Assessing the Resolution Adaptability of the Zhang-McFarlane Cumulus Parameterization With Spatial and Temporal Averaging

With increasing computational capabilities, cumulus parameterizations that are adaptable to the smaller grid spacing and temporal interval for high-resolution climate model simulations are needed. In this study, we propose a method to improve the resolution adaptability of the Zhang-McFarlane (ZM) scheme, by implementing spatial and temporal averaging to the CAPE tendency. This method allows for a more consistent application of the quasi-equilibrium (QE) hypothesis at high spatial and temporal resolutions. The resolution adaptability of the original ZM scheme, the scheme with spatial averaging, and the scheme with spatiotemporal averaging at 4-32 km grid spacings are assessed using the Weather Research and Forecasting (WRF) model by comparing to cloud resolving model (CRM) simulation results coarse-grained to these same grid spacings. We show the original ZM scheme has poor resolution adaptability, with spatiotemporally averaged subgrid convective transport and convective precipitation increasing significantly as the resolution increases. The spatial averaging method improves the resolution adaptability of the ZM scheme and better conserves total transport and total precipitation. Temporal averaging further improves the resolution adaptability of the scheme. With better constrained (although smoothed) convective transport and precipitation, both the spatial distribution and time series of total precipitation at 4 and 8 km grid spacings are improved with the averaging methods. The results could help develop resolution adaptability for other cumulus parameterizations that are based on the QE assumption.