Uncertainties of nonlinearly estimated parameters from incubations of soil organic matter

Parameters of first-order mineralization models are commonly estimated from incubation experiments by using nonlinear estimation techniques. The impact of incubation length and especially more or less small measurement errors on estimated mineralization parameters is largely unknown. The objective of this paper is to analyze the influence of errors in mineralization measurements on the nonlinearly estimated parameters, and to find out how the certainty of parameters can be enhanced. CO2 evolution from organic material (forest floor, L layer) of an acid sandy podzol under pine (Pinus silvestris L.) is taken as an example. For the nonlinear parameter estimation, Marquardt's method is used, and to evaluate uncertainties of estimated model parameters, Monte-Carlo simulations are performed. The results demonstrate that really small measurement errors in the order of random and unavoidable experimental errors may cause serious uncertainties (about 50%) in the estimated parameters. Parameter uncertainties are the same for cumulative or rate measurements and models. The evaluations based on MonteCarlo simulations show that measurement accuracy and incubation length are key factors for the certainty of estimated parameters. Any decrease of measurement errors results in a disproportionate enhancement of parameter certainty. An increase of incubation length up to about 80 % of the time needed to reach 90 % of the maximum cumulative mineralization, t(90), is optimal to minimize parameter uncertainty. This optimal incubation length is commonly not known a priori because t(90) depends on the a priori unknown mineralization kinetics. A practical way for its determination is an accompanying estimation of the parameters while the incubation is going on, and the experiment may be terminated when incubation length has reached about 80% of the estimate of t(90).