This paper describes the latest improvements applied to the Goddard profiling algorithm (GPROF), particularly as they apply to the Tropical Rainfall Measuring Mission (TRMM). Most of these improvements, however, are conceptual in nature and apply equally to other passive microwave sensors. The improvements were motivated by a notable overestimation of precipitation in the intertropical convergence zone. This problem was traced back to the algorithm's poor separation between convective and stratiform precipitation coupled with a poor separation between stratiform and transition regions in the a priori cloud model database. In addition to now using an improved convective-stratiform classification scheme, the new algorithm also makes use of emission and scattering indices instead of individual brightness temperatures. Brightness temperature indices have the advantage of being monotonic functions of rainfall. This, in turn, has allowed the algorithm to better define the uncertainties needed by the scheme's Bayesian inversion approach. Last, the algorithm over land has been modified primarily to better account for ambiguous classification where the scattering signature of precipitation could be confused with surface signals. All these changes have been implemented for both the TRMM Microwave Imager (TMI) and the Special Sensor Microwave Imager (SSM/I). Results from both sensors are very similar at the storm scale and for global averages. Surface rainfall products from the algorithm's operational version have been compared with conventional rainfall data over both land and oceans. Over oceans, GPROF results compare well with atoll gauge data. GPROF is biased negatively by 9% with a correlation of 0.86 for monthly 2.5Њ averages over the atolls. If only grid boxes with two or more atolls are used, the correlation increases to 0.91 but GPROF becomes positively biased by 6%. Comparisons with TRMM ground validation products from Kwajalein reveal that GPROF is negatively biased by 32%, with a correlation of 0.95 when coincident images of the TMI and Kwajalein radar are used. The absolute magnitude of rainfall measured from the Kwajalein radar, however, remains uncertain, and GPROF overestimates the rainfall by approximately 18% when compared with estimates done by a different research group. Over land, GPROF shows a positive bias of 17% and a correlation of 0.80 over monthly 5Њ grids when compared with the Global Precipitation Climatology Center (GPCC) gauge network. When compared with the precipitation radar (PR) over land, GPROF also retrieves higher rainfall amounts (20%). No vertical hydrometeor profile information is available over land. The correlation with the TRMM precipitation radar is 0.92 over monthly 5Њ grids, but GPROF is positively biased by 24% relative to the radar over oceans. Differences between TMI-and PR-derived vertical hydrometeor profiles below 2 km are consistent with this bias but become more significant with altitude. Above 8 km, the sensors disagree significantly, but the information content is low...

A set of global, monthly rainfall products has been intercompared to understand the quality and utility of the estimates. The products include 25 observational (satellite based), four model, and two climatological products. The results of the intercomparison indicate a very large range (factor of 2 or 3) of values when all products are considered. The range of values is reduced considerably when the set of observational products is limited to those considered quasi-standard. The model products do significantly poorer in the Tropics, but are competitive with satellite-based fields in midlatitudes over land. Over ocean, products are compared to frequency of precipitation from ship observations. The evaluation of the observational products points to merged data products (including rain gauge information) as providing the overall best results.

Coupled-dipole approximation (CDA) calculations of microwave extinction and radar backscatter are presented for nonhomogeneous (soft) ice spheres and for quasi-realistic aggregates of elementary ice crystal forms, including both simple needles and real dendrites. Frequencies considered include selections from the Dual-Frequency Precipitation Radar (DPR; 13.4 and 35.6 GHz) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI; 18.7, 36.5, and 89.0 GHz), both slated for orbit on the GPM mission.The computational method is first validated against Mie theory using dipole structures representing solid ice spheres as well as stochastically generated ''soft'' ice spheres of variable ice-air ratio. Neither the traditional Bruggeman nor Maxwell Garnett dielectric mixing formula is found to correctly predict the full range of CDA results for soft spheres. However, an excellent fit is found using the generalized mixing rule of Sihvola with n 5 0.85.The suitability of the soft-sphere approximation for realistic aggregates is investigated, taking into account the spectral dependence of backscatter and/or extinction per unit mass at key DPR and GMI frequencies.Even when spheres of nonequal mass are considered, there is no single combination of fraction and mass that simultaneously captures all the relevant radiative properties. All four aggregate models do, however, exhibit a predictable power-law dependence of the mass extinction coefficient on the total particle mass. Dual-frequency mass extinction ratios are only very weakly dependent on particle masses; moreover, the ratio is found to be approximately proportional to frequency raised to the power 2.5.The dual-frequency backscatter ratio is found to be a predictable function of the aggregate mass for particles smaller than 3 mg. Above this size, the ratio is strongly sensitive to aggregate shape, a finding that raises concerns about the utility of dual-frequency backscatter ratio measurements whenever larger particles might be present in a volume of air.The validity of the Rayleigh-Gans approximation applied to radar backscatter from snow aggregates was also examined. Although the dual-frequency backscatter ratio was reasonably well reproduced, the absolute magnitude was not.

No abstract

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5°-resolution range from approximately 50% at 1 mm h−1 to 20% at 14 mm h−1. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%–80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5° resolution is relatively small (less than 6% at 5 mm day−1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%–35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%–15% at 5 mm day−1, with proportionate reductions in latent heating sampling errors.