Estimation of cumulative fluxes of nitrous oxide: uncertainty in temporal upscaling and emission factors

Nitrous oxide (N2O) is a greenhouse gas produced mainly by the microbial breakdown of agricultural fertilizer. 'Emission factors' (EFs, the fraction of nitrogen added that is released as N2O) are based on flux chamber measurements following the application of fertilizer. These measurements are very variable in space and time so that EFs are often uncertain, but this is rarely quantified. We developed a method that simplifies the calculation of EFs, incorporates prior knowledge and quantifies the uncertainty with a Bayesian approach to fit the parameters of a lognormal model. We compared this with the standard method for interpolating, extrapolating and integrating fluxes of N2O (trapezoidal integration). We verified both methods against process-based model output where the true integral was known and against eddy covariance data where the integral was estimated more accurately because of the greater spatial and temporal coverage. We used the process-based model to simulate flux chamber data and added a lognormal spatial distribution to the model output. The lognormal model performed better than the standard method, in terms of estimating the true underlying cumulative flux more accurately. Estimates based on chamber and eddy covariance data were sometimes substantially different, but with no clear systematic bias. The Bayesian approach with the lognormal model enabled us to combine both chamber and eddy covariance data to constrain cumulative fluxes. The standard trapezoidal method typically underestimates emission factors to some extent if fluxes are lognormally distributed in space. The Bayesian approach with the lognormal model is a robust method for quantifying the uncertainty in cumulative fluxes of N2O.