Robin Hogan

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PDFs of humidity and cloud water content from
Raman lidar and cloud radar

• Robin Hogan
• Ewan OConnor
• Anthony Illingworth
• Department of Meteorology, University of Reading
  UK

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Sub-gridscale structure in GCMs

• Small-scale structure in GCMs can have large
  scale effects
• Sub-grid humidity distribution used to determine
  cloud fraction (e.g. in UM)
• Sub-grid cloud water distribution affects mean
  fluxes (crudely represented in ECMWF, not in UM)
• We use radar and lidar to make high-resolution
  measurements of water vapour and cloud content
• Raman lidar provides water vapour mixing ratio
  from ratio of the water vapour and nitrogen Raman
  returns
• Empirical relationships provide ice water content
  from radar reflectivity
• Liquid clouds are more tricky!

Chilbolton Raman lidar
Chilbolton cloud radar
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Mixing ratio comparison 11 Nov 2001
Raman lidar Unified Model, Mesoscale version
Cloud
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Small-scale humidity structure

• Correlation between adjacent range gates shows
  that small-scale structure is not random noise
• Typical horizontal cell size around 500m

Mixing ratio at 720m 6m
500m
Wind speed 6 m/s
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PDF comparison
12 UTC
15 UTC
1.6 km

• Agreement is mixed between lidar and model
• Good agreement at low levels
• Some bimodal PDFs in the vicinity of vertical
  gradients
• Further analysis required
• More systematic study
• Partially cloudy cases with PDF of liquidvapour
  content

Larkhill sonde
0.8 km
Smith (1990) triangular PDF scheme
0.2 km
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Ice cloud inhomogeneity

• Most models assume cloud is horizontally uniform
• Non-uniform clouds have lower emissivity albedo
  for same mean ? due to curvature in the
  relationships

SHORTWAVE albedo versus visible optical depth
Pomroy and Illingworth (GRL 2000)
LONGWAVE emissivity versus IR optical depth
Carlin et al. (JClim 2002)
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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)
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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? .

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Deriving extinction IWC from radar
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

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

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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

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Cirrus fallstreaks and wind shear
Unified Model
Low shear High shear
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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

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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

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Vertical decorrelation

• Variance at each level not enough, need vertical
  decorrelation/overlap info
• Only radar can provide this information aircraft
  insufficient

• Decorrelation length is a function of wind shear
• Around 700m near cloud top
• Drops to 350m in fall streaks

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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 log10 fIWC
  0.3log10d - 0.04s - 0.93

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Distance from cloud boundaries

• Can refine this further consider shear lt10
  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

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Conclusions

• We have quantified how fractional variances of
  IWC and extinction, and the vertical
  decorrelation, depend on model resolution, shear
  etc.
• Full expressions in Hogan and Illingworth (JAS,
  March 2003)
• Expressions work well in the mean (i.e. OK for
  climate) but the instantaneous differences in
  variance are around a factor of two
• Raman lidar shows great potential for evaluating
  model humidity field
• Outstanding questions
• Our results are for midlatitudes what about
  tropical cirrus?
• What other parameters affect inhomogeneity?
• What observations could be used to get the high
  resolution vertical and horizontal structure of
  liquid water content?

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