A new approach to spatiotemporal estimation of the river state

Abstract

The paper proposes a spatiotemporal method of analysis of the river state on the basis of the measurement of pollution level indicators in the context of its application in modern control systems. For the examined objects and measurements of their characteristic parameters described by differential equations, the issue of river state estimation was formulated on the basis of discrete measurements of water pollution carried out in control stations located along the river. Using such determined estimates of all control signals describing the level of pollution in the rivers, higher accuracy of water quality control was obtained in comparison with a case based solely on measurements of some easily accessible parameters. While designing the presented solution, a mathematical model of a physical object was used which was a section of a river understood as a certain mathematical abstraction binding together variables characterizing the state of the object, interaction of external signals and its reaction. It has been assumed that the dissolved oxygen (DO) concentration is the starting point at the stage of water quality status modeling as many other indicators of pollution level are associated with it. Such an indicator may be biochemical oxygen demand (BOD) which also reflects the DO consumption in rivers and represents the degradation of water quality. Having a mathematical model of pollution distribution in the river and real measurements, numerical simulations created the possibility of influencing the changes in pollution indicators (BOD and DO) in specific conditions and in a specific time. The paper verifies the compliance of the proposed mathematical model of the object with the actual representation of the local river Wislok in the Subcarpathian province in Poland.