Howland Forest, ME, USA: Multi-Gas Flux (CO 2 , CH 4 , N 2 O) Social Cost Product Underscores Limited Carbon Proxies

: Forest carbon sequestration is a widely accepted natural climate solution. However, methods to determine net carbon offsets are based on commercial carbon proxies or CO 2 eddy covariance research with limited methodological comparisons. Non-CO 2 greenhouse gases (GHG) (e.g., CH 4 , N 2 O) receive less attention in the context of forests, in part, due to carbon denominated proxies and to the cost for three-gas eddy covariance platforms. Here we describe and analyze results for direct measurement of CO 2 , CH 4 , and N 2 O by eddy covariance and forest carbon estimation protocols at the Howland Forest, ME, the only site where these methods overlap. Limitations of proxy-based protocols, including the exclusion of sink terms for non-CO 2 GHGs, applied to the Howland project preclude multi-gas forest products. In contrast, commercial products based on direct measurement are established by applying molecule-speciﬁc social cost factors to emission reductions creating a new forest offset (GHG-SCF), integrating multiple gases into a single value of merit for forest management of global warming. Estimated annual revenue for GHG-SCF products, applicable to the realization of a Green New Deal, range from ~$120,000 USD covering the site area of ~557 acres in 2021 to ~$12,000,000 USD for extrapolation to 40,000 acres in 2040, assuming a 3% discount rate. In contrast, California Air Resources Board compliance carbon offsets determined by the Climate Action Reserve protocol show annual errors of up to 2256% relative to eddy covariance data from two adjacent towers across the project area. Incomplete carbon accounting, offset over-crediting and inadequate independent offset veriﬁcation are consistent with error results. The GHG-SCF product contributes innovative science-to-commerce applications incentivizing restoration and conservation of forests worldwide to assist in the management of global warming.


Introduction
Uncertainty and high cost of typical commercial forest carbon offset protocols are unresolved [1][2][3][4][5][6], impeding widespread adoption and expansion of forest conservation projects. The main endeavor of commercial forest carbon offset trading is to assist landowners with the conservation and restoration of forests based on the net carbon sequestration and carbon credit sales for a project [7,8] while verifiably reducing net emissions. While forest restoration is recognized as a viable, economic, and readily deployable nature-based commercial solution to mitigate climate change [9][10][11][12][13][14], forest loss continues at a rate of 10 million hectares annually from 2015-2020 [15], outpacing restorative efforts. In contrast, the forest landscape conserved by carbon protocols and trading is astonishingly small, 0.03% of the available land for restoration of~0.9 billion hectares [12,15], evidence that existing methods underpinning forest carbon are not economically or ecologically viable. Forest carbon sequestration credits, typically derived from sparse forest mensuration (6-or 12-year timber inventory) [16][17][18] surveys for above-ground carbon and use of multiple, carbon denominated growth models [18][19][20], by default, exclude direct measurement of GHG's, limiting innovative commercial applications.

CO2 and CH4 Tower Fluxes
Howland has the second longest-running flux record in the United States, dating back to 1996 (the longest belonging to Harvard Forest). These 20 years of data provide a time-series long enough for robust analyses of relationships between NEE and various environmental variables. CO2 fluxes used in this study were measured above the canopy at a 29 m tower with the eddy covariance technique since 1996 (US-Ho1; "the main tower"), from 1999 to 2004 (US-Ho2; "west tower"), and from 2004 to 2007 (US-Ho3). US-Ho1 includes CH4 measurements from 2012 to 2018, and it is approximately 775 m apart from US-Ho2. The additional tower, US-Ho3, was used to monitor NEE after a shelterwood harvest [43]. Removal of biomass from the project area was negligible for the areas represented by US-Ho1,2, while US-Ho3 experienced the planned shelterwood harvest to

CO 2 and CH 4 Tower Fluxes
Howland has the second longest-running flux record in the United States, dating back to 1996 (the longest belonging to Harvard Forest). These 20 years of data provide a time-series long enough for robust analyses of relationships between NEE and various environmental variables. CO 2 fluxes used in this study were measured above the canopy at a 29 m tower with the eddy covariance technique since 1996 (US-Ho1; "the main tower"), from 1999 to 2004 (US-Ho2; "west tower"), and from 2004 to 2007 (US-Ho3). US-Ho1 includes CH 4 measurements from 2012 to 2018, and it is approximately 775 m apart from US-Ho2. The additional tower, US-Ho3, was used to monitor NEE after a shelterwood harvest [43]. Removal of biomass from the project area was negligible for the areas represented by US-Ho1,2, while US-Ho3 experienced the planned shelterwood harvest to record changes in NEE [43]. More in-depth details about flux and footprint measurements and preprocessing can be found at [38,40,41]. Preprocessed data before filtering and gap-filling can be found at the AmeriFlux website (https://ameriflux.lbl. gov/sites/site-search/#keyword=Howland (accessed on 27 March 2021) [38]. More details can be found at [44,45]. The data can be downloaded from [38].

Data Processing and Calculations
CO 2 eddy covariance data were processed with REddyProc 1.2.1 [46], which filters low turbulence data using the methodology from [47] (with the 50-percentile criterion) and then fills all the gaps produced by the filtering technique or by instrument failure with a lookup table. The soil temperature at the lowest depth was chosen as the input variable for REddyProc along with the above canopy air temperature (T air ), the vapor pressure deficit and the photosynthetic photon flux density divided by 0.47 as global radiation.
Ecosystem respiration (R eco ), its photosynthesis (gross primary productivity; GPP) and NEE are related according to the equation: In this study, R eco was estimated with REddyProc based on the nighttime approach [21,22], which fits the Lloyd and Taylor [48] model for respiration (Equation (2)) using only nighttime data, because NEE = R eco at night, and then extrapolating the parameters R ref and E 0 found in the regression to calculate daytime R eco (T ref and T 0 are fixed). Then, GPP is calculated with Equation (1) [49].
Afterward, yearly NEE, R eco and GPP sums were calculated in Python 3.7.7. In the literature, NEE can also be expressed as net ecosystem production (NEP), where NEP = NEE [50].

GHG Forest and Social Cost of CO 2 , CH 4 and N 2 O
Values in USD for the social cost of GHGs were adopted from the Interagency Working Group on Social Cost of Greenhouse Gases, United States Government [33]. The social cost values were applied to net emissions for US-Ho1 and for soil chamber measurements to introduce a new GHG social cost forest (GHG-SCF) product that integrates the three gases into a single value of merit for holistic forest management of global warming.

Howland Eddy Covariance Footprint Data
A composite footprint map was made by overlapping layers in Figure 1. The bottom layer consists of a satellite image showing the complete Howland research area redrawn from https://umaine.edu/howlandforest/about/. Then, the CARB measurements area with its plots were redrawn from [17] and overlapped. The top layers are the footprint monthly climatology maps that are in the dataset S3 downloaded from https://zenodo. org/record/4015350 with their backgrounds removed and centered at each tower location. All the Howland footprints available were used (2013 to 2017 for Ho1, and 2003 to 2008 for Ho2 and Ho3). Tower locations and reference circles were highlighted for comparison.

CARB-CAR Data, Documents and Third-Party Verification Review
CARB-CAR Forest methods exclude CO 2 measurement relying upon forest mensuration and growth models operationalized over a mandated 100-year project monitoring interval as employed by the California Air Resources Board and Climate Action Reserve [18][19][20]51]. Howland Forest protocol data for CAR 681 and CAR 1168 results and thirdparty verification documentation were obtained from the Climate Action Reserve (https: //www.climateactionreserve.org/, accessed on 16 February 2021) and the California Air Resources Board (https://ww2.arb.ca.gov/our-work/programs/compliance-offset-program, accessed on 16 February 2021) websites and documents available therein. Supplement Tables S1-S5 provide links to project data and document repositories, cumulative carbon credit performance reports with serial numbers, and historical summary of the CARB-CAR carbon offset supply chain for CAR 681 and CAR1161 and advances in Howland Forest carbon research. Regulations for satisfying AB32 compliance criteria were based on the California Code of Regulations, Title 17, Division 3, Chapter 1, Subchapter 10, Article 5, Sub article 14, Section 95,977(d). Additional information on the CARB mandatory verification process can be found here: https://ww2.arb.ca.gov/our-work/programs/complianceoffset-program/offset-verification, accessed on 16 February 2021.

Results
The results are presented in Figures 2-5 with supplemental material as indicated. Figure 2 shows the complete GHG record for Howland Forest tower sites (US-Ho1,2,3) expressed in units of gC m −2 y −1 and as tCO 2 acre −1 y −1 . Errors are graphed based on CARB-CAR relative to NEE results. Figure 3 provides the underlying annual R eco, and GPP data plotted to illustrate the large variance of the R eco /GPP ratio across sites and years. Figure 4 shows the Howland GHG record, including soil chamber data for CH 4 and N 2 O. Figure 5 monetizes the data in Figure 4 based on data provided for each gas's reported social cost for a given year and discount rate.  Table S6.   Table S6. 1999 to 2009 (10 years; at 95%, the approximate t-threshold is 2.2), consistent with [41]. US-Ho3 documents the recovery of NEE after a shelterwood harvest. The absolute and percentage error of CARB-CAR data relative to NEE data ranges from 0.65 tCO2 ac −1 y −1 , 25.7% to 75.9 tCO2 ac −1 y −1 , and 2258% for the years 2011 and 2008, respectively, if US-Ho1 yearly values are taken as the representative values. CARB-CAR protocol requires a forest inventory on a 12-year basis, reflecting the reliance on annual model simulations in lieu of empirical data (Project Design Document, page 22, Supplement Table S5, Doc # 3).  years, while (B) shows only those in the ranges (1050; 1400) and (1250; 1600) gC m y for Reco and GPP, respectively. Individual years are identified in B); years with higher GPP relative to Reco likely store more carbon relative to annual records for carbon sequestration shown; larger GPP is offset by larger Reco. Outliers in 3-A for US-Ho1 and US-Ho2 (filled blue circles) from lowest to highest GPP are US-Ho1 (2015)    soil chamber data are net negative, resulting in a net positive flux for the soil areas sa pled of 25.7 CO2e [38], based on the limited chamber data available. Mean CO2 and C measured at the three towers were −10.76 and −0.03 metric tons per hectare, respectiv while CO2, CH4 and N2O mean measured at the soil chambers were 25.8, −0.13 and −0.0 metric tons per hectare, respectively. Note, however, that the Howland forest is cons ently a sink for CH4 and N2O for the limited periods observed.       [38], based on the limited chamber data available. Mean CO 2 and CH 4 measured at the three towers were −10.76 and −0.03 metric tons per hectare, respectively, while CO 2 , CH 4 and N 2 O mean measured at the soil chambers were 25.8, −0.13 and −0.0037 metric tons per hectare, respectively. Note, however, that the Howland forest is consistently a sink for CH 4 and N 2 O for the limited periods observed. Figure 5 shows the monetization of the integrated average annual GHG social cost for forests (GHG-SCF), (gray bar) for the Howland Forest project (~557 acres) based on the measurement of CO 2 , CH 4 and N 2 O at the US-Ho1 tower, or from soil chambers, using estimates for the social cost factor (USD) for each gas for a given year (e.g., USD $52, $15,000, $19,000 for 2021, and $73, $2500, and $28,000 for 2040, for CO 2 , CH 4 and N 2 O, respectively) [33]. For illustration purposes only, the US-Ho1 measurements were extrapolated to 40,000 acres to demonstrate the potential revenue over larger forest areas. Projections account for social value estimates in 2021 and in 2040. A discount rate of 3% was applied to the values for each gas according to [33], yielding projected project average annual GHG-SCF values (USD) of $124,000 (2021 values, 557 acres) up to $12,200,000 (2040 values, 40,000 acres). Although biomass removal from the Howland Forest project areas (US-Ho1,2) was minimal over the interval of GHG flux measurements, shelterwood harvests would likely reflect the loss of canopy and the resulting reduction in GHG-SCF product value, a trend observed in [43].

Monetization of Net GHG Data Using Social Cost Factors and Revenue Projections
CARB-CAR Forest Carbon Supply Chain. Supplement Tables S1-S5 and Document S6 describe the carbon credit supply chain for CARB-CAR forest carbon projects. Supplement Table S1 identifies the transition of CAR681, an improved forest management project (IFM), from an early action project to an eligible ARB compliance project CAR1161 or CAFR5161 listed on 26 February 2015; total offset credits registered for both project numbers are available through the links provided. Supplement Tables S2 and S3 identify the date of issue for specific vintage years and serial numbers for CAR681 and CAR1161, respectively. Supplement Table S4 lists the project documents for CAR681 and CAR1161, covering project data reporting, project design, carbon pools used in calculations and verification documents with dates of entry for each into the CARB regulatory registry. A full verification report for CAR681 credits issued was uploaded on 11 March 2015 (Item 1, SCS Global Services), completing the supply chain for CARB markets for the cap-and-trade AB32 legislated system [16]. A full verification statement is not available for CAR1161 offsets. See Supplement Document S6 for additional details of the analyses presented in Supplement Tables S1-S5.

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 damage from 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 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 R eco [53] or automatic debit to stored carbon intended for carbon trading markets. US-Ho1 R eco vs. GPP for 2008, the initial year of CAR681, yielding a total of 43,687 carbon credits (−5334.7 gC m −2 y −1 ) (Supplement Table S2), falls within the lower left quadrant of the FLUXNET slope for R eco and GPP values, Figure 3B Figure 3A) emphasize the need for high-frequency monitoring as anomalous years can have disruptive impacts on project revenue [32]. US-Ho3 confirms the sensitivity of eddy covariance NEE to timber harvest and regrowth (Figure 2A,B), a trend not detected by CARB-CAR methods but a requirement to test CARB-CAR modeled harvest and growth simulations [17]. Eddy covariance data provide insights into carbon dynamics and related economics not possible with biometric surveys conducted every 6-to 12-years, typical for the Howland CARB-CAR protocol [17].
Considering CO 2 alone, Howland Forest NEE tower data, US-Ho2, in conjunction with US-Ho1, covers~95% of the shared project footprint area with CARB-CAR forest plots ( Figure 1). NEE values for US-Ho1 and US-Ho2 are comparable, lacking significant differences between the towers. The Howland two-tower NEE data confirms irreconcilable differences for carbon accounting relative to CARB-CAR data consistent with previous results [1] of offset over-crediting and overpayment by~4x relative to NEE values [1]. The aggregate CAR681 and CAR1161 time series (2015)(2016)(2017) was~2.7x the mean and~17x the standard deviation for Howland NEE over the same period, exceeding the 5% invalidation threshold cited by CARB [52] and lying outside of the natural range for 20 years of measured interannual Howland [58] and NEE forest values [23,53]. The exclusion of ecosystem respiration terms for CO 2 within the CARB-CAR protocols, critical for calculation of net forest carbon sequestration, confirm incomplete carbon accounting and likely erroneous, invalid offsets for the CARB compliance process for CAR681 and CAR1161. Absent ecosystem respiration, errors of up to 2258% per year were calculated ( Figure 2C; Supplement Table S6), emphasizing the requirement for complete carbon accounting, consistent with the well-characterized relationship between R eco and GPP (Figure 2A,B), and soil chamber measurements for CO 2 efflux ( Figure 5).
The three-gas forest eddy-covariance systems employed at Howland are comprised of commercially available single and multi-gas analyzers for eddy covariance (e.g., CO 2 and CH 4 , N 2 O) [38,[58][59][60], also applicable to soil chamber gas analyses [38]. A combination of three-gas eddy covariance tower networks of varying heights and soil chamber measurement campaigns can be scaled up across specific ecosystem landscapes by employing expanded ground networks, increasingly inclusive of CH 4 and N 2 O monitoring [61][62][63][64], scale-aware models [65], and remote sensing data [66,67] available for the US and increasingly across the planet [68]. In contrast to the diversity of GHG direct measurements and applications for Howland, the CARB-CAR protocols identify and list CH 4 and N 2 O only as sources [20], precluding determination of net budgets for these gases, and emphasizing limitations of estimation protocols that exclude direct measurement of GHGs. Equations for net GHG reductions and removal enhancements cited in [20] may apply to any GHG but are uniquely denominated for CO 2 , as source or sink, linked to carbon and tree growth equations and models to satisfy the 100-year carbon baseline and tree harvest scenarios required for CARB-CAR products. Accordingly, CARB-CAR protocol uncertainties, if employed to determine offsets for non-CO 2 GHGs, are likely higher than for CO 2 and limited to source emissions rather than net emissions for these gases.
Independent verification of emission reduction claims is critical to the integrity of GHG offset supply chains. Analysis of third-party verification of the CARB-CAR forest carbon supply chain revealed inconsistencies with CARB-CAR policy, including: (1) The CARB-CAR Howland project did not meet CARB reporting regulations for both tranches of Howland CARB offsets as an early action project (CAR681), or as an ARB compliance project (CAR1661), by noncompliance of offset verification reporting dates (Supplement Table S5, Supplement Document S6); (2) CAR misstated the actual values for a single year of NEE data (1996) [41] as seven years of seasonal Howland NEE data in support of CAR model adjustment for seasonal trends in tree growth. However, the CAR model (v. 3.2) excludes terms for soil carbon as ecosystem respiration, intrinsic to NEE data, and requires conversion of NEE micromoles m −2 s −1 to tree volume, a complex topic addressed by [69]. Details of model revisions and results were not provided, calling the validity of model results into question; (3) The Howland NEE and soil GHG records, advancing annually from 1996 to 2021, were available to CARB-CAR project owners, operators, and third-party verifiers (38,40,41,43,44,45,58,59,60) overlapping with the supply chain process from 2013 to 2019 culminating in serialized CARB verified offsets according to the AB32 mandate [70]. The Howland US-Ho1 NEE data were not reported as an independent check of the CARB-CAR annual results, a comparison that would have constrained the natural ranges for carbon sequestration offering an opportunity to proscriptively avoid CARB-CAR forest carbon sequestration uncertainties; (4) The Howland CARB-CAR project reporting exhibits errors and lapses in recordation, similar to those reported previously [1], including numerical errors, changes in reporting format from annual to discretionary mixed time intervals, and non-standard model operations resulting in uncertain values; and, (5) The raw data and detailed model outputs for the CARB-CAR projects have not been made available to the public, limiting collaboration and external verification of the project results. Instead, the CARB-CAR data and information are housed on personal computers with no central repository (Supplement Table S5, Item 10). Considering the uncertainties identified above, the CARB-CAR verification process is scientifically unjustifiable, creating avoidable offset invalidation risk for CAR681 and CAR1161. The exclusion of direct measurement protocols for forest carbon has been recently extended within the Assembly Bill AB398 [71] the successor bill to AB32 [70], by recommendation of a mandated Task Force to guide inclusion of new offset protocols. However, direct measurement of forest carbon protocols was not addressed [72].
The CARB-CAR and similar protocols could be improved by defining measurement and model results within Equation (1) universal reference framework (NEE = R eco + GPP) and incorporating independent field data for direct measurement of CO 2 . Collaboration with forest carbon sequestration field sites represented by the National Ecological Observatory and the AmeriFlux network of eddy covariance towers [73,74] may suggest improvements in the CARB-CAR protocol. Given the sources of uncertainty identified for the CARB-CAR verification process, improvements could be implemented in the near term, such as providing raw data availability for external users, inter-comparison of CARB-CAR with NEE data where possible, enforcing accounting standards, and adherence to consistent reporting formats.

Conclusions
The societal value of forests as GHG sinks can be linked with the social cost values established for GHGs emissions. Combining direct measurement of GHGs with their social