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The Cotter-Holm Slice Model (CHSM) was introduced to study the behavior ofwhether and specifically the formulation of atmospheric fronts, whoseprediction is fundamental in meteorology. Considered herein is the influence ofstochastic forcing on the Incompressible Slice Model (ISM) in a smooth 2Dbounded domain, which can be derived by adapting the Lagrangian function inHamilton's principle for CHSM to the Euler-Boussinesq Eady incompressible case.First, we establish the existence and uniqueness of local pathwise solution(probability strong solution) to the ISM perturbed by nonlinear multiplicativestochastic forcing in Banach spaces $W^{k,p}(D)$ with $k>1+1/p$ and $p\geq 2$.The solution is obtained by introducing suitable cut-off operators applied tothe $W^{1,\infty}$-norm of the velocity and temperature fields, using thestochastic compactness method and the Yamada-Watanabe type argument based onthe Gy\"{o}ngy-Krylov characterization of convergence in probability. Then,when the ISM is perturbed by linear multiplicative stochastic forcing and thepotential temperature does not vary linearly on the $y$-direction, we provethat the associated Cauchy problem admits a unique global-in-time pathwisesolution with high probability, provided that the initial data is sufficientlysmall or the diffusion parameter is large enough. The results partially answerthe problems left open in Alonso-Or{\'a}n et al. (Physica D 392:99--118, 2019,pp. 117).

The influence of stochastic forcing on strong solutions to the Incompressible Slice Model in 2D bounded domain