1. Quantifying sub-grid cloud structure and representing it GCMs
Robin Hogan
Anthony Illingworth, Sarah Kew, Jean-Jacques Morcrette, Itumeleng Kgololo, Joe Daron, Anna Townsend

2. Overview Cloud overlap from radar
Maximum-random overlap underestimates cloud radiative effect
Inhomogeneity scaling factors from MODIS
Homogeneous clouds overestimate cloud radiative effect
Dependence on gridbox size, cloud type, spectral region etc.
Vertical structure of inhomogeneity from radar
Overlap of inhomogeneities in ice clouds
Experiments with a 3D stochastic cirrus model
Trade-off between overlap and inhomogeneity errors
Representing the heating-rate profile
Priorities for radiation schemes

3. Cloud overlap assumption in models
Cloud fraction and mean ice water content alone not sufficient to constrain the radiation budget
Assumptions generate very different cloud covers
Most models now use “maximum-random” overlap, but there has been very little validation of this assumption

4. Cloud overlap from radar: example
Radar can observe the actual overlap of clouds
We next quantify the overlap from 3 months of data

5. Cloud overlap: approach
Consider combined cloud cover of pairs of levels
Group into vertically continuous and non-continuous pairs
Plot combined cloud cover versus level separation
Compare true cover & values from various overlap assumptions
Define overlap parameter: 0 = random and 1 = maximum overlap

6. “Exponential-random” overlap
Overlap of vertically continuous clouds becomes random with increasing thickness as an inverse exponential
Vertically isolated clouds are randomly overlapped
Higher total cloud cover than maximum-random overlap
Hogan and Illingworth (QJ 2000), Mace and Benson-Troth (2002)

7. Exponential-random: global impact
New overlap scheme is easy to implement and has a significant effect on the radiation budget in the tropics
Difference in OLR between “maximum-random” overlap and “exponential-random” overlap
~5 Wm-2
globally
ECMWF model, Jean-Jacques Morcrette

8. Cloud structure in the shortwave and longwave
Over black surface
Cloud structure in the shortwave and longwave
Clear air Cloud
Inhomogeneous cloud
Non-uniform clouds have lower emissivity & albedo for same mean optical depth due to curvature in the relationships
Can we simply scale the optical depth/water content?

9. Results from MODIS Reduction factor depends strongly on: ECMWF use 0.7
Cloud type & variability
Gridbox size
Solar zenith angle
Shortwave/longwave
Mean optical depth itself
ECMWF use 0.7
All clouds, SW and LW
Value derived from around a month of Sc data: equivalent to a huge gridbox!
Not appropriate for model with 40-km resolution
MODIS Sc/Cu
1-km resolution,
100-km boxes
Itumeleng Kgololo

10. Shortwave albedo Longwave emissivity Joe Daron Stratocumulus cases
Ice-cloud cases
Cumulus cases
True
Plane-parallel model
Modified model
Longwave emissivity
Stratocumulus cases
Ice-cloud cases
Cumulus cases
Emissivity
True
Plane-parallel model
Modified model
Joe Daron

11. Solar zenith angle
Asymmetry factor
Anna Townsend

12. Vertical structure of inhomogeneity
Low shear
High shear
Decorrelation length ~700m
We estimate IWC from radar reflectivity
IWC PDFs are approximately lognormal:
Characterize width by the fractional variance
Lower emissivity and albedo
Higher emissivity and albedo

13. 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
Best-fit relationship: log10 fIWC = 0.3log10d s
Hogan and Illingworth (JAS 2003)

14. 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

15. 3D stochastic cirrus model
“Generalizes” 2D observations to 3D
A tool for studying the effect of cloud structure on radiative transfer
Radar data
Slice through simulation
Hogan & Kew (QJ 2005)

16. …with increased shear
Both gridbox-mean albedo and emissivity increase for the same mean optical depth/IWP
Shear ~ 20 m s-1km-1

17. Radiative effect: control experiment
Upwelling shortwave (=60º) Upwelling longwave (Wm-2)
27 Dec 1999

18. Thin cirrus example Independent column calculation:
SW radiative effect at TOA: 40 W m-2
LW radiative effect at TOA: -21 W m-2
GCM with exact overlap
SW change: +50 W m-2 (+125%)
LW change: -31 W m-2 (+148%)
Large inhomogeneity error
GCM, maximum-random overlap
SW change: +9 W m-2 (+23%)
LW change: -9 W m-2 (+43%)
Substantial compensation of errors

19. Thin case: heating rate
Shortwave Longwave
GCM scheme with max-rand overlap outperforms GCM with true overlap due to compensation of errors
Maximum-random overlap -> underestimate cloud radiative effect
Horizontal homogeneity -> overestimate cloud radiative effect

20. Thick ice cloud example
Independent column:
SW radiative effect: 290 W m-2
LW radiative effect: -105 W m-2
GCM with exact overlap
SW change: +14 W m-2 (+5%)
LW change: -10 W m-2 (+10%)
Near-saturation in both SW and LW
GCM, maximum-random overlap
SW change: +12 W m-2 (+4%)
LW change: -9 W m-2 (+9%)
Overlap virtually irrelevant

21. Thick case: heating rate
Shortwave Longwave
Large error in GCM heating rate profile
Inhomogeneity important to allow radiation to penetrate to (or escape from) the correct depth, even though TOA error is small
Cloud fraction near 1 at all heights: overlap irrelevant
More important to represent inhomogeneity than overlap

22. Summary Cloud overlap: GCMs underestimate radiative effect
Exponential-random overlap easy to add
Important mainly in partially cloudy skies: 40 W m-2 OLR bias in deep tropics but only around 5 W m-2 elsewhere
Inhomogeneity: GCMs overestimate radiative effect
Affects all clouds, can double the TOA radiative effect
Scaling factor too crude: depends on gridbox size, cloud type, solar zenith angle, spectral region; and heating rate still wrong!
Need more sophisticated method: McICA, triple-region etc.
What about other errors?
In climate mode, radiation schemes typically run every 3 hours: introduces random error and possibly bias via errors in diurnal cycle. How does this error compare with inhomogeneity?
Is spectral resolution over-specified, given large biases in other areas? Why not relax the spectral resolution and use the computational time to treat the clouds better?