Bayesian calibration of the nitrous oxide emission module of an agro-ecosystem model

Abstract

Nitrous oxide (${\text{N}}_2\text{O}$) is the main biogenic greenhouse gas contributing to the global warming potential (GWP) of agro-ecosystems. Evaluating the impact of agriculture on climate therefore requires a capacity to predict ${\text{N}}_2\text{O}$ emissions in relation to environmental conditions and crop management. Biophysical models simulating the dynamics of carbon and nitrogen in agro-ecosystems have a unique potential to explore these relationships, but are fraught with high uncertainties in their parameters due to their variations over time and space. Here, we used a Bayesian approach to calibrate the parameters of the ${\text{N}}_2\text{O}$ submodel of the agro-ecosystem model CERES-EGC. The submodel simulates ${\text{N}}_2\text{O}$ emissions from the nitrification and denitrification processes, which are modelled as the product of a potential rate with three dimensionless factors related to soil water content, nitrogen content and temperature. These equations involve a total set of 15 parameters, four of which are site-specific and should be measured on site, while the other 11 are considered global, i.e. invariant over time and space. We first gathered prior information on the model parameters based on the literature review, and assigned them uniform probability distributions. A Bayesian method based on the Metropolis–Hastings algorithm was subsequently developed to update the parameter distributions against a database of seven different field-sites in France. Three parallel Markov chains were run to ensure a convergence of the algorithm. This site-specific calibration significantly reduced the spread in parameter distribution, and the uncertainty in the ${\text{N}}_2\text{O}$ simulations. The model’s root mean square error (RMSE) was also abated by 73% across the field sites compared to the prior parameterization. The Bayesian calibration was subsequently applied simultaneously to all data sets, to obtain better global estimates for the parameters initially deemed universal. This made it possible to reduce the RMSE by 33% on average, compared to the uncalibrated model. These global parameter values may be used to obtain more realistic estimates of ${\text{N}}_2\text{O}$ emissions from arable soils at regional or continental scales.

Introduction

Soils are the main source of nitrous oxide (${\text{N}}_2\text{O}$) in the atmosphere, via the microbial processes of nitrification and denitrification. Because of its heavy reliance on synthetic N-fertilisers, agriculture has enhanced these two processes, as a result of which agro-ecosystems contribute 55–65% of the global anthropogenic emissions of ${\text{N}}_2\text{O}$. Compared to other ecosystem types or economic sectors, they are thus responsible for the major part of the atmospheric build-up of ${\text{N}}_2\text{O}$ (Smith et al., 2007). Compared to other greenhouse gases (GHG) such as ${\text{CO}}_2$, ${\text{N}}_2\text{O}$ fluxes are of small magnitude and highly variable in space and time, being tightly linked to the local climatic sequence and soil properties. Predicting ${\text{N}}_2\text{O}$ emissions from agro-ecosystems thus requires taking into account complex processes and interactions which originate from both environmental conditions and agricultural practices Duxbury and Bouldin, 1982, Grant and Pattey, 2003, Pattey et al., 2007. This poses a serious challenge to the estimation of the source strength of arable soils, which is currently mostly based on available statistics on fertiliser ignoring these environmental factors IPCC, 2006, Lokupitiya and Paustian, 2006. On the other hand, process-based agro-ecosystem models may in principle capture these effects, and have thereby a unique potential to predict ${\text{N}}_2\text{O}$ emissions from arable soils at the plot-scale as well as at regional and continental scales Butterbach-Bahl et al., 2004, Li et al., 2001, Gabrielle et al., 2006a, Del Grosso et al., 2006. Examples of biophysical ${\text{N}}_2\text{O}$-models include DAYCENT (Parton et al., 2001), DNDC (Li, 2000), FASSET (Chatskikh et al., 2005) and CERES-EGC (Gabrielle et al., 2006b). However, a major limitation to the wide-spread use of these models lies in the fact that their predictions are highly dependent on parameter settings, and carry a large uncertainty due to uncertainties in parameter values, driving variables and model structure (Gabrielle et al., 2006a).

Although model parameterization and uncertainty analysis are widely developed in the literature on agro-ecosystem models, they are rarely considered simultaneously Monod et al., 2006, Makowski et al., 2006. Bayesian calibration makes it possible to combine the two types of analysis by providing estimates of parameters values under the form of probability density functions (pdfs), which may be also propagated to model outputs as pdfs (Gallagher and Doherty, 2007). Probability density functions are initially the expression of current imprecise knowledge about model parameter values, this prior probability is then updated with the measured observations into posterior probability distribution by means of Bayes’ theorem (Makowski et al., 2006).

In ecological and environmental sciences, Bayesian calibration has been applied to a wide range of models Hong et al., 2005, Larssen et al., 2006, Ricciuto et al., 2008, and this field is developing actively, mainly using Markov Chain Monte Carlo (MCMC) methods to estimate the posterior pdf for the model parameters. The Bayesian methodology described by Van Oijen et al. (2005) was applied to dynamic process-based forest models with the objective of calibrating model parameters with various types of observed data from forested experimental sites Svensson et al., 2008, Klemedtsson et al., 2007. In these examples, Metropolis–Hastings MCMC-algorithm was used to generate samples from the posterior parameter distributions. Although there is an increasing body of the literature on the application of Bayesian approaches to environmental sciences, the latter have not been applied to process-based model of soil ${\text{N}}_2\text{O}$ emission models, to the best of our knowledge.

The overall purpose of this paper was thus to calibrate the parameters of the ${\text{N}}_2\text{O}$ emission module of the CERES-EGC agro-ecosystem model and to quantify uncertainty of model simulations by developing a suitable Bayesian calibration method. Data sets of measured ${\text{N}}_2\text{O}$ emission rates were collected from seven field-sites in Northern France, which represent major soil types, crops and management practices of the area. The Bayesian procedure was first applied separately to each experimental site, and secondly to the ensemble of the sites. This made it possible to explore the spatial variability of model parameters, and to test whether they could be considered as universal and with which uncertainty range.