244
K. Döös et al.
7.6.3 Subgrid Parameterization Questions
Döös et al. (2011) compared the relative dispersion of 5854 pairs of surface drifters
with that of simulated TRACMASS trajectories. The coefficients were tuned in order to match the magnitude of the relative dispersion of the surface drifters after
32 days. The ‘diffusion’ parameterization, which adds a stochastic term to the trajectory in accordance with Eq. (7.38), attains realistic relative dispersion rates for
A H = 2500 m 2 /s. By calibrating the amplitude of the extra horizontal turbulent
velocities u , v (cf. Appendix B of Döös et al. 2011), also the turbulence parameterization reaches realistic values. The absolute dispersion is not much affected
when the diffusion parameterization is added, but gives far too high values for the
‘turbulence’ subgrid parameterization. The modelled trajectories with added diffusion/turbulence also manifest values of the residual velocities which are similar to
real data, but with decidedly smaller values of the Lagrangian correlation time. In
other words, realistic particle separation rates are obtained using a large diffusivity
value, but at the cost of totally changing correlation properties and energy partitioning in the frequency domain.
A more realistic representation of the unresolved scales would require a higher
order subgrid parameterization. Griffa (1996) showed that a random walk does
not describe the turbulent dispersion behaviour of ocean tracers and that a better
quantitative agreement can be reached using an Ornstein–Uhlenbeck process. This
work has been refined by Pasquero et al. (2001) who observed that the Ornstein–
Uhlenbeck model assumes Gaussian velocity distributions, while the ocean displays
exponential-like tails associated with the mesoscale dynamics (Bracco et al. 2000a).
Those tails are common to 2D turbulent flows (Bracco et al. 2000b) and to Lagrangian trajectories in an oceanic eddy-resolving model (Bracco et al. 2003). Based
on these similarities Pasquero et al. (2001) built a family of two-process stochastic
models that provided a better parameterization of turbulent dispersion in rotating
barotropic flows.
Berloff and McWilliams (2002) and Berloff et al. (2002) also explored in detail
the issue of (horizontal) stochastic parameterizations for oceanic flows, suggesting
an alternative model to the one of Pasquero et al. (2001). It is therefore to be expected that the zeroth-order Markov process used in the present study will not provide a good representation of the surface drifters. The relative dispersion rates can
hence only be tuned to match the total value at a particular moment. The shape of
the power spectrum of the modelled velocity without parameterizations is therefore
more realistic in its shape even if too weak.
7.7 Mass Transport and Lagrangian Stream Functions
The mass conservation of the TRACMASS schemes makes it possible to calculate
mass transports between different sections in the model domain. A particular water
or air mass can be isolated and followed as a set of trajectories between specific
K. Döös et al.
7.6.3 Subgrid Parameterization Questions
Döös et al. (2011) compared the relative dispersion of 5854 pairs of surface drifters
with that of simulated TRACMASS trajectories. The coefficients were tuned in order to match the magnitude of the relative dispersion of the surface drifters after
32 days. The ‘diffusion’ parameterization, which adds a stochastic term to the trajectory in accordance with Eq. (7.38), attains realistic relative dispersion rates for
A H = 2500 m 2 /s. By calibrating the amplitude of the extra horizontal turbulent
velocities u , v (cf. Appendix B of Döös et al. 2011), also the turbulence parameterization reaches realistic values. The absolute dispersion is not much affected
when the diffusion parameterization is added, but gives far too high values for the
‘turbulence’ subgrid parameterization. The modelled trajectories with added diffusion/turbulence also manifest values of the residual velocities which are similar to
real data, but with decidedly smaller values of the Lagrangian correlation time. In
other words, realistic particle separation rates are obtained using a large diffusivity
value, but at the cost of totally changing correlation properties and energy partitioning in the frequency domain.
A more realistic representation of the unresolved scales would require a higher
order subgrid parameterization. Griffa (1996) showed that a random walk does
not describe the turbulent dispersion behaviour of ocean tracers and that a better
quantitative agreement can be reached using an Ornstein–Uhlenbeck process. This
work has been refined by Pasquero et al. (2001) who observed that the Ornstein–
Uhlenbeck model assumes Gaussian velocity distributions, while the ocean displays
exponential-like tails associated with the mesoscale dynamics (Bracco et al. 2000a).
Those tails are common to 2D turbulent flows (Bracco et al. 2000b) and to Lagrangian trajectories in an oceanic eddy-resolving model (Bracco et al. 2003). Based
on these similarities Pasquero et al. (2001) built a family of two-process stochastic
models that provided a better parameterization of turbulent dispersion in rotating
barotropic flows.
Berloff and McWilliams (2002) and Berloff et al. (2002) also explored in detail
the issue of (horizontal) stochastic parameterizations for oceanic flows, suggesting
an alternative model to the one of Pasquero et al. (2001). It is therefore to be expected that the zeroth-order Markov process used in the present study will not provide a good representation of the surface drifters. The relative dispersion rates can
hence only be tuned to match the total value at a particular moment. The shape of
the power spectrum of the modelled velocity without parameterizations is therefore
more realistic in its shape even if too weak.
7.7 Mass Transport and Lagrangian Stream Functions
The mass conservation of the TRACMASS schemes makes it possible to calculate
mass transports between different sections in the model domain. A particular water
or air mass can be isolated and followed as a set of trajectories between specific