Estimation of parameters in complex 15N tracing models by Monte Carlo sampling

Abstract The most widely used method to quantify gross N transformation rates in soils is based on 15 N dilution and enrichment principles. To identify rate parameters, 15 N-tracing experiments are analysed by models that are linked to algorithms that try to minimize the misfit between modelled and observed data. In currently available 15 N-tracing models optimization algorithms are based on the Levenberg–Marquardt method that is suitable for the determination of small number of parameters. Therefore, these models are restricted to a few processes. Methods based on Monte Carlo sampling have the potential to overcome restrictions on parameter numbers but have not been tested for application in 15 N-tracing models. Here, for the first time, we use a Markov chain Monte Carlo (MCMC) method with a tracing model to simultaneously determine the probability density functions (PDFs) of the whole set of parameters for a previously published data set [Muller, C., Stevens, R.J., Laughlin, R.J., 2004. A 15 N tracing model to analyse N transformations in old grassland soil. Soil Biology & Biochemistry 36, 619–632]. We show that the MCMC method can simultaneously determine PDFs of more than 8 parameters and demonstrate for the first time that it is possible to optimize models where transformations are described by Michaelis–Menten kinetics. Setting the NH 4 + oxidation rate to Michaelis–Menten kinetics reduced the misfit by 19%. Together with monitoring diagnostics for parameter convergence, the MCMC method is a very efficient and robust technique to determine PDFs for parameters in 15 N-tracing models that contain large number of N transformations and complex process descriptions.