Figure 3
“Figure_3_ISVR.mat” contains the bubble populations calculated in this paper.  Radii (in metres) are stored in the ‘radii’ variable.  Bubble counts for 1.15 m and 2 m depth are stored in the variable ‘BSDs_mean_198’.
“Figure_3_historic.mat” contains the historic bubble populations.  Variable names include the author and year, along with either x (for radii in micrometers) or y (for bubble count), e.g. phelps97_x and phelps97_y.

Figure 4
The modelled BSDs are contained in Figure_4_model.mat.  The variable ‘BSDs’ has the BSDs for 1.15 and 2 m depth in the first and second rows respectively.  The BSDs should be multiplied by the ‘fact’ variable.  Corresponding bubble radii are in the ‘radii’ variable.
The measured BSDs are contained in Figure_4_measured.mat.  The variable ‘BSDs_mean_198’ has the BSDs for 1.15 and 2 m depth in the first and second rows respectively.  Corresponding bubble radii are in the ‘radii’ variable.  Error bars are one standard deviation, which are in the ‘stan_dev_115’ and ‘stan_dev_200’ variables for 1.15 m and 2 m depth respectively (each array has a value for each bubble radius).

Figure 5
Data are stored in Figure_5_N.mat, Figure_5_O2.mat, Figure_5_CO2.mat and Figure_5_A.mat for nitrogen, oxygen, carbon dioxide and argon respectively.  The y axis data are stored in the variables F_N, F_O, F_C and F_A for the four gases respectively.  Each dataset is multiplied by the ‘fact’ variable factor.  x axis data are stored in the ‘sat’ variable.  Linear best-fit lines are shown through each dataset.  In order for the lines to fit well onto the same plot, the fluxes are normalised by dividing each by the product of the fraction in dry air and solubility of each gas. Fractions are 0.7809, 0.2095, 350e-6 and 9.3e-3 and solubilities are 6.29e-6, 13.0e-6, 445e-6 and 14.2e-6 mol m^-3 Pa^-1 for nitrogen, oxygen, carbon dioxide and argon respectively (values from Table 6.1 of Coles thesis).  The normalised fluxes are then scaled by a value of 0.1513. 

The inset is a copy of Figure S3.13 (description below).

Figure 6
x axis values are the bubble radii shown in Table S2.1 from 16 to 187 microns.
Measured BSDs are in the file “Figure_6_measured.mat” in the variable ‘means_split’.  Data for significant wave heights of 3.1 m and 1.9 m are in the first and second rows of the ‘means_split’ variable.  Only the first 11 values in each row are plotted.
The modelled BSDs are in the files ‘Figure_6_modelled_a.mat’ and ‘Figure_6_modelled_b.mat’ for Hs of 3.1 m and 1.9 m respectively.  In each file, the ‘radii’ variable contains the bubble radii.  The y axis values for Hs=3.1 are in the the first row of variable ‘BSDs_sc112’.  The y axis values for Hs=1.9 are in the first row of variable ‘BSDs_sc55’.  Modelled BSDs are scaled by the ‘fact’ variable.  Only the x axis values corresponding the bubble radii shown in Table S2.1 (between 16 and 187 microns) are shown.

Figure S2.1 (a)
Data are in “Figure_S2_1_pulses.mat”.  The complete pulse train is contained within the variable ‘plse_train_1’.  The plotted pulses are the 3rd and 4th pulses (10 kHz and 18 kHz).

Figure S2.1 (b)
Data in “Figure_S2_1_bubbles_132.mat".  Plotted data are the first channel from the ‘active_1_6_0’ variable, low-pass filtered at 250 kHz (sample rate is 1 MHz).

Figure S2.5 (a)
Data are in “Figure_S2_5a.mat”.  x data are contained in the variable ‘S_v_mean’, y data are contained in the variable ‘y’.

Figure S2.5 (b)
Data are in “Figure_S2_5b.mat” and the variable ’S_v_surf’ (a multi-dimensional array).

Figure S3.1
Data are contained in “Figure_S3_1.mat”.  x, y and z data are in the variables ‘x_plot’, ‘y_plot’ and ‘z_plot’ respectively.  Colour data are in the variable ‘a_plot’ (bubble radius in metres).  Bubbles smaller than 20 microns or larger than 800 microns are excluded from the plot.

Figure S3.2
The lines shown in this plot are calculated from the equations in the Levich and Thorpe papers referenced in the figure caption.

Figure S3.3
Description in figure caption.

Figure S3.4
Data are contained in “Figure_S3_4.mat”.  ‘x’ variable is bubble radius in microns.  ’T_g_N’ is curve for nitrogen, ’T_g_O’ is curve for oxygen, ’T_g_C’ is curve for carbon dioxide, ’T_g_A’ is curve for argon.

Figure S3.5
As per figure caption.

Figure S3.6
BSDs are stored in .mat files Figure_S3_6a.mat, Figure_S3_6b.mat, Figure_S3_6c.mat, Figure_S3_6d.mat for panels a, b, c and d respectively.  x values are a linear range from 10 to 1200 inclusive.
The BSDs in panels a, b, c and d need to scaled by factors of 377.98, 188.64, 38.04 and 19.01 respectively.

Figure S3.7
Data for solid line are contained in “Figure_S3_7_solid.mat”.  The solid line is created from the average of the 31st and 35th columns in the ‘met_data’ variable (ignoring values less than zero), and performing a running average of width 20 over the data.
Data for the dashed line are contained in “Figure_S3_7_dashed.mat”.  The plotted data, in the variable ‘asis2u’, are the values in the second column that correspond to values in the first column between 180 and 181 (Julian day).  The data are scaled by a factor of 1.07.

Figure S3.9
x		y
12		45
13		56.25
14		37.5
15		29.0
16		37.5
17		23.7
17.75	20.9

Figure S3.10
Data are contained in “Figure_S3_10.mat” and the variable ‘d2hs’.  The plotted data are the values in the second column corresponding to values in the first column between 180.5 and 181 (Julian day).

Figure S3.12
Data are contained in “Figure_S3_12.mat”.  x, y and z values are in the ‘x_space’, ‘y_space’ and ‘z’ variables respectively.  Bubble size is in the ‘a’ variable.  Bubbles smaller than 20 microns or larger than 300 microns are not plotted.  One in every 100 bubbles are shown in the plot.

Figure S3.13
Matlab code to reproduce this plot is contained within the subfolder “Large scale model”.  The script titled “main_large_scale_model.m” should be run.  The other .m files are called by the main file and must be in the same folder.  Images of each step of the model (500 in total) can be output by uncommenting the relevant section of code and updating the save path to a valid path (it is currently “/valid/path/to/save/files/”).

Figure S3.14
Radii are the values shown in Table S2.1 from 16 to 187 microns.
Measured BSDs are in the file Figure_S3_14_measured.mat.  Variables contained BSDs for 1.15 m and 2 m depth are BSDs_uncert_115m and BSDs_uncert_2m respectively.  Within each variable, the first row is the minimum BSD and the second row is the maximum BSD.
Minimum modelled BSDs are in the file Figure_S3_14_min_model.mat in variable BSDs_sc64.  Maximum modelled BSDs are in Figure_S3_14_max_model.mat in variable BSDs_sc144. In BSDs_sc64 and BSDs_sc144, the first row is for 1.15 m depth and the second row is for 2 m depth.  Bubble radii are in the ‘radii’ variables in the .mat files.  The modelled BSDs must be scaled by the ‘fact’ factor in each .mat file.

Figure S3.15
Measured BSDs are in the file “Figure_S3_15_measured.mat” in the variable ‘BSDs_mean’.  The first and second columns correspond to 1.15 m and 2 m depth respectively.  Bubble radii are in the ‘radii’ variable. 
The modelled BSDs are in files “Figure_S3_15_modelled_x_inc.mat” and “Figure_S3_15_modelled_x_dec.mat”, where x is ‘a’ to ‘f’ for panels ‘a’ to ‘f’ respectively, and ‘inc’ and ‘dec’ correspond to an increase or decrease in the varied parameter.  Note that ‘c’ and ‘d’ are both initial jet velocity, but at different depths, so they share the same files with ‘x’ being ‘cd’.  In each file, the BSDs are stored in a variable ‘BSDs’, with the first row of data corresponding to 1.15 m depth (used for all panels except ‘d’) and the second row corresponding to 2 m depth (only used in panel ‘d’).  x axis bubble radii are in the ‘radii’ variables.  The BSDs are multiplied by the ‘fact’ variable.