Spatial-temporal variability of methane fluxes in lakes varying in latitude, area, and depth

Abstract

Many previous studies have found spatial and seasonal variabilities in CH₄ fluxes, which could significantly affect lake-wide CH₄ budgets. However, the ways in which the spatial and seasonal patterns of CH₄ fluxes vary among lakes on a global scale is largely unknown. We compiled literature on CH₄ flux data from global lakes and analyzed the spatial and seasonal variabilities for lakes varying in latitude, maximum depth, and area. Spatially, we found a significant linear relationship between the ratio of littoral to profundal fluxes and lake morphology (more related to area than depth), while globally, half of the lakes would have within 5% error of CH₄ emission estimation under single-zone sampling. Seasonally, mid-latitude lakes showed higher CH₄ fluxes in the summer and autumn, indicating the influence of temperature and autumn overturn, and the latter being largely related to maximum depth. Globally, due to abundant shallow lakes in the mid-latitude zone, approximately 99% of lakes had higher fluxes in the summer, while 75% of lakes showed errors in CH₄ emission estimation within 20% when only the summer flux was investigated. In the high-latitude lakes, CH₄ evasion during the spring ice-off period was significantly correlated with lake maximum depth, while lake area was also important when analyzing the CH₄ diffusive flux. Our study yields preliminary conclusions about spatial and seasonal patterns of CH₄ flux in different lake types, which are fundamental to building an effective sampling strategy and to determining an accurate CH₄ budget from global lakes.

1. Introduction

CH₄ is the second most impactful greenhouse gas after CO₂, and on a 100-year time horizon, the potential warming effect of CH₄ is approximately 28 times that of CO₂ [1]. The atmospheric CH₄ concentration has dramatically increased since the 1750s, and after stagnation from 2002 to 2006, it started to increase again in 2007 [2]. The accurate evaluation of the global CH₄ budget is important for developing realistic approaches to mitigate climate change. Freshwater is recognized as an important natural source of CH₄, although it covers a small fraction of the Earth's surface area [[3], [4], [5]], and lakes are estimated to contribute approximately 62% of freshwater CH₄ emissions [6]. However, few previous estimations of global lake CH₄ emissions have included the spatial and seasonal variability in CH₄ fluxes, which are considered important for lake-wide CH₄ budgets [[7], [8], [9]].

Spatially, single point or regional measurements are insufficient to accurately estimate lake-wide CH₄ fluxes into the atmosphere [[8], [9], [10]]. It is assumed that the littoral zone contributes more than 60% of CH₄ emissions in shallow lakes [11]. In contrast, the small (0.24 km²) and deep (maximum depth >10 m) Lake Gerzensee had higher CH₄ fluxes in the central region [12]. Hence, the spatial CH₄ fluxes may be different for lakes varying in area and depth. Furthermore, significant seasonal variations in CH₄ fluxes were also found to be accompanied by different seasonal temperature and water environment conditions [9,13,14]. Hence, the CH₄ flux may have different seasonal patterns in lakes in different latitude zones. In summary, we hypothesized that the spatial and seasonal variability in the CH₄ flux would show different patterns for lakes varying in latitude, area, and depth. Hence, we compiled direct measurements of spatial and seasonal CH₄ fluxes (including diffusion and ebullition) from lakes worldwide, and the spatial and seasonal CH₄ flux variability patterns were analyzed for different lake types.

2. Materials and methods

2.1. Collection of published data

The areal lake CH₄ fluxes and concentrations, including spatial or seasonal sampling, were collected from the literature. Reservoirs were excluded owing to the specific gas pathways in the dam [15], as well as saline or brackish lakes due to their unique biogeochemistry and paucity of direct measurements. The spatial heterogeneity in CH₄ fluxes was analyzed for 38 lakes with sampling sites distributed both in the littoral (nearshore) and profundal (open water) zones, while only 33 lakes explicated both the area and maximum depth data in the literature, and 41 and 40 lakes were used for area and maximum depth analysis, respectively. A total of 125 lakes, with 13, 28 and 84 lakes in low-, mid- and high-latitude areas, respectively, were selected with sampling in both the high CH₄ flux and low CH₄ flux seasons to study seasonal variability (Supplementary Table S1). The CH₄ fluxes found in the literature were mainly measured with a static or floating chamber technique, in which the chambers without bubble shields received CH₄ by both diffusion and ebullition, and the surface-water CH₄ concentrations were measured using the headspace equilibrium technique [3]. Moreover, if a study clearly stated that the chamber was used only to measure CH₄ diffusive flux, the data were also considered to represent CH₄ diffusive flux in this study. CH₄ diffusive flux was also calculated with a boundary layer diffusion model (Fick's law) in some studies (e.g., Ref. [8]).

2.2. Spatial CH₄ flux

The 38 lakes with available spatial CH₄ data were divided into littoral and profundal zones according to the description in each study. In each lake, CH₄ fluxes from the same lake zones were averaged if more than one value was available. The ratio of littoral to profundal CH₄ flux (L/P) was proposed to quantify the spatial variability in CH₄ flux. Note that the L/P of 7 deep and large lakes were calculated via CH₄ diffusive flux or surface-water CH₄ concentration because of a lack of CH₄ ebullition data. Because the data of maximum depth was more frequently offered in the collected literature than mean depth, maximum depth rather than mean depth was used in this study. In addition, to simultaneously reflect lake area and depth, the ratio between lake area (km²) and maximum depth (m) (Area/MaxDepth) was calculated as one of the lake physical parameters. We performed linear, polynomial, and smooth spline regressions to evaluate the relationship between L/P and lake physical characteristics and evaluated quadratic relationships for piecewise regressions.

To assess the representativeness of sampling sites at the lake center, we assumed that the lakes had similar areas of littoral, intermediate and profundal zones, that is, each lake zone equals 1/3 of the lake area, and the CH₄ flux from the intermediate zone was the average of the CH₄ flux in the profundal and littoral zones. According to the calculated L/P, if we hypothesize that the CH₄ flux in the profundal zone is x, then the CH₄ flux in the littoral zone is L/P*x, and the CH₄ flux in the intermediate zone is (x + L/P*x)/2. Then, whole lake CH₄ emissions estimated with both the littoral, intermediate and profundal fluxes are calculated as follows:

$$\mathrm{E}\mathrm{m}=(1/3*\mathrm{x}+1/3*\mathrm{x}*\mathrm{L}/\mathrm{P}+1/3*((\mathrm{x}+\mathrm{L}/\mathrm{P}*\mathrm{x})/2)))*\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}$$ (1)

when only the profundal flux was used to represent the whole lake, CH4 emissions could be estimated as Ep = x * area. Correspondingly, when using only the littoral zone flux, CH4 emissions were estimated to be El = x*L/P*area. We calculated the ratio of Ep/Em and El/Em to evaluate the error of CH₄ emission estimation. Please see Table S3 for the calculation processes.

2.3. Seasonal CH₄ flux

To analyze seasonal CH₄ flux from the 152 lakes, the sampling dates were divided into spring/autumn (March to May), summer/winter (June to August), autumn/spring (September to November) and winter/summer (December to February) in the Northern/Southern Hemisphere, except for lakes in tropical areas. The tropical climate shows no significant temperature differences but is characterized by higher rainfall in summer [16,17]. Tropical lakes may be flooded by river inflow or local rainfall or by both; thus, the high-water period may be delayed for months after summer rain [18]. Hence, the sampling period of tropical lakes was separated into low- and high-water seasons according to the regional climate and the timing of inundation.

For analysis of the seasonal CH₄ flux at different latitudes, the studied lakes were divided into low-latitude (<24°), mid-latitude (24°–54°), and high-latitude (>54°N) zones. The mid-latitude region included mainly subtropical and temperate climates, which had obvious seasonal temperature variability. For mid-latitude lakes, higher CH₄ emissions probably occur in summer (e.g., Ref. [10]) or during the lake turnover period in spring or autumn [19], and sampling for CH₄ more frequently occurs in summer and autumn according to our collected data. Therefore, to assess the representativeness of limited seasonal sampling, we hypothesize that the days for each season are equivalent. Then, we calculated the ratios of whole-year CH₄ emission estimation with seasonal flux in summer (Es), autumn (Ea) or both (Esa) to estimated CH₄ emission using the seasonal mean flux (Esm). In addition, the ratio of CH₄ flux in summer to that in autumn (Fsummer/Fautumn) was used to analysis the seasonal difference between summer and autumn.

Lakes at high latitudes usually had ice cover during the winter, although a small part of the gas could escape through openings in the ice owing to ice cracks caused by increased pressure and/or warm waters from inflows and frequent CH₄ bubbling [20] or from vegetation emergence through the ice [21]; most of the CH₄ was trapped in the ice and underlying water when the ice was present. If CH₄ escapes oxidation under ice, CH₄ accumulation under the ice could result in gas “storage”, and large diffusion emissions occur when the ice melts in spring [[22], [23], [24]]. Hence, we focused on the contribution of CH₄ flux during the ice melt and a comparison with that in the ice-free period. Ice-melt refers to springtime when ice starts to thaw until complete ice-off; the ice-free period includes summer and the possible autumn turnover period. Because of the large differences in the duration dates of the two periods, for example, complete thaw could take only two weeks in northern Swenden [25], the CH₄ fluxes were presented as the summary during each period, that is, the mean flux in each period multiplied by its duration days (unit of mmol per m²). Previous studies estimated the spring efflux by using bubble trapped under ice or floating chambers, as well as by sampling CH₄ dissolved in lake water immediately before and after ice melt or by monitoring CH₄ fluxes with eddy covariance [25]. Referring to the method of [26], we calculated the percentage contribution of ice-melt flux to annual CH₄ emission to reduce the uncertainty between different methods used to estimate CH₄ fluxes.

Considering the different seasonal lake environments, which result in various CH₄ emission modes, the seasonal CH₄ flux was analyzed separately among the three latitude regions. We used the Kruskal‒Wallis test to compare CH₄ fluxes among the four different seasons and a Dunn-Bonferroni test for post hoc comparisons. The Mann‒Whitney U test was conducted to compare CH₄ fluxes in the two tropical seasons. Pearson correlation and linear regression analysis were used to analyze the relationship between seasonal CH₄ flux and lake physical characteristics.

2.4. Spatial and seasonal variability in global lakes

Robust models to investigate the relationship between spatial and seasonal CH₄ fluxes and lake physical characteristics were chosen to estimate L/P or the seasonal proxy indicators (only for mid-latitude lakes) for global lakes. Lake depth data were excluded in most of the datasets on lake characteristics at the global scale [27,28], except the HydroLAKES dataset [29], which includes mean lake depth, and the Global Lake Database (GLDBv2), which includes hiatus mean and maximum depth data [30]. We developed the Fresh-Water Lake-Depth Dataset (FWLDDS) in GLDBv2 with data mostly from Wikipedia except for Chinese lakes, which were referenced from the recently created lake survey database [31]. The lakes for which at least lake area and mean or maximum depth data were available were included from the FWLDDS, and the final dataset had 5762 lakes (Supplementary Table S2). Since approximately 20% of lakes have only mean depth and lack maximum depth data, which is a key factor for predicting CH₄ flux, a linear regression model was run to predict maximum depth based on lake area and mean depth; the simulation value was significantly correlated with the measured value, suggesting the reliability of this model (Function 2).

$$\mathrm{Max}\mathrm{d}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}=2.045\times \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{h}+0.003\times \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}(\mathrm{a}\mathrm{d}\mathrm{j}{\mathrm{R}}^2=0.90,\mathrm{d}\mathrm{f}=4382,\mathrm{p}<0.0001)$$ (2)

here, lake area is in km², and maximum and mean depth are in m. Then, maximum depth data were supplemented for the HydroLAKES dataset using Function 2 based on lake mean depth and area [29].

3. Results and discussion

3.1. Spatial flux patterns

The spatial variability in the CH₄ flux had different characteristics among the various lake types. Limited by data size, although we tried multiple regression models, only the linear models between lake area, Area/MaxDepth and L/P were statistically significant with p < 0.05 but with relatively low R² (Fig. 1a & b). L/P showed a significant correlation with lake area and Area/MaxDepth, rather than maximum depth. Most lakes had higher CH₄ fluxes in the littoral zone, while higher CH₄ fluxes in the profundal zone could exist only in some, not all, small and deep lakes (see data in Supplementary Table S1). Typically, the littoral zone has abundant available organic matter in sediments originating from high productivity or influx from the watershed [9,14,32], and the increased methanogenesis rates in the littoral zone generates greater CH₄ storage during summer stratification and enhanced CH₄ emission to the atmosphere by bubbling [33]. In contrast, without abrupt water depth variation in shallow lakes, the lake currents are determined mostly by the prevailing wind direction and lake morphology, inducing erosion in the profundal zone and deposition along the shoreline and in the lake bays. The profundal sediment in large and shallow lakes may be susceptible to erosion by lake currents, inducing lower CH₄ production, such as that in Lake Taihu, which has little soft sediment in the profundal zone [14,34,35].

Fig. 1.

The ratio between CH₄ emissions in the littoral and profundal zones (L/P) in relation to lake area (a) and the ratio between lake area and maximum depth (MaxDepth) (b). The units for lake area and MaxDepth were km² and m, respectively, and all the data were natural log transformed.

Specifically, we found that L/P and Area/MaxDepth showed significant positive correlations, and when the Area/MaxDepth >1, L/P > 1 (Fig. 1b), suggesting that when the lakes tend to be larger and shallower, that is, with less lakebed slope, their CH₄ shows higher flux in the littoral zone than in the profundal zone. Håkanson (1977) [36] described a linear relationship between slope and sediment water content, which had a direct link to sediment bulk density and grain size. In addition, topography-induced water depth variations may influence the lengths of internal waves at the bottom sediment, thereby directly affecting the bottom water currents and material transmission. The steep slopes of small and deep lakes facilitate sediment migration to profundal regions, resulting in a higher proportion of easily degradable organic matter (e.g., algae) in central sediments than in the near-shore zone [16,37]. In addition, the strong seasonal stratification of deep lakes contributes to the low dissolved oxygen concentrations or anoxic conditions in deep waters [16,19,38], leading to high CH₄ production and effusion.

However, CH₄ produced in the deeper sediment is at a greater risk of oxidation in the sediment and water column, even for ebullition. A bubble model for Lake Stechlin shows that approximately 80% of CH₄ trapped in the bubbles released from the nearly 70 m deep sediment would dissolve in the hypolimnion (>40 m depth) and leave little CH₄ in the gas bubbles when reaching the surface, and less than 20% of the CH₄ mass fraction remains in the bubbles released from 40 m deep sediment when reaching the surface [39]. On the other hand, oxic CH₄ production is considered an important CH₄ source correlated to sediment area and surface mixed layer volume [[40], [41], [42], [43]]. The CH₄ concentration in the profundal zone of the large and deep lake is presumed to be determined more by oxic CH₄ production than by anoxic CH₄ production in the sediment [44]. Therefore, a deeper maximum depth may induce higher CH₄ production but also increase CH₄ oxidation in the profundal area, which is related to topography, trophic status, etc., while oxic CH₄ production may also matter, especially in the stagnation period. All the above information explains why not all small and deep lakes show higher CH₄ fluxes in the profundal zone.

Overall, the bottom topography, which could be reflected by the collocation of lake depth and area, has an influence on the deposition rate and sediment features, which are related to the spatial heterogeneity of sediment organic matter content and methanogenesis. Thus, we deem that the lake area and maximum depth should both be considered to estimate CH₄ flux spatial variability, and the linear regression model between Area/MaxDepth and L/P was used for further analysis (Fig. 1b). Nonetheless, apart from limited training data, the relatively weak correlation coefficients between L/P and lake physical characteristics may also indicate the influence of other factors, such as lake eutrophication and allochthonous carbon input from river inflow. Lake eutrophication could be a factor for high CH₄ flux in the profundal zone of deep lakes [38], and oxic CH₄ production in the surface water may also increase with the improvement of productivity, and phytoplankton especially diatoms, cyanobacteria, green algae, and cryptophytes [45,46]. On the other hand, river inflow may increase the organic matter supply to the littoral zone, resulting in high CH₄ emissions [47], and rivers could also directly bring dissolved CH₄ into the lake, which may enhance or weaken CH₄ flux spatial heterogeneity [8,23,48,49].

The estimated L/P for global lakes ranged from 0.50 to 6.30, with a mean value of 1.21 and a median value of 1.12. Generally, approximately 20% of lakes showed L/P < 1, and 64% of lakes had L/P values ranging from 1 to 1.4 (Fig. 2a). Correspondingly, only approximately 20% of lakes had Ep/Em > 1, and 20% of lakes had El/Em < 1. Almost half of the lakes showed Ep/Em ranging from 0.9 to 1.0, and El/Em ranged from 1.0 to 1.1 (Fig. 2b and c), indicating that half of the lakes showed errors of within 5% when using the littoral or profundal CH₄ flux for whole lake CH₄ emission estimation. That is, relatively low estimation error could occur for half of the global lakes when sampling only in littoral or profundal zones. However, considerable spatial sampling design should be conducted for relatively large or deep lakes.

Fig. 2.

Frequency percentage of L/P, Ep/Em, and El/Em; Ep represents the estimated whole lake CH₄ emission using CH₄ flux in the profundal zone, Em represents the estimated CH₄ emission using lake water mean CH₄ flux, and El represents the estimated lake CH₄ emission using CH₄ flux in the littoral zone. The data on the bar are the percentage of the frequency, which is calculated as the ratio of frequency in each class to the total amount of data. Please see section 2.3 for the calculation process.

3.2. Seasonal flux patterns

3.2.1. Low-latitude lakes

A total of 13 lakes with CH₄ flux measurements in both the high-water and low-water seasons were used for further analysis. Overall, low-latitude lakes had significantly higher CH₄ fluxes in the high-water season than in the low-water season (p < 0.05, Fig. 3a). Ten out of the 13 lakes in Brazil showed inconsistent conclusions. Early studies using the static chamber technique indicated approximately 34 and 4 times higher CH₄ fluxes in the high-water season than in the low-water season in the southern Pantanal [18] and Amazon [16], Brazil, respectively. The research by Marani and Alvalá (2007) [17] in the Pantanal region found that the diffusive flux showed a slight but not statistically significant seasonal variation, and the CH₄ ebullition was variable but had no seasonal pattern. Notably, studies in the lakes of low-latitude areas with both CH₄ diffusion and ebullition quantified concluded that most of the total CH₄ emissions were ebullitive (more than 90%) [17,50]. Hence, more research that includes observations of CH₄ ebullition is still needed to determine whether higher CH₄ fluxes in the high-water season are valid across global low-latitude lakes.

Fig. 3.

Seasonal variability in the total CH₄ fluxes of lakes in different climatic zones and significant seasonal diffusive CH₄ flux variability in high-latitude lakes. “■” shows the mean value. Letters above are comparison tests, values with different letters indicate significant differences, and different uppercase and lowercase letters show significant differences of p < 0.01 and p < 0.05, respectively.

CH₄ ebullition is episodic and dependent upon many factors. CH₄ bubbling from the sediment is considered to correlate with the shear stress in sediments caused by bottom currents, which in turn are influenced by wind, internal pressure gradients, and lake bathymetry [51]. Rising CH₄ bubbles can dissolve in the water column and be stored or oxidized, and water depth and temperature are two important factors controlling the transfer processes of bubbles [52]. Hence, the season with relatively high temperature but low water level may have high CH₄ ebullition flux per area, while high water level may cause anoxia in the sediment, resulting in high CH₄ production and low CH₄ oxidation. Therefore, to determine the seasonal CH₄ flux in low-latitude lakes, the high variability in lake depth and area must be considered, and more regional research is needed to analyze their influence on CH₄.

In low-latitude regions, other methods, such as satellite measurements, are complementary to the surface network of CH₄. The study by Tunnicliffe et al., 2020 [53] using a high-resolution regional inversion framework coupled with satellite measurements of CH₄ found that the Amazon and Pantanal wetlands both showed higher CH₄ emissions in the high-water season. In addition, the estimation of CH₄ emissions in the Pantanal region through regularly measured vertical atmospheric profiles revealed a large amount of CH₄ emissions during rising water levels [54]. Hence, for the whole wetland area, higher CH₄ emissions may be prevalent in the high-water season, while the situation in lakes is still ambiguous.

3.2.2. Mid-latitude lakes

To analyze seasonal patterns, a total of 28 lakes with CH₄ flux data in at least two seasons were chosen, among which 8 lakes were studied only in the summer and autumn. The CH₄ flux in mid-latitude lakes showed significant seasonal variability, with the lowest flux in winter (p < 0.005) and higher fluxes in summer and autumn than in spring (p < 0.05) (Fig. 3b). Seasonally, temperature is usually considered an important factor influencing CH₄ production and oxidation in mid-latitude lakes [55]. In the warm season, lakes may have higher sediment CH₄ production under high temperature in the sediment and the supply of newly produced autochthonous organic matter [56]. In addition, the more serious eutrophication in the warm season could inhibit CH₄ aerobic oxidation by eutrophication-created anoxic conditions [57,58]. Generally, temperature and trophic status are two main factors determining seasonal CH₄ fluxes in mid-latitude shallow lakes [9,13,56,59].

However, our results showed that the autumn CH₄ flux approached the level in summer, even with higher mean values but larger dispersion (Fig. 3b). Except for Ea/Esm, the seasonal CH₄ flux proxies (i.e., Es/Esm, Esa/Esm and Fsummer/Fautumn) all showed negative but greater correlations with maximum depth than with lake area. The significantly high CH₄ flux in autumn is likely to occur in deep lakes. For most deep lakes in the mid-latitude zone, summer stratification is a process in which much CH₄ accumulates in anoxic deep waters. Then, the large quantities of CH₄ that were stored in the anoxic hypolimnion can be effectively transported to the upper layer during rapid mixing, causing high dissolved CH₄ concentrations in the surface water and diffusive fluxes to the atmosphere in the autumn [19]. Following the complete overturn, the entire water column could be oxic, with little of the original CH₄ remaining in the water column [19], which influences the CH₄ flux in the following season. In contrast, incomplete turnover is adverse to the emission of bottom CH₄ and brings oxygen to only the middle layer, leaving the deep water anoxic with high CH₄ storage [60]. Hence, the contribution of autumn emissions is largely determined by the length of the summer stagnation period and the intensity of turnover, and both processes are related to lake topography and morphology.

Limited by the data volume, only Esa/Esm and Fsummer/Fautumn showed significant correlations with maximum depth (Fig. 4a & b). We chose the linear regression models in Fig. 4 for the analysis of Fs/Fa and Es/Esm for global lakes in the mid-latitudes. The results showed that for global lakes with latitudes between 24 and 54, only 0.11% of lakes had higher CH₄ fluxes in autumn than in summer (Fig. 5a), which is in accordance with the amount of relatively shallow lakes globally [61]. Similarly, less than 0.1% of lakes had Es/Esm <1, and 75% of lakes showed Es/Esm ranging from 1.0 to 1.4 (Fig. 5b), indicating that the summer flux is likely to overestimate the yearly CH₄ emissions, but the error for most lakes with medium depths retains a low level (within 20%). Therefore, multi-season sampling should be implemented when lakes are relatively shallow or deep.

Fig. 4.

The ratio between CH₄ flux in the summer and autumn (Fs/Fa) in relation to lake maximum depth (MaxDepth) (a) and the ratio of whole year CH₄ emission estimation with flux in summer to that with seasonal mean flux (Es/Esm) in relation to lake maximum depth (MaxDepth) (b). Note that all the data were natural log transformed.

Fig. 5.

Frequency percentages of Fs/Fa and Es/Esm. Fs and Fa are the CH₄ fluxes in the summer and autumn, respectively; Es represents the estimated whole-year CH₄ emissions using the CH₄ flux in the summer, and Esm represents the estimated CH₄ emissions using the seasonal mean CH₄ flux.

3.2.3. High-latitude lakes

A total of 84 lakes with CH₄ flux data during the ice-melt and ice-free seasons were included for the seasonal CH₄ analysis. Due to the different methods used for CH₄ flux measurement, 28 lakes included both CH₄ diffusive and ebullitive fluxes, and 61 lakes had only CH₄ diffusion data. Both CH₄ total and diffusive fluxes showed significantly higher values in the ice-free period than during the ice-melt period (p < 0.005, Fig. 3c & d). For the 28 lakes with CH₄ total flux, the contribution percentage of CH₄ flux in the ice-melt period ranged from 0% to 56%, with a mean value of 17% and a medium value of 13%. In contrast, the CH₄ diffusive flux of the 61 lakes showed ice-melt contribution percentages of 0%–83%, with mean and medium values of 30% and 21%, respectively. This result suggests that the ice-melt contribution could be overestimated when only the CH₄ diffusive flux was used.

The CH₄ total and diffusive fluxes in the ice-melt and ice-free periods all showed negative correlations with lake area and maximum depth (Table 1), indicating higher CH₄ emissions in small and shallow lakes than in large and deep lakes. The CH₄ diffusive flux showed more significant correlations to lake maximum depth and area than the CH₄ total flux, probably suggesting that the CH₄ diffusive flux is more related to lake morphology than the ebullitive flux. Nevertheless, the contribution of ice-melt CH₄ total and diffusive flux showed no significant correlation with lake depth and area, and the correlation was relatively weak for CH₄ diffusive flux compared to that of the CH₄ total flux (Table 1). All the above results suggest the obvious influence of lake depth on CH₄ ebullition during ice-off; in other words, shallow lakes tend to have higher CH₄ ebullition in the ice-melt period than deep lakes, which may significantly improve their spring CH₄ emission contribution.

Table 1.

The relationships of CH₄ fluxes in the ice-melt and ice-free periods with lake physical characteristics.

	CH4total flux			CH4diffusive flux
	Ice-melt flux	Ice-free flux	Ice-melt Contribution	Ice-melt flux	Ice-free flux	Ice-melt Contribution
Area	−0.37	−0.34	−0.18	−0.59**	−0.51**	−0.10
MaxDepth	−0.43*	−0.32	−0.35	−0.50**	−0.62**	0.12
Area/MaxDepth	−0.19	−0.21	−0.040	−0.54**	−0.41**	−0.16

The data are Pearson correlation coefficients, * represents p < 0.05; ** represents p < 0.01.

The spring ice-off may produce significant CH₄ emissions in high-latitude lakes after CH₄ accumulates under the ice, which is dependent on the length of the ice-cover season, the availability of oxygen in the winter [25] and the ice-growth rate [62]. More importantly, the CH₄ flux during spring ice-off is mostly determined by the intensity of lake turnover, which is usually complete in deep lakes [26]. Thus, we believe that the higher CH₄ flux in the ice-free period is due to most of the shallow lakes in our data (only 7 out of the 28 lakes had maximum depths greater than 10 m), and the estimation of the CH₄ flux contribution percentage in the ice-melt period should be conservative.

However, other factors may also result in the uncertainty of our estimation. A large majority of the northern lakes have been measured over short periods of only one to a few days, even in the ice-free season. Wik et al. (2016) [63] recommended that measurements of diffusive CH₄ flux and ebullition be made over at least 11 and 39 days, respectively, and scattered throughout the ice-free season. The same problem also exists for studies during the ice-cover period. According to our statistics, the number of CH₄ flux studies for high-latitude lakes in the ice-covered period (82) is much less than that in the ice-free season (150), and most studies in ice-covered lakes sampled only once or over a short time [64,65]. More importantly, a few studies have investigated spring emissions by calculating the difference between depth-integrated gas storage before the onset of ice thaw and after complete ice-off (e.g., Refs. [24,65,66]), which is termed potential spring emissions by Jansen et al. (2019) [25]. This estimation of spring emissions may have a large deviation since the possibility of CH₄ oxidation during ice-off is not included [67]. In addition, ice breaks usually occur next to the shore first; when sampling after complete ice-off, the littoral zone may have accumulated CH₄ in the bottom water, while the in situ CH₄ efflux to the air may be similar to that of the profundal area [68]. Thus, spring CH₄ emissions may be overestimated. Therefore, future research should elucidate the sampling strategy for CH₄ flux studies in ice-covered lakes.

3.3. Limitations and uncertainties

The most obvious limitation in this study is the data size. For the study of spatial CH₄ flux patterns, only 42 lakes were used, and 13 and 28 lakes were included for the seasonal CH₄ flux analysis of the low- and mid-latitude lakes, respectively, which largely explained the relatively low R² in the regression models. In fact, the spatial-temporal variability in lake CH₄ flux has received much attention, especially since CH₄ became a research hotspot. However, despite the various efforts that have been made, we found that the available data are still limited for our study objectives. For example, for spatial CH₄ analysis, first, the lake area and depth must be clearly articulated in the literature, and some small lakes at low latitudes, such as the Pantanal region, Brazil, in Bastviken et al. (2010) [7], were excluded. Second, sampling should include both the littoral and profundal zones of a lake, and inner-zone spatial analysis data were excluded in our study.

The data size also limited a more precise analysis of spatial CH₄ flux variability in different lake types. We tried a local weighted regression for L/P with lake morphology parameters and found varying forms of regression lines in different lake types. Then, we tried piecewise polynomial regression analysis and found revised U waves for lakes with log area <1 and log Area/MaxDepth <0 and U waves for the remaining part (Supplementary Fig. S1). While these relationships are not statistically significant thus far, more data are needed to examine their meaning and correction.

On the other hand, there is a lack of accurate quantitative standards for littoral, intermediate and profundal zones within lakes, and in this study, we hypothesized that these three zones were averaged in a lake. In fact, deep and shallow lakes should have different proportions of littoral and profundal zones; hence, for a shallow lake that usually had a higher flux and a larger littoral zone or a deep lake that had a higher flux and a larger profundal zone, our method would result in an underestimation of Em, and then, the El/Em for those shallow lakes and the Ep/Em for those deep lakes should be further decreased. However, the error of Em is uncertain for other lake types.

Overall, this study highlights several prospects for future work to reduce uncertainties. First, more available spatial and seasonal lake CH₄ data are still urgently needed. Second, global research on lake morphology and topography should be strengthened to provide reasonable reference standards for the quantitative separation of different lake zones.

4. Conclusions

The spatial and seasonal variabilities in CH₄ fluxes in lakes varying in latitude, area, and depth were analyzed at a global scale based on data from the literature. Spatially, most lakes showed higher CH₄ fluxes in the littoral zone, except some small and deep lakes, and the flux differences between littoral and profundal zones increased with increasing lake area or area/max depth. Globally, half of the global lakes would have a relatively low error of CH₄ emission estimation, while we emphasize the considerable spatial sampling design needed for large and deep lakes. Seasonally, more regional research is needed for low-latitude lakes due to their high variability in lake depth and area, which have different effects on CH₄. The mid-latitude lakes showed higher CH₄ fluxes in the summer and autumn, indicating the influence of temperature and autumn overturn, while the latter is related to the maximum depth. Globally, we pointed out the necessity of multi-season sampling in relatively shallower or deeper lakes. Generally, the high-latitude lakes showed significantly higher CH₄ fluxes in the ice-free period than during the ice-melt period, while the deep lakes may be the opposite. This study is fundamental to elucidating the spatial and seasonal CH₄ patterns for different lake styles and the sampling strategy for CH₄ flux studies, which is beneficial for determining accurate CH₄ budgets from global lakes.

Author contribution statement

Lingling Li: Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Bin Xue: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data.

Data availability statement

Data will be made available on request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following are the supplementary data to this article: