Cabo Verde LCS evolution¶

An extracted hyperbolic LCS (see cabo_verde_lcs) is a material curve: given its vertices at \(t_0\), the lon/lat that shrink_lines returns, its position at any other time is fixed by the flow map, \(\mathcal{M}(t) = F_{t_0}^{t}(\mathcal{M}(t_0))\) (Haller 2015, Eq. 5, doi:10.1146/annurev-fluid-010313-141322). The LCS is not re-diagnosed at each time: one curve, fixed at \(t_0\), is carried to each horizon.

The flow map \(F_{t_0}^{t}\) is the advected-position field a FlowMap stores, so the curve is evolved by interpolating that field at the curve’s vertices with FlowMap.image. The curve itself is never re-integrated.

Each family is evolved in its coherent direction, the one in which perturbations shrink. The attracting curve is therefore carried by the forward maps and the repelling curve by the backward maps. Each is evolved in the opposite direction to the one it was diagnosed on.

# Importing Parcels pulls in the holoviews/bokeh bootstrap and prints an
# alpha-version notice, neither of which belongs on the rendered page.
import matplotlib.pyplot as plt
import numpy as np
import xarray as xr
from parcels import FieldSet, Particle, ParticleSet, StatusCode
from parcels.convert import copernicusmarine_to_sgrid
from parcels.kernels import AdvectionRK4

from lcs_parcels import NeighborSeedGrid

Parcels v4 field set¶

copernicusmarine_to_sgrid tags the CMEMS A-grid with SGRID metadata; from_sgrid_conventions wraps it as a spherical FieldSet.

sgrid = copernicusmarine_to_sgrid(fields={"U": currents["uo"], "V": currents["vo"]})
fieldset = FieldSet.from_sgrid_conventions(sgrid, mesh="spherical")
z_surface = float(currents["depth"].values[0])

Recovery kernel¶

Particles that leave the domain or hit land are turned into NaN in place (Parcels would otherwise abort the run), so losses propagate as NaN through every diagnostic below. StatusCode.EndofLoop rather than StatusCode.Delete: deleting shrinks the particle array and breaks the alignment with the seed order.

def set_lost_to_nan(particles, fieldset):
    lost = particles.state >= StatusCode.Error
    particles.x = np.where(lost, np.nan, particles.x)
    particles.y = np.where(lost, np.nan, particles.y)
    particles.state = np.where(lost, StatusCode.EndofLoop, particles.state)

Snapshots¶

Each family of material lines day by day, with its own \(t_0\) position drawn faintly in every panel for reference. The axes are shared and left to autoscale, so a curve that leaves the release box stays visible.

fig, axes = plt.subplots(2, len(offset_days), figsize=(16, 6), sharex=True, sharey=True)
lcs_families = [
    (attracting_evo, "tab:blue", "attracting"),
    (repelling_evo, "tab:red", "repelling"),
]
for row, (evo, color, name) in zip(axes, lcs_families, strict=True):
    for k, ax in enumerate(row):
        ax.plot(
            evo["lon"].isel(offset=0).T,
            evo["lat"].isel(offset=0).T,
            color="0.7",
            lw=0.6,
        )
        ax.plot(
            evo["lon"].isel(offset=k).T,
            evo["lat"].isel(offset=k).T,
            color=color,
            lw=0.8,
        )
        ax.set_title(f"{name}, offset {evo['offset'].isel(offset=k).item():+.0f} d")

../_images/017398818379c97f037f73b728d8d51db86507797847e6fc1b2ff7efd7baf350.png

Cabo Verde LCS evolution¶

Currents¶

Parcels v4 field set¶

Seed grid and horizons¶

Recovery kernel¶

Advect to each horizon¶

Extract the LCS at the longest window¶

Evolve each family of material lines in its coherent direction¶

Snapshots¶

LCS-Parcels

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