State-transition matrices as an analysis and forecasting tool applied to water quality in reservoirs

Water reservoirs have the function to control the temporal variability of the water availability, thus bringing greater security over these resources. The water quality of these systems must be adequate for their multiple uses, and one of the main tools to understand it, is mathematical modelling. Given the importance of the water quality, the goal of this paper is to develop an analysis that takes into account the randomness of the variables that affect the thermal and/or biochemical regimes of a reservoir. For this, it is proposed a combination of deterministic and statistical analysis, where the probabilities of occurrence of a given event are considered. Difficult factors, such as the lack of data on the water quality and other variables, were considered, which increases the replicability of the method. The research method is divided into three groups: Modelling, Scenarios and Compilation of these scenarios. Through modelling, a base layout is created, enabling the use of scenarios, which are statistically analysed, and compiled into a state-transition matrix. With this, a more robust tool to understand the dynamics of water quality in a system is obtained, since it is not heavily dependent on field measurements and is easily adaptable and replicable.