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The viscosity parameters play a fundamental role in applications involvingstochastic primitive equations (SPE), such as accurate weather predictions,climate modeling, and ocean current simulations. In this paper, we developseveral novel estimators for the anisotropic viscosities in the SPE, using afinite number of Fourier modes of a single sample path observed within a finitetime interval. The focus is on analyzing the consistency and asymptoticnormality of these estimators. We consider a torus domain and treat strong,pathwise solutions in the presence of additive white noise (in time). Notably,the analysis for estimating horizontal and vertical viscosities differs due tothe unique structure of the SPE and the fact that both parameters of interestare adjacent to the highest-order derivative. To the best of our knowledge,this is the first work addressing the estimation of anisotropic viscosities,with the potential applicability of the developed methodology to other models.

Estimation of Anisotropic Viscosities for the Stochastic Primitive Equations