Open WL Archief (OWA)

In the first part the data validation problem is addressed. Like other environmental data, water quality data have a complex nature. They contain a considerable amount of noise due to their natural variability and the measurement error. They may contain missing values, are of ten non-normally distributed and are commonly gathered at irregular time instants. Moreover, they possess cyc1ic variations and contain nonlinear trends. With this respect, additive models are explored to model water quality data. These models are then used to design an automatic validation procedure for new observations that are acquired with a river monitoring network. Based on historical data, additive models are fitted to predict new observations and to construct prediction intervals (PI's). A new observation is dec1ared valid if it is located within the interval. Several methods were developed to derive such PI's and the PI that was based on bootstrapping studentised prediction errors was shown to be most accurate and most robust to deviations from normality. The coverage of these prediction intervals and their power to detect anomalous data are successfully established in a simulation study. The method is illustrated on two case studies in which the method detected abnormal nitrate concentrations in the water body provoked by a dry summer which was followed by an extremely wet winter periad. Currently, the Flemish environmental agency is also using our method for the validation of new observations from their physico-chemical monitoring network.

In the second part a spatio-temporal model is developed for river monitoring network data. The aim was to enable valid statistical inference based on the data that is observed at the sampling locations. Therefore the observations of the monitoring network at a certain time instant can be considered as the realisation of a finite-dimensional multivariate random variable with each dimension corresponding to each of the p sampling locations. This enables us to write the model as a p-dimensional state-space model. The state variable is defined by a Directed Acyclic Graph (DAG) that is derived from the river network topology. In reality the dependence structure based on the DAG may be obscured by environmental factors such as rainfall and climatological conditions in general. This is taken into account by embedding the state variable into an observation model. Initially, the observation model was extended with a linear model for the mean. The specification of the mean model allows the assessment of different research questions. An efficient expectation-conditional-maximisation (ECM) algorithm is proposed for parameter estimation, using the Kalman filter and smoother in both E- and CM-steps. However, many environmental processes are characterised by a nonlinear trend. To allow the estimation of such a nonlinear trend, we replaced the parametric mean model by a semiparametric model that used a smoother for the estimation of the trend component. This procedure also allows to test for trends on a smaller time scale. To detect if the local trend is significant, tests on the first derivative of the nonlinear trend are performed at each time step. This results, however, in a large number of simultaneous tests. Multiplicity is thus another problem which had to be addressed. Many environmental processes are also non-Gaussian. To handle such data, a generalisation of our spatio-ternporal model is needed. A first attempt is presented that can handle binary data. Environmental compliance is often based on threshold levels, providing a binary response to the decision maker. We made use of generalised linear mixed models (GLMM) to model such a binary response. Again, the spatio-temporal dependenee structure is introduced by using a latent state variable. In a GLMM the parameters of the mean model have a conditional interpretation. In an environmental context, however, we want to infer on the marginal mean. Therefore the marginalised version of the GLMM of Heagerty and Zeger (2000) is used. They introduced a mapping function between the conditional and marginal model components to identify a conditional model structure that allows immediate estimation of the marginal mean parameters.