Parametrizing cloud geometry and its application in a subgrid cloud-edge erosion scheme

To represent the effects of unresolved cloud processes in numerical weather prediction and climate models, parametrizations of the subgrid properties of clouds are required. In this paper, we describe a method for specifying the "cloud-edge length" within a model grid-box, which is an important parameter for approximating the subgrid mixing of air at cloud boundaries. We begin by proposing three conceptual models that predict the cloud-edge length using the grid-box cloud fraction and a length-scale to be derived empirically. The conceptual models are then evaluated using a wide range of observations and cloud-resolving models. Based on the finding that the "effective cloud spacing" approach fits both these data best, we parametrize the effective cloud spacing as a function of pressure and model resolution. An application of this parametrization to the cloud erosion scheme in the ECMWF forecast model is then demonstrated. The effective cloud spacing approach is compared to the "effective cloud scale" approach and is shown to increase cloud fraction in stratocumulus regions, while decreasing cloud fraction in cumulus regions. These cloud changes have the overall effect of decreasing the error of the modelled top-of-atmosphere net short-wave irradiance when compared to CERES observations by around 3%. Additionally, the cloud-edge length is an important parameter for approximating subgrid radiative transfer and it is hoped that this parametrization will be useful to quantify the effect of representing 3D cloud radiative transfer in global models.