Impact of atmospheric pressure variations on methane ebullition and lake turbidity during ice-cover

Methane ebullition (bubbling) from lake sediments is an important methane flux into the atmosphere. Previous studies have focused on the open-water season, showing that temperature variations, pressure fluctuations and wind-induced currents can affect ebullition. However, ebullition surveys during the ice-cover are rare despite the prevalence of seasonally ice-covered lakes, and the factors controlling ebullition are poorly understood. Here, we present a month-long, high frequency record of acoustic ebullition data from an ice-covered lake. The record shows that ebullition occurs almost exclusively when atmospheric pressure drops below a threshold that is approximately equal to the long-term average pressure. The intensity of ebullition is proportional to the amount by which the pressure drops below this threshold. In addition, field measurements of turbidity, in conjunction with laboratory experiments, provide evidence that ebullition is responsible for previously unexplained elevated levels of turbidity during ice-cover.


Introduction
Lakes are an important source of atmospheric methane (Wik et al., 2016), and ebullition from lake sediments is often the dominant source of this methane (Bastviken et al., 2004;Sanches et al., 2019). However, there are large uncertainties in measuring and predicting methane ebullition (Engram et al., 2020). Multiple environmental factors affect ebullition, including wind-induced currents (Joyce & Jewell, 2003), short wave radiative flux (Wik et al., 2014), sediment temperature variations (Fechner-Levy & Hemond, 1996), water level fluctuations (Harrison et al., 2017), and atmospheric pressure changes (Scandella et al., 2011;Varadharajan & Hemond, 2011). Most studies of ebullition have been conducted during the open-water season, when these processes often act simultaneously, rendering it difficult to discriminate between them. Ice-cover provides the opportunity to study ebullition under less complicated conditions. However, the paucity of ebullition data during ice cover constitutes a major knowledge gap, despite the prevalence of ice-covered lakes (Denfeld et al., 2018;Verpoorter et al., 2014).
In addition to contributing to atmospheric methane, ebullition from sediment can impact the local aquatic system. When bubbles migrate through sediment, they enhance porewater advection (Santos et al., 2015), mobilize and release contaminants (Fendinger et al, 1992), and cause sediment destabilization (Kavcar, 2008). As they emerge from the sediment, bubbles can entrain sediment particles in their wake, increasing turbidity in the water column (Klein, 2006). While ebullition appears to enhance turbidity during ice cover (Lawrence et al., 2016;Tedford et al., 2019a), continuous and simultaneous measurements of ebullition and turbidity have not previously been made.
We examine a one-month record of ebullition collected during ice cover at Base Mine Lake, in Alberta, Canada. During this period, water level fluctuations, temperature changes, and windinduced currents were minimal, allowing us to focus on the relationship between atmospheric pressure variations and ebullition. A downward facing echosounder was mounted below the ice to monitor ebullition continuously from a fixed area. This high frequency ebullition data revealed the dominant effect of atmospheric pressure on ebullition. We also investigated the impacts of ebullition on lake turbidity with the aid of laboratory experiments and field measurements.

Methods
Base Mine Lake (57° 1' N, 111° 37' W in Alberta, Canada) was formed by filling a mined-out oil sands pit with tailings and capped with water (Dompierre & Barbour, 2016). As part of a remediation strategy, the deposition of tailings was completed at the end of 2012. The tailings were 25 -35% solids by weight, with similar mean particle size and clay fraction as the finegrained muds found in lakes and estuaries (Dompierre & Barbour 2016). These tailings are commonly referred to either as fluid fine tailings, or simply mud. The lake exhibits seasonal thermal stratification similar to that of natural dimictic lakes, and ice-cover is typically from November to April (inclusive) also similar to natural lakes in the region (Tedford et al. 2018).
At the end of 2012, the 7.8 km 2 lake was 7 m deep, overlying a 45 m mud layer. The initial depth of the water-cap was designed to isolate the mud from re-suspension due to the direct action of wind-wave induced currents (Lawrence et al., 1991). The mud layer has been settling gradually over time (Dompierre & Barbour, 2016). By January 2018, the average depth of the water-cap was about 10 m ( Figure 1a). Degeneration of residual hydrocarbon inside the mud layer produces methane (Francis, 2020); subsequently, bubbles rise through the mud layer and then the water-cap (Figure 1b). These bubbles are typically 0.1 -1 cm diameter when they reach the water surface.
In the present study we use meteorological data, echo soundings, bottom-water temperature, and turbidity measurements from Day 40 (9 February) to Day 67 (8 March) of 2018 (Zhao et al., 2021). Meteorological data, including atmospheric pressure, have been collected at the central However, no pressure data were obtained from P1 between Day 40 and Day 47, therefore, we use the airport data for our analysis. and internal logging of the Echologger EA400 allows for long autonomous deployments under the ice, it does not record bubble locations, or size, inside the beam. Therefore, it is unable to convert ebullition intensity into volumetric methane flux as in the case of dual beam echosounders (Ostrovsky et al., 2008).
Turbidity was measured at 30-minute intervals using a RBRDuo logger with a Seapoint turbidity sensor attached to a mooring chain at P2 (Figure 1a). The total water depth at this location was approximately 11 m. The turbidity in NTU units was approximately twice the total suspended solids concentration in mg/L (Tedford et al., 2019a). On 3 October 2019, images of the lakebed were taken using a drop camera, Subsea Video Systems S-513, to facilitate our understanding of ebullition and turbidity.

Results
Variations in atmospheric pressure, ebullition intensity and turbidity under ice from 9 February (Day 40) until 8 March 2018 (Day 67) are presented in Figure 2. Ebullition intensity varies dramatically from hour to hour. The most intense ebullition events occurred during the passage of two low-pressure systems. The first system persisted from Day 43 to Day 45, and the second from Day 54 to Day 60 ( Figure 2a). During the first event, ebullition started to increase when the atmospheric pressure dropped below its long-term average, increased further as the pressure continued to drop, and then decreased as the pressure increased. Ebullition essentially ceased when the atmospheric pressure rose above its long-term average again. During the second event the pressure cycled down and up three times and ebullition peaked during each pressure trough.
During periods of above average pressure, ebullition either ceased altogether, or occurred in occasional bursts with no clear connection to atmospheric pressure.
Increased turbidity (decreased water clarity) at depth is typically associated with low-pressure events (Figure 2c). During the first event (Day 43 -45) a peak in turbidity at 8.5m coincided with a pressure trough and high ebullition. During the second event (Day 54 -60) there were three troughs in the atmospheric pressure and three corresponding peaks in ebullition intensity.
Turbidity at 8.5m peaked during the second and third pressure troughs, but did not peak during the first pressure trough on Day 54 even though ebullition peaked. Whereas, turbidity at 2.5m was not affected by ebullition or pressure. Note, the bottom-water temperature has no apparent correlation with ebullition ( Figure 2d). We conducted preliminary laboratory experiments to investigate the link between ebullition and turbidity. Following the procedures outlined in Zare and Frigaard (2018), we prepared a layer of Carbopol, a transparent gel-like material, as a surrogate for the mud. We capped the Carbopol with a layer of water to mimic Base Mine Lake (Figure 3). We injected air through a needle, 0.6 mm in diameter, into the base of the Carbopol and observed the rise of the resulting bubbles. As the bubbles rose through the water-Carbopol interface some of the Carbopol, as well as fine particles placed on the interface, were entrained into the wake of the bubbles (Figure 3a). Some of the entrained Carbopol and fine particles detrain before the bubbles rise to the water surface ( Figure 3b). We hypothesize that the same process occurs in Base Mine Lake. Turbidity at depth was affected by ebullition (8.5 m in Figure 2c), whereas higher in the water column it was not affected (2.5 m in Figure 2c). After the passage of many bubbles a conduit formed within the Carbopol (Figure 3c). Some of the overlying water (blue) entered the conduit after the release of each bubble.     Figure 1a; whereas, the location of pockmarks 2 -8 is indicated with a white square in Figure 1a. While many researchers have observed a relationship between pressure variations and methane ebullition from sediments (e.g. Walter Anthony et al., 2010;Harrison et al., 2017), to our knowledge none have observed as definitive a relationship as we have presented in Figure 2.
Our data set is special for two reasons. Firstly, given that the lake is ice-covered, and there are no inflows or outflows, pressure variations in the sediment are almost exclusively due to atmospheric pressure fluctuations. Secondly, by mounting an echo-sounder in the ice we were able to obtain a continuous record of ebullition from a fixed location for an extended period of time.
In our data record, the ebullition intensity is well approximated by: where is the predicted ebullition intensity, P is atmospheric pressure, ℎ is a threshold pressure and is a proportionality constant. As a measure of the goodness of fit between the measured ebullition, , and the ebullition predicted by (1), we use = 1 − ∑( − ) 2 ∑ 2 . The variation of with ℎ and k is plotted in Figure S1 in the supporting information. The optimal value of = 0.87, is obtained when ℎ = 97.1 and = 2.9. Applying this set of values, the result from equation (1) is shown in Figure 2b. It matches the magnitude and timing of observed ebullition well. An alternative set of values is obtained using the average atmospheric pressure ℎ = = 96.9 , and = 4.2, calculated by equating the time integral of the observed ebullition intensity over the study period with the time integral of the predicted ebullition intensity using equation (1). This latter pair of values gives = 0.79 as shown in Figure S1. A comparison between the observed ebullition intensity and predicted ebullition intensity using this pair of values is shown in Figure S2.
In addition to atmospheric pressure fluctuations, many factors have been suggested to affect methane ebullition. Seasonality in temperature can influence ebullition by affecting methane production rate and methane solubility in porewater (e.g. Fechner-Levy & Hemond, 1996;DelSontro et al., 2016). The temperature of the surface of the mud in Base Mine Lake can vary several degrees on a seasonal basis (Dompierre & Barbour, 2016), in response to the seasonal variation in the temperature of the water column (Tedford et al., 2019a). During the study period, the bottom-water temperature remains stable ( Figure 2b) and shows no correlation with ebullition. The temperature inside the mud layer varies even less. Dompierre & Barbour (2016) have shown that temperature variations inside the mud decreases exponentially with depth and the variations are negligible 4 m below the lakebed. Falling water levels, due to reservoir withdrawals, can also trigger ebullition (Harrison et al., 2017). However, due to the absence of inflow and outflow during ice cover, the water level in Base Mine Lake is stable. Finally, Joyce and Jewell (2003) observed that shear stresses caused by bottom currents, driven by surface winds, could trigger the release of bubbles. However, under ice, wind driven bottom currents are negligible.
As in natural sediment, ebullition in Base Mine Lake is subject to complex processes.
Nevertheless, based on our observations during ice cover and the effectiveness of equation (1), we conclude that most of the ebullition in Base Mine Lake can be explained using a relatively small number of principles and assumptions, namely: there is a range of depths within the mud of Base Mine Lake in which the methane concentration in the pore water is at, or near, saturation (Francis, 2020); methane bubbles are present in this zone, with sizes ranging from the size at nucleation to a critical size at which ebullition occurs (Algar et al., 2011); and methane released through ebullition is replenished by methanogenesis, but at time scales much longer than the duration of pressure events,.
During ice-cover inflows into, and outflows from, the lake are negligible, and the hydrostatic pressure exerted on the mud by the combination of water and ice is constant. Therefore, any change in atmospheric pressure changes the pressure exerted on the bubbles within the mud.
When the pressure experienced by the bubbles drops, the corresponding reduction in methane solubility (Henry's Law) results in gas moving from the pore water into the bubbles, causing them to grow. Decreasing pressure also causes bubbles to grow (ideal gas law). The idealization represented by equation (1) implies that when the atmospheric pressure drops below the pressure threshold (e.g. Figure 2, day 43), the largest bubbles reach critical size and ebullition starts.
Subsequently, when atmospheric pressure rises above the pressure threshold (e.g. day 45), the corresponding increase in methane solubility results in methane moving from the bubbles into the pore water. This, together with the reduced volume due to the increased pressure, causes ebullition to stop.
In applying equation (1) we have assumed a constant pressure threshold during our study period, and obtained results that are largely consistent with the observations presented in Figure 2.
However, for the pressure threshold to remain constant, the rate of ebullition would need to be in equilibrium with the rate of methane production. If the rate of ebullition exceeds the rate of production the store of available methane will decrease, effectively reducing the pressure threshold; whereas, if production exceeds ebullition the pressure threshold will rise. The relative success of our assumption of a constant threshold in equation (1) implies that the variation of the pressure threshold during our study period was not significant.
While the sediments in Base Mine Lake are the product of a mining operation, they have similar mean particle size and clay fraction as the fine-grained muds found in natural lakes and estuaries (Dompierre & Barbour 2016). The clear linkage between pressure and ebullition that we have observed has also been observed in natural lakes. For example, Matton & Likens (1990) observed rapid ebullition during low atmospheric pressure events in Mirror Lake, New Hampshire. In northern ice-covered lakes, Walter Anthony et al. (2010) also observed that ebullition responded to atmospheric pressure fluctuations. Scandella et al. (2011) showed a strong relationship between pressure variations and ebullition from the "gassy" sediments in Upper Mystic Lake, Massachusetts.
There are occasions (e.g. during days 40, 46, 51 and 61 in Figure 2) when sporadic ebullition occurs even though atmospheric pressure is considerably higher than the pressure threshold.
This may be a result of intermittent coalescence of bubbles inside the mud-layer causing them to reach critical size. Movements within the mud layer due to its gradual settling (Dompierre & Barbour, 2016) may facilitate coalescence and ebullition.
Ebullition in Base Mine Lake has other important impacts beyond the elevated turbidity shown in Figure 2c. Our laboratory experiments show that rising bubbles push water out of established conduits, and once the bubbles exit, the water flows back in (Figure 3c). The same process probably occurs in Base Mine Lake, enhancing the exchange of heat and dissolved contaminants between the mud layer and water column. This process provides an explanation for the enhanced mixing hypothesized by Dompierre et al. (2017) in modelling exchange between the mud and water column. The rising bubbles increase dissolved methane concentration in the water column, which leads to methane oxidation and contributes to decreasing dissolved oxygen concentration (Risacher et al., 2018). In winter, methane bubbles are frozen into the ice, along with hydrocarbon transported from the mud (Tedford et al., 2019b). The presence of bubbles causes weakening of the ice, that is apparent during augering, and may result in earlier melting. In summer, hydrocarbon transported by the bubbles reaches the lake surface, influencing heat exchange with the atmosphere (Chang, 2020;Clark et al., 2020) and the properties of windgenerated surface waves (Hurley et al., 2020).

Conclusions
Although there are extensive observations of ebullition during the open water season, under ice observations are limited. We present high-frequency ebullition data from Base Mine Lake under ice, that reveals that ebullition primarily occurs when atmospheric pressure is below a threshold.
This pressure threshold is approximately equal to the average atmospheric pressure. The timing and magnitude of major ebullition events is well reproduced by setting the ebullition intensity to be proportional to the pressure deficit below the pressure threshold. Laboratory experiments and field observations also show that these episodic ebullition events elevate turbidity at depth and can enhance exchange of contaminants between the mud layer and the water column.
Even though our results are from a single lake during ice-cover, the importance of atmospheric pressure variations is not limited to this lake, or the ice-cover season. The response of ebullition to pressure variations has been observed in natural lakes, both during ice-cover (Walter Anthony et al., 2010) and during the open-water season (Matton & Likens, 1990;Scandella et al.,2011).
Future studies are needed to refine and extend our results to other lakes and the open-water season. Our data suggests that future surveys need to sample ebullition frequently enough (at least hourly) to capture the rapid response of ebullition to pressure variations.