Autonomous Large-Scale Radon Mapping and Buoyant Plume Modeling Quantify Deep Submarine Groundwater Discharge: A Novel Approach Based on a Self-Sufficient Open Ocean Vehicle

Groundwater discharge into the sea occurs along many coastlines around the world in different geological settings and constitutes an important component of global water and matter budget. Estimates of how much water flows into the sea worldwide vary widely and are largely based on onshore studies and hydrological or hydrogeological modeling. In this study, we propose an approach to quantify a deep submarine groundwater outflow from the seafloor by using autonomously measured ocean surface data, i.e., 222Rn as groundwater tracer, in combination with numerical modeling of plume transport. The model and field data suggest that groundwater outflows from a water depth of ∼100 m can reach the sea surface implying that several cubic meters per second of freshwater are discharged into the sea. We postulate an extreme rainfall event 6 months earlier as the likely trigger for the groundwater discharge. This study shows that measurements at the sea surface, which are much easier to conduct than discharge measurements at the seafloor, can be used not only to localize submarine groundwater discharges but, in combination with plume modeling, also to estimate the magnitude of the release flow rate.


Radon transfer kinetics
The explanations and figures shown below refer to the results of Petermann et al. 2 The radon transfer between water and air depends on many factors, including: S6 -type of exchange unit (e.g., membrane, spray unit) -water pumping rate -air flow rate through the measurement chamber -volume of the measurement chamber Experiments have shown that the delay is caused by two processes: a kinetic delay and a decay delay ( Figure S 3-2). The black line represents true radon-in-water anomaly, red is the radon-inair (corrected for partitioning) in the measuring chamber (delay caused by gas transfer kinetics) and green the system measurements (it measures Po-218). The radon transfer into the system is caused by the kinetic delay (from black to red line), the decay of radon into Po-218 relates to the decay delay (from red to green line). In the observed signal we see a response delay and a smoothing of the signal relative to the input signal. For a more complex signal the input and the measurement record are shown in Figure S  is reasonable to assume that the response delay is similar as well. Filtering procedure for the radon data A data filtering procedure had to be applied as recorded 222 Rn-data was partly corrupted by electronic spikes, which where possibly caused by high-voltage sparks in one detection unit of the radon sensor unit RTM-1688.
To apply sound data filters a 3-step algorithm of if-then equations was used to filter raw data: 1. If a given 222 Rn activity concentration in air is below the measured local background, i.e. Ni <24 Bq m -3 , then set the 222 Rn activity concentration to 24 Bq m -3 ; 222 Rn activity S9 concentrations were recorded in "fast mode" with 5 min sampling time (however, the local background 222 Rn activity concentration of 24 Bq m -3 was separately recorded with a 15-min sampling time).
2. If the 222 Rn activity concentration in air Ni>15xNi-1 then set Ni to Ni-1; the factor 15 was given by the maximum slope of the radon sensor output when Rn-charged water (i.e. of about 4700 Bq m -³ reaches the membrane-equilibration tube of the Rn-monitor (RTM-1688) with the given sampling configuration (fast mode, 5 min integration time), initial water in the equilibration tube of ~76 Bq m -³, and pumped volume rate in the flow-through equilibration tube. 3 3. If the 222 Rn activity concentration in air during decline after peak maximum is: Ni>1.7xNi+1 then set Ni to Ni-1; this argument considers the physical radon decay, which implies that 59% (=1/1.7) of the initial Rn activity concentration is measured on average within a 5-min interval.
The filtered radon activity concentrations in air in the inner gas chamber of the RTM-1688 were subsequently converted into radon activity concentrations in water by multiplying all data with an Ostwald-coefficient of 0.17. The coefficient converts a radon activity concentration in air to a radon activity concentration in seawater at the given temperature and salinity during measurements

Gas ebullition
Ebullition (i.e., the spontaneous formation of gas bubbles in seawater) might strip 222 Rn out of the plume water. In order to evaluate the potential effect of ebullition on the field observations, we considered the case where the groundwater discharged at the seafloor would have been saturated with aqueously dissolved gases (such as CH4 or CO2). In this case, ebullition could happen during ascent in the water column due to decreasing pressure. Ebullition is controlled by two antagonistic processes happening during plume ascent: entrainment in the ascending plume of ambient water undersaturated with dissolved gases decreases the oversaturation in plume water, whereas decreasing ambient pressure increases the oversaturation, potentially leading to ebullition. We find S11 that ebullition is unlikely to have posed a major limitation in the current study owing to the dominant effect of dilution during most of the ascent through the water column. For the base case simulation, which predicted the volume of water entrained in the plume over its ascent trajectory, we evaluated the potential of ebullition for the conditions the most favorable to ebullition, i.e. if the discharged water would be 100% saturated with aqueously-dissolved gases and the ambient seawater would contain a total pressure of 1 atm of dissolved gases throughout the water column.
Under these conditions and assuming Henry's law, water would initially become undersaturated with dissolved gases due to entrainment of ambient seawater in the plume. Upon nearing the water surface the pressure decrease would reduce the extent of undersaturation until water would become oversaturated with dissolved gases (i.e., the total pressure of dissolved gases would exceed the ambient pressure meaning that ebullition would be theoretically possible). However, the plume water would become oversaturated only within 3.3 m of the sea surface (7 s before reaching the sea surface), with a maximum oversaturation of dissolved gases of 0.14 atm. These simulated conditions are the most favorable conditions for ebullition, and field conditions are likely to have been less favorable to this process (groundwater less than 100% saturated with dissolved gases).
Consequently, we interpret that ebullition is unlikely to have substantially affected the field measurements performed with the sensor mounted on the wave glider. S12