Quadrature Methods for the Calculation of Subgrid Microphysics Moments

AbstractMany cloud microphysical processes occur on a much smaller scale than a typical numerical grid box can resolve. In such cases, a probability density function (PDF) can act as a proxy for subgrid variability in these microphysical processes. This method is known as the assumed PDF method. By placing a density on the microphysical fields, one can use samples from this density to estimate microphysics averages. In the assumed PDF method, the calculation of such microphysical averages has primarily been done using classical Monte Carlo methods and Latin hypercube sampling. Although these techniques are fairly easy to implement and ubiquitous in the literature, they suffer from slow convergence rates as a function of the number of samples. This paper proposes using deterministic quadrature methods instead of traditional random sampling approaches to compute the microphysics statistical moments for the assumed PDF method. For smooth functions, the quadrature-based methods can achieve much greater accura...