 0.44 0.49 0.64 0.70 0.89 0.93 0.92 0.95 Discharge Ratio 4 7 10 0.29 0.29 0.30 0. 50 0. 51 0. 51 0.73 0.74 0.75 0.93 0.94 0.94 0.95 0.96 0.96 
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PAGE 1 Publication No. 58 LONGTERM PERFORMANCE OF STORMWATER DETENTION FACILITIES: A COMPARISION OF DESIGN METHODOLOGIES by Gay F.E. Goforth University of Florida Gainesville, FL 326112013 PAGE 2 LONGTERM PERFORMANCE OF STORMWATER DETENTION FACILITIES: A COMPARISION OF DESIGN METHODOLOGIES By Gary F. E. Goforth PUBLICATION No. 58 FLORIDA WATER RESOURCES RESEARCH CENTER RESEARCH PROJECT TECHNICAL COMPLETION THESIS ENGINEERING AND INDUSTRIAL EXPERIMENT STATION PROJECT NUMBER 80W31 THESIS SUBMITTED JUNE, The work upon which this thesis is based was supported in part by funds provided by the Water Research Program, Engineering and Industrial Experiment Station, University of Florida, Gainesville PAGE 3 ACKNOWLEDGEMENTS In tel' act ion i s fl l' e e ; ass u c h lowe t han k s to ma n y individuals at Black Hall and the Center For Wetlands who have contributed to the completion of this thesis and to my career at the University ofl Florida. The diversity ofl professionals in the department has provided a constant challenge to maintain an awareness of the many, yet similar, flacets ofl environmental engineering sciences. A large debt is acknowledged to Bob Dickinson who several times pulled me up .when I was close to drowning while SWMMing. Thanks also go to Steve Nix flor his help on SIT. The use ofl the computer resources at the Center For Wetlands, Black Hall and the Northeast Regional Data Center was invaluable. Thanks to Anelia Crawford flor the drafted fligures. The direction ofl this thesis is credited to Dr. J. P. Heaney; the stability ofl the content is credited to Dr. W. C. Huber; the inflluence of Dr. H. T. Odum is reflected in the holistic approach to the problem assessment and solutions. Theil' guidance and attention are greatly appreciated. Certainly the greatest debt is owed to my wifle, Karen. Her patience, sacrifice, programming and typing ability and overall good spirits in the flace of adversity will be florever appreciated. ii PAGE 4 I \. TABLE OF CONTENTS ACKNOWLEDGEMENTS . . . i i LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS . . . . v vii x ABSTRACT .X i i I NTRODUCT I ON . . 1 1 3 6 CASE GENERAL OVERVIEW .. ..... SYSTEM DESCRIPTION . . . DEFINITION OF CONTROL UNIT .. ... CLASSIFICATION OF METHODS STUDY . CATCHMENT CHARACTERIZATION RAINFALLRUNOFF CHARACTERIZATION data .... SYNOP. . Quantity .... BASIN CHARACTERIZATION Flow Conditions .. Removal ...... Theory Settling. Comparison Flow Conditions .8 1 1 1 1 1 2 1 2 1 3 1 5 23 23 24 24 29 METHODOLOGIES. .. ... 32 ANALYTICAL. . 32 EMPIRICAL . . 33 SIMULATION. . 36 STORM. .. .... ....... 36 SWI'1M . .. ... 36 Overview. . . 36 Data Input Block 38 Data Input Storage/Treatment Block 39 Constant Simulation 45 Variable Di$charge Simulation ... 46 Removal Mechanism .................. 47 OneYear versus.25Year Simulation. 50 Block Results. . 50 Storage/Treatment Block Results. 52 iii PAGE 5 STATISTICAL TECHNIQUES Event Definition ............ Traditional Design of Flood Control Basins. Aggregate Statistical Methods .. Data Input. . . Capture Performance Results Removal.,. . . Analysis Using Simulated Data COMPARISONS. .. DISCUSSION . GENERAL APPLICATION OF METHODOLOGIES APPENDIX A Program Listing and Data Input APPENDIX B BASIN Development and Listing APPENDIX C Detention Time. REFERENCES BIOGRAPHICAL SKETCH iv 70 70 72 74 75 80 83 84 87 9 1 93 97 1 03 1 05 1 1 2 1 1 5 PAGE 6 Table 1. 2. 3. 4. 5. 6. 7. 8. 9. LIST OF TABLES Case study catchment characteristics. SYNOP results of 24.6 years of Atlantal Georgia rainfall. Relationships between pollutant loads and flow volume (FLOW). Comparison! of Runoilil Block results using hourlYI daily and weekly rainfall input. SYNOP results of 24.6 years of simulated runoflf data. Determination of normalized volume ratios (Vb/Vro). Calculation oil constant discharge rates (Qc) (Ti = 111.17 hours; Vro = 18022 cubic feet>. Comparison of mean runoff event parameters for 1953 with the 24.6year record (minimum interevent time = 4.0 hours). Runoff Block 24.6year simulation summary. 10. Examples of Storage/Treatment Block summaries. 11. 12. 13. Estimates of flow pollutant removal function of basin discharge rate: capture efficiency efficiency (R) as a volume and constant simulation"results. (C) and Estimates of fllow capture efficiency (C) and pollutant removal" efficiency (R) as a function of drawdown height and rate (Vb/Vro=1.61): 1953 simulation results. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro = 1.61): 1953 simulation results. v 1 2 1 6 35 38 41 42 46 52 51 53 54 65 66 PAGE 7 14. Computer costs simulations. 71 15. Determination normalized volume ratios. 76 16. Estimates capture (C) as a function of basin volume and constant discharge rate: statistical results. 80 17. Comparison simulated mean event statistics with rainfall conversion values. 85 18. Estimates of flow capture ef.piciency, (C) as a function of basin volume and discharge rate: statistical results with simulated runoff means. 19. Estimates of hydraulic volume and detention time of control units associated with a single rainfall event. vi 86 94 PAGE 8 LIST OF FIGURES Figure 1. 2. 3. 4. 5. 6. 7. 8. 9. Representation of the hydrologic cycle. Discretized subsystems of the hydrologic c y c 1 e. Pro c e sse s de fin i n g ( the per for ma n ceo r a control unit. Schematic of Case Study catchment area. Characterization Or the various methodologies. Comparison of theoretical and observed distributions or interevent times ror Minneapolis/St. Paul airport. SYNOP values for mean event volume and duration as a function of minimum interevent time. SYNOP values for mean event intensity and interevent time as a function of minimum i ntereven t time. A comparison Or rainfall and runoff time series depicting the reduction in number of events and the reduction in the event volume. 10. Definition of interception and storage for storm events. 11. 12. 13. 14. Representation of a time series of runoff rlows. Development of overflow rate in an ideal iettling basin. Effluent concentrations for a firstorder removal process in n completely mixed plugs. Removal efficiency for a firstorder removal process demonstrating the effect of increased vii 4 5 5 7 9 1 4 1 7 1 8 20 21 22 25 28 PAGE 9 turbulence; n=1 for and n=1 for completely mixed. 28 15. Effluent responses to a step input. 30 16. Comparison or real and plug flow reactor volumes for a firstorder reaction. 30 17. stage relationships as calculated by BASINi constant and variable' discharge. 40 18. Time series of constant influent pollutant concentration. 44 19. Removal eQ.uation used in SIT Block. 48 20. Comparison of effluent concentrations under ideal plug flowl ideal completely mixed and as calculated with SWMM SIT completely mixed routingi step input of pollutant. 49 21. Solution surface of flow capture efficiency (C) as a function of basin volume and constant discharge rate: 1953 simulation results. 55 22. Solution surface of pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: 1953 simulation results. 56 23. Pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: 1953 and 24.6year simul tion results. 57 24. Pollutant removal efficiency (R) as a function of basin volume under variable di'scharge conditions: 1953 simulation results. 61 25. Solution surface of pollutant removal efficiency (R) as a function of drawdown height and drawdown rate (Vb/Vro = 1.61): 1953 simulation results. 63 26. Pollutant removal efficiency (R) as a function of drawdown height and constant discharge rate (Vb/Vro. = 1.61): 1953 simulation results. 64 27. Solution surface of pollutant removal efficiency (R) as a function of outlet height viii PAGE 10 and outlet diameter (Vb/Vro = 1.61): simulation results. 1953 28. Pollutant removal (R) as a function of outlet height and outlet diameter 67 (Vb/Vro = 1.61): 1953 simulation results. 68 29. Distribution of the largest sample value from a sample size n from an exponential distribution. 73 30. Normal probability plot Kentucky River data. 73 31. Relationship of capture efficiency (C) with normalized basin .volume, normalized discharge rate and mean volume coefficient of variation. 79 32. Solution surface of flow capture (C) as a of basin volume and constant discharge rate: 1953 statistical results. 33. Flow capture as a function basin volume and constant discharge rate: 1953 statistical results. 81 82 34. Comparison 89 35. Comparison of pollutant removal efficiency. 90 B1. Development of BASIN. C1 Various control unit configurations: steadystate conditions. C2 Various control unit configurations: nonsteadystate conditions. ix 1 04 1 07 11 0 PAGE 11 a, b ai A c C cO Cro CV dr Dr Dro e H Hd hp k I ir Ir Iro kO ki L LIST OF SYMBOLS USED coerricients or runorr power percentage Or flow passing through basin i crosssectional area Or rlow errluent concentration rlow volume capture erriciency inrluent concentration runorr conversion ractorcoerricient Or variation individual rainrall event duration mean rainrall event duration mean runorr event duration base or natural logarithm height or settling zone height at which discharge begins and ends height or particle entering settling zone rirstorder reaction coerricient percent Or catchment area that is impervious individual rainrall event intensity mean rainrall event intensity mean runorr event intensity initial rirstorder reaction coerricient linear rlow coericient or basin i length or rlow element x PAGE 12 n N G Qc GcTi/Vro R SA SIT t td Ti v V Vb Vb/Vro Ve Vi vo vp Vr Vro Vs xo turbulence coefficient return period for design storm volumetric flow rate constant discharge rate normalized discharge rate pollutant removal efficiency surface area of settling zone storage/treatment elapsed time detention time of system mean interevent time velocity of flow volume of flow element empty volume of basin normalized basin volume effective volume volume of basin i overflow rate (surface loading rate) particle settling velocity mean rainfall event volume (per unit surface area) mean runoff event volume (per unit surface area) volume of settling zone percentage of particles with vp less than vo xi PAGE 13 Abstract Thesis Presented to the Graduate Council the University Florida in Partial the Req,uirements the Degree Master or Engineering LONGTERM PERFORMANCE OF STORMWATER DETENTION FACILITIES: A COMPARISON OF DESIGN METHODOLOGIES by Gary F. E. Gororth June 1981 Chairman: James P. Heaney MaJor Department: Environmental Engineering Sciences A general overview empirical, analytical, statistical and simulation techniq,ues ror evaluating stormwater detention systems is presented. The benerits and limitations of these methods in designing a control device water quality improvement are emphasized. A detailed analysis compares continuous simulation utilizing the Protection Agency's Storm Water Management Model with the statistical techniques advanced by Hydroscience, Inc. The general dynamics or storage and rlow xii PAGE 14 elements are discussed, emphasizing the importance of detention time in defining a time frame for evaluating systems. Chairman u xiii PAGE 15 ''I INTRODUCTION GENERAL OVERVIEW In the urban environment, combined and separate storm sewer overflows contribute the same amount of contaminants to receiving waters as do secondary treatment efrluents (Heaney, et al. 1975, C. E. Q. 1978>' Presently, simple storage/treatment devices, i. e. one or two component systems such as a stormwater detention basin, provide a costerrective tool for quantity as well as quality control Or these storm flows. While the design Or these devices has traditionally been based upon a single storm event, the additional information provided by longterm analyses has recently encouraged their adaptation. The engineer or planner concerned with the design of a detention facility for the quality control of stormwater runoff has a variety of solution methodologies available: empirical approaches utilizing average annual values; analytical methods based on solutions to the flow governing equations; simulators amenable to rigorous search techniques; and statistical techniques involving rainfallrunoff parameter distributions. No one method, or coordinated coupling of methods, has been documented as the most costefrective for PAGE 16 2 all applications. This is in part due to the lack of an available longterm data base, but also reflects the lack of comparative studies. This thesis evaluates methodologies available for analyzing the longterm performance of stormwater runoff control devices. A detailed description of these methods is not the intent. The manuals referenced for each provide that service. Rather, the benefits and limitations of these methods in designing a control device for water quality improvement are emphasized. three criteria: The comparison consists of 1. problem assessment, i. e. how does the particular method define the system; 2. ease of application, e. g. data or computer r equ i rements, or c umb ersome tec hn i ques, and associated costs; and 3. accuracy of results, both absolute and relative to data requirements. Because the longterm performance of detention facilities has not been well documented, there is no available data base to definitively compare the accuracy of the methods. ObJectively, this study presents an opportunity to establish relative estimates of the longterm performance of storage/treatment devices for stormwater quality control. The optimal design of a control device will depend on problem specific constraints such as discharge quality standards and economic considerations. PAGE 17 SYSTEM DESCRIPTION The following definition of a system is presented as a framework to maintain conceptual consistency. A system is any structure, device, scheme, or procedure, real or abstract, that interrelates in a given time reference, an input, cause, or stimulus, of matter, energy or information, and an output, effect, or response, of information, energy, or matter. (Dooge 1973, p. 4) This functional interrelationship of inputs and outputs for 3 a given time reference provides a basis for addressing water quality problems in a spectrum of hydrologic units, from urban stormwater systems to lakes threatened with cultural eutroph ication. Before evaluating the performance of a particular system, the hierarchy of systems which influence that performance must be recognized. A classical representation of the hydrologic cycle is presented in Figure 1. Storages and flows of water are the principal elements in the system, although the influences of solar energies, land morphologies and other factors are implicitly included. The system depicted in Figure 1 can be partitioned into discrete subsystems defined by characteristic storages and flows, as shown in Figure 2. These subsystems can be further subdivided into individual components, or contT'ol units, whose boundaT'ies similarly reflect the storages and flows emphasized. The basic hydrologic characteristics which define the performance of a control unit, as depicted in Fi g UT'e 3,are: PAGE 18 4 I , I ",_.;., == OCEAN .., : f 't' , _____ .,... j Ground Water ,', .. ,',M".. ..... ':1 :,",: .... ",.': .. ..:. ..... ,.:, ........... ... Figure 1. Representation of the hydraulic cycle. PAGE 19 Figure 2. Figure 3. Throughfo II lf!.lL Aquifers Streams, lakes, and rivers Precipito lion Oceans Discretized subsystems of the hydraulic cycle. Variables Variables characterizing characterizing E:lement af physical system Inflow outllow processes processes Processes defining the performance of a control unit. 5 PAGE 20 1. The source oP the mass, the unit's place in the system and its relation to other units; 2. 3. the dynamic storage and Plow conditions; and the removal mechanism. DEFINITION OF CONTROL UNIT 6 The Pollowing analysis centers on the longterm pollutant removal effectiveness of a hypothetical detention facility. The control unit is a single basin which receives the stormwater runoff Prom an urban catchment, and discharges to an undescribed receiving water. A schematic oP the system is presented in Figure 4. The data source is a 24.6year record oP hourly rainfall values obtained from the National Weather Service. The system boundaries 6f the control unit are drawn at the inlet and outlet. As such, it is not Just the rainfall which is the forcing function, but the runoff, a result of the rainfall's interaction with the catc hment. The pollutant source is the constituent contaminants of the runoff sand, debris, dust, etc. The removal mechanism responsible for pollutant control is sedimentation, and the removal characteristic is based on the treatment time in the basin. The removal kinetics are defined by the hydraulics within the basin, as determined by basin geometry and the inflow and discharge characteristics. These are the major influences on control efPiciency and become the design parameters. PAGE 21 RRAINFALL RoRUNOFF ETEVAPOTRANSPIRATION I INFILTRATION W WIDTH OF CATCHMENT' L LENGTH OF CATCHMENT OF :DETENTION FACILITY' 0DISCHARGE TO RE;CEIVING WATER Figure 4. Schematic of Case Study area. 7 PAGE 22 ; CLASSIFICATION OF METHODS Several methodologies are available ror estimating the longterm performance of stormwater detention facilities. The approaches are all models of the same complex process, yet differ conceptually and mechanistically. Figure 5 is a schematic depicting the relationship of the various methodologies. For the purpose of this thesis, the following classifications will be used: 1. Analytical approaches utilize some combination of the general mass continuity equation and the advectivedispersion equation to describe the rlows, storage, and pollutant removal characteristics Or a control unit. 2. Empirical approaches are derived from or guided by experience. Although literally implying the lack of a 8 theoretical background, the expression is used to denote methods which have been developed in scientific and engineering practice. 3. Two types of statistical techniques are widely used (Chow 1964). Frequency analysis methods are based on approximating the value of a random variable with a probability density function, from which frequencies of occurrence may be assigned. Regression and correlation analyses deal with the description of the relationship between two or more variables. PAGE 23 9 f (v ,q) EMPIRICAL ANALYTICAL SIMULATION t STATISTICAL Figure 5. Characterization of the various methodologies. PAGE 24 10 4. Digital simulation methods were developed to exploit the ability of highspeed computers to manipulate mathematical expressions. The main objective of these methods is to deterministically model the dynamic processes in a physical system. Rarely does a definitive demarcation exist between solution methodologies; there are overlaps and extensions from one to the next. As a modell each method represents simplificationsl compromising between ease of application and accuracy. The empirical and statistical approaches provide firstcut approximations based on a small data The more complicated simulations are generally regarded as more accuratel although they may have extensive data or computational PAGE 25 CASE STUDY CATCHMENT CHARACTERIZATION Usersupplied catchment data are input for most models. The extent of the data collection is dependent on the requirements of the particular method employed. As indicated in Figure 4, there are no streams, lakes or groundwater flows. For simplicity, there was no initial abstraction, areas of depression storage or other consumption of water. The flow routing geometry was kept as simple as possible. Conceptually, the catchment was a sloping plane with no gutter or pipe networks. All the runoff flowed directly to a dummy outlet on the downslope side. The runoff from the entire catchment was routed to the proposed basin, and was subsequently discharged to a local receiving water. The data were based on observed values for a drainage basin in Gainesville, Florida, and are presented in Table 1 (Huber, et al. 1981>' In an actual catchment, waste characteristics would be obtained by running column settling tests on runoff samples. PAGE 26 Table 1. Case study catchment characteristics. Total area = 24.7 acres Impervious area :::: 37 percent No depression storage or initial abstraction Average catchment slope:::: 0.040 ft/ft :::: 211 ft/mile Maximum infiltration = 2.5 in/hr Minimum infiltration = 0.52 in/hr Evaporation:::: 0.1 in/day Population density = 500 people/square mile RAINFALLRUNOFF CHARACTERIZATION Rainfall Data ,As the storages and flows of water are the principal elements in the catchment system, rainfall is the driving force. Longterm rainfall data are available on several 12 time bases, e. g. continuous gages or discrete hourly, daily, monthly or yearly records. Rainfall data are characterized by volume (depth over the catchment area), average intensity, duration and time between events. The rainfall data source utilized for this study was the National Weather Service (NWS) tape for 24.6 years (June 1948 December 1972) OT hourly rainfall at Atlanta, Georgia. The standard NWS format is to record hourly rainTal1 values in hundredths oT an inch on days when there is rain. Days without rain are not recorded on the tape. Hourly data Tor the first day oT each month are recorded regardless of whether it rained or not. PAGE 27 \ ..... j 13 SVNOP For methods requiring average event statistics, hourly rainfall data may be analyzed with SVNOP, a computer package developed by Hydroscience, Inc. (1979) to determine synoptic statistics of data time series. Rainfall volumes, intensities, durations and interevent times are the principal parameters evaluated in SVNOP. Available options include complete statistics on an event basis and time basis, e. g. yearly averages. Cumulative conditional probabilities (i. e. I given that rain has occurred) and return periods for hourly magnitudes are also calculated, based on the California method of probability plotting. The grouping of hourly data into storm events is based on the minimum number Or dry hours between rainfalls, an input variable termed the minimum intervent time. Assuming that the storm events occur as a Poisson process, the time between events is exponentially distributed. The exponential distribution is a special case Or the gamma distribution with the coefficient of variation equal to unity. Figure 6 demonstrates the relationship between theoretical and observed results for the cumulative distribution Or interevent times. The gamma distribution has been widely applied in hydrology (Haan 1977). To define events, the minimum interevent time is varied to obtain a value close to unity for the coefficient of variation (cv) associated with the interevent time. The SVNOP manual PAGE 28 F gure 6. 99 w/ V w 98 :J 1 g 97 Z w > 96 I / V"00i; / .j / j (.!) 0 95 r/; {/ i'l/'1.25 1 PAGE 29 15 recommends an initial trial of three hours for the minimum interevent time. SYNOP was run on the entire 24.6year record Or Atlanta rainfall to determine the storm statistics. The results of these runs, presented in Table 2 and Figures 7 and 8, give some idea of the sensitivity of the, results to the choice of the minimum interevent time. The computer costs averaged $6.25 per run. eight hours speciried as the minimum number of dry hours defining an event, the coerficient of variation for the mean interevent time was 1.004. Values for the means of the parameters were taken from this run, e. g. the mean volume (Vr) of a rainfall event was 0.495 inches. Notice that Vr does not the product of 11' and Dr. This is because Vr is the mean of the products of the individual events' intensity (ir) and duration (dr), which is not necessarily to the product of the mean intensity (Ir) and the mean duration (Dr), i. e. Vr = mean (irdr) which is not the same as (mean ir)(mean dr) = IrDr. Runoff Quantity The interaction Or rainfall and the catchment generates runoff. The of runoff is determined by the influence of infiltration, evaporation, consumption patterns and land use (Eagleson 1970). The watershed system response to these interactions has been evaluated by hydrologists for many years. A comparison of rainfall and runoff time PAGE 30 " ( cTable 2. SYNOP results or 24.6 years of Atlanta, Georgia rainfall. Minimum # Number Volume cv Duration cv Intensity cv Interevent cv of dry hours Vr Dr Ir time Ti (in) (hr) (in/hr) (hr) 3 3215 0.367 1.540 4.642 1. 126 0.078 1.372 66. 73 1.269 5 2596 O. 454 1.424 6.646 1.124 0.077 1.348 82. 62 1.067 8 2381 0.495 1.384 7.824 1.134 0.077 1.356 90. 10 1.004 12 2134 O. 552 1.332 9.817 1. 143 0.074 1.334 100. 55 0.917 0' PAGE 31 17 0.6 1.5 Z 0 1.4 tr CC c 0.5 1.3 .. lIW a :E 1.2 ::> I1 Z 0 0.4 W > 00 MEAN VOLUME 1.1 U Z A A CV LL PAGE 32 18 1.5 Z 0 .... 0.078 1.4 t( .c. "0::: c: .0.077 1.3 ,. >tJ... I0 en 0.076 1.2 Z IW Z IW Z 0.075 1.1 () z 00 MEAN INTENSITY I..l.. lJ... 0.074 CV 1.0 W W 0 ::E () 0.073 0.9 0 3 6 9. 12 MINIMUM INTEREVENT TIME, hr U t... 110 00 MEAN INTER EVENT 1.5 .r::. Z .. &A CV 0 W 100 ti 1.4 I0:: !=. 90 1.3 f Z W lJ... > 80 1.2 0 W 0:: IW Z I70 1.1 W Z () lJ... Z 60 lJ... 1.0 W W 0 ::?: u 5 0.9 3 6 9 12 MINIMUM INTEREVENT TIME, hr Fi gu re 8 SYNOP values fo r mean event intensity and interevent time as a function of minimum L.interevent time. PAGE 33 series. presented in Figure 9. depicts two phenomena characteristic of the rainfallrunoff process: 19 1. a reduction in the number of events due to the capture of low volume storms by the indigenous catchment storage capacity. e. g. depression storage and soil moisture capac i ty i and. 2. a reduction in the volume of the events due to the catchment storage and flow interception, e. g. infiltration rates. Analyses that deal with single runoff events are not sufficient to characterize these phenomena because the catchment storage and interception capacities are functions of antecedent soil moisture conditions. and are not constant. It becomes to retain as much, information as possible on the time between successive events. The event duration defines the reference time frame for differentiating between storage and inter.ceptor elements. A storage element can detain up to a maximum runoff volume per event. i. e. its detention time is greater than the event duration. An interceptor. on the other hand. can capture up to a maximum flow rate before bypassing Stormwater runoff control devices can also be characterized by storage and interception capacity. as presented in Figure 10. A representation of a time series of runoff flows is presented in Figure 11. a series of flow pulses separated by PAGE 34 <; FEB MAR I I II 0.0 II 2.0 I:l 'M JZ.i 1.0 JZ.i 0.0 APR MAY .1 I I JI J11 II. JUN 1.1 20 Maximum storage Minimum storage Figure 9. A comparison of rainfal I and runoff time series depicting the reduction in number of events and the reduction in the event volume. PAGE 35 a) INTERCEPTION b) STORAGE D EI"] TIME c) INTERCEPTION AND STORAGE 0: W0Z1F gure 10. Definition of interception and storage for storm events. TIME 21 PAGE 36 22 U') '+0 ... 0 ...J lL. 4.0 .lL.. lL. 0 2.0 Z ::> a:: 0 0 20 30 r 130 140 150 160 170 TIME, hr Figure 11. Representation of a time ser.ies of runoff flows. PAGE 37 23 relatively long peroiods oT no Tlow. The determination of runoff characteristics is a maJor step in the solution process and is where the methods vary the most .. The approaches compared here offer a sharp contrast in the representation of the rainfallrunoff process. The statistical and empirical approaches summarize runoff generation via linear conversion factors applied to rainfall statistics. On the other hand, the simulation technique utilizes some of the most refined concepts in deterministic hydrology. BASIN CHARACTERIZATION Flow conditions U The input to the basin is the runoff from the catchment area. The time series of runoff events depicted in Figure 11 suggests two realms of kinetics: rapid, relatively wellmixed during the runoTf event, followed by slower (less dispersion, turbulence> kinetics and possibly quiescent conditions during dry weather. Characterizing this time series of discontinuous flows entering the basin is a maJor obstacle in solution methods. Basin discharge may be either variable, as in the case of gravity drainage, or constant, via a pump or outlet restriction. systems, 1. e. Negative feedback is inherent in gravity when the water level is high, the outflow is high, and as such, tends stabilize the flow. It is PAGE 38 24 difficult to deal with this nonlinearity analyticallYi it is Tar easier to analyze a constant discharge rate. There has been no evidence to suggest that one is better than the other Tor pollutant removal. Removal Theory of settling Pollutant removal via settling is the most widely useful operation in water and wastewater treatment (Fair, Geyer and Okun 1968, Liptak 1974). In the design oT sedimentation basins, basic assumptions are incorporated: 1. inlet zone the influent is transformed to a uniform vertical distribution of particles. 2. settling zone there is steady, uniform flow and quiescent, discrete and unhindered settling. 3. bottom zone solids which enter the bottom zone are not resusp end ed. 4. outlet zone solids that do not enter the bottom zone leave in the effluent. These four zones and particle settling paths are shown in Figure 12. The maJor design parameter is the overflow rate (vo), defined as vo = H/td = (Vs/SA)/(Vs/Q)' = O/SA (1) where H is the depth of the settling zone ( L J, td is the detention time of the settling zone ( T J, Vs is the volume of the settling zone [ L3 J, PAGE 39 Q _.INLET ZONE H SURFACE AREA = SA PERPENDICULAR TO FLOW CROSS SECTIONAL AREA = A Vo BOTTOM ZONE OUTLET ZONE TRAVEL TIME = L 1/ = L Q/A LA V = = Q Q H H Q OVERFLOW RATE = Vo = = = t if/Q SA Figure 12. Development of overflow rate in an ideal 5 e ttl i n g ba 5 in. 25 PAGE 40 26 SA is the the settling zone ( L2 J, and Q is the in the_settling zone [ L3/T J. The settling is slow, such that it is the removal rates that important, than the state (Rich 1974). ideal conditions, settle at a velocity (vp) by Stoke's Law, and are removed iT vp is greater than vo. Additional particles are removed which enter the settling zone at a height (hp) less than The total basin removal is given by 'to R = (1xo) + (l/vo) vp dx (3 ) where R is the pollutant removal eflTiciency, and xo is the proportion oT particles with vp less than vo. Rarely do detention perTorm ideal conditions. Most OTten, design eTfliciencies are due to violations ideal assumptions caused by short circuiting and turbulence, which alter the kinetics flrom ideal quiescent conditions. Short circuiting is induced through thermal currents, wind action, influent inertia, etc. Resuspension of solids may occur as the .plow rate exceeds the scouring velocity. Thomas and McKee derived the PAGE 41 27 effect of longitudinal dispersion in a basin consisting of n completely mixed plugs (Fair, Geyer and Okun, 1968>' Figure 13 presents the relative effluent concentrations for an instantaneous injection of dye undergoing a first order decay as it passes through the basin. A completely mixed basin is shown as n=1, while an ideal plug 'Plow basin (n=infinity) would be represented by a spike at t/td ofun i t y. The net effect of altering the flow regime from quiescent to more turbulent conditions is the reduction of the reaction coefficient k (Fair, Geyer and Okun 1968; Rich 1974) Although there is no way to predict before operation the reduction for a particular basin, the phenomena can be represented as in Figure 14, where the reduction of k is given as k/kO = (1clcO)**n where k is the reaction coefficient, kO is the reaction coefficient under quiescent conditions, c is the effluent concentration, cO is the initial pollutant concentration, and n is the coefficient indicating the degree of turbulence, which increases as the flow regime diverges from ideal conditions. (4 ) Plug flow conditions are represented by n=O where k=kO and the pollutant decays according to cleO = e**(kt) or, R = 1c/eO "'" le**(kt). ( 5) PAGE 42 :t Relative time, t/td Figure 13. Effluent concentrations for a firstorder removal process in n completely mixed plugs. 1.0 o (.) 0.9 "(.) 0.8 .. 0.7 cj Z 0.6 8.5 W 0.4 '\ \ 1\ \1 \ \ r... l'.: rf!!:' I" In: > 0.3 ti 0.2 iiJ 0.1 0:: 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 FIgure 14. RELATIVE TIME, t/td Removal effIcIency for a firstorder removal process the effect of increased turbulence; for quiescent and n=l for completely mixed. 28 PAGE 43 Comparison Flow Conditions Plug flow and completely mixed removal regimes deTine the extremes of pollutant removal performance. By definition, the hydraulic regime in each plug is complete mixing. Therefore, under static conditions, e. g. a column 29 settling test, there is no difference between the two. The applicability oT transferring column settling test results to dynamic conditions was recently reexamined by White ( 1976). In tank studies, he observed reasonable agreement with column tests, although the results were highly dependent on the waste characteristics. The effect of longitudinal dispersion on plug flow performance has been studied to correlate plug flow and complete mixing under dynamic conditions PAGE 44 1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 INFLUENT EFFLUENT Dd plug flow, Yr' 0 x large dispersion VT"' 0.2 x a 0,5 a. b. intermediate amount of dispersion Dd "'VL'O 025 x Dd complete mix, L (l) Vx Figure 15. Effluent responses toa step input. 100 '* I "/ v. (I) lcomplete mixing) first Qrder "'I I .......... 64 i',.. Ill'." 200 K" ''', " ....... ylOO r... Ii 10 >. K r50 (lines of equal volume i. or holdlnll time) II _: lI1...... b( 20 .......... r. Lt'><' ...... !i"'r, 10 r.: rfr0,25 " r....... ,,2 .... ><... 0,0625 .... .......... .. 0 (plug lIow) ./ ..... t:". Q,QI Q,l Figure 16. Comparison of real and plug flow volumes foria firstorder reaction. 30 PAGE 45 31 These two solutions represent the removal erficiency extremes. The lower removal efficiency of complete mixing is a result or the basin concentration being continuously mixed with the inrluent, yielding a dilution or the influent but a concurrent increase in the basin concentration. In plug fiowl the basin effluent more clearly reflects the removal process occurring in the separate plugs. The difference between the steadystate solutions for firstorder reactions is graphically presented in Figure 16, which compares the volume of an ideal plug flow basin to the volume of a basin with dispersion yielding the same removal efficiency (Weber 1972>' From Figure 16 it is possible to predict the effect of implementing dispersion reducing mechanisms such as baffles. For example, by reducing the U dispersion factor from infinity (completely mixed) to 1. 0, the volume necessary to provide 90 percent removal is reduced by a factor of 2. There has been no widely used method for sizing SIT facilities with longterm stormwater quality control as the rna in 0 b J e c t i ve. Heaney, et al. (1979) presented the mechanics for determining the optimal combination of SIT for steady state conditionsl subJect to economic constraints. PAGE 46 t'lETHODOLOG I ES ANALYTICAL Analytical models are developed from a combination Of the general mass continuity and advectivedispersion equations. They range in complexity from simple steadystate approximations to more complicated variable flow solutions. The complexity of solution for detailed problems intimidates users and prohibits widespread application. Customarily, a simplification of the system's dynamic processes is necessary to obtain a solution. The analytical approach to stormwater detention facilities has been advanced by Medina (1976). Constant and variable (linear) flow and storage conditions were stUdied. Conservative and nonconservative pollutant routing were i"ncluded. Effluent concentrations were derived for "simple" forcing functions. Application of this method requires the runoff flows and pollutants be converted to one of the input functions for which solutions have been derived. The solutions are limited in application due to their complexity and sensitivity to storage and flow conditions, i. e. the need to reduce the complexity of the dynamics to facilitate the analytical solution. The complexity of these solutions PAGE 47 precludes their application to stormwater runoff events without the use of detailed simulation. EMPIRICAL A widely used method for characterizing the rainfallrunoff process is the application of a conversion ractor to mean rainfall values. Conversion factors are catchment specific and have been correlated to 33 imp ervi ousness, land use, pop u lat i on dens i ty and depress i on storage (Hydroscience, Inc. 1979, Chow 1964). L..Jhile this method accounts for an average reduction in the volume of storms, it does not correct for the decreased number of events, 1. e. it doesn't account for the small volume storms that are retained in the catchment storage. Empirical relationships for runoff water quality have also been developed. Receiving water studies have determined runoff coefficients for with nutrient loadings based on land use (Reckhow 1980). In the urban arena, Smolenyak (1979) determined coefficients of the power equation load = a(flow)**b where load is the pollutant load in the runoff [ M J, flow is the runoff flow [ L3/T 3, and a, b are coefficients. PAGE 48 Values determined from data in the Urban RainfallRunoff Quality Data Base are presented in Table 3. The practice of water quality control via settling is 34 inherent in most applications of natural waters. Water and wastewater treatment employ several variations of settling basins. Natural hydrologic systems incorporate detention for' both the storage of kinetic energy and the deposition of sediment load. As a result of the implementation of reservoirs, siltation studies have contributed to the identification oT the relationships between sedimentation and hydraulic parameters. The most popular sediment trap studies are those of Brown, Brune, Churchill and Camp (Ward and Haan 1977). Chen (1976) presents the historical development of theoretical analyses of sediment retention. These methods require the removal assessment of detention facilities based on an annual time frame. As there was no way to reconcile this with the stochastic nature of runoff eventsl these empirical methods were not investigated further. A recent review by Nixl et al (1980) summarizes the benefits in utilizing detention facilities for stormwater quality improvement. Several combinations of empirical and statistical approaches were suggested for design purposes. PAGE 49 35 ( TABLE 3 Relationships beb/een Pollutant Loads and Flo\'! Volume (FLOW). Dependent R2 S;g. Level No. of Model Load = a(FLOW)b Variable FTest Events Reg. Coef. a b BOO .2S .99 SO 34.0 1.12 COO .76 .99 157 29.S LOS NH3N .99 20 .215 .72 NITN .SO .99 21 .119 .80 NTOT .57 .99 103 .0400 .71 \ .. ./ ORGN .S8 .99 40 .S56 1.04 TOTN .74 .99 37 .304 1. 07 OOP .S3 .99 34 .064S .98 TOP .46 .99 119 .0104 .78 TOTOP .27 .90 11 .OSOO .. 55 TOTP .66 .99 53 .426 1.5 TPHOS' .91 .99 S .105 1. 05 "TOTS .69 .99 41 279 1. 41 TSS .56 .99 260 44.2 1.10 Source: Smolenyak 1.979 PAGE 50 36 SIMULATION Several models are available ror the simulation or the rainrallrunofr process and detention pond performance. Simulation is amenable to a trial and error routine. leading to search techniques for determining an acceptable design. STORM The Storage. Treatment and Overflow Model (STORM) of the Corps of Engineers models wetweather flow through separate storage and treatment facilities (U.S.A.C.O.E. 1974>' Runoff quantity is generated from an empirical conversion factor applied to rainfall excess. Runoff quality is generated as a function of land use. While flow is routed through the treatment plant, there is no capacity to model the quality improvement provided by detention. SWMM Overview The Storm Water Management Model (SWMM) is one of the most comprehensive and well documented models available for the analysis and design of urban stormwater systems (Huber et al. 1980). SWMM was developed by Metcalf and Eddy, Inc., the University of Florida and Water Resources Engineers, Inc. under a contract for the Environmental Protection Agency. Version I was released in 1971 and has been continually undergoing revision and updating. This study PAGE 51 L utilized Version III, released in 1980, and also incorporated rurther rerinements. While the model allows ror extensive watershed simulation, this study restricted the analysis to a simpliried Runorr Block and concentrated on the Storage/Treatment Block. The Runorr Block deterministically models the 37 rainrallrunorT process in a catchment. Physical data such as depression storage, inriltration rates, soil characteristics, catchment area, ground slope, gutter network, evapotranspiration rates and hourly rainrall values are included as the model input. Pollutant buildup and washorr runctions are available, as is pollutant generation based on catchment land use. The RunoTf Block generates hydrographs and pollutographs as options. Several inherent adJustment ractors are available ror calibration oT the mod e 1. The Storage/Treatment (S/T) Block Or SWMM models the rlow and pollutant routing through a storage and/or treatment device which can be either a detention or nondetention unit. Geometric and hydraulic relationships, e. g. depth to surface area, and evaporation rates, and incoming flows are included as data input ror the SIT block. Discharge can be modeled as either constant or variable outrlow. The package provides ror a variety Or removal mechanisms and rlow routing options, capable Or tracking both stormwater rlows and constituent pollutants. PAGE 52 38 Data Input Tor Runoff Block The Runoff Block accepts hourly rainfall data in the National Weather Service (NWS) format. No gutter or pipe networks were used in the example catchmenti all runoff exited the area via a dummy outlet. The impervious area was modeled separately from the pervious area. Runoff generated on either area went directly to the dummy outlet without passing through the other area. Also, theT'e were no areas of depression storage in the modeled catchment. The data input for the Runoff Block consisted of the catchment characteristics presented in Table 1. A complete listing of the data input is given in Appendix A. Currently, continuous SWMM can only be run with hourly rainfall input. As an aside, the hourly rainfall data were transformed into daily and weekly records. StmM Runoff Block was run on the first 19 months of the Atlanta data and the results are compared in Table 4. Table 4. Comparison of Runoff Block results using hourly. daily, and weekly rainfall input. Rainfall Average Total Infilt. Evap. Runoff Time step Intensity Rainfall ( in) (in) ( in) HOURLY HOURLY 81.68 51.72 6. 39 28. 68 DAILY DAYTOT/Dr 80. 53 50. 46 8. 18 28. 00 WEEKLY WEEKTOT/2Dr 81.62 51.73 6. 11 28. 62 PAGE 53 39 Reasonable agreement was obtained, suggesting that if hourly data were not available, continuous SWMM could be run using daily or weekly rainfall data. Data Input for Storage/Treatment Block The basin geometry and hydraulic characteristics required as input data for the SIT block were obtained from a separate computer program, BASIN, written for that purpose. BASIN calculates stage to surface area, stage to volume and stage to discharge relationships for basins given the dimensions, side slope and outlet configuration. Examples are provided in Figure 17. The program development and listing is provided in Appendix B. As a reference, basin volumes (Vb) were normalized to the mean runoTf volume per event (Vro), yielding a normalized volume ratio (Vb/Vro). Currently, SWMM does not define storm event statistics, so the SYNOP program was employed. This involved running the Runoff Block with the complete 24.6year (June 1948 December 1972) rainfall record and generating 24. b years of simulated runoff data. These data were transformed to the Tormat of the NWS rainfall data, which is compatible with the SYNOP input format. As with the rainfall data, the minimum interevent time was varied to obtain the coefficient of variation (cv) for the interevent time close to unity. these runs are presented in Table 5. The results of PAGE 54 40 9 30 (, OJ OJ 000 25 (1) 0 8 ill 40 () 0 :.0 20 :::I .. () PAGE 55 t r Table 5. SYNOP results of 24.6 years of simulated runoff data. Minimum' Number Volume CV Duration Oro (hr) CV Intensity I ro CV Interevent Time Ti (h r) CV of dry hrs Vro 3 4 5 8 12 2124 1998 1903 1760 1646 ( j n) ( in/hr) 0.180 1.253 4.507 0.964 0.041 1.057 101.35 1.172 0.192 1.221 4.980 0.978 0.041 1.058 101.75 1.114 0.201 1.196 5.428 0.989 0.041 1.063 113.13 1.070 0.217 1.194 6.438 1.030 0.040 1.073 122.32 0.999 0.274 1.181 7.448 1.093 0.039 1.052 130.80 0.940 PAGE 56 L 42 A minimum interevent time of four hours resulted in a cv of 1.000. The mean runoff volume per event (Vro) was determined to be 18022 cubic feet, based on the mean depth of 0.201 inches over 24.7 acres. The number of events was reduced from 2381 rainfall events (Table 2) to 1998 runoff events. Continuity is checked by comparing the product of the mean event volume and the total number of events with the amount of runorf generated by the Runoff Block,' (0. 194 events) =: 383.61 inchesi from Runoff, 388 inches. Test volumes (Vb) were obtained from BASIN to closely approximate ratios (Vb/Vro) Or 0.5, 1.0, 2.0, 4.0, 10. O. For example, a Vb/Vro ratio or 0.50 implies that the empty basin volume is 50 percent of the mean storm event volume. The basin volumes used are presented in Table 6. Table 6. Determination of normalized volume ratios (Vb/Vro). Basin volume (Vb) feet) 7744 15014 29064 74420 167835 Normalized volume ratio Vb/Vro 0.430 O. 833 1. 613 4. 129 9.313 PAGE 57 43 The input data for the Runoff Block are provided in Appendix A. The SIT Block utilized the runoffvalues generated from the Runoff Block. To save execution time and money, the Runoff Block was run once and the output stored on an interface data disk. The interface data set served as the input to SIT for the subsequent simulations. A constant suspended solids concentration aT 100 mgll was assigned to the influent. This was chosen as opposed to generating pollutants rrom the catchment area for four reasons: 1) it avoids concern over how the pollutants are generated; 2) it provides a base value (100 mg/l) ror ruture comparisons; 3) it provides a blockedorf step input as shown in Figure 18; and, 4) a constant inrluent concentration establishes that the percent of flow bypassed is numerically equal to the percent Or the pollutant bypassed. The actual flow condition in a basin is neither plug flow nor completely mixed, but somewhere between, termed "intermediate mixing". The complete mixing option of SIT was chosen for the rlow routing regime for its analytical and computational simplicity, resulting in lower simulation costs than the plug flow method. Two options of basin discharge were explored: variable outflow based on hydraulic head above an outlet, and a PAGE 58 It.. g,?; 20 O:::!J... t Z O ti .0::: ZlW Z ::::>W It) !J...Z zO t) t Figure 18. Time series of constant influent pollutant concentration. 44 PAGE 59 45 drawdown scheme which emptied the basin at a constant rate (see Figure 17). The pumping option was run comparison with the statistical technique. while the variable discharge option was utilized for application to basins with gravity drainage. Constant Discharge Simulation A variable volume, constant unit was simulated by using the pumping option of SIT. As a reference, the constant drawdown rate was normalized as QcTi/Vro where Qc is the drawdown rate in cubic feet per hour, Ti is the mean interevent time in hours, and Vro is the mean volume in cubic (Hydroscience. 1979>' As Ti and Vro are constants determined from SYNOP, variable values the ratio drawdown rates. These rates were calculated to yield ratios of 1, 2, 4, 7, and 10 and are presented in Table 7. It was assumed that drawdown occurs whenever there is water in the basin. The of drawdown height (Hd) and drawdown rate on capture and removal efficiencies was analyzed. PAGE 60 u Table 7. Calculation constant discharge rates (Oc) (Ti = 111. 17 hours; Vro = 18022 cubic reet>. Normalized discharge ratio OcTi/Vro 1 2 4 7 10 Drawdown rate (Oc) (cubic reet/hr> 162 324 648 1135 1621 Variable Discharge Simulation A variable volume. variable outrlow control unit was simulated with the SIT Block by utilizing a power equation 46 ror basin discharge based on hydraulic head. This simUlates the hydraulics in a basin with gravity drainage. The outlet characteristics were arbitrarily assigned as a six inch circular opening placed one root above the bottom. Instead or a solution surrace. as was provided in the constant discharge simUlations, a single removal curve was determined ror basin perrormance versus basin volume. In an analogous manner to the drawdown height and rate combinations. outlet elevation and crosssectional area were recognized as design parameters Tor basin and were analyzed. Evaporation in the SIT unit was arbitrarily assigned a value OT O. 1 inch per day. PAGE 61 Removal Mechanism A removal equation was chosen oT the Torm R = Rmax(le**(kt where R is the pollutant removal eTTiciency. Rmax is the maximum removal eTTiciency. k is the Tirstorder rate coeTTicient [ lIT J. and t is the treatment time [ T J. 47 (9) Fair. Geyer and Okun (1968) presents general removal curves with k near 1.4 per hour Tor TSS and 0.50 per hour Tor BOD. with Rmax oT 0.75 and 0.45. respectively. For design purposes. values Tor Rmax and k would be determined Trom column settling tests with representative pollutants. Values oT 1.0 and 0.6 per hour. respectively. were arbitrarily assigned Tor these parameters. In the SIT Block. removal is accounted Tor once per time step, the length oT the time step, one hour. as the treatment time. The removal equation is presented in Figure 19. Because the time step was held constant throughout the simulation there was a constant percent removal (45 percent) oT pollutant per time step. A comparison oT eTfluent concentrations for removal governed by this equation in an ideal plug flow basin, an ideal completely mixed basin and the SIT'complete mixing regime is presented iri Figure 20. As shown. the SIT results lie within the extremes of pollutant removal efTiciency provided by ideal plug flow and complete mixing. PAGE 62 48 1.00 ) 0.9 0.8 0.7 Removal (R) = l.O(1_eO 6t) i t(hr) R 0.6 0.25 0.143 0.50 0.259 1.00 0.451 0:: 2.00 0.699 3.00 0.835 >0.5 4.00 0.909 () 'S.OO 0.952 Z W 0.451 () lL.. 0.4 lL.. W ..J 0.3 0 W 0:: 0.2 0.1 0.0 0 2 3 4 5 TRE.ATMENT TIME hr .'0 Figure 19. Removal equation used in SWMM SIT Block. PAGE 63 Figure 20. Comparison of effluent concentrations under .deal pl"ug flow, ideal comp1etely mixed and as calculated with SWMM SIT completely mixed routing; step input of pollutant. PAGE 64 50 Oneyear Versus 24.6year Simulation The initial decision to use one year of data as opposed to the full 24.6year history was based on economic considerations; mistakes and debugging were expensive enough without extra data the costs. The 12 months of the input record (June 1,1948 May 31, 1949) were utilized to get the simulator running. It was realized that if a IItypical" year's simUlation adeq,uately reproduced longterm basin the costs the analysis would be reduced by as much as an order magni tude. A IItypicalli year, 1953, was chosen on the basis of similar synoptic statistics, as determined by the SYNOP run of the 24.6year data. A comparison 1953 runoff parameters with those the 24.6year time series is presented in Table 8. The adeq,uacy of one year's simulation for describing the longterm basin was analyzed in a series simulations; the results are presented b.elow. Block Results A variety of summary print are available in the Runoff Block, from detailed hourly results to the total simulation summary, as presented in Table 9. On the hypothetical catchment, 704 inches (60 percent) of the total 1179 inches of rain left via infiltration. A total of 388 inc hes (33 percent) ac cumu lated as runoff, wh i 1 e 150 inc h es PAGE 65 r C Table 9. Runoff Block 24.6year simulation summary. TOTAL PRECIPITATION (RAIN PLUS SNOW) TOTAL INFILTRATION TOTAL EVAPORATION TOTAL GUTTER/PIPE/SUBCAT FLOW AT INLETS TOTAL WATER REMAINING IN GUTTER/PIPES TOTAL WATER REMAINING IN SURFACE STORAGE $ ERROR IN CONTINUITY. /. OF TOTAL PRECIP MILLION INCHES OVER CUBIC FEET TOTAL BASIN 105. 512 63. 106 7.846 34.830 0.000 0.000 0.256 1176.79 703.83 87. 51 388.47 o. 00 0.00 * RUNOFF SIMULATION ENDED NORMALLY * \J1 PAGE 66 Table 8. Comparison of mean runoff event parameters Tor 1953 with the 24.6year record (minimum inter event time = 4.0 hours). 24.6year 1953 Volume (in) 0.201 0.217 cv 1.222 0.948 Duration (hr) 5. 066 6. 190 cv 0.972 1.087 Intensity (in/hr) 0.043 0.044 cv 1.148 1.164 Interevent time (hr) 111. 71 104.83 cv 1.000 0.986 (8 percent) were lost to evaporation. Mass continuity was preserved within 0.3 percent over the total 24.6year simulation. Storage/Treatment Block Results The format Tor the SIT results are similar to the runoff output with more emphasis on quality parameters. Again, as shown in Table 10, the results were presented to facilitate continuity checks. 52 PAGE 67 Table 10. Examples of Storage/Treatment Block summaries. DETEtolTION UNIT CHARACTERISTICS: POLLUTANT ROUTING METHOD : COMPLETELY MIXED RESIDUALS DRAWOFF SCHEME: NEVER DRAWN OFF 0.0 DEPTHAREASTORAGEFLDW RELATIONSHJPS DEPTH, FT. SURFACE AREA, SQ. FT. 0.0 O. 50 1. 00 1. 25 1. 50 2.00 2.50 3. 00 3. 50 4.00 4. 50 GOVERNED BY PUMPING PUMPED 5000.0 5304. 0 5t.J1b.O 5775. 0 5']36.0 6264. 0 6600. 0 6944. () 7296.0 7656.0 8024. 0 STORAGE, CU. FT. O. 0 2576. 0 5306. 0 6729. 9 8193.7 11243.7 14459. 7 17845.7 21405.7 25143. 7 29063. 7 DEPTH AT WHICH FIRST PUMPING RATE DEGINS, FT. : 0.0 O. 0 O. 45 O. 45 O. 0 DEPTH AT WHICH SECOND PUMPING RATE BEGINS, FT. : FIRST PUMPING : SECOND PUMPING RATE,CFS : DEPTH AT WHICH ALL PUMPING STOPS, FT. : UNrr PARAMETER VOLUME CAT K(,K/\ (CU. Ff. ) LE}!1. '1 INFLOW, TOTAL O. 11).56E+07 O. INFLOW,NET O. 1386E+07 O BYPASS O. 7027E+05 0.0 TREATED OUTFLOW O. 136f1.E+07 O. 1422E+04 RESIDUAL FLOW 0.0 0.0 REMOVED BY DECAY 0.:29131:=:+04 REMAIN. TOT; VOL. O. 5283E+04 O. 3216E'01 EVAPORATION 0.1700E+05 53 PAGE 68 54 Constant Discharge Simulation Performance results from the constant discharge simulations are presented in Figures 21, 22 and 23, and in Table 11. Table 11. Estimates capture (C) and pollutant removal (R) as a of basin volume and constant discharge rate: simulation results. Normalized Volume Ratio Normalized 0.43 0.83 1.61 4.13 9.31 Discharge ratio 1953 24.6 yr 1953 1953 24.6 yr 1953 1953 25yr 1 C 0.344 0.331 0.476 0.613 0.640 0.852 1.000 0.952 R 0.343 0.322 0.476 0.598 0.638 0.847 0.989 0.941 2 C 0.398 R 0.373 O. 552 O. 721 0.527 0.690 0.945 1.000 0.906 0.961 4 C 0.468 0.461 0.621 0.804 0.795 0.962 1.000 0.993 R 0.373 0.383 0.532 0.712 0.705 0.864 0.905 0.896 7 C 0.542 0.699 0.839 0.971 1.000 R 0.365 0.524 0.661 0.792 0.817 10 'C 0.611 0.608 0.744 0.868 0.876 0.982 1.000 0.999 R 0.342 0.351 0.483 0.603 0.619 0.713 0.728 0.736 indicates that simulation was not run. The 1953 simulations duplicated the results of the 24.6year simulations within five percent over the entire spectrum basin volumes and discharge rates. Figure 21 presents the solution surface capture efficiency as a of drawdown rate and basin volume. PAGE 69 U 55 10.0 r, 9.0 8.0 7.0 o ::> 6.0 .0 > W 5,0 ::::> 1 0 > C\ 4.0 W N 1 PAGE 70 ( 56 10,0 ,...._____ , 9.0 8.0 7.0 0 $ "6.0 ..c > .. W 5,0 :::::> ..J 0 > 0 4.0 W N. .J 0::: 3.0 0 Z 2.0 1.0 +53 0.40 +37 0, I 2' NbRMALIZED DISCHARGE, QcTi IVro Figure 22 Solution surface of pollutant removal efficiency (R) as a function of basin volume.and constant discharge rate: 1953 simulation results. 10 PAGE 71 U 57 1.0 r., 1953 RESULTS A 25YEAR RESULT 0.9. 0.8 0.7 0.6 0:: .. 0.5 >() Z W () 0.4 lJ.. 0.43 lJ.. W I 0.3 0 W 0:: 0.2 1.0 0.0 o 2 3 4 5 6 7 8 9 10 NORMALIZED DISCHARGE. Qcl1 IVro Figure 23. Pollutant removal efficiency (R) as a function of basin volume and constant discharge rate: 1953 and 24.6year. simulati6n results. PAGE 72 Isopleths of percent capture were drawn by linear interpolation between calculated values. As expected, flow capture was greater as the drawdown rate increased, due to an increase in the effective volume. Also, as the basin volume increased, the capture efficiency increased due to less bypass. The vertical distance between the isoquants represents the sensitivity of capture performance to basin volume; the smaller the distance, the greater the sensitivity. for drawdown rates greater than 4.0, there appears to be uniform sensitivity to basin volume. The lowest sensitivities occur at the lower drawdown rates (QcTi/Vro less than 2.0). The isoquants converge slightly toward the upper end of the abscissa. The horizontal 58 distance separating the isoquants represents the sensitivity of capture performance to the drawdown rate. The isoquants become parallel to the abscissa above QcTi/Vro of 4.0, implying relative insensitivity to drawdown rate. Sensitivity is increased as the drawdown rate is decreased. Figure 22 presents the solution surface for pollutant removal efficiency as a function of basin volume and drawdown rate. Unlike the solution surface of capture performance, the isoquants in Figure 22 slope upward after an initial negative slope. The result is a solution surface which allows more than one drawdown rate at a specific basin volume to achieve the same removal performance. This demonstrates the performance tradeoff of providing a larger PAGE 73 59 errective volume by emptying the basin providing a longer treatment time. although bypassing more r low. Combinations of basin volume and drawdown rate yielding equivalent removal erriciencies are depicted along i soquants. For e x amp Ie, the rem 0 val per for ma n ceo b t a in e d b Y a Vb/Vro of 4.1 and a QcTi/Vro of 2.0 was the same as a Vb/Vro of 9.3 and a normalized discharge rate of 4.0. The. greatest removal occurred in the region of large basin volumes (Vb/Vro ) 4.0) and low drawdown rates (GcTi/Vro < 4.0), Figure 23 presents the removal performance in a different manner than in Figure 22. There is no increase in information by presenting the results in this way, although ( ) "" the communication or information is improved. For example, in Figure 23. it is than in Figure 22 to see that the sensitivity of removal to drawdown rate increases as the volume ratio increases. Combinations of basin volume and drawdown rates yielding equivalent removal as well as the sensitivity of the removal performance to drawdown rate are demonstrated. For example, the sensitivity of performance to drawdown is represented as the slopes of the and is seen to increase as the volume ratio increases. As the volume ratio increases, the maximum removal erficiency for each volume occurs at decreasing drawdown rates. The 1953 performance curve for a Vb/Vro of 9.3 is depicted as a straight line. This represents a divergence (5 percent at L; PAGE 74 60 GcTi/Vro = 1.0) from the 24.6year results, possibly due to the lack of a large storm during 1953. All of the curves converge to 4.3 percent removal at GcTi/Vro of 0.0, that is, in the case where there is no outlet. Longterm removal efficiency would undoubtedly be smaller for this case, tending to zero percent. Variable Discharge Simulations The effect of basin volume on capture and removal performance in basins with variable outflow rates was analyzed by running the SWMM SIT Block on five sets of basin geometry and hydraulic characteristics. The results presented in Figure 24 follow an intuitive removal relationship with increased removal as the storage capacity I increases. The regions below Vb/Vro of 0.43 and above Vb/Vro of 9.31 were not explored because of the unlikeliness of such a small volume ratio. The resultant removal curve is neither an exponential nor a power equation for the range observed. Only three 24.6yearsimulations were run due to their low marginal benefit, i. e. the oneyear simulations gave estimates close enough to the 24.6year results to avoid spending the extra money for the longterm simulations. The costs of the runs averaged $0.60 for oneyear and $6.25 for 24.6year simulations. PAGE 75 L" 61 1.00 r, 0.9 0.8 0.7 1953 RESULTS 0.6 ... 25 YEAR RESULT 0:: .. )00.5 U 25year 1953 2 Vb/Vro C R C R W U 0.43 0.903 0.241 0.904 0.251 I.!004 I.!' W 0.83 0.898 0.529 1.61 0.967 0.643 0.952 0.641 4.13 1. 000 0.860 .J 9.31 1.000 0.916 1.000 0.918 0.3 0 :?: w .... n:: 0.2 0.1 :3 4 5. 6 7 8 9 10 2 NORMALIZED VOLUME, Vb/Vro Figure 24. Pollutant removal efficiency (R) as a function of basin volume under variable discharge conditions.: 1953 simulation results. PAGE 76 62 Optimal Basin Design During preparation of the initial performance solution surfaces, it was recognized that the heights at which discharge began and ended would combine with the discharge rate to affect basin performance. Intuitively, increasing the height would decrease the capture efficiency, but due to the completelymixed flow routing regime, the remaining volume would provide dilution of the influent. Combinations of drawdown height (Hd) and rate (Qc) and similarly outlet diameter and invert height, were simulated in an attempt to develop guidelines for the optimal design of detention facilities. A basin with a Vb/Vro of 1.61 was utilized for these simulations. The results from the constant drawdown simulations indicated that a basin with this ratio had the greatest performance sensitivity (26 percent capture and 11 percent removal) over the range of drawdown rates. In the variable discharge runs, a basin with a Vb/Vro of 1.61 yielded results in the knee of the removal curve. It was felt that a basin with this ratio was sensitive enough to reflect the effect of height and discharge combinations on basin performance. The results of the constant drawdown rate simulations are presented in Figures 25 and 26 and Table 12. The solution surface in Figure 25 indicates that maximum performance is achieved by a normalized discharge ratio PAGE 77 U 63 4.0 '" +60 ,/ '" '" ,/ '" ,/ / ,/ ,/ / ./ / / / / 3.0 / / 71 + / / .. / / / / I, 0 :c j' j .. Z 2.0 76 0 + ...:> ,/ ,/ W ..J W Z ;: 0 Cl 1.0 0.75 ,/ 0:: ,/ ,/ Cl .......0.70 0.0 .L.I...L..'_..L.I...I... __ '_t:... __ L_L::;;..J'_L_' o "Figure 25. 2 4 6 8 10 12 14 16 18 20 NORMALIZED DISCHARGE, QcTi IVro Solution surfa6e of pollutant removal efficiency (R) as a function of drawdown height and drawdown rate (Vb/Vro = 1.61): 1953 s.imulation results. PAGE 78 0. 1.0 64 0.9 0.8 0.7 0.6 a:: .. 0.5 >() Hd (fi) SYMBOL z W 0 0 () I.J.. I A I.J.. W 2 0 ...J 3 0.3 4 "0 W 0:: 0.2 1.0 0.00 NORMALIZED DI,SCHARGE, QcTi IYro Fi g u re Pollutant efficiency (R) as a function of drawdown height and constant di;charge rat'e (Vb/Vro = .1.61): simulation results. PAGE 79 Table. 12. Estimates of flow capture efficiency (C) and pollutant removal efficiency (R) as a function of drawdown height and rate (Vb/Vro = 1.61): 1953 simulation results. Normalized Discharge Ratio 1 C R 2 C R 4 C R 7 C R 10 C R 12 C R 15 C R 18 C R 20 C R o 0.613 O. 598 O. 721 0.690 0.804 O. 712 O. 839 O. 661 O. 868 0.603 O. 883 O. 570 0.900 O. 520 * Drawdown Height (ft) 1 O. 578 O. 578 0.679 O. 679 O. 756 O. 734 0.804 O. 752 0.837 O. 761 0.860 O. 766 O. 874 O. 749 O. 885 O. 730 2 0.517 0.517 0.610 O. 610 0.687 0.687 O. 749 O. 728 O. 778 O. 738 O. 795 O. 744 O. 831 O. 763 0.845 O. 758 O. 851 O. 761 3 * * 0.717 O. 694 O. 745 O. 713 O. 765 O. 727 O. 776 O. 731 indicates that simulation was not run. 4 * * O. 610 O. 597 0.648 O. 621 0.663 O. 636 or 12.0 with an Hd of one foot. Removal efficiencies for basins with complete drawdown (Hd of 0.0) were lower than limited drawdown (Hd greater than 0.0) for all but the 65 lowest rates. The general trend of the isoquants indicates that similar performance can be achieved by a low drawdown PAGE 80 66 ratio and low height as well as a higher ratio and a corresponding higher drawdown elevation. Figure 26 more clearly presents the removal performance associated with each height. As the height increased, maximum removal occured at drawdown rates. As the drawdown rate increased, removal efficiency increased until a maximum was reached, after which, further increase in drawdown rate yielded decreased removal. The results of the variable outflow simulations are presented in Figures 27 and 28 and Table 13. Table 13. Estimates of fIow capture efficiency (C) and pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro=1. 61): 1953 simulation results. Outlet Outlet Elevation (ft) Diameter (ft) 0 1 2 2. 5 3 4 0.0 C 0.043 0.043 0.043 0.043 0.043 0.043 R 0.043 0.043 O. 043 0.043 0.043 0.043 0.25 C 0.887 0.845 O. 775 O. 721 0.635 R O. 708 O. 763 O. 737 O. 696 0.619 O. 50 C 0.976 0.'952 0.922 0.900 0.876 0.678 R 0.293 0.641 O. 737 O. 753 O. 757 0.625 1. 00 C 1.000 1.000 1.000 1.000 0.995' O. 951 R 0.018 0.460 0.650 O. 705 O. 747 O. 791 1. 50 C 1.000 1.000 1.000 R 0.690 O. 734 O. 798 indicates that simulation was not run. PAGE 81 G 67 4.0 3.0 .,. ,.;" / ,; .... 'to.. Z / .0 ........ /" 2.0 ./ /' ::> ,/ ./ W ,/' ....J ,/ w ./ Iw ....J I:::) 0 I.'" 1.0 0,0 __ ___________ ______ ____ L __ 0.0' 0.25 0,5 1.0 1.5 OUTLET DIAMETER) ft Figure 27. Solution surface of pollutant removal efficiency (R) as a function of outlet height and outlet diameier (Vb!Vro =' 1.61): simulation results. PAGE 82 ,0 68 1.00 , 0.9 0.6 0: .. >0.5 U Z W U Hd ( f t) SYMBOL l.L.. 0.4 l.L.. 0 0 W I I IJ. 2 0 0.3 0 3 :;E W 4 0: 0.0 L.. __ ...J__ 0.0 0.25 0.50 1.00 1.50 OUTLET DIAMETER) ft FIgure 28. Pollutant removal efficiency (R) as a function of outlet height and outlet diameter (Vb/Vro = 1.61): 1953 simu1ation results. PAGE 83 69 The capture performance describes intuitive results. As the outlet height increases, the flow captured decreases. As the outlet diameter increases, the capture efficiency increases. The preliminary increase in removal efficiency as the outlet height increases (holding diameter constant) demonstrates the effect of dilution in a completely mixed basin. Capture efficiency decreases, but the remaining volume undergoes continuous pollutant decay, creating a sizeable dilution potential for the influent. For each outlet diameter, a unimodal removal curve was observed as the outlet height increased. This reflected the effect ori removal efficiency of decreased capture performance combined with increased dilution. As the outlet diameter increased for a constant outlet elevation, the capture efficiency increased. As observed before, the removal performance peaks and then decreases as the diameter increases, again reflecting the tradeoff of capture and treatment. The maximum removal was observed at an outlet height of 4.0 feet and an outlet diameter of 1.5 feet. Even though the effective volume is small, the rate of discharge was so great that 100 percent of the year's runoff flows were captured. This suggests that a basin with a large outlet, possibly a weir, offers the best capture and removal performance. This is a different case than a basin with no PAGE 84 ) 70 outlet. With no outlet the maximum depth is maintained (minus evaporation, etc. losses) and any runoff is immediately bypassed with no treatment. With a large outlet below the maximum depth, the runoff will pass through the basin and receive some degree of treatment by dilution. Extrapolating these results to areas outside the solution surface, the limiting maximum removal configuration would be a drawdown rate as high as the maximum inflow rate, with the discharge height at the top of the basin, i. e. no bypass, but all the runoff would be diluted to some degree as it passed through the basin. These trends suggest that optimal quality control would be provided by a basin that is partially full of water to provide dilution. This conclusion is based on the supposition that pollutant removal follows the exponential removal curve and that there is complete mixing in the basin. The latter assumption is hardly appropriate for sedimentation. The computer costs associated with the simulations are presented in Table 14. STATISTICAL TECHNIGUES Event Definition A preliminary task in statistical analysis is the grouping of raw data into independent events. A common1y used method is the separation of hourly rainfall values by a minimum number of hours with no rain. Serial PAGE 85 Table 14. Computer costs or simulations. Procedure Cost Dollars Runorf Block 24.6year Oneyear Storage/Treatment Block 24.6year Synop Oneyear Interface 24.6year runo;; 3.25 O. 75 6.25 0.60 1. 25 1. 75 Average costs for low priority execution on the University or Florida system. Normal priority is approximately four times as much. autocorrelation has been used to deTine this minimum interevent time (Medina 1976). Howard (1976), Hydroscience 71 (1979) and others have suggested that rainfall events occur as a Poisson process, and the time between events is exponentially distributed. The exponential distribution is a special case oT the gamma distribution with the coeT;icient 0; variation (standard deviation divided by the mean) equal to unity. A cumulative distribution of time between events was presented in Figure 6. The gamma function has been widely applied in (Haan 1977). PAGE 86 72 Traditional Design or Flood Control Basins L The traditional sizing or stormwater detention has been based on the control a single "design" storm event. These basins are designed to capture the runorr resulting a storm expected to occur for a given duration on the average once every N years (Haan 1977 >. Typical values of N range from 150, although incorporation of downstream risk assessment governs the value of N. The typical design storm analysis employs ranking particular storms (e. g. annual maximum 60 minute and 24 hour rainralls) over a time period and assigning an extreme value probability distribution to the resultant sequence. From this distribution, return periods are assigned to storms of given magnitudes and dUTations. Figure 29 depicts the relationship between the paTent distribution and resulting extreme value distTibutions. Figure 30 presents a cumulative extreme probability distribution (normal) used to determine the return peTiod of Tiver flood flows. Because this method does not retain infoTmation on the time between events, theTe is a loss of information and the method is said to be inefficient in terms of the data (Haan 1977). One unobtainable parameteT whose value is necessary for accurate flow routing is the effective volume, defined as the actual stoTage volume available at the beginning of a storm, which is a function of antecedent conditions. Bome municipalities require that PAGE 87 .25 .15 p (y) 16 Y (days) 73 Figure 29. Distribution of a sample size n the largest sample value from from an exponential distribution. 1.01 1.11 ...... II .. II HI+i 1'1'''''' :j 110 "0 II. 100 1/1 .... 0 u. 0 0 VI 0 70 0 .Q 00 !: a '0 I. .0 }trh '0 '0 l.ri" 1'. 0,\ 0.. 0,," '0 RETURN PERIOO ( Y") 2 5 10 20 50 100 200 PERCENT GREATER THAN 'rO ..., .. r t +. .;,..;..;., : t )0 20 10 o,m 0.1 0,1 .;..t .'1=FR= +t" ASSUMED HISTOR!CAL ,J.+ t=:q::r:;::,. +H'.. '=: HF In+, .1+ I+., 10 )0 40 ,0 .0 )b IU u .. ,. lOt. PERCENT LESS THAN Figure 30. Normal probabi I ty plot of Kentucky River data. PAGE 88 u 74 ponds be built to contain the runoff from urbanized areas (subdivisions, parking lots, etc.) resulting .prom a design storm. The Rational Method, an extension of design storm concept, is widely used for this purpose. The design storm method is relatively straightforward and does not require computer solution, hence it receives high ratings on ease of application, though as Haan (1977) points out, there is no direct theoretical connection between the solution and the underlying mechanisms governing the storm events. While this method is successTully used for flood control design, no criteria have been established Tor determining a design storm for quality control. Aggregate Statistical Methods Independently, two groups have developed statistiial approaches for designing urban stormwater detention facilities. Howard (1976) presented the theoretical framework for analyzing the interevent times and volumes of combined sewer overflows resulting from various storage/treatment His derivation was based on approximating intensity, duration and interevent time as independent and exponentially distributed random variables. As part of a study evaluating the longterm performance of stormwater control devices, Di Toro, et al. (1979) derived an analytical expression for the effective volume of a stormwater detention facility available at the beginning PAGE 89 75 of a storm event. Like Howard's method, this technique retains information on the time between events, an important parameter for flow routing analyses. The method is based on the SYNOP results for rainfall event statistics: intensity, depth, duration and interevent time; converting them to runoff values; setting up the respective equations for effective volume and solving them. The result is a set of graphs which enable the user to plot the solution surface for percent of flow captured (e) and effective volume (Ve), as a function of the constant drawdown rate (Oc) and the ratio of the empty basin volume (Vb) to the mean runoff volume (Vro). The algorithm requires repetitive application to obtain an optimal basin size for maximum capture efficiency. The method presents a straightforward procedure for a simple catchment, single basin system (Dever, 1980), Data Input The Atlanta rainfall event statistics were obtained from the previous runs of SYNOP. Runoff event parameters were obtained from the rainfall values via a linear conversion factor. The STORM equation was used to determine the volume conversion factor, based on the percent imperviousness for the catchment, ero = O. 15 + 0.75I (10) where ero is the runoff conversion factor, and PAGE 90 76 I is the perc.nt of the catchment area that is impervious. With 1=0.37 for the catchment data, Cro=0.4275. The conversions produced a mean runoff volume of 19000 cubic feet based on the mean event depth of 0.212 inches over the catchment area of 24. 7 acres. The mean event volume is similar to the value obtained by the SWMM simulation (18022 cubic feet). A$mentioned earlier, the conversion method does not account for the reduction in the number of events resulting from catchment capture. This results in a total of 504 inches of runoff for the entire 24.6year record, as compared with the 388 inches obtained by the Runoff Block. Vb/Vro ratios were calculated to correspond to the volumes used in the simulations. The resulting ratios are presented in Table 15. Table 15. Determination of normalized volume ratios. Basin volume Normalized volume ratio (cubic feet) Vb/Vro 7744 O. 41 15014 O. 79 29064 1. 53 92420 3. 74 167835 8. 83 PAGE 91 77 There was a misrepresentation oT the normalized discharge ratio in Di Toro's work. 1. The product QcTi was expressed as the average drawdown between storms. The concept oT average drawdown between storms implies that mass continuity be preserved. With no bypass, the average volume entering the basin is to the average runoTT volume, and represents a limiting value oT the average longterm drawdown between storms. The average drawdown would be even less iT the average volume entering the basin is less than the average runoTT volume, due to bypass. IT the product oT Qc and Ti were truly the average drawdown between storms, then the ratio (QcTi/Vro) would always be less than or to unity; yet relationships are developed Tor values up to inPinity. 2. The product oT ac and Ti would only the average drawdown between storms iT the time series was completey homogeneous, with mean event volumes occurring at mean interevent intervals. For all other time series: a. the product oT Gc and Ti has no relationship to averag e va I ueSi b. the product oT Qc and Ti is always greater than the true average drawdown between stormsi and, r U PAGE 92 l G 78 c. the ratio (QcTi/Vro) is not bounded by continuity constraints. This is why values greater than unity are realized. The average drawdown concept developed by Hydroscience, Inc. is a plausible yet erroneous expression. The ratio QcTi/Vro is used in this study merely as a normalized discharge rate. A solution surface of capture performance was prepared as a function of basin volume and pumping rate. The grid was created by using Figure 31 (see arrows) as follows: 1. enter the lower graph at the respective volume ratio (Vb/Vro)i 2. move horizontally until intersecting with the normalized discharge curve (QcTi/Vro)j 3. move to the upper graph at the effective volume ratio (Ve/Vro), the common side between the graphs; 4. continue up until intersecting the runoff volume f coefTicient oT variation curve (cv); and 5. Tinally move horizontally and exit at the estimate of capture efficiency (C). This process was repeated for 25 combinations OT volume sizes and drawdown rates. PAGE 93 (.) NORMALIZED E'FFECTIVE VOLUME J Ve/Vro 1.0 r__ ,1.0 ___ 2::; ..:...0 __ =.3:r:.O ____ 4:.:,::.0=___ 5:.::;.0 0.8 0.2 >a () w z C/) w C/) () >0.6 0.4 tt co w :z w 0 0:: I0:4 0.6 :::> u le:{ a.. a:: PAGE 94 lJ L Capture Results The results are presented in Figures 32 and 33 and Tab Ie 16. Table 16. Estimates flow capture efficiency (C) as a function of basin volume and constant discharge rate: statistical results. Normalized Discharge Ratio Normalized Volume 1 2 4 7 10 Ratio O. 41 0.22 0.23 0.24 0.30 0.30 O. 79 0.40 0.47 O. 48 0.49 0.49 1.53 0.61 0.68 O. 70 O. 70 O. 71 3.92 0.86 0.90 O. 91 0.92 0.92 4.63 0.90 0.93 0.93 0.94 0.94 80 Isopleths of capture efficiency were drawn which emphasized the apparent insensitivitiy the performance to varying pump i ng rates. This relationship exists due to the combined shapes of the upper and lower curves. The capture efficiency is most sensitive to the coefficient of variation and volume ratio (Ve/Vro) at the lower end of the Ve/Vro axis. However, at the lower end of the Ve/Vroaxis, the effective volume ratio is relatively insensitive to the pumping rate, For the lines converge near a QcTi/Vro of 1. O. Conversely, where the volume is most sensitive to the pumping rate, at the upper end of the Vb/Vro axis, the percent capture is least sensitive to effective volume, for PAGE 95 'L; 81 10.0 .9.0 8.0 I7.0 0 $ ........ 6.0 .c 'r> ... W 5.0 ::::J Il 0 +92 > 0 W 4.0 N . +91 0.90 l PAGE 96 L 82 1.0 Vb/Vro=5.00 0.9 3.83 0.8 0.7 L50 0.6 C,) .. >C,) Z 0.5 0.77 W U lJ.. lJ.. W 0.4 W 0:: ::::> I0.40 a.. 0.3 C,) 0.2 0.1 0.0 "_L_I.. __ .l..._...l_L __ L.._l_L __ l_..J o 2 3 4 5 6 7 8 9 10 NORMALIZEOOISCHARGE QcT! IVro Figure 33. FJowcapture efficienct as a function of basin volume and constant discharge rate: 1953 statistical results. PAGE 97 83 the slopes are the The greatest overall sensitivity lies in the "middle" region the graphs. The maximum variation any given volume was an 11 percent increase 64 percent to 75 percent a ratio of 1.6. The largest Vb/Vro ratio available in Figure 31 is 5.0. This limitation precluded a complete comparison with simulation results, where Vb/Vro ratios up to 9.3 were analyzed. Removal A maJor weakness of using the statistical method for estimating control is the inherent assumption of absolute pollutant removal efficiency. In the design of a detention facility for control, the determination of a removal efficiency is the primary obJective. It was to assign a removal expression. It was tempting to use the constant removal value incorporated during each time step in the SIT simulation, however, the two terms are not conceptually The statistical method essentially treats the removal mechanism in the basin as a black box in which the constant removal to the total captured flow during the complete time history. The simulation employs time steps to route the flow the basin, and the constant removal term applies only to the volume within the basin during that time step. This implies that for any runoff volume which remains in the basin longer PAGE 98 than one time step, the total efficiency will be than the constant removal 84 To make an estimate of efficiency would be the solution in this study. an estimate of efficiency can be obtained by taking the product of the percent and an assigned constant The solution will have the same shape as the capture in 32, but the value of the will be by the factor. Analysis Using Simulated Runoff Data For further study, the statistical analysis was on obtained the SWMM simulation. The values by SYNO? for the data the Rtinoff Block (see Table 5) of SWMM to the converted values in Table 17. differentes were noted. The most obvious is that 24 percent events modeled in the statistical method than the simulation. This affects the total amount of by the two methods .. The simulation yields 308 inches of runoff while the use of a conversion yields 504 inches of 30 runoff the period. This is not apparent of the estimates of mean volume, is only a 5. 47 in the PAGE 99 Table 17. Comparison of simulated runoff mean event statistics with rainfall conversion values. Simulated Number of events 1920 Volume (in) 0.201 cv 1.222 Duration (hr) 5.066 cv 0.972 Intensity (in/hr) 0.043 cv 1. 148 Interevent time (hr) 111.71 cv 1.000 Minimum interevent 4 time (hr) to yield cv near 1. 0 Conversion 2381 0.212 1.384 7.824 1.134 0.032 1.356 90. 10 1.004 8 two methods. This is an interesting point. Because the statistical method deals with basin volumes normalized to 85 the mean event volume, the 30 percent continuity difference between the methods is not reflected in the flow capture solution surface. This implies that satisfying the continuity equation may not be a requisite for a good solution methodology. An important difference is that the minimum interevent time was reduced from 8 hours to 4 hours to obtain a coefficient of vari.tion for interevent time close to unity. At first, this appears to be due to the presence of an effective detention time inherent in the PAGE 100 86 catchment storage, characterized by the attenuation of magnitude and lengthening of duration. The values for the mean duration contradicts this thought, being two hours less than the rainfall mean.. This decreased duration may be the result of roundoff error in transferring runoff data into the NWS format for subsequent SYNOP runs. Flows less than 0.125 cubic feet per second are y'ounded down to 0.0 inches per hour, baSed on a catchment area of 24.7 acres. Volume ratios and pumping rates calculated from these new values are identical to those used in SWMM, as the same SYNO? run was the basis for those values. The performance determination was repeated on these new volume ratios and pump ing rates. The results are summarized in Table 18. Table 18. Estimates of flow capture efficiency (C) as a function of basin volume and discharge rate: statistical results with simulated runoff means. Normalized Volume Ratio O. 43 O. 83 1. 61 4.13 5. 00 Normalized Discharge Ratio 1 2 4 7 10 0.28 0.28 O. 29 0.29 O. 30 O. 44 0.49 O. 50 0.51 O. 51 0.64 O. 70 O. 73 O. 74 O. 75 O. 89 O. 93 O. 93 0.94 0.94 0.92 0.95 0.95 0.96 O. 96 PAGE 101 ) 87 Because of the low sensitivity of flow capture efficiency to small changes in either volume or drawdown ratio, the solution surface obtained is almost identical to Fi g ure 32. The only computer costs associated with the statistical technique were for the SYNOP runs, which averaged $6.50 for rainfall and $1.75 for runoff data. COMPARISON In comparing the methods, it is necessary to recognize that the statistical, empirical and analytical techniques are firstcut approaches, while the simulation yields a greater design and analysis flexibility, although requiring a larger data input. As emphasized earlier, there was no established data base to definitively compare the results obtained. However, certain aspects of the statistical and simulation methodologies can be compared. Both techniques utilize the same rainfall data. The simulation generates its own runoff data, while the statistical technique relies on a conversion factor. With no established data base, there was no way to say whether the simulated runoff values are more accurate than the statistical conversions. However, previous implementations of SWMM which tested \ predicted runoff with documented values reinforce the assumption that the simulation results are accurate. Both methods allow calibration of results with observed data when PAGE 102 88 present. Mean event runorr values obtained rrom the two methods dirrered by only 5 percent, but the dirrerent'number or events (2381 ror the statistical method versus 1920 ror the simulation> resulted in the statistical method predicting 30 percent more total runorf over the 24.6 year record. Figure 34 is a comparison of the rlow capture solution surfaces obtained from the simulation and statistical methods. For dischage ratios less than 1.0 the two methods are in reasonable agreement. However, at discharge rates above this ratio the estimates diverge, with the statistical estimates predicting up to 20 percent less capture than the simulation results. Figure 35 is a comparison Or the estimates of removal efficiencies obtained from the simulation and statistical methods, where r is the constant removal term employed by the statistical technique. The most striking dirference is the shape of the isoquants. The simulation estimates reflect the combination of rlow bypass and treatment time in the slopes or the isoquants. The ability to depict this fundamental property Or storage/treatment devices is relinquished by the statistical method with the direct inclusion of a removal expression, r. Estimates of r yielding comparable removal as the simulation results ranged rrom near unity at discharge ratios than 1.0 to less than 0.8 at higher drawdown rates. PAGE 103 ( L 89 10.0 r, o :> .c > W ::E ::> .J o > 9.0 8.0 7.0 6.0 5,0 o W 4.0 N .J PAGE 104 90 10.0 r, 9.0 8.0 7.0 0 ;;; "..c 6.0 > ... w ::::> 5,0 :.J 0 G > 0 W 4.0 N I 0:: 3.0 .0 Z 2.0 ___ 1.0 .. 0.50 40 0.0 0 NORMALIZED DISCHARGE, QcTl /Vro Figure 35. Comparison of pollutant removal efficiency. PAGE 105 L/ DISCUSSION This analysis was concerned with comparing solution methodologies. Because there are no actual data to obtain removal characteristics or calibrate the results, the results are not meant to stand alone, but are a runction Or the assumptions involved. It was relt that empirical and analytical methods were applicable for determining longterm perrormance of stormwater detention facilities. Application of analytical methods to stormwater runoff events may be obtained with computer simulation (Medina 1980). Continuous simUlation was found to provide the most detailed performance analysis. SWMM can handle complicated rlow networks and SIT combinations, and give detailed summaries for any time period. The simulation provided more interesting (i. e. no explicit relationship between capture and removal performance) relationships between the overall removal efficiency and the basin parameters. There was a noticeable removal performance tradeoff between increasing the effective volume at the beginning of a storm and increasing the pollutant treatment time. These relationships were closer to observed results than the constant removal results of the statistical method (Heaney J PAGE 106 92 1975 >. The simulation permits a sensitivity analysis of basin parameters and pumping strategies, while there is limited mechanism for this in the statistical technique. This feature allows the simulation to be used to search for the optimal basin characteristics for pollutant removal. The relative effectiveness of the statistical technique in estimating flow capture performance for the hypothetical catchment was demonstrated by comparison with the results from the simulation. Conversion of rainfall volume was within 5 percent of the simulated results, although total volume of runoff over the 24.6 year record was 30 percent higher in the statistical method. The statistical method in the form utilized precludes determination of pollutant removal efficiency. Modifications are needed to account for variable removal efficiency within the detention facility. PAGE 107 GENERAL APPLICATIONS OF METHODOLOGIES A spectrum Or hydrologic control units is depicted in Figures 1 and 2. An example Or these units and estimates or their volumes and detention times associated with a single rainfall event are enumerated in Table 19. Both hydrologic storages and transport elements are classified as control units. While flows of water are not generally recognized as control elements, they possess the same characteristics necessary for pollutant removal, e. g. even though a detention facility is stationary, the volume ofwater passing through it is not. The hydrologic and functional characteristics alluded to in Figure 3 are 'inherent in all water bodies, whether it is a river reach which has a detention time of less than a day or a water supply reservoir with a detention time on the order ofmonths. The classificati6n ofa hydrologic unit as a storage or rlow is based on a relative time scale; a flow element turns over "faster" than a storage device. This time dependence dictates the reaction kinetics and is the basis for recognizing a spectrum of water bodies in Table 19. In all cases, the actual mechanisms or removal are not altered, but rather, the inherent kinetics which determine PAGE 108 94 Table 19. Estimates OT hydraulic volume and detention time of various control units associated with a single rainTall event. Percent of Even!; Va 1 ume 1. interception by above ground structures I") "'. the initial abstraction volume 3. the transport through the soil via inTi1tration 4. the overTlow runoTT 5. the Tlow in gutters 6. areas OT depression storage in the basin 7. evapotranspiration 8. the Plow in stream channels and Tlood plains 9. detention Tacilities 10. ponds and lakes 11. the ultimate receiving water; here we recognize an even larger system, either subsurTace, oceanic or atmospheric. Source: modiTied Trom Medina 1976. 05 05 3060 2035 1030 010 010 1030 015 1035 520 Decention Time 07 days 03 hours 512 hours 118 hours 118 hours 01 month 012 hours 09 days 010 days 0.11000 years 110000 years the extent Or perrormance are changed. The hydrologlc kinetics dictate the predominance or dirTusive ,transport or turbulent advective transport (Rich 1974). The omission OT the time scale criteria in evaluating system perTormance presented diTriculties in the early works PAGE 109 on lake eutrophication (Vollenwieder 1968, Dillon 1975, Reckhow 1978). The derivation of the first models began with the mass continuity equation but quickly veered to empirical concepts. Vollenwieder (1968) originally developed a general expression for the trophic state of lakes based on aerial loading and mean depth. The same 95 empirical model was used for all water bodies, ranging from urban ponds with detention times on the order of days, to mammoth lakes with detention times of hundreds of years. The early predictive models were based on data gathered from a number of large, public lakes threatened with water quality problems. Later studies revealed a set of lakes whose trophic conditions were considerably different than predicted. In one study, Dillon (1975) compared the phosphorus concentrations in two lakes of similar depths. Their areal phosphorus loadings and, hence, their predicted phosphorus levels, differed by a ractor of twenty. Due to the difference in detention times, 26 days versus 1738 days, the observed concentrations in the lakes were similar. It was recognized that detention time, which had been neglected in the early models, was a fundamental factor in the lake concentration of phosphorus. The influence of detention time was obscured in the earlier studies as a result of using a one year time frame on lakes with detention times greater than one year. In 1973, Vollenwieder incorporated the detention time concept in the trophic state model with PAGE 110 96 an rate, as the ratio mean depth to detention time (Vollenwieder 1976). Other intuitively detention time the continuity and similar to the ones which Vollenwieder and others ultimately arrived at (Reckhow 1978, Schnoor 1975). It is possible to apply the solution methodologies analyized in this thesis to problems of a nature. The solution process should follow the .same as was presented: 1. identify the system; a. unit's place in system; b. influencing processes; 2. ide n t i f y ma J 0 flo w san d s tor age s ; and, 3. recognize the time dependence on removal mechanisms i. e. detention time, which affects the performance of the reaction kinetics. PAGE 111 0000 0001 OOUl 0003 0004 0005 00U6 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 Oll17 0018 0019 0020 0021 I '022 \",:/023 0024 0025 0026 0027 0028 0029 Ou30 0031 0032 Ll033 0034 0035 0036 0037 0038 0039 0040 0041 0042 Q 0 3 0044 0045 0046 APPENDIX A. PROGRAM LISTING AND DATA INPUT \ Table Al Runoff Block Simulation IISWMM JOB (2006,3400,100,20,0), 'GARY F. GOFORTH',CLASS=1,REGION=512K, II MSGLEVEL=(I,l) I*PASSWORD 2,RAIN I*ROUTE PRINT REMOTE6 II EXEC FORTXCLE,LPARM='LIST,NOMAP,OVLY',OPTIONS='NOSOURCE,NOMApi IIFORT.SYSIN DO SUBROUTINE COMBIN RETURN END SUBROUTINE TRANS RETURN END SUBROUTINE RECEIV RETURN END SUBROUTINE EXTRAN RETURN END SUBROUTINE STRT RETURN END /*INCLUDE /*INCLUDE /*INCLUDE /*INCLUDE /*INCLUDE RHYDfWl RHYDR02 RHYDR03 GUTTERl GUTTER2 1* /ILKED.SYSLMOD DO SPACE=(CYL,(5,1,1 //LKED.SYSUTI DD SPACE=(CYL,(5,Z /ILKED.LlB DO DSN=UF.A0063473.S\JMM,DISP=SHR I/LKED.SYSIN DO INCLUDE LIB(MAIN) INCLUDE LIB(GRAPH,CURVE,PINE,PPLOT,SCALE,HYSTAT) OVERLAY ALPHA INCLUDE LIB(RUNOFF,RBDATA,CTRAIN) INSERT OVERLAY BETA INCLUDE LlB(HYDR2,GAt.1P,QSHED,\JSHED) INCLUDE LIB(MELT,AREAL,FINDSC,GQUAL,HCURVE) INSERT \'JSHED OVERLAY BETA INCLUDE L I BC PRIHR3) //GO.FTOIFOOl DO UNIT=SYSDA,SPACE=(TRK,(SO,10, II VOL G S ERg \J 0 R K a 1 DC [3 G ( R E C F M:: V [3 S 0 L 'K S I Z E ::I 4 2 40 B U F NO = 1 ) //GO.FT02FOOI DO UNIT=SYSDA,SPACE=(TRK,(SO,lO, / / VOL=SER=\JORKOl,DC8=( RECF1,1=VBS, BLKS I ZE=4240, BUFNO=1) //GO.FTU3F001 DO UNIT=SYSOA,SPACE=(TRK,(SO,lO, 17 II VOL=SER=WORKOl,DCB=(RECFM=V8S,BLKSIZE=4240,BUFNO=1) f .. 1.,_/ 97 PAGE 112 Table AI (cont.) //GO.FT04F001 DD SYSOUT=A,DCD=(RECFM=FSA,LRECL=133,BLKSIZE=133) IIGO.FT08FOU1 DD UfJIT=SYSDA, II DSN=UF.AOOG3473.RAlfJA,SPACE=(TRK,(100,50),RLSE), I I 0 I S P = ( N HJ C AT L G ) I 0 C B = ( R E C F Iv! = VB S,B L KS I Z E = 4 2 4 0, BJ F N 0 = 1 ) IIGO.FT09FOOI DO UtJIT=SYSDA,SPACE=(TRK,(50,lO, II /IGO,FT10F001 DD UNIT=SYSDA, // DCB=(RECFM=FB,LRECL=80,BLKSIZE=GIGO), /1 DISP=SHR,DSt'J=UF.B0063400.SG.RAIN IIGO.SYSIN DO 10 8 8 9 123 4 RUNOFF 8 9 9 8 o 8 o o TH t SIS A S t MULAT I OfJ RUN OF T\JENTYF I VE YEARS OF HOURLY RAINFALL (ATLANTA AIRPORT) ON 10 HA THROUGH A BASIN. 1 0 0 60.0 1 25.0 0 0 0.5 7 31 12 72 090451ATLANTA, GEORGIA 9 9 G 98 o 48 1 0 OU40 OU49 o l) 50 OU51 0052 OU53 0054 0055 0056 0057 005H 0059 0060 0061 000L 00G3 0064 0065 0066 0067 1 1 1 103724.7 37.0 0.04 0.0130.25 0.0520.184 2.5 0.52 0.00115 0 00G9 0 1 0070 EtJDPROGRAM 0071 1* END OF WORK FILE PAGE 113 Ouoo OU01 0002 0003 0004 0005 0006 0007 0008 0009 0010 Oll11 OU12 OU13 OU14 0015 OU16 0017 0018 0019 0020 OU21 00L2 '.J 024 ." '0025 0026 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 OU40 0041 0042 0043 0044 0045 0046 0047 )48 '.J049 0050 0051 005:l Table A2 StoragelTreatment Block Simulation 99 I/SWMM JOB (2006,3400,200,50,0),'GARY F. GOFORTt1',CLASS=1,REGION=512K, II I*PASSWORD 2,RAIN I*ROUTE PRINT REMOTE6 II EXEC FORTXCLE,LPARM='LIST,MAP,OVLY',OPTIONS='NOSOURCE,NOMAP' IIFORT.SYSIN DD SUBROUT I tJE COtB IN RETURN END SUBROUTINE TRANS RETURN END SUBROUTINE RECEIV RETURN END SUBROUTINE EXTRAN RETURN END SUBROUTINE RUNOFF RETURN END 1* IIJC LUD E urn TDNT* /*INCLUDE 5TRT&&& /*INCLUDE STRDAT* I*INCLUDE PLUGS* 1* I/LKED.SYSLMOD DD SPACE=(CYL,(S,l,l IILKED.SYSUTI DO SPACE=(CYL,(S,2 /ILKED.LIB DO DSN=UF.A0063473.SWMM,DISP=SHR IILKED.SYSIN DO INC L U 0 ELI B 01 A I r J) I NCLUOE LI B (GRAPH, CURVE, PI fJE, PPLOT, SCALE, HYSTAT) OVERLAY ALPHA INCLUDE LIB(CONTRX,STCOSX) INSERT Sl,S2. OVERLAY BETA INCLUDE LIB{EQUATX,INTERX) IIGO.FTOIFOOI DO UNIT=SYSDA,SPACE=(TRK,(SO,lO, I I VO L=S ER=\IORKO 1, DCB=( R ECFM=VBS, B LKS I Z E=4 2 40, BUFNO=I) IIGO.FT02FOOI DO II IIGO.FT03FOUI DO UNIT=SYSDA,SPACE=(TRK,(SO,lO, II VOL=SER=WORKOl,DCB=(RECFM=VBS,BLKSIZE=4240,BUFNO=1) IIGO.FT04FOOl'DD SYSOUT=A,DCB=(RECFM=FSA,LRECL=133,BLKSIZE=133) IIGO.FT08FOOl DD UNITaSYSDA,SPACE=(TRK,(SO,50, II VOLSER=WORK01,DCB=(RECFM=VBS,BLKSIZE=4240,BUFNO=1) IIGO.FT09FOOI DO UrJIT=SYSDA,SPACE=(TRK,(50,10, II VOL=SER=WORKOl,DCB=(RECFM=VBS,BLKSIZE=4240,BUFNO=1) IIGO.FTIOFOOI DD UNIT=SYSDA, II DCB=(RECFM=VBS,BLKSIZE=4240,LRECL=80,BUFNO=1), II DISP=SHR,DSN=UF.A0063473.RAINAA IIGO.SYSIN DO 10 8 10 B 10 8 10 8 10 8 10 8 10 8 10 8 1 ? h PAGE 114 Table A2 (cont.) 100 l OU54 STORAGE 0055 BASIN ONE 0056 0057 B1. 0 1 1 1 0 OU58 Cl 530101 0.0 0 0 0 0059 01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ,0060 01 0.1 0.1 0.1 0.1 00G1 Ell OU62 F1 BASIN 0063 F2 10000.0 1 100 100 100 0064 G1 1.0 0065 G2 0 0 1 0066 G2 0067 G3 1.666E04 OOG8 G3 1.0 1.0 0069 HI OU70 11 1 2 3 0071 13 0.0 5000 a 0072 13 0.5 5304 a 0073 13 1.0 5616 0 0074 13 1.25 5775 3.151 0075 13 1.5 5936 4.457 'I U76 13 2.0 6264 6.303 13 2.5 6600 7.719 0078 1 3 3.0 G944 8.913 0079 13 3.5 7296 9.965 0080 13 4.0 7656 10.912 0081 13 4.5 8024 11.791 OU82 I 3 0033 15 0.0 0.0 0.450 0.450 0.0 0084 16 0.0 0085 /*INCLUOE Gl 0086 ENOPROGRAM 0087 / END OF \WRK FILE. PAGE 115 Table A3 Program Listing of Interface Program 1 01 l 0000 IIFLY JOB (2006,3400,lOO,5,0),FLY,CLASS=1,REGION=512K, 0001 II MSGLEVEL=(l,l) 0002 I*PASS\JORD 2,RAI N 0003 I*ROUTE PRINT rcp 0004 II EXEC WATFIV 0005 $JOB 0006 DIMENSION OUTFlW(24l,FLOH(24),POLl(24) 0007 DIMENSION IFLmJ(24) 0008 DIMENSION IDATE(24) 0009 Dlt .. 1ENSI01J ISAVECIO),tJDIM(lO) 0010 CHARACTER SOURCE*4(S),PNAME*4(2,2),PUNIT*4(2,2) 0011 CHARACTER TITLEl*4(40),TITLE2*4(40) 0012 LEND=721231 0013 LOCAT=090451 0014 NQSDUM=l 0015 READ(lO) TITLEl 0016 READ(lO)' IDATEZ,ZZERO 0017 READ(lO) TITLE2 0018 REAO(lO) (SOURCE(K),K=l,S),NSTEP,OELT,INLETS,NQSDUM,TAREA 0019 READCIO) (ISAVE(K),K=l,INLETS) o 0 2 0 REA D ( 1 0) P N AM E ( K, K W ) K = 1 2 ) K \ J = 1 N Q S DUM) 0021 RfAD(10) PUNIT(K,KW),K=1,2),KW=1,NQSDUM) 0022 READ(10) (NDIM(K),K=l,NQSDUM),QCONV 0023 10 ITFLOW=O 0024 DO 250 J=l,24 a a 2 5 REA D ( 1 0 ) AT I ME 1, I D ATE ( J ) T I tv! E I, 0 U T F UH J ) PO L L( J ) C********************* CONVERT CFS TO HUIWREDTHS OF AN INCH **** 0027 C FLOvJ(CFS) 3GOOSEC 100% 121N PER FOOT / ( 43S60FT2 PER ACRE 0028 C 24.7 ACRES) = FLOW 4.015124 o 0 2 9 2 0 0 F L mJ( J ) = 0 U T F UH J ) 4 0 15 1 2 4 o U3 0 C OU31 C********** COfJVERTING TO INTEGER AND ROUNDING UP ( >0.5) *********** 0032 I F LmJ( J ) = I F I X ( F LmJ( J ) ) OU33 DIFF=(FLOW(J)FLOAT(IFLOW(J) 0034 IFCDIFF.GE.0.5) IFLOW(J)=IFLOW(J)+l 0035 C 0036 ITFLOW=ITFLOW+IFLOW(J) 0037 250 CONTINUE 0038 JDATE=IDATE(l) 0039 INT=JDATE/IOO 0040 .INT1=lrn*100 0041 INT2=JDATEINTI IF(INT2.EQ.1)GO TO 280 0043 IF(ITFLOH.LT.l)GO TO 10. o U 4 4 2 8 0 R I T E ( 8 3 U 0) L 0 CAT J D ATE, ( I F L 0\ H J ) J = 1 1 2 ) L 0 CAT J 0 ATE, ( I F L mJ( J ) 0045 IJ=13,24), 0046 300 FORMAT(2IG,'1',1213,/,216,'Z',1213) 0047 IF CJDATE.LT.LEtlD) GO TO 10 0048 350 CONTINUE 0049 STOP 0050 END ,,0051 $ENTRY 0052 //GO.FT08FOOI DD UNIT=SYSDA, 0053 II DSN=UF.BOU63400.S6.RAINC,SPACE=(TRK,(125,10),RLSE), o 0 5 4 / I DIS P = (t J E \I CAT L G ) ,DC B = (f( E C F M = F B, lJ L K S I Z E ::: 6 1 GO, L R E C L = [: 0 ) 0055 IIGO.FTI0FOOI DO UNIT=SYSDA, 0056 II DCB=CRECFM=VBS,LRECL=BO,BLKSIZE=4240,BUFNO=1), o U 5 7 / / DIS P = S H R D S '" U F A 0 0 G 3 4 7 3 R A I r J A 1*rn,1 PAGE 116 Table A4 SYNOP Execution 0000 IISYNOP JOB (200G,3400,SO,5,O),'GRIZZLY',CLASS=1 0001 I*PASSIJORD 0002/*kOUTE PRINT OUU3 II EXEC FORTXCLE,SUBLIB1='CIRCA.FORTLIB',LPARM='LIST,NOMAP' 0004 IIFORT.SYSIN DD 0005 1* 0006 IILKED.LIB DO DSN=UF.A0063473.SYNOP,DISP=SHR 0007 IILKED.SYSIN DO 0008 INCLUDE LIB(MAIN) OU09 INCLUDE LIB(COAD2,SETIA,NUMER,IDATE,SHELL,SHELR,DAIDA) 0010 IIGO.SYSIN DO 0011 90451 004110 0012 IIGO.FT10F001 DO UNIT=SYSOA,OISP=SHR,OStJ=UF.B0063400.S6.RAINC, 0013 II OCB=(RECFM=FB,LRECL=80,BLKSIZE=61GO) 0014 IIGO.FT11F001 DO UNIT=SYSOA,SPACE=(TRK,(20,10, 0015 II VOL=SER=WORK01,DCB=(RECFM=FB,LRECL=80,DEN=3,BLKSIZE=800) I 1016 1* OF WORK FILE 1 02 PAGE 117 L, G APPENDIX B BASIN Development and Listing BASIN is a small BASIC program written to generate hydraulic relationships variety Or basin geometries. This is necessary as input to the Storage/Treatment Block Or SWMM. The development BASIN is depicted in Figure B1. The wetted area of a basin is a function the basin side slope and the depth. The resulting stagesurface area relationship is integrated over the basin depth to yield the stagevolume relationship. I BASIN also calculates the stagedischarge relationship based on gravity drainage. 10 20 30 40 50 60 70 80 90 100 110 120 130 140 BASIN INPUT "WHAT ARE THE DEPTH, BASE, LENGTH, AND SLOPES?"iD,B,L, S1,82,S3,S4 INPUT "WHAT ARE THE DIMENSIONS OF THE OUTLET DIAMETER AND HEIGHT?";PI,HT FOR D1=0 TO D VOL=B*D1*L+Dl*D1*D1/3*(S1*S2+S2*S3+S3*S4+S4*S1)+ D1*D1/2*(B* PAGE 118 L B \ y __ 1. \ = dt?s' en .. w 0:: C/) 0 dmax DEPTH 0 .. W ,(9 0:: :c () en Cl 0 dmax DEPTH Fi.gure B1. Development of BASIN. 104 SA = BL + kId + k 2 d 2 kl = B(sl + 83 ) + L(82 + 84 ) k2 = 8182 + 8283 + 8384 + 8481 dV = SAdd V = S SAdd V = BLD + k3d2 + k 4 d3 k3 = kl/2 k4 = k2/3 > .. w ::> .J 0 > 0 DEPTH Q = k (d d )1/2 6 0 dmax k6 = (CE)SA 1 (2g)I/2 out et PAGE 119 APPENDIX C Detention Time The concept hydraulic detention time is widely applied in many areas science and engineering. Typically, storage/treatment are designed under steady state and uniform conditions. In practice, detention present in estimating a hydraulic detention time due to characteristics which violate ideal assumptions. A simplirication rrequently employed in reservoir design and lake studies is averaging the rlow ovei a relatively long time interval, usually a year, and assuming that the change in volume over the time interval is zero, implying a steady state condition. The and storages in urban stormwater detention are characterized by a smaller (less than one year) time scale, due to quicker turnovers. As a result, there is a need to examine the rlow routing process on a smaller time scale in order to analyze the treatment characteristics Or the control unit. PAGE 120 Behind td=V/Q: SteadyState Conditions Under unirorm flow conditions, the velocity Or water in a control unit is equal to 106 v==Q/A (Cl) where v is the velocity r LIT J, Q is the flow [ L3 IT J, and A is the crosssectional area Or .plow [ L2 J. The length or time (t) required to travel a distance (L) is t==L/v (C2) Assuming that the same steady and unirorm rlow conditions prevail in a detention basin, the travel time (detention time) is td == L/v == L/(Q/A) == (LA)/Q == vIa (C3) where V is the basin volume in [ L3 J Figure C1 shows some common configurations of control units at steady state conditions. For a system composed Or bas ins ins e r i e s ( C 1 b ) the tot a 1 d e ten t i on t i me i s the sum of the individual basin detention times. For parallel basins (Clc), the average detention time ror the system is the sum of the product Or the percentage or total flow traversing each circuit and the detention time or that circuit. In Figure Clc, the percentage Or flow passing through basin 1 is (alQ/Q), and the detention time is PAGE 121 1 v IQ I =td = VIQ a) VI I / Va td = VI/Q + V2/Q b) VI Q Q td = VI/Q+V2/Q V2 a2Q a2.Q c) KQ Q (I+K )Q Q td = ('.)(:!! ... E) VI V2 I+K. Q Q d) Fi 9 u r e C 1. V a rio usc 0 n t r 0 1 u nit con fig u rat ion s : steadystate conditions. 1 07 PAGE 122 \ 108 (Vl/alG). The 1 to the system detention time is (alG/G) (Vl/alG) = V1/O (C4) calculations basin 2 yields the system detention time td = Vl/G + V2/Q (CS) Expanding this concept to multiple tank in td = summation i=l to n (Vi/G) (C6) a system containing a loop, as in Cld, the detention time is to the weighted sum of the tanks' detention times and the detention time. The passing the system without is Q/(l+k)G = 1/(1+k) (C7) k is the while the is kG/(l+k)G = k/(l+k) (C8) The system detention time is td = (1/(1+k(Vl/Q+V2/Q) (C9) PAGE 123 Notice that the rlow in the recycle system receives less treatment time than the rlow through basins in series. Hence, settling basins are rarely designed with recycle. Analysis or NonsteadyState Conditions By employing rinite dirrerence techniques, equations ror detention times or the in Figure Cl may be 109 developed ror nonsteadystate conditions. Using the average volume during the time interval dt, the expression dv/dt by derinition is zero. The rlow passing through a tank is described by both an inflow and a outflow term. By derining the instantaneous rlow as the mean or the inflow and outrlow magnitudes, the average rlow over a time interval can be determined as the mean instantaneous rlow. Q = (in + out)/2 Q(ave) = (0 at t + Q at t+dt)/2 (CI0) Expanding this concept to average detention time, td(ave) = V(ave)/O(ave) (C11) Control unit configurations under nonsteady but linear rlow conditions are presented in Figure C2, where the errluent is proportional to the amount Or storage. The detention time may be represented as td = (2V) I (O+kV) (C12) PAGE 124 ,,... 1 1 0 v I K,V. (:. td = V/OtKV) a) I .E.1 VI V td = 2V, Q + KIVI + 2V2 KIV, + K2V2 b) VI Q K,VI+K2V2 2V, + 2V2 td = oIQI'+KIVt o2Q+K2V2 I..eV2 ....:::0 a2Q K2V2 K2V2 KJVt K2 V2 td = R+St (A) VI V2 S :.' Fjgure C2. Various control configurations: nonsteadystate conditions. PAGE 125 111 For a series or linear units, the system detention time is equal to the sum or the components# detention times. td = summation Trom i=l to n [(2V(i I (k(il)V(il)+k(i)V(i] For parallel tanks the detention time is td = summation rrom i=l to n C(2a(i)V(i I (a(i)Q + k(i>VCi] (C13) (C14) For tanks with recycle, the rlow recycled is proportional to the volume in basin 2. The amount flowing in the system (8) is 8 = (Q+2klVl+2k2V2+k3V2)/4 (C15) The amount passing straight through the system (St) is (k3V2), and the recycle Tlow (R) is (k2V2>. The detention time is td = St+R)/S)(A) (C16) where A = Vl/(Q+k2V2+klVl + (2V2)/(klVl+k2V2+k3V2 It is emphasized that these equations will describe steady state systems and will reduce to the equations in Figure Cl when in.plows equal 'out.plows. Also, these equations are equally valid .por any system which can be described by similar (linear) kinetics. PAGE 126 L REFERENCES 1. Council on Environmental Quality. Environmental Quality. The Ninth Annual Report OT the Council on Environmental Quality, Non Point Sources. December 1978. 2. Chow, V. T Ed., Handbook oT Applied Hydrology A Compendium oT Waterresources Technology. McGrawHill Book Company, New York, N. Y., 1964. 3. Dever, R. Discussion on Stormwater Interception and Storage by Dominic Di Toro. oT the Environmental Engineering Division. ASCE. Vol. 106, No. EE4. April 1980. 4. Dillon, P. The Phosphorus Budget OT Cameron Lake, Ontario: The Importance oT Flushing Rate to the Degree oT Eutrophy oT Lakes. Limnology and Oceanography, Vol. 20, 1975, pp. 2839. 5. Di Toro, D. M., and M. Sma 11. Stormwater Interception and Storage, oT the Environmental Eng i neer i ng Di vi s ion. ASCE, vo 1. 105, No. EEL February 1979, pp. 4354. 6. C.!., Linear Theory or Hydrologic Systems, Technical BUlletin No. 1468, Agricultural Research Service, USDA, D. C., 1973. 7. Eagleson. P. S Dynamic Hydrology. McGrawHill Book Company, New York, New York, 1970. 8. Fair, G. M C. Geyer, and D. A. Okun, Water and Wastewater Engineering, Vol. 2, Water Purification and Wastewater Treatment and Disposal, Wiley and Sons, Inc., New York, New York, 1968. 9. Haan, C. T., Statistical Methods in Hydrology, The Iowa State University Press, Amos Iowa, 1977. 10. P., W. C. Huber, H. Sheikh, M. A. Medina, 11. R. Doyle, W. A. Peltz, and E. Darling. Urban Stormwater Management Modeling and DecisionMaking, EPA Report No. 670/275022, National Environmental 'Research Center" Cincinnati, Ohio, May 1975. Heaney, P., Economic/Financial Analysis OT Urban Water Quality Management Problems, EPA Grant No. R802911024, Municipal Environmental Research Laboratory, Cincinnati, Ohio. March 1979. PAGE 127 L/ 113 12. Howard, C. D. D., of Storage and Treatment Plant Overflows, Journal of the Environmental Engineering Division, ASeE, Vol. 102, No. EE4, August 1976, pp. 709722. 13. Huber, W. C., J. P. Heaney, and S. J. Nix, Stormwater Management Model User's ManualVersion III, EPA Draft Report, National Environmental Research Center, Cincinnati, Ohio, 1980. 14. Huber, W. C., P. L. Brezonik, J. P. Heaney, G. F. Goforth, M. C. Cullem and D. J. Pollmann, An Environmental Study of Hogtown Creek in Gainesvil.le, Fla., Final Report to Florida Dept. of Environmental Regulation, Gainesville, Fla., March 1981. 15. Hydroscience, Inc., A Statistical Method for the Assessment of Urban Stormwater, EPA440/379023, Office of Water Planning and Standards, Washington, D. C., May 1979. 16. Liptak, B. G., Environmental Engineers' Handbook, VOl.1 1: Water Pollution, Chilton Book Company, Radner, Pennsylvania, 1974. 17. Med ina, M. A., Jr., Interaction of Urban Stormwater Runoff, Control Measures and Receiving Water Response, Dissertation presented to the Graduate Council of the University of Floridain partial fulfillment of the reguirements for the degree of Doctor of Philosphy, Gainesville, Florida, 1976. 18. Medina, M.A., Discussion on Water Quality Trap Efficiency of Storm Water Management Basins, by R. H. McCuen, Water Resources Bulletin, Vol. 17, No. 1, February 1981. 19. Nix, S. J., J. P. Heaney, and W. C. Huber, Water Quality Benefits of Detention, Chapter 12 of APWA Manual, January 1981. 20. Reckhow, K. H., Lake Quality Discriminant Analysis, Water Resources Bulletin, Vol. 14, No.4, August 1978. 21. Reckhow, K. H., M. N. Beaulac and T. Simpson, Modeling Phosphorus Loading and L.ke Response Under Uncertainty: A Manual and Compilation of Export Coefficients, EPA Clean Lakes Section, Washington, D. C., June 1980. 22. Rich, L. G. I Environmental Systems Engineering, McGrawHill Book Company, New York, New York, 1974. PAGE 128 114 23. Sc hnoor, J. L., and D. J. 0 'Conner, A Simp liT i ed Approach Tor Eutrophication Modeling of Lakes, A Papaer Presented at the 51st. Annual ConTerence OT WPCF, Anaheim, CaliTornia, October 1978. 24. Small, M. and D. M. Di Toro, Stormwater Treatment Systems, Journal OT the Environmental Engineering Division, ASCE, Vol. 105, No. EE3, June 1979, pp. 557569. 25. Smolenyak, K., Urban WetWeather Pollutant Loadings, A thesis presented to the Graduate Council OT the University OT Florida in partial fulfillment of the requirements for the Degree or Master Or Engineering, University of Florida, Gainesville, Florida, 1979. 26. Sonzogni. W. C., P. C. Uttormark and G. F. Lee, A Phosphorus Residence Time Model: Theory and Application, Water Resources Research, Vol. 10, March 1975, pp. 429435. 27. U. S. Army Corps Or Engineers, Urban Stormwater Runoff STORM, Generalized Computer Program, 723S8L2520, 28. H. E.C., May 1974. Vollenweider, R. A., Water Management Research, DECOReport 6872, Paris, 1968. 29. Vollenweider, R. A., and P. J. Dillon, The Application of the Phosphorus Loading Concept to Eutrophication Research, Canada Centre for Inland Waters, National Research Council of Canada, 1974. 30. Vollenweider, R. A., Advances in Defining Critical Loading Levels for Phosphorus in Lake Eutrophication Men. Ita!., Idrobio1., 1976. 31. Ward, A. J., C. T. Haan and B. J. Barfield, Simulation of the Sedimentology OT Sediment Detention Basins, OWRT B046KY, Water Research Institute, Lexington, Kentucky, June 1977. 32. Weber, W. J., Physicochemical Processes ror Water Guality Control, New York, New York, 1972. 33. White, J. B., and M. R. AlIos, Experiments on Wastewater Sedimentation, Journal WPCF, Vol. 48, No.7, July 1976, pp. 17411751. PAGE 129 BIOGRAPHICAL SKETCH Gary Frank Edmon Goforth was born on December 12, 1956. Just outside the prison walls in Huntsville, Texas. He grew up in Texas and Indiana and has lived in Florida since 1966. He enrolled at the University Florida in 1975, and received a Bacheior of Science in Engineering (Environmental Engineering) in 1979. He subsequently entered the Graduate School at the University of Florida, working on a Master of Engineering Degree in Environmental Resources Management. He was a member of Tau Beta Pi and Kappa Phi Kappa honorary societies, the Water Pollution Control Federation, the American Water Works Association, and the Aircraft Owners and Pilots Association. To support his academic habit, he worked throughout his undergraduate and graduate career. Beginning as a haberdasher, he has monitored the effects thermal effluent from a nuclear power plant on a saltwater marsh, researched tertiary treatment of domestic waste in a freshwater marsh, and assessed the impact of urbanization on the water quality of an urban stream. He has coauthored several annual reports associated with these proJects. In 1980, he married a wonderful little Polish girl, Karen. 115 