Our understanding of biosphere–atmosphere exchange has been considerably enhanced by eddy covariance measurements. However, there remain many trace gases, such as molecular hydrogen (H₂), that lack suitable analytical methods to measure their fluxes by eddy covariance. In such cases, flux-gradient methods can be used to calculate ecosystem-scale fluxes from vertical concentration gradients. The budget of atmospheric H₂ is poorly constrained by the limited available observations, and thus the ability to quantify and characterize the sources and sinks of H₂ by flux-gradient methods in various ecosystems is important. We developed an approach to make nonintrusive, automated measurements of ecosystem-scale H₂ fluxes both above and below the forest canopy at the Harvard Forest in Petersham, Massachusetts, for over a year. We used three flux-gradient methods to calculate the fluxes: two similarity methods that do not rely on a micrometeorological determination of the eddy diffusivity, K, based on (1) trace gases or (2) sensible heat, and one flux-gradient method that (3) parameterizes K. We quantitatively assessed the flux-gradient methods using CO₂ and H₂O by comparison to their simultaneous independent flux measurements via eddy covariance and soil chambers. All three flux-gradient methods performed well in certain locations, seasons, and times of day, and the best methods were trace gas similarity for above the canopy and K parameterization below it. Sensible heat similarity required several independent measurements, and the results were more variable, in part because those data were only available in the winter, when heat fluxes and temperature gradients were small and difficult to measure. Biases were often observed between flux-gradient methods and the independent flux measurements, and there was at least a 26% difference in nocturnal eddy-derived net ecosystem exchange (NEE) and chamber measurements. H₂ fluxes calculated in a summer period agreed within their uncertainty and pointed to soil uptake as the main driver of H₂ exchange at Harvard Forest, with H₂ deposition velocities ranging from 0.04 to 0.10 cm s⁻¹.

We present an evaluation of aircraft observations of the carbon and greenhouse gases CO₂, CH₄, N₂O, and CO using a direct-absorption pulsed quantum cascade laser spectrometer (QCLS) operated during the HIPPO and CalNex airborne experiments. The QCLS made continuous 1 Hz measurements with 1σ Allan precisions of 20, 0.5, 0.09, and 0.15 ppb for CO₂, CH₄, N₂O, and CO, respectively, over > 500 flight hours on 79 research flights. The QCLS measurements are compared to two vacuum ultraviolet (VUV) CO instruments (CalNex and HIPPO), a cavity ring-down spectrometer (CRDS) measuring CO₂ and CH₄ (CalNex), two broadband non-dispersive infrared (NDIR) spectrometers measuring CO₂ (HIPPO), two onboard gas chromatographs measuring a variety of chemical species including CH₄, N₂O, and CO (HIPPO), and various flask-based measurements of all four species. QCLS measurements are tied to NOAA and WMO standards using an in-flight calibration system, and mean differences when compared to NOAA CCG flask data over the 59 HIPPO research flights were 100, 1, 1, and 2 ppb for CO₂, CH₄, N₂O, and CO, respectively. The details of the end-to-end calibration procedures and the data quality assurance and quality control (QA/QC) are presented. Specifically, we discuss our practices for the traceability of standards given uncertainties in calibration cylinders, isotopic and surface effects for the long-lived greenhouse gas tracers, interpolation techniques for in-flight calibrations, and the effects of instrument linearity on retrieved mole fractions.

Abstract. We have examined the utility of retrieved column-averaged, dry-air mole fractions of CO₂ (XCO₂) from the Greenhouse Gases Observing Satellite (GOSAT) for quantifying monthly, regional flux estimates of CO₂, using the GEOS-Chem four-dimensional variational (4D-Var) data assimilation system. We focused on assessing the potential impact of biases in the GOSAT CO₂ data on the regional flux estimates. Using different screening and bias correction approaches, we selected three different subsets of the GOSAT XCO₂ data for the 4D-Var inversion analyses, and found that the inferred global fluxes were consistent across the three XCO₂ inversions. However, the GOSAT observational coverage was a challenge for the regional flux estimates. In the northern extratropics, the inversions were more sensitive to North American fluxes than to European and Asian fluxes due to the lack of observations over Eurasia in winter and over eastern and southern Asia in summer. The regional flux estimates were also sensitive to the treatment of the residual bias in the GOSAT XCO₂ data. The largest differences obtained were for temperate North America and temperate South America, for which the largest spread between the inversions was 1.02 and 0.96 Pg C, respectively. In the case of temperate North America, one inversion suggested a strong source, whereas the second and third XCO₂ inversions produced a weak and strong sink, respectively. Despite the discrepancies in the regional flux estimates between the three XCO₂ inversions, the a posteriori CO₂ distributions were in good agreement (with a mean difference between the three inversions of typically less than 0.5 ppm) with independent data from the Total Carbon Column Observing Network (TCCON), the surface flask network, and from the HIAPER Pole-to-Pole Observations (HIPPO) aircraft campaign. The discrepancy in the regional flux estimates from the different inversions, despite the agreement of the global flux estimates suggests the need for additional work to determine the minimum spatial scales at which we can reliably quantify the fluxes using GOSAT XCO₂. The fact that the a posteriori CO₂ from the different inversions were in good agreement with the independent data although the regional flux estimates differed significantly, suggests that innovative ways of exploiting existing data sets, and possibly additional observations, are needed to better evaluate the inferred regional flux estimates.

Hristov et al. (1) argue that our study “pro- vides a comprehensive, quantitative analysis of anthropogenic methane sources,” but that the conclusion “that US EPA [US Environ- mental Protection Agency] estimates for live- stock methane emissions are grossly under- estimated appears to be unsubstantiated by . . . [a] ‘bottom-up’ approach” outlined in their letter.

In this reply, we discuss the information provided by atmospheric methane data about methane emissions, and comment on the chal- lenge of connecting “bottom-up” and “top- down” estimates, a conclusion shared Hristov et al. (1).

Our study (2) used both near-surface and airborne atmospheric measurements of CH4 concentrations to characterize the total mass of methane added to the atmosphere by sur- face emissions, discretized in space and time. We conclude that total United States meth- ane emissions in 2007–2008 were 33.4 ± 1.4 TgC/yr (44.5 TgCH4/yr), 45–57% above the most recent US EPA baseline estimate for those years (3). Furthermore, we estimate “the magnitude of emissions with spatial pat- terns similar to animal husbandry and ma- nure” (2) at 12.7 ± 5.0 TgC/yr (16.9 TgCH4/ yr), 11–156% above baseline EPA estimates for those sectors (best estimate 84% above EPA). Our conclusions are generally consis- tent with previous more limited top-down studies examining total United States (e.g., ref. 4) and regional livestock/manure meth- ane emissions (e.g., ref. 5).

Hristov et al. (1) argue that “the validity of this ‘top-down’ approach can be verified by a relatively simple ‘bottom-up’ method using current livestock inventories and enteric or

manure methane emission factors.” The authors build this estimate for enteric fermen- tation by multiplying the US Department of Agricuture (USDA) livestock inventory esti- mates for 2013 (note that our study covers 2007–2008), by “assumed” feed dry matter intake and “assumed” methane production rates. “With the above assumptions,” Hristov et al. estimate methane emissions from en- teric fermentation comparable to the US EPA’s inventory for 2011. Similarly, the authors use USDA livestock inventories and Intergovernmetal Panel on Climate Change (IPCC) (6) manure methane emissions fac- tors to estimate United States manure emis- sions that are 35% lower than EPA inven- tory numbers.

The estimates of Hristov et al. (1) there- fore require a series of assumptions, for which errors compound as several factors are multiplied and added. Feed matter intake and emission factors both have substantial uncertainties (6), as do the IPCC manure methane emission factors (6). Given these uncertainties, which are inherent in all bot- tom-up inventories, we strongly disagree that “the validity of [our] ‘top-down’ ap- proach can be verified” using the Hristov et al. estimates (1).

The method we applied is especially suited to quantifying large-scale total emissions, and uncertainties increase for sector- and region- specific estimates [as outlined above and in our study (2)]. Even in light of these uncer- tainties, the total emissions with spatial pat- terns consistent with animal husbandry are still likely to be substantially above EPA esti- mates. Conversely, bottom-up inventories are strongest at detailing individual emission

types, but uncertainties compound at larger scales, such as the national scale examined here. This difference is precisely why we ar- gue that careful, detailed assessments are needed to reconcile the emissions clearly vis- ible from atmospheric observations with bot- tom-up emissions inventories. Hristov et al. (1) also note a “need for a detailed inven- tory . . . to more accurately estimate . . . emis- sions.” On this point we strongly agree.

Scot M. Millera,1, Anna M. Michalakb, and Steven C. Wofsya
aDepartment of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138; and bDepartment of Global Ecology, Carnegie Institution for Science, Stanford, CA 94305

Wetlands comprise the single largest global source of atmospheric methane, but current flux estimates disagree in both magnitude and distribution at the continental scale. This study uses atmospheric methane observations over North America from 2007 to 2008 and a geostatistical inverse model to improve understanding of Canadian methane fluxes and associated biogeochemical models. The results bridge an existing gap between traditional top-down, inversion studies, which typically emphasize total emission budgets, and biogeochemical models, which usually emphasize environmental processes. The conclusions of this study are threefold. First, the most complete process-based methane models do not always describe available atmospheric methane observations better than simple models. In this study, a relatively simple model of wetland distribution, soil moisture, and soil temperature outperformed more complex model formulations. Second, we find that wetland methane fluxes have a broader spatial distribution across western Canada and into the northern U.S. than represented in existing flux models. Finally, we calculate total methane budgets for Canada and for the Hudson Bay Lowlands, a large wetland region (50–60°N, 75–96°W). Over these lowlands, we find total methane fluxes of 1.8±0.24 Tg C yr⁻¹, a number in the midrange of previous estimates. Our total Canadian methane budget of 16.0±1.2 Tg C yr⁻¹ is larger than existing inventories, primarily due to high anthropogenic emissions in Alberta. However, methane observations are sparse in western Canada, and additional measurements over Alberta will constrain anthropogenic sources in that province with greater confidence.

Natural gas (NG) is a potential “bridge fuel” during transition to a decarbonized energy system: It emits less carbon dioxide during combustion than other fossil fuels and can be used in many industries. However, because of the high global warming potential of methane (CH4, the major component of NG), climate benefits from NG use depend on system leakage rates. Some recent estimates of leakage have challenged the benefits of switching from coal to NG, a large near-term greenhouse gas (GHG) reduction opportunity (1–3). Also, global atmospheric CH4 concentrations are on the rise, with the causes still poorly understood (4).