Table 1 Average CH₄ surface fluxes from Lake Hallwil and gas transfer velocities.

Model			F_surf,G⁵ (mmol m⁻² day⁻¹)	k₆₀₀ (m day⁻¹)	k_CH4 (20 °C) (m day⁻¹)	F_surf (20 °C) (mmol m⁻² day⁻¹)
Flux chamber⁶			0.6	(1.8)……0.6	(1.8)……0.6	(0.6)……0.18
Hallwil relationship⁶	k_600,m = 2 * U₁₀	(cm h⁻¹)	0.8	0.8	0.8	0.24
MacIntyre et al.¹⁰
Positive buoyancy flux	k_600,m = 1.74 * U₁₀ − 0.15	(cm h⁻¹)	0.7	0.7	0.7	0.21
Negative buoyancy flux	k_600,m = 2.04 * U₁₀ + 2	(cm h⁻¹)	1.3	1.3	1.3	0.39
Combined buoyancy flux	k_600,m = 2.25 * U₁₀ + 0.16	(cm h⁻¹)	1.0	1.0	0.9	0.27
Vachon and Prairie¹⁷	k_600,m = 1.48 * U₁₀ + 2.51 + 0.39 * U₁₀ * log₁₀(A_surf)	(cm h⁻¹)	1.4	1.4	1.3	0.39

Average CH₄ surface fluxes estimated by Günthel et al.⁵, F_surf,G, are compared to gas transfer velocities and correct CH₄ surface fluxes at 20 °C. Donis et al.⁶ published the same value as Günthel et al.⁵ for the flux chamber measurements and 0.8 mmol m⁻² day⁻¹ for the MacIntyre model with positive buoyancy flux. k₆₀₀ is the gas transfer velocity for CO₂ at 20 °C, k_CH4 (20 °C) the gas transfer velocity of CH₄ at 20 °C, and F_surf (20 °C) the surface flux of CH₄ at 20 °C calculated by us. F_surf (20 °C) is calculated from k_CH4 (20 °C) and using for the surface concentration 0.3 mmol m⁻³ in Lake Hallwil^5,6. U₁₀ is the wind speed 10 m above the lake surface and A_surf is the surface area of the lake. Details on the calculations are provided in Supplementary Note 2.
Note that Günthel et al.⁵ used wind speed data from 15 April to 28 July but not from August. We applied here the same to allow direct comparison. The average U₁₀ of these data is 1.69 m s⁻¹. In case of flux chambers, the numbers in brackets use the values of Günthel et al.⁵ and the surface concentration 0.3 mmol m⁻³ in Lake Hallwil^5,6. Bold numbers assume that the flux chamber data of Donis et al.⁶ used by Günthel et al.⁵ represent k₆₀₀ and not F_surf, as is supported in the main text and in Supplementary Note 2.

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