Analysis of parameter uncertainty of a flow and quality stormwater model

Distribution-Based Calibration of a Stormwater Quality Model

Stormwater quality models are usually calibrated using observed pollutographs. As current models still rely on simplified model concepts for pollutant accumulation and wash-off, calibration results for continuous pollutant concentrations are highly uncertain. In this paper, we introduce an innovative calibration approach based on total suspended solids (TSS) event load distribution. The approach is applied on stormwater quality models for a flat roof and a parking lot for which reliable distributions are available. Exponential functions are employed for both TSS buildup and wash-off. Model parameters are calibrated by means of an evolutionary algorithm to minimize the distance between a parameterized lognormal distribution function and the cumulated distribution of simulated TSS event loads. Since TSS event load characteristics are probabilistically considered, the approach especially respects the stochasticity of TSS buildup and wash-off and, therefore, improves conventional stormwater quality calibration concepts. The results show that both experimental models were calibrated with high goodness-of-fit (Kolmogorov–Smirnov test statistic: 0.05). However, it is shown that events with high TSS event loads (>0.8 percentile) are generally underestimated. While this leads to a relative deviation of −28% of total TSS loads for the parking lot, the error is compensated for the flat roof (+5%). Calibrated model parameters generally tend to generate wash-off proportional to runoff, which is indicated by mass-volume curves. The approach itself is, in general, applicable and creates a new opportunity to calibrate stormwater quality models especially when calibration data is limited.

An inexact chance-constrained programming model for water quality management in Binhai New Area of Tianjin, China

In this study, an inexact-chance-constrained water quality management (ICC-WQM) model is developed for planning regional environmental management under uncertainty. This method is based on an integration of interval linear programming (ILP) and chance-constrained programming (CCP) techniques. ICC-WQM allows uncertainties presented as both probability distributions and interval values to be incorporated within a general optimization framework. Complexities in environmental management systems can be systematically reflected, thus applicability of the modeling process can be highly enhanced. The developed method is applied to planning chemical-industry development in Binhai New Area of Tianjin, China. Interval solutions associated with different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help decision makers identify desired policies under various system-reliability constraints of water environmental capacity of pollutant. Tradeoffs between system benefits and constraint-violation risks can also be tackled. They are helpful for supporting (a) decision of wastewater discharge and government investment, (b) formulation of local policies regarding water consumption, economic development and industry structure, and (c) analysis of interactions among economic benefits, system reliability and pollutant discharges.

Uncertainty in urban stormwater quality modelling: the influence of likelihood measure formulation in the GLUE methodology

In the last years, the attention on integrated analysis of sewer networks, wastewater treatment plants and receiving waters has been growing. However, the common lack of data in the urban water-quality field and the incomplete knowledge regarding the interpretation of the main phenomena taking part in integrated urban water systems draw attention to the necessity of evaluating the reliability of model results. Uncertainty analysis can provide useful hints and information regarding the best model approach to be used by assessing its degrees of significance and reliability. Few studies deal with uncertainty assessment in the integrated urban-drainage field. In order to fill this gap, there has been a general trend towards transferring the knowledge and the methodologies from other fields. In this respect, the Generalised Likelihood Uncertainty Evaluation (GLUE) methodology, which is widely applied in the field of hydrology, can be a possible candidate for providing a solution to the above problem. However, the methodology relies on several user-defined hypotheses in the selection of a specific formulation of the likelihood measure. This paper presents a survey aimed at evaluating the influence of the likelihood measure formulation in the assessment of uncertainty in integrated urban-drainage modelling. To accomplish this objective, a home-made integrated urban-drainage model was applied to the Savena case study (Bologna, IT). In particular, the integrated urban-drainage model uncertainty was evaluated employing different likelihood measures. The results demonstrate that the subjective selection of the likelihood measure greatly affects the GLUE uncertainty analysis.