A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds

The three-dimensional structure of clouds is known to be important for determining their radiative effects, but it is difficult to obtain this structure directly from observations. In this paper a stochastic model is described that is capable of simulating the structural properties unique to cirrus: fallstreak geometry and shear-induced mixing. We first present an analysis of time-height cloud radar sections from southern England to extract the cirrus parameters of interest. It is found that horizontal power spectra of the logarithm of ice-water content (estimated from radar reflectivity factor and temperature) typically exhibit a spectral slope of around -5/3 near cloud top that decreases with depth into the cloud, to values as low as -3.5 in some cases. This decrease can be explained by wind shear coupled with a spread of particle fall speeds leading to a homogenization that acts preferentially at smaller scales. The power spectra exhibit a distinct scale break, becoming flat at scales larger than around 50 km (the 'outer scale'). The orientation of the fallstreaks may be predicted from the profile of mean wind and mean ice fall speed. We then describe the stochastic model, which takes as input profiles of the mean and fractional standard deviation of ice-water content, spectral slope, outer scale and wind speed. It first generates an isotropic 3-D fractal field by performing an inverse 3-D Fourier transform on a matrix of simulated Fourier coefficients with amplitudes consistent with the observed I-D spectra. Random phases for the coefficients allow multiple realizations of a cloud with the same statistical properties to be generated. Then horizontal slices from the domain are manipulated in turn to simulate horizontal displacement and changes to the spectra with height. Finally the field is scaled to produce the observed mean and fractional standard deviation of ice-water content. Vertical 2-D slices extracted from the domain are very similar in appearance to cloud radar observations. Radiative-transfer calculations using the independent column approximation are used to show that the different fallstreak orientation resulting from different wind shears can change mean top-of-atmosphere radiative fluxes by in excess of 45 W m(-2) in the shortwave and 15 W m-2 in the long-wave. The effect of wind shear to induce horizontal mixing causes an additional but smaller radiative effect. We also investigate the biases that would be expected from the assumptions made in the radiation schemes of general-circulation models (GCMs). It is found that there is some compensation between the errors arising from the assumptions of horizontal homogeneity and maximum-random overlap; if a GCM were to improve the overlap assumption but still assume clouds to be horizontally homogeneous then the total error in cloud radiative effect would be likely to increase.