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

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.

💡 Research Summary

This paper tackles two long‑standing challenges in low‑Earth‑orbit (LEO) satellite link analysis: (1) the limited fidelity of three‑dimensional atmospheric refractivity fields reconstructed from sparse radiosonde measurements, and (2) the numerical instability of existing non‑uniform plane‑wave (NPW) ray‑tracing algorithms when the atmospheric loss terms are extremely small. To address the first issue, the authors replace radiosonde‑based interpolation with a high‑resolution complex‑valued refractivity model derived from a regional numerical weather prediction (NWP) system (the Korea Integrated Model, KIM). Using the MPM93 formulation, temperature, pressure, humidity, cloud liquid/ice mixing ratios, and precipitation are converted into a complex refractivity Ñ = Ndry + Nwv + Ncloud + Nrain at 18 GHz. The resulting extinction coefficient κ ranges from 4.79 × 10⁻¹⁰ to 2.24 × 10⁻⁷, indicating a weakly lossy medium but still sufficient to generate NPW behavior. The KIM‑based field exhibits far finer horizontal gradients (≈11 km spacing) than the radiosonde‑based field, especially under heavy precipitation associated with Typhoon Kong‑re.

The second challenge concerns the NPW formulation of Chang et al., which suffers from severe subtractive cancellation when κ ≪ n, causing underflow in double‑precision arithmetic. The authors propose a reformulation that introduces auxiliary variables a = n₁² − κ₁², b = n₁κ₁, c = cos(θᵢ − ψᵢ) and r = ac/b, enabling stable evaluation of the apparent refractive indices N and K for both incident and transmitted waves. In the second medium, the NPW dispersion relations reduce to quartic equations in N² and K²; physically admissible roots are selected by enforcing the relation K = sign(N² − n² + κ²). All calculations remain within standard double precision, eliminating the need for long‑double arithmetic.

Validation proceeds in two parts. First, a single‑interface test varies κ₂ over three orders of magnitude while keeping n₁ = 1.0001, n₂ = 1.0002, and κ₁ = 10⁻⁸. The proposed algorithm accurately reproduces K₂ cos αₜ ≈ κ₂ even for κ₂ ≈ 10⁻⁹, whereas Chang’s method yields erroneous attenuation due to cancellation. Second, realistic LEO downlink simulations are performed over a 2‑Nov‑2024 typhoon scenario. Three ray‑tracing approaches are compared: (i) the conventional uniform‑plane‑wave (UPW) approximation, (ii) Chang’s method executed in long‑double precision, and (iii) the new stable NPW algorithm. All three produce virtually identical ray trajectories and cumulative path‑loss curves; boresight‑angle errors differ by less than 0.01°, confirming that, for the weakly lossy atmosphere considered, the UPW model captures the essential physics. The key observation is that the effective attenuation term K cos α closely matches the intrinsic loss κ, because variations in the attenuation direction compensate differences between K and κ.

Performance-wise, the stable NPW algorithm achieves a 24‑fold speedup relative to the high‑precision benchmark while retaining double‑precision stability. Consequently, the method is suitable for real‑time link budgeting, handover optimization, and large‑scale constellation simulations where computational efficiency is critical.

In summary, the paper demonstrates that (a) high‑resolution NWP‑based complex refractivity fields markedly improve atmospheric modeling over radiosonde interpolation, and (b) despite the theoretical existence of NPW effects, their impact on LEO link metrics (refraction angle, path loss, boresight error) is negligible under typical weak‑loss conditions. Therefore, practitioners can continue to rely on the simpler UPW ray‑tracing approach for most LEO link analyses, while the newly proposed fast and numerically stable NPW ray tracer offers a rigorous alternative for validation or for scenarios with unusually high atmospheric loss.