Statistical Distribution of TSS Event Loads from Small Urban Environments

Abstract

Results from a long-term stormwater quality monitoring program were used to derive total suspended solids (TSS) event load distributions at four small urban environments (flat roof, parking lot, residential catchment, high traffic street). Theoretical distribution functions were fitted to the empirical distribution functions obtained. Parameters of the theoretical distribution functions were optimized with respect to a likelihood function to get both optimized parameters and standard errors. Kolmogorov-Smirnov and Anderson-Darling test statistics were applied to assess the goodness-of-fit between empirical and theoretical distribution. The lognormal distribution function was found to be most expressive to approximate empirical TSS event load distributions at all sites. However, the goodness-of-fit of the statistical model strongly depends on the number of events available. Based on the results of a Monte-Carlo-based resampling strategy, around 40 events should be considered.

Hydraulic, wash-off and sediment transport experiments in a full-scale urban drainage physical model

“…Several empirical equations and models have commonly been used in the literature to model urban wash-off 3,[8][9][10] . However, the prediction accuracy of these lumped formulations is still quite limited 11,12 .…”

Distribution-Based Calibration of a Stormwater Quality Model

“…Instead of replicating single-event characteristics or pollutographs, the approach aims to minimize the difference between observed and simulated TSS event load distribution. Since observed TSS event load distributions can be well approximated with theoretical distribution functions [22], the calibration uses a site-specific parameterized lognormal distribution as reference (cf. Section 2.3).…”

“…Leutnant et al [22] use TSS event load data from Leutnant et al [24] and describe site-specific empirical TSS event load distributions by means of theoretical distribution functions. The authors demonstrated that the two-parameter lognormal distribution approximates the empirical TSS event load distribution well and can therefore be used to probabilistically describe TSS event loads.…”

“…In their study, parameters of the lognormal distribution are optimized with respect to a likelihood function and the goodness-of-fit is evaluated by means of Kolmogorov-Smirnov and Anderson-Darling test statistics. Table 3 shows the general lognormal distribution formula and optimized parameter for µ (meanlog) and σ (sdlog) for sites FR and PL taken from Leutnant et al [22]. Table 3.…”

“…Table 3. Lognormal distribution function and optimized parameters to describe TSS event load distribution for site FR and PL from Leutnant et al [22].…”