Initial 3D isotropic fractal field

1
A 3D stochastic cloud model for investigating the
impact of cirrus inhomogeneity on radiative
transfer Robin J. Hogan and Sarah F.
Kew Department of Meteorology, University of
Reading, UK Email r.j.hogan_at_reading.ac.uk
3. Formulation of stochastic cloud model

• A 1D power spectrum indicates variance at each
  scale but with no phase information.

• An initial fractal cloud-like field can be
  generated by essentially performing an inverse 3D
  Fourier Transform on the 1D power spectrum, but
  introducing random phases for the Fourier
  components.
• In practice this is more complicated as we need
  to add artificial scale breaks in the 1D spectrum
  to account for different grid spacing and domain
  sizes in the x, y and z directions.

Initial 3D isotropic fractal field
1. Introduction

• The importance of ice clouds on the earths
  radiation budget is well recognized.

• Ice cloud inhomogeneity can affect both mean
  longwave (Pomroy and Illingworth 2000) and
  shortwave fluxes (Carlin et al. 2002).
• Most GCMs assume cloud is horizontally uniform,
  but non-uniform clouds have lower emissivity and
  albedo for same mean optical depth due to
  curvature in the relationships.

Simulated cirrus cloud (isosurface of IWC)

• At each height we then
• Translate to simulate fallstreaks.
• Change the spectral slope to simulate mixing.
• Scale to get the right mean and variance.
• Exponentiate to produce a lognormal distribution.
• Threshold at a certain IWC value to represent
  gaps in the cloud.

• High resolution observations are required to
  characterize the horizontal inhomogeneity of
  cloud water content and radiative properties.
• However, vertical decorrelation information is
  also required and this can only be derived from
  radar aircraft data are insufficient.

• Cross-sections through the simulated field look
  encouragingly similar to the IWC field from the
  original radar image

• Stochastic models are useful for quantifying the
  radiative effect of cloud structure but existing
  models have tended to concentrate on
  boundary-layer clouds (e.g. Cahalan et al. 1994,
  DiGuiseppe and Tompkins 2003, Evans and Wiscombe
  2004).
• Here we present the first stochastic model
  capable of representing the important structural
  features unique to cirrus fallstreak geometry
  and shear induced mixing.
• Preliminary radiative transfer calculations
  demonstrate the sensitivity of fluxes to
  fallstreak orientation, which is determined by
  wind shear.

4. Radiative properties of inhomogeneous cirrus

• A thinner cloud, modelled on a case from 17 July
  1999, is now used to demonstrate the effect of
  wind shear on radiative fluxes

Stratocumulus simulation for comparison
Observed shear 2 m s-1 km-1
Higher shear 20 m s-1 km-1
Slice through simulation
2. Analysis of cloud radar data
Emissivity

• We use the 94-GHz radar at Chilbolton, England.
  The case shown is from 27 Dec 1999 and
  demonstrates the effect of wind shear on
  fallstreak geometry.

Emissivity
Reflectance
Met Office model
Reflectance

• Numerous published empirical relationships exist
  to estimate ice water content (IWC) from radar
  reflectivity factor, and we find that the
  resulting PDFs may usually be represented by a
  lognormal distribution (Hogan and Illingworth
  2003)

Reflectance

• The changes to mean emissivity and albedo with
  shear correspond to changes in longwave and
  shortwave flux of 20-30 W m-2, of the same order
  as the error incurred in climate models due to
  not representing cirrus inhomogeneity at all.
• By contrast, stratocumulus structure has little
  effect in the longwave as the higher optical
  depth means that the cloud behaves as a black
  body also the temperature contrast with the
  ground is much less.

MODIS reflectance

• Spectral analysis of ln(IWC) reveals a spectral
  slope of close to 5/3 at cloud top which
  steepens lower down in the cloud due to
  preferential mixing at smaller scales.

5. Implications for spaceborne radar and lidar

• We can use the stochastic model to simulate
  synergistic radar/lidar retrievals.
• It is found that footprints within 1.5 km of each
  other (from an altitude of 700 km) are needed for
  the error due to mismatch to be less than 25 (1
  dB).

Spread of fall speeds (due to turbulence or size
distribution) leads to homogenisation of
fallstreaks and steeper power spectrum
CloudSat radar and Calipso lidar to be launched
in 2005

• At each height we characterize the cloud by these
  parameters
• Mean IWC
• Fractional variance of IWC, fIWC (tends to be
  higher near cloud boundaries)
• Power spectrum slope
• Scale break (usually found to be around 50 km)
• Horizontal wind speed (to estimate horizontal
  displacement)