Parameterizing ice cloud inhomogeneity and the overlap of

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

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 • But for ice clouds the vertical decorrelation is also important Lower emissivity Relationship between optical depth and emissivity Pomroy and Illingworth (GRL 2000) Higher emissivity

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

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 .

Deriving extinction & IWC from radar log. Z r log 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 • Regression in log-log space provides best estimate of log from a measurement of log. Z (or d. BZ) • 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.

For inhomogeneity use the SD line log. Z • • log 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

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

Vertical decorrelation: effect of shear • Low shear region (above • High shear region (below 6. 9 km) for 50 km boxes: – decorrelation length = 0. 69 km – IWC frac. variance f. IWC = 0. 29 – decorrelation length = 0. 35 km – IWC frac. variance f. IWC = 0. 10

Ice water content distributions Near cloud base Cloud interior Near cloud top • 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

Results from 18 months of radar data Fractional variance of IWC Vertical decorrelation length Increasing shear • 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. 3 log 10 d - 0. 04 s - 0. 93

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

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 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?