Algorithm Overview
The objective of the 3A11 algorithm is to derive monthly oceanic rainfall over 5o latitude by 5o longitude grid box using TRMM TMI data.
Monthly rainfall estimates have been derived from SSM/I brightness temperature histograms using probability distribution functions for over ten years (Wilheit et al., 1991, Chang and Chiu, 1998). The emission signal from the rain drops is used to extract the rainfall information. This technique has been extended to using the TMI Level-1B data for rain estimates as the at launch algorithm.
The histogram approach is based on the observation that rain rate can be modeled statistically by a mixed distribution, a discrete probability of no rain and a log-normal distribution for the raining part. The parameters of the rain rate probability distribution function (pdf) can be related to the brightness temperature histogram using the results of radiative transfer calculations. A combination of TMI channels, namely, twice the 19-GHz minus the 21-GHz vertical channel is used to minimize the effect of varying water vapor. The observed monthly histograms are compared with histograms computed from assumed Log-normal parameters which are varied until satisfactory agreement between the two histograms is reached. Freezing height needed by the radiative transfer calculation is derived from scattergrams of the 19 and 21 GHz TMI brightness temperature. The derived TMI rain-rate indexes are then multiplied by a correction factor to account for the beam-filling bias (Wilheit et al., 1991; Chiu et al., 1993). Wang (1995), using airborne radar data to drive a simulation, derived this correction factor which depends on the freezing level height and the footprint size.
In addition to brightness temperature histograms, several instantaneous rain rate histograms are also calculated. The probability distribution fit to the rain rate histograms is now being tested. These histograms derived from different TMI channels with different sensitivity to rain rate may widen the dynamic ranges in the rain estimates.
For operational purpose, this program is divided into three parts. The first part involves ingesting the TMI Level-1b data and generating an intermediate histogram file. This histogram accumulates the monthly data by individual data granule. Since the intermediate histogram is solely used for internal operation, no discussion will be given here. The second part of the program computes monthly rain estimates from the intermediate histogram. The third part converts the monthly rain estimates to HDF output file.
File Format
There is one output for level 3A data product for TMI, 3A11. The granule size is one month. Derived rainfall parameters are (1) monthly rainfall, (2) probability of rainfall, (3) chi square fit value, (4) freezing level height, (5) mean rain rate on rain, (6) mean brightness temperature when it is not raining, and (7) standard deviation of rain rate. Quality flags are also included in the data file. The detailed file content of 3A11 can be obtained from the Volume 4 ? Levels 2 and 3 File Specifications provided by the TRMM Data and Information System (TSDIS).
Known Deficiencies
3A11 using the combination channel of 19 and 21 GHz. These channels are subject to saturation for high rain rate cases. Current technique accounts for part of the effect. Resolution is now being worked on. Addition of the 10 GHz data will help to resolve this issue. Also, this algorithm is slightly sensitive to the known TB calibration errors. The Current calibration problem with TMI Level-1B data will not have large impact on the estimated rain (ca. 10%).
Planned Improvements
Work is underway to validate the results of 3A11 by comparing with rainfall climatology, available ‘truth’ data, and SSM/I derived rain estimates. Any shortcomings of the algorithm will be addressed to the best of our ability. For the next data release, we expect to improve the iteration procedure in the retrieval software. Also quality flags with more physical meaning will be added to the data set.
References
Chang, A.T.C. and L. S. Chiu, 1998: Non-systematic Errors of Monthly Oceanic Rainfall Derived from SSM/I, Mon. Wea. Rev., in press.
Chiu, L.S., A.T.C. Chang, and J.Janowaik, "Comparison of monthly rain rates derived from GPI and SSM/I using probability distribution functions," Journal of Applied Meteorology, 32, 323-334, 1993.
Wang, S. A., 1995: Modeling the Beamfilling Correction for Microwave retrieval of Oceanic Rainfall, Ph. D. Dissertation, Dept of Meteorology, Texas A&M University, College Station, TX, 99pp.
Wilheit, T.T., A.T.C. Chang and L.S. Chiu, 1991: Retrieval of monthly rainfall indices from microwave radiometric measurements using probability distribution functions. J. Atmos. Oceanic Tech., 8, 118-136.