Supplement of Technical note: Mobile open dynamic chamber measurement of methane macroseeps in lakes

Methane (CH4) seepage (i.e., steady or episodic flow of gaseous hydrocarbons from subsurface reservoirs) has been identified as a significant source of atmospheric CH4. However, radiocarbon data from polar ice cores have recently brought into question the magnitude of fossil CH4 seepage naturally occurring. In northern high latitudes, seepage of subsurface CH4 is impeded by permafrost and glaciers, which are under an increasing risk of thawing and melting in a globally warming world, implying the potential release of large stores of CH4 in the future. Resolution of these important questions requires a better constraint and monitoring of actual emissions from seepage areas. The measurement of these seeps is challenging, particularly in aquatic environments, because they involve large and irregular gas flow rates, unevenly distributed both spatially and temporally. Large macroseeps are particularly difficult to measure due to a lack of lightweight, inexpensive methods that can be deployed in remote Arctic environments. Here, we report the use of a mobile chamber for measuring emissions at the surface of ice-free lakes subject to intense CH4 macroseepage. Tested in a remote Alaskan lake, the method was validated for the measurement of fossil CH4 emissions of up to 1.08× 104 g CH4 m−2 d−1 (13.0 L m−2 min−1 of 83.4 % CH4 bubbles), which is within the range of global fossil methane seepage and several orders of magnitude above standard ecological emissions from lakes. In addition, this method allows for low diffusive flux measurements. Thus, the mobile chamber approach presented here covers the entire magnitude range of CH4 emissions currently identified, from those standardly observed in lakes to intense macroseeps, with a single apparatus of moderate cost.


S1. Response time and data interpretation
The concentration read by the detector has a certain delay, due to the gas residence time from the chamber to the detector. However, if the detector is close to the chamber and the tubing of a reduced diameter, this time is very short; i.e., from 1.6 to 2.0 s in our case. However, even if it can be assumed that a bubble entering the chamber is immediately mixed within the chamber, the detectors have an inherent response time. This effect causes a certain delay and a buffer time, between the actual concentration read by the detector (CD) and CC. To take this delay into account a standard mixing model can be used (Eq. S12), where θ is the response time of the system In Eq. (S1), θ was determined from experimental data, using several step CD increases observed in the field. The adjustment was done through excel, minimizing the Root Mean Square Error (RMSE) between experimental CD data and Eq. (S2), where CD,0 is the initial reading of the detector (at time 0), and CC is the actual concentration in the chamber.
After CC was determined, Eq. (5) was used to determine instantaneous F along the transects. Alternatively, Eq. (6) was used to determined mean flux over a transect section. In the case of instantaneous F, during transects, and despite the relatively high signal to noise ratio of detectors used; i.e., ratio of the mean to the standard deviation, F was subject to a significant noise, and a first data smoothening of CC was necessary, followed by a second smoothening of dCC/dt (Eq. S7). In both cases we opted for a pondered smoothening described by Eq. S3, where X´ is the smoothened variable X, in this case CC or dCC/dt.
As it will be shown in the Results and Discussion section, peak fluxes were detected, which corresponded to step increases of CC (ΔCC), caused by bubbles reaching the chamber. These abrupt increases offer a unique opportunity to quantify the CH4 mass content of the bubbles (MB). It should be noticed that since these step increases were observed in a few seconds, the amount of CH4 lost through detector extraction or entering the chamber can be neglected over that short time, as far a as single and clear increase was observed. Thus, MB was determined during the field experiment according to Eq. (S4).

= ∆ • (S4)
From MB, the volume of the bubbles (VB) and their equivalent spherical diameter (dB) at atmospheric pressure were determined, assuming that the CH4 content in the bubbles (%CH4) is known, according to Eq. (S5) and (S6), respectively.
where 16 is the molecular weight of CH4 (g), R is the universal gas constant (L atm mol -1 K -1 ), T is the temperature (K) and P is the atmospheric pressure (atm).
Since bubble volume and diameters are important for mass transfer determination during their migration to the lake surface, the actual bubble volume (V'B) at a given depth (D) within the water column is given by Eq. (S7).
where  is the water volumetric mass density (kg m -3 ), g is the standard gravity (m s -2 ), and 101,325 is the conversion factor from Pa to atm.