Abstract:Rainfall-runoff models can be classified into three types: physically based models, conceptual models, and empirical models. In this latter class of models, the catchment is considered as a black box, without any reference to the internal processes that control the transformation of rainfall to runoff. In recent years, some models derived from studies on artificial intelligence have found increasing use. Among these, particular attention should be paid to Support Vector Machines (SVMs). This paper shows a comparative study of rainfall-runoff modeling between a SVM-based approach and the EPA's Storm Water Management Model (SWMM). The SVM is applied in the variant called Support Vector regression (SVR). Two different experimental basins located in the north of Italy have been considered as case studies. Two criteria have been chosen to assess the consistency between the recorded and predicted flow rates: the root-mean square error (RMSE) and the coefficient of determination. The two models showed comparable performance. In particular, both models can properly model the hydrograph shape, the time to peak and the total runoff. The SVR algorithm tends to underestimate the peak discharge, while SWMM tends to overestimate it. SVR shows great potential for applications in the field of urban hydrology, but currently it also has significant limitations regarding the model calibration.

Stormwater runoff is often contaminated by human activities. Stormwater discharge into water bodies significantly contributes to environmental pollution. The choice of suitable treatment technologies is dependent on the pollutant concentrations. Wastewater quality indicators such as biochemical oxygen demand (BOD 5 ), chemical oxygen demand (COD), total suspended solids (TSS), and total dissolved solids (TDS) give a measure of the main pollutants. The aim of this study is to provide an indirect methodology for the estimation of the main wastewater quality indicators, based on some characteristics of the drainage basin. The catchment is seen as a black box: the physical processes of accumulation, washing, and transport of pollutants are not mathematically described.Two models deriving from studies on artificial intelligence have been used in this research: Support Vector Regression (SVR) and Regression Trees (RT). Both the models showed robustness, reliability, and high generalization capability. However, with reference to coefficient of determination R 2 and root-mean square error, Support Vector Regression showed a better performance than Regression Tree in predicting TSS, TDS, and COD. As regards BOD 5 , the two models showed a comparable performance. Therefore, the considered machine learning algorithms may be useful for providing an estimation of the values to be considered for the sizing of the treatment units in absence of direct measures.

Residential water consumption has been analysed by monitoring a water distribution system in a small town of about 1200 inhabitants, Piedimonte San Germano, in southern Italy. The design of a water distribution system is usually undertaken with reference to the maximum water required by customers-one of the most onerous operating conditions to which an hydraulic network is exposed. The aim of the present work has been to contribute to the characterisation of the peak water demand through statistical inferences on a large data sample collected from the system under consideration. Specifically, the data have been analysed for the effect of resampling the raw data with respect to time interval on the estimate of peak demand factor. Formulae are suggested to estimate the maximum flow demand for small towns, in relation to the number of users. In addition, statistical inferences have shown that the stochastic, maximum flow demand is described by the log-normal and Gumbel models. With reference to small residential areas, the parameters of such statistical distributions have been estimated. These have shown that the coefficient of variation (CV) of the peak water demand is a function of the number of users. Although these results are only directly applicable to the specific context from which they have been obtained, the comparison with the sparse data available in the technical literature leads to the belief that the proposed relationships could be extended to other small residential areas.

Peak water demand is one of the most stringent operative conditions for a Water Distribution System (WDS), not only for the intensity of the event itself, but also for its recurring nature. The estimation of the maximum water demand is a crucial aspect in both the design and management processes. Studies in the past have tackled this issue with deterministic approaches, even if peak phenomena are distinctly random. In this work, probabilistic models have been developed to study and forecast the daily maximum residential water demand. Some probability distributions have been tested by means of statistical inferences on different data samples related to three monitored WDS. The parameter estimations of the proposed equations have been related to the number of supplied users. Furthermore, this work investigates time scaling effects on the effectiveness of the proposed distributions and relations. Corrective factors that take into account the effect of time averaging step on the above-mentioned parameters have been proposed.

Residential water demand is a random variable which influences greatly the performance of municipal water distribution systems (WDSs). The water request at network nodes reflects the behavior of the residential users, and a proper characterization of their water use habits is vital for the hydraulic system modeling. This study presents a stochastic approach for the characterization of the daily residential water use. The proposed methodology considers a unique probabilistic distribution - mixed distribution - for any time during the day, and thus for any entity of the water demanded by the users. This distribution is obtained by the merging of two cumulative distribution functions taking into account the spike of the cumulative frequencies for the null requests. The methodology has been tested on three real water distribution networks, where the water use habits are different. Experimental relations are given to estimate the parameters of the proposed stochastic model in relation to the users number and to the average daily trend. Numerical examples for a practical application have shown the effectiveness of the proposed approach in order to generate the time series for the residential water demand

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