1. Robin Hogan & Anthony Illingworth Department of Meteorology University of Reading UK Parameterizing ice cloud inhomogeneity and the overlap of inhomogeneities using cloud radar data

2. Relationship between optical depth and emissivity Ice cloud inhomogeneity Cloud infrared properties depend on emissivity Most models assume cloud is horizontally uniform In analogy to Sc albedo, the emissivity of non-uniform clouds is less than for uniform clouds Pomroy and Illingworth (GRL 2000) Lower emissivityHigher emissivity But for ice clouds the vertical decorrelation is also important

3. Cloud radar and ice clouds Cloud radars can estimate ice parameters from empirical relationships with radar reflectivity, Z (liquid clouds more difficult due to drizzle). Can evaluate gridbox-mean IWC in models, but newer models are also beginning to represent sub-grid structure Here we use radar to estimate gridbox variances and vertical correlation of inhomogeneities We use 94-GHz Galileo radar that operates continuously from Chilbolton in Southern England

4. Fractional variance We quantify the horizontal inhomogeneity of ice water content (IWC) and ice extinction coefficient () using the fractional variance: Barker et al. (1996) used a gamma distribution to represent the PDF of stratocumulus optical depth: Their width parameter is actually the reciprocal of the fractional variance: for p( ) we have = 1/f.

5. Deriving extinction & IWC from radar Regression in log-log space provides best estimate of log from a measurement of logZ (or dBZ) log Z r log But by definition, the slope of the regression line is r log / log Z (where r is the correlation coefficient), so f is underestimated by a factor of r 2 0.45. Use ice size spectra measured by the Met-Office C-130 aircraft during EUCREX to calculate cloud and radar parameters: =0.00342 Z 0.558 IWC =0.155 Z 0.693

6. For inhomogeneity use the SD line The standard deviation line has slope of log / log Z We calculate SD line for each horizontal aircraft run Mean expression =0.00691 Z 0.841 (note exponent) Spread of slopes indicates error in retrieved f & f IWC log Z log

7. Cirrus fallstreaks and wind shear This is a test … Low shear High shear Unified Model

8. Vertical decorrelation: effect of shear Low shear region (above 6.9 km) for 50 km boxes: –decorrelation length = 0.69 km –IWC frac. variance f IWC = 0.29 High shear region (below 6.9 km) for 50 km boxes: –decorrelation length = 0.35 km –IWC frac. variance f IWC = 0.10

9. Ice water content distributions PDFs of IWC within a model gridbox can often, but not always, be fitted by a lognormal or gamma distribution Fractional variance tends to be higher near cloud boundaries Near cloud baseCloud interior Near cloud top

10. Results from 18 months of radar data Variance and decorrelation increase with gridbox size –Shear makes overlap of inhomogeneities more random, thereby reducing the vertical decorrelation length –Shear increases mixing, reducing variance of ice water content –Can derive expressions such as log 10 f IWC = 0.3log 10 d - 0.04s - 0.93 Fractional variance of IWCVertical decorrelation length Increasing shear

11. Distance from cloud boundaries Can refine this further: consider shear <10 ms -1 /km –Variance greatest at cloud boundaries, at its least around a third of the distance up from cloud base –Thicker clouds tend to have lower fractional variance –Can represent this reasonably well analytically

12. Conclusions We have quantified how the fractional variances of IWC and extinction, and the vertical decorrelation, depend on model gridbox site, shear, and distance from cloud boundaries Full expressions may be found in Hogan and Illingworth (JAS, March 2003) –Note that these expressions work well in the mean (i.e. OK for climate) but the instantaneous differences in variance are around a factor of two Outstanding questions: –Our results are for midlatitudes: what about tropical cirrus? –Our results for fully cloudy gridboxes: How should the inhomogeneity of partially cloudy gridboxes be treated? –What other parameters affect inhomogeneity?