Five lakes of different trophic states and depths were selected for the study (Table 1). Lake Baldegg (66 m depth) is located in an agricultural area dominated by pig farms. After 34 years of artificial aeration and mixing, it is still eutrophic with total phosphorus (TP) concentrations of ∼ 25 mgP m-3. Lake Hallwil is the shallowest of the investigated lakes (48 m) and is presently recovering from its eutrophic past (TP ∼ 12 mgP m-3) after 30 years of artificial aeration. Lake Aegeri is oligotrophic (TP ∼ 6 mgP m-3) and located in a catchment dominated by pastures and forests. Lake Geneva is the largest lake in central Europe by volume. It is still meso-eutrophic (TP ∼ 20 mgP m-3) and the areal O2 consumption rate is among the highest measured in Swiss lakes (Müller et al., 2012a; Schwefel et al., 2016). Lake Zug (197 m) is eutrophic, permanently stratified below ∼ 100 m depth (meromictic), and has a TP value of ∼ 30 mgP m-3 in the productive epilimnion. In Lake Zug, only one set of cores for porewater analysis, CH4 analysis, and bulk sediment parameters was collected from the permanently oxic part (> 4 mgO2 L-1 throughout the year) at 62 m water depth.

Sediment cores were retrieved with a Uwitec gravity corer equipped with a PVC tube (6.5 cm inner diameter, 60 cm length). The PVC tube has pre-drilled holes (diameter 2 mm) at 5 mm intervals. The holes were sealed with adhesive tape prior to sampling. Sediment cores were taken along a depth gradient (Table 1). Porewaters were sampled on site immediately after retrieval. A total of 10–50 µL of sediment porewater was retrieved by punctuating the adhesive tape and horizontally inserting a MicroRhizon filter tube (1 mm diameter, 0.20 µm pore size; Rhizosphere Research Products, Wageningen, Netherlands). The sampling resolution was 5 mm for the first 5 cm of sediment, ≤ 1 cm between 5 and 10 cm of sediment, ≤ 2 cm between 10 and 20 cm of sediment, and ≤ 3 cm below 20 cm of sediment. The porewater retrieval time was between 10 and 30 s and samples were immediately analyzed to minimize oxidation. Each porewater sample was analyzed once with two capillary electrophoresis devices each equipped with a capacitively coupled contactless conductivity detector (CE-C4D) (calibrated for anions and cations) directly at the lake shore. Full separation of ions of interest (NH4+, Mn(II), Fe(II), SO42-, NO3-, NO2-) was achieved within 6 min by applying a voltage of 15 kV and a current of 0.5 µA. The background electrolyte solution and all calibration standards were freshly prepared before sampling with ultrapure water (Merck) and the corresponding salts. All five-point calibrations were checked against a multi-ion standard (Fluka), and standard deviations of all measurements were < 5 %. The procedure is described in detail by Torres et al. (2013).

Methane samples were collected from additional sediment cores retrieved on the same day and location. Core liners had holes of 1.2 cm diameter pre-drilled staggered at 1 cm vertical intervals and covered with adhesive tape. Immediately after retrieval the cores were sampled in 1 cm steps from top to bottom by cutting the tape and inserting a plastic syringe where the tip was cut off. Two cubic centimeters of sediment was transferred into 125 mL serum flasks containing 2 mL of 7 M NaOH and capped with a septum stopper. Each CH4 sample was analyzed three times in the headspace by gas chromatography (Agilent) using a 1010 Supelco Carboxene column with a standard deviation of 0.1 to 1.3 %.

Additional sediment cores were extruded and sampled in 0.5 to 1 cm sections. Water content was calculated from the weight difference before and after freeze drying, and the porosity was estimated from the density and the respective TOC content (Och et al., 2012). Freeze-dried sediments were ground in an agate mortar and further analyzed for TOC / TN with a Euro EA 3000 elemental analyzer (Hekatech). Net sedimentation rates were determined based on the assumption of constant rate of supply with γ-ray measurements of 210Pb and 137Cs with a Canberra GeLi borehole detector and/or by varve counting, which was possible in all cores except the cores from Lake Hallwil. The net sedimentation rates were further validated by the characteristic 137Cs peaks of the Chernobyl fallout (1986) and the bomb spike of 1963. As TOC content and net sedimentation rates were not determined from our sediment cores in Lake Geneva, literature data were used to calculate the total organic carbon mass accumulation rate (TOC-MAR, gC m-2 yr-1). By comparing our coring sites to sites published by Span et al. (1990), Vernet et al. (1983) and Loizeau et al. (2012) we estimated an average net sediment accumulation rate of 1000 g m-2 yr-1 with a TOC content of 1.1 %, resulting in TOC-MAR of 11 gC m-2 yr-1 for the deep basin. Although TOC content and net sedimentation can vary drastically due to turbidites and the inflow of the Rhone River, we deem this estimate to be representative of the deep undisturbed central basin of Lake Geneva.

Sediment traps were deployed in lakes Baldegg and Aegeri from March 2013 until the end of November 2014 to determine TOC gross sedimentation rates. In Lake Hallwil, sediment traps were deployed from January 2014 to December 2014 (see Supplement Table S1). The sediment trap material was collected every 2 weeks. The traps consisted of two cylindrical PVC tubes with an inner diameter of 9.2 cm and were positioned at 15 m water depth and 1 m above the sediment surface. For the calculation of the gross sedimentation, only data from the lower trap were used. The collected material was weighed, freeze-dried, and analyzed for TOC and TN with the same methods as the sediment.

Porewater fluxes were calculated from vertical porewater concentration gradients with a one-dimensional reaction-transport model (Müller et al., 2003) that was adapted from Epping and Helder (1997) and extended from O2 to other parameters. The fluxes (J) of reduced compounds (CH4, NH4+, Fe(II), and Mn(II)), denoted in mmol m-2 d-1, were multiplied by 32/1000 to be converted into equivalent O2 fluxes (gO2 m-2 d-1) based on redox stoichiometry and summed up in Fred (Eq. 1). S(-II) was considered negligible as we detected dissolved Fe(II) in all cores. Fred=2⋅JCH4+2⋅JNH4+0.5⋅JMn(II)+0.25⋅JFe(II), where Fred represents the total O2 required per area to oxidize all reduced compounds released by the sediment (Matzinger et al., 2010). As total phosphorus concentration and hypolimnetic O2 consumption rate did not change during the past years, sediment diagenetic processes are assumed to be in quasi-steady state. Although seasonally varying deposition rates of OC and varying O2 concentrations may alter Fe(II) and Mn(II) concentration gradients, the fluxes of NH4+ and CH4 dominating Fred did not change systematically with the seasons.

Total organic carbon mass accumulation rate in the lake sediment (TOC-MAR, in gC m-2 yr-1) at each coring site was calculated from the sedimentation rate (SR, in cm yr-1), porosity (ϕ), dry density (ρdry in g cm-3), and TOC (mg g-1) for each 5 mm interval (Och et al., 2012) (Eq. 4). Porosity and dry density are calculated for each sampling interval individually (Eqs. 1 and 3): ϕ=Vw/(Vw+Vs), with Vw and Vs being the volumes of water and sediment, while the sediment volume can be calculated from its weight (Ws) and the dry density (Eq. 2): Vs=Ws/ρdry. The dry density is estimated according to the empirical relationship between TOC content (in %) and density of geogenic sediments (Och et al., 2012), drydensity=-0.0523⋅TOC+2.65. The TOC-MAR values were then averaged from 2 to 10 cm sediment depth. The first 2 cm were excluded to neglect freshly deposited matter as this material still passes through intense and rapid degradation. The lower TOC-MAR calculation depth of 10 cm was chosen to remain within the time frame where steady-state conditions can be assumed (Radbourne et al., 2017). TOC-MAR=SR⋅ρdry⋅1-ϕ⋅10000⋅(TOC/1000)

The porewater concentration profiles of the reduced compounds CH4, NH4+, Fe(II), and Mn(II) measured at different depths in Lake Baldegg, Lake Aegeri, Lake Hallwil, and Lake Geneva are presented in Fig. 1, and for Lake Zug in Fig. S1 (see Supplement). The highest overall porewater concentrations occurred in Lake Baldegg (Fig. 1a) and the lowest in Lake Geneva (Fig. 1d) in spite of its high productivity. A distinct pattern of increasing porewater concentrations with increasing sampling depth was apparent in Lake Baldegg and to a lesser extent in Lake Aegeri (Fig. 1a, b). Nitrate concentrations in the overlying water of the sediment core were on average 101 µmol L-1 in Lake Baldegg, 23 µmol L-1 in Lake Aegeri, 61 µmol L-1 in Lake Hallwil, 32 µmol L-1 in Lake Geneva, and 20 µmol L-1 in Lake Zug and steeply declined to zero within the first centimeter of the sediment.

The trend of increasing ion concentrations with lake depth observed in the porewater was also reflected in the areal fluxes of the reduced compounds from the sediment to the lake bottom waters (Table 2). The fluxes were positive from the sediment to the bottom water in all lakes at all depths. Fluxes measured at the same locations on up to five different dates between March and October varied by 34 % in Lake Baldegg and by 84 % in Lake Aegeri for CH4, as well as by 80 % in Lake Baldegg and by 65 % in Lake Aegeri for NH4+. The fluxes of Mn(II) (66 and 72 %) and Fe(II) (46 and 88 %) also showed a high variability. This temporal variation is likely due to local heterogeneity of the sediment and seasonal variations of both the supply of OC, e.g., algae blooms, and the O2 concentration at the sediment–water interface. However, the relative importance of these driving factors could not be determined, and no clear seasonal pattern was detected.

A summary of all fluxes and Fred is given in Table 2. In Lake Baldegg the highest fluxes of CH4, NH4+, and Fe(II) of all lakes and a clear increase with sampling depth were observed. Fluxes at the deepest site agreed well with earlier measurements from dialysis samplers (Urban et al., 1997). In the oligotrophic Lake Aegeri fluxes of CH4 and NH4+ were small at the shallow sites and similar to those observed in other oligotrophic lakes (Frenzel et al., 1990; Carignan et al., 1994), while at the deepest location considerably higher fluxes were measured for CH4. Fluxes in Lake Hallwil did not show an overall increase with lake depth. In Lake Geneva, the smallest fluxes of CH4, NH4+, and Fe(II) were observed in spite of its high productivity, without systematic variations with lake depth. NH4+ and CH4 contributed 85 to 98 % to the O2 consuming capacity, while Fe(II) and Mn(II) played only a minor role. Müller et al. (2012a) estimated Fred for a range of eutrophic lakes to be 0.36 ± 0.12 gO2 m-2 d-1, based on a relationship between hypolimnetic O2 consumption rates and mean hypolimnion depths. Fred values observed at 24 m (0.28 gO2 m-2 d-1) and 40 m (0.34 gO2 m-2 d-1) depth in the eutrophic Lake Baldegg (see Table 2) matched the modeled value. Fred at the deepest site of Lake Baldegg (0.49 gO2 m-2 d-1) agreed with a previous observation of 0.55 gO2 m-2 d-1. Likewise, in Lake Hallwil, Fred varied between 0.18 gO2 m-2 d-1 and 0.25 gO2 m-2 d-1, matching earlier measurements of 0.28 gO2 m-2 d-1 (Müller et al., 2012a). In Lake Aegeri, Fred was clearly higher at the deepest sampling site than at the shallower sites. At 34 and 49 m water depth, Fred was 0.07 gO2 m-2 d-1, and thus typical for a deep oligotrophic lake. At 79 m, a markedly higher Fred of 0.26 gO2 m-2 d-1 was observed. In eutrophic Lake Geneva, Fred varied between 0.02 and 0.09 gO2 m-2 d-1, which is surprisingly low for a productive lake. In summary, we did not observe a direct relationship between the trophic state of the lake and the fluxes of reduced substances.

Determination of sedimentation rates from core dating revealed increasing sediment deposition with increasing lake depth in Lake Baldegg and at the deepest site of Lake Aegeri. The sediment TOC content was around 3.4 % and varied only little between the different coring sites and lakes (see Table 2), except for Lake Geneva with an estimated 1.1 % TOC. Consequently, mass accumulation rates varied substantially and increased with depth in Lake Baldegg and to a lesser extent in Lake Aegeri. We attribute this observation to sediment focusing, which has also been documented by Urban et al. (1997) for Lake Baldegg. Sediment focusing transports fine, freshly settled organic-rich material from the shallower to the deeper parts of a lake and consequently increases TOC-MAR with lake depth (Lehman, 1975). Carignan and Lean (1991) documented that porewater fluxes increased with lake depth caused by the focusing of labile particulate OC into the deeper part of the lake. A study at oligotrophic Little Rock Lake also showed elevated NH4+ concentrations at the deepest site due to a greater supply of fine-grained organic particles caused by sediment focusing (Sherman et al., 1994). In eutrophic Lake Zug, Maerki et al. (2009) found that NH4+ fluxes increased proportionally with the sediment contents of TOC and total nitrogen (TN), indicating a link between fluxes of reduced substances and TOC-MAR. In lakes Baldegg and Hallwil, geochemical focusing, caused by recurring redox-sensitive dissolution and precipitation of Mn and Fe phases, is an additional process that increases Fe(II) and Mn(II) concentrations with lake depth (Urban et al., 1997; Schaller and Wehrli, 1996).

Sediment focusing increased TOC-MAR by ∼ 104 % in the deepest part of Lake Baldegg and by ∼ 43 % in Lake Aegeri. Since Fred depends on the sedimentation regime and bottom-water O2 availability, this explains the spatial variability of Fred in these two lakes. No sediment focusing was observed in Lake Hallwil, which is in agreement with a previous study by Bloesch and Uehlinger (1986). In consequence, extrapolating measurements performed at the deepest sites of lakes to the entire lake area can significantly overestimate the average contribution of reduced sediment compounds to AHM if sediment focusing is active.

All lakes investigated have a predominance of autochthonous OC input, implied by similar C / N ratios (7.0–9.9), a proxy for the origin of OC (see Table 2), and a permanently oxic hypolimnion (see Fig. S2). As a consequence, the burial efficiency of OC, defined as the ratio between TOC-MAR and OC gross sedimentation rate (deposition rate of OC onto the sediment surface) by Sobek et al. (2009) should be rather similar in these lakes. Based on gross TOC sedimentation data from sediment traps (see Table S1) and TOC-MAR values (Table 2), burial efficiencies at the deepest sampling locations were calculated from sediment trap data of lakes Baldegg (50 %), Hallwil (41 %), and Sempach (46 %). All values were close to the average value of 48 % determined from 27 sediment cores from 11 lakes by Sobek et al. (2009). Consequently, a similar proportion of gross OC sedimentation is buried and contributes to the formation of Fred and TOC-MAR in all studied lakes. An exception is Lake Aegeri, with a surprisingly high burial efficiency of OC of 77 % calculated for the deepest site. However, this is caused by the exceptional bathymetry. The deepest site is located in a small trough with surrounding steep slopes predestined for sediment slides and remobilization of settled particles. The locally high ratio of sediment area to water volume presumably leads to the annual development of an anoxic deep water layer which increases OC burial, but is not representative of the whole lake.

As primary production and hypolimnetic O2 concentrations did not change considerably during the last decade, the burial efficiency and thus TOC-MAR and Fred generation likely remained unchanged. Furthermore, porewater profiles do not capture the effects of rapid initial mineralization occurring within the top few millimeters of the sediment, but mirror the slower processes of anaerobic degradation of buried OC and Fred. Hence, in Fig. 2 we related Fred to the corresponding TOC-MAR at each sampling location. Additional datasets from earlier measurements in various lakes were added to complement the relationship.

Figure 2 reveals two characteristic facts concerning the release of reduced compounds from lake sediments: (i) a distinct increase in Fred was observed when TOC-MAR exceeded ∼ 10 gC m-2 yr-1 and (ii) Fred increased proportionately with TOC-MAR between 10 and 45 gC m-2 yr-1 up to ∼ 0.50 gO2 m-2 d-1 in all seasonally mixed lakes investigated. The highest Fred value was measured at the deepest point of Lake Baldegg with 0.49 gO2 m-2 d-1 at a TOC-MAR of 45 gC m-2 yr-1, despite much higher TOC-MAR in Rotsee. The mineralization of sediment OC appeared to be the main driver of Fred independent of the cause of TOC accumulation. The areal accumulation of TOC per time is controlled by gross sedimentation (which is related to primary production), O2 concentration in the bottom water, biological factors like grazing and bioturbation, and physical parameters such as sediment focusing (Sobek et al., 2009). At low TOC-MAR, the total flux of reduced substances was very low (e.g., lakes Baikal, Erie, and Superior, Fig. 2), as only little carbon remained for anaerobic degradation, and the reduced substances diffusing up from deeper sediment strata were quantitatively oxidized in the upper sediment layers

Given that all investigated lakes are seasonally mixed and have a permanently oxic hypolimnion, the likely driving factors for the positive relationship between Fred and TOC-MAR are (i) hypolimnetic O2 concentrations, and (ii) the quality and quantity of OC. An influence of temperature and benthic production can be ruled out as all sampling stations were located in the cold hypolimnia well below the thermocline. Generally, high O2 concentrations lead to a high fraction of aerobic OC mineralization and hence decrease in TOC-MAR as OC is decomposed by oxygenases and other reactive oxygen species (Maerki et al., 2006; Sobek et al., 2009; Stumm and Morgan, 1996). Furthermore, elevated hypolimnetic O2 concentrations increase the oxidation of reduced compounds near or within the top sediment layer and thus increase the regeneration of alternative electron acceptors such as NO3- and SO42- (Urban et al., 1997). In contrast, low O2 concentrations or even temporally anoxic conditions increase OC burial and thus TOC-MAR and prompt the production of reduced compounds (Sobek et al., 2009).

Low TOC-MAR occurred in lakes with low primary production and low allochthonous input. In the oligotrophic lakes Superior and Baikal, TOC-MAR was 4 and 7 gC m-2 yr-1 (see Table S2), respectively, and the resulting Fred from the sediment was close to zero (Och et al., 2012; Klump et al., 1989; Remsen et al., 1989; Richardson and Nealson, 1989). In addition to low gross sedimentation of OC, the high sediment O2 penetration depth (of around 1–3 cm) causes a long exposure time to oxic conditions and thus oxic mineralization of a large fraction of the deposit (Maerki et al., 2006; Martin et al., 1993; Li et al., 2012). In consequence, the TOC buried in lakes like Superior and Baikal is already highly mineralized and therefore does not generate significant amounts of reduced substances. However, low TOC-MAR values were also observed in Lake Geneva. Although Lake Geneva is highly productive, its hypolimnetic O2 concentration remained high throughout the year (see Fig. S2) (Schwefel et al., 2016). Randlett et al. (2015) concluded that ∼ 75 % of the OC in Lake Geneva was mineralized aerobically at the sediment surface. Measurements performed by Schwefel et al. (2017) further confirmed that > 96 % of the OC in Lake Geneva is mineralized aerobically within the water column or at the sediment surface. As the buried OC only generated low Fred of 0.03 to 0.09 gO2 m-2 d-1 (see Table 2), we concluded that the material was already recalcitrant. In contrast to the other lakes investigated, in Lake Geneva high porewater concentration and sediment penetration of SO42- enhanced the degradation of OC and actively diminished Fred by oxidation of CH4 and formation of iron sulfides. Norði et al. (2013) showed the efficiency of anaerobic CH4 oxidation by SO42- and a reactive Fe(III) pool which in turn reduced the flux of CH4 out of the sediment. Sediment core measurements at 210 and 240 m but in proximity to the Rhone River delta by Randlett et al. (2015) showed that at even higher TOC-MARs of 20 to 30 gC m-2 yr-1 (2 to 3 times the rate estimated for the open lake), Fred values remained at similarly low values of 0.04 to 0.05 gO2 m-2 d-1. This case highlights the importance of OC quality, as refractory OC can be sequestered and offset TOC-MAR without a noticeable increase in Fred. Consequently, lakes with a higher input of land-derived organic material should show a higher offset in TOC-MAR values as more recalcitrant OC is buried without a direct effect on Fred.

While TOC-MAR values were similar at all three stations in Lake Aegeri, Fred peaked at the deepest point. In addition to a likely sediment focusing, a small anoxic bottom layer developed at the end of summer stratification at the deepest location (see Fig. S2) due to the steep topography. This condition diminishes oxic mineralization of settled OC and thus supports the formation of higher Fred.

Under the assumptions that primary production even under ideal circumstances can generate only a limited amount of OC of around ∼ 400 to 500 gC m-2 yr-1 (Wetzel, 2001) and that allochthonous, soil- and land-plant-derived OC is comparatively less accessible for mineralization, Fred is expected to converge at an upper bound even at high total TOC-MAR. As shallower lakes with a high primary production tend to become anoxic during the stratification period and thereby start accumulating reduced substances in the deepest part of the hypolimnion, Fred should not further increase as the concentration gradients between sediment and water would flatten as the oxic–anoxic interface moves from the sediment into the bottom water. The high Fred values encountered in Lake Baldegg (∼ 0.49 gO2 m-2 d-1) supposedly represent an upper boundary of Fred, as it is an example of a highly eutrophic lake with an additional supply of OC to the deepest part by sediment focusing while only retaining an oxic hypolimnion due to artificial aeration. At the highest TOC-MAR value of ∼ 170 gC m-2 yr-1 measured in the seasonally anoxic Rotsee (RO), Fred remained at 0.46 gO2 m-2 d-1 (measured after lake mixing in the oxic hypolimnion), showing no further increase in Fred, while measurements performed at the end of summer stagnation and an anoxic hypolimnion revealed a Fred value of 0.26 gO2 m-2 d-1. However, whether Fred consistently levels off at high TOC-MAR remains to be verified by measurements in additional eutrophic lakes with an oxic hypolimnion and high TOC-MAR.

The increasing fraction of aerobically mineralized OC with increasing O2 availability in eutrophic lakes is further supported by a systematic decrease in Fred with increasing mean hypolimnion depth (zH) in productive lakes, shown in Fig. 3. During the stratified period, the hypolimnetic O2 reservoir in eutrophic lakes with a small zH is quickly exhausted, enforcing a higher OC burial rate and increased anaerobic mineralization and thus the formation of reduced substances, e.g. in Rotsee, Türlersee, and Pfäffikersee. In these lakes Fred becomes the dominant fraction of AHM with values of ∼ 0.40 gO2 m-2 d-1. In the deep Lake Geneva, the hypolimnetic O2 inventory increases with zH, and the lakes' resilience to O2 depletion rises. Consequently, more O2 is available for aerobic remineralization of OC, and hence less or more degraded OC is buried. Hence, Fred diminishes with increasing zH. Coherently, very deep eutrophic lakes such as Lake Geneva are well protected from anoxia. Lake Baldegg deviates from this general correlation in Fig. 3 due to the high sediment focusing, which caused the sedimentation rate to increase by a factor of 1.9 compared to the shallower sites. Likewise, sediment focusing might increase Fred in other lakes. However, it is unclear to what extent sediment focusing increases Fred and TOC-MAR, for example in Lake Sempach (Urban et al., 1997). These findings complement and extend the observation presented in Müller et al. (2012a) that AHM of fully productive lakes increased linearly with their mean hypolimnion depth if zH < ∼ 25 m, with a similar contribution of reduced compounds from the sediments of all lakes. A closer look at the fluxes of reduced compounds produced by the deposited organic matter in the sediment, however, revealed that they also depend on the concentration of O2 that the material was exposed to.