Fig 1.
Schematic of the set-up and instrumentation used in the experiments (not to scale).
The aquarium (0.5 × 0.5 × 0.5 m) was located ~20 m below the rain generator. Particle image velocimetry (PIV) was used to characterize the turbulent flow field in the water. For this, microscopic seeding particles were illuminated from the side using a laser light sheet and observed with a camera through the front window. The field of view of the PIV camera (21 × 12.5 cm on average) is shown as a grey rectangle, the region of interest (ROI) of the PIV measurements (21 × 8 cm on average) is marked by the red dashed line and the size of the interrogation areas is exemplified by blue (pass 1) and purple (pass 2) dashed lines. Four sensors for dissolved oxygen (O2 probes) were used to establish an oxygen mass balance in the aquarium to estimate the gas transfer velocity. A pressure sensor located at the bottom of the aquarium was used to estimate the rain rate from the temporal increase in water level. Atmospheric pressure (Patm) was recorded by the oxygen and temperature data logger.
Table 1.
Summary of experimental results.
Fig 2.
Gas transfer velocity versus rain rate (R) with linear regressions (solid lines) and the resulting equations shown as legends.
a) Gas transfer velocity for oxygen at in situ temperature (kO2), b) Normalized gas transfer velocity (k600) and comparison to previous studies [10, 22, 23]. The data from [10] were fitted with a linear regression to obtain the expression k600 = 0.42R + 13.3 (r2 = 0.97).
Fig 3.
Details of the dissipation rate modeling process.
a) Power-law relationship between the coefficient a (Eq (9)) and the rain rate (R) (solid line). b) Modeled versus measured dissipation rates for all evaluated rain rates (R) (symbols) and at all evaluated sampling depths (colorbar). The dashed line shows a 1:1 relationship.
Fig 4.
Normalized gas transfer velocities k600 versus surface renewal model (Eq (11) for energy dissipation rates sampled at z = 7.5 cm depth.
At this depth, we estimated the value of the coefficient A as 2.31, Sc is the Schmidt number (here equal to 600). The dashed line shows a 1:1 relationship.
Fig 5.
Measured (k600) versus predicted (k600_mod) gas transfer velocities (symbols) and a 1:1 plot (dashed line).
The slope of a linear regression (grey line) was 1.6 ± 0.18 (r2 = 0.85, n = 13, p < 0.0001). Error bars represent the uncertainty of a factor of 2 in the measured dissipation rates.
Fig 6.
Observed gas transfer velocity (k600) versus kinetic energy flux of rain (FKE).
The solid line shows a second-order polynomial fit according to the equation provided in the legend. Results from [22, 23]. The data from were taken from [22] and fitted to a polynomial curve to get the expression k600 = -30.6 FKE2 + 91.7 FKE + 3.47 (r² = 0.99) (S10 Fig). The data from [23] were taken from [10] and the polynomial curve was fitted to get the expression k600 = -26.9 FKE2 + 84.7 FKE +5.91 (S11 Fig).
Fig 7.
Comparison of dissipation rate profiles estimated by different methods in the present study, and estimated in other studies for similar rain rates: PIV-based dissipation rates (Eq 8) for R = 39 mm h-1 (blue circles) and in the absence of rain (blue crosses); the single-point dissipation obtained from the ADV data (red triangle); profiles of the first 10 cm obtained by [11]at 40 mm h-1 (grey triangles) and data from [10] measured at 43 mm h-1 (grey squares).