Spatial and Temporal Correlates of Greenhouse Gas Diffusion from a Hydropower Reservoir in the Southern United States

Emissions of CO2 and CH4 from freshwater reservoirs constitute a globally significant source of atmospheric greenhouse gases (GHGs), but knowledge gaps remain with regard to spatiotemporal drivers of emissions. We document the spatial and seasonal variation in surface diffusion of CO2 and CH4 from Douglas Lake, a hydropower reservoir in Tennessee, USA. Monthly estimates across 13 reservoir sites from January to November 2010 indicated that surface diffusions ranged from 236 to 18,806 mg·m−2·day−1 for CO2 and 0 to 0.95 mg·m−2·day−1 for CH4. Next, we developed statistical models using spatial and physicochemical variables to predict surface diffusions of CO2 and CH4. Models explained 22.7% and 20.9% of the variation in CO2 and CH4 diffusions respectively, and identified pH, temperature, dissolved oxygen, and Julian day as the most informative predictors. These findings provide baseline estimates of GHG emissions from a reservoir in eastern temperate North America, a region for which estimates of reservoir GHGs OPEN ACCESS


Introduction
Hydropower is an important renewable component of national energy portfolios in many countries.Although hydropower traditionally has been considered to be carbon neutral [1], recent investigations suggest that the reservoirs created by large hydropower dams emit greenhouse gases (GHG), primarily carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) [2,3].For example, Barros et al. [4] estimated that hydropower reservoirs release to the atmosphere 48 Tg of carbon as CO2 and 3 Tg of carbon as CH4 each year, based on extrapolation of emissions estimates from 85 globally distributed hydropower reservoirs.This carbon emission rate comprises 4% of the total net carbon emitted from the surfaces of all natural and human-created freshwater bodies and therefore represents a significant component of the global carbon cycle [4].Emissions of GHGs from reservoirs occur via three main pathways.First, accumulation of dissolved GHGs in the water column, primarily originating from microbial metabolism, leads to passive diffusion from the reservoir surface to the atmosphere [2,5].Second, gas bubble ebullition from the sediments of the reservoir also contribute to GHG emissions, particularly in the form CH4 from shallow areas of reservoirs [6][7][8][9].More recent investigations have documented the ebullition of microbubbles generated from oxic production of CH4 in the water column is also a source of GHG emission from reservoirs [10].Third, the rapid decrease in pressure as water leaves the reservoir, passes through the hydroelectric turbine, and is expelled into the tailrace allows GHGs to diffuse into the atmosphere.The relative contribution of GHGs from these three pathways varies from reservoir to reservoir and across seasons, and depends on various factors related to reservoir morphometry, age, and dam operation [3,4,11].Nevertheless, surface diffusion often is the dominant contributor of GHG emissions [3,8,11], and is the focus of this study.
Many environmental factors contribute to the spatial and temporal variation in GHG surface diffusion.From a spatial perspective, surface diffusion of GHGs varies among reservoirs distributed along broad geographic gradients.For example, mean annual air temperature is a key factor affecting GHG emissions, with low-latitude tropical reservoirs typically emitting GHGs at greater rates per unit area than high-latitude temperate and boreal reservoirs [4].Additionally, nutrient loading from the upstream catchment also contributes to variation in GHG emissions among reservoirs receiving drainage from agricultural versus natural land cover [3].Emissions of GHGs also vary along environmental gradients within reservoirs.For example, ebullition occurs most often in shallow areas where bubbles remain intact.Bubbles originating from deeper areas can dissolve in the water column before reaching the reservoir surface resulting in greater passive diffusion [6][7][8]12].Longitudinal position within the reservoir is also important, with shallow river delta habitats in the upper reservoir typically producing more GHGs than deeper reservoir habitats nearer the dam [3].From a temporal perspective, GHG emissions vary among years and among seasons within a year.Emissions of GHGs correlate negatively with reservoir age because new reservoirs generally contain larger pools of labile organic carbon from inundated terrestrial vegetation relative to older reservoirs [13].Emissions of GHGs also vary within a year due to seasonal changes in temperature, nutrient availability, hydrology, and stratification-turnover dynamics [3,14].
Identifying the spatial and temporal drivers of GHG emissions within and among reservoirs is an important step in developing a predictive framework that can be used to forecast future GHG emissions of existing reservoirs as well as those reservoirs currently under construction or planned for construction.The ability to identify environmental correlates of GHG emissions requires data on GHG emissions from environments and geographic regions that have not previously been studied.In particular, many of the investigations of GHG emissions by reservoirs have taken place in tropical or boreal regions [4,15].Fewer studies have been undertaken in reservoirs at mid-latitudes (but see [3,16,17]) even though approximately 30% of all reservoirs occur at these latitudes throughout the world [4].Also lacking are studies of seasonal variation in GHG emissions along environmental gradients within a single reservoir (but see [3]) [12].
The overall objective of this study was to evaluate spatial and temporal variation in GHG emissions from Douglas Lake, a hydropower reservoir in the southeastern United States.First, we measured fluxes of CO2 and CH4 from the reservoir to the atmosphere via surface diffusion.Measurements were made across seasons and throughout the reservoir to document spatial and temporal variation in diffusion rates.Second, we developed statistical models to quantitatively characterize environmental correlates of CO2 and CH4 surface diffusion in both space and time.To do this, we used a recently-developed statistical algorithm, Random Forests [18], which can identify non-linear and threshold relationships between predictor variables and the response variable.By developing statistical models, our goal was to elucidate environmental drivers of variation in CO2 and CH4 emissions within a reservoir.Such statistical models can be used to predict GHG emissions in other unsampled reservoirs in this geographic region, and possibly forecast GHG emissions following future environmental changes such as increased nutrient loading or rising air temperatures.

Study Site and Field Sampling
Douglas Lake is located in eastern Tennessee and was formed in 1943 following the construction of Douglas Dam on the French Broad River in the upper Tennessee River basin (Figure 1).Douglas Dam is 61 m in height and 520 m wide and is equipped with four Francis-type hydropower turbines with a total electricity generation capacity of 111 megawatts.Douglas Lake covers 115 km 2 and is managed by the Tennessee Valley Authority (TVA) primarily for flood storage and hydroelectric generation, but it is also used extensively for recreational activities [19].The reservoir is a warm monomictic system and pool elevation fluctuates seasonally by approximately 13.4 m, with maximum drawdown occurring from December through February.Water quality deficiencies include low concentrations of dissolved oxygen, particularly in the hypolimnion during summer stratification [20].Field measurements were made monthly at 13 sites from January to November 2010, excluding February (Figure 1).During each monthly sampling campaign, all 13 sites were sampled over four or fewer consecutive days between the hours of 800 and 1800.Sites were distributed among six lentic main lake locations within Douglas Lake placed at increasing distances from Douglas Dam (M1-M6); four lentic cove locations within Douglas Lake placed at increasing distances from Douglas Dam (C1-C4), and three lotic locations on the Nolichucky River (U1), French Broad River (U2), and Pigeon River (U3) upstream of Douglas Lake.This distribution of sites captured spatial variation in environmental characteristics known to affect GHG production and surface diffusion [3,9,12].

CO2 and CH4 Emissions and Physicochemical Variables
We estimated CO2 and CH4 emissions using the thin boundary layer (TBL) method following a standard protocol outlined by the International Hydropower Association [20].This method uses GHG concentration gradients at the water surface and semi-empirical equations to indirectly estimate GHG flux.Greenhouse gas diffusion estimates using the TBL method can be less accurate under certain conditions than direct measurement of diffusion using floating chambers [21], but still can provide useful estimates of GHG diffusion, particularly when a large number of locations and/or open windy lake locations are sampled [22].Water samples were collected from within 0.5 m of the reservoir surface in 125-mL serum bottles sealed with butyl stoppers and preserved with potassium chloride (KCl).Samples were returned to the laboratory where headspace gas chromatography was used to measure the concentrations of dissolved CO2 and CH4 [23].Two or three water samples were collected from each site on each sampling date, and the mean concentrations of gases in these subsamples were calculated and used in the following TBL calculations to estimate surface diffusions.
Gas diffusion from the water surface to the atmosphere can be estimated as the product of the concentration gradient between the surface water and air and a gas exchange coefficient (k) for CO2 (Equation (1)) and CH4 (Equation ( 2)).

CO diffusion = water[CO ] − air[CO ] × k
(1) Greenhouse gas concentrations from the water surface were calculated as the partial pressure of the gas (CO2 or CH4), which require data on water salinity, water temperature, air temperature, and atmospheric pressure.Gas exchange coefficients were calculated using the Schmidt number for each gas (CO2 or CH4), wind speed, and temperature.Air and water temperatures were measured at each site when water samples were collected.Wind velocity and atmospheric pressure measurements were acquired from a National Oceanic and Atmospheric Administration weather station located 34 km east of Douglas Dam [24].Concentrations of CO2 and CH4 in the atmosphere were assumed to be 388 ppm and 1.8 ppm, respectively, based on recent global estimates [25].We calculated monthly estimates of reservoir-wide diffusion of CO2 and CH4 by multiplying reservoir surface area (115 km 2 ) by the area-specific diffusion rates averaged across the ten lentic sites (M1-M6 and C1-C4).These reservoir-wide estimates assume that the ten lentic sampling locations capture the spatial variation in CO2 and CH4 surface diffusion; this method has been used in previous estimates of reservoir-wide GHG emissions [3].
In addition to GHG emissions, measurements of temperature, dissolved oxygen (O2), conductivity, and pH were made from the surface and bottom of the water column on each sampling date from each site using a multiparameter data sonde (Model 6820 V2; YSI Inc.; Yellow Springs, OH, USA).Additional water samples were collected from the surface and bottom of the water column on each sampling date from each site using a van Dorn water sampler; then samples were analyzed for dissolved organic carbon (DOC), ammonium (NH4 + ), nitrate (NO3 − ), soluble reactive phosphorus (SRP), and total phosphorus (TP) concentrations using standard methods [18].

Data Analysis
We calculated sample averages and 95% confidence intervals for surface and bottom values of physicochemical variables and surface concentrations of CO2 and CH4 for each month (sites pooled) and for each site (months pooled) to summarize the spatial and temporal variation in GHG flux from Douglas Lake.We also calculated sample averages and 95% confidence intervals for surface concentrations and diffusive fluxes of CO2 and CH4 for each month (sites pooled) and for each site (months pooled) to summarize and visualize the spatial and temporal variation in GHG flux from Douglas Lake.
We developed statistical models to identify environmental correlates of CO2 and CH4 surface diffusions across the reservoir and among seasons.The Random Forests algorithm generates a regression tree using a random subset of the observations (i.e., samples) and environmental predictor variables.This procedure is repeated many times (i.e., 1000 times for the present analysis) and the response variable is predicted using a composite of all regression trees (i.e., the forest).This recently-developed statistical algorithm is useful for characterizing nonlinear relationships between predictor variables and the response variable, modeling high order and complex interactions among predictor variables, and accommodating missing values of predictor variables [26].These properties make Random Forests models more accurate and informative than more traditional techniques (e.g., multiple linear regression) when modeling complex ecological responses [26].We screened a total of 23 environmental predictor variables measured during field sampling for use as predictors in the random forest models.We calculated pairwise correlation coefficients of all 23 variables and removed highly correlated (R >0.7) variables, retaining the variable from each pair that was hypothesized to be more causally linked to GHG fluxes (e.g., SRP instead of TP).We also removed CO2 and CH4 concentrations, wind speed, and surface water temperature because these variables are used directly in the TBL equations and would artificially inflate model performance if included as predictors.Sixteen variables were retained as predictors in the Random Forests models (Table 1).These variables were used to develop separate models for CO2 and CH4.Model performance was evaluated as the percent of variance explained, and statistical significance was evaluated by testing for linear relationships between model-predicted and observed GHG fluxes.We quantified the importance of predictor variables as the decrease in node impurity standardized from zero to one [26].Lastly, we created partial dependence plots to visualize the independent effects of each of the five most important predictor variables for the CO2 and CH4.Partial dependence plots are useful for identifying non-linear or threshold relationships between predictors and the response.Because Random Forests models are a composite of many separate regression trees built from a random subset of the predictors, partial dependence plots can effectively display the relationship between the response and a single predictor variable, while factoring out the effects of the remaining predictor variables [26].Statistical analyses were performed in the R programming environment using the randomForest library [27].
Table 1.Importance of 16 environmental predictor variables in explaining variation in surface diffusion of CO2 and CH4 based on thin boundary layer (TBL) estimation at six lentic main lake sites (M1-M6), four lentic cove sites (C1-C4), and three upstream lotic sites (U1-U3).Variable importance was measured as the decrease in node impurity of each Random Forests model with values standardized from 0 to 1.

Physicochemical Conditions of Douglas Lake
Physicochemical factors (averaged across seasons) varied across sampling sites at Douglas Lake (Table 2).Main lake sampling sites increased in depth from a seasonal average of 2.5 m in the upstream-most site (M1) to 25.2 m in the downstream-most site (M6).Upstream lentic sites were the shallowest (~1.5 m) and cove sites were of moderate depths, ranging from 4.8 to 15.7 m.Surface temperatures averaged across seasons were generally consistent across sites, ranging from 20.7 °C to 27.6 °C.Bottom temperatures averaged across seasons were lowest in the deep downstream-most site (M6).Likewise, O2 concentrations at the surface were consistently high across sites (7.4 to 10.0 mg•L −1 ), whereas bottom O2 concentrations varied across sites (3.1 to 8.9 mg•L −1 ) and were lowest in the downstream-most main lake sites due to thermal stratification during the summer.DOC concentrations were consistent across sites at the surface (2.1 to 4.9 mg•L −1 ), but were more variable across sites at the bottom (1.7 to 6.9 mg•L −1 ).Concentrations of NH4 + , NO3 − , SRP, and TP as well as pH varied across sites, but did not show consistent upstream-to-downstream, lentic-to-lotic, or main lake-to-cove trends.
Physicochemical factors (averaged across sites) varied seasonally (Table 3).Depth at all sites except the lotic upstream sites peaked in the spring, declined steadily through the summer, and were lowest in the winter due to management of pool elevation by the TVA.Mean monthly surface temperatures ranged from 3.2 °C in January to 29.6 °C in July.Bottom temperatures showed a similar seasonal trend, but the maximum temperature in August (25.7 °C) was lower than surface temperature during that month due to thermal stratification.Concentrations of O2 at the surface ranged from 7.5 mg•L −1 in August to 12.7 mg•L −1 in March.At the bottom of the water column, O2 concentrations ranged from 3.0 mg•L −1 in August to 12.9 mg•L −1 in March.DOC at the surface and at the bottom ranged from 1.3 to 3.6 mg•L −1 from January to September, but were higher in October and November (range of 6.8 to 7.1 mg•L −1 ).Surface NH4 + concentrations ranged from 13.1 to 50.1 µg N•L −1 across months, but did not exhibit noticeable seasonal cycles.Bottom NH4 + concentrations, bottom and surface concentrations of NO3 − , and bottom and surface concentrations of SRP were variable across months but did not exhibit noticeable seasonal cycles.

CO2 and CH4 Emissions from Douglas Lake
Reservoir-wide estimates of surface diffusion ranged from 27,137 kg•day −1 in January to 2,091,331 kg•day −1 in July for CO2 and 0 kg•day −1 in March and April to 71 kg•day −1 in July for CH4.Area-specific rates of CO2 surface diffusion varied spatially with the low rates ranging from 2480 to 6471 mg•m −2 •day −1 in the downstream-most main lake sites (M2-M6) and cove sites (C1-C4), whereas higher rates ranging from 12,177 to 18,806 mg•m −2 •day −1 occurred in the upstream-most lentic main lake site (M1) and the three upstream lotic sites (U1-U3) (Figure 3A).Area-specific rates of CH4 surface diffusion also increased from downstream to upstream within the lentic main lake and cove sites, ranging from 0.25 mg•m −2 •day −1 at the downstream-most main lake site (M6) to Our evaluation of surface diffusion of CO2 and CH4 indicates that Douglas Lake is a net emitter of both of these GHGs, regardless of season or location within the reservoir.Emissions of CO2 were four to five orders of magnitude greater than emissions of CH4, which is consistent with previous studies of reservoir GHG emissions [11,22].Our estimates of surface diffusion averaged across seasons and reservoir locations (7067 and 0.34 mg•m −2 •day −1 for CO2 and CH4, respectively) fall within the range of previously reported rates of surface diffusion of these gases from other reservoirs throughout the world.Specifically, our estimates are similar to those from reservoirs in the Western United States [11], Canada [28][29][30], and Scandinavia [31], but are lower than estimates from tropical reservoirs [32].These comparisons match the low-to-high latitude decline in GHG emissions reported by Barros et al. [4].Only a few studies have reported GHG emissions from reservoirs in the eastern United States.Beaulieu et al. [3] and Jacinthe et al. [33] reported higher emission rates, which could be a consequence of the higher agricultural land use (and consequent higher nutrient loading) surrounding their study reservoirs in Ohio and Indiana, respectively, compared to Douglas Lake.
Much recent research has focused on documenting among-reservoir variation in GHG emissions and identifying broad scale environmental drivers of this variation, such as latitude, net primary production, and reservoir morphology [4,11,34].Less is known about environmental gradients driving variation in GHG emissions within a single reservoir.Our findings suggest that surface diffusion of CO2 and CH4 increases from downstream to upstream locations in the reservoir.This pattern has been documented in previous studies and has been attributed to shallow depths and greater nutrient and carbon availability from tributary influxes in upstream areas of the reservoir, particularly at the river delta [3].Interestingly, we did not observe strong differences in GHG flux between deeper main lake and shallower cove locations located at similar longitudinal positions.This finding suggests that input of nutrients and labile carbon from the three major tributaries (Nolichucky, French Broad, and Pigeon Rivers), and not factors associated strictly with shallow water, is important in generating higher levels of GHG surface diffusion in shallow upstream areas.
Identifying seasonal variation in GHG emissions from hydropower reservoirs is also a key research need.We show that surface diffusion of CO2 and CH4 generally increases during the summer months, as observed in previous studies [22,31,32].This pattern is consistent with higher temperatures throughout the water column and elevated rates of microbial metabolism, producing more CO2 and CH4 in bottom sediments and the water column [5,8,35].Interestingly, we observed high surface concentrations and subsequent diffusion rates of CH4 in January as well.This seasonal anomaly was apparent for the most downstream main lake and cove sites.Future work should focus on elucidating causes of this high CH4 diffusion in January and exploring GHG fluxes in nearby reservoirs for similar seasonal anomalies.

Modelling Spatial and Temporal Variation in GHG Emissions
The Random Forests models were statistically significant (p < 0.0001) and explained 22.7% of the variance in CO2 surface diffusion and 20.9% of the variance in CH4 surface diffusion.Surface pH, Julian date, bottom DOC, distance upstream from the dam, and surface DOC were the five most important predictors of CO2 diffusion, whereas bottom temperature, surface O2, surface pH, surface DOC, and Julian date were the five most influential predictors of CH4 diffusion (Table 1).Partial dependence plots revealed nonlinear relationships between environmental predictors and surface diffusions of CO2 and CH4 (Figure 4).Specifically, surface diffusion of CO2 was highest when surface pH was less than eight and between Julian dates ranging from one to 180.Surface diffusion of CO2 also increased notably between 40 and 70 km upstream from the dam.Surface diffusion of CH4 was positively associated with bottom temperature, with diffusion increasing at temperatures of 25 °C and higher.Surface diffusion of CH4 also declined notably when surface O2 was above 7 mg•L −1 and when surface pH exceeded 7.5.
Multivariate statistical models have been applied to various questions related to global change biology [36,37], but they have had only limited application in studies of reservoir GHG emissions [4].Our results suggest that multivariate statistical models can explain a moderate amount of variation (20.9% to 22.7%) in CO2 and CH4 fluxes, using spatial factors and commonly-measured physicochemical factors as predictor variables.This lack of strong predictive capability could be due to several factors.First, we used TBL estimates of surface diffusion as the response variable, yet surface diffusion rates based on such estimates are inherently less accurate than direct measurements with floating chambers [21].Second, diurnal cycling of CO2 and CH4 can influence rates of surface diffusion [5,38,39]; however, we did not include predictor variables to account for such diel variation.Third, although we included a variety of environmental variables as predictors, including other unmeasured environmental factors in statistical models would likely improve model performance.For example, structural and metabolic characteristics of lake-bottom sediments are known to be important drivers of GHG production and emissions in lakes and reservoirs [8,35].Further, including temporally varying drivers such as tributary discharge and reservoir turnover rate would also likely improve model performance [3,10].Nevertheless, relationships between GHG fluxes and the most influential predictor variables matched predictions based on known physicochemical properties as well as previous studies aimed at identifying environmental correlates of reservoir GHG emissions.For example, our partial dependence plots showed the negative relationship between CO2 flux and surface pH expected due to the known relationship between CO2 speciation and pH [5].Other investigators have also noted a relationship between CO2 flux and pH in reservoirs of the Western United States [10].Likewise, CH4 flux was positively associated with water temperature at the bottom of the reservoir and negatively associated with dissolved oxygen concentrations-factors that drive benthic microbial metabolism and anaerobic respiration pathways, respectively [5].  1 for a summary of variable importance for all 16 predictor variables.
Fundamental physicochemical relationships suggested by the results of our models indicate that our statistical models provide an essential first step toward developing and refining more precise and accurate statistical models which we view as an important goal in future studies of reservoir GHG emissions.In particular, further work should focus on measuring additional environmental variables that are hypothesized to be causally linked to GHG production in pelagic and benthic environments of the reservoir, as well as those variables linked to the flux of GHG via the key pathways.For example, sediment nutrient and oxygen conditions should be measured and used as causal predictors of CH4 production and subsequent surface diffusion.Also, microbial abundance and functional composition in the pelagic zone in part determine the degree to which rising CH4 bubbles are oxidized to CO2 [14,38], and therefore may be precise and accurate predictors of CO2 and CH4 fluxes.Lastly, the use of recently developed and flexible statistical algorithms, such as Random Forests, allows investigators to identify nonlinear and threshold relationships between predictor and response, which is more informative than traditional correlative analyses based on linear regression [26].
Although our statistical models did not predict as precisely needed for the purpose of predicting or forecasting GHG emissions in other study systems, further refinement of statistical models like the ones we present here should be useful for several generally-applicable reasons.First, statistical models will improve understanding of cause-effect relationships between environmental and spatial factors and fluxes of GHGs.Second, models incorporating predictor variables compiled in a spatially continuous manner across a body of water (e.g., depth from digitized bathymetric maps) can be used to project GHG emissions in a spatially continuous manner.This approach can improve the precision of whole-reservoir emissions estimates over those estimates made from a small number of sampling stations placed in representative habitats and then extrapolated to the entire reservoir.Third, precise statistical models can be used to forecast emissions under future environmental conditions associated with reservoir aging [4] and/or changes in climate [40], nutrient loading [31], dam operations [3], or yet other unknown factors.Such models will be useful for life cycle analyses aimed at estimating the complete carbon footprint of hydropower projects starting with construction, extending through their operational lifetime, and ending with their decommissioning [34,41].Lastly, although we developed a statistical model to predict spatial and seasonal variation in GHG emissions within a reservoir, this approach could easily be applied to broad-scale studies of variation in GHG emissions among reservoirs within a region, across a continent, or the entire globe.Such broad-scale studies will aid in better understanding broad scale drivers such as climate, reservoir type, or natural and human land cover.Estimates from such broad-scale studies will improve global estimates of GHG emissions from freshwater lakes and reservoirs necessary for understanding global carbon cycling and climate change.Moreover, forecasting among reservoir variation in GHG emissions can inform regional development of hydropower resources and provide estimates of cumulative GHG emissions from multiple reservoirs [42,43].

Conclusions
Although hydropower facilities are frequently viewed as a green source of energy, a growing body of literature suggests that GHG fluxes from their reservoirs contribute globally significant amounts of GHGs to the atmosphere [3,4,15].The present study provides two important contributions.First, our findings provide baseline estimates of GHG emissions from a reservoir in temperate North America-a region for which data are limited, despite having a relatively large number of hydropower-generating reservoirs.Second, we demonstrate the utility of statistical models as predictive tools for studying GHG emissions.Hydropower resources throughout the world are being developed rapidly, and additional development is planned.This development is particularly rapid in Asia and South America [44,45], but recent interest in expanding hydropower resource use in the United States and Canada is also being evaluated [46][47][48][49].Deeper understanding and prediction of GHG flux within and among reservoirs is essential to forecast the potential impact of regional hydropower development scenarios [43] on the global carbon cycle and the consequent implications for anthropogenic climate change.

Figure 2 .
Figure 2. Surface concentrations of (A,B) CO2 and (C,D) CH4 from Douglas Lake as functions of (A,C) longitudinal position and (B,D) month of the year.Error bars represent 95% confidence intervals around the sample average.

Figure 3 .
Figure 3. Surface diffusion of (A,B) CO2 and (C,D) CH4 from Douglas Lake as functions of (A,C) longitudinal position and (B,D) month of the year.Error bars represent 95% confidence intervals around the sample average.

Figure 4 .
Figure 4. Partial dependence plots derived from Random Forests models showing the relationship between the five most influential environmental correlates (horizontal axes) and surface diffusion of (A,B) CO2 and (E-G) CH4.Inset numbers in each panel show variable importance.See Table1for a summary of variable importance for all 16 predictor variables.

Table 2 .
Spatial variation in physicochemical variables of Douglas Lake.Values are sample averages with 95% confidence intervals in parentheses.Confidence intervals for sample averages represented by a single sample (i.e., no seasonal replication) are denoted with NAs.

Table 3 .
Seasonal variation in physicochemical variables of Douglas Lake.Values are sample averages with 95% confidence intervals in parentheses.Confidence intervals for sample averages represented by a single sample (i.e., no spatial replication) are denoted with NAs.