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We investigate a discretization of a class of stochastic heat equations onthe unit sphere with multiplicative noises. A spectral method is used for thespatial discretization and the truncation of the Wiener process, while animplicit Euler scheme with non-uniform steps is used for the temporaldiscretization. Some numerical experiments inspired by Earth's surfacetemperature data analysis GISTEMP provided by NASA are given.

A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere