The Sensitivity of Rainfall Estimation to Error Assumptions in a Bayesian Passive Microwave Retrieval Algorithm

Abstract

he Goddard profiling algorithm (GPROF) uses Bayesian probability theory to retrieve rainfall over the global oceans. A critical component of GPROF and most Bayes theorem?based retrieval frameworks is the specification of uncertainty in the observations being utilized to retrieve the parameter of interest. In the case of GPROF, for any sensor, uncertainties in microwave brightness temperatures (Tbs) arise from radiative transfer model errors, satellite sensor noise and/or degradation, and nonlinear, scene-dependent Tb offsets added during sensor intercalibration procedures. All mentioned sources impact sensors in a varying fashion, in part because of sensor-dependent fields of view. It is found that small errors in assumed Tb uncertainty (ranging from 0.57 K at 10 GHz to 2.29 K at 85 GHz) lead to a 3.6% change in the retrieved global-average oceanic rainfall rate, and 10%?20% (20%?40%) shifts in the pixel-level (monthly) frequency distributions for given rainfall bins. A mathematical expression describing the sensitivity of retrieved rainfall to uncertainty is developed here. The strong global sensitivity is linked to rainfall variance scaling systematically as Tb varies. For ocean scenes, the same emission-dominated rainfall?Tb physics used in passive microwave rainfall retrieval is also responsible for the substantial underestimation (overestimation) of global rainfall if uncertainty is overestimated (underestimated). Proper uncertainties are required to quantify variability in surface rainfall, assess long-term trends, and provide robust rainfall benchmarks for general circulation model evaluations. The implications for assessing global and regional biases in active versus passive microwave rainfall products, and for achieving rainfall product agreement among a constellation of orbiting microwave radiometers [employed in the Global Precipitation Measurement (GPM) mission], are also discussed.