Time series analysis by state space models applied to a water quality data in Portugal

Abstract

Time series analysis by state space models provide a very flexible tool for analysing dynamic phenomena and evolving systems, and have significantly contributed to extending the classical domains of application of statistical time series analysis. In this study, in the context of a surface water quality monitoring problem in a river basin, it is proposed an approach for the structural time series analysis based on the state space models associated to the Kalman filter. The main goals are to analyse and evaluate the temporal evolution of the environmental time series, and to identify trends or possible changes in the water quality on a dynamic monitoring procedure. The data concerns the River Ave's hydrological basin located in the Northwest of Portugal, where monitoring has become a priority in water quality planning and management because its water has been in a state of obvious environmental degradation for many years. As a result, the watershed is now monitored by seven monitoring sites distributed along the River Ave and its main streams. For the modeling process we consider the monthly dissolved oxygen concentration dataset between January 1999 and January 2014. The framework of the state space models shows versatility to incorporate unobserved components, such as trends, cycles and seasonals, that have a natural interpretation and represent the salient features of the environmental time series under investigation. From the environmental point of view, the proposed approach allows to obtain pertinent findings concerning water surface quality interpretation and change point, thus highlighting the potential value of this type of analysis, and it is also relevant to identify unanticipated changes that are important in the management process and for the assessment of water quality.A. Manuela Gonc¸alves was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the FCT-Fundac¸ao para a Ciência e aTecnologia, through the Project PEstOE/MAT/UI0013/2014. Marco Costa was supported by Portuguese funds through the CIDMA-Centre for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ”FCT-Fundac¸ao para a Ciência e a Tecnologia”, within project UID/MAT/04106/2013