CO₂ flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

Abstract. Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO₂) 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 CO₂ fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO₂ fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO₂ concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO₂ 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 CO₂ 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 CO₂ 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 CO₂ 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 CO₂ 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. CO₂ 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 CO₂ flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO₂ flux dynamics. The underestimation effect by linear regression was observed to be different for CO₂ uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO₂ balances than in the individual fluxes. To avoid serious bias of CO₂ flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.