Determination of a Pollutants Source in an Estuary through the Inverse Problems Technique

A great challenge today is conciliation of water resources utilization with the expansion of cities and human activities. Considering that the water quality of a given water body is necessarily evaluated through the analysis of some biological, physical and chemical parameters, mathematical and computational models able to describe the behavior of such parameters can be an useful tool, given their ability to generate scenarios and, as a consequence, the possibility to support decisions regarding water resources management. In this work, Inverse Problems techniques are applied to estimate the source parameters (intensity and position) of a hypothetical conservative pollutant released in estuarine waters. The studied case here is the estuary of Macaé River, located in the brazilian southeast coast. The pollutant transport was modeled by the advection-diffusion equation, here solved by the Finite Element Method and the Finite Difference Method. The hydrodynamics parameters were assumed known and the mesh applied to the domain was defined according to the discretization method used to solve the direct problem. For estimation of source position here were used the Luus-Jaakola (LJ), the Particle Collision Algorithm (PCA) and the Ant Colony Optimization (ACO) Methods, and to estimate the source intensity was used the Golden Section Method. Besides, a sensibility analysis of hypothetical sampling sites position regarding the source parameters (intensity and position) was performed. In this study, synthetic pollutant concentrations with and without noise were used. For the noiseless data, all methods have successfully achieved the objective function in more than 90% of executions. Considering the number of estimates from different points on the location and also the computational cost, the PCA Method showed the highest performance. On the other hand, for the data with ± 5% of noise, all methods had efficiency greater than 85%. Considering the number of estimates from different points on the location, and also the computational cost, again the PCA method showed the best performance. The results of this study demonstrated the potentiality of the Inverse Problems technique to estimate with satisfactory accuracy the location and intensity of a given pollutant source released in estuarine environments, something that can also contribute to possible environmental liabilities identification.