Spatial Non-Stationary Models for Precipitation with Elevation in the Dependency Structure - A Case Study of Annual Precipitation in Hordaland
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In this work, we construct spatial statistical models for interpolation of precipitation in areas characterised by orographic precipitation. The models are built as latent Gaussian models. We use the stochastic partial differential equation (SPDE) approach to spatial modelling to reduce the computational cost. The methodology integrated nested Laplace approximation (INLA) is used for inference and interpolations. The aim of the study is manifold. Firstly, the study has applied purposes. We aim to construct a good model for interpolation of precipitation in areas characterised by orographic precipitation, and for prediction of the total precipitation in catchment areas, i.e., the areal precipitation. Such a model should be able to quantify the uncertainty of the interpolations, and have a good predictive performance. It is also desired to get a better understanding of the physical precipitation process in this kind of terrain, e.g., how precipitation varies with elevation. Secondly, the study has a statistical purpose. We aim to obtain a better knowledge about non-stationary and stationary modelling of spatial processes. In particular, we wish to examine how large degree of non-stationarity there has to be in a process, before it is detectable and relevant for the predictive performance. We compare a stationary model and a non-stationary model with dependency structure varying with elevation. Simple toy examples are used to explore the consequences of having dependency structure that varies with elevation. A case study is carried out, using annual observations of precipitation in Hordaland. It is also performed a simulation study, in order to further explore the effect of non-stationarity, and its impact on predictions of precipitation. The results showed that a non-stationary model has a slightly better predictive performance when doing interpolations of precipitation in areas characterised by orographic precipitation. However, there are still some large errors when using the non-stationary model to predict areal precipitation in catchments located at high elevations. The results also showed that the predictive performance of both models became noticeably better when an observation was included inside the catchment areas. Further, the results showed that when the degree of non-stationarity in the process is small, a stationary model has good predictive performance.