#### 4.2. Comparison With Numerical Models

[13] We performed two numerical simulations of the 5-L release, one by a single CO_{2} droplet simulation incorporating dissolution rates and buoyancy forces calibrated by laboratory and field studies to determine the initial sizes of droplets, and another by a turbulent two-phase cloud model [*Chen et al.*, 2003] to predict droplet cloud dynamics.

[14] The early single droplet observations [*Brewer et al.*, 2002] were described by a very simple spherical buoyancy equation applicable for a drag coefficient of 1:

Where u is the terminal rise velocity, g is gravity, r is the droplet radius, and *ρ*_{sw} and *ρ*_{CO2} are the changing in situ densities of seawater and liquid CO_{2} respectively. This approach was criticized [*Zhang*, 2005], but strongly supported in a rebuttal by *Alendal et al.* [2006]. The droplet sub-model used here for the slip velocity (u) and diameter-shrinking rate () is of the form:

Where *m*, *ρ*, and *C* are the mass of the droplet, the density, and the CO_{2} concentration respectively. The subscripts *c*, *cs*, and *s* indicate CO_{2}, CO_{2} droplet surface, and seawater respectively. *Sh*_{e} and *C*_{d} are the effective Sherwood number and effective drag coefficient respectively. The dotted symbols are derivatives with respect to time. The last two parameters play a key role in the prediction of droplet dissolution and rising velocity. Here the experimental data based values of *Sh*_{e} and *C*_{d} given by *Chen et al.* [2003] are used in the simulations.

[15] Field and laboratory observations, and model predictions, show that the droplets formed rapidly after free liquid release range from 8 to 10 mm diameter. Over the observed CO_{2} cloud ascent from the release depth of 1,000 m to 850 m (4.8°C) we calculate from the droplet sub-model that a droplet with an initial diameter of 10 mm will decrease in size to 4.7 mm, and the rise velocity will decrease from 0.11 m/s to 0.08 m/s. A droplet with an initial 8 mm diameter will decrease to 1 mm, and the velocity decrease is from 0.10 m/s to 0.02 m/s.

[16] We use droplet number density (number/m^{3}) to visualize the CO_{2} cloud dynamics from the two-phase modeling simulations. With initial diameters of 8–10 mm set randomly droplets disperse horizontally due to local water velocities, while rising vertically (Figure 3b). Our simulations of vertical sections are well matched to the sonar images for up to 15 minutes from release not only for the height of the CO_{2} cloud but also for cloud width. The simulated cloud rises slowly with a slightly lower velocity in comparison with that detected by sonar at 25 minutes. This may be due to a downward flow predicted in the model by locally dense CO_{2} enriched sea water [*Chen et al.*, 2005]. Because of a relatively smaller computation domain in the horizontal (20 m × 20 m) than the vertical (200 m), the open boundary conditions at top and bottom make the modeled flow field sensitive to the small negative buoyancy effect. This predicted downward flow developed to a detectable level in comparison with the droplet rise velocities after about 20 minutes, when CO_{2} dissolution caused the small droplets to rise with lower velocity. In the real ocean no significant down-welling was observed, since the small size of the release produced negligible local density increases. We note that in earlier published work [*Brewer et al.*, 2002] a small programming error in the simple model used lead to a slight exaggeration of rise rate for small droplets late in the plume development.

[17] For modeled horizontal sections simulations agreed well with the ROV sonar record with modeled and observed scales of 12 × 12 m^{2} in cloud/droplet areas. The cloud dilutions detected by the ROV sonar correspond to simulations with maximum droplet number densities of 620, 160, and 80 at each sampled time (5, 15, and 25 minutes) respectively.