Biogeosciences CO 2 flux determination by closed - chamber methods can be seriously biased by inappropriate application of linear regression

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO 2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO 2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO 2 fluxes are not constant during the closed chamber experiment , and no linear increase or decrease of CO 2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO 2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO 2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO 2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO 2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO 2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO 2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO 2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO 2 flux dynamics. The underestimation effect by linear regression was observed to be different for …