## 4 Discussion  
The three-gas flux inventory (CO\({}_{2}\), CH\({}_{4}\), N\({}_{2}\)O) for the Howland Forest [38] demonstrates the commercial promise of expanding direct measurement of forest GHGs, an area of research with limited results [27; 54]. The Howland forest project provides an example of net GHG emission footprints coupled with external factors, such as the social cost of GHG emissions [33; 55; 56], across select areas of the Howland site, resulting in a single value of merit for holistic forest management of global warming. The Howland Forest was a net sink for CO\({}_{2}\) and CH\({}_{4}\), except for 2014 during the 2012 to 2016 interval for US-Ho1 Figure 4A). Soil accumulation chamber data also consistently demonstrated a sink for CH\({}_{4}\) and N\({}_{2}\)O but a source for CO\({}_{2}\) (Figure 4A). While CH\({}_{4}\) and N\({}_{2}\)O emissions are 11,200 (Figure 4A) and 828,000 (Figure 4B) orders of magnitude lower than corresponding CO\({}_{2}\) fluxes, respectively, they have higher social cost factors relative to CO\({}_{2}\) (USD $51) of $1500 (28-36x CO\({}_{2}\)) and $18,000 (265-298x)x CO\({}_{2}\)), respectively, calculated for the year 2021 with a 3% discount rate [33]. Projected GHG social cost forest (GHG-SCF) offset products for the Howland project area of 557 acres and extrapolated, for illustration purposes only, to 40,000 acres for 2021 and 2040. Figure 5A-D ranges from (USD) $12,000 (2021, 557 acres) to $12,000,000 (2040, 40,000 acres) (Figure 5A-D). Thus, the contribution of small forest fluxes of non-CO\({}_{2}\) GHGs can result in comparatively large revenue benefits that should not be ignored [38] in forest management programs. The GHG-SCF, as employed in this study, is intended to reflect the societal value of reducing emissions of GHG forest species by one metric ton per year. In principle, the GHG-SCF product includes the value of all climate change impacts, including (but not limited to) changes in human health effects, net agricultural productivity, property damagefrom increased flood risk and natural disasters, risk of conflict, environmental migration, and the value of ecosystem services, including those provided by forests [33]. Presently, the variables and mechanisms, such as soil composition, site land-use history, species and age of trees, seasonality, rainfall, and topography, regulating forest GHG gas exchange are not well understood, emphasizing the importance of expanded monitoring of diverse forests [29; 54; 57]. Direct measurement of GHG-SCF should be an integral part of the realization of green policies (e.g., Green New Deal), providing links to established policy criteria to reduce GHG emissions [33] employing nature-based solutions [12]. The importance of forest carbon respiration to validate net carbon sequestration for Howland is emphasized in Figure 3A,B, showing annual steps in \(\mathrm{R_{eco}}\) relative to GPP. Figure 3A,B demonstrates that for every annual interval of photosynthetic uptake of CO\({}_{2}\) (GPP), there is an obligatory response embodied in \(\mathrm{R_{eco}}\)[53] or automatic debit to stored carbon intended for carbon trading markets. US-Ho1 \(\mathrm{R_{eco}}\) vs. GPP for 2008, the initial year of CAR681, yielding a total of 43,687 carbon credits (\(-5334.7\)\(\mathrm{g\ cm^{-2}\ y^{-1}}\)) (Supplement Table S2), falls within the lower left quadrant of the FLUXNET slope for \(\mathrm{R_{eco}}\) and GPP values, Figure 3B, lower than most annual intervals. The CAR681 2008 value would require \(\mathrm{R_{eco}}\) and GPP values of 2667, in the case of the identity line relationship (e.g., \(\mathrm{R_{eco}}\) = GPP; NEE = 0), clearly outside of the Ho1-3 values; requiring higher values for GPP if considering the regression line for all Ho1-3 data (red regression line). US-Ho1, 2016, showed the highest GPP relative to \(\mathrm{R_{eco}}\), while US-Ho3 values for 2004-2006 exhibit high respiration relative to GPP.