Statistics of Arctic cloud downwelling infrared emissivity

Time series of optical depth of Arctic stratus clouds are investigated for scaling properties and biases with respect to a plane-parallel model. The study is based on 3 years of infrared spectrometer and microwave radiometer measurements made at the Atmospheric Radiation Measurement North Slope of Alaska site. Power spectra of radiance and radiance emissivity are found to indicate scaling with a spectral coefficient on the order of 5/3 over 0.5-10 hours, consistent with the Kolmogorov-Obukhov prediction [Kolmogorov, 1941] for three-dimensional turbulence. Irradiance emissivities inferred from the data set, using an independent column approximation and 6-hour time intervals, are further analyzed to find reduction factors for the same mean optical depth in a plane-parallel representation. These factors are estimated to average 0.82 in March and 0.48 in September but with a high degree of variability: The most inhomogeneous quarters of these data sets exhibit reduction factors of 0.57 (March) and 0.20 (September). Observed reduction factors for radiance and irradiance are found to depend primarily on the ratio of mean optical depth to variance, a result consistent with exact results for a gamma distribution of cloud thickness.