An Accurate Parameterization of the Radiative Properties of Water Clouds Suitable for Use in Climate Models

A new parameterization of the radiative properties of water clouds is presented. Cloud optical properties for both solar and terrestrial spectra and for cloud equivalent radii in the range 2.5–60 µm are calculated from Mie theory. It is found that cloud optical properties depend mainly on equivalent radius throughout the solar and terrestrial spectrum and are insensitive to the details of the droplet size distribution, such as shape, skewness, width, and modality (single or bimodal). This suggests that in cloud models, aimed at predicting the evolution of cloud microphysics with climate change, it is sufficient to determine the third and the second moments of the size distribution (the ratio of which determines the equivalent radius). It also implies that measurements of the cloud liquid water content and the extinction coefficient are sufficient to determine cloud optical properties experimentally (i.e., measuring the complete droplet size distribution is not required). Based on the detailed calculations, the optical properties are parameterized as a function of cloud liquid water path and equivalent cloud droplet radius by using a nonlinear least-square fitting. The parameterization is performed separately for the range of radii 2.5–12 µm, 12–30 µm, and 30–60 µm. Cloud heating and cooling rates are computed from this parameterization by using a comprehensive radiation model. Comparison with similar results obtained from exact Mic scattering calculations shows that this parameterization yields very accurate musts and that it is several thousand times faster. This parameterization separates the dependence of cloud optical properties on droplet size and liquid water content, and is suitable for inclusion into climate models.