date: Tue, 10 Aug 2004 12:03:14 -0600
from: Tom Wigley
subject: effective sensitivity
to: Sarah Raper
This is a multi-part message in MIME format.
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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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