Oxic methanogenesis is only a minor source of lake-wide diffusive CH4 emissions from lakes

natural


CH4-fluxes from the sediments in the SML of Lake Hallwil
and Günthel et al. 2019 3 determined the CH4-flux from sediments into the water column, Fsed, in the SML of Lake Hallwil by averaging Fsed estimates from two sediment cores. One of these cores was collected at 3 m and the other at 7 m water depth.
Because the SML extends from 0 to 5 m water depth only the core from 3 m water depth is from the SML.  13 C of the CH4 in the pore water of the cores from 3 m and 7 m differs substantially between the two cores (see Figure 5b in 4

Wind based models and chamber measurements: Günthel et al. 2019 and Donis et al. 2017 have mistakenly used gas transfer coefficients for CH4-fluxes
We have calculated gas transfer coefficients of CO2 at 20°C, k600, and CH4-fluxes from the lake surface, Fsurf, in Lake Hallwil using different wind based models for k600 (Table 1) (Table 1). Note that in their mass balance for Lake Hallwil Donis et al.  (Table 1). Our calculations can easily be confirmed using the average wind speed, because the applied models of k600 depend linearly on wind speed.
The wind data provided to us by Günthel Table 1) and Fsurf for this model is 3.3 times smaller (0.21 mmol m -2 d -1 see Table 1). The value published by Donis et al. 2017 4 is slightly larger than 0.7, probably because they averaged CH4-fluxes divided by CH4,av, which does not result in exactly the same value as the average kCH4. Independent of this speculation on the procedure applied by  Table 1  (ii) Why does this factor 0.3 agree so very well with the value of the surface concentration of CH4 that was already missing in the flux calculations of the wind based models?

The Hallwil relationship as most reliable estimate of the average k600 and Fsurf
The mass balance in Lake Hallwil was based on average CH4 surface fluxes for the time period between April and August.

NOM and NOMC in Lake Hallwil
The mass balance of Donis et al. 2017 4 and Günthel et al. 2019 3 for Lake Hallwil considers CH4 emissions at the lake surface, CH4 fluxes from sediments, and additional contributions that were small (vertical turbulent transport of CH4) or were not measured and are highly uncertain (dissolution of microbubbles). These additional contributions are neglected in the following (explanation see supplement A). Because the neglected terms are sources of CH4 in the SML, the values estimated by us are upper limits of the NOM. Note that methane oxidation, which was not measured independently, is not required because we consider net production and not gross production. The results of the mass balance are -9summarized in Supplementary Table 1. The balance is based on the Hallwil relationship (explanation see above) and indicates that net-production of CH4 contributes ~17% to overall emissions, i.e. NOMC = 17%.

Supplementary Table 1: Estimation of NOMC in Lake Hallwil.
The columns provide CH4 fluxes at the lake surface, Fsurf, and total CH4 emissions, Fsurf,tot, for different methods for estimating surface fluxes, the total CH4 sediment flux, Fsed,tot , estimated from the sediment flux from the core collected at 3 m water depth, Fsed = 2.8 mmol m -2 d -1 , net-production of methane in oxic waters NOM = Fsurf,tot -Fsed,tot , and the contribution of NOM to the total methane emission NOMC = NOM / Fsurf,tot. The surface area of Lake Hallwil is Asurf = 9.9·10 6 m 2 and the area of the sediments in the SML (0-5 m water depth) is Ased = 0.

Estimation of sediment fluxes from mesocosm experiments
The sediment flux in the mass balances for Lake Stechlin by Günthel et al. 2019 3 are underestimated and oxic metanogenesis is therefore overestimated. Sediment fluxes were calculated by assessing oxic production from mesocosm experiments and by using these estimates of CH4-production in a mass balance for the lake closing the balance to determine the sediment flux. CH4 surface fluxes from the mesocosms were utilized to calculate CH4 production within the mesocosms. However, Fsurf from the mesocosm was overestimated because the gas transfer coefficient used in the mesocosms was taken to be the same as  The data clearly indicate that turbulence in the open water of the lake is substantially larger than in the mesocosm and therefore strongly suggest that the gas transfer coefficient should be smaller in the mesocosm than in the lake. In the following, we estimate k600 in the mesocosm by scaling k600 for the open water using the relation k600 ~  ¼ and the ratio between  in the lake and  in the mesocosm, i.e. a ratio of 5 as lower and of 10 as upper limit. Hence,  Table 2).

Supplementary Table 2: Assessment of sediment fluxes from the mesocosm-and lake measurements conducted 2014 in the South Basin of Lake Stechlin
Gas transfer coefficients for the open water from the lake were k600,L = 5.115 cm hr -1 (Supplementary Table 4

NOMC in Lake Stechlin
We used the sediment fluxes from Supplementary Table 2 to re-evaluate the mass balances from Lake Stechlin (Supplementary Table 3 Table 3 below). In the South Basin NOMC agrees very well between the years 2014 and 2016 and the average NOMC is 29% and 36% for the upper and lower bound of sediment fluxes, respectively. In the North Basin NOMC ranges between 26% and 33% and is therefore very similar to NOMC in the South Basin.

Supplementary Table 3: Lake Stechlin: NOMC estimated from the mass balance of CH4 in 2014, 2016 and 2018 in the South and North Basin.
Total emissions Fsurf,tot = Fsurf · Asurf were calculated from the average Fsurf determined for the North Basin from chamber measurements (2016Chamber, June-July 2016; chamber data Supplementary Table 4 Table 3 indicated as 2016Ch_20J, also included in Figure   1 and Supplementary Figures 4 and 5).
Note that the overestimation of the surface fluxes by the "Stechlin relationship" has also consequences for the estimated sediment fluxes, because these were determined based on surface fluxes from 2014 that were derived from the "Stechlin relationship". Using a wind

Comment on the sediment flux in the
and Asurf is the surface area, kCH4 the gas transfer coefficient for CH4, and CH4,equ the atmospheric equilibrium concentration of CH4. Equ. (3) assumes, as did also DelSontro et al.
NOMCCH4,meas are only slightly larger than NOMC (Supplementary Table 5) Table 1): Fsurf from the "Hallwil relationship" that is based on the chamber measurements in Lake Hallwil 4 . Fsed, from the CH4 pore water concentrations in the sediment core collected at 3 m water depth (Fsed = 2.8 mmol m -2 d -1 , Supplementary Table 1). Lake Stechlin (Supplementary Table 3 Table 4): Fsed derived from CH4 pore water measured in a single sediment core by 1 , considering the CH4 gradient in the top 2 cm and at 5 cm depth, (Fsed = 0.08 mmol m -2 d -1 and Fsed = 0.26 mmol m -2 d -1 ) providing upper and lower limit of NOMC, respectively; Fsurf from specific wind model of 1 ; Lake Cromwell: Data from 3 . Additional Lakes (Supplementary Table 5  Hallwill by an order of magnitude.

The ratio Ased/VSML for the lakes investigated by
Here we estimate Ased and RAV assuming that the lakes are radially symmetric, i.e.  Supplementary Table 5.