Low-frequency (LF) communication operates within a frequency band defined by the International Telecommunication Union (ITU), spanning from 30 kHz to 300 kHz, with wavelengths ranging from 1000 m to 10,000 m [
1]. Renowned for its extensive coverage; capability of spanning tens of thousands of kilometers; and remarkable penetration through various media like rocks, soil, and seawater, LF communication serves as a vital tool for command and control communication across vast land areas, including deep bunkers and tunnels. Additionally, LF propagation remains resilient against anthropogenic interference and nuclear detonation, making it important for communications under extreme environmental conditions. To establish and ensure the reliability of LF communication systems, in-depth studies on low-frequency propagation characteristics have always been a theme of the past, present, and future.
In 1925, Appleton proposed the magneto-ionic theory [
2], laying the theoretical foundation for the propagation of radio waves in the ionosphere. Subsequently, Booker extended this theory [
3], and Bracewell discovered the relationship between ionospheric variations and solar angles [
4]. The Cavendish Laboratory conducted significant research on LF propagation. Finally, Budden systematically summarized these findings in his book
Radio Waves in the Ionosphere, contributing to the continuous improvement and maturation of LF propagation theory [
5]. Based on the work of these pioneers, Wang combined the latest database to analyze in detail four LF skywave propagation prediction methods, comparing them with the measured field strength, and discussed the factors affecting skywave propagation in 1999 [
6]. In 2000, Warrington and Jones used the summertime ionospheric model to predict the LF skywave field strength and compared it with the measured field strength to determine the validity of the model [
7]. In 2002, Liu et al. calculated and compared the geometric parameters of LF skywave propagation based on the distribution models of different atmospheric refractive indices [
8]. In 2004, Wakai used the wave-hop method to predict the field strength of skywaves, ground waves, and synthetic waves within 60 kHz to 500 kHz within 4000 km and then compared it with the measured field strength to verify the effectiveness of the method [
9]. In 2006, Wakai used the same method to predict the skywave field strength of 40 kHz and 60 kHz in Japan and compared it with the measured field strength [
10]. In 2008, Wang qualitatively and quantitatively discussed the seasonal variation in LF skywave field strength based on a huge LF skywave database [
11]. In 2010, Shigeru and Kurihara proposed the development of a receiver system with higher sensitivity and resolution to reduce interference due to the existence of high-order ionospheric reflection mode in LF propagation and multiple noises in long-distance propagation [
12]. In 2012, Feng and his team proposed a formula for calculating the reflection coefficient of vertically polarized waves under isotropic conduction conditions based on the oblique reflection propagated by low ionospheric LF propagation, which was well verified [
13]. In 2017, Pal et al. qualitatively explained LF propagation anomalies by studying the effect of sudden stratospheric warming events in 2009 on LF signals in the Earth–Ionosphere Waveguide (EIWG) [
14]. In the same year, Zhou et al. combined the Finite-Difference Time-Domain (FDTD) method with the Parabolic Equation (PE) method to analyze the propagation characteristics of LF radio waves at short propagation distances with high propagation angles [
15]. In 2019, Melchinov predicted relatively accurately the seasonal variation in LF radio waves on the radio propagation path of frozen soil [
16]. In 2020, based on the wave-hop theory and FDTD method, Zhou et al. studied the time-delay characteristics of a one-hop skywave in an EIWG within 200 km under different ionospheric conditions and different calculation methods [
17]. In 2021, Gasdia and Marshall developed software (released as the LongwaveMode Propagator.jl) similar to the Long Wave Propagation Code (LWPC) but more stable in mode selection than LWPC [
18]. In 2022, Mu et al. verified the effects of multiple multi-path delay estimation algorithms in different channel environments and obtained the delay characteristics of LF multi-hop skywaves [
19]. In the same year, Zhao et al. combined the atmospheric model with the International Reference Ionosphere (IRI) model and then used the improved FDTD method to analyze the characteristics of LF skywave signals [
20]. In 2023, Gao et al. proposed an LF propagation prediction model that considered the geomagnetic effect based on the wave-hop method, which was used to predict the one-hop skywave field strength under different conditions [
21].
To address the demands of engineering applications while balancing computational complexity and efficiency and to refine the prediction methods for 40 kHz LF skywave propagation, this study adopts the ITU-R P.684 method (identified as ITU in the following text) as a foundation. Utilizing the Kriging method, we reconstruct real-time data from four ionospheric parameter observation stations and further enhance the electrical characteristic parameters using a global 16-level classification of surface properties. With these inputs, we predict the field strength of 40 kHz signals across a 2000 km range. Subsequently, we conduct spatiotemporal and comprehensive analyses, comparing different methodologies.