Error analysis of TMI rainfall estimates over ocean for variational data assimilation

An intercomparison of retrieval errors from different Tropical Rainfall Measuring Mission (TRMM) passive microwave rainfall products was carried out to assess the definition 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 kin) 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 min h(-1)) and around 50% at high rain rates (20-50 min 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 approximate to 27 x 40 km(2)) resolution. The impact of spatial averaging on retrieval errors was simulated using fits 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 first 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 final 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 suffice to calculate rainfall retrieval errors at the model resolution.