Abstract
An error model for Bayesian Monte Carlo retrieval algorithms which explicitly accounts for uncertainty introduced by the use of a finite database of realizations, as well as uncertainties associated with the modelling and measurement components of the retrieval is described. The model provides a rigorous estimate of the uncertainty in all retrieved parameters as well as a breakdown of this uncertainty into two components attributable to an imperfect database, and modelling and measurement uncertainties, respectively. This error information is critical for algorithm development, model validation and, in particular, in variational data assimilation where the relative accuracy of the observations and the background forecast determines how much the latter is modified in the assimilation process.
Using the error model, uncertainties in the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) instantaneous surface rainfall product (2A12) are found to range from 40 to 60 percent in rainfall up to 20 mm h^−1^.. In heavier rain, uncertainties rapidly increase due to heavy attenuation in all TMI channels which requires surface rainfall to be inferred solely from the non‐unique relationship between surface rain rate and the ice‐scattering signature in the strongly coupled 37 and 85 GHz brightness temperatures. In light rain, the fact that the database attempts to approximate nature's infinite cloud probability density function by a finite set of realizations, and the inherent inability of the TMI brightness temperatures to completely distinguish between all cloud profiles in the database, dominate retrieval uncertainties. Between 4 and 10 mm h^−1^ both error components are comparable while measurement and model uncertainties dominate in heavier rainfall. Preliminary attempts to incorporate radar reflectivity data to reduce profile database uncertainties show promise, but can lead to a compensating increase in the modelling and measurement‐error component.
Results highlight the need for studying sources of systematic error in the cloud database such as errors in cloud microphysical assumptions, beam‐filling errors, or biases in the radiative‐transfer calculations used to simulate brightness temperatures for each profile. In addition, the utility of the error model for estimating uncertainties in any Bayesian Monte Carlo retrieval algorithm is demonstrated. Copyright © 2002 Royal Meteorological Society.