In Lake Hallwil, the contribution of oxic methanogenesis to overall diffusive CH4 emissions has been estimated to be 90%6 or 63–83%5, but we show here that NOMC ~ 17%.
In the mass balance of the SML extending from 0 to 5 m water depth5,6, Günthel et al.5 used an average sediment flux of Fsed = 1.75 mmol m−2 day−1, averaging flux estimates of Donis et al.6 from two sediment cores, one collected at 3 m and the other at 7 m water depth. The δ13C of the CH4 in the pore water of these two cores differ substantially6, indicating differences in production and oxidation of CH4 between the sediments in the SML and at 7 m water depth. The estimate of Fsed in the SML should therefore be based on the core collected at 3 m water depth. Using the approach of Donis et al.6, the correct Fsed derived from the data of this core is Fsed = 2.8 mmol m−2 day−1 (Peeters et al.9, see Supplementary Note 2.1 for details).
Günthel et al.5 and Donis et al.6 apparently have erroneously used gas transfer coefficients instead of proper CH4 fluxes to calculate emissions. This conclusion is demonstrated by the perfect agreement between the values published erroneously as CH4 fluxes, Fsurf, by Günthel et al.5 and the values of the gas transfer coefficients of CH4 at 20 °C, kCH4, calculated by us (Table 1). The values published by Donis et al.6 as CH4 fluxes are very similar to these kCH4 and therefore also do not represent CH4 fluxes but gas transfer coefficients (for details, see Supplementary Note 2.2).
The gas transfer coefficient of CH4 must be multiplied by the difference between the surface concentration (0.3 mmol m−3, ref. 6) and the atmospheric equilibrium concentration of CH4 (CH4,equ = 0.003 mmol m−3 at 20 °C9), i.e. by ~0.3 mmol m−3, to obtain Fsurf. Fsurf is therefore ~3.3 times smaller than the values of the gas transfer coefficients erroneously taken by Günthel et al.5 and Donis et al.6 as CH4 fluxes (Table 1 and details in Supplementary Note 2.2).
Donis et al.6 and Günthel et al.5 used values obtained from measurements with floating chambers to calculate emissions, but these values claimed to represent Fsurf appear to be in fact values for transfer coefficients, suggesting the same mistake as in the case of the wind models. Donis et al.6 stated: “Average flux (April–August 2016) is equal to 0.8 ± 0.2 mmol m−2 d−1 from MacIntyre relationship for positive buoyancy and to 0.6 ± 0.3 mmol m−2 d−1 from chamber measurements. The latter, not significantly different from the wind-based relationship, was used for the mass balance”. Günthel et al.5, co-authored by D. Donis, claim that the “MacIntyre relationship for positive buoyancy”10 provides an average value of 0.7 for Fsurf, but in fact 0.7 is the average value for kCH4 in unit m day−1 (0.7 m d−1, see Table 1) and Fsurf for this model is 3.3 times smaller (0.21 mmol m−2 d−1, see Table 1). The value by Donis et al.6 for the MacIntyre relationship10 is even slightly larger than 0.7 and therefore clearly incompatible with Fsurf but is rather a gas transfer coefficient as is obvious in the case of Günthel et al.5. The good agreement between the value for the gas transfer coefficient obtained from the MacIntyre model for positive buoyancy flux10 and the values from the chamber measurements suggests that the values from the chamber measurements are not gas fluxes but also gas transfer coefficients (see Supplementary Note 2.2 for more details).
Donis et al.6 derived from their chamber measurements the wind-based model “Hallwil relationship” specifically for Lake Hallwil. The establishment of this Hallwil relationship required that Donis et al.6 calculated gas transfer coefficients from their chamber measurements. In their Supplementary Fig. 4, Donis et al.6 show that the values from their chamber measurements agree well with those from the Hallwil relationship (Supplementary Fig. 2 and Supplementary Note 2.2). Note, however, that the values for the Hallwil relationship are in fact gas transfer coefficients and not Fsurf, supporting that also the values from the chamber measurements represent gas transfer coefficients and not Fsurf (Supplementary Fig. 2 and Supplementary Note 2.2 for more details). This conclusion implies that the values from the chamber measurements by Donis et al.6 must be multiplied by ~0.3 mmol m−3 to give proper CH4 fluxes, which are then ~3.3 times smaller than the CH4 fluxes used in the mass balances of refs. 5,6.
Because there are only four chamber measurements available for 2016 and one of them was exceptionally low (see ref. 6 and Supplementary Note 2.2), the Hallwil relationship is considered here to provide the most reliable estimate of the average k600 in Lake Hallwil and therefore applied to calculate the average surface CH4 flux for April to August 2016, i.e., Fsurf = 0.24 mmol m−2 d−1 (see Table 1 and Supplementary Note 2.2). The reliability of the Hallwil relationship was confirmed by Günthel et al.5 and by Hartmann et al.11 comparing different estimates of surface fluxes in the South Basin of Lake Stechlin.
With Fsed = 2.8 mmol m2 day−1 and Fsurf = 0.24 mmol m2 day−1, NOM = 416 mol day−1 and the contribution of NOM to total emissions is NOMC = 17% (Supplementary Table 1 in Supplementary Note 2.3 includes also additional estimates of NOMC). The low value of NOMC suggests that most of CH4 in the SML originates from the sediments, which is consistent with the δ13C isotopic composition of CH4 in Lake Hallwil9. The uppermost CH4 in the sediment core from the SML is characterized by δ13C about –59‰, which corresponds very closely to the δ13C of the CH4 in the open water of the SML ranging from −62‰ to −58‰ (Figs. 4 and 5 both in ref. 6). Thus the δ13C values suggest that the CH4 from the uppermost pore water in the sediment of the SML is the source of the CH4 in the open water and do not indicate a reduction of the δ13C expected in case of substantial CH4 production.
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