Enhancing Long Wave Propagation Prediction Capability through the Integration of International Reference Models

The propagation characteristics of very low frequency (VLF, 3–30 kHz) and low frequency (LF, 30–300 kHz) electromagnetic waves in the Earth–ionosphere waveguide are critical to long-distance communication, navigation, and timing. To address limitations of traditional long-wave propagation models (LWPC), e.g., the static representation of ionospheric parameters, this study presents an optimized scheme incorporating international reference models. This approach improves the predictive accuracy of long-wave propagation models by integrating three international reference models. Specifically, the International Reference Ionosphere (IRI) model provides high-resolution ionospheric parameters. These are coupled with the NRLMSIS model to calculate neutral atmospheric densities, enabling accurate derivation of electron collision frequency. Additionally, updated geomagnetic parameters from the International Geomagnetic Reference Field (IGRF-13) model are incorporated. Validation using measured data from the VTX station across six propagation paths shows that the optimized model enables spatiotemporally continuous modeling of ionospheric electron density and collision frequency and eliminates non-physical parameter discontinuities in the original model during dawn–dusk transition periods, with the equivalent reflection height exhibiting physically consistent continuous dynamic evolution. During daytime, the correlation coefficient between predicted and measured field strengths improved from a range of －0.505 to 0.566 to a new range of 0.638 to 0.964, while the RMSE over the six paths decreased from 0.0779 to 0.0189, which indicates a significant improvement in predictive performance. This study presents a more reliable numerical framework for VLF/LF propagation prediction, thereby conferring substantial practical value for engineering applications.