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*Subject*: Time for model equilibration*From*: kenc@llnl.gov (Ken Caldeira)*Date*: Tue, 26 May 1998 17:59:37 -0700

Dear colleagues, As per our discussion of model equilibration time scales at the US OCMIP meeting at NCAR last week, the simplest approach is to look at a one-box reservoir equilibrating with an overlying atmosphere: (1) d a / d t = k (a0 - a(t)) , which has the solution (2) a(t) = a0 + a1 E^(-k t) . If we then add radioactive decay, we then have (3) d b / d t = k (b0 - b (t)) - kdecay b(t) , the solution is (4) b(t) = (k / (k + kdecay)) b0 + b1 E ^ (- ( k + kdecay) t) If we think that the e-folding time for the equilibration of a stable tracer is on the order of 1 kyr, and the decay of 14C is about 5.7 kyr, then the e-folding time for the combined system to approach steady-state is about 85% (i.e., 1/(1/(1 kyr) + 1/(5.7 kyr)) of that of the non-decaying tracer. If Jorge's results converged only 92 % after 6000 yr, this suggests an e-folding time-scale of about 2400 yrs for the central North Pacific. With radioactive decay considered, the e-folding time to approach a 14C solution should be about 1700 yr, which means that the 14C would be 97 % converged after 6000 yr. (Does this mean there could still be a 30 o/oo error?) Cheers, Ken <---------------------------> Ken Caldeira Climate System Modeling Group Lawrence Livermore National Laboratory 7000 East Ave., L-103 Livermore CA 94550 USA tel: (925) 423-4191 (new area code!) fax: (925) 422-6388 e-mail: kenc@LLNL.gov

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