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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. Relationship between optical depth and emissivity.

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parameterizing ice cloud inhomogeneity and the overlap of inhomogeneities using cloud radar data
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
Ice cloud inhomogeneity

Relationship between optical depth and emissivity

  • But for ice clouds the vertical decorrelation is also important

Lower emissivity

Higher emissivity

  • 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)

cloud radar and ice clouds
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
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
Deriving extinction & IWC from radar

rlog

logZ

  • But by definition, the slope of the regression line isrlog/logZ(where r is the correlation coefficient),so f is underestimated by a factor ofr2  0.45.
  • Regression in log-log space provides best estimate of log from a measurement of logZ(or dBZ)

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
For inhomogeneity use the SD line

log

logZ

  • 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
cirrus fallstreaks and wind shear
Cirrus fallstreaks and wind shear
  • This is a test …

Unified Model

Low shear

High shear

vertical decorrelation effect of shear
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
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
Results from 18 months of radar data

Fractional variance of IWC

Vertical decorrelation length

  • 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 log10fIWC = 0.3log10d - 0.04s - 0.93

Increasing shear

distance from cloud boundaries
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
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?