Find eddies as objects, not just as a field

flow_deformation() returns the Okubo-Weiss parameter as a number per cell. This takes the next step: it groups the connected cells where rotation beats strain into individual eddies, and describes each one. A cell then carries not "how eddy-like is the flow here" but "you are inside an eddy, it turns this way, and it is this big".

Usage

detect_eddies(
  env_dat,
  u = "UO",
  v = "VO",
  threshold = 0.2,
  min_cells = 4L,
  measures = c("in_eddy", "polarity", "radius"),
  per = c("km", "m"),
  suffix = ""
)

Arguments

env_dat: an sf POINT object with one row per location and time step, as datamatch's access functions return
u: name of the eastward velocity column, in m/s
v: name of the northward velocity column, in m/s
threshold: multiple of the standard deviation of Okubo-Weiss below which a cell counts as rotational. Positive; 0.2 follows the literature
min_cells: smallest connected region kept, in cells
measures: any of "in_eddy", "polarity" and "radius"
per: distance unit for the radius, "km" or "m"
suffix: appended to each measure to name its column

Value

env_dat with one column per requested measure. in_eddy is 1, 0 or NA; polarity and radius are NA outside an eddy

Details

That distinction matters ecologically, because the two polarities do opposite things. A cyclonic eddy upwells at its core, lifting nutrients and often concentrating plankton; an anticyclonic one downwells, and its core is typically poorer. A covariate that only says "eddy" averages the two together and can easily find nothing.

How eddies are identified

The Okubo-Weiss criterion of Isern-Fontanet et al. (2003): a cell belongs to an eddy where \(W < -\alpha\sigma_W\), with \(\sigma_W\) the standard deviation of \(W\) over that time step and \(\alpha\) the threshold argument. The published value is 0.2, which is the default. It is a relative threshold, recomputed per step, so a quiet month still yields eddies — the criterion asks which parts of this flow are most rotational, not whether the flow is energetic in absolute terms.

Connected regions are then labelled, and those smaller than min_cells are discarded as noise. On a 1/12-degree product an eddy of oceanographic interest spans many cells; a two-cell patch is more likely to be a numerical artefact of the differencing than a feature.

What each measure is

in_eddy is 1 inside an identified eddy and 0 outside.
polarity is +1 for cyclonic rotation and -1 for anticyclonic, from the sign of the eddy's mean vorticity. In the northern hemisphere cyclonic is counter-clockwise and upwelling at the core.
radius is the equivalent radius of the eddy, \(\sqrt{A/\pi}\) for its area \(A\), in per units. Real eddies are not discs, so this is a size, not a shape. See below for what it does and does not measure.

Cells outside any eddy get 0 for in_eddy and NA for the others, because they have no eddy to describe. Cells where there was nothing to judge get NA for all three: the outermost ring, where the central difference has no neighbours, and anywhere the velocity itself is missing, which over a masked product is land. Those are not the same as being outside an eddy, and in_eddy does not report them as 0 – a fabricated zero over land is indistinguishable from a measured one, and would be used as though it were.

Radius measures the patch, not the eddy

The threshold is a multiple of \(\sigma_W\) for the whole time step, so it is one absolute level applied to every eddy in the field at once. A strong eddy has \(|W|\) far below that level over nearly its whole core and loses almost nothing to it; a weak one only dips below it near its centre, and the patch that survives is a fraction of the feature. Two eddies of the same physical size can therefore report very different radii if one is spinning faster than the other.

On a field of Gaussian vortices with cores of 25 to 60 km, raising threshold from 0.05 to 1.5 moves the reported radius of the strongest eddy by 3 percent and that of the weakest by more than half. radius is comparable between eddies of similar strength, and between time steps only where \(\sigma_W\) is stable. Where the question is size as such, treat it as an index rather than a measurement, and hold threshold fixed across everything being compared.

What this is not

Detection per time step, with no identity between steps. Nothing here tracks an eddy through its life, so there is no age, no lifespan and no propagation speed, and the same physical eddy carries unrelated labels in consecutive steps. eddy_id is therefore deliberately not returned: it would invite exactly that mistake.

The Okubo-Weiss criterion is also known to be permissive in strongly strained flow and sensitive to the smoothness of the velocity field. It finds rotation-dominated regions, which is a good working definition of an eddy and not the same thing as a closed-contour eddy from altimetry.

References

Isern-Fontanet J, Garcia-Ladona E, Font J (2003). Identification of marine eddies from altimetric maps. Journal of Atmospheric and Oceanic Technology 20(5), 772-778. doi:10.1175/1520-0426(2003)20<772:IOMEFA>2.0.CO;2

Examples

if (FALSE) { # \dontrun{
env <- detect_eddies(env)

# Cyclonic cores upwell, so they are the ones worth separating out.
upwelling <- env$in_eddy == 1 & env$polarity > 0
} # }