| Abstract Scope |
This paper proposes a stochastic surrogate model for the precipitating quasi-geostrophic (PQG) equations, which reduces the computational cost and maintaining mathematical and physical fidelity. By utilizing a Markov jump stochastic process, the stochastic surrogate model, SPQG, efficiently simulates the phase-transition dynamics of water, providing a computationally favorable option over the conventional iterative-inversion methods required in PQG. To retain the model's mathematical precision and inherent physics, calibration is performed using potential vorticity (PV) as a predictor for the transition rates between saturated and unsaturated states in the Markov process. This calibration embeds the original PQG data correlations between clouds and high-PV regions into the model. Moreover, to improve the capability in capturing the underlying thermodynamics, the SPQG model uses a Gaussian kernel for data smoothing, as well as an adaptive method for better accuracy of the cloud fraction. |