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*Subject*: 14C time constants, yet again*From*: kenc@llnl.gov (Ken Caldeira)*Date*: Thu, 28 May 1998 16:26:26 -0700

Folks, Rick is right that considering the gas equilibration can introduce a longer time constant. The effective residence time of water in the mixed-layer (relative to gas-exchange-isotopic equilibration time-scales) can have a big effect on the 14C equilibration time-constant for the deep ocean, with short residence times (i.e., lack of equilibration with the atmosphere) leading to long deep ocean equilibration time scales ... In Mathematica, I analytically solved a simple two-box model with the following equations, where 'a' is the 14C in the surface box, and 'b' is the 14C for the deep box. I ignored radioactive decay in the surface box to make the equations more tractable. d a / d t = kgas (a0 - a[t]) + km (b[t] - a[t]) d b / d t = kd (a[t] - b[t]) - kdecay b[t], where a0 is the atmospheric delta 14C kgas is the inverse time constant for 14C equilibration (~1/(8 yr)) km is the inverse time constant for surface mixing with the deep ocean (~1/(10 yr) ???) kd is the inverse time constant for deep mixing with the surface ocean (~1/(2400 yr) ???) kdecay is the C14 decay inverse time constant (~1/(5700 yr)) Solving this system, the dominant inverse time constant for deep ocean equilibration is: kequil = (sqrt((kd + kdecay + kgas + km)^2 - 4 (kd kgas+kdecay (kgas+km))) - - (kd + kdecay + kgas + km))/2 , which for the above parameter values yields ~1/(2459 yr), slightly longer than the deep-North-Pacific equilibration time for a non-decaying tracer that equilibrates rapidly with the atmosphere! With the other values above held constant, if km = 1/(1yr), 1/kequil = 4511 yr if km = 1/(100 yr), 1/kequil = 1782 yr if kgas = 1/(0.8 yr), 1/kequil = 1782 yr if kgas = 1/(80 yr), 1/kequil = 4524 yr The upshot of this is that, as Rick Murnane pointed out, that gas exchange and vertical structure can introduce longer time constants than my previous 1-box result indicated, and a more sophisticated model is probably needed to predict actual convergence time scales. Has anybody run Maier-Reimer's model for a very long time and examined convegence rates for 14C? What does this mean for the simulated time required to reach a meaningful deep ocean 14C result? 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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