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The Unified Model Cloud Scheme.

The Unified Model Cloud Scheme. Damian Wilson, Met Office. A PDF cloud scheme. q T = q sat (T L ). q T =q+l. .  = q T - q sat (T L ). This formulation is only valid if condensation is rapid, hence no supersaturation. T L =T - L/c p l.

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The Unified Model Cloud Scheme.

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  1. The Unified Model Cloud Scheme. Damian Wilson, Met Office.

  2. A PDF cloud scheme qT = qsat(TL) qT=q+l   = qT - qsat(TL) This formulation is only valid if condensation is rapid, hence no supersaturation. TL=T - L/cp l l = qT -qsat(T) = qT - qsat(TL + L/cp l) l = qT - [ qsat(TL) +  L/cp l] where  is the chord gradient l = aL [qT - qsat(TL)] where aL = [1+  L/cp]-1

  3. Mathematical formulation l = aL [ qT - qsat(TL) ] Write in terms of a gridbox mean and fluctuation. l  aL [<qT> - qsat(<TL>)] + aL [ qT’ -  TL’ ] l  Qc + s If we know the distribution G(s) of ‘s’ in a gridbox then we can integrate across the distribution to find C and <l>.

  4. The Smith parametrization G(s) Cloudy Clear s=-Qc s bs We parametrize G(s) to be triangular with a width given by bs = aL[1-RHc]qsat(<TL>) When -QC=bs we have -aL [<qT> - qsat(<TL>)] = aL[1-RHc]qsat(<TL>) or <RH> = RHc.

  5. Implementation • Values of C and l can be solved analytically. • But at what temperature should aL be calculated? This problem arises from the linear approximation we made earlier. We need a form of ‘average’ aL. • We calculate  and <aL> asthe gradient of the chord between T, qsat(T) and TL, qsat(TL). • This means that there is an iteration to find the value of <l> (but not necessary for C).

  6. Important issues What is the shape of the PDF? What is the skewness? How does the PDF change with time, C, …? Is the PDF adequately described by simple parameters? Cloudy s= –Qc s=aL [ qT’ -  TL’ ] Analysis should be performed in the ‘s’ framework. What is the width of the PDF?

  7. Consequences of PDF shape. C The shape of the PDF determines how C and <l> vary with Qc. Remember, though, that it is also possible for the shape to change with time or as a function of C or the physical process which is occuring. 1 bs = f(C) Triangular shape Top-hat shape 0.5 Skewed 0 Qc Larger RHc

  8. Summary • The Met Office cloud scheme uses a qT and TL framework to formulate a PDF description of cloud fraction and condensation. Other cloud schemes can be presented similarly using qT and TL ideas. • It relies on the assumption of instantaneous condensation and evaporation. • The resulting behaviour of cloud fraction and condensate depends critically on how the shape of the PDF is parametrized. • Is the shape sensible?

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