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Initial 3D isotropic fractal field An initial fractal cloud-like field can be generated by essentially performing an inverse 3D Fourier Transform on the 1D power spectrum, but introducing random phases for the Fourier components. In practice this is more complicated as we need to add artificial scale breaks in the 1D spectrum to account for different grid spacing and domain sizes in the x, y and z directions. Radar data Slice through simulation Observed shear: ~2 m s -1 km -1 Higher shear: ~20 m s -1 km -1 CloudSat radar and Calipso lidar to be launched in 2005 Inhomogeneous cloud Clear air Cloud A 3D stochastic cloud model for investigating the impact of cirrus inhomogeneity on radiative transfer Robin J. Hogan and Sarah F. Kew Department of Meteorology, University of Reading, UK Email: r.j.hogan@reading.ac.uk Cloud top -5/3 Cloud base -3.5 Shear-induced mixing at small scales Scale break at ~50 km Spread of fall speeds (due to turbulence or size distribution) leads to homogenisation of fallstreaks and steeper power spectrum Spectral analysis of ln(IWC) reveals a spectral slope of close to –5/3 at cloud top which steepens lower down in the cloud due to preferential mixing at smaller scales. Near cloud base Cloud interior Near cloud top 2. Analysis of cloud radar data The importance of ice clouds on the earth’s radiation budget is well recognized. 1. Introduction 4. Radiative properties of inhomogeneous cirrus 3. Formulation of stochastic cloud model Ice cloud inhomogeneity can affect both mean longwave (Pomroy and Illingworth 2000) and shortwave fluxes (Carlin et al. 2002). Most GCMs assume cloud is horizontally uniform, but non-uniform clouds have lower emissivity and albedo for same mean optical depth due to curvature in the relationships. Lower emissivity and albedo Higher emissivity and albedo High resolution observations are required to characterize the horizontal inhomogeneity of cloud water content and radiative properties. However, vertical decorrelation information is also required and this can only be derived from radar; aircraft data are insufficient. Stochastic models are useful for quantifying the radiative effect of cloud structure but existing models have tended to concentrate on boundary-layer clouds (e.g. Cahalan et al. 1994, DiGuiseppe and Tompkins 2003, Evans and Wiscombe 2004). Here we present the first stochastic model capable of representing the important structural features unique to cirrus: fallstreak geometry and shear induced mixing. Preliminary radiative transfer calculations demonstrate the sensitivity of fluxes to fallstreak orientation, which is determined by wind shear. We use the 94-GHz radar at Chilbolton, England. The case shown is from 27 Dec 1999 and demonstrates the effect of wind shear on fallstreak geometry. Numerous published empirical relationships exist to estimate ice water content (IWC) from radar reflectivity factor, and we find that the resulting PDFs may usually be represented by a lognormal distribution (Hogan and Illingworth 2003): At each height we characterize the cloud by these parameters: Mean IWC Fractional variance of IWC, f IWC (tends to be higher near cloud boundaries) Power spectrum slope Scale break (usually found to be around 50 km) Horizontal wind speed (to estimate horizontal displacement) A 1D power spectrum indicates variance at each scale but with no phase information. At each height we then: Translate to simulate fallstreaks. Change the spectral slope to simulate mixing. Scale to get the right mean and variance. Exponentiate to produce a lognormal distribution. Threshold at a certain IWC value to represent gaps in the cloud. Simulated cirrus cloud (isosurface of IWC) Cross-sections through the simulated field look encouragingly similar to the IWC field from the original radar image: A thinner cloud, modelled on a case from 17 July 1999, is now used to demonstrate the effect of wind shear on radiative fluxes: Slice through simulation Reflectance Emissivity Reflectance MODIS reflectance Stratocumulus simulation for comparison The changes to mean emissivity and albedo with shear correspond to changes in longwave and shortwave flux of 20-30 W m -2, of the same order as the error incurred in climate models due to not representing cirrus inhomogeneity at all. By contrast, stratocumulus structure has little effect in the longwave as the higher optical depth means that the cloud behaves as a black body; also the temperature contrast with the ground is much less. 5. Implications for spaceborne radar and lidar We can use the stochastic model to simulate synergistic radar/lidar retrievals. It is found that footprints within 1.5 km of each other (from an altitude of 700 km) are needed for the error due to mismatch to be less than 25% (1 dB). Met Office model

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