A Mean-Variance Approach for Describing Organic Matter Decomposition

Organic matter decomposition models based on a continuous distribution of reactive types can be modified to include both the mean (k̄) and the variance (s2k) of the distribution. This mean-variance approach to modeling is useful for describing how the parameters of a distribution affect the expected value of the decomposition rate. A gamma distribution of organic matter reactivities is a particularly useful model of the initial distribution g(k, 0). It is characterized by two parameters, v and 1/a, which describe the shape and scale of the distribution, respectively. Analysis of decomposition isopleths for combinations of mean and variance reveals that more reactive organic matter mixtures plot higher than less reactive ones within a [k̄, s2k ] co-ordinate system, and the decomposition rate is constrained by a line drawn from the origin to a tangential point on its isopleth. The slope of this line is equal to 1/a, the scale parameter of its gamma distribution. As decay proceeds, the rate constant of the total mixture decreases with the slope of its tangential line, and the variance tends toward zero more rapidly than the mean. This is due to the preferential removal of the more reactive organic matter components, causing the distribution to shift to the left. A mean-variance decomposition model may lead to more accurate estimates of the short-term decomposition rate but only for organic matter mixtures characterized by large values of v or 1/a.