Bayesian approach for uncertainty quantification in water quality modelling: The influence of prior distribution

Mathematical models are of common use in urban drainage, and they are increasingly being applied to support decisions about design and alternative management strategies. In this context, uncertainty analysis is of undoubted necessity in urban drainage modelling. However, despite the crucial role played by uncertainty quantification, several methodological aspects need to be clarified and deserve further investigation, especially in water quality modelling. One of them is related to the “a priori” hypotheses involved in the uncertainty analysis. Such hypotheses are usually condensed in “a priori” distributions assessing the most likely values for model parameters. This paper explores Bayesian uncertainty estimation methods investigating the influence of the choice of these prior distributions. The research aims at gaining insights in the selection of the prior distribution and the effect the user-defined choice has on the reliability of the uncertainty analysis results. To accomplish this, an urban stormwater quality model developed in previous studies has been employed. The model has been applied to the Fossolo catchment (Italy), for which both quantity and quality data were available. The results show that a uniform distribution should be applied whenever no information is available for specific parameters describing the case study. The use of weak information (mostly coming from literature or other model applications) should be avoided because it can lead to wrong estimations of uncertainty in modelling results. Model parameter related hypotheses would be better dropped in these cases

On the Mitra-Wan Forest Management Problem in Continuous Time

The paper provides a continuous time version of the well known discrete time Mitra-Wan model of optimal forest management, where a forest is harvested to maximize the utility of timber flow over an infinite time horizon. Besides varying with time, the state variable (describing available trees) and the other parameters of the problem vary continuously also with respect to the age of the trees. The evolution of the system is given in terms of a partial differential equation and later rephrased as an ordinary differential equation in an infinite dimensional space. The paper provides a classification of the behavior of optimal and maximal programs when the utility function is linear, convex, or strictly convex and the discount rate is positive or null. Formulas are provided for modified golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann policies, and the optimality or maximality of such programs is discussed. In all different sets of data, it is shown that the optimal (or maximal) control is necessarily something more general than a function, i.e. a positive measure. In particular, in the case of strictly concave utility and null discount, when the Faustmann policy is not optimal, it is shown that optimal paths converges over time to the golden rule configuration, while in the case of strictly concave utility and positive discount the Faustmann policy is shown to be not optimal, contradicting the corresponding result in discrete time

Urban Storm-Water Quality Management: Centralized versus Source Control

The continuous growth of urban areas and the increasing public awareness of the environmental impacts of storm water have raised interest on the quality of the receiving water bodies. In the past two decades, many efforts have been directed at improving urban drainage systems by introducing mitigation measures to limit the negative environmental impacts of storm water. These mitigation measures are generally called best management practices (BMPs), sustainable urban drainage systems, or low impact developments, and they include practices such as infiltration and storage tanks that reduce the peak flow and retain some of the polluting materials. Choosing the best mitigation measure is still a controversial topic. To gain insight on the best technique, this study compares different distributed and centralized urban storm-water management techniques, including infiltration and storage facilities. The main objective of this study is to use modeling to assess the effects of the different urban drainage techniques. To this end, a homemade model that was developed in previous studies is applied. This model enables us to simulate both combined sewer systems and ancillary structures such as storm tanks or infiltration trenches to determine water quantity and quality characteristics. A long-term simulation is employed to account for the effects of sediments in BMPs, which generally reduce the hydraulic capacity. The results allow us to draw some conclusions on the peculiarities of BMP techniques, on the possibility of integrating different techniques for improving efficiency, and on BMP maintenance planning

Implementation of pressure reduction valves in a dynamic water distribution numerical model to control the inequality in water supply

The analysis of water distribution networks has to take into account the variability of users’ water demand and the variability of network boundary conditions. In complex systems, e.g. those characterized by the presence of local private tanks and intermittent distribution, this variability suggests the use of dynamic models that are able to evaluate the rapid variability of pressures and flows in the network. The dynamic behavior of the network also affects the performance of valves that are used for controlling the network. Pressure Reduction Valves (PRVs) are used for controlling pressure and reducing leakages. Highly variable demands can produce significant fluctuation of the PRV set point, causing related transient phenomena that propagate through the network and may result in water quality problems, unequal distribution of resources among users, and premature wear of the pipe infrastructure. A model was developed in previous studies and an additional module for pressure control was implemented able to analyze PRVs in a fully dynamic numerical framework. The model was demonstrated to be robust and reliable in the implementation of pressure management areas in the network. The model was applied to a district of the Palermo network (Italy). The district was monitored and pressure as well as flow data were available for model calibration

A BMA Analysis to Assess the Urbanization and Climate Change Impact on Urban Watershed Runoff

Abstract A reliable planning of urban drainage systems aimed at the mitigation of flooding, should take into account the possible change over time of impervious cover in the urban watershed and of the climate features. The present study proposes a methodology to analyze the changing in runoff response for a urban watershed accounting several plausible future states of new urbanization and climate. To this aim, several models simulating the evolution scenario of impervious watershed area and of climate change were adopted. However, it is known that an evolution scenario represents only one of all possible occurrence and it is not necessary the true future state, therefore it is needed to find the plausible forecast of the future state by taking into account and combining several possible evolution models. According to this aim, in the present study the Bayesian Model Averaging (BMA) approach was applied to several evolution models for climate variables. The Bayesian Model Averaging is a statistic multi-model method that computes a weighted average of the series of available competing models forecast overcoming the problem of arbitrary selecting of single best model and, consequently, the relative requirements of uncertainty analysis. The weighted average is the probability density function (pdf) of the quantity to be forecasted, while the weights correspond to the comparative performance of the models over training period of observation. After the application of BMA, for a given probability, the impervious area extension and the design rainfall event were identified and used as input data for a numerical model based on the SWMM software which was adopted to simulate the behavior of the urban drainage-system adopted as case study. Particularly, the proposed procedure was applied with reference to the Sicilian climate regions (southern Italy)

Energy, water and environmental balance of a complex water supply system

The present paper describes the analysis of water and energy balance in a complex urban water supply system. The analysis was carried out employing Life Cycle Analysis (LCA) methodologies. The LCA approach was integrated with the analysis of the system energy and water balance. For a real size water supply system, based on the results of the individual LCAs, the current baseline was constructed highlighting the water, energy and environmental (in terms of CO2eq emissions in the atmosphere) costs of supplied water. Then, three different mitigation measures have been evaluated: the first is based on energy production by installation of photovoltaic systems; the second is based on energy recovery by means of hydraulic turbines, exploiting the available pressure potential to produce energy; the third based on energy optimization of pumping stations by installing inverter systems, replacement of rotors with optimized blade profiles and installation of automation systems and self-control. Also the possibility of substituting some of the pipes of the water supply system was considered in the recovery scenario in order to reduce leakages and recovery the energy needed for leakages transport and treatment. The analysis of the results shown that energy recovery scenario is the most reliable solution even without any pipe substitution. Thanks to the recovery of energy and limiting the environmental impact of the system, the CO2eq production per cubic meter of supplied water was reduced from 0.41 to 0.07 kg CO2eq/m3 of supplied water

Three-dimensional numerical simulations on wind- and tide-induced currents: The case of Augusta Harbour (Italy)

The hydrodynamic circulation in the coastal area of the Augusta Bay (Italy), located in the eastern part of Sicily, is analysed. Due to the heavy contamination generated by the several chemical and petrochemical industries active in the zone, the harbour was declared a Contaminated Site of National Interest. To mitigate the risks connected with the industrial activities located near the harbour, it is important to analyse the hydrodynamic circulation in the coastal area. To perform such analysis, a parallel 3D numerical model is used to solve the Reynolds-averaged momentum and mass balance, employing the k-? turbulence model for the Reynolds stresses. The numerical model is parallelized using the programing technology - Message Passing Interface (MPI) and applying the domain decomposition procedure.The Augusta Bay circulation is mainly due to the relative contribution of the wind force acting over the free surface and the tidal motion through the mouths. Due to the geometric complexity of the domain and the presence of several piers along the coast, a curvilinear boundary-fitted computational grid was used, where cells corresponding to land areas or to wharfs were excluded from the computation. Comparisons between numerical results and field measurements were performed. Three different simulations were performed to selectively isolate the effect of each force, wind and tide, acting in the considered domain. The current in the basin was successfully estimated on the basis of the numerical results, demonstrating the specific role of wind and tidal oscillation in the hydrodynamic circulation inside the harbour

A Hybrid optimization method for real-time pump scheduling

Session S6-02, Special Session: Evolutionary Computing in Water Resources Planning and Management IILinear, non-linear and dynamic programming, heuristics and evolutionary computation are amongst the techniques which have been applied to obtain solutions to optimal pump-scheduling problems. Most of these either greatly simplify the complex water distribution system or require significant time to solve the problem. The scheduling of pumps is frequently undertaken in near-real time, in order to minimize cost and maximize energy savings. However, this requires a computationally efficient algorithm that can rapidly identify an acceptable solution. In this paper, a hybrid optimization model is presented, coupling Linear Programming and Genetic Algorithms. The resulting hybrid optimization model has demonstrated more rapid convergence with respect to the traditional metaheuristic algorithms, whilst maintaining a good level of reliability