A Load Model Based on Antecedent Dry Periods for Pollutants in Stormwater

By Soonthornnonda, Puripus Christensen, Erik R

ABSTRACT: A load model for stormwater constituents is proposed that describes mass retained on the drainage area after previous storms, as a function of a weighted sum of previous antecedent dry periods. It was used to compute the event load for 14 constituents- zinc, copper, cadmium, nickel, chromium, lead, mercury, silver, total suspended solids (TSS), E. coli, fecal coliform, total soluble phosphorus, total phosphorus, and 5-day biochemical oxygen demand. The results show acceptable fits for most constituents based on over 400 rain events (2000 to 2004) in Milwaukee, Wisconsin. Considering the retained pollutant mass after one previous storm rather than assuming the area to be clean after the previous storm gives more accurate results for all constituents, except TSS and silver. The model can be used for mixed land-use areas. The ratios of deposition fluxes of zinc and individual metals were determined at a major parking lot producing a profile characteristic of automobile emissions. Water Environ. Res., 80, 162 (2008).

KEYWORDS: load model, stormwater constituent, antecedent dry period, land use, pollutant mass, deposition flux.

doi:10.2175/106143007X220888

(ProQuest: … denotes formulae omitted.)

Introduction

Common sources of urban runoff include dry and wet atmospheric deposition, accumulation of street refuse (litter, dirt, organic residues, and vehicular traffic emissions), vegetation, urban area erosion, and road deicing chemicals (Adams and Papa, 2000). The quality of stormwater runoff in each drainage area depends on land use. Runoff from traffic-related drainage areas can display high, levels of heavy metals and chloride. By comparison, residential runoff typically has high levels of nutrients and bacteria (Soonthornnonda and Christensen, 2005). Further characterization of runoff quantity and quality is desirable to obtain predictive models and evaluate the need for treatment before discharge into receiving waters.

Sartor et al. (1974) simulated washoff of stormwater pollutants from street surfaces by an exponential model. They found that the removed pollutant mass was related to the volume of rainfall during a rainfall event. Alley (1981) developed an exponential washoff model for effective impervious surfaces, in which the predicted amount of constituent washoff was a direct function of the total volume of storm runoff. Charbeneau and Barrett (1998) proposed a model that predicts pollutant load using event mean concentration for single-land-use catchments. Otiier runoff quality analysis models have been widely developed to predict runoff volumes, mass loads, and concentrations (Brezonik and Stadelmann, 2002; Niehus, 1997); however, to our knowledge, there is no model that specifically considers the influence of each of several dry periods before a storm event on the calculated load. Although Alley and Smith’s (1981) model included antecedent condition parameters, it was tested only for nitrogen, lead, and solids, and only for a single land-use-type drainage area with little pervious area runoff. Only eight periods of runoff were considered. Kim et al. (2005) created a washoff model for predicting the mass emission rates of highway metals during first-flush runoff. Their model has four parameters-none of which appears to have a direct relationship to land use or runoff coefficient. Kim et al. (2005) reported that average daily traffic, antecedent dry period, total rainfall, average rainfall intensity, and runoff coefficient are the main variables that affect total lead mass load. Barrett et al. (1998) reported that a low runoff coefficient resulting from infiltration produces a large reduction in the pollutant load of highway runoff. An appropriate treatment of antecedent conditions, runoff coefficient, and land use in load models has not been satisfactorily demonstrated, to date. Even though many computer load models for continuous simulation are available (i.e., Modeling of Urban Sewers [MOUSE] and Stormwater Management Model [SWMM] [Elliott and Trowsdale, 2007]), important conditions, such as closed-form solution for simulation of multiple sequential dry periods or comprehensive simultaneous parameter estimation for several drainage areas, are not included.

The main objective of this paper is to develop a load model for urban runoff constituents with emphasis on zinc, copper, cadmium, nickel, chromium, lead, mercury, silver, 5-day biochemical oxygen demand (BOD5), total suspended solids (TSS), E. coli, fecal coliform, total soluble phosphorus (TSP), and total phosphorus. The model contains a buildup component, including consideration of runoff coefficient, drainage area, land use, and one to three antecedent dry period(s) before a given storm event and a washoff component reflecting intensity and duration of the storm. A comprehensive parameter estimation scheme is included. Other objectives are to determine runoff coefficients for sampling areas, evaluate constituent concentrations relative to their guideline values or limits, and estimate the contribution of traffic-related sources to zinc, copper, cadmium, nickel, chromium, and lead in urban runoff. More than 400 storm events will be considered in 18 watersheds of Milwaukee, Wisconsin, during the period 2000 to 2004.

Background

The Milwaukee Metropolitan Sewerage District (MMSD) (Wisconsin) has conducted a voluntary stormwater monitoring program since 2000, which includes sampling and analysis of stormwater runoff quality. Samples were collected from 2000 to 2004, at 18 monitoring sites. This program has focused on 33 constituents of mixed land-use drainage areas. Statistical analysis of these sampling data has been done by Soonthornnonda and Christensen (2005). The results showed that stormwater samples were found to have significantly higher pollutant concentrations (i.e., metals, TSS, and nutrients) than either the Wisconsin Pollutant Discharge Elimination System (WPDES) limits or National Pollutant Discharge Elimination System (NPDES) and National Water Quality Criteria (EPA NWQC) guideline levels. Soonthornnonda and Christensen (2005) reported that the length of the antecedent dry period (t^sub d^) was a significant parameter determining pollutant concentrations and loadings, as a result of the gradual accumulation of pollutants during the dry period before a storm.

Materials and Methods

Study Area. The MMSD receives sanitary and stormwater flows from 28 communities (population 1.1 million) with an area of 1094 km^sup 2^. According to the MMSD voluntary stormwater monitoring program (2000 to 2004), 18 sites in 8 communities of 1104 ha (11.04 km^sup 2^) were selected from the total district area (MMSD, 2003). Individual drainage areas ranged from 1.92 to 608 ha. Table 1 summarizes land-use features of the 18 sampling sites.

Stormwater Sampling. The sampling method used in this study (MMSD, 2003) followed recommendations for stormwater discharge permits by the Wisconsin Department of Natural Resources (WDNR, 2002). The first sample was taken at a specified time triggered by a certain water level in the stormwater sewer. The trigger point level varied from site to site, as a result of adjustments based on baseline flow. A second sample was taken 2 hours later. Sampling was conducted between April and November each year, from 2000 to 2004. All samples were analyzed by the MMSD (2007). Metals were analyzed based on U.S. Environmental Protection Agency (U.S. EPA) (Washington, D.C.) method 6010 (U.S. EPA, 1996), except mercury, where method 245.1 was used (U.S. EPA, 1994). Standard Methods (APHA et al., 1998) were used to analyze BOD^sub 5^ (5210B), E. coli (9223B), fecal coliform (9222D), and TSS (2540D). Unless otherwise specified, total metals concentrations (i.e., both soluble and particulate fractions) are considered.

Runoff Coefficient An area velocity sensor (ISCO Model No. 2150, Teledyne Iseo Inc., Lincoln, Nebraska) was used to measure runoff discharges and velocities at sites. Runoff discharges were obtained during the period 2000 to 2004. A rain gauge station for each monitoring site was selected based on the minimum distance to each site.

Runoff coefficients for each storm event were calculated . regardless of the depression storage volume as a ratio of runoff volume to rainfall volume.

Statistical Methods. The program SPSS 13.0 (SPSS Inc., Chicago, Illinois) (Noonan, 2006) was used to compute descriptive statistics, and SigmaPlot 8.0 (SYSTAT Software Inc., Point Richmond, California) (Gall, 2006) was used to generate box plots for MMSD stormwater data from 2000 to 2004. Statistical results were evaluated against WPDES limits in WDNR (2003). The NPDES guidelines in U.S. EPA (2000) or EPA NWQC guidelines in U.S. EPA (1986) and U.S. EPA (2006) were used in the case of nonavailability of WPDES limits. A summary of stormwater monitoring constituents and their guidelines or limits is shown in Table 2.

Load Model. Washoff models proposed by Alley (1981) and Sartor et al. (1974) have been used by a number of researchers. In these models, the rate of pollutant removed from an effective impervious surface is assumed to be proportional to the amount remaining on this surface. The amount of pollutant washoff predicted is a function of the volume of storm runoff or rainfall and initial amount of pollutant. The initial amount of pollutant is a function of the maximum amount of pollutant on the effective impervious area and time since the last period of street sweeping or storm runoff (Alley and Smith, 1981). Alley and Smith (1981) stated that it was an important assumption in their model that effective impervious surfaces were the predominant source of stormwater loads and that the watershed had uniform land use. With regard to antecedent dry conditions, they recognized that the surface load (L^sub e^) after the previous period of storm runoff or street sweeping should be considered, and they gave an expression for the equivalent accumulation time (t^sub e^) in terms of L^sub e^ and buildup parameters. However, L^sub e^ was not expressed in terms of parameters for previous storm(s) and associated antecedent dry period(s). Many complex load models that use continuous simulation (i.e., SWMM, Hydrologie Simulation Program-Fortran [HSPF], and Source Loading and Management Model [SLAMM]) do not give better information for the accumulation rate of constituents on the drainage area. The accumulation rate is often obtained by trial and error during data calibration, with little, if any, actual direct measurements (Pitt et al., 2004).

To overcome the above limitations, the modified model, described below, includes multiple subwatersheds, each with a specific runoff coefficient and land-use factor. Antecedent dry conditions are considered, in terms of an equivalent accumulation time reflecting the antecedent dry period and up to two appropriately reduced previous antecedent dry periods.

The model, which relates the load per event (P) of a given pollutant to the runoff coefficient, average rainfall, antecedent dry period, and land-use factor for a site, is as follows:

The storm duration (Deltat) is determined as the period of time between the starting point of each storm hydrograph and the point where 10% of discharge peak value has occurred at the recession limb of the hydrograph.

The effective area is beta A. The pollutant mass accumulated at the beginning of the storm event (j) is alpha a beta A f(t^sub d^). If a load (L^sub e^) is remaining on the drainage area after the previous storm, L^sub e^ should be added to this expression. In this model, the expression in the square bracket in eq 1, optimum approximately 78%, represents the fraction of the initial pollutant mass washed off after the runoff event.

If the accumulation of pollutant mass between storm events j – 1 and j does not depend on t^sub d^, f(t^sub d^) may be written as a constant, as follows:

However, if the accumulation of pollutant mass between storm events j – 1 and j is dependent on t^sub d^ j, f(t^sub d^) may be written as follows:

Where it is assumed that the surface is clean after the previous storm j – 1.

Advancing one step further, the pollutant mass retained after storm event j – 1 may be included in the model, and f(t^sub d^) is the following:

Where it is assumed that the surface is clean after storm j – 2.

The pollutant masses retained after storm events j – 1 and j – 2 may also be included in the model, and f(t^sub d^) becomes the following:

The assumption is here that the surface is clean after storm j – 3. The model expressed by eqs 3 to 5 is a linear buildup model. In eq 5 and its extensions to further dry periods (i.e., t^sub d,j- 3^), the effective antecendent dry period is written as a sum of the preceding dry period followed by downweighted or reduced previous dry periods. For a sufficient number of terms, the actual previous dry periods become downweighted, such that their contribution is small and the assumption of initial clean surfaces (i.e., after storm j – 3) is inconsequential.

In case of significant removal of pollutants by wind or pollutant decay during buildup, the general expression for buildup may be written as follows:

This equation is a version of the buildup model considered by Charbeneau and Barrett (1998), modified to include the runoff coefficient beta. The expression for f(t^sub d^), corresponding to eqs 3 to 5, and including pollutant removal according to eq 6 during buildup, are in the same order.

Note that these equations become eqs 3 to 5 when Kt^sub d^ [much less than] 1, which we assume here to be the case, as a result of frequent rainfall events in the Midwest of the United States. The antecedent dry period (t^sub d^) was defined as the dry period before any runoff event, in which both tiie previous peak discharge and the current peak discharge are >/=5 % of the overall average peak flow during rainfall events from 2000 to 2004. By using this definition, values of t^sub d^ will be more realistic by disregarding minor runoff events.

Land-use factors alpha (i.e., mass load at specific site divided by mass load for all regions) were estimated as a measure of that site’s relative contribution to the pollutant load. The pollutant deposition flux on a surface is alphaa. The values of a and c were deteimined by a least-squares fit of calculated to measured loads for all areas, with alpha = 1. Next, alpha values for individual drainage areas were estimated based on average factors needed to give a better fitting model. The factor alpha for a drainage area can be determined from the following:

and the uncertainty of the mean deltaA is given by the following:

Multiplication of the overall calculated load with alpha will then ensure that the new calculated points are centered around the line Y = x in the log-log loading plot.

Measured loads P^sub m^ were determined as follows:

Values of P^sub m^ based on eq 17 were compared with those based on a limited data set (n = 12 storms, representing the full range of storm variability), with approximately six measurements during each storm event. Results indicated that loads calculated from eq 17 were overestimated by a factor of 1.54 +- 0.15 (average +- standard error of mean, n = 12). Thus, the use of eq 17 to estimate measured loads may be acceptable, especially because load uncertainties typically are one cycle (a factor of 10) in log-log load plots.

Pollutant concentrations in stormwater runoff are difficult to model because of many uncertain factors, such as source strength, dispersion, runoff percolation, and so forth. However, order-of- magnitude estimates can be made for some metals where the major source is known. For example, automobile tires are a major source of zinc (Christensen and Guinn, 1979), and aqueous concentrations can be calculated as the emission rate times the number of vehicle kilometers traveled in the watershed during the antecedent dry period divided by the runoff volume.

By contrast, ratios between deposition fluxes alphaa can, in some cases, be modeled reasonably well, based on known emission rates (i.e., rates of zinc from tire wear and copper from brake linings [Brewer, 1997; Legret and Pagotto, 1999]).

Results

Monitoring Results. Results of the descriptive statistics calculations indicate that the mean concentrations of chromium, copper, lead, zinc, and TSS exceed WPDES limits, NPDES guidelines, and EPA NWQC guidelines at several sites, including site 15 (1-94 runoff). Box plots of zinc concentrations are shown in Figure 1, with similar plots for BOD^sub 5^, E. coli, and total phosphorus for all 18 sites. Most zinc concentrations exceed the NPDES guideline of 0.117 mg/L. The mean concentrations of total phosphorus at sites 9, 17, and 18 were found to exceed the WPDES limit of 1 mg/L. The mean concentrations of BOD^sub 5^ at sites 8, 9, 13, 17, and 18 were relatively high and exceed the WPDES limit of 30 mg/L. Most E. coli bacteria counts exceed the EPA NWQC guideline of 126 colony-forming units (CFUs)/100mL.

Runoff Coefficients. Runoff coefficients were computed as total runoff volume divided by total rainfall volume. Coefficients ranged from 0.00096 to 16.1. The mean coefficients for the 18 monitoring sites ranged from 0.0052 to 3.88. The median coefficients ranged from 0.0036 to 3.71 (Table 1). The mean coefficient over all sites was 0.87 +- 0.33, and the median was 0.13. Coefficients were greater than 1.0 at sites 6, 7, 8, and 18. Typically, runoff coefficients vary for different storm events, being larger for larger storms and shorter dry periods between storms (less influence of depression storage and limited infiltration), but would not exceed a value of one, nor would uiey be very small for urban areas.

Three possible explanations of obtaining runoff coefficients larger than one for these sites are illegal discharges of sanitary wastewater, groundwater infiltration, and underestimated drainage areas. Substantial contribution from sanitary wastewater should influence the water quality (higher concentrations of nutrients, BOD^sub 5^, and E. coli). The substantial contribution from groundwater would also influence water quality; for example, concentrations of heavy metals (i.e., zinc, copper, lead, and chromium) would be lower because of a dilution effect. The results in Figure 1 do not support these hypotheses.

It is more likely that these four drainage areas (sites 6, 7, 8, and 18) have been underestimated. We have recently confirmed this for sites 6 and 7, from the fact that the drainage piping networks extend significantly beyond the originally indicated drainage areas for these sites. The extension is in rough proportion to the amount by which the runoff coefficient exceeds unity. The low values of measured runoff coefficient may be the result of infiltration in unsaturated soil at low rainfall (sites 1, 9, 10, and 14) and overestimated drainage areas (i.e., site 15). The value much smaller than 1 (0.033) of the runoff coefficient for site 15 is confirmed by the fact that the slopes and outfalls for drainage pipes of site 15 indicate that the effective drainage area is much smaller than the one that was indicated originally. Despite these modifications, the product …A remains valid, even for … > 1, because … is multiplied by the same factor by which A is divided. Concentrations of Zinc and Copper in Stormwater. Regarding the estimation of metal concentrations in runoff volume, consider zinc and copper from site 15 during the 6-hour rainfall event from August 12, 2002, 6:00 p.m., to August 13, 2002, 12:00 a.m. (midnight). Assuming that a 1.5-km stretch of the 6-lane 1-94 freeway is the source and that the freeway system in Milwaukee includes 1100 lane km (700 lane miles), the fraction of total zinc and copper deposition is 8.04 x 10^sup – 3^.

The primary source of copper in urban runoff is automobile brake linings (McCuen, 2004). The average brake wear rate is 8.8 mg/ vehicle km (Warner et al., 2002). The average brake lining is assumed to have a copper concentration of 79 000 mg/kg (7.9%) (Brewer, 1997; Legret and Pagotto, 1999). Thus, the average deposition rate of copper is 8.8 x 0.079 = 0.70 mg/vehicle km. Christensen and Guinn (1979) reported that the average deposition rate of zinc is 3.0 mg/vehicle km.

Consequently, with an antecedent dry period of 8.6 days, 1.685 x 107 vehicle freeway km (1.047 x 107 vehicle freeway miles) traveled per day, a runoff volume of 1274 m^sup 3^, zinc concentration of 2.73 mg/L, and copper concentration of 0.63 mg/L are obtained, compared with measured event mean concentrations of 2.23 and 0.51 mg/L, respectively. Hydraulic and pollutant data are from the MMSD (2003) and highway data from the Texas Transportation Institute (2005). Because of several uncertainties, for example, in contributing freeway length and amounts of zinc and copper deposition in the watershed, the agreement between measured and calculated values should only be taken as an indication within an order of magnitude, that zinc and copper from highways appear to be a significant source of zinc and copper in runoff.

Constituent Loads. Event mass loads of zinc, copper, cadmium, nickel, chromium, lead, mercury, silver, BOD^sub 5^, TSS, E. coli, fecal conform, TSP, and total phosphorus were estimated according to eqs 1 to 5 and also using eqs 7 to 9. Results using eqs 1 to 5 are shown in Table 3, which presents the deposition coefficient a and R^sup 2^ from the model fit. The model performed better for all constituents, except TSP, when t^sub d^ was included in the buildup term. This indicates that the release of soluble phosphorus may be more dependent on storm duration and intensity than accumulation during dry periods. The R^sup 2^ values for all constituents, except TSS and silver, based on an assumption of a clean surface after the last storm in eq 3, are less than the R^sup 2^ values obtained from eq 4, suggesting that the load retained after the previous storm is significant and that constituents such as metals, phosphorus, and bacteria, associated with smaller particles, are more likely to be trapped on the drainage area at die end of the previous storm than bulk TSS. Figure 2 shows a comparison of measured and predicted loads of zinc, BOD^sub 5^, E. coli, and total phosphorus. The load model based on the retained mass after two previous storms (eq 5) gave less accurate results, as shown in Table 3.

An average of 78% removal of pollutant mass (i.e., tiie square bracket in eq 1) was selected as an optimum, giving c values for all constituents of approximately 0.6 cm^sup -1^. Alley (1981) reported that a runoff volume of 12.7 mm would wash off 90% of a pollutant from effective impervious surfaces, regardless of duration and whether or not the runoff was uniform. The corresponding c is 1.81 cm^sup -1^. Charbeneau and Barrett (1998) found that approximately 85% of TSS was actually removed. Alley (1981) reported that average c values for eight storms based on total runoff ranged from 0.63 cm^sup -1^ (nitrogen) to 1.30 cm^sup -1^ (suspended solids). Grottker (1987) found c values based on effective rainfall ranging from 0.21 cm^sup -1^ (cadmium) to 3.20 cm^sup -1^ (nickel).

There was some improvement in the model fit, as shown by an increasing R^sup 2^, when losses of copper, nickel, and mercury during buildup according to eqs 7 to 9 were included. The optimal K values were 0.036 day^sup -1^ for copper and nickel and 0.2 day^sup – 1^ for mercury. Thus, characteristic times for losses 1/K (days) were 28 days for copper and nickel and 5 days for mercury. The reason for the shorter time for mercury is probably that this element exists in many volatile compounds and therefore is more likely to undergo relatively rapid losses.

Land use factors alpha (mass load at specific site divided by mass load for all regions) were estimated as a measure of that site’s relative contribution to the pollutant load. These factors, based on eqs 1 and 4, are shown in Figures 3 and 4. Factors (alpha) for many metals were greater than 1.0 at sites 4,5,15, and 18. Also, alpha factors for BOD^sup 5^ and total phosphorus were greater than 1 at site 4. The values of alpha factors for E. coli and fecal coliform were greater than 1 at 10 sites (4, 6, 7, 8, 9, 12, 13, 14, 17, and 18). The land-use factor can be used as a parameter to understand the relative contribution of pollutant load in each stormwater catchment A catchment with significant highway(s) and parking lot(s) will give a high alpha value for metals, as seen in Table 1 and Figure 3. Catchments with residential, open lands, or recreational areas display high alpha values for BOD^sub 5^, total phosphorus, E. coli, and fecal coliform (Table 1 and Figure 4).

Deposition fluxes alphaa of copper, cadmium, and lead based on eqs 1 and 4, at site 15, were 5.96 x 10^sup -3^, 5.84 x 10^sup – 5^, and 2.47 x 10^sup -3^ kg/ha/d, respectively. Deposition fluxes of copper, cadmium, and lead at site 18 were 2.31 x 10^sup -3^, 3.46 x 10^sup -5^, and 8.93 x 10^sup -4^ kg/ha/d, respectively. By comparison, Harrison and Johnston (1985) reported that deposition fluxes of copper, cadmium, and lead on the verges of a major highway in northwest England range between 1.43 x 10^sup -4^ and 2.07 x 10^sup -3^, 1.43 x 10^sup -5^ and 2.43 x 10^sup -4^, and 3.29 x 10^sup -4^ and 0.016 kg/ha/d, respectively. Thus, fluxes of cadmium and lead at sites 15 and 18 were within the ranges reported above. The deposition fluxes of copper at sites 15 and 18 were just above the above-mentioned range. The load model gave deposition fluxes of zinc of 0.0236 (site 15) and 0.0102 (site 18) kg/ha/d. Sabin et al. (2005) determined atmospheric deposition rates in Los Angeles, Calfornia, of 10 and 43 [mu]g/m^sup 2^/d (1.0 x 10^sup -4^ and 4.3 x 10^sup -4^ kg/ha/d) within a 5-ha area of limited local metal sources for copper and zinc, respectively, further indicating that local inputs generally are significantly higher than atmospheric inputs.

Relationship between Mass Loads of Zinc, Copper, and Other Metals in Stormwater Runoff. Ratios between zinc and copper deposition fluxes alphaa are 4.0 (site 15), 4.7 (site 16), and 4.4 (site 18). These three sites have significant automobile traffic. The ratio between the average zinc and copper vehicle deposition rates is 3.0 mg Zn/vehicle km/0.70 mg Cu/vehicle km = 4.3. Also, the ratio between zinc and copper concentrations at site 18, at t^sub d^ = 25 days in Figure 5, is (1.43 mg/L)/(0.3 mg/L) = 4.77. This is in agreement with the ratio between the range of ratios of zinc and copper deposition fluxes alphaa (4.0 to 4.7) and average zinc and copper vehicle deposition rates (4.3), which, with the linear correlation of metal concentrations versus antecedent dry period, as illustrated in Figure 5, indicate that the measured zinc and copper in fact is derived from automobile traffic.

Table 4 summarizes the comparison of ratios between concentrations of zinc and other metals with ratios of deposition fluxes (eqs 1 and 4) of zinc and other metals (copper, cadmium, nickel, chromium, and lead) at sites 6, 15, 16, and 18. Ratios of deposition fluxes at sites 18 and associated concentration ratios from Figure 5 are assumed to be indicators of traffic-related sources. Table 4 shows that all metals at these sites can be viewed as having automobiles as a main source, except chromium at site 6, 15, and 16; cadmium and nickel at site 6; and lead at site 6. Possible nonautomotive sources of selected metals include metal plating (chromium and nickel), asphalt paving (nickel), and insecticide application (cadmium) (Colman et al., 2001).

Discussion

The main new points developed here are the following:

(1) A new dry-period-based load model for pollutants in urban runoff, in which the influence of each dry period before a storm event on the calculated load can be evaluated; and

(2) Demonstration of the fact that including not only the immediately preceding dry period, but also a weighted contribution from one additional preceding dry period improves the model fit for the following constituents: zinc, copper, cadmium, nickel, chromium, lead, mercury, BOD^sub 5^, bacteria, TSP, and total phosphorus.

The additional term reflects the load retained on the drainage area after the previous storm. Only the model fits for TSS and silver are not improved by the consideration of an additional dry period.

Previous models as developed by, for example, Alley and Smith (1981) and Kim et al. (2006) are limited to parameters such as nitrogen, lead, TSS, and chemical oxygen demand and do not express the calculated load in terms of a closed-form expression with previous dry periods as parameters. Also, only Alley and Smith (1981) compare models with different antecedent dry conditions (nitrogen, lead, and TSS).

Although the developed model can consider maximum pollutant buildup on the drainage area resulting from removal by wind or decay, we find that a linear model appears to be sufficient for the data considered here, based on linear metal concentrations versus the dry period in Figure 5, except perhaps for mercury, and, to a lesser extent, copper and nickel. Data for the bacteria concentrations versus the dry period (not shown) also support a linear model, up to t^sub d^ = 25 days. It may be expected that exponential buildup terms, as in eqs 7 to 9, would apply to drier climates with long antecedent dry periods, as is found in the southwestern United States. In addition to introducing new theoretical and practical aspects mentioned above, this work can also serve as basis for comparisons with load estimates for other drainage areas.

Conclusions

We have outlined a framework for modeling loads of runoff constituents, such as zinc, copper, cadmium, nickel, chromium, lead, mercury, silver, BOD^sub 5^, TSS, E. coli, fecal coliform bacteria, TSP, and total phosphorus, in an urban watershed with several separate subdrainage areas, each with a specific runoff coefficient and main land use. The antecedent dry period is an important predictor of loads to receiving waters for most constituents, except TSP. Both concentrations and loads of pollutants should be considered in the establishment of guideline limits for the watershed. The main conclusions of this work are as follows:

(1) The load model of Alley and Smith (1981), which was developed for a mainly impervious area of single land use is expanded to apply for multiple subwatersheds of different runoff coefficients and land use. The model is valid for a wide range of runoff coefficients. Land use is modeled by a multiplicative parameter alpha, for which an efficient statistical estimation procedure has been developed. The model determines an average constituent deposition rate, a (kilograms per hectare per day or CFU per hectare per day), and a specific rate alphaa for each subarea. The total antecedent dry period is included as an effective accumulation time that considers the residual load from the previous storm or street cleaning. This is done by adding one or two previous dry period(s) to the antecedent dry period, weighted according to the intensity and duration of the following storm(s). Considering just one previous dry period appears to be sufficient. High metal fluxes are found near major throughways, such as I-94, highway 794, and by major parking lots. Phosphorus and bacteria deposition rates are high in certain residential, recreational, and institutional areas, and near the Milwaukee County Zoo.

(2) Runoff coefficients show little variability by event for a given urban area. However, for residential areas and open lands, these coefficients can be quite small at low rainfall, indicating depression storage

(3) Metal concentrations in runoff are high compared with NPDES guidelines near I-94 and the Miller Park East parking lot. Several BOD^sub 5^ concentrations exceed the WPDES limit (30 mg/L) in residential areas. Most E. coli concentrations exceed the EPA NWQC guideline for recreational waters (126 CFU/100mL). While most mean total phosphorus values are below the WPDES limit of 1 mg/L, there are several single measurements above this value.

(4) Considering ratios between deposition fluxes and concentrations at the Miller Park East parking lot, a characteristic metals profile is developed for zinc, copper, cadmium, nickel, chromium, and lead coming from automotive sources. The zinc/copper ratio (4.4 to 4.8) is consistent with automobile emission from tires (zinc) and brake linings (copper). The metals profile is descriptive of metal deposition near I-94 and other urban sites, except that chromium, nickel, and cadmium, in some cases, appear to have additional sources.

Credits

This work is supported by the Milwaukee Metropolitan Sewerage District (M03023P01) (Wisconsin). We also thank Christopher Magruder, Mary Singer, and Urbain Boudjou from MMSD for providing all data and helpful discussion.

Submitted for publication December 14, 2006; revised manuscript submitted May 18, 2007; accepted for publication July 16, 2007.

The deadline to submit Discussions of this paper is May 15, 2008.

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* Department of Civil Engineering and Mechanics, P.O. Box 784, University of Wisconsin-Milwaukee, Milwaukee, WI 53201; e-mail: erc@uwm.edu.

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