An Importance Sampling Method for Lagrangian Stochastic Modeling of Atmospheric Turbulence
摘要
Accurately representing atmospheric turbulence requires capturing its highly non-Gaussian probability density functions (PDFs), which are poorly represented by traditional turbulence closure models. The recently proposed Lagrangian Stochastic Subgrid Turbulence Model (LSSTM) directly simulates turbulence PDFs using particle-based stochastic differential equations (SDEs), but its Monte Carlo formulation is subject to high sampling variance and computational cost. In this study, we introduce an importance sampling (IS) framework for LSSTM that reduces variance by modifying the drift of the governing SDEs to tilt their invariant distribution, combined with adaptive resampling to prevent weight degeneracy. A sampling weight proportional to vertical velocity fluctuations is proposed to improve the estimation of turbulent fluxes while preserving stability in non-turbulent regions. Validation with one-dimensional diffusion processes demonstrates variance reductions of 30–80% across statistical moments and tail probabilities. Applied to dry convective boundary layer simulations, IS improves the accuracy of turbulence statistics, reduces systematic biases in mean profiles, and achieves up to 50% variance reduction in vertical fluxes and up to 60% in rare-event probabilities. These results demonstrate that IS substantially enhances the efficiency and robustness of LSSTM, providing a practical pathway toward affordable PDF-based turbulence modeling.