Interpolation and optimal monitoring in space and time

<font size="2">This thesis shows how statistics can be used for both analysing data and for determining the (optimal) design for collecting data in environmental research. An important question is often where to place monitoring stations to meet the objective of measuring as good as possible. In this thesis it is shown how existing monitoring networks can be adjusted on the basis of quantitative criteria. These criteria are based on aspects of spatial(-temporal) interpolation.A case study of climate variables in Jalisco State of Mexico is used to investigate the use of interpolation techniques. The climate variables monthly maximum temperature and monthly mean precipitation are predicted on a regular grid of points on the basis of measurements at climate stations. Four forms of kriging and three forms of thin plate splines are discussed. From these techniques, trivariate regression-kriging and trivariate thin plate splines performed bestThe optimal adjustment of existing monitoring networks is investigated for three case studies with different criteria. In the first place, a monitoring network adjustment is investigated for estimation of the semivariance function, whereby the criterium is based on the theory of optimal design of experiments. Secondly, we develop and apply a methodology to reduce an existing monitoring network to find an optimal configuration of a smaller network. In this case a criterion based on locally weighted regression with two different weight functions is used. The methodology is applied to the Dutch national SO ₂ network and offers the possibility to include different politically relevant options in the model by weight criteria. As a third case study, a monitoring network for groundwater level is considered. It focusses on a possible reduction of the number of measurementsat this monitoring network without losing much information about the groundwater level at the different piezometers. Investigation of a reduction of the number of measurements is based on a geostatistical spatial-temporal model. The results show that the monitoring effort of the network can be reduced.Finding optimal designs involves several optimization problems. In this thesis several methods are developed and applied to solve these problems. For small problems full enumeration of all possible configurations is possible with a branch-and-bound algorithm. In this way, it is ensured that the global optimum is found. If full enumeration of all possible monitoring networks is impossible, a search algorithm is applied to find a (sub)-optimal solution