Title: 
Dynamic modelling of receiving waters, affected by rain.

Abstract: 

This talk will present an overview of some of my modelling efforts 
for receiving waters, influenced by the transient impact of rain. 

First the background for launching these investigations is given, 
followed by an introduction to the oxygen dynamics, that have been focused 
on, namely photosynthesis and the interaction with organic matter. 
Then an example of pre-filtering the input data to obtain more precise 
estimates is given, along with a natural progression of estimating this 
filter along with the parameters in a state space model. The first method 
was primarily focused on finding the best model for photosynthesis. 
The advantage of estimating the filter directly is that the model can 
then be used for on-line monitoring purposes. Thus immediate assessment 
of receiving waters, as well as of data quality, is possible. 

After this, the linear resrvoir model is introduced and applied, first 
to a hydraulic model, then to a model containing the dynamics of the 
hydraulics, oxygen and organic matter. 
It is well known from models of reactor hydraulics, usually pertaining 
to waste water treatment plants, that modelling the reactor as a series 
of totally mixed reactors, will mathematically merge towards a description 
for plug flow when the number of reactors in the series goes towards 
infinity. In hydraulogy this is called a linear reservoir model. 
In the example presented here, it is shown that two reservoirs are 
sufficient to describe the dynamics. Particularly, the hydraulic model 
show good results.