Relationship between radar reflectivity and the time scale of warm rain formation in a global cloud-resolving model

The connections between radar reflectivity and the time scale of warm rain formation are examined within a global cloud-resolving model. The parameterizations formulae of auto-conversion and accretion processes in the model reveal specific relationships between the time scale for auto-conversion and radar reflectivity of cloud water as well as between the time scale for accretion and radar reflectivity of rain water. The overall time scale for warm rain formation, determined by combined contributions from these processes, is found to relate with total radar reflectivity in the manner that varies with cloud-rain composition between auto-conversion and accretion limits. The global statistics from the model output reveals that the time scale is closely related with the total radar reflectivity, thus suggesting that the radar reflectivity is a gross measure of the warm rain time scale. The relationship developed is applied to both model-simulated and CloudSat-observed radar reflectivities to compare the time scales of warm rain formation between observation and the model. Comparison of the time scale so derived reveals significant differences between the model and CloudSat observations. These differences suggest that the simulated cloud-rain composition in the model is biased toward larger rain water contents and smaller content of cloud water compared to reality due to an accelerated cloud-to-rain water conversion in the model.