## 2 Materials and Methods
### Carbon Isotopocules and \({}^{iso}\)NEE  
The isotopocules \({}^{13}\)C\({}^{16}\)O\({}_{2}\), and \({}^{18}\)O\({}^{12}\)C\({}^{16}\)O data were measured between April and October from 2011 to 2013 at the Harvard Forest and quality-controlled as the dataset \"hf209-10\" [17] downloaded from [[https://harvardforest1.fas.harvard.edu/exist/apps/datasets/showData.html?id=209](https://harvardforest1.fas.harvard.edu/exist/apps/datasets/showData.html?id=209)]([https://harvardforest1.fas.harvard.edu/exist/apps/datasets/showData.html?id=209](https://harvardforest1.fas.harvard.edu/exist/apps/datasets/showData.html?id=209)) where a detailed explanation of the measurement system can be found. It has \({}^{13}\)CO\({}_{2}\) isoflaves and \({}^{12}\)CO\({}_{2}\) fluxes obtained at irregular intervals of around 40 min with an approximate 50% of missing data that were used to calculate \({}^{13}\)C yearly budgets. The isotopocules molar mixing ratios were measured by a quantum cascade laser spectrometer, which runs in a temperature-controlled enclosure. Then, they were calibrated on a 40-min interval by linear interpolation between two cylinders: a high span gas cylinder containing roughly 450 ppm CO\({}_{2}\) in air, and a low span cylinder containing roughly 350 ppm CO\({}_{2}\) in air. The total CO\({}_{2}\) molar mixing ratio (to dry air) and the isotope ratios were calculated from the individual isotopocule molar mixing ratios measured by the spectrometer. Eddy and storage fluxes for each isotopocule and for total CO\({}_{2}\), plus the eddy and storage isofluaves, were calculated by EC using wind data from the sonic anemometer that is operated as part of the existing long-term eddy flux measurement system. The results were priced in $50 tC\({}^{13}\)O\({}_{2}\) and $5150 tC\({}^{13}\)O\({}_{2}\) pricing scenarios (see pricing information below) with extrapolations to 300 ha and 40,468 ha, based solely on numerical projection to illustrate potential project revenue with increasing land area. To explore the relationship between \({}^{13}\)C and NEE from both datasets (\"US-Ha1 28-years\" and \"hf209-10\"), hourly \({}^{13}\)CO\({}_{2}\) means were used. All regressions and statistics were calculated using Python 3.7 and SciPy 1.4.1 library ([[https://docs.scipy.org/doc/](https://docs.scipy.org/doc/)]([https://docs.scipy.org/doc/](https://docs.scipy.org/doc/))). Isotopic measurements for \({}^{13}\)C are expressed as ratios in per mil (%) in standard notation relative to Vienna Pee Dee Belemmite (VPDB) standard [45]. The purpose of employing metric tons of \({}^{13}\)C\({}^{16}\)O\({}_{2}\), as defined for t\({}^{12}\)CO\({}_{2}\), is to further partition and quantify soil CO\({}_{2}\) respiration since \(R_{exo}\) as reported for NEE represents both soils based heterotrophic (R\({}_{h}\)) and vegetation based autotrophic (R\({}_{a}\)) carbon efflux measured during the night when GPP = 0. In contrast, isotopic flux partitioning (IFP) [16; 17; 18; 46] utilizes the inherent discrimination against the heavier carbon isotope (\({}^{13}\)C) resulting in fractionation at the leaf level by the Rubisco enzyme during photosynthesis between atmospheric and plant matter of up to \(\sim\)29 per mil (%) for plants with the C3 photosynthetic mode [26]. The isotopic imprint of reduced or isotopically lighter \({}^{13}\)C composition remains locked in plant matter until it is transferred to the atmosphere as \({}^{13}\)CO\({}_{2}\) during decomposition by microbes (e.g., R\({}_{a}\)) differentiating inspired from isotopically heavy tropospheric CO\({}_{2}\). The fractionation occurs instantaneously at the leaf level imprinting organic matter as substrate for respiration and isotopic measurement. The actual \(\delta^{13}\)C of vegetation and subsequent release of soil CO\({}_{2}\) via respiration for a given sample will vary across the temporal changes in atmospheric \(\delta^{13}\)C and rainfall experienced during growth among other factors [26].