Assessment of random errors in multi-plot nitrous oxide flux gradient measurements

- A novel method calculated random errors of flux-gradient measurements of N2O fluxes.
- Errors of fluxes greater than 45 ng N m−2 s−1 were on average 9% of the measured flux.
- N2O fluxes close to zero had errors of similar magnitude to the flux.
- The value of random errors of 30-min N2O fluxes increased only with eddy diffusivity.
- Errors represented on average ±5.5% of the total annual N2O emissions.

The multi-plot flux-gradient (FG) technique is well-suited for non-intrusive measurements of agricultural N2O emissions for individually-treated field-scale plots across growing seasons at high temporal and spatial resolution. The degree of random error associated with N2O flux measurements is unknown; knowledge of these errors will increase confidence in the flux measurements and strengthen comparisons of total N2O emissions between treatments. An error estimation routine was developed to determine the random error (σ) associated with FG-measured fluxes (σF). The combination of a moving-block bootstrapping technique and the filtering method of Salesky et al. (2012) estimated the σ values for each variable used in calculating individual 30-min FG-derived fluxes. This error analysis was applied to a year-long dataset where a four-plot FG system measured N2O fluxes semi-continuously in a soybean field in Southwestern Ontario, Canada, with each plot having different treatments affecting N2O emissions. Errors of the concentration differences contributed the largest proportion to the σF values. The individual 30-min σF values did not correlate with the magnitude of the flux but were positively correlated with turbulence conditions. Random errors of N2O fluxes greater than 45 ng N m−2 s−1 had values representative of 9% of the measured flux, whereas error of fluxes close to zero frequently exceeded the value of the measured flux. Cumulating the errors over the experiment reduced the degree of error associated with the cumulated total N2O emissions with an average value of 31.5 g N ha−1, which represented on average ±5.5% of the total N2O emissions. The proposed framework is applicable to other scalar fluxes being determined by the flux-gradient method.