Radar data assimilation experiments with a microphysical bulk formulation based on scaling normalization

We address here the problem of optimization of the microphysical information extracted from a simulation-system composed of high resolution numerical models and multi-parameter radar data or other available measurements. As a tool in the exploration of this question, we propose a bulk microphysical scheme based on the general approach of scaling normalization of particle size distribution (PSD). This approach does not rely on a particular functional form imposed on the PSD and naturally leads to power law relationships between the PSD moments providing an accurate and compact PSD representation. To take into account the possible evolution of the shape/curvature of the distribution, ignored within standard one- and two- moment microphysical schemes, we propose a new three-moment scheme based on the two-moment scaling normalization. The methodology of the moment retrieval included in the three-moment scheme can also be useful as a retrieval algorithm combining different remote sensing observations. The developed bulk microphysical scheme presents a unified formulation for microphysical parameterization using one, two or three independent moments, suitable in the context of variational data assimilation.

The effectiveness of the scheme with different combinations of independent moments is evaluated by comparison with a very-high resolution spectral model on representative microphysical processes: rain sedimentation and evaporation. Various assimilation experiments are presented in the context of a column time-dependent model used to simulate the passage of precipitating cells over a short period of time. When all the predicted moments are observed and assimilated, the minimization converges very well, even with 40% observation error. In this case, the reflectivity factor, which is related to the sixth moment, can be retrieved with 0.2 dB accuracy. When only the reflectivity is observed, the total number of concentration (related to the zeroth moment) can not be recovered. However, the constant relative humidity can be obtained with 1% accuracy. When simpler one-moment and two-moment schemes are used to retrieve the precipitation structure from the observed reflectivity, the model error strongly projects on the non-observed moments of the PSD.