Oxygen has been monitored in a small urban creek for a two months period. The purpose of the data collection is to use statistical modelling to obtain a better understanding of the phenomena governing the oxygen concentration. The long term goal is to influence the process of urban runoff to achieve oxygen concentration suitable for fish. Oxygen fluctuates significantly on a diurnal basis. Furthermore the purpose is to establish a model by which we are able to use rain data to estimate extreme values for comparison with standards for minimum oxygen concentration. The experience is that the fluctuations cannot be explained adequately on a deterministic basis alone. Significant stochastic variation has to be accounted for.
Data from a small stream is used to identify a dynamic model of the oxygen level as a function of solar radiation, water depth, and rain. The model is formulated in continuous time as two coupled stochastic differential equations. The continuous time formulation makes it possible directly to interpret the parameters of the model. Hence the model is useful for monitoring the actual state of the stream.
In this paper a grey box modelling approach, which is a statistical method taking the known physical relations into account, is used. This approach is closely related to the continuous time formulation. The parameters of the model are estimated using discrete time data and a maximum likelihood method. In evaluating the likelihood function a Kalman filter is used.
The dynamic model makes it possible to assess the transient impact of the urban runoff due to rain events, as well as the effect due to solar radiation. The ultimate outcome of the analysis is to determine the required size and location of storage basins to be constructed in the sewer system, in order to decrease combined sewer outflows and extreme oxygen depletion during rain.