The Build-Up Wash-Off (BUWO) method is a hydrological modeling approach used to simulate the accumulation and removal of pollutants, such as sediment, nutrients, and contaminants, from impervious surfaces in urban areas during rainfall events. This method is commonly employed in the field of stormwater management and urban water quality assessment. It helps estimate the quantity and quality of runoff from urban areas and the subsequent pollutant loads entering receiving water bodies. Build up may be a function of time, traffic flow, dry fallout and street sweeping. During a storm event, the material is then washed off into the drainage system. Although the bulid-up Wash-off option is conceptually appealing, the reliability and credibility of simulation may be difficult to establish without local data for calibration and validation (Huber and Dickinson, 1988). 

The Michaelis-Menten Build-Up Equation is a mathematical model used to describe the accumulation of pollutants on impervious surfaces in urban areas over time. In the context of urban stormwater management and water quality modeling, the Michaelis-Menten Build-Up Equation is used to estimate how a specific pollutant, such as sediment, heavy metals, or nutrients, accumulates on impervious surfaces (e.g., roads, parking lots) as a function of time, especially during dry weather periods. The equation is often used in conjunction with the Build-Up Wash-Off (BUWO) method to model the buildup and subsequent wash-off of pollutants during rainfall events. The general form of the Michaelis-Menten Build-Up Equation is as follows (Huber and Dickinson, 1988 and Neitsch, Arnold, Kiniry, and Williams, 2009) :

\begin{aligned} &\text{SED}=\frac{\text{SED}_{\max } \times t_d}{\left(t_{\text {half }} + t_d\right)} \\\\ &\begin{aligned} & \mathrm{ SED }=\text { Solids Build Up ($\mathrm{kg}/$curb $\mathrm{km})$ td days since $S E D=0$ } \\ & \mathrm{SED}_{\text {max}}=\text { Maximum Accumulation of Solids Possible for the Land Type ($\mathrm{kg}/$curb $\mathrm{km})$ } \\ & \mathrm {t_{\text {half }}}=\text { Length of Time needed for Solids to Increase from 0 to half of $\mathrm{SED}_{\mathrm{max}}$ (days)} \\ & \mathrm {t_d}= \text {Time dry in days} \\ \end{aligned} \end{aligned}

The Huber-Dickinson equation is a commonly used mathematical model for simulating the wash-off of pollutants from impervious surfaces in urban areas during rainfall events. It's named after its developers, W.C. Huber and R.E. Dickinson, who introduced the model in the 1988 publication titled "Stormwater Management Model User's Manual, Version III." The Huber-Dickinson equation is particularly associated with the United States Environmental Protection Agency's (EPA) Storm Water Management Model (SWMM), which is widely used for stormwater management and urban hydrology modeling. The equation estimates the wash-off of pollutants as a function of various factors, including rainfall characteristics, land use, and the pollutant load on impervious surfaces. The general form of the Huber-Dickinson Wash-Off equation is as follows (Huber and Dickinson, 1988 and Neitsch, Arnold, Kiniry, and Williams, 2009):

\begin{aligned} &\text Y_{\text {sed}}=\text{SED}_{0} \times \left(1-e^{-k k \cdot t}\right) \\\\ &\begin{aligned} & \mathrm{Y}_\text{sed}=\text{Cumulative Amount of Solids Washed Off at Time t $(\mathrm{kg} /$curb $\mathrm{km})$} \\ & \mathrm{SED}_0=\text{Amount of Solids Build Up on the Impervious Area at the Beginning of the Precipitaiton Event $(\mathrm{kg} /$curb $\mathrm{km})$} \\ & \mathrm{kk}=\text{urb}_{\text {coef }} \times \mathrm{q}_{\text {peak }} \\ & \quad \mathrm{urb_\text{coef}} = \text {Wash Off Calibration Coefficient $\left(0.039-0.39 \mathrm{~mm}^{-1}\right)$} \\ & \quad \mathrm{q}_{\text {peak }}=\text {Peak Event Flow Rate $(\mathrm{mm} / \mathrm{hr})$} \\\\ & \mathrm{Y}_{\mathrm{sed}} \times \mathrm{L}_{\text {curb }} = \text {Sediment Load} \\ & \quad \mathrm{L}_{\text {curb }} = \text {Length of Curb (curb $\mathrm{km})$} \\ \end{aligned} \end{aligned}

Street cleaning is a common practice in urban areas to manage the accumulation of solid debris and litter in street gutters. While it has traditionally been believed that street cleaning positively impacts the quality of urban runoff, there has been a scarcity of data available to quantitatively assess this influence. Previous studies, such as those conducted under the EPA Nationwide Urban Runoff Program (NURP), have generally indicated limited improvements in runoff quality as a result of street sweeping unless carried out on a daily basis (EPA, 1983b). The equation or model for street sweeping or pollutant removal during street cleaning operations can vary and is typically developed based on local practices, equipment types, cleaning frequencies, and specific pollutant removal efficiencies associated with the street sweeping process. These equations or models may not have a standardized or widely accepted form, as they often depend on the unique characteristics of the street cleaning operations in a particular area.

This BUWO Method includes four parameters to describe the street sweeping operations within the subbasin. The Density specifies the total length of street curb whether or not the curb is subject to sweeping operations. The density should consider whether the street has curbs on one side or both sides of the street. The Sweeping Percentage specifies the percentage of the curb length subject to sweeping. The percentage should account for the possible presence of parked cars which result in missed curb. The Efficiency Percentage specifies the efficiency of the sweeping equipment at removing accumulated sediment. Finally, the Interval specifies the number of days between scheduled sweeping operations.

The general form of the Huber-Dickinson street sweeping removal equation is as follows (Huber and Dickinson, 1988 and Neitsch, Arnold, Kiniry, and Williams, 2009):

\begin{aligned} & \mathrm {SED} = \text{SED}_{0} \times \left(1-\text{fr}_{av} \times \text{reff}\right) \\\\ &\begin{aligned} & \mathrm{SED}= \text {Amount of Solids Remaining after Sweeping $(\mathrm{kg} / \mathrm{curb} \mathrm{km}$ )} \\ & \mathrm{SED}_0=\text {Amount of Solids Present prior to Sweeping $(\mathrm{kg} / \mathrm{curb} \mathrm{km}$ )}\\ & \mathrm{fr}_{a v}=\text {Fraction of the Curb Length Available for Sweeping}\\ & \mathrm{reff} =\text {Removal Efficiency of the Sweeping Equipment} \\ \end{aligned} \end{aligned}

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include the initial time, half time, maximum solid amount, density, sweeping percentage, efficiency percentage, interval, and wash-off coefficient.

A tutorial using the BUWO simulation can be found here: TBD.

A Note on Parameter Estimation

Street sweeping parameters exhibit variability and are typically tailored to local conditions, accounting for factors like equipment types, cleaning frequencies, and the efficiency of pollutant removal during the street sweeping process.