The following describes the methodology for both this dataset (methane) as well as the nitrous oxide dataset because the analyses were completed concurrently. Please see Related Datasets section below for N2O results.

Water sampling
Samples were collected using specially-designed 12L Niskin® bottles connected to a rosette with a Sea-Bird SBE 911Plus CTD package integrated into the system. The bottles were designed by John Bullister (NOAA Pacific Marine Environmental Laboratory (PMEL)) to specifically minimize contamination for trace gases, in particular chlorofluorocarbons and sulfur hexafluoride (Bullister and Wisegarver, 2008). Seawater was dispensed using Tygon® tubing from the bottles into the bottom of 240 mL borosilicate bottles to at least two times overflowing ensuring the absence of bubbles.

Sample preservation
The samples were preserved using 200 microliters of saturated mercuric chloride solution, crimp-sealed and stored in the dark at room temperature until analysis.

Analysis
Analysis of methane (CH4) and nitrous oxide (N2O) was conducted simultaneously using a gas chromatography method (del Valle & Karl, 2014; Wilson et al., 2014), typically 1 to 6 months after sample collection. Briefly, the water sample was transferred under positive pressure (supplied by helium gas) from the glass vials to a purge chamber fitted with a porous frit. The sample was then purged with ultra-high purity helium and the gas stream passed through a Nafion® dryer (Perma Pure LLC) and a Drierite® trap (VWR) to remove water vapor and then passed through an Ascarite trap to remove CO2, before being trapped on a packed sample loop (Porapak Q 80/100; Sigma-Aldrich) immersed in liquid nitrogen. After sparging for 10 minutes, the sample loop was heated and injected onto an analytical column (30 m x 0.32 mm GS-CarbonPLOT capillary column; J&W Scientific) within a gas chromatograph (Agilent 7890A) equipped with a flame ionization detector (FID) and an electron capture detector (ECD). The carrier flow was alternated from the FID to the ECD using a Dean’s switch® (Agilent Technologies) which allowed the quantification of both CH4 and N2O from a single sample. The oven temperature was typically maintained at 38°C, although this subsequently was decreased to 30°C in August 2016 to better resolve the CH4 peak when partial overlap with an O2 peak occurred.

Calibration
Calibration of the analytical system was conducted using gaseous standards purchased from Scott-Marin (CH4: 20.15 ± 1% ppmv; N2O: 4.81 ± 2% ppmv in a balance of N2) and NOAA (CH4: 1965.32 ppbv; N2O: 357.56 ppbv in a balance of air). From March 2016 onwards, the calibration for CH4 and N2O was compared against reference standards prepared by John Bullister at NOAA PMEL on behalf of SCOR Working Group #143. In all instances, standards were injected prior to the purge and trap set-up and therefore passed through the purge chamber and gas drying apparatus. A linear curve was applied to the CH4 calibration values and a polynomial curve was fitted to the N2O calibration values.

Precision and Accuracy
The precision of CH4 measurements for surface seawater with concentrations of 2.57 ± 0.07 (SD) nmol kg-1 (n=14), as calculated by the coefficient of variation, was 3%. The accuracy of CH4 measurements was evaluated by analyzing filtered (0.2 μm) seawater samples that had been equilibrated with atmospheric air at a range of set temperatures between 19–27°C which were maintained using a water bath. The measured values agreed to within 2.4 ± 0.9% of predicted values. The precision of N2O measurements in surface seawater, with concentrations of 6.47 ± 0.14 (SD) nmol kg-1 (n=14), as calculated by the coefficient of variation was 2%. Using the same air-equilibrated seawater set-up, as described for CH4, the accuracy of N2O measurements was 2.6 ± 1.9% of predicted values.

Calculation
The sea-air flux (F, μmol m-2 d-1 ) of CH4 and N2O was calculated as :
F = k (Cw -Ceq)
where k is the gas transfer velocity (m d-1), Cw is the ambient concentration of the gas dissolved in water (μmol m-3), and Ceq is the concentration of the gas at equilibrium with the atmosphere. Ceq was determined from the solubility equations for N2O (Weiss and Price, 1980) and for CH4 (Wiesenburg & Guinasso, 1979), and using the atmospheric concentrations measured at the NOAA Mauna Loa Observatory and available online from NOAA's Global Monitoring Laboratory (Lan & Keeling, 2025; Dlugokencky et al., 2016). The wind speed data, used to calculate k, for January 2009 to May 2016 were taken from the Woods Hole Oceanographic Institution-Hawaii Ocean Time-series Site (WHOTS) mooring (Upper Ocean Processes Group, 2024) and normalized to a height of 10 meters above sea surface (Smith, 1988). The wind data from July–December 2016 derive from the Blended Sea Winds data product for the coordinates 22°45' N and 158°00' W (Zhang et al., 2006). k was determined for each gas using the wind speed parameterization of Wanninkhof (2014) and the Schmidt numbers for each gas, calculated using the updated empirical temperature dependence formulations (Wanninkhof, 2014). To calculate the sea-air fluxes, the mean k value for the week prior to sample collection was used.