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

Dhanoa, M.S., Louro, A., Cardenas, L.M., Shepherd, A., Sanderson, R., Lopez, S., France, J.
Atmospheric environment 2020 pp. 117500
agricultural land, atmospheric chemistry, carbon dioxide, greenhouse gas emissions, greenhouse gases, inventories, lognormal distribution, nitrous oxide
In this study, we draw up a strategy for analysis of GHG field data. The distribution of greenhouse gas (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 mean of carbon dioxide (CO₂) and nitrous oxide (N₂O) flux data measured in an agricultural field. The option of transforming CO₂ flux data to the Box-Cox scale in order to make the distribution normal, was also investigated. The results showed that average CO₂ value estimates from GEV are less affected by data in the long tail compared to the sample mean. The data for N₂O flux were much more complex than CO₂ 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 CO₂ sample mean of 65.62 (mean log-scale 65.89) kg CO₂–C ha⁻¹ d⁻¹ was reduced to GEV mean of 60.14 kg CO₂–C ha⁻¹ d⁻¹. The arithmetic N₂O sample mean of 1.038 (mean log-scale 1.038) kg N₂O–N ha⁻¹ d⁻¹ was reduced to GEV mean of 0.01571 kg N₂O–N ha⁻¹ d⁻¹. Our analysis suggests that GHG data should be analysed using the GEV method, including a Box-Cox transformation when negative data is present, 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 help minimise any biases in the data.