Sediment fluxes rather than oxic methanogenesis explain diffusive CH4 emissions from lakes and reservoirs

Methane emissions from lakes and reservoirs are a major natural source in the global budget of atmospheric CH4. A large fraction of these emissions are due to diffusive transport of CH4 from surface waters to the atmosphere. It was suggested recently that CH4 production in the oxic surface waters is required to compensate for diffusive CH4 emissions from lakes. In contrast, we demonstrate here that typical diffusive CH4-fluxes from sediments in shallow water zones, Fsed,S, suffice to explain CH4 emissions to the atmosphere. Our analysis is based on the combination of an exceptional data set on surface concentrations of CH4 with a mass balance model of CH4 that is focused on the surface mixed layer and considers CH4-fluxes from sediments, lateral transport, gas exchange with the atmosphere, and includes temperature dependencies of sediment fluxes and gas exchange. Fsed,S not only explains observed surface CH4 concentrations but also concentration differences between shallow and open water zones, and the seasonal variability of emissions and lateral concentration distributions. Hence, our results support the hypothesis that diffusive fluxes from shallow sediments and not oxic methanogenesis are the main source of the CH4 in the surface waters and the CH4 emitted from lakes and reservoirs.

Section S1: Information on investigated systems, measurements and data 32 All methane samples were measured using the head space technique and gas Lower Lake Konstanz (LLC), Lake Ammer, and Lake Uberlingen see Encinas Fernadez et al. Section S1.1 Overview on the systems studied 48 Characteristic properties of the different systems investigated are provided in Table S1.   The number of surface measurements collected during the different campaigns in the different 89 lakes is listed in Table S2. These surface measurements were used to calculate the average 90 surface concentration of CH 4 in the entire basin and in the littoral for the different campaigns.  Section S1.3 Cross-shore transect in Lake Uberlingen 103 The sampling points along the cross-shore transect in Lake Uberlingen are depicted in Fig.   104 S7.  (Table S3).

117
The four terms on the right hand side of S1a describe (i) the change of C(r,t) with time 144 due to lateral transport, (ii) the source of CH 4 due to the flux from the sediments, (iii) the loss 145 of CH 4 due to gas exchange with the atmosphere, and (iv) net production of CH 4 , 146 respectively. To test our hypothesis that sediment fluxes are sufficient to compensate 147 emissions, i.e. that net production is not required to close the mass balance, we simulate the 148 methane concentrations assuming no net production, i.e. P(r,t) = 0.

149
In equations S1a and S1b C(r,t) is the concentration of CH 4 as function of r and time t,  The models were implemented in MATLAB. The partial differential equations were 265 solved using the method of lines by discretizing the spatial coordinate and solving the 266 resulting coupled system of ordinary differential equations using the ode15s solver of In the following we re-analyze the data of Donis et al. 1  evidence for substantial oxic methane production.

287
The following sections provide details on our re-analysis of the data of Donis et al. 1 .

288
We first estimate the CH 4 flux from the shallow sediments based on the pore water profile of

297
In the following we demonstrate that Donis et al. 1  The total flux from the sediments of the littoral zone within the mixed surface layer (Zone 2: 336 0-5m, see Table 2   Using the correct sediment area and the sediment flux correctly estimated from the 347 pore-water concentration measured within the top 3 cm of the sediment core one obtains in 348 the mixed surface layer a total source of CH 4 due to sediment fluxes of: S sed,total = 2.8·10 -3 mol 349 m -2 d -1 · 7.11 10 5 m 2 = 1990 mol d -1 , which is 10 times larger than the total source due to  Table 2 353 The mass balance argument by Donis et al. 1 implicitly assumes steady state conditions. As  Hence, the following discussion of emissions from Lake Hallwil is based on calculations for a 359 water temperature of 20°C.

360
Gas exchange at the lake surface is determined from the relation:  Table S3.