A comprehensive analysis of uncertainties in warm rain parameterizations in climate models based on in situ measurements

Abstract

Because of the coarse grid size of Earth system models (ESM), representing warm-rain processes in ESMs is a challenging task involving multiple sources of uncertainty. Previous studies evaluated warm-rain parameterizations mainly according to their performance in emulating collision-coalescence rates for local droplet populations over a short period of a few seconds. The representativeness of these local process rates comes into question when applied in ESMs for grid sizes on the order of 100 kilometers and time steps on the order of 20-30 minutes. We evaluate several widely used warm-rain parameterizations in ESM application scenarios. In the comparison of local and instantaneous autoconversion rates, the two parameterization schemes based on numerical fitting to stochastic collection equation (SCE) results perform best. However, because of Jessen's inequality, their performance deteriorates when grid-mean, instead of locally-resolved, cloud properties are used in their simulations. In contrast, the effect of Jessen's inequality partly cancels the overestimation problem of two semi-analytical schemes, leading to an improvement in the ESM-like comparison. In the assessment of uncertainty due to the large time step of ESMs, it is found that the rain-water tendency simulated by the SCE is roughly linear for time steps smaller than 10 minutes, but the nonlinearity effect becomes significant for larger time steps, leading to errors up to a factor of 4 for a time step of 20 minutes. After considering all uncertainties, the grid-mean and time-averaged rain-water tendency based on the parameterization schemes are mostly within a factor of 4 of the local benchmark results simulated by SCE.