Modeling Radio Wave Propagation Over Irregular Terrain via the Split-Step Parabolic Equation Approach
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Bibliographic record
Abstract
Modeling electromagnetic wave propagation over complex terrain is essential for a wide range of applications, including wireless communications, radar systems, and remote sensing. This paper presents an advanced terrain-aware propagation model based on the split-step parabolic equation (SSPE) method, which offers high computational efficiency and accuracy for simulating wave behavior in such environments. This study enhances the classical SSPE formulation by incorporating high-resolution models and spatially varying refractive index profiles to capture the effects of terrain-induced diffraction and ducting. To mitigate numerical instability and ensure accuracy in steep terrain transitions, we implement terrain-following transformations and adaptive spatial discretization. Additionally, an impedance boundary condition is used to account for surface conductivity and permittivity variations, enabling realistic modeling over mixed land and sea paths. Comparisons with canonical solutions and benchmark scenarios are conducted to validate the numerical implementation. Sensitivity analyses are performed to examine the influence of terrain resolution, refractivity gradients, and ground parameters on propagation loss. The methodology also supports frequency scaling and can be extended to accommodate range dependent meteorological inputs. The developed SSPE-based terrain propagation model is intended for integration into broader electromagnetic environment simulators and is designed to operate efficiently for long-range, low-angle propagation scenarios at very high frequency through microwave frequencies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it