Sequestering carbon and improving soil fertility; Validation of an improved method for estimating CO2 flux

• Constrained cubic spline interpolation may be ideal for estimating flux.
• Natural cubic spline interpolation may be used to identify outliers.
• Cross validation may be suitable for comparing interpolation techniques.

Carbon dioxide flux to the atmosphere is the major pathway whereby carbon is lost from agricultural soils. Linear interpolation has traditionally been used to estimate soil CO2 flux in lab-based studies but the resulting curves are not representative of biological systems. The objective of this study was to examine the effectiveness of linear, natural cubic spline and constrained cubic spline interpolation models for estimating CO2 flux from contrasting soils under different management regimes. Cross-validation techniques were employed to examine the predictive accuracy, overshoot/undershoot behavior, smoothness and deviation of cumulative CO2 flux estimates of each approach. The predictive accuracy of the interpolation models differed with soil type and between amended and unamended soils. Predictive accuracy also decreased with increased interval length though being sensitive to the nature of the region being estimated. Linear interpolation accurately predicted most measured data points and had a low spread of potential cumulative CO2 flux values (between 154% and − 54%) but produced non-smooth curves. Natural cubic spline interpolation produced relatively smooth curves but had low predictive accuracy and high variability in potential cumulative CO2 flux values (between 528% and − 617%). Constrained cubic spline interpolation produced the smoothest curves while its predictive accuracy and spread of potential cumulative CO2 flux (between 175% and − 53%) was comparable to that of linear interpolation. These results demonstrate that the constrained cubic spline interpolation technique offers improvements over linear interpolation for estimating soil CO2 flux.