An Empirical Cumulus Parameterization Scheme for a Global Spectral Model

Abstract

Realistic vertical heating and drying profiles in a cumulus scheme is important for obtaining accurate weather forecasts. A new empirical cumulus parameterization scheme, based on a procedure to improve the vertical distribution of heating and moistening over the tropics is developed. The empirical cumulus parameterization scheme (ECPS) utilizes observed profiles of Tropical Rainfall Measuring Mission (TRMM) based apparent heat source (Q₁) and the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis based apparent moisture sink (Q₂). A dimension reduction technique through rotated principal component analysis (RPCA) is performed on the vertical profiles of heating and drying over the convective regions of the tropics, to obtain the dominant modes of variability. Analysis suggests that most of the variance associated with the observed profiles can be explained by retaining the first three modes. The ECPS then applies a statistical approach, in which Q₁ and Q₂ are expressed as a linear combination of the first three dominant principal components which distinctly explain variance in the troposphere as a function of the prevalent large-scale dynamics. The principal component (PC) score, which quantifies the contribution of each PC to the corresponding loading profile, is estimated through a multiple screening regression method which yields the PC score as a function of the large-scale variables.
The profiles of Q₁ and Q₂ thus obtained are found to match well with the observed profiles. The impact of the ECPS is investigated in a series of short range (1-3 day) prediction experiments, using the Florida State University global spectral model (FSUGSM, T126L14). Comparisons between short range ECPS forecasts and those with the modified Kuo scheme, show a very marked improvement in the skill in ECPS forecasts. This improvement in the forecast skill with ECPS emphasizes the importance of in- corporating realistic vertical distributions of heating and drying in the model cumulus scheme. This also suggests that in the absence of explicit models for convection, the proposed statistical scheme improves the modeling of the vertical distribution of heating and moistening in areas of deep convection.