Beyond the logistic growth model for nitrous oxide emission factors from agricultural soils

Measurement of nitrous oxide emission in the dairy farm is a time-consuming process. The alternative approach is to run a realistic process-based model. The NZ-DNDC model is capable of generating reasonable results in a short time. The model is driven by weather and soil parameters that have a high degree of temporal (weather) and spatial (soil properties) variability. This variability in soil and weather parameters leads to uncertainty in the predicted nitrous oxide emissions. This paper examines the possibility of developing a simplified model to investigate the effects of variation in individual weather or soil parameters on nitrous oxide emission. This study undertakes to apply the logistic growth model with secondary growth effects to model the growth of the nitrous oxide emission factor with environmental variables. The generalized model considered here allows for the inclusion of secondary growth with the addition of only one extra parameter, unlike many bi-logistic growth models which double the number of parameters. The model has the capability to generate the generalized logistic behavior as well as a number of different realistic growth and decay behaviors. A nonlinear least-squares regression algorithm is described that provides parameter estimates from time-series growth data. This is an iterative process that starts with an initial realistic guess of the parameters. The modified technique presented here computes the correction term which is multiplied to the old parameter to get the new value. This is a more robust technique that allows for a little non-linearity around the solution. Model sensitivity and robustness are discussed in relation to error structure in the data. Taxonomy and examples of systems of greenhouse gas emission that exhibit secondary growth or decay are presented. The model is shown to be superior to the simple logistic model for representing many growth processes.