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. --------------020706030906080104040905 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit 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. 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