Statistical relationships between higher-order moments of probability density functions (PDFs) are used to analyze top-of-atmosphere radiance measurements made by the Atmospheric Infrared Sounder (AIRS) and radiance calculations from the ECMWF Re-Analysis (ERA) and the Modern-Era Retrospective Analysis for Research and Applications (MERRA) over a 10-yr period. The statistical analysis used in this paper has previously been applied to sea surface temperature, and here the authors show that direct satellite radiance observations of atmospheric variability also exhibit stochastic forcing characteristics. The authors have chosen six different AIRS channels based on the sensitivity of their measured radiances to a variety of geophysical properties. In each of these channels, the authors have found evidence of correlated additive and multiplicative (CAM) stochastic forcing. In general, channels sensitive to tropospheric humidity and surface temperature show the strongest evidence of CAM forcing, while those sensitive to stratospheric temperature and ozone exhibit the weakest forcing. Radiance calculations from ERA and MERRA agree well with AIRS measurements in the Gaussian part of the PDFs but show some differences in the tails, indicating that the reanalyses may be missing some extrema there. The CAM forcing is investigated through numerical simulation of simple stochastic differential equations (SDEs). The authors show how measurements agree better with weaker CAM forcing, achieved by reducing the multiplicative forcing or by increasing the spatial correlation of the added noise in the case of an SDE with one spatial dimension. This indicates that atmospheric models could be improved by adjusting nonlinear terms that couple long and short time scales.
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