Numerical studies of connectivity and Lagrangian transport in the world’s oceans

Particles transport can be used to study flow fields on different scales in geophysics. Tracer and inertial particle transport can highlight the connectivity between different locations in the ocean or describe changes in flow fields based on the visualization of the flow by tracers. Of particular interest are long-range transport properties to either identify changes in flow paths due to climate change or to study the transport of seeds over long distances to identify sources of plants in different parts of the world. Such studies require particle tracking algorithms which are capable to work properly on a global scale of the Earth, i.e. on a spherical geometry. 

We have created a sophisticated software tool that simulates the movement of large numbers of tracer and inertial particles within interpolated oceanic velocity fields, in our examples based on the publicly available HYCOM data. Built in C++ and parallelized with Intel Threading Building Blocks (Intel TBB), it achieves high performance when dealing with substantial computational loads. To accelerate nearest-neighbor searches, we organize the grid points into a kd-tree, making it quick to locate grid points near any particle. We then interpolate the eastward and northward velocity components using a Gaussian-shaped weight function — an effective choice that avoids the singularities sometimes encountered in inverse distance interpolation. Since planar projections can introduce significant distortions on a global scale, we also account for Earth’s spherical geometry. Specifically, we solve two-dimensional tracer equations and the Maxey–Riley equation for inertial particles on a local tangent plane. Afterward, we revert the computed particle positions to latitude-longitude coordinates via an azimuthal equidistant projection, mitigating large-scale errors in simulations that may span thousands of kilometers.

The software is capable of simulating the dispersal of seeds and algae by ocean currents, easily managing hundreds of thousands of particles under varied initial conditions. It reconstructs connectivity maps between distant coasts, identifies transport barriers through finite-time Lyapunov exponent calculations, and can compute derivatives of the velocity field — such as divergence, vorticity, and the Okubo–Weiss parameter — broadening its range of oceanographic applications.

We highlight the software’s capabilities with two representative examples. First, we track the origins of particles (such as plant seeds) and explore their possible routes to Hawaii. Second, we assess the likelihood that harmful algal blooms could drift into the Baffin Bay during the warmest parts of the summer.