Parameterizing Ice Cloud Inhomogeneity and the Overlap of Inhomogeneities Using Cloud Radar Data

Abstract

Cloud variability on scales smaller than the gridbox size of numerical forecast and climate models is believed to be important in determining the radiative effects of clouds, and increasingly attempts are being made to parameterize these fluctuations in the radiation schemes of current models. In order to calculate the radiative effects of an inhomogeneous cloud, a model needs to know not only the degree of variability within a gridbox but also the degree to which the inhomogeneities in vertically adjacent levels are overlapped. In this paper these two parameters are derived for ice clouds from an 18-month midlatitude 94-GHz cloud radar dataset and parameterized in terms of horizontal gridbox size (d), the vertical shear of the horizontal wind (s), and the vertical position in the cloud. The vertical decorrelation length ?z0 (i.e., the depth over which the correlation coefficient of either ice water content or optical extinction coefficient in separate vertical levels falls to e?1) is found to be well represented in the mean by log10?z0 = 0.3 log10d ? 0.031s ? 0.315, where ?z0 and d are in kilometers and s is in meters per second per kilometer. As expected, higher shear results in more rapid decorrelation, although the rms deviation from this expression is around a factor of 2.5. It is found that the probability distribution of ice water content within a gridbox is usually well represented by a lognormal or gamma distribution. The fractional variance in ice water content (fIWC) may be expressed to within a factor of 2 by log10fIWC = 0.3 log10d ? 0.04s ? 0.93, valid for d < 60 km, above which fIWC is constant with increasing d. The expression for the fractional variance of visible extinction coefficient is the same except with the ?0.93 term replaced by ?0.96. The s dependence indicates a tendency for increased shear to result in decreased cloud variability. This can be explained by the presence of ice fallstreaks in a sheared flow: a parcel of air in the middle of a cloud is alternately fed from above by ice-rich and ice-poor air, resulting in a homogenization of the layer at a rate dependent on the shear. A more complicated formula is derived to express the dependence of fIWC on the vertical position within the cloud; it is found that fractional variance tends to be largest at cloud top and decreases into the interior before increasing again in the lowest third of the cloud. Thicker clouds tend to have lower fractional variance. No significant dependence on temperature or absolute altitude was found for either fIWC or ?z0.