Glider Path Design and Control for Reconstructing Three-Dimensional Structures of Oceanic Mesoscale Eddies

TL;DR

This work advances reconstructing the three-dimensional hydrographic fields of oceanic mesoscale eddies using underwater gliders by (i) adopting Thin Plate Spline interpolation with a three-dimensional blocking scheme to enable fast, accurate 3D reconstructions; (ii) introducing a data-driven glider path design framework to select formation patterns that minimize RMSE across candidate paths; and (iii) developing an adaptive, two-dimensional path-control method that balances fidelity to the designed pathway with progress toward a destination under ocean currents. Key contributions include a TPS-based interpolation with a 3D blocking strategy that reduces computational complexity to $O(B^{-2} n^3)$, a training-data–driven path-design approach identifying center and parallel formations as effective, and a DE-based path-control framework that robustly guides gliders along designated trajectories even in strong currents. The experiments, using CESM and GLORYS-derived eddy fields, demonstrate improved RMSEs over IDW and Kriging, validate path-design choices, and show that the control framework maintains mission progress, making real-time, high-resolution 3D eddy reconstructions more feasible for oceanography and climate studies.

Abstract

Underwater gliders offer effective means in oceanic surveys with a major task in reconstructing the three-dimensional hydrographic field of a mesoscale eddy. This paper considers three key issues in the hydrographic reconstruction of mesoscale eddies with the sampled data from the underwater gliders. It first proposes using the Thin Plate Spline (TPS) as the interpolation method for the reconstruction with a blocking scheme to speed up the computation. It then formulates a procedure for selecting glider path design that minimizes the reconstruction errors among a set of pathway formations. Finally we provide a glider path control procedure to guide the glider to follow to designed pathways as much as possible in the presence of ocean current. A set of optimization algorithms are experimented and several with robust glider control performance on a simulated eddy are identified.

Figures (8)

• Figure 1: Three dimensional structure of the temperature ($^\circ \text{C}$) and salinity (g/kg) fields of a simulated mesoscale eddy, where the three axes represent longitude, latitude and depth, respectively.
• Figure 2: Two dimensional demonstration of the blocking scheme. For $R_{11}$, the green parts are the overlaps of two regions and the red part is the overlap of four regions. $d_{11}\left( \mathbf{x}_1 \right) = | x_{1,1}-E_{\text{long,}1}^{U} | | x_{1,2}-E_{\text{lat,}1}^{U} |$, $d_{11}\left( \mathbf{x}_2 \right) = | x_{2,1}-E_{\text{long,}1}^{L} | | x_{2,2}-E_{\text{lat,}1}^{U} |$ and $d_{12}\left( \mathbf{x}_2 \right) = d_{22}\left( \mathbf{x}_2 \right) = 0$.
• Figure 3: (a) The projection of the underwater gliders' trajectory on the sea level (4 different path designs) and (b) its diving and climbing motions on the vertical section.
• Figure 4: Flowchart of glider path control, where the optimization problem solves the adaptive objective function \ref{['eq:weighted average']}.
• Figure 5: Vertical reconstruction RMSES with respect to the depth for temperature ($^\circ \text{C}$, left panels) and salinity (g/kg, right panels) fields with different path designs (a) and different number of gliders (b).