Seasonal methane dynamics in high-elevation lakes in the Sierra Nevada California : the role of elevation , temperature , organic matter , and inorganic nutrients

Freshwater lakes are important but poorly constrained sources of methane (CH4) to the atmosphere due to high, but variable, rates of CH4 production, as well as limited and inconsistent measurements worldwide. Highelevation lakes have been particularly overlooked—despite their large numbers in mountain ranges around the world, and despite CH4 dynamics at high elevations may be altered by rapid increases in temperature due to climate change. We examined variations in surface CH4 concentrations and diffusive fluxes, temperature, dissolved organic matter (DOC), and inorganic nutrients in five montane lakes spanning multiple elevations in the Sierra Nevada of California. Over two years, we found strong and consistent seasonality in CH4 concentrations in lakes; higher concentrations were typically observed in the warmest months and lower concentrations in fall. Changes in CH4 concentrations were significantly related to temperature in the majority of the individual lakes (r2 = 0.430.81) and related to elevation (r2 = 0.39) and DOC (r2 = 0.30) across lakes. Methane concentrations in lakes at elevations <3000 m were strongly related to temperature, nitrite concentrations and elevation (r2 = 0.90), whereas at elevations >3000 m, CH4 correlated with dissolved inorganic nitrogen to dissolved inorganic phosphorus ratios and elevation (r2 = 0.48). Our results expand on our understanding of temporal variations in CH4 and demonstrate substantial seasonality in CH4 concentrations and diffusive fluxes in freshwater lakes—suggesting that temporal variation should be considered in large-scale estimates, and may be a predictable function of elevation, temperature, organic matter, and nutrients.


Introduction
Methane (CH4) is a potent greenhouse gas with great influence on the world's climate (Hoegh-Guldberg et al. 2018;Reay et al. 2018). While anthropogenic emissions have increased atmospheric CH4 concentrations over the last century, an important baseline contribution of CH4 to the atmosphere comes from natural ecosystems (Conrad 2009;Kirschke et al. 2013). Methane emissions from freshwater lakes are a particularly significant, but poorly constrained, component of natural CH4 emissions. For example, the contribution of freshwater ecosystems (lakes and rivers) to the global CH4 budget is estimated to range from 12% to 32% (with uncertainties ranging from 2% to 47%) of natural emissions (Saunois et al. 2016). More specifically, current estimates of the global CH4 total emissions from freshwater lakes and impoundments range an order of magnitude, from 69 to 204 Tg CH 4-C yr -1 (DelSontro et al. 2018). These uncertainties stem partly from the substantial spatial and temporal variability in CH4 cycling across and within freshwater lakes, as well as significant under-sampling of this variability.
For instance, only a few hundred lakes have been sampled for CH4 emissions out an estimated total of 304 million lakes globally (Downing 2009;Bastviken et al. 2011), and only a handful of studies have measured CH4 variation over time (Xing et al. 2005;Casper et al. 2009;Palma-Silva et al. 2013;Natchimuthu et al. 2014;Martinez-Cruz et al. 2015). Clearly, additional studies are needed of the spatial and temporal heterogeneity in CH4 emissions from these ecosystems, as well as their potential controls (Tranvik et al. 2009;Bastviken et al. 2011;Reay et al. 2018).
Variations in CH4 concentrations in lake water columns are driven by microbial CH4 production (predominantly via methanogenesis in sediments) and consumption via microbial CH4 oxidation in surface sediments and the water column (Bastviken et al. 2004). Both of these processes can be altered by changes in environmental conditions and, in general, temperature seems to have a strong positive effect on both of them (Zeikus and Winfrey 1976;Duc et al. 2010;Palma-Silva et al. 2013;Lofton et al. 2014;Marotta et al. 2014;Sepulveda-Jauregui et al. 2018). Moreover, ecosystem-level analyses seem to indicate that as temperatures rise, CH4 lake concentrations and fluxes will also increase (Natchimuthu et al. 2014;Yvon-Durocher et al. 2014;Rasilo et al. 2015). However, much of our understanding of temperature regulation of CH4 concentrations in freshwater is derived from laboratory-or field-based experimental temperature manipulations. While these studies are extremely useful for isolating the effects of temperature from other variables, in situ temperature may vary in concert with other seasonally changing environmental properties, such as lake organic carbon (C) inputs and nutrients concentrations. For example, the quantities and types of organic C present in lakes during the year influence CH4 production (Conrad 1999), and this in turn is regulated by nutrient availability (Sepulveda-Jauregui et al. 2018). For CH4 consumption, on the other hand, temperature may only play a role when neither CH4 nor DO concentrations are limiting (Harrits and Hanson 1980;Liikanen et al. 2002;Martinez-Cruz et al. 2015). Collectively, these environmental factors may interact to influence CH4 production, consumption, and emissions. The degree to which temperature-versus other environmental factors-affects CH4 emissions from lakes remains largely unknown. Further characterization of this response is necessary as it could result in a positive climate feedback as global temperatures increase.
High-elevation regions are predicted to experience increased air temperatures, reduced lake ice cover, reduced snow-albedo, and changes in cloud cover as a result of climate change (Mountain Research Initiative EDW Working Group et al. 2015;O'Reilly et al. 2015;Sadro et al. 2019). Temperate montane lakes therefore could be disproportionately affected by climate change-including both increases in average temperatures, as well as changes in seasonal variability (e.g., reduced ice cover and a longer growing season). Importantly, high-elevation lakes can exhibit high CH4 concentrations and fluxes (McCrackin and Elser 2011), but CH4 cycling is rarely characterized in these lakes. Their contribution to the CH4 budget may be underrepresented in comparison to tropical or boreal lakes due to a lack of measurements (Saunois et al. 2016), even though they represent around 10% of lakes globally (Verpoorter et al. 2014). The Sierra Nevada of California is home to thousands of such lakes (Melack and Stoddard 1991;Sickman et al. 2003), and this region already displays a long-term warming trend . Snow-albedo feedbacks and changes in the type of precipitation will likely further increase warming and reduce snow pack melt in the decades to come (Walton et al. 2016;Sun et al. 2019).
Further reduction in snowpack melt and rain could also affect high-elevation lakes by altering nutrient inputs into freshwater lakes from snowmelt (Williams et al. 2001;Sickman et al. 2003). At the same time, increased nutrient loading from atmospheric deposition has been shown to alter algal communities and trophic dynamics in highelevation ecosystems (Baron et al. 2000;Elser et al. 2007;Elser et al. 2009).
Atmospheric deposition is a significant source of nutrients to the Sierra Nevada (Aciego et al. 2017) , where changes in nutrient limitation may already be occurring due to human activity in the adjacent San Joaquin Valley (Sickman et al. 2003). Such changes could consequently impact CH4 cycling in lakes by altering organic C sources and quantities to these ecosystems (Tranvik et al. 2009;West et al. 2016;Reay et al. 2018;Moser et al. 2019). Finally, recent research indicates that the combination of increased temperature and nutrient concentrations can strongly enhance lake CH4 production and ebullition (Davidson et al. 2018;Sepulveda-Jauregui et al. 2018). An improved understanding of the effects of environmental variation on CH4 emissions in this ecosystem will help us account for future changes in CH4 fluxes and better predict longterm climate trends.
We used large natural variations in temperature over time and with increasing elevation to determine the potential importance of temperature controls on CH4 emissions from montane lakes. High-elevation lakes in the Sierra Nevada represent an ideal experimental system for examining temperature effects on CH4 emissions within natural freshwater ecosystems because of these strong natural variations. Over two years, we quantified CH4 concentrations and diffusive emissions in five lakes spanning an elevation gradient in the Sierra Nevada, California (Fig. 1). In addition to temperature variation, we measured two main categories of environmental variation that are likely to affect CH4 emissions: nutrient (ammonium, nitrite, nitrate, phosphate) concentrations and availability and organic C production and properties (dissolved organic C and specific UV absorbance at 254 nm). Our aim was to answer the following research questions: 1) To what degree do CH4 concentrations vary spatially over an elevation gradient and temporally over the seasons in high-elevation lakes, and how does this compare with other lake types? and 2) how much of the variation in CH4 concentrations within and among lakes can be explained by seasonal fluctuations in environmental parameters (independently or collectively) such as temperature, nutrients and organic C concentrations, as well as lake intrinsic characteristics (e.g., elevation)? We hypothesized that temperature and nutrient concentrations would have the greatest effect on CH4 concentrations in surface lake water, especially at higher elevations where temperatures are rapidly increasing, and landscapes characteristics contribute less allochthonous nutrient sources to lakes.

Methane measurements
Methane concentrations were measured via headspace equilibration and gas chromatography. In brief, triplicate water samples were collected directly into 170 ml glass vials, capped with halogenated butyl stoppers, and crimped with aluminum seals to avoid gas loss. Twenty-five ml of water was then replaced with 25 ml of air collected on site, while air samples were collected into 12-mL Labco Exetainer vials (Labco Ltd., Lampeter, Ceredigion, UK). One hundred seventy mL glass vials containing water and headspace were shaken for 2 minutes to reach equilibration, and the headspace was collected with a gas-tight syringe; headspace gas samples were immediately transferred into 12-mL Exetainer vials. Triplicate samples were later analyzed using a Shimadzu GC-2014 gas chromatograph with flame ionization detection (FID) for CH4 (Weiss 1981). Samples were analyzed within 2-3 months of collection (a time period of up to 15 weeks has been tested and found to result in no significant change in CH4 concentrations, with 2% or less decrease in 5 ppm CH4 concentration from storage).
Methane standards (Air Liquide, Houston, Texas USA) ranged from 1.5 to 333 ppm and bracketed every 15 samples; standard curve r 2 values ranged from 0.997 -0.999 across different runs. Headspace CH4 concentration measurements were then used to calculate CH4 concentration in lake water based on Henry's law of equilibrium (Yamamoto et al. 1976).

Diffusive methane fluxes
Diffusive CH4 fluxes were calculated with the following equation: where F is the flux, k is the gas transfer coefficient, Cw is the dissolved CH4 concentration in the water, and Ca is the concentration of CH4 in the air. The parameter k was estimated from wind-speed data collected from meteorological stations (White Wolf, Tuolumne Meadows, and Tioga Pass stations, each selected for their close proximity to Lukens, Cathedral, and Gaylor Lakes respectively) in Yosemite National Park maintained by the California Department of Water Resources (http://cdec.water.ca.gov) and the relationship developed by Cole and Caraco (1998) for low-wind speeds: where k600 is the gas coefficient normalized to Schmidt number (Sc) 600, and U10 is the wind speed adjusted to 10 m following Amorocho and DeVries (1980).
The k600 values were converted to k values using the equation from Bartosiewicz et al. (2015): where k is the gas transfer coefficient, c equals -0.67 according to Guérin et al. (2007), and Sc is calculated following Wanninkhof (2014). While there are acknowledged uncertainties associated with calculating k from wind-speed models, we aimed to provide an estimate of diffusive emissions from high-elevation lakes that is lacking in the literature. However, these estimated diffusive fluxes were not included in further statistical analyses.

Nutrients and organic matter
For nutrient measurements, water collected in the lakes was filtered (0.22 µm) and analyzed for NH4 + , NO2 -, NO3 -, and PO4 3-. Ammonium and NO2were analyzed using a Trilogy Laboratory Fluorometer (Turner Designs; San Jose, CA, USA) with NH4 + and NO2modules using the fluorescent method of Holmes et al. (1999)  Apparent oxygen utilization (AOU) was calculated from the following equation: where O2,sat is the saturation oxygen concentration dependent on temperature and salinity and O2 is the observed oxygen concentration.

Statistical analyses
We tested relationships between CH4 concentrations in lake surface water and the following individual environmental variables using linear regression: T, DO, NO2 -, NO3 -, NH4 + , PO4 3-, ratios of dissolved inorganic nitrogen to dissolved inorganic phosphorus (DIN:DIP), DOC, SUVA254nm, and elevation. We also used these same variables in standard multiple-linear regression analyses to predict CH4 concentrations.
Predictor variables and multi-linear models were selected based upon adjusted R 2 values, Aikake Information Criteria (AIC) of goodness of fit, and model significance. A priori significance level was defined as α<0.05. We ran multi-linear regressions for the pooled data as well as for mid-elevation (Lukens, Upper and Lower Cathedral Lakes) and upper-elevation (Lower and Upper Gaylor Lakes) lakes separately. Data were assessed to ensure they met the assumptions of regression (independence of observations, homoscedasticity, and normality of residuals). Methane concentrations were natural-log-transformed due to non-normality of residuals and heteroscedasticity, but the predictor variables met all linear regression assumptions previously mentioned.

Methane concentrations and diffusive fluxes within and across lakes
Methane concentrations and fluxes in lakes are often measured at single time points, even though they may have a highly dynamic nature. In our study, CH4 concentrations showed large variations across lakes and over time, ranging from 16 to 3679 nM ( Fig.   2a). All of these values were supersaturated, indicating that all lakes were net sources of CH4 to the atmosphere at all times (Table 1). Within individual lakes, the highest and most variable CH4 concentrations were found in Lukens and Lower Gaylor Lakes.
Lukens is located at the lowest elevation and generally showed the highest CH4 concentrations-although the single highest value was observed in Lower Gaylor, the majority of concentrations >500 nM occurred in Lukens Lake ( Diffusive CH4 fluxes ranged from 0.007 to 2.3 mmol m -2 day -1 (Fig. 2b, Table 1).

Seasonal and elevational variation in methane and temperature
Along with variation in CH4, temperature showed expected seasonal and elevational variation within and across lakes. We observed similar seasonal trends in all lakes, where peak temperatures occurred in late July and early August, and temperatures were lowest at the end of the sampling season in October through November for both 2016 and 2017 (Fig. 2c) Given coincident seasonal variations in CH4 concentrations and temperature, consistent differences between lakes at different elevations, and previous work demonstrating temperature effects on CH4 emissions, we analyzed potential relationships between temperature and CH4 concentrations (Fig. 3a). Within individual lakes, CH4 concentrations correlated with seasonal temperature variations in lake water in Lukens (r 2 = 0.65, p<0.005, n = 12), Lower Cathedral (r 2 = 0.53, p<0.05, n = 8) and Upper Cathedral Lake (r 2 = 0.81, p<0.005, n = 8). Methane concentrations were not significantly related to temperature in Upper Gaylor Lake, and were inversely related to temperature in Lower Gaylor Lake (r 2 = 0.43, p<0.05, n = 11). Data pooled across all lakes showed no significant correlation between CH4 concentrations and temperature, likely due to the different patterns observed in the individual lakes. In particular, lower elevation lakes with more substantial temperature variation showed stronger correspondence between temperature and CH4. We therefore analyzed relationships with elevation and found that elevation was the most significant factor determining CH4 concentrations in the water-overall, the lower the elevation, the higher the CH4 concentration in the lake (r 2 = 0.39, p<0.005, n = 49). Temporal variations within individual lakes are superimposed on this overall pattern.

Organic matter production and composition
To examine potential relationships between CH4 concentrations and organic C dynamics, we measured DOC and SUVA in 2017, and DO in 2016 and 2017. DOC followed an elevational trend (Table 1); Lukens Lake presented the highest DOC values We also measured DO, as it (1)  July and the highest in October (Fig. 4a). Dissolved oxygen ranged from 6.0 to 8.0 mg L -1 in Lukens Lake, 6.0 to 7.8 mg L -1 in Lower Cathedral Lake, and 5.0 to 7.7 mg L -1 in Upper Cathedral Lake. Gaylor Lakes, located at the highest elevation, presented the highest DO, with Lower Gaylor ranging from 5.0 to 8.7 mg L -1 and Upper Gaylor ranging from 6.0 to 8.9 mg L -1 . Methane concentrations were inversely correlated with DO in Lukens Lake (r 2 = 0.69, p<0.005, n = 11), while correlations for the other lakes individually or using pooled data across all five lakes were not significant. Given that variations in temperature likely affect observed DO concentrations, we calculated apparent oxygen utilization (AOU) from the difference between DO values expected in equilibrium with the atmosphere at different temperatures versus those observed.
Apparent oxygen utilization showed consistent seasonal trends in most of the lakes ( Figure 4b). However, CH4 concentrations were not significantly related to AOU.

Inorganic nutrients dynamics
We measured three forms of dissolved inorganic nitrogen (DIN; ammonium, nitrite, and nitrate), as well as dissolved inorganic phosphorus (DIP; phosphate). High-elevation lakes are typically nutrient depleted (Sickman et al. 2003;Moser et al. 2019), and the lakes in this study are no exception, with low concentrations of all measured inorganic nutrients (Fig. 5).
Ammonium concentrations were low and variable (0.18 to 2.83 µM, with the majority of NH4 + concentrations <1.5 µM), but in contrast to CH4, NH4 + concentrations did not display a seasonal trend and CH4 was not significantly related to NH4 + (Fig. 5a). Both NO2and NO3concentrations were also low over the period studied, typically ranging from 0 to 1 µM ( Fig. 5b and 5c). Nitrite trends in the lakes differed from year to year.
In 2016, overall variation was higher, and there were no discernible seasonal trends; in 2017, all NO2concentrations were uniformly <0.3 µM, and we observed a seasonal

Multi-linear model for CH4 concentrations in high-elevation lakes
Given the seasonal and elevation-related patterns observed in high elevation lakes, we tested for statistically significant relationships between CH4 and potential explanatory variables using multiple linear regression. Pooling all lakes together showed that the only significant predictor variable across all lakes was elevation (Table 2); however, individual lakes displayed strong temperature responses, especially at lower elevations.
As a result, we classified lakes into two elevational bands (mid-and upper elevation) to better understand relationships at different elevations ( Table 2). The multilinear regression in the mid-elevation band showed that CH4 concentrations in lake water were significantly correlated to temperature, elevation, and NO2 -; in the upper-elevation lake band, CH4 concentrations were significantly related to elevation and DIN:DIP ratios.
Methane concentration in individual lake surface water and in the pooled lake data was consistently related to elevation, as well as in the elevation band regressions. Contrary to our hypothesis, CH4 concentrations in mid-elevation lakes, but not upper-elevation lakes, were positively correlated to temperature over the growing season.

Seasonal variation in methane
Our findings have multiple implications for our understanding of CH4 biogeochemistry in freshwater ecosystems. First and most fundamentally, significant seasonal variability was clearly evident in CH4 concentrations in Sierra Nevada lakes, as highest CH4 concentrations were observed in the warmest months, and lowest CH4 concentrations were typically observed at the end of the sampling season before winter. Field site accessibility prevented taking measurements during the winter and spring seasons, but Greene et al. (2014) and Jammet et al. (2015) showed that there can be significant CH4 release during ice-off due to the build-up of CH4 under ice throughout winter and spring. While this phenomenon was not captured here and could be significant, it underlines our over-arching finding that dissolved CH4 can be highly variable over time. temperatures were observed-a finding shared for a single shallow pond in Sweden (Natchimuthu et al. 2014), and for a single subtropical lake in China (Xing et al. 2005).
Contrarily, Martinez-Cruz et al. (2015) found the opposite pattern for thirty Alaskan Lakes, where CH4 concentrations were on average lower during the summer and higher during the wintertime due to changes in lake ice cover. Taken together, these limited data indicate that seasonal CH4 variations can be significant, and our results provide additional context from five contrasting, high-elevation lakes in the Sierra Nevada.
Third, changes in the length of the growing season will likely increase overall CH4 diffusive flux if periods of high CH4 concentrations in lake water expand in time. This may be especially relevant for high-elevation lakes, where warmer air temperatures will increase the lake ice-free period, increase water temperature, and potentially increase organic matter and nutrient inputs from the surrounding watershed-at least in the short-term (Moser et al. 2019;Sadro et al. 2019). In line with this idea, our results showed that CH4 concentrations in high-elevation lakes were most strongly correlated with elevation, with higher average CH4 concentrations at lower elevations. Elevation can be a proxy for temperature, as lower elevations showed the lowest mean temperatures (see below). If high-elevation lakes shift to resemble lower-elevation lakes, the strong correlation with elevation suggests increased CH4 concentrations.
However, both organic C concentrations and composition, as well as nutrient concentrations, may also vary with elevation. In general, lakes at higher elevation tend to be more oligotrophic, as allochthonous sources of C and nutrients become more scarce in alpine and sub-alpine regions (Urmy and Warren 2019). We therefore evaluated organic matter and nutrients as potentially relevant factors for CH4 cycling in lakes that are also elevation dependent.

Relationships between methane, organic matter production and composition, and dissolved nutrients
The quality and quantity of organic matter can affect methanogenesis in lakes because organic matter provides substrates for CH4 production, and affects oxygen availability in sediments due to heterotrophic aerobic respiration (Tranvik et al. 2009;Grasset et al. 2018;Sepulveda-Jauregui et al. 2018). We found that patterns in DOC and SUVA254nm were consistent with lake elevation and watershed characteristics (Table 1). In particular, Lukens Lake is located at the lowest elevation with a surrounding meadow, and likely has a larger input of allochthonous C, while Lower and Upper Cathedral Lakes are at higher elevation where allochthonous C would be relatively lower. Lower and Upper Gaylor Lakes are located above the tree line where DOC levels tend to be lower (Moser et al. 2019). Consistent with this, DOC concentrations were the highest at the lowest elevation and decreased with increases in elevation (Table 1). The specific UV absorbance at 254 nm is a useful measure to perceive changes in organic C over the growing season. Low SUVA254nm is indicative of overall low molecular weight (Chowdhury 2013) and low percent aromaticity (Weishaar et al. 2003). Allochthonous sources of organic C are often complex molecules (aliphatic polymers, humic substances) that are mainly degraded under aerobic conditions, whereas autochthonous sources can be mineralized under both aerobic and anaerobic conditions (Zehnder and Svensson 1986;Hulthe et al. 1998;Bastviken et al. 2004). In our study, the inverse correlation between CH4 concentrations and SUVA254nm values (Supplemental Fig. 2) suggests that simple C molecules favor enhanced CH4 production.
High-elevation lakes are also often oligotrophic, such that changes in nutrient concentrations can affect the overall ecology of the lake. Higher nutrient input to lakes can alter lake community structure and enhance primary productivity and CH4 production (Tranvik et al. 2009;West et al. 2016;Reay et al. 2018). Overall, we found low concentrations of all dissolved inorganic nutrients-consistent with oligotrophic conditions prevalent in high-elevation lakes. Although both nitrogen (N) and phosphorus (P) may be limiting nutrients in freshwater ecosystems (Elser et al. 2007), P availability is particularly relevant to the CH4 paradox (i.e., the observation of consistent supersaturation of CH4 in freshwater and marine oxic surface waters; Karl et al. 2008;Tang et al. 2014). Several studies have proposed that biological mechanisms other than traditional methanogenesis produce CH4 (Grossart et al. 2011;Bogard et al. 2014;Tang et al. 2016;Bižić et al. 2020) and one mechanism that may be particularly important in oligotrophic ecosystems is the demethylation of methyl phosphonate. This can be performed by multiple groups of bacteria using C-P lyase genes during the degradation of DOM (Repeta et al. 2016;Yao et al. 2016;Wang et al. 2017), and has been observed in both freshwater (Yao et al. 2016;Wang et al. 2017) and marine (Karl et al. 2008;Metcalf et al. 2012;Carini et al. 2014;Repeta et al. 2016) ecosystems.
In our study, we found low but detectable PO4 3concentrations through most of the icefree season in most lakes. This result is consistent with a long-term study of Emerald Lake in the Sierra Nevada (Sickman et al. 2003). We focused on inorganic nutrient concentrations because previous work has shown that ecological changes associated with nutrient enrichment can affect CH4 fluxes, and changes in bioavailable P could affect CH4 production via methyl phosphonate breakdown. In particular, we might expect that low P availability overall, or in comparison to N, might result in increased microbial methylphosphonate breakdown, and therefore increased CH4 production.
However, we did not observe significant relationships between CH4 concentrations and DIP.
Instead, CH4 was related to dissolved nitrite, nitrate, and DIN:DIP ratios within some individual lakes and in multiple linear regression (Supplemental Fig. 1, Table 2). While CH4 concentrations were not as consistently related to inorganic nutrients as they were to temperature and elevation, they still displayed significant correlations in some of the high-elevations lakes studied here (Supplemental Fig. 1). Higher elevation lakes exhibit lower nutrient and DOC concentrations than mid-elevations lakes (Moser et al. 2019;Urmy and Warren 2019); in this area, microbial activities may be constrained by nutrient concentrations. Previous studies have found that alpine ecosystems are highly sensitive to modest N deposition (Baron et al. 2000;Wolfe et al. 2003;Vinebrooke et al. 2014). Consistently, lakes in this study were likely N-depleted for the majority of the season, which may explain why CH4 concentrations were predicted to be higher when N was more available either in the NO2form or as a higher DIN:DIP ratio.

Methane dynamics in relation to elevation and temperature
We found significant relationships between CH4 concentrations and elevation and temperature. Highest CH4 concentrations were observed at the lowest elevation lake and decreased with elevation. While associated with elevation, temperature was also correlated with CH4 concentrations measured over time in the mid-elevation lakes (<3000 m, Lukens, Upper and Lower Cathedral Lakes). In our study, lakes located at different elevations with different mean temperatures showed distinct seasonal patterns in temperature and CH4 concentrations. Likewise, lakes sampled in earlier work also varied in the strength of CH4-temperature relationships (Xing et al. 2005;Casper et al. 2009;Palma-Silva et al. 2013;Natchimuthu et al. 2014), but showed that temperature increases have overall a corresponding positive response on lake CH4 concentrations (Natchimuthu et al. 2014;Marotta et al. 2014;Yvon-Durocher et al. 2014;Rasilo et al. 2015). Our data provide additional evidence of positive temperature-CH4 relationships in several lakes.
Collectively, these observations lend support to the hypothesis that CH4 concentrations are typically closely related to temperature, but other factors that vary seasonally or with elevation may also be important in regulating CH4 concentrations in lakes. In particular, CH4 concentrations were correlated with temperature, elevation, and NO2in mid-elevation lakes. In contrast, the lack of a temperature response in the upper- concentrations.
Methane ebullitive fluxes were not measured in this study but can be a major contribution to total lake CH4 emissions, especially in shallow lakes (Bastviken et al. 2004;DelSontro et al. 2016 Table 2. Multi-linear regression models for methane (CH4) surface concentrations as a function of environmental parameters measured in five Sierra Nevada montane lakes.

Tables and figures
Abbreviations: NO2 -= nitrate and DIN:DIP = dissolved inorganic nitrogen to dissolved inorganic phosphorus ratio.