robin hogan & anthony illingworth department of meteorology university of reading uk...
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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?