An analytical assessment of greenhouse gas impacts on HF propagation using the Appleton-Beynon approach

Abstract

In 1940, Edward V. Appleton and William J. G. Beynon derived an analytical formulation for the ground range of a high-frequency (HF) radio wave propagating through a simplified ionosphere represented by a single parabolic layer. This formulation allows direct estimation of two key radio propagation parameters: the skip distance and the maximum usable frequency (MUF). Using this approach, we quantify the expected long-term impact of increasing greenhouse gas concentrations, specifically CO2, on these parameters for propagation through the F2 layer. Future CO2 abundances are taken from three SSP scenarios (SSP2-4.5, SSP3-7.0, SSP5-8.5) projected for the year 2100, and F2-layer long-term changes are derived using trends from WACCM-X simulations. Our resultsshow that the combined expected decrease in hmF2 and foF2 leads to an increase in skip distance and a decrease in MUF. The skip distance can increase up to ~600 km for high signal frequencies under the solar activity leveland season considered in this study, while the MUF would decrease up to 4 MHz due to the dominant effect of foF2 reduction over that of hmF2 lowering. These effects are similarly obtained for day and night conditions. A comparison with PHaRLAP ray tracing indicates that, despite the simplifications made, skip distance errors remain low for present conditions, suggesting that Appleton´s formulation provides a good first approximation of future changes. The results highlight how simplified analytical models can offer valuable insight for modern problems in ionospheric climate change and HF propagation forecasting.