70 



EKDAHL AND KEELING 



am 



= 6 years 



TABLE 1 



PARAMETERS FOR RESERVOIR MODELS 



Five-Reservoir Model: Standard Case 



Transfer times 



*Atmosphere — surface ocean layer 



(air— sea) 

 *Deep ocean — surface ocean layer 

 Mass of inactive carbon in reservoirs 

 *Surface ocean layer 

 tTotal ocean 



Short-lived land biota 



Long-lived land biota 

 *Total land biota 



Atmosphere 



T dm = 1500 years 



N 



mo 



2.0 N 



N mo + N do 



ao 

 63.0 NL 



ao 



N eo = 0.0459 (N eo + N bo ) 

 N bo = 0.9541 (N eo + N bo ) 



N eo + N bo = 2-65 N ao 

 N ao = 6.156 x 10 17 g 



Inactive-carbon production rates 

 for land biota 

 Short-lived 

 Long-lived 



F eo = 3.0 x 10 16 gyear" 1 

 F bo = 2.6 x 10 16 gyear" 1 



Six-Reservoir Model: All Cases 



Transfer time 



Upper atmosphere — lower 

 atmosphere 



Mass of inactive carbon in reservoirs 

 Upper atmosphere (stratosphere) 

 Lower atmosphere (troposphere) 



t u \ = 2 years 



N 



0.15N, 



uo "•■* J '^ao 

 Ni = 0.85 N ao 



* Parameters were varied in nonstandard cases. 



tFor nonstandard cases this mass varies slightly to conform to the 

 model equations given in Appendix C of the next paper (part II). 

 (These equations assign constant values to the concentrations of 

 carbon in the surface and deep-ocean layers and to the total volume 

 of ocean water; the calculated value of Nj thus depends on the ratio 

 N mo /N ao which may vary from case to case.) 



Eqs. 4 and 5. We have verified that the system of equations for the six-reservoir 

 model is mathematically stable for any set of positive transfer coefficients at any 

 oscillation frequency. Also, we have determined that linearizing the governing 

 transfer equations is justified because of the small relative variations in carbon 

 distribution during the period of interest (prior to nuclear weapons testing). 

 Accordingly (see Appendix A), we have derived for the six-reservoir model with 

 an oscillating stratospheric source, the transfer-function ratio Zi (to)/Zi (0), ap- 

 propriate to the lower atmosphere, and obtained the attenuation and phase shift as 

 a function of the frequency to based on a representative set of model parameters 

 (Table 1). For comparison we have also computed the attenuation and phase 

 shift for the one-parameter model of Grey and Damon 25 and a five-reservoir 



