Summary:

## Calculating 13C and 14C Flux

The general formula for calculating the flux of 13C (CF_13C) and total carbon (CF_totC) is:

CF_13C = (CF_totC * CS_13C_up / CS_totC_up) * f_frac

Where:
- CS_13C_up and CS_totC_up are the masses of 13C and total C in the upstream pools, respectively.
- f_frac is the fractionation factor.

If f_frac = 1.0, there is no fractionation, and the 13C and total C fluxes are proportional to the upstream masses.
Values of f_frac < 1.0 indicate discrimination against the heavier 13C isotope, while f_frac > 1.0 indicates a preference for 13C.

Currently, f_frac is always set to 1.0 when calculating 13C flux.

For 14C flux, no fractionation is used, as the measurements are typically corrected for 14C fractionation by referencing them to 13C ratios.