Path Integrals and Keeling Plots

Consideration is temporarily restricted to the case where 5p is constant through the canopy Taking the ensemble average of Eq. (32) and assuming (reasonably) that the covariance of fluctuations in c and 8 can be neglected relative to the mean products C d and CqSq, Eq. (32) yields 

Let /a and be the fractions of the total COj exchange due to assimilation and respiration, respectively, so that for a moving fluid particle, /a = 4 Adt)/( pdt) and similarly for f,. The definitions imply +fn= 1, with A usually larger than 1 and negative (when respiration is smaller in magnitude than assimilation). Using Eq. (32), it follows that 

Eeyuation (37) generalizes a relationship by Yakir and Wang (1996), who considered gradients above the canopy. It implies that if 5a and dp are uniform through the canopy (including both plant and soil surfaces), then measurements of 5a, 5p, and 5p can be used to partition the overall CO2 exchange into assimilation to plants and respiration from soil and plants. Of the three isotopic compositions, 5p is obtained from profiles of 5 and c in the air with Eq. (36), and 5a and 5p can be obtained from measurements on plant and soil material in the case of C. The situation for 0 is more complicated (Farquhar et al, 1993 Ciais and Meijer, 1998). 

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