94 BACASTOW AND KEELING 



LAND-BIOTA GROWTH FACTOR 



lr is not clear to us how best to model an increasing land biota, either to 

 explain past perturbations in the carbon cycle or to make future predictions. 

 Lacking detailed information on plant responses to changes in atmospheric C0 2 

 concentration, we have assumed the flux from the atmosphere to the long-lived 

 biota, F a h, and the return flux, Fb a , to be proportional to the total carbon in 

 the long-lived biota, N5. The model thus conforms to an intuitive picture that 

 the long-lived biota grows and respires in proportion to the mass of long-lived 

 plants. Roughly in accordance with the response of annual plants in glass- 

 houses, 24- ^ } we further assume that the flux from the atmosphere increases as 

 the logarithm of the atmospheric carbon mass, N a . Thus we write 



F a b = F bo 



'♦"■(£)](£) 



'°(^) 



Fba = F b or 7 iL < 3 > 



where F^o is the preindustrial (steady state) value of F a b and Fb a > and N a0 and 

 Nbo are preindustrial values of N a and N^,. The factor j3 is an adjustable 

 parameter that reflects the degree of C0 2 fertilization; it will be called the biota 

 growth factor. For small increases in N a and Nb, as have occurred up to now, if 

 Eqs. 2 and 3 hold, the net flux to the long-lived biota is given to a close 

 approximation by 



/Na"Nao\ 



Fab - Fba ^-^j (4) 



i.e., if the atmospheric C0 2 concentration increases by x %, the long-lived biota 

 assimilates carbon at a net rate |3x% higher than in the preindustrial atmosphere. 

 The formulations of the fluxes to and from the short-lived biota, F ae and 

 F ea , are similar, except that F ae is taken as proportional to the carbon mass of 

 the long-lived biota, Nb, because well over half the short-lived biota growth is 

 associated with long-lived plants: 



F --4 + ' h (£)](£) 



F ea - Feo (^) (6) 



where F e0 is the preindustrial value of F ae and F ea , and N e0 is the preindustrial 

 value of N e . Because Eq. 5 implies a considerably greater restraint on the growth 

 of short-lived plants than a similar expression with F ae proportional to the 

 carbon mass of the short-lived biota, N e , the growth factor,/?, is considerably 

 larger for a given uptake of industrial C0 2 than if both biota reservoirs grew in 



