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ocmip stuff -- Murnane ---equilibration time scales continued



>HI Ken -
>
>Could you do me a favor and send this to the ocmip mailing list?  I don't
>seem to have reply rights!
>
>Thanks,
>
>Rick
>
>>Date: Thu, 28 May 1998 18:07:40 +0200
>>From: LMCE list server <listserv@lsce.saclay.cea.fr>
>>Subject: Returned mail: Private list 'ocmip-all'
>>To: rmurnane@sargasso.bbsr.edu
>>
>>  Sorry, you are not a subscriber to the list, or your address has changed.
>>  So, you are not allowed to send mail to this list.
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>>
>
>>Date: Thu, 28 May 1998 13:08:44 -0400
>>To: ocmip-all@lsce.saclay.cea.fr
>>From: Richard Murnane <rmurnane@sargasso.bbsr.edu>
>>Subject: Re: Time for model equilibration
>>
>>Hi -
>>
>>I would guess that this approach only gives a lower bound for
>>equilibration.  In the GCM's a water parcel is subducted and isolated from
>>the atmosphere before isotopic equilibration with the atmosphere.  My
>>feeling is that the isotopic equilibration time scale (t) for an ocean GCM
>>is on the order of the (vertical) diffusion time scale for ocean.  For
>>example, if you've got a 1 cm^2/sec diffusion coefficient and a 4 km deep
>>ocean:
>>
>>t = 400000^2/1/3.14*10^7 = 5000 years
>>
>>where 3.14*10^7 is the number of seconds in a year.
>>
>>Rick
>>
>>>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
>>
>>
>
>
>_______________________________________________________________________
>
>Richard J. Murnane
>Science Program Manager
>Risk Prediction Initiative
>Bermuda Biological Station for Research, Inc.
>Ferry Reach
>St. George's  GEO1
>BERMUDA
>
>Phone:  (441) 297-1880 ext. 246
>FAX:    (441) 297-2890
>internet:  rmurnane@bbsr.edu
>On the Web? try URL http://www.bbsr.edu/rpi/
>_______________________________________________________________________
>

<--------------------------->
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