An Analysis of Uncertainties in Warm Rain Parameterizations in Climate Models Based on in Situ Measurements

Warm rain generated by the collision-coalescence of droplets is an important process that modulates the total water budget and thereby radiative effects of marine boundary layer clouds. Because of the coarse grid size of Earth system models (ESM) and use of bulk parameterization schemes, 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 localized droplet populations over a short period of time, e.g, 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. The objective of this paper is to evaluate the performance and uncertainties of several widely used warm-rain parameterizations in ESM application scenarios. To achieve this goal, in situ measured droplet size distributions (DSDs) from the ACE-ENA field campaign are used to drive a numerical stochastic collection equation (SCE) solver, which is used as a benchmark for uncertainty evaluation. In the comparison of local and instantaneous autoconversion rates, the two parameterization schemes based on numerical fitting to SCE results (KK2000 and Chiu2021) 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 (SB2001 and Liu2007), 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. This paper reveals how three major sources of uncertainties in the warm rain parameterization interfere with each other to determine the error for grid-mean time-averaged warm rain simulations in ESM.