5 Characterisation of the dynamics at stake

It is of interest to better understand the geophysical at stakes in the different velocity products to characterise the dynamics that are represented in each field. Few analyses are proposed as diagnostics to help the characterisation of the current products

5.1 Regional mesoscale surface dynamics characterisation (applied to SST / current)

Surface dynamics characterisation have been applied to \subsubsection{Spatial Anisotropy} Spatial anistropy provides useful informaation on the scale and the pattern present in a given region. As the diagnostics can run on images, it enables to compare statistically the patterns from the velocity product with the one derived from SST observation that will be regarded as the truth.

To do so, the directional variogram of the SST will be compared with the one from the velocity product. The directional variogram equation is given by:

\[\gamma(h, \theta) = \frac{1}{2N(h, \theta)} \sum_{i=1}^{N(h, \theta)} \left[ z(\mathbf{x}_i) - z(\mathbf{x}_i + h\mathbf{e}_\theta) \right]^2 \]

where:

\[\begin{split} \begin{align*} \gamma(h, \theta)&: \text{Variogram value at lag distance } h \text{ in direction } \theta \\ N(h, \theta)&: \text{Number of data pairs separated by distance } h \text{ in direction } \theta \\ z(\mathbf{x}_i)&: \text{Value of the variable at location } \mathbf{x}_i \\ z(\mathbf{x}_i + h\mathbf{e}_\theta)&: \text{Value of the variable at a location } h \text{ units away from } \mathbf{x}_i \text{ in direction } \theta \\ \end{align*} \end{split}\]

An ellipsoid is fit to the variogram and enables to quantitatively compute maps of scales of the most energetic processes in different directions.

5.2 Spatial / temporal variance

A simple spatial or temporal variance analysis can also give insight of the variability of the velocity field in space or time. The temporal and spatial scale at stakes can be intercompared with results from other velocity products or SST observations.

5.3 Low frequency signal

Performing long-term advection on a basin scale will reveal the low frequency signal. The most commonly used diagnostics is looking at the area of aggregation of particles that have been launched homogeneously on a whole basin. These areas of aggregation areas and the time it took for particles to aggregate can be compared with what have been observed in the Atlantic or Pacific ocean using plastic debris as tracers.