A strategy for modelling heavy-tailed greenhouse gases (GHG) data using the generalised extreme value distribution: Are we overestimating GHG flux using the sample mean?

In this study, we draw up a strategy for analysis of greenhouse gas (GHG) field data. The distribution of GHG flux data generally exhibits excessive skewness and kurtosis. This results in a heavy tailed distribution that is much longer than the tail of a log-normal distribution or outlier induced skewness. The generalised extreme value (GEV) distribution is well-suited to model such data. We evaluated GEV as a model for the analysis and a means of extraction of a robust average of carbon dioxide (CO ₂) and nitrous oxide (N ₂O) flux data measured in an agricultural field. The option of transforming CO ₂ flux data to the Box-Cox scale in order to make the distribution normal was also investigated. The results showed that average CO ₂ estimates from GEV are less affected by data in the long tail compared to the sample mean. The data for N ₂O flux were much more complex than CO ₂ flux data due to the presence of negative fluxes. The estimate of the average value from GEV was much more consistent with maximum data frequency position. The analysis of GEV, which considers the effects of hot-spot-like observations, suggests that sample means and log-means may overestimate GHG fluxes from agricultural fields. In this study, the arithmetic CO ₂ sample mean of 65.6 (mean log-scale 65.9) kg CO ₂–C ha ⁻¹ d ⁻¹ was reduced to GEV mean of 60.1 kg CO ₂–C ha ⁻¹ d ⁻¹. The arithmetic N ₂O sample mean of 1.038 (mean log-scale 1.038) kg N ₂O–N ha ⁻¹ d ⁻¹ was substantially reduced to GEV mean of 0.0157 kg N ₂O–N ha ⁻¹ d ⁻¹. Our analysis suggests that GHG data should be analysed assuming a GEV distribution of the data, including a Box-Cox transformation when negative data are observed, rather than only calculating basic log and log-normal summaries. Results of GHG studies may end up in national inventories. Thus, it is necessary and important to follow all procedures that contribute to minimise any bias in the data.