the unified model cloud scheme

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The Unified Model Cloud Scheme.

Damian Wilson, Met Office.


A PDF cloud scheme

TL=T - L/cp l

qT=q+lqT = qsat(TL)

= qT - qsat(TL)

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

This formulation is only valid if condensation is rapid, hence no supersaturation.


Mathematical formulationl = 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>.

( )

[ ] ( )

c

c

s

s Q

s

c

s Q

C G s ds

l Q s G s ds


The Smith parametrization

s

G(s)

s=-Qcbs

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.

Cloudy

Clear


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> as the 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).


Important issues

s= –Qc

Cloudy

What is the width of the PDF?

What is the skewness?

What is the shape of the PDF?

Is the PDF adequately described by simple parameters?Analysis should be performed in the ‘s’ framework.

s=aL [ qT’ - TL’ ]

How does the PDF change with time, C, …?


Consequences of PDF shape.

Qc

C

1

0

0.5

Larger RHc

Triangular shapeTop-hat

shapeSkewed

bs = f(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.


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?

the unified model cloud scheme

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