| Abstract: |
The Global Precipitation Measurement (GPM) Microwave Imager (GMI) is the radiometric calibration transfer standard for the intersatellite radiometric calibration of the NASA GPM constellation radiometers. Because these radiometers are not identical, the GPM Intersatellite Calibration (XCAL) Working Group has developed a robust double difference (DD) technique to estimate the brightness temperatures (Tb) bias, which is applied to constellation radiometers before being input into a single satellite radiometer rain retrieval algorithm (GPROF). Also, for this rain retrieval, it is important to provide the uncertainty of the bias estimates.
This paper describes the development of a generic uncertainty estimation model, which is associated with the DD biases between GMI and a given constellation radiometer. As an example, we use the XCAL DD between GMI and the TRMM Microwave Imager (TMI).
First, the overall uncertainty is partitioned into separate and mostly independent sources that include: statistical sampling confidence, geophysical field spatial variability, radiative transfer model (RTM) physics, geophysical parameter errors, Rayleigh-Jeans approximation versus Planck Function and uncertainty in calibration reference (GMI).
Next, various analyses were performed to determine the uncertainty from each source. For example, from rigorous statistical principles, it is possible to calculate the number of independent samples required to estimate the DD bias within ±0.05 K with 96% confidence. On this basis, the required sampling strategy was established. Next, to investigate the impact of the second source (spatial averaging or “box size”), a number of different boxes (e.g., 0.25°, 0.5°, 1°, etc.) were used to average the individual radiometer Tb’s before calculating the DD and the standard deviations (std) for a large number of boxes were calculated. The smallest box size that yielded the minimum std was selected.
The next two sources (RTM physics and input environmental parameters) were not independent; therefore, they were evaluated using Monte Carlo simulations. Estimates of the std of the environmental parameters were known from the literature for the NOAA GDAS model and the ECMWF ERA-I model and each was used in separate simulations, with two different sets of atmospheric physics and two sets of ocean surface physics. Results were combined using the root sum squared method. Next, the uncertainty associated with the Rayleigh-Jean approximation to the Planck function was evaluated by calculating the standard deviation of the difference in calibration bias derived using the two sets of geophysical parameters.
Finally, the estimated individual independent uncertainties, along with the GMI calibration uncertainty (obtained from published data), were combined using the root sum squared method. In this paper, results for each uncertainty source will be shown and net residual uncertainty between GMI and TMI Tb’s for corresponding channels will be given.
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