[1] Spaceborne precipitation radars are usually designed to operate at attenuating wavelengths, mostly at X, Ku and Ka band. At these frequencies and above, convective rainfall can cause severe attenuation. Moreover, raindrops and precipitating ice can give rise to appreciable multiple scattered radiation which apparently tends to enhance the nominal attenuated reflectivity. In order to properly describe radar observations in such conditions, apparent reflectivity has to be modeled taking into account both path attenuation and incoherent effects. To this aim, a general definition of volume radar reflectivity is introduced, and a Monte Carlo model of backscattered specific intensity is implemented. The numerical model is applied to synthetic profiles, extracted from a mesoscale cloud-resolving model simulation and representing intense and heavy convective precipitation at a developing and mature stage. Realistic appearance of these average profiles is argued by resorting to radar measurements available in literature. Spaceborne apparent reflectivity due to multiple scattering is shown to be significantly different from the attenuated one for the near-surface layers of mature convection at Ku band and even for growing convection at Ka band. A discussion about this discrepancy is carried out at Ku band showing its possible impact for estimated rain rate profiles. If precipitation incoherent effects are formally treated as perturbation factors of the specific attenuation model, constrained single-frequency inversion techniques are shown to be suitable to minimize rain rate retrieval errors due to multiple scattering phenomenon.

This article explores the uncertainties associated with evaluating a global atmospheric model with radar reflectivity observations. A forward operator for radar reflectivity (ZmVar) is described and used for the comparison of the ECMWF global numerical weather prediction model short-range forecasts with radar data from CloudSat. A sensitivity study is performed to determine which differences can be attributed to either specific radar forward operator assumptions or to deficiencies in the global model. The results show that model-derived reflectivities are particularly sensitive to the definition of subgrid precipitation fraction, as precipitation dominates the radar reflectivity signal, but also to the choice of particle size distribution and scattering properties of the different hydrometeor categories. However, there are a number of consistent differences in the reflectivity comparison that are significantly larger than can be explained by the sensitivity tests. This suggests that these discrepancies are due to deficiencies in the model cloud and precipitation frequency of occurrence and hydrometeor water contents. These include too frequent occurrence at high altitudes, too low occurrence in the Southern Hemisphere storm track and an overestimate of rain in warm-phase low cloud. The study shows the value of CloudSat for evaluating the model in terms of radar reflectivity and highlights the importance of taking into account forward operator uncertainties for both model evaluation and data assimilation applications.

SUMMARYAn intercomparison of retrieval errors from different Tropical Rainfall Measuring Mission (TRMM) passive microwave rainfall products was carried out to assess the de nition of observation error for experiments of rainfall assimilation in a variational framework. Depending on algorithms and their spatial resolution and sampling, a large variety of error estimates occurred. The error propagation to the European Centre for Medium-Range Weather Forecasts (ECMWF) model grid (here 45 and 60 km) was investigated from error simulations and observed data with and without accounting for spatial error correlation.All algorithms used in this study (TRMM standard product 2A12 V.5 and two alternative algorithms, namely PATER and BAMPR) employ a Bayesian retrieval framework. The Bayesian errors obtained from each algorithm from different case-studies showed values well above 100% at low rain rates (0.1 mm h ¡1 ) and around 50% at high rain rates (20-50 mm h ¡1 ) at the original product resolution and sampling. These Bayesian errors corresponded very well with those from an independent evaluation which was carried out by comparing TRMM microwave radiometer (TMI) estimates to precipitation radar retrievals at the same (here ¼27 £ 40 km 2 ) resolution. The impact of spatial averaging on retrieval errors was simulated using ts to the Bayesian errors and realistic log-normal rainfall probability distributions. By neglecting spatial correlation, the range of errors is reduced from 70-200% to 20-50% at low rain rates and from 25-70% to 5-20% at high rain rates. To account for spatial data correlation, TMI observations were rst averaged to the ECMWF model grid. Then the decorrelation of rain rates as a function of separation distance from all products was calculated. The introduction of spatial error correlation affected both error reduction and dispersion of errors per rain-rate interval. The nal error estimates ranged from 50-150% at low rain rates to 20-50% at high rain rates. The analysis suggests that once the spatial correlation pattern of a product is known, the probability density distribution of real observations inside the model grid does not produce larger scatter and therefore a simple scaling may suf ce to calculate rainfall retrieval errors at the model resolution.

The retrieval errors of cloud and precipitation hydrometeor contents from spaceborne observations are estimated at microwave frequencies in atmospheric windows between 18 and 150 GHz and in oxygen absorption complexes near 50–60 and 118 GHz. The method is based on a variational retrieval framework using a priori information on the cloud, atmosphere, and surface states from ECMWF short-range forecasts under different weather regimes. This approach was chosen because a consistent description of the model state and its uncertainties is provided, which is unavailable for other methods. The results show that the sounding channels provide more stable, more accurate, and less biased retrievals than window channels—in particular, over land surfaces and with regard to snowfall. Average performance estimates showed that if sounding channels are used, 80% of all retrievals are within 100% error limits and 60% of them are within 50% error limits with regard to rainfall. For snowfall, the sounding channels produce 60% of all retrievals with errors below 100% for rates smaller than 1 mm h−1, and 50%–80% of the cases have errors below 50% for more intense snowfall.

[1] A cloud model-based statistical retrieval technique for estimating surface precipitation and cloud profiles over ocean, called Bayesian Algorithm for Microwave Precipitation Retrieval (BAMPR), is described. The inversion scheme, based on the Bayesian estimation theory, is trained by a CRD obtained by inputting the numerical outputs of a mesoscale microphysical model into a three-dimensional radiative transfer model. Since the performances of the retrieval are strictly dependent on the a priori information given by the CRD, the generation of the database itself, and the coupling between the forward and the inverse problem are carefully discussed. Particular emphasis is given to the database representativeness of the meteorological event under investigation and to the quantification of modeling errors. The retrieval uncertainties are provided with the estimates themselves by choosing the Minimum Mean Square technique as a Bayesian inversion method. As an example, the algorithm is applied to some case studies in the Tropics using the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager data. The analysis is focused on the evaluation of the CRD performances with respect to the various events (i.e., a tropical cyclone, a tropical storm, a summer front, and some isolated convective cells in the Atolls region) and different CRDs (i.e., two hurricanes from the University of Wisconsin Nonhydrostatic Modeling System and a tropical squall line from the Goddard Cumulus Ensemble model). A detailed examination is carried out on the case of the hurricane Bonnie on 25 August 1998, which is discussed by using TRMM official products as a comparison.