The Broadband Radiative Transfer Parameterization Considering The Vertical Variation Of Microphysical Properties In Warm Clouds

It is essential to propose a rapid radiative transfer scheme which can be used to accurately simulate cloud radiation effect in current climate modelling.Observations show that cloud microphysical properties(including liquid water content and droplet radius)vary with altitude in clouds.The variation leads to vertically inhomogeneous optical properties inside clouds and then affect radiative transfer calculation.However,current climate models cannot consider this important character due to their coarse vertical resolution.Therefore,it is significant to efficiently calculate the radiation effect related to the vertical variation of cloud microphysical properties in climate models.To include the effect of vertical variation of cloud microphysical properties,new multi-layer solar and infrared radiative transfer schemes are proposed.In these schemes,exponential expressions are applied to represent the vertically inhomogeneous inherent optical properties.The variable coefficient solar and infared radiative transfer equations can be solved by the perturbation method coupled with the Eddington approximation and the infrared two-stream discrete ordinate method,respectively.The adding method based on the four invariance principles is used to handle solar and infrared radiative transfer in a multi-layer inhomogeneous atmosphere.In order to investigate their accuracy and computational efficiency,We applied both new solar and infrared schemes into the Canadian Climate Center radiative transfer model and compared the results to conventional radiative transfer schemes based on the Eddington approximation and infrared two-stream discrete ordinate method.According to the results,conclusions can be summarized as follow:(1)Ignoring the vertical variation of cloud microphysical properties leads to a significant bias of 5.77 W/m~2for the downward solar flux,8.97 W/m~2for the upward solar flux,-0.27 K/day for the solar heating rate.The new solar scheme can reduce the bias related to the vertical variation.The maximum bias of the new solar scheme is only 0.05 W/m~2for the downward flux,0.22 W/m~2for the upward flux,0.05 K/day for the heating rate.(2)Ignoring the vertical variation of cloud microphysical properties basically have no influence on infrared downward flux.However,it will cause high bias in the calculation of infrared upward flux and infrared heating rate.The bias of infrared two-stream discrete ordinate method can be up to 1.51 W/m~2for the upward flux,-0.94 K/day for the heating rate.While the maximum bias of the new infrared scheme is only-0.23 W/m~2for the upward flux,-0.07 K/day for the heating rate.(3)In terms of computational efficiency,the new solar scheme is approximately three times more computationally expensive compared to the conventional Eddington approximation considering the algorithm itself.The new infrared scheme is approximately four times more computationally expensive compared to the conventional two stream discrete ordinate method.When applying them to the full radiative transfer model,the computational time for the new solar and infrared scheme is double as compared to the conventional Eddington approximation and infrared two-stream discrete ordinate method.Therefore,the new solar and infrared schemes are very suitable to be applied into climate simulations to consider the radiation effect related to the vertical variation of cloud microphysical properties.