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

Abstract

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 assimilation of SSM/I and TMI rainfall rates in the ECMWF 4D‐Var system

“…The methodology is similar to the one proposed by Marécal and Mahfouf (2002) where Total Column Water Vapour (TCWV) retrievals in rainy areas from a simplified 1D-Var assimilation are introduced in the 4D-Var system. An improved methodology for the estimation of rain rate retrieval errors proposed by Bauer et al (2002) is used. Three one-month experiments are undertaken: a control run (no rain rate assimilation), a TMI run (assimilation of TMI-derived rain rates) and a SSM/I run (assimilation of SSM/I-derived rain rates).…”

“…The spatial correlations are very consistent between the two retrievals, since both TMI and SSM/I retrievals are calibrated from the PR. As mentioned by Bauer et al (2002), the more rapid spatial decorrelation noticed in their study with other algorithms comes from the 85.5 GHz channel that is not considered in PATER-type algorithms. It is interesting to note that the correlation at 100 km is about 0.3, whereas it was only 0.2 in results presented by Bauer et al (2002).…”

“…(b) Estimation of retrieval errors Rainwater contents w (g m −3 ) produced by the PATER algorithms are converted into rain rate R (mm h −1 ) from a relation proposed by Bauer et al (2002):…”

“…This is a compromise between computing time and stability of the statistics. The polynomial fit used in Bauer et al (2002) is kept (with different coefficients):…”

“…Some considerations on the chosen methodology are given in section 2. A central aspect of this study concerns the definition of rain rate retrieval errors, described in section 3 based on the work of Bauer et al (2002). A slightly modified version of the 1D-Var is presented in section 4 to accommodate more efficiently the large number of SSM/I rainfall rate observations.…”