Spatio-temporal geostatistical modeling of Gneiting applied to surface albedo (Brazil)

A B S T R A C T
Several science areas have data coming characterized by variations in space and time that are measured using statistical procedures that take into account or not the existing interactions between the dimensions of space and time. Gneiting, in 2002, proposed a model that is based on the construction of non-separable stationary covariance functions, given the condition of being positive definite, which can be used to model the covariance matrix used in kriging. The southern mesoregion of Minas Gerais is very important to Brazilian agribusiness due to the planting of coffee cultivar and also because it has an extensive pasture area, allowing the creation of cattle, horses, and pigs and, for this reason, it is essential to study factors that impact on the climate of this region as the Earth's surface albedo, which is defined as the ability of a surface to reflect solar radiation. This article's objective is to apply the covariance model presented by Gneiting to the Geostatistical modeling of a set of real data on the albedo of the Earth's surface in the mesoregion in question using ordinary kriging to predict data of this nature. We choose to use the linear kriging predictor as it has the property of being best linear unbiased prediction (BLUP). We conclude that the exponential-cauchy family belonging to the class of covariance functions presented by Gneiting obtained a lower MSE in the adjustment of the covariance matrix of the linear kriging predictor and, therefore, can be used to predict the Earth's surface albedo.
Keywords: Albedo, space-time, covariance, Gneiting