| Note copyright and disclaimer restrictions. | © Wm James 1999-2002`  |   Questions?  |  Updated 02/01/28 |
| Cite: "James, Wm. (2000). 05-661,05-662 Web site. U. of Guelph, Sch. of Eng'rg. www.eos.uoguelph.ca/ webfiles/james"  | 

05-662 Water pollution control planning (for UCT students, CIV530Z  is a programme of individual study on a specialized topic - examination by report/s and possibly an oral) is a graduate engineering course, comprising the six even-numbered modules below: 2. philosophy underlying public water pollution; 4. methods of developing area-wide pollution control plans and sustainable use plans in Ontario and elsewhere; 6. introduction to BMPs and the SLAMM model; 8.  introduction to the WASP model; 10. Urban litter in drainage systems;  12. examination of quantitative and non-quantitative information in the context of planning. No field trips are planned for Jan-Apr 2000. More info is provided in module 0.   

Current modules in this website are for January to April 2002.   

module 7

contents

RUNOFF

Introduction
Overview of Quality Procedures
Quality Simulation Credibility
Required time resolution
Quality Constituents
Land Use Data
Buildup
Available buildup studies
Buildup Formulations
Buildup Data
Washoff
Washoff Formulation
Effects of washoff parameters
Related Buildup-Washoff Studies
Street Cleaning
Constituent Fractions
Available Information
Effect in RUNOFF Module
Precipitation Chemistry
Effect of rain pollutants in RUNOFF Module
Urban Erosion
Universal Soil Loss Equation
Erosion Simulation
Rainfall Factor and Maximum Thirty Minute Intensity
Erosion Area
Slope Length Gradient Ratio
Cropping Management Factor
Control Practice

SLAMM - this section is copyrighted and provided by Dr Pitt

Additions to Existing Module 7 - Observed Pollutant Buildup and Washoff (or why I developed SLAMM)

For subject click on the asterisk

Introduction *
Street Dirt Accumulation *
Methodology for Street Dirt Accumulation Measurements *
Street Surface Particulate Sampling Procedures *
Street Dust and Dirt Pollutant Characteristics *
Summary of Observed Accumulation Rates *
Washoff of Street Dirt *
Background *
Yalin Equation *
Sartor and Boyd Washoff Equation *
Street Dirt Washoff Observations and Comparisons with the Yalin, and Sartor and Boyd Washoff Equations *
Small-Scale Washoff Tests *
Washoff Equations for Individual Tests *
Comparison of Particulate Residue Washoff Using Previous Washoff Models and Revised Washoff Model *
Summary of Street Particulate Washoff Tests *
Observed Particle Size Distributions in Stormwater *
"First-Flush" of Stormwater Pollutants from Pavement *
References *
Reading and links *
Comment on Assignment A7 *

Assignment A7

Introduction

Pedagogic note: Learning objectives for this module include exploring the basic uncertainty in stormwater quality simulation. We restrict ourselves here to the somewhat detailed method used in SWMM RUNOFF. Thus in this section I have cut and paste material originally written by Wayne Huber for the SWMM documentation, but somewhat edited for the version of the manuals which I produce locally for my students. Hence the figure, table and equation numbers. As the material is for SWMM simulation it should be read selectively. My intention here is to show that even these so-called detailed methods are based on noisy observations, and have more unexplained variance than they have determinism - see for example  Figure 4-34. Non-linear buildup of street solids. Note that the inherent uncertainty is not (as it "should oughtta be") reported in SWMM computed results.Thus sensitivity, calibration and error analysis (SCEA) is an important part of modelling. Instead of covering SCEA in detail on this page, click here to link to an unfinished, preliminary, draft booklet on SCEA for SWMM modelling. You are required to summarize the main points of your potential interest in this topic, and tie your discussion to potential applications to problems in your areal.

Source: Storm Water Management Model version 4 User's manual, by Wayne C Huber and Robert E Dickenson, USEPA first printed August 1988. RUNOFF module quality routines, taken from various pages therein. Rearranged by W James, 1999.

----excerpts from SWMM manual starts (I have made numerous cuts and simplifications)

Simulation of urban runoff quality is very inexact. The many difficulties of simulation of urban runoff quality are discussed by Huber (1985, 1986) [*References not yet added to this page 00.01.25 - see Bill's version of the manuals]. Very large uncertainties arise both in the representation of the physical, chemical, biological and sociological processes and in the acquisition of data and parameters for model algorithms. The true mechanisms of buildup involve factors such as wind, traffic, atmospheric fallout, land surface activities, erosion, street cleaning and other imponderables. Although efforts have been made to include such factors in physically-based equations (James and Boregowda, 1985), it is unrealistic to assume that they can be represented with enough accuracy to determine a priori the amount of pollutants on the surface at the beginning of the storm. Equally naive is the idea that empirical washoff equations truly represent the complex hydrodynamic (and chemical and biological) processes that occur while overland flow moves in random patterns over the land surface.

Such uncertainties can be dealt with in two ways. The first option is to collect enough calibration and verification data to calibrate the model equations used for quality simulation. Given sufficient data, the equations used in SWMM can usually be manipulated to reproduce observed concentrations and loads. This is essentially the option discussed at length in the following sections. The second option is to abandon the notion of detailed quality simulation altogether and use either (a) a constant concentration applied to quantity predictions (i.e., obtain storm loads by multiplying predicted volumes by an assumed concentration) (Johansen et al., 1984) or (b) a statistical method (Hydroscience, 1979; Driscoll and Assoc., 1981; EPA, 1983b; DiToro, 1984). Two ways in which constant concentrations can be simulated in SWMM are by using a rating curve (equation 4-116) with an exponent of 1.0 or by assigning a concentration to rainfall. Statistical methods are based in part upon strong evidence that storm event mean concentrations (EMCs) are lognormally distributed (Driscoll, 1986). The statistical methods recognize the frustrations of physically-based modeling and move directly to a stochastic result (e.g. a frequency distribution of EMCs), but they are even more dependent on available data than methods such as those found in SWMM. That is, statistical parameters such as mean, median and variance must be available from prior information. Furthermore, it is harder to study the effect of controls and catchment modifications using statistical methods.

The main point is that there are alternatives to the approaches used in SWMM; the latter can involve extensive effort at parameter estimation and model calibration to produce quality predictions that may vary greatly from an unknown "reality." Before delving into the arcane methods incorporated in SWMM and other urban runoff quality simulation models, you should try to determine whether or not the effort will be worth it in view of the uncertainties of the process and whether or not simpler alternative methods might suffice. The discussions that follow provide a comprehensive view of the options available in SWMM, which are more than in almost any other comparable model in the public domain, but the extent of the discussion should not be interpreted as a guarantee of success in applying the methods.

Overview of Quality Procedures

Methods for estimation of urban runoff quality constituents are reviewed extensively by Huber (1985, 1986). Many constituents can appear in either dissolved or solid forms (e.g. BOD, nitrogen, phosphorus) and may be adsorbed onto other constituents (e.g. pesticides onto "solids") and thus be generated as a portion of such other constituents. To treat this situation, any constituent may be computed as a fraction ("potency factor") of another. For instance, five percent of the suspended solids load could be added to the (soluble) BOD load. Or several particle size - specific gravity ranges could be generated, with other constituents consisting of fractions of each.

Up to ten quality constituents may be simulated in the RUNOFF Module. All are user-supplied, with appropriate parameters for each. All are transferred to the interface file for transmittal to subsequent SWMM modules, but not all may be used by the modules; see the documentation for each module.

Up to five user-supplied land uses may be entered to characterize different subcatchments. Street sweeping is a function of land use, and individual constituents. Constituent buildup may be a function of land use or else fixed for each constituent. Considerable flexibility thus exists.

When channel/pipes (links) are included, quality constituents are routed through them assuming complete mixing within each gutter/pipe (link) at each time step. Scour, deposition or decay-interaction during routing is simulated in the TRANS module and not at all in the RUNOFF Module.

Output consists of pollutographs (concentrations versus time) at desired locations along with total loads, and flow-weighted concentration means and standard deviations. In addition, summaries are printed for each constituent describing its overall mass balance for the simulation for the total catchment, i.e., sources, removals, etc. These summaries are the most useful output for continuous simulation runs.

In the following material, the processes described above are discussed in more detail. 

Quality Simulation Credibility

Although the conceptualization of the quality processes is not difficult, the reliability and credibility of quality parameter simulation is very difficult to establish. In fact, quality predictions are almost useless without local data for calibration and validation. If such data are lacking, results may still be used to compare relative effects of changes, but parameter magnitudes (e.g. predicted concentrations) will forever be in doubt. This is in marked contrast to quantity prediction for which reasonable estimates of hydrographs may be made in advance of calibration.

Moreover, there is disagreement in the literature as to what are the important and appropriate physical and chemical mechanisms that should be included in a model to generate surface runoff quality. The objective in the RUNOFF Module has been to provide flexibility in mechanisms and the opportunity for calibration. But this places a considerable burden on you to obtain adequate data for model usage and to be familiar with quality mechanisms that may apply to the catchment being studied. This burden is all too often ignored, leading ultimately to model results being discredited.

In the end then, there is no substitute for local data, that is, observed rain, flow and concentrations, with which to calibrate and verify the quality predictions. Without such data, little reliability can be placed in the predicted magnitudes of quality parameters.

Required Degree of Temporal Detail

Early quality modeling efforts with SWMM emphasized generation of detailed pollutographs, in which concentrations versus time were generated for short time increments during a storm event (e.g. Metcalf and Eddy et al., 1971b). In most applications, such detail is entirely unnecessary because the receiving waters cannot respond to such rapid changes in concentration or loads. Instead, only the total storm event load is necessary for most studies of receiving water quality. Time scales for the response of various receiving waters are presented in Table 4-17 (Driscoll, 1979; Hydroscience, 1979). Concentration transients occurring within a storm event are unlikely to affect any common quality parameter within the receiving water, with the possible exception of bacteria. The only time that detailed temporal concentration variations might be needed within a storm event is when they will affect control alternatives. For example, a storage device may need to trap the "first flush" of pollutants.

Table 4-17. Required Temporal Detail for Receiving Water Analysis.. Required Temporal Detail, Receiving Water Analysis. (Driscoll, 1979; Hydroscience, 1979)

The significant point is that calibration and verification ordinarily need only be performed on total storm event loads, or on event mean concentrations. This is a much easier task than trying to match detailed concentration transients within a storm event.

Quality Constituents

The number and choice of constituents to be simulated must reflect your needs, potential for treatment and receiving water impacts, etc. Almost any constituent measured by common laboratory or field tests can be included, up to a total of ten. 

Land Use Data

Each subcatchment must be assigned only one of up to five user-supplied land uses. The number of the land use is used as a program subscript, so at least one land use data must be entered. Street sweeping is a function of land use and constituent (discussed subsequently). Constituent buildup may be a function of land use depending on the type of buildup calculation specified for each. 

One of the most influential of the early studies of stormwater pollution was conducted in Chicago by the American Public Works Association (1969). As part of this project, street surface accumulation of "dust and dirt" (DD) (anything passing through a quarter inch mesh screen) was measured by sweeping with brooms and vacuum cleaners. The accumulations were measured for different land uses and curb length, and the data were normalized in terms of pounds of dust and dirt per dry day per 100 ft of curb or gutter. These well- known results are shown in Table 4-18 and imply that dust and dirt buildup is a linear function of time. The dust and dirt samples were analyzed chemically, and the fraction of sample consisting of various constituents for each of four land uses was determined, leading to the results shown in Table 4-19.

Table 4-18. Measured Dust and Dirt (DD) Accumulation in Chicago by the APWA in 1969 (APWA, 1969).

Table 4-19. Milligrams of Pollutant Per Gram of Dust and Dirt (Parts Per Thousand By Mass) For Four Chicago Land Uses From 1969 APWA Study Milligrams of Pollutant Per Gram of Dust and Dirt (Parts Per Thousand By Mass) For Four Chicago Land Uses From 1969 APWA Study (APWA, 1969).

From the values shown in Tables 4-18 and 4-19, the buildup of each constituent (also linear with time) can be computed simply by multiplying dust and dirt by the appropriate fraction. 

Of course, the whole buildup idea essentially ignores the physics of generation of pollutants from sources such as street pavement, vehicles, atmospheric fallout, vegetation, land surfaces, litter, spills, anti-skid compounds and chemicals, construction, and drainage networks. Lager et al. (1977a) and James and Boregowda (1985) consider each source in turn and give guidance on buildup rates. But the rates that are (optionally) entered into the RUNOFF Module only reflect the aggregate of all sources.

Available buildup studies

The 1969 APWA study (APWA, 1969) was followed by several more efforts, notably AVCO (1970) reporting extensive data from Tulsa, Sartor and Boyd (1972) reporting a cross section of data from ten US cities, and Shaheen (1975) reporting data for highways in the Washington, D.C. area. Pitt and Amy (1973) followed the Sartor and Boyd (1972) study with an analysis of heavy metals on street surfaces from the same ten US cities. More recently, Pitt (1979) reports on extensive data gathered both on the street surface and in runoff for San Jose. A drawback of the earlier studies is that it is difficult to draw conclusions from them on the relationship between street surface accumulation and stormwater concentrations since the two were seldom measured simultaneously.

Amy et al. (1975) provide a summary of data available in 1974 while Lager et al. (1977a) provide a similar function as of 1977 without the extensive data tabulations given by Amy et al. Perhaps the most comprehensive summary of surface accumulation and pollutant fraction data is provided by Manning et al. (1977) in which the many problems and facets of sampling and measurements are also discussed. For instance, some data are obtained by sweeping, others by flushing; the particle size characteristics and degree of removal from the street surface differ for each method. Some results of Manning et al. (1977) will be illustrated later. Surface accumulation data may be gleaned, somewhat less directly, from references on loading functions that include McElroy et al. (1976), Heaney et al. (1977) and Huber et al. (1981a).

Ammon (1979) summarized many of these and other studies, specifically in regard to application to SWMM. For instance, there is evidence to suggest several buildup relationships as alternatives to the linear one, and these relationships may change with the constituent being considered. Upper limits for buildup are also likely. Several options for both buildup and washoff are investigated by Ammon, and his results are partially the basis for formulations in this version of SWMM. Jewell et al. (1980) also provide a useful critique of methods available for simulation of surface runoff quality and ultimately suggest statistical analysis as the proper alternative. Many of the problems and weakness with extensive data and present modeling formulations are pointed out by Sonnen (1980) along with guidelines for future research.

To summarize, many studies and voluminous data exist with which to formulate buildup relationships, most of which are purely empirical and data-based, ignoring the underlying physics and chemistry of the generation processes. Nonetheless, they represent what is available, and modeling techniques in SWMM are designed to accommodate them in their heuristic form.

Buildup Formulations

Most data, as will be seen, imply linear buildup since they are given in units such as lb/ac-day or lb/100 ft curb-day. As stated earlier, the Chicago data that were used in the original SWMM formulation assumed a linear buildup. However, there is ample evidence that buildup can be nonlinear; Sartor and Boyd's (1972) data are most often cited as examples (Figure 4-34). More recent data from Pitt (Figure 4-35) for San Jose indicate almost linear accumulation, although some of the best fit lines indicated in the figure had very poor correlation coefficients, ranging from 0.35 <= r <= 0.9. Even in data collected as carefully as in the San Jose study, the scatter (not shown in the report) is considerable. Thus, the choice of the best functional form is not obvious. Whipple et al. (1977) have criticized the linear buildup formulation included in SWMM, although it is somewhat irrelevant since you may insert your own desired initial loads, calculated by whatever procedure desired. However, this is a useful option only for single-event simulation.

The proper choice of the proper functional form must ultimately be your responsibility. The program provides three options for dust and dirt buildup and three for individual constituents, namely: 1. power-linear, 2. exponential, or 3. Michaelis-Menton.

Figure 4-34. Non-linear buildup of street solids. (After Sartor and Boyd, 1972, p. 206.)

Linear buildup is simply a subset of a power function buildup. The shapes of the three functions are compared in Figure 4-36 using the dust and dirt parameters as examples, and a strictly arbitrary assignment of numerical values to the parameters. Exponential and Michaelis-Menton functions have clearly defined asymptotes or upper limits. Upper limits for linear or power function buildup may be imposed if desired. "Instantaneous buildup" may be easily achieved using any of the formulation with appropriate parameter choices. For instance, if it were desired to always have a fixed amount of dust and dirt available, DDLIM, at the beginning of any storm event (i.e., after any dry time step during continuous simulation), then linear buildup could be used with DDPOW = 1.0 and DDFACT equal to a large number ³ DDLIM/DELT. Linear buildup is fastest in terms of computer time.

Figure 4-35. Buildup of street solids in San Jose. (After Pitt, 1979, p. 29.)

  It is apparent in Figure 4-36 that different options may be used to accomplish the same objective (e.g. nonlinear buildup); the choice may well be made on the basis of available data to which one of the other functional forms have been fit. If an asymptotic form is desired, either the exponential or Michaelis-Menton option may be used depending upon ease of comprehension of the parameters. For instance, for exponential buildup the exponent (i.e., DDPOW for dust and dirt of QFACT(2,K) for a constituent) is the familiar exponential decay constant. It may be obtained from the slope of a semi-log plot of buildup versus time. As a numerical example, if its value were 0.4 day^-1, then it would take 5.76 days to reach 90 percent of the maximum buildup (see Figure 4-36).

Figure 4-36. Comparison of linear and three non-linear buildup equations. Dust and dirt, DD is used as an example. Numerical values have been chosen arbitrarily.

For Michaelis-Menton buildup the parameter DDFACT for dust and dirt (or QFACT(3,K) for a constituent) has the interpretation of the half-time constant, that is, the time at which buildup is half of the maximum (asymptotic) value. For instance, DD = 50 lb at t = 0.9 days for curve 4 in Figure 4-36. If the asymptotic value is known or estimated, the half-time constant may be obtained from buildup data from the slope of a plot of DD versus t . (DDLIM- DD), using dust and dirt as an example. Generally, the Michaelis-Menton formulation will rise steeply (in fact, linearly for small t) and then approach the asymptote slowly.

The power function may be easily adjusted to resemble asymptotic behavior, but it must always ultimately exceed the maximum value (if used). The parameters are readily found from a log-log plot of buildup versus time. This is a common way of analyzing data, (e.g. Miller et al., 1978; Ammon, 1979; Smolenyak, 1979; Jewell et al., 1980; Wallace, 1980).

Prior to the beginning of the simulation, buildup occurs over DRYDAY days for both single event and continuous simulation. During the simulation, buildup will occur during dry time steps (runoff less than 0.0005 in./hr or 0.013 mm/hr) only for continuous simulation.

For a given constituent, buildup may be computed: 1. as a fraction of dust and dirt, or 2. individually for the constituent. If the first option is used then the rate of buildup will depend upon the fraction and the functional form used for a given land use. In other words, the functional form could vary with land use for a given constituent. If the second option is used (1 £ KALC £ 3) the buildup function will be the same for all land uses (and subcatchments) for a given constituent. Of course, each constituent may use any of the options. Catchment characteristics (i.e., area or gutter length) may be included through the use of parameters JACGUT or KACGUT.

Units for dust and dirt buildup parameters are reasonably straightforward and explained in Table 4-20. For example, if linear buildup was assumed using the Chicago APWA data (APWA, 1969), values for DDFACT could be taken directly from Table 4-17 for different land uses. Parameters JACGUT would equal zero. A limiting buildup (DDLIM) of so many lb/100 ft-curb could be entered if desired, and for linear buildup, DDPOW = 1.0.

 Buildup Data

Data with which to evaluate buildup parameters are available in most of the references cited earlier under "available studies." Manning et al. (1977) have perhaps the best summary of linear buildup rates; these are presented in Table 4-23. It may be noted that dust and dirt buildup varies considerably among three different studies. Individual constituent buildup may be taken conveniently as a fraction of dust and dirt from the entries in Table 4-22, or they may be computed explicitly. It is apparent that although a large number of constituents have been sampled, little distinction can be made on the basis of land uses for most of them.

As an example, suppose options METHOD = 0 and KALC = 0 are chosen and "all data" are used from Table 4-23 to compute dust and dirt parameters. Since the data are given as lb x curb-mile-1 x day-1, linear buildup is assumed and commercial land use DD buildup (average for all data) would be DDFACT = 2.2 lb / (100-ft curb - day) (i.e., 2.2 = 116/52.8, where 52.8 is the number of hundreds of feet in a mile). DDPOW would equal 1.0 and no data are available to set an upper limit, DDLIM. Parameter JACGUT = 0 so that the loading rate will be multiplied by the curb length for each subcatchment. Constituent fractions are available from the table. For instance, QFACT values for commercial land use would be 7.19 mg/g for BOD₅, 0.06 mg/g for total phosphorus, 0.00002 mg/g for Hg, and 0.0369 106 MPN/g for fecal coliforms. Direct loading rates could be computed for each constituent as an alternative, e.g. with KALC = 1 for BOD₅ and KACGUT = 0, parameter QFACT(3,K) would equal 2.2 x 0.00719 = 0.0158 lb / (100-ft curb - day).

 Table 4-23a. Nationwide Data on Linear Dust and Dirt Buildup Rates and on Pollutant Fractions (after Manning et al., 1977, pp. 138-140.)

Table 4-23b.

It must be stressed once again that the generalized buildup data of Table 4-23 are merely informational and are never a substitute for local sampling or even a calibration using measured concentrations. They may serve as a first trial value for a calibration, however. In this respect it is important to point out that concentrations and loads computed by the RUNOFF Module are usually linearly proportional to buildup rates. If twice the quantity is available at the beginning of a storm, the concentrations and loads will be doubled. 

Almost all of the above loading data are from samples of storm water, not combined sewage. Although some loadings may be inferred from concentration measurements of combined sewage (e.g. Huber et al., 1981a; Wallace, 1980), they are not directly related to most surface accumulation measurements. Thus, if buildup data alone are used in combined sewer areas, buildup rates will probably be multiples of the values listed. The proper factor will most easily be found by calibration with local concentration measurements. Alternatively, the dry-weather flow mixing and scour routines in the TRANSport module may be used to increase combined sewer concentrations. However, mixing of dry-weather flow with storm water has a negligible effect on concentrations during high flows, and the scour routine is highly empirical and adds a second calibration step. Hence, the easiest option for combined sewers is probably to calibrate as described earlier. Calibration may also be achieved using the rating curve approach.

When snowmelt is simulated, some of the ten constituents may be used to represent deicing chemicals. Applications of such chemicals varies depending upon depth of snowfall and local practice. Loading rates are discussed in SWMM Snowmelt Routines and in other references (Proctor and Redfern and J.F. MacLaren, 1976a, 1976b; Field et al., 1973; Richardson et al., 1974; Ontario Ministry of the Environment, 1974). For instance, guidelines of the type proposed by Richardson et al. (1974) are used in many cities and are given in Table 4-24. Summaries are also given by Manning et al. (1977) and Lager et al. (1977a).

   Table 4-24. Guidelines for Chemical Application Rates for Snow Control. (Richardson et al., 1974.)

Washoff is the process of erosion or solution of constituents from a subcatchment surface during a period of runoff. It the water depth is more than a few millimeters, processes of erosion may be described by sediment transport theory in which the mass flow rate of sediment is proportional to flow and bottom shear stress, and a critical shear stress can be used to determine incipient motion of a particle resting on the bottom of a stream channel, e.g. Graf (1971), Vanoni (1975). Such a mechanism might apply over pervious areas and in street gutters and larger channels. For thin overland flow, however, rainfall energy can also cause particle detachment and motion. This effect is often incorporated into predictive methods for erosion from pervious areas (Wischmeier and Smith, 1958) and may also apply to washoff from impervious surfaces, although in this latter case, the effect of a limited supply (buildup) of the material must be considered.

Washoff Formulation

Ammon (1979) reviews several theoretical approaches for urban runoff washoff and concludes that although the sediment transport based theory is attractive, it is often insufficient in practice because of lack of data for parameter (e.g. shear stress) evaluation, sensitivity to time step and discretization and because simpler methods usually work as well (still with some theoretical basis) and are usually able to duplicate observed washoff phenomena. Among the latter, the most oft-cited results are those of Sartor and Boyd (1972), in which constituents were flushed from streets using a sprinkler system. It would appear that an exponential relationship could be developed to describe washoff of the form:

(4-133)

• where POFF = cumulative amount washed off at time, t,
• PSHED_o = initial amount of quantity on surface at t = 0, and
• k = coefficient.

Alternatively, since the amount remaining, PSHED(t), equals PSHED_o - POFF, then:

(4-134)

• where PSHED(t) = quantity remaining on surface at time, t,
• PSHED_o = initial amount of quantity, and
• k = coefficient.

It is clear that the coefficient, k, is a function of both particle size and runoff rate. An analysis of the Sartor and Boyd (1972) data by Ammon (1979) indicates that k increases with runoff rate, as would be expected, and decreases with particle size.

The Sartor and Boyd data lend credibility to the washoff assumption that the rate of washoff (e.g. mg/sec) at any time is proportional to the remaining quantity:

(4-135)

The solution of equation 4-135 is equation 4-134. This was first proposed by Mr. Allen J. Burdoin, a consultant to Metcalf and Eddy, during the original SWMM development. The coefficient k may be evaluated by assuming it is proportional to runoff rate, r:

(4-136)

• where RCOEF = washoff coefficient, in.^-1, and
• r = runoff rate over subcatchment, in./hr.

Burdoin assumed that one-half inch of total runoff in one hour would wash off 90 percent of the initial surface load, leading to the now familiar value of RCOEF of 4.6 in.^-1. (The actual time distribution of intensity does not affect the calculation of RCOEF.)

Sonnen (1980) estimated values for RCOEF from sediment transport theory ranging from 0.052 to 6.6 in.^-1, increasing as particle diameter decreases, rainfall intensity decreases, and as catchment area decreases. He pointed out that 4.6 in.^-1 is relatively large compared to most of his calculated values. Although the exponential washoff formulation of equations 4-135 and 4-136 is not completely satisfactory as explained below, it has been verified experimentally by Nakamura (1984a, 1984b), who also showed the dependence of the coefficient k on slope, runoff rate and cumulative runoff volume.

This exponential formulation did not adequately fit some data, and as a "correction," availability factors of the form

(4-137)

• where AV = availability factor, and
• a,b,c = coefficients,

were multiplied by equation 4-133 in order to match measured suspended solids concentrations in Cincinnati and San Francisco (Metcalf and Eddy et al., 1971a). The primary difficulty is that use of equations 4-135 and 4-136 will always produce decreasing concentrations as a function of time regardless of the time distribution of runoff. This is counter-intuitive, since it is expected that high rates during the middle of a storm might indeed produce higher concentrations than those preceding. This may be explained by observing that concentrations are calculated by dividing the load rate (e.g. mg/sec) to obtain the quantity per volume (e.g. mg/L). Thus,

(4-138)

• where C = concentration, quantity/volume,
• Q = A × r = flow rate, cfs,
• A = subcatchment area, ac, and
• r = runoff rate, in./hr.,

and the constant incorporates conversion factors. Clearly, the concentration will always decrease with time since the runoff rate, r, divides out of the equation and the quantity remaining, PSHED, continues to decrease. This problem is overcome in SWMM by making washoff at each time step, POFF, proportional to runoff rate to a power, WASHPO:

(4-139)

• where POFF = constituent load washed off at time, t, quantity/sec (e.g. mg/sec),
• PSHED = quantity of constituent available for washoff at time, t, (e.g. mg),
• RCOEFX = washoff coefficient = RCOEF/3600, (in/hr^)-WASHPO × sec^-1, and
• r = runoff rate, in./hr.

It may be seen that if equation 4-139 is divided by runoff rate to obtain concentration, then concentration is now proportional to rWASHPO-1. Hence, if the increase in runoff rate is sufficient, concentrations can increase during the middle of a storm even if PSHED is diminished. (Equation 4-139 was first suggested in a 1974 report to the Boston District Corps of Engineers, authorship unknown).

There are two parameters to be determined, RCOEF and WASHPO. Availability factors of the form of equation 4-137 are no longer used since there is sufficient flexibility for calibration using only equation 4-139.

Effects of Parameters

In subroutine QSHED of the RUNOFF Module, washoff load rates (e.g. mg/sec) are computed instantaneously at the end of a time step using equation 4-110. They are subsequently combined with other possible inflow loads to a gutter/pipe (link) or inlet (node) before dividing by the total inflow rate to obtain a concentration. The remaining constituent load on the subcatchment at the end of a time step is determined by using the average power of the runoff rate over the time step,

4-114)

This calculation is done prior to application of equation 4-139. The average (trapezoidal rule) approximates the integral of rWASHPO over the time step.

That the load rate of sediment is proportional to flow rate as in equation 4-139 is supported by both theory and data. For instance, sediment data from streams can usually be described by a sediment rating curve of the form

(4-141)

• where G = sediment load rate, mg/sec,
• Q = flow rate, cfs, and
• a,b = coefficients.

Due to a hysteresis effect, such relationships may vary during the passing of a flood wave, but the functional form is evident in many rivers, e.g. Vanoni (1975), pp. 220-225, Graf (1971), pp.234-241, and Simons and Senturk (1977), p. 602. Of particular relevance to overland flow washoff is the appearance of similar relationships describing sediment yield from a catchment e.g. Vanoni (1975), pp. 472-481. The exponent b in equation 4-141 corresponds to the exponent WASHPO in equation 4-139, and the presence of the quantity PSHED in equations 4-139 reflects the fact that the total quantity of sediment washed off a largely impervious urban area is likely to be limited to the amount built up during dry weather. Natural catchments and rivers from which equation 4-141 is derived generally have no source limitation.

The use of rating curves in their own right is an option in the RUNOFF Module. At this point, however, results from sediment transport theory can be used to provide guidance for the magnitude of parameters WASHPO and RCOEF in equation 4-139. Values of the exponent b in equation 4-141 range between 1.1 and 2.6 for rivers and sediment yield from catchments, with most values near 2.0. Typically, the exponent tends to decrease (approach 1.0) at high flow rates (Vanoni, 1975, p. 476). In the RUNOFF Module, constituent concentrations will follow runoff rates better if WASHPO is higher. A reasonable first guess for WASHPO would appear to be in the range of 1.5-2.5.

Values of RCOEF are much harder to infer from the sediment rating curve data since they vary in nature by almost five orders of magnitude. The issue is further complicated by the fact that equation 4-139 includes the quantity remaining to be washed off, PSHED, which decreases steadily during an event. At this point it will suffice to say that values of RCOEF between 1.0 and 10 appear to give concentrations in the range of most observed values in urban runoff. Both RCOEF and WASHPO may be varied in order to calibrate the model to observed data.

The preceding discussion assumes that urban runoff quality constituents will behave in some manner similar to "sediment" of sediment transport theory. Since many constituents are in particulate form the assumption may not be too bad. If the concentration of a dissolved constituent is observed to decrease strongly with increasing flow rate, a value of WASHPO < 1.0 could be used.

Although the development has ignored the physics of rainfall energy in eroding particles, the runoff rate, r, in equation 4-139 closely follows rainfall intensity. Hence to some degree at least, greater washoff will be experienced with greater rainfall rates. As an option, soil erosion literature could be surveyed to infer a value of WASHPO if erosion is proportional to rainfall intensity to a power.

Related Buildup-Washoff Studies

Several studies are directly related to the preceding discussions of the SWMM RUNOFF Module water quality routines. Some of these have been mentioned previously in the text, but it is worthwhile pointing out those that are particularly relevant to SWMM modeling as opposed to data collection and analysis (although most of the studies do, of course, utilize data as well). The following discussion is by no means exhaustive but does include several studies that have simulated water quality using buildup-washoff mechanisms, rating curves or both.

The U.S. Geological Survey (USGS) has performed comprehensive urban hydrologic studies from both a data collection and modeling point of view. For example, their South Florida urban runoff data are described and referenced in the EPA Urban Rainfall-Runoff Quality Data Base (Huber et al., 1981a). Urban rainfall-runoff quantity may be simulated with the USGS distributed Routing Rainfall-Runoff Model (Dawdy et al., 1978; Alley et al., 1980a) which includes simulation of water quality. This is accomplished using a separate program that uses the quantity model results as input. These efforts are described by Alley (1980) and Alley et al. (1980b). Alley (1981) also provides a method for optimal estimation of washoff parameters using measured data. The USGS procedures are based in part upon earlier work of Ellis and Sutherland (1979). These four references all discuss the use of the original SWMM buildup-washoff equations. An application of SWMM RUNOFF and TRANSport modules to two Denver catchments during which buildup-washoff parameters were calibrated is described by Ellis (1978) and Alley and Ellis (1979).

Work at the University of Massachusetts has developed procedures for calibration of SWMM RUNOFF Module quality (Jewell et al., 1978a) and for determination of appropriate washoff relationships (Jewell et al., 1978b). Jewell et al. (1980) and Jewell and Adrian (1981) reviewed the supporting data base for buildup-washoff relationships and advocate using local data to develop site specific equations for buildup and washoff. Most of their suggested forms could be simulated using the available functional forms in SWMM.

Since several other models use quality formulations similar to those of SWMM, their documentation provides insight into choosing proper SWMM parameters. In particular, most of the STORM calibration procedures (Roesner et al., 1974, HEC, 1977a,b) can be applied also to SWMM (with WASHPO = 1). Inclusion of water quality simulation in ILLUDAS (Terstriep et al., 1978; Han and Delleur, 1979) also is based on SWMM procedures. Finally, modified SWMM routines have been used to simulate water quality in Houston (Diniz, 1978; Bedient et al., 1978).

Street Cleaning

Street cleaning is performed in most urban areas for control of solids and trash deposited along street gutters. Although it has long been assumed that street cleaning has a beneficial effect upon the quality of urban runoff, until recently, few data have been available to quantify this effect. Unless performed on a daily basis, EPA Nationwide Urban Runoff Program (NURP) studies generally found little improvement of runoff quality by street sweeping (EPA, 1983b).

The most elaborate studies are probably those of Pitt (1979, 1985) in which street surface loadings were carefully monitored along with runoff quality in order to determine the effectiveness of street cleaning. In San Jose, California (Pitt, 1979) frequent street cleaning on smooth asphalt surfaces (once or twice per day) can remove up to 50 percent of the total solids and heavy metal yields of urban runoff. Under more typical cleaning programs (once or twice a month), less than 5 percent of the total solids and heavy metals in the runoff are removed. Organics and nutrients in the runoff cannot be effectively controlled by intensive street cleaning -- typically much less than 10 percent removal, even for daily cleaning. This is because the latter originate primarily in runoff and erosion from off-street areas during storms. In Bellevue, Washington (Pitt, 1985) similar conclusions were reached, with a maximum projected effectiveness for pollutant removal from runoff of about 10 percent.

The removal effectiveness of street cleaning depends upon many factors such as the type of sweeper, whether flushing is included, the presence of parked cars, the quantity of total solids, the constituent being considered, and the relative frequency of rainfall events. Obviously, if street sweeping is performed infrequently in relation to rainfall events, it will not be effective. Removal efficiencies for several constituents are available in tables (Pitt, 1979). Clearly, efficiencies are greater for constituents that behave as particulates.

Within the RUNOFF Module, street cleaning (usually assumed to be sweeping) is performed (if desired) prior to the beginning of the first storm event and in between storm events (for continuous simulation). Unless initial constituent loads are input (or unless a rating curve is used) a "mini- simulation" is performed for each constituent during the dry days prior to a storm during which buildup and sweeping are modeled. Starting with zero initial load, buildup occurs according to the method chosen. Street sweeping occurs at intervals of CLFREQ days. (During continuous simulation, sweeping occurs between storms based on intervals calculated using dry time steps only. A dry time step does not have runoff greater than 0.0005 in./hr (0.013 mm/hr), nor is snow present on the impervious area of the catchment.) Removal occurs such that the fraction of constituent surface load, PSHED, remaining on the surface is

(4-143)

• where REMAIN = fraction of constituent (or dust and dirt) load remaining on catchment surface,
• AVSWP = availability factor (fraction) for land use J, and
• REFF = removal efficiency (fraction) for constituent K.

The removal efficiency differs for each constituent as seen in published tables, from which estimates of REFF may be obtained. The effect of multiple passes must be included in the value of REFF. During the mini-simulation that occurs prior to the initial storm or start of simulation "dust and dirt" is also removed during sweeping using an efficiency REFFDD. It is probably reasonable to assume that dust and dirt is removed similarly to the total solids. A non-linear effect is exhibited, in which efficiencies tend to increase as the total solids on the street surface increase. The RUNOFF Module algorithm does not duplicate this effect. Rather, the same fraction is removed during each sweeping.

The availability factor, AVSWP, is intended to account for the fraction of the catchment area that is actually sweepable. For instance, Heaney and Nix (1977) demonstrate that total imperviousness increases faster as a function of population density than does imperviousness due to streets only. Thus, the ratio of street surface to total imperviousness is one measure of the availability factor, and their relationship is

(4-144)

• where AVSWP = availability factor, fraction, and
• PD_d = population density over developed area, persons/ac.

Such a relationship is reasonably a function of land use. Although a value of AVSWP must be entered for each land use, the equation of Heaney and Nix (1977) was developed only for an overall urban area. Thus, extrapolation to specific land uses should be done only with caution, but equation 4-144 is probably suitable for use on a large, aggregated catchment, such as might be used for continuous simulation.

An alternative approach may be found in Pitt (1979) in which the issue of parked cars is dealt with directly. Pitt shows that the percentage of curb left uncleaned is essentially equal to the percentage of curb occupied by parked cars. Thus, if typically 40 percent of the curb (length) is occupied by parked cars, the availability factor would be about 0.60. In many cities, parking restrictions on street cleaning days limit the length of curb occupied during sweeping.

Parameter DSLCL merely establishes the proper time sequence for the "mini-simulation" prior to the start of the storm (or continuous simulation). A hypothetical sequence of linear buildup and street sweeping prior to a storm is sketched in Figure 4-37.

Figure 4-37. Hypothetical time sequence if linear buildup and street sweeping.

 Eventually an equilibrium between buildup and sweeping will occur. For the example shown in Figure 4-37, this is when the removal, 0.32.PSHED, equals the weekly buildup, 0.3 x 106.7, or PSHED = 6.56 x 106 mg. If sweeping is scheduled for the day of the start of the storm (DSCL = CLFREQ) it does not occur. (An exception would be when the first day of a continuous simulation is a dry day. Sweeping would then occur during the first time step.)

The SWMM user should bear in mind that although the model assumes constituents to build up over the entire subcatchment surface, the surface load, PSHED, is simply a lumped total in, say, mg (for NDIM = 0), and there are no spatial effects on buildup or washoff. Hence, if it is assumed that a particular constituent originates only on the impervious portion of the catchment, loading rates and parameters can be scaled accordingly. Likewise, AVSWP can be determined based on the characterization of only the impervious areas described above. However, if a constituent originates over both the pervious and impervious area of the subcatchment (e.g. nutrients and organics) the removal efficiency, REFF, should be reduced by the average ratio of impervious to total area since it is independent of land type. The availability factor, AVSWP, differs for individual land uses but has the same effect on all constituents.

As previously discussed, the original SWMM RUNOFF Module quality routines were based on the 1969 APWA study in Chicago (APWA, 1969). A particular aspect of that study that led to modifications to the first buildup-washoff formulation was that the Chicago quality data (e.g. Table 4-18) were reported for the soluble fraction only, i.e., the samples were filtered prior to chemical analysis. Hence, they could not represent the total content of, say, BOD₅ in the stormwater. In calibration of SWMM in San Francisco and Cincinnati, 5 percent of predicted suspended solids was added to BOD₅ to account for the insoluble fraction. This provided a reasonable BOD₅ calibration in both cities.

The Version II release of SWMM (Huber et al., 1975) followed the STORM model (Roesner et al., 1974) and added to BOD₅, N and PO₄ fractions of both suspended solids and settleable solids. Adding a fraction from settleable solids is double counting, however, since it is no more than a fraction of suspended solids itself. Furthermore, all the fractions in SWMM and STORM were basically just assumed from calibration exercises as opposed to being measured from field samples.

Agricultural models, such as NPS (Donigian and Crawford, 1976), ARM (Donigian et al., 1977) and HSPF (Johanson et al., 1980) also relate other constituent mass load rates and concentrations to that of "solids," usually "sediment" predicted by an erosion equation. The ratio of constituent to "solids" is then called a "potency factor" and for some constituents is the only means by which their concentrations are predicted. The approach works well when constituents are transported in solid form, either as particulates or by adsorption onto soil particles. This approach can also be used in SWMM. For instance, one constituent could represent "solids" and be predicted by any of the means available (i.e., buildup-washoff, rating curve, Universal Soil Loss Equation). Other constituents could then be treated simply as a fraction, F1, of "solids." The fractions (potency factors) are input. As a refinement, two or more constituents could represent "solids" in different particle size ranges, and fractions of each summed to predict other constituents. Again, this approach will not work well for constituents that are transported primarily in a dissolved state, e.g. NO₃.

Available Information

In an effort to evaluate potency factors for various constituents in both urban and agricultural runoff, Zison (1980) examined available data and developed regression relationships as a function of suspended solids and other parameters. His only urban catchments were three from Seattle, taken from the Urban Rainfall-Runoff-Quality Data Base (Huber et al., 1981a), for which several water quality and storm event parameters were available. Unfortunately, statistically meaningful results could only be obtained using log-transformed data, and simple fractions of the type required for input are seldom reported. Zison (1980) acknowledged this and suggested that model modifications might be made or piecewise-linear approximations made to the power function relationship. In any event, Zison related the total constituent concentration (not just the nonsoluble portion) to other parameters. Hence, for their use in SWMM< the buildup-washoff portion would need to be "zeroed out," (easily accomplished), as suggested earlier.

Other reports also provide some insight as to potential values for the constituent fractions. For instance, Sartor and Boyd (1972), Shaheen (1975) and Manning et al. (1977) report particle size distributions for several constituents. However, the distributions refer principally to fractions of constituents appearing as "dust and dirt," not to fractions of total concentration, soluble plus nonsoluble. Finally, Pitt and Amy (1973) give fractions (and surface loadings) for heavy metals.

If constituent fractions are used in SWMM, local samples should identify the soluble (filterable) and nonsoluble fractions for the constituents of interest. Alternatively, the fractions may be avoided altogether by treating the buildup-washoff or rating curve approach as one for the total concentration, thus eliminating the need to break constituents into more than one form.

Effect in RUNOFF Module

The fractions entered act only in "one direction." That is, nothing is subtracted from, say, suspended solids if it is a constituent that contributes to others. When the fractions are used, they can contribute significantly to the concentration of a constituent. For instance, if 5 percent of suspended solids is added to BOD₅, high SS concentrations will insure somewhat high BOD₅ concentrations, event if BOD₅ loadings are small.

Units conversions must be accounted for in the fractions. For instance, if a fraction of SS is added to total coliforms, units for F1 would be MPN per mg of SS. In general, F1 has units of the "quantity" of KTO (e.g. MPN) per "quantity" of constituent KFROM (e.g. mg).

The contributions from other constituents are the penultimate step in subroutine QSHED. The occur after the Universal Soil Loss Equation calculation, and the the to-from constituents can include the contribution from erosion if desired. Only the contribution from precipitation comes later and thus cannot be included in the constituent fractions. Rather it is added to the constituent load at the end of the chain of calculations, as described below.

There is now considerable public awareness of the fact that precipitation is by no means "pure" and does not have characteristics of distilled water. Low pH (acid rain) is the best known parameter but many substances can also be found in precipitation, including organics, solids, nutrients, metals and pesticides. Compared to surface sources, rainfall is probably an important contributor mainly of some nutrients, although it may contribute substantially to other constituents as well. In particular, Kluesener and Lee (1974) found ammonia levels in rainfall higher than in runoff in a residential catchment in Madison, Wisconsin; rainfall nitrate accounted for 20 to 90 percent of the nitrate in stormwater runoff to Lake Wingra. Mattraw and Sherwood (1977) report similar findings for nitrate and total nitrogen for a residential area near Fort Lauderdale, Florida. Data from the latter study are presented in Table 4-28 in which rainfall may be seen to be an important contributor to all nitrogen forms, plus COD, although the instance of a higher COD value in rainfall than in runoff is probably anomalous.

In addition to the two references first cited, Weibel et al. (1964, 1966) report concentrations of constituents in Cincinnati rainfall (Table 4-20), and a summary is also given by Manning et al. (1977). Other data on rainfall chemistry and loadings is given by Betson (1977), Hendry and Brezonik (1980), Novotny and Kincaid (1981) and Randall et al. (1981). A comprehensive summary is presented by Brezonik (1975) from which it may be seen in Table 4-29 that there is a wide range of concentrations observed in rainfall. Again, the most important parameters relative to urban runoff are probably the various nitrogen forms.

Uttormark et al. (1974) provide annual nitrogen (and phosphorus) precipitation loading values (kg/ha-yr) for many cities regionally for the U.S. and Canada. It should be remembered that considerable seasonal variability may exist. These may be easily converted to precipitation concentrations required for SWMM input if the local rainfall is known, since 10 x kg/ha-yr / cm/yr = mg/l. For instance, annual NH₃-N + NO₃-N loadings at Miami are almost 2 kg/ha-yr, and annual rainfall is 60 in. (152 cm). From the above, the inorganic nitrogen concentration is 10 x 2/152 = 0.13 mg/l which compares quite favorably with the sum of NH₃-N and NO₃-N concentrations for two of the three Ft. Lauderdale storms given in Table 4-28. For a better breakdown of nitrogen forms, see Table 17 of Uttormark et al. (1974).

(after Mattraw and Sherwood, 1977)

Table 4-29. Representative Concentrations in Rainfall.

aRange for three storms ^bAverage of 35 Storms ^cSum of NH₃-N, NO₂ –N, NO₃-N

Effect of rain pollutants in RUNOFF Module

Constituent concentrations in precipitation are input. All runoff, including snowmelt, is assumed to have at least this concentration, and the precipitation load is calculated by multiplying this concentration by the runoff rate and adding to the load already generated by other mechanisms. It may be inappropriate to add a precipitation load to loads generated by a calibration of buildup-washoff or rating curve parameters against measured runoff concentrations, since the latter already reflect the sum of all contributions, land surface and otherwise. But precipitation loads might well be included if starting with buildup-washoff data from other sources. They also provide a simple means for imposing a constant concentration on any RUNOFF Module constituent.

For single event simulation, use of precipitation concentrations is a simple way in which to account for the high concentrations of several constituents found in snowpacks (Proctor and Redfern and James F. MacLaren, 1976b). It would be inappropriate for continuous simulation, however, since such high concentrations in runoff would not be expected to persist over the whole year.

If this is the only method used to simulate melt quality, however, a constant predicted concentration will result. Also, caution should be used if simulating particulates (e.g. suspended solids) or heavy metals since high concentrations in a snowpack do not necessarily mean high concentrations in runoff, since the material may rapidly settle during overland flow. For instance, the very high lead concentrations (2 - 100 mg/l) found in snow windrows in urban areas are greatly reduced in the melt runoff (0.05 - 0.95 mg/l), (Proctor and Redfern and James F. Maclaren, 1976b).

Erosion and sedimentation are often cited as a major problem related to urban runoff. They not only contribute to degradation of land surfaces and soil loss but also to adverse receiving water quality and sedimentation in channels and sewer networks. Several ways exist to analyze erosion from the land surface (e.g. Vanoni, 1975), the most sophisticated of which include calculations of the shear stress exerted on soil particles by overland flow and/or the influence of rainfall energy in dislodging them. In keeping with the simplified quality procedures included in the rest of the RUNOFF Module, a widely-used empirical approach, the Universal Soil Loss Equation (USLE), has been adapted for use in SWMM. Full details and further information on the USLE are given by Heaney et al. (1975).

 Universal Soil Loss Equation

The USLE was derived from statistical analyses of soil loss and associated data obtained in 40 years of research by the Agricultural Research Service (ARS) and assembled at the ARS runoff and soil loss data center at Purdue University. The data include more that 250,000 runoff events at 48 research stations in 26 states, representing about 10,000 plot-years of erosion studies under natural rain. It was developed by Wischmeier and Smith (1958) as an estimate of the average annual soil erosion from rainstorms for a given upland area, L, expressed as the average annual soil loss per unit area, (tons per acre per year):

(4-148)

• where R = the rainfall factor,
• K = the soil erodibility factor,
• LS = the slope length gradient ratio,
• C = the cropping management factor or cover index factor, and
• P = the erosion control practice factor.

This equation represents a comprehensive attempt at relating the major factors in soil erosion. It is used in SWMM to predict the average soil loss for a given storm or time period. It is recognized that the USLE was not developed for making predictions based on specific rainfall events. There are many random variables which tend to cancel out when predicting individual storm yields. For example, the initial soil moisture condition, or antecedent moisture condition, is a parameter which cannot routinely be determined directly and used reliably. It should be understood by the SWMM user that equation 4-145 enables land management planners to estimate gross erosion rates for a wide range of rainfall, soil, slope, crop, and management conditions.

Erosion Simulation:

If erosion is to be simulated, it is so indicated by parameter IROS. Note that at least one other (arbitrary) quality constituent must be simulated along with "erosion." No particular soil characteristics (e.g. particle size distribution) are assigned to the erosion parameter, and its title is "EROSION," with units of mg/l, in the output. Erosion may be added to another constituent, e.g. suspended solids, if desired using parameter IROSAD. However, the erosion parameter will also always be maintained as an individual parameter throughout the RUNOFF Module.

Other input parameters are:

1. the maximum 30-minute rainfall intensity of the storm (single-event) or of the simulation period (continuous), RAINIT, 
2. the area of each subcatchment subject to erosion, ERODAR, 
3. the flow distance in feet from the point of origin of overland flow over the erodible area to the point at which runoff enters the gutter (link) or inlet (node), ERLEN, 
4. the soil factor K, SOILF, 
5. the cropping management factor C, CROPMF, and
6. the control practice factor P, CONTPF.

The source and use of these parameters is described below.

Rainfall Factor and Maximum Thirty Minute Intensity

The rainfall factor, R, of the equation 4-148 is the product of the maximum thirty minute intensity and the sum of the rainfall energy for the time of simulation. Rainfall energy, E, is given by an empirical expression by Wischmeier and Smith (1958):

(4-149)

• where E = total rainfall energy for time period of summation, 100-ft-ton/ac,
• RNINHR_j = rainfall intensity at time interval j, in./hr, and
• DELT = time interval, hr, such that the product RNINHR x DELT equals the rainfall depth during the time interval.

The summation was performed over all time intervals with rainfall for a year for the original USLE development; contours of R over the U.S. are given by Wischmeier and Smith (1965). However, it can also be performed for an individual storm. In SWMM this is performed on a time step basis; that is, E is evaluated at each time step using the rainfall intensity at that time step (no summation). The rainfall factor, R, is then

(4-150)

where RAINIT = maximum average 30 minute rainfall intensity for the storm (single event) or the period of simulation (continuous) in./hr.

RAINIT must be found from an inspection of the input hyetograph prior to simulation. Computed in this manner, the rainfall factor does not account for soil losses due to snowmelt or wind erosion. The units of R (100-ft-ton- in/ac-hr) are generally meaningless since the soil factor, K, is designed to cancel them. But the indicated units for RAINIT and RNINHR (in/hr) must be used.

Erosion Area:

Parameter ERODAR represents the area of the subcatchment subject to erosion. This would ordinarily be less than or equal to the pervious area of the subcatchment and could indicate land that is barren or under construction.

Soil Factor:

The soil factor, K, is a measure of the potential erodibility of a soil and has units of tons per unit of rainfall factor, R. A soil erodibility may be used to find the value of the soil factor once five soil parameters have been estimated. These parameters are: percent silt plus very fine sand (0.05 - 0.10 mm), percent sand greater than 0.10 mm, organic matter (O.M.) content, structure, and permeability. To use a nomograph, enter on the left vertical scale with the appropriate percent silt plus very fine sand. Proceed horizontally to the correct percent sand curve, then move vertically to correct organic matter curve. Moving horizontally to the right from this point, the first approximation of K is given on the vertical scale. For soils of fine granular structure and moderate permeability, this first approximation value corresponds to the final K value and the procedure is terminated. If the soil structure and permeability is different than this, it is necessary to continue the horizontal path to intersect the correct structure curve, proceed vertically downward to the correct permeability curve, and move left to the soil erodibility scale to find K. For a more complete discussion of this topic, see Wischmeier et al. (1971).

A preferable and often simpler alternative to the use of a nomograph is to refer directly to the soil survey interpretation sheet for the soil in question, on which may be found the value of the soil factor. Since this is site-specific local information, it is highly recommended. Local Agricultural Research Service and Soil Conservation Service offices are available to obtain the soil survey interpretation sheets and to provide much other useful information.

Slope Length Gradient Ratio:

This parameter is an empirical function of runoff length and slope and is given by

(4-151)

• where LS = slope length gradient ratio,
• ERLEN = the length in feet from the point of origin of overland flow to the point where the slope decreases to the extent that deposition begins or to the point at which runoff enters a defined channel, e.g. inlet (node), and
• WSLOPE = the average slope over the given runoff length, ft/ft.

Parameter ERLEN is entered with the erosion parameters. The slope, WSLOPE, is the same as for runoff calculations.

In using the average slope in calculating the LS factor, the predicted erosion will be different from observed erosion when the slope is not uniform. Meyer and Kramer (1969) show that when the slope is convex, the average slope prediction will underestimate the total erosion, whereas for a concave slope, the prediction equation will overestimate the erosion. If possible, to minimize these errors, large eroding sites should be broken up into areas of fairly uniform slope.

Cropping Management Factor:

This factor is dependent upon the type of ground cover, the general management practice and the condition of the soil over the area of concern. The C factor (CROPMF) is set equal to 1.0 for continuous fallow ground which is defined as land that has been tilled and kept free of vegetation and surface crusting. Values for the cropping management factor are given in Table 4-30 (Maryland Dept. of Natural Resources, 1973). Again consultation with local soils experts is recommended.

(Maryland Dept.of Natural Resources, 1973)

aAs recommended by manufacturer

This is similar to the C factor except that P (CONTPF) accounts for the erosion-control effectiveness of superimposed practices such as contouring, terracing, compacting, sediment basins and control structures. Values for the control practice factor for construction sites are given in Table 4-22 (Ports, 1973). Agricultural land use P factor values are given by Wischmeier and Smith (1965).

The C and P factors are the subject of much controversy among erosion and sedimentation experts of the U.S. Department of Agriculture (USDA) and the Soil Conservation Service (SCS). These factors are estimates and many have no theoretical or experimental justification. It has been suggested that upper and lower limits be placed on these factors by local experts to increase the flexibility of the USLE for local conditions.

The P factors in the upper portion of Table 4-31 were designated as estimates when they were originally published. SCS scientists have found no theoretical or experimental justification for factors significantly greater than 1.0. Surface conditions 4, 6, 7 and 8 (P<1.0) of Table 4-30 also are estimates with no experimental verification.

Table 4-31. Erosion Control Practice Factor, P, for Construction Sites (Ports, 1973).

-----excerpt ends

Bill still has to insert linked titles to figs and tables

Burton, G.A. and R. Pitt. Manual for Evaluating Stormwater Runoff Effects, A Tool Box of Procedures and Methods to Assist Watershed Managers. CRC/Lewis Publishers, New York. Expected publication in 2000.

Street Dirt Accumulation

At very long accumulation periods relative to the rain frequency, the wind losses may approximate the deposition rate, resulting in very little loading increases. For Bellevue, Washington, with interevent rain periods averaging about 3 days, steady loadings were observed only after about 1 week (Pitt 1985). In Castro Valley, California, the rain interevent periods were much longer (ranging from about 20 to 100 days) and steady loadings were never observed (Pitt and Shawley 1982).

Early measurements of across-the-street dirt distributions made by Sartor and Boyd (1972) indicated that about 90 percent of the street dirt was within about 30 cm of the curb face (typically within the gutter area). These measurements, however, were made in areas of no parking (near fire hydrants because of the need for water for the sampling procedures that were used), and the traffic turbulence was capable of blowing most of the street dirt against the curb barrier (or over the curb onto adjacent sidewalks or landscaped areas) (Shaheen 1975). In later tests, Pitt (1979) and Pitt and Sutherland (1982) examined street dirt distributions across-the-street in many additional situations. They found distributions similar to Sartor and Boyd’s observations only on smooth streets, with moderate to heavy traffic, and with no on-street parking. In many cases, most of the street dirt was actually in the driving lanes, trapped by the texture of rough streets. If extensive on-street parking was common, much of the street dirt was found several feet out into the street, where much of the resuspended (in air) street dirt blew against the parked cars and settled to the pavement. Figure 4 shows across-the-street distributions of street dirt, both before and after street cleaning for a relatively busy roadway (having no parking) in Bellevue, WA (Pitt 1985). Only about 20% of the street dirt was near the curb before street cleaning, while 90% was within about 8 ft. After cleaning, the load was even more evenly distributed, as the street cleaner preferentially removed street dirt near the curb and blew some dirt out into the street.

Methodology for Street Dirt Accumulation Measurements

The street dirt sampling procedures described here were developed by Pitt (1979) and were extensively used during many of the EPA’s Nationwide Urban Runoff Program (NURP) projects (EPA 1983) and other street cleaning performance studies and washoff studies (Pitt 1987). These procedures were developed to be much for flexible and more accurate indicators of street dirt loading conditions than previous sampling methods used during earlier studies (such as Sartor and Boyd 1972, for example).

The sample storage cans were labeled with the date, the test area’s name, and an indication of whether the sample was taken before or after the street cleaning test or if it was an accumulation (or other type) of sample. Finally, the lids of the sample cans were taped shut and transported to the laboratory for logging-in, storage, and analysis.

Street Dust and Dirt Pollutant Characteristics

Solomon and Natusch (1977) also examined urban particulates near roadways and homes in urban areas. They found that lead concentrations in soils were higher near roads and houses. This indicated the capability of road dust and peeling house paint to contaminate nearby soils. The lead content of the soils ranged from 130 to about 1,200 mg/kg. Koeppe (1977), during another element of the Champaign-Urbana lead study, found that lead was tightly bound to various soil components. However, the lead did not remain in one location, but it was transported both downward in the soil profile and to adjacent areas through both natural and man-assisted processes.

Summary of Observed Accumulation Rates

Table 1 summarizes many accumulation rate measurements obtained from throughout North America. In the earliest studies (APWA 1969; Sartor and Boyd 1972; and Shaheen 1975), the initial street dirt loading values after a major rain or street cleaning were assumed to be zero. Calculated accumulation rates for rough streets were therefore very large. Later tests measured the initial loading values close to the end of major rains and street cleaning and found that they could be relatively high, depending on the street texture. When these starting loadings were considered for the earlier measurements, the re-calculated accumulation rates were much lower. The early, uncorrected, Sartor and Boyd accumulation rates that ignored the initial loading values were almost ten times the corrected values shown on this table. Unfortunately, most urban stormwater models used these very high early accumulation rates as default values.

 The most important factors affecting the initial loading and maximum loading values shown on Table 1 were found to be street texture and street condition. When data from many locations are studied, it is apparent that smooth streets have substantially less loadings at any accumulation period compared to rough streets for the same land use. Very long accumulation periods relative to the rain frequency result in high street dirt loadings. During these conditions, the wind losses of street dirt (as fugitive dust) may approximate the deposition rate, resulting in relatively constant street dirt loadings. At Bellevue, WA, typical interevent rain periods average about three days. Relatively constant street dirt loadings were observed in Bellevue because the frequent rains kept the loadings low and very close to the initial storage value, with little observed increase in dirt accumulation over time (Pitt 1985). In Castro Valley, CA, the rain interevent periods were much longer (ranging from about 20 to 100 days) and steady loadings were only observed after about 30 days when the loadings became very high and fugitive dust losses caused by the winds and traffic turbulence moderated the loadings (Pitt and Shawley 1982).

Background

where p_s = specific density of particle, g/cm3

K_j = factor relating the standard rain to the actual rain

Table 3. Kj Values used in Yalin Sediment Transport Model (Sutherland and McCuen 1978)

t = rain duration

Particulate residue washoff predictions for Bellevue conditions were made using the Sutherland and McCuen modification of the Yalin equation, and the Sartor and Boyd equation. Three particle size groups (<63, 250-500, and 2000-6350 m m), and three rains, having depths of 5, 10, and 20 mm and 3-hour durations, were considered. The gutter lengths for the Bellevue test areas averaged about 80 m, with gutter slopes of about 4.5 percent. Typical total initial street dirt loadings for the three particle sizes were: 9 g/curb-meter for <63 m m, 18 g/curb-meter for 250-500 m m, and 9 g/curb-meter for 2000-6350 m m. The actual Bellevue net loading removals during the storms was about 45 percent for the smallest particle size group, 17 percent for the middle particle size group, and -6 percent (6 percent loading increase) for the largest particle size group. The predicted removals were 90 to 100 percent using the Sutherland and McCuen method, 61 to 98 percent using the Sartor and Boyd equation, and 8 to 37 percent using the availability factor with the Sartor and Boyd equation. The ranges given reflect the different rain volumes and intensities only. There were no large predicted differences in removal percentages as a function of particle size. The availability factor with the Sartor and Boyd equation resulted in the closest predicted values, but the great differences in washoff as a function of particle size was not predicted.

The Bellevue street dirt washoff observations included effects of additional runoff volume and particulates originating from non-street areas. The additional flows should have produced more gutter particulate washoff, but upland erosion materials may also have settled in the gutters (as noted for the large particles). However, across-the-street dirt loading measurements indicated that much of the street dirt was in the street lanes, not in the gutters, before and after rains. This dirt distribution reduces the importance of these extra flows and particulates from upland areas. The increased loadings of the largest particles after rains were obviously caused by upland erosion, but the magnitude of the settled amounts was quite small compared to the total street dirt loadings.

Small-Scale Washoff Tests

Table 4 presents the site data along with the basic rain and runoff observations obtained during these tests. All tests were conducted for about two hours, with total rain volumes ranging from about 5 to 25 mm. The test code explanations follow:

Table 4. Experimental Levels for each Test Factor

Figure 8, Figure 9 and Figure 10 are plots of total solids, suspended solids, and filterable solids concentrations during these tests. The total solids concentrations varied from about 25 to 3000 mg/L, with an obvious decrease in concentrations with increasing rain depths during these constant rain intensity tests. No concentrations greater than 500 mg/L occurred after about two mm of rain. All concentrations after about 10 mm of rain were less than 100 mg/L. Total solids concentrations were independent of the test conditions. A wide range in runoff concentrations was also observed for SS, with concentrations ranging from about 1 to 3000 mg/L. Again, a decreasing trend of concentrations was seen with increasing rain depths, but the data scatter was larger because of the experimental factors. The dissolved solids (<0.45 m m) concentrations ranged from about 20 to 900 mg/L, comprising a surprisingly large percentage of the total solids loadings. For small rain depths, dissolved solids comprised up to 90 percent of the total solids. After 10 mm of rain depth, the filterable residue concentrations were all less than about 50 mg/L.

 Manual particle size analyses were also conducted on the suspended solids washoff samples, using a microscope with a calibrated recticle. Figure 11, Figure 12 and Figure 13 are examples of particle size distributions for three tests. These plots show the percentage of the particles that were less than various sizes, by measured particle volume (assumed to be similar to weight). The plots also indicate median particle sizes of about 10 to 50 m m, depending on when the sample was obtained during the washoff tests. All of the distributions showed surprisingly similar trends of particle sizes with elapsed rain depth. The median size for the sample obtained at about one mm of rain was much greater than for the samples taken after more rain. The median particle sizes of material remaining on the streets after the washoff tests were also much larger than for most of the runoff samples, but were quite close to the initial samples’ median particle sizes. The washoff water at the very beginning of the test rains, therefore, contained many more larger particles than during later portions of the rains. Also, a substantial amount of larger particles remained on the streets after the test rains. Most street runoff waters during test rains in the 5 to 15 mm depth category had median suspended solids particle sizes of about 10 to 50 m m. However, dissolved solids (less than 0.45 m m) made up most of the total solids washoff for elapsed rain depths greater than about five mm.

These particle size distributions indicate that the smaller particles were much more important than indicated during previous tests. As an example, the Sartor and Boyd (1972) washoff tests (rain intensities of 50 mm/h for two hour durations) found median particle sizes of about 150 m m which were typically three to five times larger than were found during these lower-intensity tests. They also did not find any significant particle size distribution differences for different rain depths (or rain duration), in contrast to the Toronto tests, which were conducted at more likely rain intensities (3 to 12 mm/hr for two hours).

• High rain intensity and smooth streets: 0.20

If a selected model requires available loading values instead of the total loading values, then a procedure must be used to adjust the total loading values (such as attempted by the availability term in STORM and SWMM). In all cases, the k term must be appropriate for the model form. However, the use of an available loading value for N_o requires the use of a substantially larger k term compared to using the total loading value.

The filterable residue washoff models, however, were all based on total measured filterable residue loadings. These different preferred model forms for particulate and filterable residue were most likely caused by the differences in washoff efficiencies for different sized particles. Particulate residues were not nearly as efficiently removed during the washoff tests and were better related to much reduced "available" particulate residue loading values. Filterable residues in contrast, were much more efficiently removed and related well to total loadings (not much filterable residue was left on the streets after the washoff tests, making the available loadings very similar to the total loadings for filterable residue). Table 8 contains the availability relationship for suspended solids.

Maximum Washoff Capacity

Figure 21a. Maximum washoff capacity for smooth streets (based on Pitt 1987 and Sartor and Boyd 1972 measurements).

 

The resulting sheetflow concentrations associated with these maximum washoff values depends on the rain durations at these average rain intensities. As an example, for typical 6 hour durations, the resulting concentrations are very similar to the fitted line on the suspended solids concentration vs. rain depth plot shown on Figure 9 (about 100 mg/L for 1 to 2 mm rains, decreasing to about 10 mg/L for rains of about 25 mm in depth). For very large rains, having sustained high rain intensities, the available street dirt loading would most likely be limiting.

Comparison of Particulate Residue Washoff Using Previous Washoff Models and Revised Washoff Model

This discussion briefly compares the washoff observations obtained during these washoff tests with predicted washoff values obtained using the Sartor and Boyd (1972) washoff model (with and without the "availability" factor). Table 9 shows the predicted washoff values along with the observed values for the conditions that occurred during the washoff tests. In all cases, serious over-predictions in street dirt washoff resulted by using these common washoff models. Even with the availability factor, the predicted Sartor and Boyd washoff quantities were almost two to more than five times greater than observed. Without the availability factor, the modeled washoff quantities were at least five times greater than the observed values. The residuals (all reflecting over-predictions) of these modeled estimates ranged from 0.2 to 7 g/m² when using the availability factor, compared to residuals mostly less than 0.05 g/m² when the model developed from these washoff tests was used. Lower residuals obtained by using the revised model could be expected because these data were not independent from the data used in developing the revised washoff model.

Summary of Street Particulate Washoff Tests

 Observed Particle Size Distributions in Stormwater

Figures 22, 23,   24 are grouped box and whisker plots showing the particle sizes (in m m) corresponding to the 10^th, 50^th (median) and 90^th percentiles of the cumulative distributions. If 90% control of SS is desired, for example, then the particles larger than the 90^th percentile would have to be removed by a sedimentation device. The median particle sizes ranged from 0.6 to 38 m m and averaged 14 m m. The 90^th percentile sizes ranged from 0.5 to 11 m m and averaged 3 m m. These particle sizes are all substantially smaller than have been typically assumed for stormwater. In all cases, the New Jersey samples had the smallest particle sizes, followed by Wisconsin, and then Birmingham, AL, which had the largest particles. The New Jersey samples were obtained from gutter flows in a residential semi-xeroscaped neighborhood, the Wisconsin samples were obtained from a public works yard in Milwaukee, and the Birmingham samples were collected from a long-term parking area.

"First-Flush" of Stormwater Pollutants from Pavement

An example of first flush from a relatively simple watershed is shown in Figures 25, 26, 27 (Shaheen 1975). The test watershed was a portion of the Washington, D.C. beltway (I495), almost totally paved and guttered. This relatively small, but common rain (about 0.1 inch) produced peak flows of about 24 gal/min. The event had a relatively constant rain intensity and classical hydrograph shape with a rapid rise and drop. This event also had a pronounced first flush, with high concentrations of total solids, suspended solids, and lead at the beginning of the event, decreasing to about half. Constituents more associated with filterable fractions (soluble zinc and soluble lead) had little change over the period of the event. In contrast, another event at the same location is shown in Figures 28 and 29. The initial rainfall was about the same as for the other event, but significantly increased after about 2 hours. The hydrograph shows an initial rise and drop corresponding to the first part of the event, but the majority of the runoff occurred later in the event. The concentrations also showed an initial period of relatively high values, and then dropped, but later significantly increased when the rain intensity increased. The period of high concentrations (and high pollutant yields) occurred about two hours after rain started, conflicting with the first flush "theory." The concept of treating the first ½ inch of runoff from each event is usually successful, as almost all rains produce less than this amount, and about 80% of annual flows in many parts of North America, not because capturing the first flush allows treatment of a significantly more polluted and smaller portion of the runoff.

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Reading and links

Assignment A7

1) The only assignment associated with this module supplement is to examine possible errors in modeling that may occur through the selection of incorrect model routines dealing with accumulation and washoff of particulates.

Assignment A7:

This sounds tougher than it is: very crudely estimate the uncertainty inherent in a SWMM RUNOFF overland flow quality simulation. The easiest way to do this, probably, would be to run a very simple application using (say) PCSWMM2000 or any version of SWMM. You can also do this by trying to account for the scatter in the Sartor and Boyd data. Best would be to use both approaches.

Either way you must prepare a background review article in which you discuss the inherent scatter and poor correlations in the buildup and washoff formulations. You must write about the likely processes of pollutant buildup, and how they could conceivably be correlated with the number of vibrations of a silicon molecule in a vault somewhere (i.e. the passage of time). Similarly with washoff and how it is correlated with overland flow intensity. Try to estimate the variance in Sartor and Boyd's plots. Suggest how this variance can be used to estimate some of the uncertainty in the computed pollutant concentrations.

If you can manage to run the program choose a catchment area of 1 ha, slope of 4%, and 100% impervious, one outlet and no conveyances. Assume asphalt or concrete surface. Plot as dependent variable settleable or suspended solids, either peak concentration or event mean concentration, or both. Vary the buildup and washoff parameters.Make some reasonable conclusions about unceratinty and how modellers could nevertheless proceed.