Robin Hogan & Anthony IllingworthDepartment of Meteorology

University of Reading UK

Parameterizing ice cloud inhomogeneity and the overlap of inhomogeneities using cloud radar data

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 emissivity Higher emissivity

• But for ice clouds the vertical decorrelation is also important

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 .

exp)(

1)( 1p

2/ IWCf IWCIWC 2

/ f

Deriving extinction & IWC from radar

• Regression in log-log space provides best estimate of log from a measurement of logZ (or dBZ)

logZ

rlog

• But by definition, the slope of the regression line is rlog/logZ (where r is the correlation coefficient), so f is underestimated by a factor of r2 0.45.

Use ice size spectra measured by the Met-Office C-130 aircraft during EUCREX to calculate cloud and radar parameters:

=0.00342 Z0.558

IWC =0.155 Z0.693

For inhomogeneity use the SD line

• The “standard deviation line” has slope of log/logZ

• We calculate SD line for each horizontal aircraft run• Mean expression =0.00691 Z0.841 (note exponent)

• Spread of slopes indicates error in retrieved f & fIWC

logZ

log

Cirrus fallstreaks and wind shear

• This is a test …

Low shear

High shear

Unified Model

Vertical decorrelation: effect of shear

• Low shear region (above 6.9 km) for 50 km boxes:– decorrelation length = 0.69 km

– IWC frac. variance fIWC = 0.29

• High shear region (below 6.9 km) for 50 km boxes:– decorrelation length = 0.35

km

– IWC frac. variance fIWC = 0.10

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 base Cloud interior Near cloud top

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 log10 fIWC = 0.3log10d - 0.04s - 0.93

Fractional variance of IWC Vertical decorrelation length

Increasing shear

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 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?