Spatial analysis is usually based on the assumption of stationarity. The violation of the stationarity assumption is very likely in monitoring networks which are spread over large regions. In the present study a meteorological monitoring network of Pakistan is consid- ered that is clearly non-stationary. Pakistan has much diversity in spatial and seasonal variation of the climate. The most important variables that have an impact on the precip- itation are temperature, humidity, wind speed and elevation.
The economy of Pakistan is highly supported from the agricultural sector; the occur- rence of monsoon (June-September) rainfall being of vital importance for the said sector.
The accurate prediction of precipitation in Pakistan provides useful information for decision making. Moreover, the selection of optimal monitoring design can increase the prediction accuracy.
This dissertation focuses on three major objectives: identification of homogeneous cli- mate regions in Pakistan, accurate space-time interpolation of precipitation during mon- soon season and selection of optimal monitoring network sampling design for interpolation of precipitation with and without external drift variables.
We identify homogeneous climate regions, whereby monthly average temperature, pre- cipitation, wind speed, humidity and elevation are supposed to aect the climate variation.
The geographic coordinates are transformed by using the Lambert projection method and are combined with the mentioned meteorological data. The various clustering methods are used to observe homogeneous regions in Pakistan, it is concluded that partition around medoid clustering method is appropriate for the selection of homogeneous climate regions in Pakistan if the Lambert projection transformation is applied to geographical coordi- nates.
As the precipitation data is always positively skewed, assuming Gaussianity for precipita- tion provides illogical results. Therefore, we make Box-cox transformation of precipitation data and then apply the Hierarchical Bayesian space-time interpolation method to both the transformed and non-transformed data. The comparison for transformed and non- transformed precipitation interpolation suggests that hierarchical Bayesian interpolation by using transformed precipitation produces more accurate results as compared to non- transformed precipitation.
Moreover, the comparison between the space-time kriging, which is special case of Bayesian maximum entropy method, is made with hierarchical Bayesian interpolation us- ing transformed precipitation data, it is concluded that transformed hierarchical Bayesian interpolation gives better accuracy as compared to space-time kriging.
As we know that every natural process is connected with other natural processes, similarly the amount of precipitation is also dependent on the temperature, wind speed, humidity, elevation, latitude and longitude. To account for the eects of these natural processes on the amount of rainfall we include monthly data of temperature, wind speed and humidity as environmental covariates and elevation, latitude and longitude as spatial covariates. The generalized additive model is used to account for the eect of covariates and the output of this model is divided into two parts: trend component and residual component. The trend component is assumed to be deterministic and is modeled by using a spatial artificial neurel network (SANN). The residual component is assumed to be a random field and is modeled in a hierarchical Bayesian interpolation framework by using purely spatial non-stationary covariance model and spatio-temporal covariance model respectively, estimated by practile swarm optimization criteria. For interpolating the amount of precipitation at ungauged lo- cations the interpolated residual of ungauged locations and the predicted trend component for ungauged locations are added for respective ungauged sites, and are back-transformed to original scale. The comparison between two covariance models suggests that the spatio- temporal covariance model provides a smaller mean square error as compared to the purely spatial covariance model.
For the selection of an optimal spatial design the robust covariance matrix estima- tion criterion is used by including external drift (covariates) and without covariates. It is concluded that the design with external drift minimizes the mean square error of prediction.