On the methane paradox: Transport from shallow water zones rather than in situ methanogenesis is the major source of CH₄ in the open surface water of lakes

1 Introduction

Lakes are considered to be major natural sources of methane (CH₄), contributing a large fraction of the global CH₄ emissions to the atmosphere [Michmerhuizen and Striegl, 1996; Luyssaert et al., 2012; Bastviken et al., 2011]. However, the quantification of the global CH₄ emissions from lakes and the controls and contributions of the different CH₄ pathways from aquatic systems to the atmosphere are currently studied worldwide [Bastviken et al., 2011; Hofmann, 2013; Grossart et al., 2011; Prairie and del Giorgio, 2013; Bogard et al., 2014; Tang et al., 2014; Blees et al., 2015; Encinas Fernández et al., 2014].

Global emissions of CH₄ are typically estimated by categorizing CH₄ emissions per unit surface area according to lake size and multiplying these areal CH₄ emissions by the global surface area of lakes within the respective size category [Bastviken et al., 2011; Bastviken et al., 2004; Kirschke et al., 2013]. Therefore, global CH₄ emissions from lakes depend on the estimated global surface area of lakes in different size categories [Bastviken et al., 2011; Cole et al., 2007; Conrad, 2009; Downing et al., 2006; McDonald et al., 2012]. Furthermore, the estimates of areal CH₄ emissions are complicated by the large spatial heterogeneity of CH₄ emissions [Hofmann, 2013; Blees et al., 2015; Murase et al., 2005] and the multiple pathways and sources that can contribute to CH₄ emissions [Grossart et al., 2011; Prairie and del Giorgio, 2013; Bogard et al., 2014; Bastviken et al., 2004; Karl and Tilbrook, 1994; Walter et al., 2007; DelSontro et al., 2011; Carmichael et al., 2014; Carini et al., 2014].

CH₄ in lakes mainly originates from anaerobic carbon mineralization in anoxic sediments [Segers, 1998]. Most of the CH₄ produced in anoxic sediments is oxidized by methanotrophic bacteria at anoxic-oxic interfaces [Conrad, 2009; Bastviken et al., 2002; Utsumi et al., 1998a; Utsumi et al., 1998b]. Observations from several lakes show that in the oxic epilimnion, CH₄ concentrations are typically oversaturated and higher than in the oxic hypolimnion [Luyssaert et al., 2012; Bogard et al., 2014; Blees et al., 2015; Schulz et al., 2001]. This phenomenon, called the “methane paradox” [Reeburgh, 2007], has been taken as an indication of the in situ production of CH₄ in oxic waters [Bogard et al., 2014; Schulz et al., 2001]. Anoxic microzones were proposed as sites of in situ CH₄ production in generally oxic waters [Schulz et al., 2001]. Methanogenic Archaea attached to photoautotrophs were detected and identified as possible candidates responsible for causing elevated CH₄ concentrations in the oxic metalimnion [Grossart et al., 2011]. Recently, it has been suggested that methanogenesis in oxic surface waters is closely linked to algal dynamics and driven by acetoclastic production [Bogard et al., 2014]. A positive correlation between CH₄ and Chl-a concentrations across diverse open-water aquatic ecosystems was presented as support of this hypothesis [Bogard et al., 2014]. The possible metabolic pathways for CH₄ production in oxic waters and field evidence of oxic methane production have recently been reviewed by Tang et al. [2016]. These authors conclude that oxic methane production may be an important source of CH₄ in lakes but the fate of the produced methane and its relevance for the overall methane emissions from lakes requires additional research. According to Bogard et al. [2014], “oxic water methanogenesis is a significant component of the overall CH₄ budget in a small, shallow lake” and “this pathway (oxic water methanogenesis) may be the main CH₄ source in large, deep lakes …”

However, elevated CH₄ concentrations in oxic surface waters of the pelagic zone do not necessarily originate from the in situ production of CH₄ but could alternatively be explained by the lateral transport of CH₄ from littoral zones [Hofmann, 2013; Bastviken et al., 2004; Rudd and Hamilton, 1978; Murase et al., 2003]. CH₄ concentrations in the littoral zone (here, the shallow water zone) can be expected to be particularly high because the production rate of CH₄ in anoxic pore waters of sediments increases with temperature [Murase et al., 2005; Bastviken et al., 2008], and temperatures are higher in littoral than profundal sediments. Furthermore, CH₄-rich pore water in littoral sediments is regularly released into the water column during resuspension events associated with surface waves [Hofmann et al., 2010]. In this study, we utilize one of the world's largest data sets on CH₄ distributions within lakes to test whether CH₄ from shallow water zones (hypothesis A) or the in situ production of CH₄ in oxic surface water, i.e., production within the anoxic microzones and production due to methanogenic bacteria (hypothesis B), is the more likely explanation for the methane paradox. If CH₄ from the shallow water zone is the major source of the CH₄ in the surface water of the deepwater zone, (a) CH₄ concentrations in the shallow water zone must be higher than in the deepwater zone and (b) the ratio of CH₄ from the shallow water zone to CH₄ from the deepwater zone, f_CH4,s/d, should increase with increasing surface area of the deepwater zone because CH₄ introduced from the shallow water zone is more strongly diluted in a larger deepwater zone. In contrast, if the dominant source of CH₄ in the surface water is in situ production, one does not necessarily expect significant differences between CH₄ in shallow water and deepwater zones, and an increase in the ratio f_CH4,s/d with increasing surface area of the deepwater zone cannot be easily explained. If the in situ production of CH₄ is linked to Chl-a [Bogard et al., 2014], CH₄ concentrations in individual lakes should vary with seasonal changes in Chl-a, whereas the trophic state of a lake, i.e., the annual mean biomass, may influence both the oxic in situ production of CH₄ and the CH₄ concentrations in the shallow littoral zone via production in the sediments.

2 Methods

3 Results

3.1 Properties of Methane Concentration Distributions as Measured in Different Basins

In all the basins, surface CH₄ concentrations were horizontally heterogeneous and sensitive to the 1 m deep surface water temperature (Figure 1 and Table S1). The median values and the range of CH₄ concentrations in the horizontal distributions differ substantially between lake basins and for different surface water temperatures (Figure 1). In the comparatively small lakes, Königseggsee, Illmensee, and Mindelsee, the CH₄ concentrations ranged between ~0.06 and ~3.9 μM (Figures 1a, 1b, and 1d). In the similarly sized but very shallow Rohrsee, the CH₄ concentrations exhibited the greatest variability (~0.4 and ~20 μM; Figure 1c) and the highest maximum lake-wide median concentration (~8.7 μM). In the three basins of LLC and in Lake Ammer, which have larger surface areas than that of Rohrsee, the CH₄ concentrations were lower than those in Rohrsee and ranged between 0.5 and 16 μM (Figures 1e–1h). The lowest CH₄ concentrations (median 0.14 μM) and the lowest horizontal heterogeneity in the CH₄ concentrations (V_CH4 < 0.05 μM²) of all basins were measured in ULC (Figure 1i), the largest and deepest basin with the smallest f_A,s/t. In the basins in which several surveys were conducted at different temperatures, the greatest variability and the highest median CH₄ concentrations were observed during the summer season, when temperatures were high (Figures 1a, 1c, 1e, and 1f). An exception is the horizontal heterogeneity in the CH₄ concentrations in Illmensee, which peaked in late fall (V_CH4~0.48 μM²) during overturn (Figure 1b).

3.2 CH₄ Concentrations in the Shallow Water and Deepwater Zones of the Different Basins

The CH₄ distributions of the individual surveys in all the basins, as shown in Figure 1, were analyzed further by distinguishing between measurements in shallow water and deepwater zones and averaging the respective CH₄ concentrations to obtain CH_4,s, CH_4,d, CH_4,t, and CH_4,w. The two different estimates of the mean basin-wide methane concentrations, CH_4,t and CH_4,w, are highly correlated (p value <0.001, R² = 99.96%) and have essentially the same values (the coefficients of the regression line are a = −0.009 μM and b = 0.999; Figure 2a and Table 2a). Therefore, statistical analyses involving mean basin-wide CH₄ concentrations provide the same results regardless of whether they use CH_4,t or CH_4,w. The excellent agreement between CH_4,t and CH_4,w indicates that the sampling stations associated with the different surveys of the different basins provide representative coverage, with the number of samples from shallow water and deepwater zones being proportional to their respective surface areas.

Table 2. Assessment of the Relationship Between CH₄ Concentrations and Lake Morphology, Temperature, and Chl-a Concentrations

Linear Models
	a (μM)	b		p Value		R2 (%)	NRMSE (%)
(a) CH4,w = a + b · CH4,t	−0.009	0.999		<0.001		100	0.5
(b) VCH4 = a + b · CH4,t	−1.80	2.22		<0.001		80.9	11.99
(c) fCH4,s/d = a + b · Ad	1	3.03 × 10−8		<0.01		71.0	19.21
MLM considering CH4,t, At, fA,s/t, and T
	a	b (m−2)	c (°C−1)	p value for At or fA,s/t	p value for T	R2 (%)	NRMSE (%)
(d1) ln(CH4,t) = a + b · At	0.17	−7.47 × 10−9		0.57		0.01	26.26
(d2) ln(CH4,t) = a + b · At + c · T	−0.94	−1.49 × 10−8	0.08	0.24	0.02	17.4	24.37
(e1) ln(CH4,t) = a + b · fA,s/t	−0.99	2.27		<0.01		38.1	20.77
(e2) ln(CH4,t) = a + b · fA,s/t + c · T	−2.61	2.66	0.1	<0.01	<0.01	63.7	16.16
MLM applied to seasonal data of CH4,0–6 m, Chl-a,0–6 m, and T0–6 m
(f) ln(CH4,0–6 m) = a + b · ln(Chl-a,0–6 m ) + c · T0–6 m
	a	b (−)	c (°C−1)	p value for Chl-a,0–6 m	p value for T0–6 m	R2 (%)	NRMSE (%)
Königseggsee	−1	−0.6	0.13	0.05	<0.01	76.1	18.15
Illmensee	−3.14	0.7	0.09	0.04	<0.01	83.7	13.38
Mindelsee	−2.9	−0.05	0.13	0.91	0.05	29.4	21.62

Across diverse lake morphologies and seasons (as indicated by water temperature), the horizontal heterogeneity in the CH₄ concentration increases with the lake-wide average CH₄ concentration; i.e., log(V_CH4) and log(CH_4,t) are positively correlated (p value <0.001, R² = 80%). According to the regression model, V_CH4 increases slightly more rapidly than quadratic with CH_4,t (Figure 2b and Table 2b). Thus, the standard deviation of the CH₄ concentrations measured during individual surveys ( ) is approximately proportional to CH_4,t, which supports the suitability of using the logarithm of CH_4,t in correlation analyses and MLM.

In all the basins, the ratio f_CH4,_s/d is on average larger than 1, suggesting that the mean CH₄ concentration in the shallow water zone is typically larger than the mean CH₄ concentration in the deepwater zone. The values of f_CH4,s/d in the different surveys in each basin range from (in brackets are mean values) 0.72 to 1.14 (1.03), 0.78 to 2.08 (1.17), and 1.35 in Königseggsee, Illmensee, and Mindelsee, respectively. Larger values of f_CH4,s/d were observed in the northern, central, and southern basins of LLC and in Lake Ammer: 0.87–1.41 (1.16), 0.97–1.45 (1.23), 2.02–2.08 (2.05), and 1.38, respectively. The deepest and largest basin, ULC, has the largest value of f_CH4,s/d = 3.18 of all the lakes. According to a t test, the mean f_CH4,s/d for the different basins is significantly larger than 1 (p value <0.05). Furthermore, the mean f_CH4,s/d value significantly increased with the surface area of the deepwater zone (p value <0.05, R² = 68%). Rohrsee was not included in this analysis because it does not have a deepwater zone. If A_d becomes very small, i.e., A_d → 0, f_CH4,s/d is expected to approach 1 because transport and mixing will readily remove differences in CH₄ concentrations between the deepwater zone and the adjacent shallow water zone. Considering the mean f_CH4,s/d value from all basins except Rohrsee and forcing the linear regression through f_CH4,s/d = 1 at A_d = 0 (Table 2c) reveals a significant positive relationship between f_CH4,s/d and A_d (p value <0.005, R² = 71%).

3.3 Relationship Between CH₄, Morphometry, Chl-a, and Water Temperature

The relationship between the surface water CH₄ concentrations and lake morphometry was assessed using MLM that consider the basin-wide mean CH₄ concentrations at a 1 m water depth (CH_4,t), the morphometric parameters A_t and f_A,s/t, and the basin-wide mean water temperature at 1 m water depth (T). The application of MLM reveals that ln(CH_4,t) is not correlated with the total surface area A_t (p value >0.5) and that A_t could only explain less than 1% of the variance in ln(CH_4,t) (Table 2d1 and Figure 3a). Including T as an additional independent variable in the model (Table 2d2 and Figure 3b) increases the explained variance to ~17%. However, this increase in explained variance results from a significant correlation between ln(CH_4,t) and T (p value <0.02), whereas ln(CH_4,t) and A_t remain uncorrelated (p value >0.2; Table 2d2 and Figure 3b). In contrast to the morphometric parameter A_t, the ratio f_A,s/t is significantly correlated with ln(CH_4,t) (p value <0.01), explaining 38% of the variance in ln(CH_4,t) (Table 2e1 and Figure 3c). The MLM considering f_A,s/t and T as independent variables (Table 2e2 and Figure 3d) even explains 64% of the variance in ln(CH_4,t) and indicates a significant correlation between ln(CH_4,t) and both of the independent variables f_A,s/t and T (p value <0.01 in both cases; Table 2e2 and Figure 3d). The coefficient c describing the dependence of ln(CH_4,t) on T is positive (c = 0.1°C⁻¹; Table 2e2), suggesting that the average basin-wide surface CH₄ concentrations increase exponentially with the surface water temperature.

The relationship between CH₄ and Chl-a concentrations was investigated with MLM separately considering individual lakes, i.e., Königseggsee, Illmensee, and Mindelsee, and using seasonally resolved and vertically averaged (mean of the top 6 m) data on CH₄ concentrations (CH_4,0–6 m), Chl-a concentrations (Chl-a,_0–6 m), and water temperatures (T_0–6 m).

According to the MLM applied to the data from Königseggsee, ln(CH_4,0–6 m) is significantly correlated with ln(Chl-a,_0–6 m) and with T_0–6 m (p value ~0.05 and p value <0.01, respectively; Table 2f and Figure 4a). The MLM explains ~76% of the variance of ln(CH_4,0–6 m) (Table 2f). Coefficient b describing the slope of the relationship between ln(CH_4,0–6 m) and ln(Chl-a,_0–6 m) is negative (b = −0.60; Table 2f), suggesting that the CH₄ concentrations increase with T_0–6 m but decrease with increasing Chl-a concentrations.

In the case of the data from Illmensee, the MLM also indicate that ln(CH_4,0–6 m) is significantly correlated with ln(Chl-a,_0–6 m) and with T_0–6 m (p value = 0.04 and p value <0.01, respectively; Table 2f and Figure 4b). The MLM explains ~84% of the variance in ln(CH_4,0–6 m; Table 2f). However, coefficient b is positive in Illmensee (b = 0.69; Table 2f), suggesting that the CH₄ concentrations increase with increasing Chl-a concentrations, which is the opposite of the results for Königseggsee.

In Mindelsee, ln(CH_4,0–6 m) is not significantly correlated with ln(Chl-a,_0–6 m) (p value >0.9; Table 2f and Figure 4c) but is with T (p value ~0.05; Table 2f). Temperature explains ~30% of the variance in the ln(CH_4,0–6 m) time series (Table 2f).

Hence, the MLMs provide three opposing results with respect to the relationship between CH₄ and Chl-a concentrations: a significant negative correlation in Königseggsee, a significant positive correlation in Illmensee, and no correlation in Mindelsee.

With respect to the relationship between ln(CH_4,0–6 m) and T_0–6 m, the MLMs provide consistent results for the three lakes: the coefficient c describing the slope of the relationship between ln(CH_4,0–6 m) and T_0–6 m is positive in all the three lakes (c = 0.13°C⁻¹, c = 0.09°C⁻¹, and c = 0.13°C⁻¹, respectively), indicating that the CH₄ concentrations increase exponentially with water temperature.

4 Discussion

The CH₄ concentration distributions as measured in the surface water of all basins are spatially heterogeneous (Figure 1), supporting the findings of earlier studies [Hofmann, 2013; Blees et al., 2015; Murase et al., 2005] that demonstrated that individual measurements from lakes may result in misleading estimates of mean basin-wide CH₄ concentrations and emissions [Hofmann, 2013]. The heterogeneity of the CH₄ concentrations in the horizontal distributions increases with increasing CH₄,_t (Figure 2b). Therefore, spatially resolved measurements are required to reduce uncertainties in the estimate of the mean basin-wide CH₄ concentration, especially in lakes with high CH₄ concentrations.

The spatial distributions of CH₄ confirm that in all the basins, the average surface CH₄ concentrations are higher in the shallow water zone than in the deepwater zone (Table S1). Thus, a fundamental requirement of hypothesis A, i.e., that CH₄ from shallow water zones is a major source of the CH₄ concentrations in the surface water of the deepwater zone, is fulfilled. The comparatively high CH₄ concentrations in the shallow water zones can be explained by the frequent release of CH₄-rich pore water during resuspension events (Figure S2) associated with hydrodynamic forcing in shallow waters [Hofmann et al., 2010] and by high anaerobic CH₄ production in the sediments due to the comparatively high temperatures at shallow water depths [Murase et al., 2005; Bastviken et al., 2008; Thebrath et al., 1993]. Moreover, since temperature dependence of CH₄ production is larger than the one from CH₄ oxidation [Dunfield et al., 1993], the input of CH₄ from the shallow anoxic sediments and thus from the shallow water zone would be even more pronounced with increasing temperature.

According to hypothesis A, CH₄-rich water is transported from the shallow water zone to the deepwater zone and diluted within the deepwater zone. Because vertical mixing across the thermocline is greatly reduced under stratified conditions (Figures S1 and S2a), the lateral transport of CH₄-rich water from shallow water to deepwater zones should lead to elevated near-surface CH₄ concentrations in the deepwater zone, thus explaining the methane paradox. The dilution of CH₄ in the deepwater zone increases with increasing horizontal extent of the deepwater zone. Therefore, the ratio between the CH₄ concentrations in the shallow water and deepwater zones should increase with the surface area of the deepwater zone. This implication of hypothesis A is supported by the significant positive correlation between f_CH4,s/d and A_d (Table 2c).

According to hypothesis B, the dominant source of CH₄ in surface waters of lakes is the in situ production of CH₄ within the oxic water column. In situ production in the deepwater zone could explain the methane paradox if the in situ production of CH₄ is larger near the lake surface than in deeper layers. However, the observation of significant differences between CH_4,s and CH_4,d cannot be easily explained if hypothesis B is true because near the water surface, the distribution of both, the anoxic microzones and the methanogenic Archaea, is expected to be similar in the shallow water and deepwater zones. Even more difficult to explain is why the ratio f_CH4,s/d increases with A_d if the CH₄ production in the water column is responsible for the CH₄ concentrations in the surface water of the deepwater zone.

To support the link between oxic water column methanogenesis and algal dynamics, Bogard et al. [2014] presented a positive correlation between the logarithms of CH₄ and Chl-a concentrations. However, the correlation analysis was based on a data set combining measurements from open oceans, several freshwater lakes, and mesocosm experiments. Considering only their data for freshwater lakes, the logarithms of CH₄ and Chl-a concentrations are not correlated (p value >0.01; R² = 10% using all the data for freshwater lakes from Bogard et al. [2014]). The data therefore do not provide evidence for the link between oxic in situ production of CH₄ and algal dynamics in lakes. Furthermore, a correlation between CH₄ and Chl-a concentrations is not conclusive to support such a link because sediment-borne CH₄ may also be correlated with Chl-a concentrations, as organic material is the source of anaerobic CH₄ production in the sediments. However, in contrast to CH₄ production in sediments, methanogenesis in oxic waters linked to algal dynamics should depend not only on the annual mean concentrations of Chl-a but also on the seasonal changes in Chl-a, e.g., increases during spring bloom development and decreases thereafter during the clear water phase. However, our seasonally resolved data from three lakes do not show a consistent relationship between CH₄ and Chl-a concentrations (Figure 4 and Table 2f).

The above discussion indicates that our data are consistent with hypothesis A but are comparatively difficult to explain with hypothesis B and do not provide evidence for in situ CH₄ production in oxic waters linked to algal dynamics in lakes. Hypothesis A assumes that the shallow water zone is a major source of CH₄ in lakes and consequently implies that basin-wide mean surface CH₄ concentrations do not necessarily depend on the surface area of the lake but rather on the relative contribution of the surface area of the shallow water zone to the surface area of the entire lake. This implication of hypothesis A is confirmed by our results from MLM. The MLMs indicate that the logarithm of CH_4,t is not correlated with A_t but with the aspect ratio f_A,s/t, thus further indicating that the shallow water zones contribute a major fraction of the overall CH₄ concentrations in lakes.

The flux of CH₄ to the atmosphere depends on the gas exchange velocity k, the atmospheric equilibrium concentration of CH₄ at the surface water's temperature and salinity (CH_4,equ), and the surface water concentration of CH₄. Distinguishing between shallow water and deepwater zones suggests that the average CH₄ flux is given by F_CH4 = (k_s A_s · (CH_4,s − CH_4,equ) + k_s A_d · (CH_4,d − CH_4,equ))/A_t, where k_s and k_d are the gas exchange velocities in the shallow water and deepwater zones, respectively. Assuming that k_s and k_d are approximately the same and using CH_4,w ≈ CH_4,t (Table 2a), F_CH4 = k_s(CH_4,t − CH_4,equ). Thus, the conclusion that f_A,s/t rather than A_t is a better predictor of CH_4,t also applies to the average basin-wide diffusive flux of CH₄ into the atmosphere. Note that not only CH₄ concentrations but also ebullition fluxes are elevated in the shallow water zone [Bastviken et al., 2004]. In shallow sediments, the oversaturation required for the development of gas bubbles is less than in deep sediments because of the differences in hydrostatic pressure. Furthermore, the high temperatures in shallow water zones support a higher production of CH₄. Thus, ebullition may also be related to f_A,s/t, and the estimates of lake-wide CH₄ fluxes due to diffusion and ebullition may benefit from a categorization according to the aspect ratio f_A,s/t rather than using A_t, as is commonly done in estimations of global emissions from lakes [Bastviken et al., 2004; Bastviken et al., 2011].

Our data indicate a significant correlation between CH₄ concentrations and water temperature, consistent with Marotta et al. [2014] and Yvon-Durocher et al. [2014]. Neglecting temperature compilations in CH₄ data sets and their statistical analysis [e.g., Bogard et al., 2014] may lead to unreliable conclusions. The application of MLM to the surface data from several basins and to the seasonal data from individual lakes suggests that CH₄ concentrations increase exponentially with T at a rate of 0.09–0.13°C⁻¹. This increase implies that an increase of T from 4 to 20°C would change the CH₄ concentrations by a factor of 4 to 8. Undersampling in the cold winter season and averaging the available data on CH₄ emissions may therefore lead to an overestimation of the annual mean CH₄ emission.

5 Conclusion

In summary, the correlation analysis of CH₄ and Chl-a does not provide evidence for methanogenesis in oxic water columns linked to algal production in lakes, indicating that this process is not as important for lacustrine CH₄ emissions as recently suggested [Bogard et al., 2014]. CH₄ from shallow water zones in lakes is an important source of CH₄ concentrations in the surface water of deepwater zones [Hofmann, 2013; Bastviken et al., 2004; Murase et al., 2005]. Consistent with this finding, the ratio of the surface area of shallow water zones to the overall surface area is a better predictor of basin-wide CH₄ concentrations than the total surface area itself. CH₄ concentrations increase exponentially with water temperature, which implies that compilations of CH₄ data in large data sets and their statistical analysis must consider water temperature in order to provide meaningful results.

Our data indicate that global estimates of CH₄ emissions from lakes require seasonally and spatially resolved CH₄ data and that methanogenesis in oxic water columns is not linked to algal growth. Furthermore, the CH₄ generated in shallow water zones is a major source of basin-wide diffusive CH₄ emissions from lakes. Statistical analyses of our data consistently suggest that a categorization of CH₄ fluxes according to the ratio between the surface area of the shallow water zone and the total surface area may help to improve global estimates of CH₄ emissions from lakes.