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

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

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

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

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

“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)

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

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?

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

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

Solar zenith angle Asymmetry factor Anna Townsend

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

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 - 0.04s - 0.93 Hogan and Illingworth (JAS 2003)

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

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)

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

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

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

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

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

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

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?