Ship waves induce methane ebullition in the littoral zone of a large lake

Methane (CH4) ebullition is a major emission pathway in lakes. However, ebullition remains difficult to assess, and data from large lakes are scarce. This study investigates ebullition in the littoral zone of a large lake, demonstrating that ship waves, even after traveling long distances, regularly trigger gas bubble releases from the sediments in shallow waters. Although these ebullitions events occur only during the short time intervals of ship-wave passages, they lead to substantial CH 4 emissions. Comparing several littoral sites, we assess the frequency and extent of ship-wave-induced ebullition events and contrast them with ebullition caused by a storm event. Our findings reveal a strong cross-correlation between pressure drops due to ship waves and ebullition fluxes, highlighting ship-wave-induced pressure changes as a significant yet understudied driver of CH 4 emissions in lakes. With ship traffic on lakes steadily increasing, understanding ship-wave-induced ebullition is essential for improving estimates of lake-wide CH 4 emissions. 1 Article type: Letter 1 2 Title: Ship waves induce methane ebullition in the littoral zone of a large lake 3 4 Running head: Ship waves induce methane ebullition 5 6 Author names: Ole Lessmann1, Karla Martinez-Cruz1, Lea Loraine Ropella1, Nora Tutas1, Frank 7 Peeters1 8 9 Affiliation: 1Environmental Physics, Limnological Institute, University of Konstanz, Mainaustr. 10 252, D-78464 Konstanz, Germany 11 12 Corresponding author: Ole Lessmann, [email protected] 13 14 Author Contribution Statement 15 OL: Conceptualization, Investigation, Formal analysis, Software, Visualization, Project 16 administration and Writing (Original draft; Review and Editing). KMC: Conceptualization, 17 Investigation and Writing (Review and Editing). LLR: Investigation, Formal analysis and Writing 18 (Review and Editing). NT: Investigation, Formal analysis and Writing (Review and Editing). FP: 19 Conceptualization, Formal analysis, Software, Resources, Visualization, Project administration, 20 Supervision, Funding acquisition and writing (Review and Editing). 21 Scientific Significance Statement 22 Methane (CH4) ebullition is a major pathway in global CH 4 emissions from lakes, yet it remains 23 poorly understood, particularly in large lakes where data are scarce. Based on continuous 24 recordings of ebullition fluxes at several sites in the littoral zone of Lake Constance, we 25 demonstrate that ship waves are an important driver of ebullition events. Ship -wave-induced 26 ebullition events have short durations, but contribute a large fraction of overall CH 4 ebullition. 27 Although ebullition events due to ship waves occur only in shallow waters, they are a substantial 28 source of basin-wide CH4 emissions almost on the same order as the diffusive CH 4 emissions. As 29 boating on inland waters continues to rise, our study highlights the need to account for ship-wave-30 induced ebullition in future estimates. 31 32 Data Availability Statement 33 Data will be made available in the Zenodo repository. 34 35

36 Methane ( CH4) ebullition is a major emission pathway in lakes. However, ebullition remains 37 difficult to assess, and data from large lakes are scarce. This study investigates ebullition in the 38 littoral zone of a large lake, demonstrating that ship waves, even after traveling long distances, 39 regularly trigger gas bubble releases from the sediments in shallow waters. Although these 40 ebullitions events occur only during the short time intervals of ship -wave passages, they lead to 41 substantial CH4 emissions. Comparing several littoral sites, we assess the frequency and extent of 42 ship-wave-induced ebullition events and contrast them with ebullition caused by a storm event. 43 Our findings reveal a strong cross -correlation between pressure drops due to ship waves and 44 ebullition fluxes, highlighting ship -wave-induced pressure changes as a significant yet 45 understudied driver of CH4 emissions in lakes. With ship traffic on lakes steadily increasing, 46 understanding ship-wave-induced ebullition is essential for improving estimates of lake-wide CH4 47 emissions. 48 49

ebullition flux; methane emission; bubble traps; ship waves; Lake Constance 50

51 Methane ( CH4) is an important greenhouse gas, contributing strongly to human -made global 52 warming and driving climate change (IPCC 2021). Freshwater systems (e.g., lakes, ponds, 53 reservoirs, and rivers) are responsible for approximately 36–82% of the natural and 16–44% of the 54 total global CH4 emissions (Rosentreter et al. 2021; Jackson et al. 2024). Although estimates of 55 global CH4 emissions from freshwater systems differ substantially between studies, lakes are 56 undoubtedly one of the largest sources (Rosentreter et al. 2021). 57 The main CH4 emission pathways from lakes include ebullition, diffusion across the water -58 atmosphere interface, plant -mediated fluxes, and release of stored CH4 during water column 59 turnover (Michmerhuizen et al. 1996; Bastviken et al. 2004; Encinas Fernández et al. 2014). 60 Ebullition describes the release of bubbles from the sediment. A gas phase forms in the sediment 61 when the combined equilibrium partial pressures of all gases exceed the total ambient pressure. 62 This process requires high rates of gas production within the sediment, typically driven by 63 microbial CH4 production. Bubble release occurs when the gas pressure is sufficient to break up 64 the sediment matrix. Ebullition is often triggered by sudden drops in hydrostatic pressure, e.g., 65 during water level regulation or pumping operations in reservoirs (Harrison et al. 2017; Encinas 66 Fernández et al. 2020) and during water level drops caused by ship lock operations and ship 67 passages in rivers (Maeck et al. 2014). 68 Compared to deep-water conditions, CH4 production is higher in sediments of the shallow littoral 69 due to warmer temperatures (Conrad 2023) and increased organic matter input (Praetzel et al. 70 2020). Additionally, the lower ambient pressure in shallow waters reduces the CH4 production 71 required for gas phase formation. As a result, ebullition is more common in shallow littoral zones 72 than in deep profundal zones. Furthermore, CH4-rich bubbles rising from shallow waters lose less 73 CH4 to the ambient water during their brief ascent to the lake surface than those released from 74 greater depths (McGinnis et al. 2006). Consequently, CH4 emissions to the atmosphere from 75 ebullition fluxes are expected to be substantially larger in shallow than in deep-water regions. 76 Ebullition is often the dominant CH4 emission pathway in lakes, contributing an estimated 56% of 77 global annual CH4 emissions from these systems (Johnson et al. 2022). However, the drivers of 78 ebullition remain poorly understood (Savignano et al. 2024). Additionally, ebullition data from 79 lakes and especially from large and deep lakes are scarce (Bastviken et al. 2004; DelSontro et al. 80 2016; Praetzel et al. 2021). Therefore, understanding and quantifying ebullition in large lakes 81 remains a critical research gap. 82 In this study, we investigate ebullition in the littoral zone of large pre -alpine Lake Constance and 83 demonstrate that many of the observed ebullition events were associated with passages of ship 84 waves. Even when the ship waves were generated at great distances from the shore, the pressure 85 changes at the sediment surface associated with the passages of ship waves were typically sufficient 86 to trigger release of CH4-rich bubbles from the sediment in the littoral zone. We compare the 87 frequency and magnitude of ship -wave-induced ebullition events at different littoral sites and for 88 ship waves originating from the same route. Additionally, we present data showing ebullition 89 triggered by wind waves and discuss how these events differ from ship-wave-induced ebullition. 90 91

92 Study site 93 Measurements were conducted in Upper Lake Constance (9°30’ E, 47°30’ N), a large pre -alpine 94 lake in Europe (surface area ~470 km 2, maximum depth ~251 m). Instruments were deployed at 95 three littoral sites (Fig.1): At Obere Güll (OG) and Lipbachmündung (LM) from June 27 to July 6 96 2022 and at Bottighofen (BH) from July 11 to August 6, 2024 . Water depths at deployment were 97 2.0 m (OG), 1.7 m (LM) and 2.5 m (BH). Average temperatures during the measuring period were 98 20.2°C (OG), 21.6°C (LM) and 22.9°C (BH). 99 Wave measurements 100 High-resolution pressure time series (16 Hz) were measured using pressure sensors (PDCR 1730, 101 Teramess) with logger units developed at the University of Konstanz. The instruments were 102 deployed ~0.5 m above the sediment. Time series of water surface elevations were derived from 103 pressure time series by correcting for the wavelength -dependent attenuation of pressure 104 disturbances with depth (Hofmann et al. 2008). Waves were identified applying a zero-up-crossing 105 algorithm (IAHR 1989) to the detrended elevation time series. The wave field was characterized 106 by maximum wave height, H max, (wave height of the largest wave), and significant wave period, 107 Tsig (mean wave period of the largest third of the waves) within 1-minute intervals. The passage of 108 a surface wave trough is accompanied by a pressure decrease in the water column. For 109 characterising this pressure decrease, we defined P dec, the magnitude of the maximum pressure 110 decrease at the sediment surface associated with the passage of the wave with maximum wave 111 height within a 1-minute time interval. 112 Ebullition flux measurements 113 Ebullition fluxes from the sediment were measured using ebullition flux funnels (EFF) that were 114 custom manufactured at the University of Konstanz. Gas bubbles released from the sediment are 115 caught by an inverted funnel and directed into a cylindrical column where they displace the water. 116 The pressure difference between the gas phase in the column and the surrounding water is recorded 117 at 1 Hz and is used to determine the gas volume of the captured bubbles. The change in gas volume 118 over time provides the ebullition flux, F eb. Attached to the EFFs we deployed loggers 119 (AQUAlogger® 520, Aquatec) for measuring ambient total pressure and temperature every 30 s. 120 These data were used to convert the measured gas volumes to gas volumes at standard conditions 121 (1 atm, 20°C), assuming a molar volume of 24.0838 mol L -1. Ebullition fluxes were determined 122 from these time series by calculating the rate of gas -volume change per time employing a 30 s 123 (corresponding to 30 values) differential filter and smoothing the resulting time series of rates with 124 a boxcar filter using a moving average of 3 minutes (corresponding to 180 values). The ebullition 125 flux was calculated by dividing the volume change per time by the cross -sectional area (0.65 m 2) 126 of the EFF. 127 Exposure of littoral zones to ship waves 128 Shoreline exposure to ship waves was estimated using a simple empirical model. Ship motion 129 creates a characteristic wave pattern and the wave packets with the largest wave heights propagate 130 at an angle of approximately 35° relative to the direction of the ship track (Sorensen 1997). For 131 each location along the shoreline, the model determines whether and from which points along the 132 ship’s route waves can reach the shore. The distance travelled by the ship waves was estimated as 133 the shortest distance from their generation point along the ship’s route to the shore, without 134 accounting for diffraction effects. Ship -wave arrival times were determined from the distance 135 travelled by the wave packets and their group velocity. The latter was estimated to be 41% of the 136 ship speed at wave generation assuming propagation as deep-water waves (Crawford 1984) during 137 most of the wave’s path. 138 The shipping routes relevant to this study include the catamaran ferry route between Konstanz and 139 Friedrichshafen and the car ferry route between Konstanz and Meersburg (Fig. 1). During the study 140 period, the catamaran ferries operated hourly between 06:00 and 19:00 h on weekdays (Monday –141 Friday) and between 08:00 and 19:00 h on weekends (Saturday–Sunday). Additional evening trips 142 were scheduled on Fridays and Saturdays at 20:00 and 22:30 h (westbound) and at 21:00 and 23:30 143 h (eastbound). According to the ship -wave-exposure model, waves from westbound catamaran 144 ferries reached the stations BH, LM and OG after traveling approximately 2.4 km, 3.9 km and 8.8 145 km respectively, while waves from eastbound catamaran ferries reached station LM after traveling 146 ~4.6 km. The car ferries operated in intervals of 15–20 minutes during the day, and hourly at night. 147 Only waves from southwestbound car ferries reached station OG after traveling ~4.4 km. 148 149

150 Ebullition events and ship-wave passages 151 At all stations, ebullition shows characteristic patterns of regularly occurring short -term events 152 with relatively large ebullition fluxes (Fig. 2, 3). These ebullition events have a duration of several 153 minutes and are typically associated with the passage of ship waves at the measuring stations (Fig. 154 2). Ships and routes responsible for the waves reaching the different shore sites were identified 155 based on the wave period and the predicted wave arrival time. Catamaran ferries, traveling at 32–156 34 km h-1, generate waves with periods typically exceeding 4 s (Fig. 2D, H), whereas car ferries, 157 traveling at ~20 km h-1, generate waves with periods of 2.8–3.7 s (Fig. 2H). Observed and predicted 158 wave arrival times agreed well for all car and catamaran ferry routes (Figs. 2C, G). 159 Ebullition events at station OG (Fig. 2E) were associated with waves from the southwestbound car 160 ferry and the westbound catamaran ferry. However, the ebullition fluxes corresponding to 161 catamaran ferry waves were substantially larger than those corresponding to car ferry waves. At 162 station LM, the ebullition flux exhibited two peaks per hour (Fig. 2A), corresponding to the 163 passages of catamaran waves generated on the eastbound and westbound route. In contrast, the 164 ebullition fluxes at stations OG and BH show only a single peak per hour due to catamaran waves 165 (Fig. 2E, 3), as these sites are exposed only to waves generated on the westbound route. Ebullition 166 events not only reflect the hourly pattern in the schedule of the catamaran ferries, but also the 167 differences in these patterns between days (Fig. 3). 168 The passages of surface waves are associated with a periodic pressure decrease at the sediment 169 surface, which most likely is responsible for triggering ebullition. The pressure decrease at the 170 sediment surface, indicated by negative P dec, increases with H max but also depends on the wave 171 period, which determines the attenuation of the amplitude of pressure fluctuation with depth. This 172 effect is evident at LM at 09:40 h, when surface waves with large H max but small Tsig resulted in a 173 low-magnitude Pdec, and, despite the large H max, the induced F eb was smaller compared to waves 174 with larger Pdec (Fig. 2A–D). 175 Cross-correlation between Pdec and Feb shows the most negative correlation coefficients at zero lag 176 (r = -0.11 (BH), r = -0.34 (LM), p < 0.01) confirming that ebullition fluxes are linked to the pressure 177 decreases at the sediment surface (Fig. S1). Additional distinct peaks of negative correlation 178 coefficients occur at lags of 1 hour and 24 hours at both stations, with further lags at approximately 179 21 and 42 minutes at station LM (Fig. S1). The patterns in the cross-correlations between Pdec and 180 Feb reflect the patterns in the auto -correlations of P dec and of F eb, which are consistent with the 181 hourly and diurnal patterns in the ship-wave arrival times. 182 The mean ebullition flux during a catamaran -wave-induced ebullition event was estimated using 183 the fluxes within a 7 -minute interval centered on the peak flux during the event. On average, 184 ebullition fluxes associated with catamaran waves were 0.017 mL m -2 s-1 for the westbound and 185 0.012 mL m-2 s-1 for the eastbound catamaran routes at station LM, and 0.025 mL m-2 s-1 at station 186 BH (Table 1). The average ebullition flux during times not associated with the passages of 187 catamaran waves were 0.004 mL m-2 s-1 at LM (excluding a storm event, see Fig. 4) and 0.002 mL 188 m-2 s-1 at BH. 189 Additional ebullition events 190 Ebullition occurred not only during ship-wave passages but also during a strong wind event (wind 191 speeds reaching 10 m s -1) on June 30, 2022, between 22:20 and 24:00 h. At station LM, Tsig was 192 ~4.6 s, and Hmax reached 0.7 m during this event, leading to a Pdec of up to 0.21 dbar. Feb increased 193 in parallel with P dec reaching a maximum flux of 0.46 mL m-2 s-1 at 23:00 h (Fig. 4). Afterwards, 194 Feb decreased more rapidly than Pdec and ceased around 23:30 h. Pdec and Hmax remained elevated 195 until 24:00 h, indicating continued wave action that no longer triggered ebullition. The mean 196 ebullition flux during the 100-minute duration of the storm was 0.090 mL m-2 s-1, over three times 197 larger than that from catamaran waves. In contrast, surface waves and ebullition fluxes at site OG 198 remained unaffected by this storm event. 199 Not all surface waves associated with substantial pressure decrease caused peaks in the ebullition 200 flux (e.g., station OG around 9:20 h , Fig. 2E). Conversely, ebullition events also occurred 201 spontaneously without connections to surface waves (e.g., during the night, Fig. S2). 202 203

204 The patterns of ebullition events suggest that the pressure decrease during the passage of surface -205 waves is the mechanism driving ebullition. Ebullition fluxes are typically larger the larger the 206 pressure decrease, e.g., during the first half of the storm event and between sites. At station BH, 207 the mean ebullition flux associated with the passage of catamaran waves and the corresponding 208 pressure decrease are both significantly larger than at station LM (Fig. S3). However, the amount 209 of gas available in the sediment plays a role in limiting the ebullition flux. This is suggested by the 210 substantial reduction in ebullition fluxes during the second half of the storm event, likely due to 211 prior CH4 depletion from ebullition (Fig. 4). Hence, exhaustion of the CH4 pool in the sediment 212 resulting from previous ebullition and differences in CH4 production across seasons and sites, may 213 contribute to the variability of ebullition fluxes. In the absence of pressure decreases from surface 214 waves, the accumulation of CH4 in the sediment may generate sufficient gas pressure for triggering 215 ebullition (Fig. S2). 216 Ebullition fluxes associated with catamaran waves occur only during short time intervals, 217 accounting for ~13% of the day at LM and ~7% of the day at BH. Note that catamaran waves from 218 the eastbound and westbound route reach LM, but only those from the westbound route reach BH. 219 Despite these short time intervals of impact, the daily mean ebullition flux associated with 220 catamaran waves contributes on average 41% (LM) and 46% (BH) of the respective total daily 221 mean ebullition flux, because the average flux during the passages of catamaran waves is 3 (LM) 222 to 11 (BH) times higher than during the rest of the day (Table 1). At LM, the daily mean ebullition 223 flux for periods unaffected by catamaran waves is 60% larger than at BH, suggesting higher CH4 224 production at LM than at BH (Table 1). CH4 depletion cannot be responsible for the differences in 225 daily mean ebullition fluxes between the sites, because the daily mean flux associated with 226 catamaran waves is higher at LM than at BH. These results support the conclusion that the larger 227 average ebullition flux at BH, compared to LM, results from differences in the trigger (Pdec) induced 228 by catamaran waves. 229 CH4 fluxes were estimated from ebullition fluxes, assuming 80% CH4 in the gas . This fraction, 230 measured in gas bubbles released from littoral sediments in Upper Lake Constance, aligns with 231 CH4 fractions in bubbles from shallow sediments reported in other studies (Maeck et al. 2014; 232 Sepulveda-Jauregui et al. 2015). Note that bubbles typically lose little CH 4 while rising from 233 shallow depths to the surface (McGinnis et al. 2006). Accordingly, the daily mean CH4 flux 234 associated with catamaran waves from the westbound route was 3.3 mmol m -2 d-1 at LM and 4.8 235 mmol m-2 d-1 at BH and from the eastbound route 2.2 mmol m-2 d-1 at LM (Table 1). These values 236 are within the range of mean CH4 ebullition fluxes reported for the shallow zone (< 3 m depth) of 237 small lakes (1.1 mmol m-2 d-1) and ponds (4.6 mmol m-2 d-1) in Canada (DelSontro et al. 2016). 238 Basin-wide CH4 emissions due to catamaran-wave-induced ebullition were estimated based on the 239 area of the shallow water zone exposed to catamaran waves that may induce ebullition. Exposed 240 shore zones were identified by applying the ship -wave-exposure model to the catamaran routes. 241 The area of the shallow water zone exposed to catamaran waves that travelled up to 9 km (Fig. 1B) 242 — the largest wave travel distance for which we have confirmed ebullition measurements — and 243 assuming bubble release from 0.5 to 3.0 m water depth, is 4.36 km 2 for the eastbound route and 244 4.56 km2 for the westbound route. Using these areas and the daily mean CH4 fluxes from station 245 LM as lower limit, basin -wide daily mean CH4 emissions associated with catamaran waves are 246 estimated to be ~25 kmol d-1 or ~400 kg d-1. These represent about 43% of the daily mean diffusive 247 CH4 emission of 940 kg d-1 from Upper Lake Constance. The latter was estimated from the basin-248 wide mean CH4 surface concentration of 0.2 µmol L -1 in the northern basin of Upper Lake 249 Constance (Encinas Fernández et al. 2016) and a gas transfer velocity of 0.6 m d-1 for CH4 at 20°C, 250 assuming wind speeds below 4.2 m s -1 (Liss and Merlivat 1986; Schwarzenbach et al. 2003). The 251 estimation above demonstrates that CH4 ebullition induced by catamaran waves accounts for a 252 large fraction of basin -wide CH4 emissions. Note, that the basin -wide CH4 ebullition associated 253 with catamaran waves is rather underestimated, because additional ebullition likely occurs from 254 depths greater than 3 m and from other shoreline stretches. Also, CH4 ebullition induced by all ship 255 waves must be larger than that by catamaran-waves alone. 256 During the strong wind event lasting less than 2.5 hours, ebullition caused a release of 18 mmol 257 CH4 m-2, which corresponds to the release by catamaran -wave-induced ebullition over 3.5 days. 258 However, wind events of similar magnitude are not very common in Lake Constance, i.e., between 259 May and October, wind events with wind speeds exceeding 7 m s-1 only occur ~4 times per month. 260 261

262 Although ship-wave-induced ebullition events are limited to the shallow littoral and occur only 263 during the short time intervals of ship -wave passages, the resulting daily mean ebullition fluxes 264 and the associated CH4 emissions can be substantial. Additionally, short and infrequent strong wind 265 events can trigger large CH4 ebullition fluxes at wind -exposed shorelines. Hence, quantifying 266 annual lake-wide CH4 emissions associated with ebullition in large lakes is challenging not only 267 due to the spatial heterogeneity of ebullition events but also because of their large temporal 268 variability across different time scales. 269

270 We thank the scientific workshop facilities at the University of Konstanz, especially Thomas 271 Schuchhardt, Oliver Hamburger, and Georg Heine for the construction and maintenance of the 272 pressure loggers and the ebullition flux funnels. We wish to express our gratitude to Devin 273 Jachtmann for dedicated data collection efforts, to Beatrix Rosenberg and Anton Pranger for 274 technical assistance in the field, and to Soo Hyun Im for valuable support in manuscript 275 preparation. This manuscript benefitted from wind speed data provided by the German 276 Meteorological Service. The authors acknowledge using ChatGPT to correct grammatical errors. 277 This research was conducted as part of the project SuBoLakes (Sustainable Boating on Lakes in 278 Germany), which was financially supported by the German Federal Environmental Foundation 279 (Deutsche Bundesstiftung Umwelt, DBU) under project No. 35825/01. 280 281 Figure 1. Bathymetric maps of Lake Constance illustrating the location of study sites and ship routes. A) 282 Overview of Lake Constance, showing the locations of the three measurement stations: Obere Güll (OG), 283 Bottighofen (BH) and Lipbachmündung (LM), as well as the ship tracks of the catamaran ferry and the car 284 ferry. B) Enlarged section of Upper Lake Constance, displaying ship tracks (solid lines), the propagation of 285 ship waves (dashed lines), and littoral zones exposed to waves generated on the catamaran routes. 286 287 Figure 2. Time series of ~5 hrs of ebullition flux (A, E), pressure decrease at the sediment surface (B, F), 288 maximum wave height (C, G), and significant wave period (D, H) on June 29, 2022, at stations OG and LM. 289 Predicted ship-wave arrival times are marked for the catamaran ferry (westbound and eastbound) and the 290 car ferry (southwestbound). 291 292 Figure 3. Ebullition flux pattern at station BH on four days with varying ship schedules. Predicted ship-293 wave arrival times are marked for the westbound catamaran ferry. A large peak reaching 0.175 mL m -2 s-1 294 is truncated around 18:00 h in panel A due to the axis scaling. 295 296 Figure 4. Time series of 2.5 hrs of ebullition flux and pressure decrease at the sediment surface (inverted) 297 (A), maximum wave height (B), and significant wave period (C), overnight from June 30 to July 1, 2022, at 298 station LM during a storm event. 299 Table 1 Ebullition fluxes and CH4 fluxes evaluated for different time periods with and without passages of 300 catamaran waves at stations LM and BH. 301 Time period of evaluation Daily mean duration (hrs) Average ebullition flux (mL m-2 s-1) Daily mean ebullition flux (mL m-2 d-1) Daily mean CH4 ebullition flux (mmol m-2 d-1) LM BH LM BH LM BH LM BH all day 24 24 0.0047 0.0036 403.8 314.6 13.4 10.5 passages of catamaran waves westbound 1.6 1.6 0.0171 0.0245 97.9 143.1 3.3 4.8 eastbound 1.6 — 0.0117 — 66.8 — 2.2 — all day, excluding passages of catamaran waves 20.8 22.4 0.0036 0.0022 267.4 175.9 8.9 5.8 302

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U.S. Army Corps of Engineers, Upper Mississippi River - 373 Illinois Waterway System Navigation Study, ENV Report 4. 50 pp. 374 1 Supplementary Figures 1 Supplementary Figure S1 2 3 Supplementary Figure S1 . Cross -correlation of the ebullition flux and the pressure decrease at the 4 sediment surface for stations BH and LM at daily (A, C) and hourly (B, D) timescales. Cross-correlations 5 are based on time series with 3 -minute averages consisting of a total of 12491 data points (BH) and 1656 6 data points (LM). 7 2 Supplementary Figure S2 8 9 Supplementary Figure S2. Time series of ebullition flux (A), pressure decrease at the sediment surface 10 (B), maximum wave height (C), and significant wave period (D), overnight from July 2 to July 3, 2022, at 11 station LM. Ebullition peaks at 01:50 and 04:50 h are not associated with a pressure decrease suggesting 12 that they occur spontaneously without a specific external trigger. In contrast, the other ebullition peaks, near 13 midnight and from 08:00 h onwards, are associated with pressure decreases linked to passages of surface 14 waves. 15 3 Supplementary Figure S3 16 17 Supplementary Figure S3 . Maximum pressure decrease at the sediment surface (A) and maximum 18 ebullition flux (B) during catamaran-wave-induced ebullition events at stations LM and BH for the eastbond 19 and westbound catamaran routes. Sample sizes are: LM east (n = 98), LM west (n = 95), and BH west (n = 20 350). The figure shows the median, upper and lower quartiles, minimum and maximum values (excluding 21 outliers), and individual outliers. Statistically significant differences between the datasets were determined 22 using a two-sample t-test and are indicated by an asterisk (* p < 0.01). 23