Variational assimilation of radar reflectivities in a cirrus model. II: Optimal initialization and model bias estimation

In this paper the microphysical model of cirrus clouds introduced in a related study is used to assimilate radar data. A variational approach is developed, based on a method of optimal estimation which makes use of the gradient information provided by the adjoint of the model to minimize a quadratic cost function. Multiple experiments to probe different solutions to the assimilation problem are conducted using both synthetic rellectivities and real observations. Various model and environment parameters are tested as control variables. Results indicate that specific humidity is a viable control variable at cloud levels. Even though this field is only indirectly related to the radar signal, information about the ambient humidity in which the cloud formed may be extracted from the radar reflectivities by using the cloud model in conjunction with the observations. The adjustment of the specific-humidity profile brings the model solution closer to the observed values by increasing the crystal number concentration. Systematic errors in the prognostic variables are also estimated as part of the optimization process by including a model bias term in the cost function. This is equivalent to relaxing the assumption of 'perfect' model, and allows for better assimilation results when both model bias evaluation and optimal initialization are performed.