Abstract
Microphysical schemes based on the scaling normalization of the particle size distribution (PSD) are cast into a variational data assimilation method to assess their ability to retrieve the precipitation structure and humidity from moments of the PSD that can be derived from radar- and ground-based disdrometer measurements. The sedimentation and evaporation, which are the main processes below the cloud base, are examined. Various identical twin 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. The relative humidity profile is assumed constant. The feedback of the microphysical processes on the thermodynamic fields is ignored. Observations are generated from a three-moment scheme having the zeroth, third, and sixth moments of the PSD as prognostic variables. The model is discretized in terms of the logarithms of the predictive moments, which render the adjustment of the model variables easier to the observations. An upper bound for the characteristic diameter for the sixth moment is however necessary to prevent numerical instabilities from developing during the data assimilation process.
The tangent linear model of the three-moment scheme reproduces well the difference between two nonlinear integrations over the assimilation window (8 min), which validates the use of its adjoint in the minimization of the cost function that measures the misfit between observations and corresponding model variables. A weak smoothness penalty function should be added to the cost function when noisy observations are assimilated.
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 sixth moment is observed, the total number of concentration (related to the zeroth moment) cannot 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 sixth moment, the model error strongly projects on the nonobserved moments of the PSD.
Welfare and Trade without Pareto
