Extrapolated CO2 fluxes over the entire Horseshoe area using different distribution model for the seep density of each flow rate category and their respective distribution

Three ROV dives (GFL-ROV-PL776-07, GFL-ROV-PL778-09; GFL-ROV-PL785-16) were visually inspected to map, count and classify seep outlets of every active site in the entire Horseshoe area. A dedicated survey was performed in site B0 to quantify flow rates: a small funnel (530ml total volume) with volumetric graduation marks was used to measure flow rates on each event noted. The funnel was also deployed on site C1, D1, E0 and G0. Observed seeps were classified into 3 categories based on their flow rate (SI Table 2): low flow rate < 10 ml s-1, medium flow rates between 10 and 40 ml s-1 and high flow rates > 40 ml s-1. We calculated the number of seeps per category, average and standard deviation of the flow rate for each of the 3 categories. Density of seeps on site B0 was then calculated for each flow rate category and defined as follows:
density of seep category i di = Number of seeps with flow rates in ith category / B0 surface area (m²)
Aerial distribution of each flow rate type was defined as:
distribution disti(%) = Number of seeps with flow rates in ith category / Total number of seeps in B0
Where i designates the low, medium and high flow rate categories.
Extrapolation over the entire Horseshoe area was performed using a similar approach to Schissel et al, 2024 (Schissel, C., Allen, D. & Dieter, H. Methods for Spatial Extrapolation of Methane Measurements in Constructing Regional Estimates from Sample Populations. Environmental Science & Technology 58, 2739-2749, doi:10.1021/acs.est.3c08185 (2024)). First, flow rates in each category were modeled following a random normal distribution, with mean and standard deviation values taken as the ones measured in B0. Random samples were then generated.
The density of each flow rate category was modeled using two types of random distribution: 1) normal distribution with mean and standard deviation as observed in B0, and 2) beta distribution with mean and variance as observed in B0 but with minimum and maximum values between 0 and the maximum density observed. Negative values are removed from further calculating steps.
The only density estimates and distributions available originate from B0, which accounts for 30% of the surface of the Horseshoe area, and no other values were available, we therefore kept the B0 measurements as baseline values for the density distribution but considered areal distribution as random. Areal distribution of flow rates categories for each of the seep sites (dist) were hence modeled in 3 different ways: totally random number, Dirichlet distribution and normal distribution with mean as the observed value in B0 and standard deviation as one third of this mean value, as no standard deviation was available. Therefore, each seep sites (from A0 to G0) has a set of 3 distribution values, all of them between 0 and 1, and whose sums equals to 1.
Fluxes were then calculated as the product of distribution, density, flow rates and area for each category and each site, as follows:
Total Flux :  [distiA0,…,distiG0] * [Fi x di] * [AreaA0,…, AreaG0]
With for each i category (low, medium, low), disti is the areal distribution of all flow rates categories in one seeping area, Fi the flow rate for the i category, di the seeping density for the i category in the seeping area considered, Area, the areal extent of the seep site (A0 to G0, Figure 1), and * designating the matricial product.
Simulations were then run for an increasing number of samples from 100 to 100000 to assess error variability. All statistical evaluations were performed using R, and the MCMCpack package (https://doi.org/10.32614/CRAN.package.mcmc). All information can be found in Cathalot et al, 2025 submitted to Nature Geoscience (DOI to be provided upon publication).