Simulating the equivalent radar reflectivity of cirrus at 94 GHz using an ensemble model of cirrus ice crystals: a test of the Met Office global numerical weather prediction model

In this paper an ensemble model of ice crystals previously used to simulate the short-wave scattering properties of cirrus is now applied to simulate its equivalent radar reflectivity (Z(e)) at 94 GHz. It is shown that the ensemble model conserves the mass of aggregating ice crystals when compared against in situ derived mass-dimensional (m-D) relationships. The ensemble model derived m-D relationship is applied to the Rayleigh-Gans approximation to obtain a new parametrized radar reflectivity forward model for general circulation models (GCMs). The derived forward model is parametrized as a function of ice mixing ratio and in-cloud temperature, and it is shown that the forward model error is generally well within +/- 2 dBZ(e) using a linear fit; this new parametrization negates the need for an 'effective diameter'. The Met Office Unified global Model (MetUM) predictions of ice water content (IWC) and Z(e) are compared against profiled in situ microphysical probe estimates of IWC and Z(e), based on in situ estimates. The in situ IWC profiles were obtained from a midlatitude cirrus case during an airborne campaign around the UK. The paper demonstrates that towards cloud-bottom and cloud-top the MetUM prediction of IWC is generally within and outside the experimental uncertainty, respectively. The MetUM forward simulation of Z(e) assumes two particle size distributions (PSDs) of differing shapes and it is shown that the broader PSD simulates Z(e) better when compared against Z(e) based on in situ estimates for all altitudes. For the same case the PSD assumed in the CloudSat retrieval of IWC is also investigated and it is speculated that it could be too narrow towards cloud-bottom. The paper demonstrates the need for consistent PSDs when forward modelling Z(e) at 94 GHz, and the forward radar model error in the MetUM should be better characterized. Copyright (C) 2011 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.