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Note that our z-axis is directed toward the bottom of the ocean. 



Also, we use g, cm, sec and cal, so the heat conductivity lamda 



is numercially equal to the heat diffusivity K. Values for 



diffusivity were set at either 1.18 or 1.9 cm 2 /sec. (Special 



scenarios investigated values of 0.2 and 4.0 cm^/sec.) 



The temperature change in the thermocline ( ^ T) is determined 



by the diffusion equation: 



c aA T(z,t) = k a 2 A T(z,t) 

 3- t 6 z 2 



The boundary conditions for a T are: 



A T = A T m at z = H m 

 and zero heat flux at the bottom of the thermocline: 

 UA T = at z = H + H m . 



Thus it is assumed that no energy escapes through the lower 

 boundary of the thermocline. Note that a T m and a T are 

 temperature changes of the mixed layer and the thermocline 

 between the initial time (1880) and time t. It is assumed that 

 in the year 1880 a T m = A T = ° and thus that the ocean 

 temperature was in a state of equilibrium with the atmosphere at 

 that time. 



Required input data are atmospheric CO2 levels on a yearly 

 or longer time period. Five-year estimates were obtained from 

 the ORNL, or alternatively, by multiplying a fixed-retention 

 factor times the interpolated five-year estimates of carbon 



