Ephemerality of discrete methane vents in lake sediments

1 Introduction

Emissions from submerged sediments in lakes, rivers, wetlands, and oceans contribute to atmospheric methane, but the nature and magnitude of the release remain uncertain. Owing to their buoyancy and high methane content, bubbles emitted from the sediment transport methane more efficiently than waters containing dissolved methane, and field studies suggest that ebullition is often the dominant mode of methane transfer to the atmosphere [Martens and val Klump, 1980; Kuipphet and Martens, 1982; Keller and Stallard, 1994; Bastviken et al., 2004; Walter et al., 2006; Bastviken et al., 2011; Maeck et al., 2013a]. Ebullitive emissions are episodic and spatially heterogeneous, which complicates upscaling of flux estimates [Greinert, 2008; Ostrovsky et al., 2008; Greinert et al., 2010; DelSontro et al., 2011; Wik et al., 2011; Maeck et al., 2013b; Walter Anthony and Anthony, 2013; Wik et al., 2013; DelSontro et al., 2015].

The episodicity of methane venting may be driven by either the methane source or an external forcing, depending on which operates on a faster time scale [Maeck et al., 2013b]. For example, drops in hydrostatic or atmospheric pressure trigger ebullition from methane-generating lake sediments [Scandella et al., 2011] and marine sediments [Martens and val Klump, 1980; Kuipphet and Martens, 1982; Chanton et al., 1989], possibly even in the presence of methane hydrates [Torres et al., 2002]. Spatial heterogeneity in methane venting often manifests as hyperactive vents or vent clusters, sometimes referred to as hot spots [Walter et al., 2006; Wik et al., 2011; DelSontro et al., 2015]. These focused release points may be associated with enhanced microbial methanogenesis [Ostrovsky et al., 2008; DelSontro et al., 2011; Maeck et al., 2013a; Wik et al., 2013], sediment morphological features like pockmarks [Bussmann et al., 2011], a geologic source [Walter Anthony et al., 2012], dissociating gas hydrates [Westbrook et al., 2009; Berndt et al., 2014; Skarke et al., 2014], or rapidly degrading permafrost [Shakhova et al., 2014]. The persistence of bubble outlets and the spacing and variability between them can potentially be used to distinguish the mechanisms controlling ebullition [Greinert, 2008; Wik et al., 2011], but observations of these critical parameters are sparse and inconclusive.

Ebullitive fluxes are sometimes measured using bubble traps deployed at discrete locations over an extended time period, but capturing hot spot ebullition or the episodicity of venting events can be challenging with this approach [Walter et al., 2006; Varadharajan and Hemond, 2012; Maeck et al., 2013b; Walter Anthony and Anthony, 2013; Wik et al., 2013]. Hydroacoustic surveys from ships [Ostrovsky et al., 2008; Greinert et al., 2010; DelSontro et al., 2011, 2015; Skarke et al., 2014; Weber et al., 2014] cover large areas but only at discrete times and therefore cannot be used for continuously quantifying fluxes. Short- and long-term seafloor deployments of hydroacoustic sensors [Greinert, 2008] can detect ebullitive events at specific locations but require careful calibration to infer spatially resolved fluxes. Here we extend the hydroacoustic approach to acquire long-term, high-resolution methane emission records from a lake bottom to test hypotheses about the driving forces for ebullition events and the mechanisms controlling spacing and persistence of gas vents.

2 Multibeam Sonar Deployment

An Imagenex 837B DeltaT 260 kHz rotating multibeam sonar was deployed on a benthic lander in the deepwater basin (18–19 m) of Upper Mystic Lake (UML), an eutrophic kettle lake north of Boston, MA (Figure 1). The sonar surveyed in a horizontal plane ≈1.5 m above the lake's bottom and ≈8–9 m below the depth of observed thermoclines to collect data over a 9 month period in a ≈330 m² area. The sediments within this region are organic rich (20–40%) [Spliethoff and Hemond, 1996] and remain anoxic and at roughly constant temperature beneath the 4–6°C hypolimnetic water [Varadharajan, 2009]. The previously measured sediment accumulation rate of 0.5 cm/yr is expected to be homogeneous within the basin due to relatively flat bathymetry, and freeze cores from within the basin show strikingly similar depth profiles of arsenic concentration [Spliethoff and Hemond, 1996]. Over the scale of the lake, deposition rates are expected to be faster near the periphery and the northern end, where water flows in from a forebay. An identical sonar was calibrated in a 1300 m³ freshwater tank at the University of New Hampshire to convert the sonar signals into estimates of the instantaneous flow rate from bubble streams (Figure 1d), which were then integrated to calculate the flux associated with ebullition episodes (see Methods and supporting information).

3 Temporal Signature of Methane Venting

Episodicity observed in spatially averaged daily flux from the sonar data confirms that strong venting episodes can be triggered by drops in hydrostatic pressure (Figure 2a), although the negative correlation of ebullition rate with hydrostatic pressure and its rate of change (R²=0.5 and 0.1, respectively) is weak, primarily because not all hydrostatic pressure drops trigger ebullition episodes. For example, the releases in late February and late April 2012 are both followed by month-long periods of relative quiescence, despite several ≈0.3 m hydrostatic drops that had earlier been enough to trigger large methane releases. The duration of these quiescent periods reflects the time for sediments to recharge the trapped bubbles to a size large enough to be susceptible to mobilization by hydrostatic triggering.

Hydrostatic triggering of ebullition may be explained mechanistically as a response to changes in effective stress. With falling hydrostatic pressure, total stress is reduced, forcing gas-charged sediments into a more tensile effective stress state. At a critical stress, gas-filled cavities then dilate near-vertical conduits to the sediment's surface [Boudreau et al., 2005; Jain and Juanes, 2009], and the critical stress may be modeled assuming that the sediment-water matrix is elastic [Algar et al., 2011a, 2011b] or plastic [Scandella et al., 2011]. The timing and relative magnitude of many of the peak ebullition events can be reproduced using a numerical model [Scandella et al., 2011] that captures this process and that is tuned with another UML data set (Figures 2a and 2b). The tuning parameter, the ebullition number, controls the episodicity of methane fluxes and reflects the balance between the tensile strength of the sediment-water matrix and the characteristic hydrostatic pressure variations. The model can capture the features of most large ebullition events, although it does not fully reproduce the long quiescent periods during March and May 2012 (Figures 2a and 2b).

The high temporal resolution, together with the large areal coverage and long duration of the sonar record, allows for a more detailed analysis of ebullition dynamics that had previously been possible with bubble-trap methods. High-frequency flux measurements (binned at 1 min) show that approximately 98% of the flux measurements follow a lognormal distribution over 3 orders of magnitude (0.1–100 mL/m²/d) (Figure 2c, see supporting information). Lognormally distributed measurements typically arise from processes controlled by the product of independent factors, which in this setting may include the bubble mobilization rate over the observation area and heterogeneity in conductivity of dynamic gas escape pathways.

Further insight into processes controlling ebullition is furnished by the distribution of interarrival times between bubble-release events—“events” are bubble-release sequences that persist with breaks no longer than 2 s (given 5 s moving-average filtering). Distributions of interarrival times may be analyzed using the hazard function

(1)

where f(τ) is the probability density function of interarrival times τ, and F(τ) is the cumulative density function [Stapelberg, 2009]. h(τ) quantifies the probability of an event occurring conditioned on a given amount of time having passed since the last event. For a Poisson process, events are independent and have uniform probability, corresponding to constant h since the events have no memory of previous arrivals. For a Weibull process—a model often used in reliability engineering to model component failures—the hazard function is a power law, h(τ) = (β/λ)(τ/λ)^{β − 1}, where β and λ are the shape and scale parameters, respectively. A decreasing power law (β < 1) corresponds to strong temporal clustering, while an increasing power law (β > 1) is associated with more regularly periodic arrivals [Stapelberg, 2009].

In UML, ebullition events are characterized by decaying power laws. For events collected from a 64 m² averaging area, the decay in both high- and low-flux regimes is well fit by β≈0.4, which reflects mild temporal clustering (Figure 2d). At the fine-scale resolution of the sonar (0.25 m²), h(τ) shows two distinct regimes characterized by different power law scalings. For short-term interarrival times (τ < 5 min), the decay has a slope less than −1, indicating stronger short-term clustering than possible with a Weibull process, which requires β > 0. The power law regime does not extend over all τ but instead transitions to a regime of more gradual decay over long interarrival times (τ > 5 min), consistent with reestablishment of sediment cohesion and healing of vent conduits. Over long τ, the high-flux regime shows even more gradual decay in h(τ) than the low-flux regime, implying a larger role for independent arrivals.

4 Spatial Signature of Methane Venting

The spatial structure of methane venting is found to depend on the overall flux regime (high flux versus low flux). Daily gas flux maps during high-flux periods reveal gas release from densely spaced outlets, while the low-flux periods are associated with sparser venting (Figure 3a). The ubiquity of venting across the observation area during high-flux periods may reflect the relative homogeneity of methanogenesis, whose controlling parameters (sediment accumulation and temperature) are fairly homogeneous above the meter scale in the deepwater basin [Spliethoff and Hemond, 1996].

During high-flux periods, ebullition events occur in clusters of enhanced activity, although, over time, events appear throughout the field of observation. While some locations vent gas at over 3 times the spatiotemporal mean flux of 10 mL/m²/d (Figure 3b), these contribute only 1% of the total flux, suggesting a minimal role for hot spots. Instead, gas appears to be released through independent, near-vertical conduits or conduit networks linked to outlets, where the scale of lateral transport or significant heterogeneity in sediment properties is less than the resolution of the sonar, 0.5 m. Such a laterally dense network of release pathways should develop in sediments that generate methane throughout their bulk. In this case, transport from the sediment matrix toward release pathways would be diffusion limited to a distance on the scale of centimeters in the days to weeks between ebullition events. The outlet and conduit spacing may also be controlled by heterogeneity in the chemistry and mechanics of the sediments, though our results show that such heterogeneity does not give rise to persistent outlets spaced more than 0.5 m apart.

A spatial clustering analysis of the observed methane-flux signal yields additional clues about the system's self-organization. Our analysis is based on the radial distribution function (RDF), g(r), which detects clustering as a function of interpoint distance r [Illian et al., 2008] (see Methods and supporting information). The analysis yields g > 1 for short-range (r < 1 m) events over short time periods (10 min and 1 h samples), indicating a high areal density of events relative to a completely spatially random (CSR) process. The short-range clustering is balanced by long-range spacing (g < 1 for r > 1 m). This signature of short-range clustering and long-range spacing was strongest for 10 min samples and became progressively weaker for longer duration samples, eventually decaying to a homogeneous RDF (g(r)≈1) over daily samples (Figure 3d). This clustering signature indicates that gas is vented from nearby, distinct outlets within a short period of time (see Methods and supporting information).

Compared with the high-flux regime, low-flux periods show both stronger variability and longer persistence in the structure of the heterogeneity. For a given observation duration, the coefficient of variation (CV) across space is more than twice the CV from high-flux periods (Figure 3c). The spatial structure of this variability is evident in the RDF, which exhibits short-range spatial clustering that is similar to the clustering observed during high-flux periods, except that it extends to r≤2 m and persists over timescales as long as 1 day (Figure 3e, see supporting information).

The ephemeral nature of spatial clustering evidenced by the RDF is consistent with the spatial localization of short-term temporal clustering observed in h(τ) and is likely associated with the same process. Ebullition events may trigger “aftershock” events by mechanically disturbing nearby sediments that contain critically stressed gas pockets. Due to the compliance of the sediments and the small magnitude of deformation associated with bubble passage, this mechanism would likely require that trapped bubbles be spaced only a few centimeters apart.

The decay of clustering over progressively longer periods indicates that individual outlet clusters are active for a short time but do not persist to dominate the long-term flux pattern. Instead, independent outlets or clusters subsequently become active at intermediate, independent locations until the domain is filled with emission sites approximating a CSR pattern. The clustering pattern in the RDF decays faster during high-flux periods, suggesting that higher fluxes arise primarily from more frequent initiation of spatially independent events. The spatial independence of new arrivals over long time periods is consistent with the conceptual model that long-term, large-scale fluxes are driven by hydrostatic pressure drops, which act equally over the sediment surface to liberate trapped gas.

5 Conclusions

In summary, the high spatial and temporal resolution afforded by the sonar data allows discernment of discrete ebullitive episodes and vent locations, and the long deployments permit analyses over months' long periods. Our analysis shows that specific methane vents in UML do not repeatedly dominate fluxes during ebullitive episodes; instead, vents are frequently forming and closing off throughout the homogeneous sediments that make up the seep field in the lake's deep basin. This finding challenges the idea that sediment vents, once established, will continue to be the preferential loci over the scale of meters. While these results may not directly apply to settings with more heterogeneous geology [Hornbach et al., 2004; Walter Anthony et al., 2012; Skarke et al., 2014] or sediment deposition patterns [Bussmann et al., 2011; DelSontro et al., 2011; Maeck et al., 2013a; DelSontro et al., 2015], they suggest that the acquisition of longer and more spatially comprehensive data sets on ebullition events in such settings may better constrain the relative importance of hot spot versus distributed methane emissions from submerged sediments for both local and global flux estimates.