Estimating Uncertainty in GPCP and TRMM Multi-Satellite Precipitation Estimates
One of the high-priority problems in satellite precipitation estimation is developing algorithms for estimating the errors in precipitation retrievals by individual sensors and subsequent multi-satellite combinations. Classically, we distinguish between "random" and "bias" errors, which do and do not, respectively average to zero over a "big enough" time/space sample. The current operational GPCP and TRMM multi-satellite algorithms are nearly unique in estimating random error for the monthly precipitation estimates from individual sensor systems (including gauge), following Huffman, and then making multi-sensor combinations. No routinely operational global precipitation produces estimates of bias error. Subsequently, a similar scheme has been followed to provide random error estimates for the Multi-satellite Precipitation Analysis (MPA) being computed in real time and after real time for TRMM. The Huffman algorithm for random error is briefly reviewed, including a discussion of the limitations imposed on the algorithm by standard monthly precipitation data sets. Starting from a very simple theoretical treatment of the histogram of precipitation samples in a month, an equation is developed that depends on the estimated average precipitation rate for the month, the number of samples in the month, and two constants. The constants are set separately for each source of precipitation estimate (such as "raingauge") by calibration at selected ground sites. We discuss recent work validating the random error estimates to highlight the successes and limitations of this first-generation approach. We then consider what information is needed from the individual sensor algorithms to facilitate additional accuracy in the estimation of random errors across the time/space span of climate regimes which a global estimation system must handle. In addition, the thorny issue of estimating bias is raised. Finally, the role of error estimates (and the qualitative errors!) in creating combinations of precipitation estimates from different individual sensors is discussed. This issue is particularly important when fine scales in space and time are being considered, say the 0.25 x 0.25-deg 3-hourly estimates in the MPA.