Initial 3D isotropic fractal field

1. Clear air Cloud Radar data Slice through simulation Inhomogeneous cloud Cloud top -5/3 Scale break at ~50 km Lower emissivity and albedo Cloud base -3.5 Shear-induced mixing at small scales Higher emissivity and albedo Near cloud top Near cloud base Cloud interior 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 3. Formulation of stochastic cloud model • A 1D power spectrum indicates variance at each scale but with no phase information. • 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. Initial 3D isotropic fractal field 1. Introduction • The importance of ice clouds on the earth’s radiation budget is well recognized. • 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. Simulated cirrus cloud (isosurface of IWC) • 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. • 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. • Cross-sections through the simulated field look encouragingly similar to the IWC field from the original radar image: • 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. 4. Radiative properties of inhomogeneous cirrus • A thinner cloud, modelled on a case from 17 July 1999, is now used to demonstrate the effect of wind shear on radiative fluxes: Stratocumulus simulation for comparison Higher shear: ~20 m s-1 km-1 Observed shear: ~2 m s-1 km-1 Slice through simulation 2. Analysis of cloud radar data Emissivity • 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. Emissivity Reflectance Met Office model Reflectance • 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): Reflectance • 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. MODIS reflectance • 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. 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). Spread of fall speeds (due to turbulence or size distribution) leads to homogenisation of fallstreaks and steeper power spectrum CloudSat radar and Calipso lidar to be launched in 2005 • At each height we characterize the cloud by these parameters: • Mean IWC • Fractional variance of IWC, fIWC (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)