Variational assimilation of radar reflectivities in a cirrus model. I: Model description and adjoint sensitivity studies

This paper presents an ice microphysics model to be used in variational assimilation of cloud-radar data. The model predicts the vertical and temporal evolution of the parameters of a modified gamma size distribution describing an ice-cloud crystal population, given an initial atmospheric state. Microphysical variables are mapped onto radar reflectivities using an explicit radar forward model. Evolution equations take into account microphysical processes relevant to ice-crystal growth, such as vapour-diffusion growth, aggregation, and gravitational sedimentation. The thermodynamic and dynamic state is specified from a numerical forecast or a radiosonde sounding and is assumed constant over the model integration time. Due to this assumption, the model provides no feedback to the environmental state and thus cannot be used for long-term cloud forecasts. However, when the model is integrated over a short time interval, and the atmospheric conditions are close to water saturation at cloud levels, the model is shown to compare well with observations. An adjoint of a linearized version of the cloud model is derived and applied to investigate model sensitivities to input variables and model parameters. Results show a large sensitivity of model outputs to temperature and selected parameters related to the crystal fall-velocity parametrization.