Non-linear and nonparametric modelling of seasonal environmental data
It is of great importance in today’s society to examine the condition of the environment, which includes monitoring trends in major rivers. The initial impetus for this work was provided by the Scottish Environmental Protection Agency (SEPA) who were interested in modelling and testing trends in water quality on the River Clyde, in the light of some major improvements to sewage treatment works on the river. The models and tests used included both parametric and nonparametric procedures, culminating in the use of nonparametric smoothing techniques to describe the trends in water quality on the river.
This thesis introduces a range of nonlinear nonparametric modelling procedures which are used to model trends in water quality on the River Clyde. Inferential techniques are developed to provide model selection criteria. The models are then further developed by introducing extra covariates and accounting for the spatial correlation which exists along the river.
Chapter 1 gives the background of the SEPA problem and outlines the aims and objectives of the thesis. Chapter 2 uses parametric modelling techniques to explore trend changes in water quality on the River Clyde. These results are compared with modelling approaches which have been developed by SEPA. Chapter 3 reviews some of the most commonly used tests within the water quality setting and these are then applied to the River Clyde data.
As a result of the analysis in Chapter 2 and 3 it became apparent that the trends in water quality are best described in a smoothly varying manner. Chapter 4 introduces nonparametric regression techniques which can be used to model the trends. Chapter 5 develops nonlinear nonparametric modelling techniques which are then applied to the river data. The flexibility of this model class is highly desirable as it allows for the modelling of smoothly changing trends and the seasonality to be varied or fixed as required. Initial checks show the models fit the data well, but it is important to test the models to discover the best fitting model at particular locations.
Chapter 6 begins by testing the nonparametric trend against both the no-effect and linear trend models. An approximate F-test and quadratic form test are then developed to compare models to discover the best fitting model at a particular station along the river. A simulation study is then carried out in order to validate the tests under suitable conditions. These produce very promising results as the size of the tests is well controlled and the power is high.
Chapter 7 extends the techniques of Chapter 5 by including more covariates to the models. Models are then developed for different sections of the river and a single overall model is developed for the river. Creating a model for all the measurement stations introduces a high degree of spatial correlation and this can be accounted for by using generalised least squares techniques. The best overall model for the River Clyde is then developed using the testing procedures developed in Chapter 6.