Temperature prediction analysis considering an optimal distribution of stations: clusters or randomly

Global mean surface air temperature is the most used measure of the climate system. Nowadays, due to the climate change problem, the interest of predicting climatic values in areas without stations has increased a lot and has been developed new interpolation methods. If we associate temperature stations with their spatial coordinates, along with other variables, it is possible to identify them by means of a spatio-temporal stochastic process. Two are the objectives in this work. Firstly, to predict the mean temperature throughout Catalonia taking into account the total number of stations (180). Secondly, to analyse the goodness of prediction reducing the number of stations gradually. At first, we consider less randomly chosen stations (160, 100, 80) and then we select stations, which are in clusters. We specified spatial log-Gaussian process models. Models are estimated using Bayesian inference for Gaussian Markov Random Field (GMRF) through the Integrated Nested Laplace Approximation (INLA) algorithm. The results allow us to quantify the minimum number of stations which are needed to do the best prediction of the mean temperature in Catalonia as well as to know the best distribution of these stations. We believe the methods shown in this study may contribute to improve prediction studies and to reduce computational cost of these predictions.