Ecological Archives E090-192-A2

Carlos A. Sierra, Henry W. Loescher, Mark E. Harmon, Andrew D. Richardson, David Y. Hollinger, and Steven S. Perakis. 2009. Interannual variation of carbon fluxes from three contrasting evergreen forests: the role of forest dynamics and climate. Ecology 90:2711–2723.

Appendix B. A probabilistic argument to explain less carbon storage under the variable climate scenario.

In general, STANDCARB models the effect of temperature T on autotrophic and heterotrophic respiration using a Q10 factor and an equation of the form:

(B.1)

Where R represents the respiration rate of a given carbon pool, and R10 the respiration rate of that pool at 10°C. Equation B.1 is a convex function with respect to temperature.

Because we are interested in obtaining a measure of central tendency using equation (B.1), we can calculate either the expected value of the function, i.e., E[f(T)], or evaluate the function at the expected value of the random variable, i.e., f(E[T]). These two cases correspond to the variable and constant climate scenarios used in our simulations, respectively.

(B.2)

Equation B.2 is commonly known as Jensen’s inequality in probability theory. From this equation we can infer that the average respiration rate will always be higher under the variable climate scenario than the respiration rate of the average temperature. This respiration function will also produce larger respiration fluxes with small but finite probabilities because the resultant probability distribution for respiration is skewed to larger values.


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