Parameterizing correlations between hydrometeor species in mixed‐phase Arctic clouds

Mixed‐phase Arctic clouds, like other clouds, contain small‐scale variability in hydrometeor fields, such as cloud water or snow mixing ratio. This variability may be worth parameterizing in coarse‐resolution numerical models. In particular, for modeling multispecies processes such as accretion and aggregation, it would be useful to parameterize subgrid correlations among hydrometeor species. However, one difficulty is that there exist many hydrometeor species and many microphysical processes, leading to complexity and computational expense. Existing lower and upper bounds on linear correlation coefficients are too loose to serve directly as a method to predict subgrid correlations. Therefore, this paper proposes an alternative method that begins with the spherical parameterization framework of Pinheiro and Bates (1996), which expresses the correlation matrix in terms of its Cholesky factorization. The values of the elements of the Cholesky matrix are populated here using a “cSigma” parameterization that we introduce based on the aforementioned bounds on correlations. The method has three advantages: (1) the computational expense is tolerable; (2) the correlations are, by construction, guaranteed to be consistent with each other; and (3) the methodology is fairly general and hence may be applicable to other problems. The method is tested noninteractively using simulations of three Arctic mixed‐phase cloud cases from two field experiments: the Indirect and Semi‐Direct Aerosol Campaign and the Mixed‐Phase Arctic Cloud Experiment. Benchmark simulations are performed using a large‐eddy simulation (LES) model that includes a bin microphysical scheme. The correlations estimated by the new method satisfactorily approximate the correlations produced by the LES.