Robin HoganRobin HoganAnthony Illingworth, Sarah Kew, Jean-Anthony Illingworth, Sarah Kew, Jean-Jacques Morcrette, Itumeleng Kgololo, Jacques Morcrette, Itumeleng Kgololo, Joe Daron, Anna TownsendJoe Daron, Anna Townsend

Quantifying sub-grid Quantifying sub-grid cloud structure and cloud structure and

representing it GCMsrepresenting it GCMs

OverviewOverview• 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

Cloud overlap assumption in Cloud overlap assumption in modelsmodels

• 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

Cloud overlap from radar: Cloud overlap from radar: exampleexample

• Radar can observe the actual overlap of clouds

• We next quantify the overlap from 3 months of data

“ “Exponential-random” Exponential-random” overlapoverlap

• 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)

Exponential-random: global Exponential-random: global impactimpact

New overlap scheme is easy to implement and has a significant effect on the radiation budget in the tropics

ECMWF model, Jean-Jacques Morcrette

Difference in OLR

between “maximum-

random” overlap

and “exponentia

l-random” overlap

~5 Wm-2

globally

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?

Cloud structure Cloud structure in the in the

shortwave and shortwave and longwavelongwave

Clear air Cloud

Results from MODISResults from MODIS• Reduction factor

depends strongly on:– 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

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MODIS Sc/Cu

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• Stratocumulus cases• Ice-cloud cases• Cumulus cases

• True• Plane-parallel model• Modified model

• True• Plane-parallel model• Modified model

Shortwave Shortwave albedoalbedo

Longwave Longwave emissivityemissivity • Stratocumulus cases

• Ice-cloud cases• Cumulus cases

Joe Daron

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Albedo as a function of Asymmetry Factor

Polycrystals(0.74)Columns(0.8)Water(0.85)Plates(0.9)

Solar zenith angleSolar zenith angle

Asymmetry factorAsymmetry factor

Anna Townsend

Vertical structure of Vertical structure of inhomogeneityinhomogeneity

Decorrelation length ~700m

Lower emissivity and albedo

Higher emissivity and albedo

Low shearLow shearHigh shearHigh shear

We estimate IWC from radar reflectivity

IWC PDFs are approximately lognormal:Characterize width by the

fractional variance

Results from 18 months of Results from 18 months of radar dataradar data

• 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 - 0.04s - 0.93

Fractional variance of IWC Vertical decorrelation length

Increasing shear

Hogan and Illingworth (JAS 2003)

• “Generalizes” 2D observations to 3D

• A tool for studying the effect of cloud structure on radiative transfer

Radar data Slice through simulationHogan & Kew (QJ 2005)

3D stochastic 3D stochastic cirrus modelcirrus model

Thin cirrus exampleThin 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

Thin case: heating rateThin case: heating rate

• 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

Shortwave Longwave

Thick ice cloud exampleThick 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

Thick case: heating rateThick case: heating rate

• 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

Shortwave Longwave

SummarySummary• 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?