# Minimizing the Impact of Changes to the CO2 Diffusion Gradient

CO2 moves out of the soil primarily by diffusion, and the diffusion rate depends on the CO2 concentration gradient in the upper layers of soil. Increasing CO2 concentration in the chamber affects the gradient, and will suppress the CO2 flux. Therefore, accurate measurements of soil CO2 flux require that the CO2 concentration in the chamber is the same as the CO2 concentration in the air.

This presents us with a paradox: An increase in CO2 concentration in the chamber causes a reduction in the diffusion rate, but you need the CO2 concentration to increase in the chamber to measure the flux rate. So, we deal with this problem using a model.

Early studies often used a linear regression to determine the CO2 flux. Experimental data show, however, that linear regression results in significant underestimation of CO2 flux, and that the underestimation is greater for porous soil.

Therefore, we use an exponential function to account for the altered diffusion gradient (Equation 1), where C’ is the instantaneous water vapor dilution corrected chamber CO2 mole fraction. With the initial slope (∂C’/∂t at t=0) of the fitted function (Equation 2), the flux is estimated at the time of chamber closing, when C is close to the ambient level.

(1)

$C\prime ={C\prime }_{s}+\left[{C\prime }_{\left(0\right)}-{C\prime }_{s}\right]{\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}e}^{-at}$

(2)

$\frac{\partial C\prime }{\partial t}=a\left[{C\prime }_{s}-{C\prime }_{\left(0\right)}\right]{\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}e}^{-at}$

where Cs is the CO2 concentration in the soil surface layer communicating with the chamber (µmol mol-1), and a is a rate constant (s-1).

Calculating the flux from the measured data, then, is accomplished with the following equation:

${F}_{c}=\frac{{10VP}_{0}\left(1-\frac{{W}_{0}}{1000}\right)}{RS\left({T}_{0}+273.15\right)}\frac{\partial C\prime }{\partial t}$

where Fc is the soil CO2 flux rate (µmol m-2 s-1), V is volume (cm3), P0 is the initial pressure (kPa), W0 is the initial water vapor mole fraction (mol mol-1), S is soil surface area (cm2), T0 is initial air temperature (°C), and ∂C'/∂t is the initial rate of change in water-corrected CO2 mole fraction (µmol mol-1 s-1).

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