A Stormwater Management Framework for Predicting First Flush Intensity and Quantifying its Influential Factors

Abstract

Despite numerous applications of Random Forest (RF) techniques in the water-quality field, its use to detect first-flush (FF) events is limited. In this study, we developed a stormwater management framework based on RF algorithms and two different FF definitions (30/80 and M(V) curve). This framework can predict the FF intensity of a single rainfall event for three of the most detected pollutants in urban areas (TSS, TN, and TP), yielding satisfactory results (30/80: $accuracy_{average}$ = 0.87; M(V) curve: $accuracy_{average}$ = 0.75). Furthermore, the framework can quantify and rank the most critical variables based on their level of importance in predicting FF, using a non-model-biased method based on game theory. Compared to the classical physically-based models that require catchment and drainage information apart from meteorological data, our framework inputs only include rainfall-runoff variables. Furthermore, it is generic and independent from the data adopted in this study, and it can be applied to any other geographical region with a complete rainfall-runoff dataset. Therefore, the framework developed in this study is expected to contribute to accurate FF prediction, which can be exploited for the design of treatment systems aimed to store and treat the FF-runoff volume.

Appendix A. Supplementary information

1.1 A.1 SWMM Model Description and Implementation

SWMM simulates the hydrograph and pollutograph for a real storm event (for a single and long-term event) based on the rainfall and other meteorological inputs, and system characteristics (catchment, conveyance, and storage/treatment) for urban and peri-urban watersheds. SWMM has been designed in blocks or operating units. Each block can be used individually or in a cascade, and an executive block coordinates its outputs. The runoff block, as well as the transport block, were utilized for this study. By using inlet hydrographs generated from the runoff unit, the transport block executes the flow and pollutant routing through the drainage network.

To simulate the runoff from urban surfaces, the kinematic-wave equation was chosen. Furthermore, the water losses taken into account were represented by the depression storage on the impervious portion of the watershed and the infiltration process. The latter was modeled by evaluating, for each subcatchment, the percentage of the impervious and pervious area obtained from the land-use map. The infiltration model adopted in this work was based on Horton’s equation, whose parameter values have been chosen according to the representative values reported in the literature in relation to soil type. Eight parameters of the runoff block of SWMM were used to calibrate the hydraulic-hydrologic model: the depth of depression storage on impervious ($Dstore-Imperv$) and pervious ($Dstore-Perv$) portions of the subcatchment, Manning’s coefficient for overland flow over the impervious ($N-Imperv$) and pervious ($N-Perv$) portions of the subcatchment, the percent of the impervious area without depression storage ($\%Zero Imperv$), and the infiltration parameters of Horton’s equation.

Pollutant build-up within a land-use category is described by a mass per unit of subcatchment area. The amount of build-up is a function of the number of dry weather days antecedent to the rainfall event. The build-up function follows a growth law that asymptotically approaches a maximum limit:

$$\begin{aligned} M_a(d_{adp}) = \frac{Accu}{Disp} \cdot A \cdot P_{imp} (1-e^{Disp \cdot d_{adp}}) \end{aligned}$$

(12)

where $M_a(d_{adp})$ represents the pollutant build-up during the antecedent dry period [kg/ha]; Disp is the parameter that measures the disappearance of accumulated solids due to the action of wind or vehicular traffic [1/d]; $P_{imp}$ is the impervious area fraction; Accu the parameter that characterizes the solids build-up rate [kg/(ha d)]; $\frac{Accu}{Disp} \cdot A \cdot P_{imp}$ presents the maximum asymptotic limit of the build-up curve. The pollutant wash-off over different land uses takes place during wet periods, and it is described by the differential equation:

$$\begin{aligned} \frac{dM_d(t)}{dt} = -Arra \cdot i(t)^{wash} \cdot M_a(t) \end{aligned}$$

(13)

where $\frac{dM_d(t)}{dt}$ is the wash-off load rate [kg/h]; Arra is the wash-off coefficient [$mm^{-1}$]; i(t) is the runoff rate [mm/h]; wash is the wash-off exponent, a parameter that controls the influence of rainfall intensity on the amount of leached pollutants. Four parameters of the runoff block were identified for the calibration of the water-quality model. For the build-up function: the parameter that characterizes the solids build-up rate (Accu) and the parameter that identifies the disappearance of accumulated sediments due to the wind or vehicular traffic (Disp). For the wash-off function: the wash-off coefficient (Arra) and the wash-off exponent (wash).

1.2 A.2 Exploratory Data Analysis: Indices and Results

Spearman, Kendall and Phik coefficients are able to capture non-linear correlations. Spearman exploits monotonicity, while Kendall measures ordinal associations. Both coefficients have values in domain $[-1, 1]$, where -1 indicates a perfect negative correlation, +1 a perfectly positive correlation, and 0 no correlation. The formulas are defined in Eqs. (14) and (15), respectively.

$$\begin{aligned} \rho = 1 - \frac{6 \sum {d_i^2}}{n(n^2-1)} \end{aligned}$$

(14)

$$\begin{aligned} \tau = \frac{(\text {number of concordant pairs}) - (\text {number of discordant pairs})}{ \left( {\begin{array}{c}n\\ 2\end{array}}\right) } \end{aligned}$$

(15)

For Spearman’s $\rho$, $d_i$ is the difference between the two ranks of each observation, and n is the number of observations. For Kendall’s $\tau$, the definition of concordant and discordant pairs is needed: a pair of values $(x_i, y_i), (x_j, y_j), i < j$ is concordant if $x_i < x_j$ and $y_i < y_j$ or if $x_i > x_j$ and $y_i > y_j$.

The Phik coefficient Baak et al. (2020) is also a non-linear correlation coefficient that was refined to work consistently with continuous and categorical variables.

The corresponding correlation heatmaps are reported in Figs. 5 and 6

Fig. 5

Correlation heatmap computed with Kendall coefficient

Fig. 6

Correlation heatmap computed with Phik coefficient