A Subspace Pursuit Method to Infer Refractivity in the Marine Atmospheric Boundary Layer

Abstract

Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well modeled by a partial differential equation (PDE): a Helmholtz equation. A natural way to solve the MABL characterization inverse problem is to minimize what is observed and what is predicted by the PDE. However, this optimization is difficult because it has many local minima. We propose an alternative solution that relies on the properties of the PDE but does not involve solving the full forward model. Ducted environments result in an EM field which can be decomposed into a few propagating, trapped modes. These modes are a subset of the solutions to a Sturm-Liouville eigenvalue problem. We design a new objective function that measures the distance from the observations to a subspace spanned by these eigenvectors. The resulting optimization problem is much easier than the one that arises in the standard approach, and we show how to solve the associated nonlinear eigenvalue problem efficiently, leading to a real-time method.

Gaussian Process Regression for Estimating EM Ducting Within the Marine Atmospheric Boundary Layer

“…We use an adaptation of PETOOL, an SSPE solver developed by Ozgun et al (2011), that specifies a Leontovich surface impedance condition at the lower boundary (Gilles et al, 2019). The continuity of the tangential components of the electric and magnetic fields in this boundary condition is satisfied by assuming that the ocean free surface at z = 0 m is a flat, finite conductor with a homogeneous dielectric constant.…”

Characterizing Evaporation Ducts Within the Marine Atmospheric Boundary Layer Using Artificial Neural Networks

“…To enforce continuity of the tangential components of the electric and magnetic fields at this boundary, the ocean surface is assumed to be a finite conductor with a homogeneous dielectric constant that can be calculated by using the semi‐empirical Debye expression (Ryan, ): where the far‐infrared dielectric constant of water, ϵ ir , is 4.9, and the relaxation time, τ , ionic conductivity, σ , and static dielectric constant of sea water, ϵ 0 , are obtained using thermodynamic data consist with the South China Sea ‐ 100% humidity at ocean surface, surface temperature of 29.7 ° C , and ocean salinity of 35 ppt. We use code adapted from PETOOL that specifies this Leontovich surface impedance condition at the lower boundary (Gilles et al, ).…”

A hybrid numerical model for long-range electromagnetic wave propagation

“…This recursive process continues until the field exits the computational domain or a certain threshold is reached. The 2W-SSPE method was implemented in an open-source software, called PETOOL [15,16], which was then used in various studies [17][18][19][20]. Although terrain modeling with a staircase approximation provides reliable results in most situations, the accuracy of the 2W-SSPE method might degrade if there are curved/slanted surfaces over the terrain profile.…”