How to estimate dispersion in stratified flows
There are lots of studies considering Lagrangian dispersion. One critical aspect is the addition of random displacement to the deterministic particle track in order to consider subgrid-scale processes. Your measure of dispersion seems acceptable except for the fact that it might be dependent on the resolution of your flow field. In order to compare your dispersion with other areas or times, you might need to scale it by the horizontal diffusivity of the flow. Some studies that could be helpful are Mariano et al. (2002), Proehl et al. (2005), Lynch &amp; Smith (2010).