Equation summary

The value of C_dry is the instantaneous water-corrected chamber CO₂ mole fraction called C'(t), as described in the LI-8100A (see equation 1‑18), LI-8250 (see equation A‑16), and 8200-01 Smart Chamber (see equation C‑15) manuals, given here as equation 9‑1.

9‑1

Its initial value is computed from the intercept of a linear regression of the first 10 points after the chamber closes. This is used as a parameter in the nonlinear regression that fits the equation 9‑1 to the C'(t) vs t data between the end of the deadband and the end of the observation. This regression yields values needed to obtain the soil CO₂ efflux rate. The discussion below describes how the appropriate slope of C_dry is computed and used to compute the final variables.

Computing the slope of C_dry requires a three-step process:

1. Fit C_dry vs E_time.
2. This is called function f(t), which is shown in equation 9‑1.
2. Compute time to such that

9‑2

1. where C₀ is the initial value of C_dry.
3. Compute the slope from the derivative of f(t) at time t₀.

9‑3

Standard error of this slope (used for the value of ∂C_dry/∂t) is given by

9‑4

where

9‑5

y_i are the individual C_dry values, f(t_i) are the computed C_dry values at Etime t_i, and n is the number of points used.

9‑6

where t is the mean E_time. The coefficient of determination R² of the fit (used of the value of CrvFit) is given by

9‑7

where

9‑8

where y is the mean C_dry value.

Flux is computed from equation 9‑9.

9‑9

The coefficient of variation (CV in %) of the flux F_c (used for the value of flux) is estimated by

9‑10

where E_p, E_t, and E_w are the assumed absolute errors or pressure, temperature, and water measurements. E_p, E_t, and E_w are all assumed to be 1.0.