[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.

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.

[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.

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[1] A statistical methodology to combine measurements from space-borne microwave radar and radiometers is proposed. The approach is fairly general, even though the combination technique is here tailored for the two instruments onboard the Tropical Rainfall Measuring Mission (TRMM) satellite specifically devoted to rainfall measurements, that is, the Precipitation Radar (PR) and the TRMM Microwave Imager (TMI). Two combined retrieval algorithms are proposed, both derived from the previously developed Bayesian algorithm for microwave-based precipitation retrieval from passive sensors (BAMPR-P), which is based on a Bayesian inversion method and is trained by a modeled cloud radiation database. The first combined technique, called BAMPR-C (BAMPR combined), operates in the narrower common swath aiming at exploiting the simultaneous measurements of PR and TMI instruments. Within BAMPR-C the hydrometeor profiles, retrieved from TMI, are used as a constraint for the PR-based inversion: this two step cascade allows us to overcome the difficulty to take into account the different scan geometries of TMI and PR. The second combined technique is called BAMPR-B (BAMPR broadening) and aims at improving the TMI-only retrieval outside the common swath. In this approach, first optimal retrieved profiles are generated by reversing the order of the previous two steps of BAMPR-C cascade within the common swath. Then the resulting profile data set and the corresponding TMI brightness temperatures are used to define the cloud radiation database to be employed outside the common swath for the TMI-only retrieval, achieving the so-called radar swath synthetic broadening. Numerical internal tests, using simulated data, are illustrated to quantify the features of the proposed synergetic algorithms. Finally, an application to measured TRMM data for a selected case study (hurricane Bonnie on August 1998) is shown and discussed.