NWP-based Atmospheric Refractivity Modeling and Fast & Stable Non-uniform Plane Wave Ray-Tracing Simulations for LEO Link Analysis

TL;DR

This work addresses two main challenges in LEO link analysis: inaccuracies in 3D atmospheric refractivity from sparse data and numerical instability in non-uniform plane-wave ray tracing. It combines NWP-derived, complex-valued refractivity maps with a fast, numerically stable NPW ray-tracing algorithm that operates in standard double precision. The authors demonstrate that non-uniform plane-wave effects have negligible impact on boresight error and path loss compared to uniform-plane-wave models, even under heavy precipitation, while achieving substantial speedups over high-precision methods. The study supports the continued use of uniform-plane-wave ray tracing for practical LEO analyses and points to physics-informed super-resolution to further enhance refractivity fidelity.

Abstract

Existing low-Earth-orbit (LEO) communication link analyses face two main challenges: (1) limited accuracy of 3D atmospheric refractivity reconstructed from sparsely sampled radiosonde data, and (2) numerical instability in previous non-uniform plane-wave ray-tracing algorithms (i.e., underflow under standard double precision), where non-uniform plane waves inevitably arise at complex-valued dielectric interfaces, is caused by extremely small atmospheric loss terms. To address these issues, we reconstruct a high-resolution 3D complex-valued refractivity model using numerical weather prediction data, and develop a fast and numerically stable non-uniform plane-wave ray tracer. The method remains stable in double precision and delivers a 24-fold speedup over high-precision benchmarks. Comparisons show that boresight-error deviations and path-loss differences between the rigorous method and the uniform-plane-wave approximation remain negligible, even under heavy precipitation. Although rays in a lossy atmosphere experience different phase- and attenuation-direction vectors-forming non-uniform plane waves-the resulting effective attenuation along the path is nearly identical to that predicted by the uniform-plane-wave model. These findings justify the continued use of uniform-plane-wave ray tracing in practical LEO link analyses.

Figures (8)

• Figure 1: Refraction of (a) uniform and (b) non-uniform plane waves at a dielectric interface.
• Figure 2: Windy weather forecast windy on 2 November 2024, 00:00 KST: (a) precipitation and (b) cloud distribution.
• Figure 3: Real part of complex atmospheric refractivity at 5 km altitude over South Korea, reconstructed from (a) radiosonde stations (black circles) using IDW and (b) KIM data.
• Figure 4: (a) 3D $\kappa$ map from the KIM data and (b) boresight error for the two atmospheric refractivity models.
• Figure 5: Results using Chang’s method: (a), (c); and using the proposed method: (b), (d). NPW with $\alpha_{\mathrm{i}} = 10^{\circ}$ is incident and refracts into the second medium. Vertical dashed lines in (b) and (d) denote the fixed value $\kappa_{1}=10^{-8}$.