This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matérn model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such covariance structure. We find parameter conditions ensuring positive definiteness. We discuss other possible models and illustrate our findings through a simulation study, where we explore the performance of maximum likelihood estimation method for the parameters of the new covariance function. A data illustration then follows, through a bivariate data set of temperatures and precipitations, observed over a large portion of the Earth, provided by the National Oceanic and Atmospheric Administration Earth System Research Laboratory.

本文针对球面上的双变量随机场提出了一类新的协方差函数，其性质与在欧几里得空间中提出的双变量Matérn模型相同。新的类取决于球面上的测地距离；它允许对具有这种协方差结构的任何二元高斯随机场的分量进行索引可微性（在均方意义上）和分形维数。我们找到确保正定性的参数条件。我们讨论了其他可能的模型，并通过模拟研究说明了我们的发现，在该研究中，我们探索了针对新协方差函数参数的最大似然估计方法的性能。然后，通过对地球大部分地区观察到的温度和降水的双变量数据集进行数据说明，