1. Investigating Cloud Inhomogeneity using CRM simulations.
James Manners
© Crown copyright 2005

2. Aims
To assess which scaling factors (if any) can be used to represent the inhomogeneity in a variety of cloud types using CRM simulations.
To characterise the distribution of liquid water (& ice) & if possible determine a link between the scaling factor & model variables.
© Crown copyright 2005

3. Why scaling factors?
Cahalan et al. 1994, “The Albedo of Fractal Stratocumulus Clouds”:
The area-average albedo of an inhomogeneous cloud field is less than that of a uniform cloud having the same microphysical parameters and the same total liquid water.
Corrected by a “Reduction factor”:
τ’ = χ τ
Assuming lognormal statistics: log χ = mean( log W ) – log (mean W),
where W is horizontal liquid water path.
Cairns et al. 2000, “Absorption within Inhomogeneous Clouds and Its Parameterization in GCMs”:
Cloud inhomogeneity has different effects on absorption and on the transmission of the direct beam – the reduction factor above cannot correctly deal with albedo and absorption at the same time.
“Renormalisation” of the optical properties may solve this:
k’ = k / ( 1 + V )
ω’ = ω / [ 1 + V( 1 – ω ) ]
g’ = g [ 1 + V( 1 – ω ) ] / [ 1 + V( 1 – ωg ) ]
where V is relative variance of the droplet density distribution (again assumed to be lognormal).
© Crown copyright 2005

4. Method
Take a snapshot of a large CRM covering ~ global model gridbox with resolutions of ~ 50 – 200m in the horizontal (preferably similar to the UM in the vertical).
Use the offline E-S radiation code to calculate fluxes in each column. Gridboxes are assumed to be completely clear or completely cloudy depending on whether the condensed water content is > 1E – 6 kg/kg.
First run (designated “Full IPA”), using the actual condensed water mixing ratios.
Second run (“Homogeneous cloud”), replace water mixing ratios with a mean in-cloud value for each layer.
Mean the fluxes & heating rates over the domain.
This simulates the effect of the homogeneous cloud seen in the UM whilst retaining the correct cloud overlap (overlap assumptions will be looked at later).
Apply scaling factors to the “homogeneous cloud” and repeat to find the best match for TOA and surface fluxes (& heating rate profile).
© Crown copyright 2005

5. First CRM: Deep tropical convection
200m resolution, 25km x 25 km
© Crown copyright 2005

6. Full IPA
Homogeneous cloud

7. Effect on heating rates
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8. Mean TOA and surface fluxes
Full IPA Homog. Cloud Homog Cloud *0.44
TOA Reflected SW:
Surf. Direct SW Down:
Surf. Diffuse SW Down:
Net Surface SW:
TOA LW Up:
Surface LW Down:
Simple scaling of condensed water mixing ratio by 0.44 corrects the total fluxes and improves the heating rate profile in this case.
This is just a ‘best fit’ – we need to be able to predict the scaling factor from the cloud properties.
© Crown copyright 2005

9. Cloud liquid water distribution
At each level find PDF of liquid water mixing ratio.
From the statistics of the distribution, calculate ‘reduction factor’ (Cahalan) and relative variance (Cairns).
2D Power spectra are also calculated to indicate how the variance is distributed with scale.
© Crown copyright 2005

10. Scaling factors calculated at each level
Scaling factors decrease with height as the relative variance increases.
Possibly linked to cloud fraction?
Mean reduction factor (χ = 0.55) is too big.
Mean Cairns value 1/(1+V) = 0.45 is a good fit if applied only to the optical depth.

11. Heating rates using 1/(1+V) scaling to opt. depth at each level
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12. Heating rates using mean Cairns scaling to all optical properties
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13. Sub-tropical Stratocumulous sheet: 30km * 12.5km, resolution 50m.
Full IPA
Homogeneous cloud

14. Scaling factors calculated at each level
Mean reduction factor (χ = 0.82) is slightly too small but using the whole profile gives a good fit.
Link to cloud fraction appears more significant…

15. Heating rates using χ scaling to optical depth at each level
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16. Plan Repeat analysis for a large range of cloud types.
Find the best fitting scaling factors:
Are these consistent for convective / stratiform cloud?
Can they be calculated from the water distribution?
Can they be linked to cloud fraction, vertical velocity etc.?
How are they related to domain size – can they be scaled using a particular power spectrum slope?
Need to consider:
Effect of zenith angle (using 30 degrees at present).
Different factors for SW/LW (perhaps related as suggested by Rossow et al.).
© Crown copyright 2005