date: Tue, 10 Aug 2004 12:03:14 -0600
from: Tom Wigley <wigley@cgd.ucar.edu>
subject: effective sensitivity
to: Sarah Raper <sraper@awi-bremerhaven.de>

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Sarah,

I keep going over this, but usually not very well.

Tell me whether this is the way Seff is determined.

A simple*global* EBM is .....

C dT/dt +  lambda*T = Q - F

where T is global-mean temp, C is a heat capacity, F is
the flux below the ocean mixed layer, Q is forcing. In the
TAR this is written (my notation is different) as .....

dH/dt  +  T/S = Q                             ....(1)

where H is ocean heat content so dH/dt is the flux into
the ocean. 'S' is the sensitivity, which, in this formulation
is called the effective sensitivity (which I could write as
Seff). This is, of course, only an approximate representation.

I've said this before, but I think this breaks down if there
is land and ocean. For a two-box case, the  equations are ...

dH/dt + lambda1*Toc = Q + k(Tland - Toc)        ....(2)
lambda2*Tland = Q + k(Toc - Tland)                  ....(3)

where 1 = oc and 2 = land. The 'k' has to involve relative
areas in practice.

The issue is whether (2) and (3) can be converted to look
like (1), involving only global T and a global sensitivity. The
answer, I think,  is 'no' -- so I think (1) is fundamentally flawed.

As an extreme case, if Tland and Toc are very similar then
one might be able to ignore the k term in (2). Comparing this
with (1) implies that what one is backing out is closer to the
ocean sensitivity than the global sensitivity. I note that in
the Table I sent you, Seff is usually less than the MLO
sensitivity, which fits.

It is possible to convert (2) and (3) to an equ. involving
only global T and global effective sensitivity (and R, the sens.
ratio) but it is very messy. From this formulation, effective
sensitivity is in general time dependent -- which also fits.

Tom.

PS The GSIC paper went off today. See attached.




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////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
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