The electric field strength analysis of Czech Republic (CZE) (270 kHz) and Monte Carlo (MCO) (216 kHz) broadcast signals, collected with a 10 min sampling frequency by a receiver located in central Italy from 1996 to 2004, is presented. The distance from transmitter to receiver ranges from 515 km (MCO) to 818 km (CZE). The daytime data and the nighttime data were extracted and then in the daytime data the data collected in winter (21 December to 21 March) were separated from the data collected in summer (21 June to 21 September). Under the hypothesis that the simple addition of the ground wave and sky wave contributions holds, at first, the analysis was focused on the comparison between the experimental and theoretical values of these waves. The theoretical values were calculated by the ground wave (GRWAVE) algorithm and the wave hop theory, respectively. Ratios between the experimental and theoretical values ranging from a few tenths of decibels to some decibels were obtained. Then the analysis of the sunspots' influence on the sky wave propagation mode was performed, and the electric field strength of the two radio signals reveals a reduction of some decibels in sunspot maximum years with respect to the values during the sunspot minimum years. In addition, an influence of the sunspots also was recognized for the ground wave propagation mode.
 Recently, several disturbances in VLF/LF radio signals connected with seismicity have been presented [Bella et al., 1998; Biagi et al., 2001a, 2001b, 2004; Biagi and Hayakawa, 2002; Hayakawa and Sato, 1994; Hayakawa et al., 1996, 2002; Molchanov and Hayakawa, 1998]. These results have been obtained by studying the electric field strength and/or the phase of radio signals collected for long periods, with a sampling period of some seconds or minutes. The data collected, regardless of the connection with seismicity, can give a contribution to the study of the VLF/LF radio wave propagation. In addition, a detailed comprehension of the radio data recorded is very helpful to better reveal possible seismic effects on the radio signals.
 Here we present an analysis of the electric field strength (amplitude) of two LF (216 and 270 kHz) radio signals collected in Italy from 1996 to 2004 at distances of 500–800 km from the transmitters. The radio data were sampled in order to investigate possible seismic effects.
2. Receiver and Radio Stations
 In 1995, some of the authors of the present paper designed and built a receiver able to measure the amplitude of LF radio signals at field sites where the noise is very low. It was decided to sample radio signals used for broadcasting and to collect the data in central Italy. A place that is the mouth of a natural cave (Amare cave) located in the central Apennines on the southern slope of the Gran Sasso chain was chosen. On the basis of the best reception, the LF broadcasting stations Monte Carlo (MCO) and Czech Republic (CZE) were selected. Their location, radiated power, and frequency are indicated in Table 1.
Table 1. Key Parameters of the Broadcasting Stations
Radiated Power, kW
 The monitoring equipment is composed of a 1-m-long vertical antenna and a data recording system consisting of (1) analogue units with an amplifier module with a five-step selectable amplification, a frequency filter with an uncertainty of 1%, and an analog-to-digital (A/D) converter and (2) a digital unit with a divider, a decade scaler, and an exponent counter. The A/D converter and the digital unit are detailed by Bella et al. . A 12-V battery connected to solar cells supplies the power. The analog voltage output is sampled every 10 min, and its digital value is stored in solid-state memory. The conversion factor from the voltage measured by the receiver to the amplitude at the receiving antenna was estimated in several laboratory tests, and it makes the instrumental zero equal to 0.20 mV/m.
 At the beginning of 1996, the receiver was put into operation in the previous site, named AS, and located 515 km away from the MCO (216 kHz) broadcasting station and 818 km away from the CZE (270 kHz) broadcasting station. Figure 1 shows the locations of the transmitters and of the receiver.
3. Preliminary Data Analysis
 The trends of the amplitude of the radio signals obtained during 1 year and during 1 week are shown in Figure 2. A systematic decrease of the signals toward the instrumental zero value at nighttime appears clearly on the 1-week trends and is related to an interruption of 3–4 hours in the radio broadcasts after 1:00 a.m. local time (local time = UT + 1 hour).
 The LF signals are characterized by the ground wave and the sky wave propagation modes. The ground wave provides a rather stable signal. On the contrary, the sky wave is greatly variable from day to night and, at daytime, from winter to summer. Therefore, as a first step, we separated the daytime data from the nighttime ones. In order to obtain at first data sets always related to the daytime and to nighttime regardless of the season and then each set with the same number of data per day, we selected the range from 0900 to 1400 UT for the daytime and the range from 2100 to 0000 UT for the nighttime. This last choice resulted, in addition to the previous conditions, in the quoted interruption in the radio broadcasts. Then in the daytime data we separated the data collected in winter (21 December to 21 March) from the data collected in summer (21 June to 21 September). Figures 3 and 4show the nighttime, daytime, winter daytime, and summer daytime trends of the amplitude of the two radio signals from February 1996 to December 2004. Some interruptions appear in the previous trends, and they are related to a lack of data as a consequence of problems with the electric power at the receiver. The mean value for each nighttime, winter daytime, and summer daytime data set was estimated, and these values are reported under the section named Electric Field Strength (experimental values) of Table 2 for the CZE radio signal and of Table 3 for the MCO radio signal.
Table 2. Theoretical and Experimental Values of the Electric Field Strength for the CZE (270 kHz) Radio Signal at AS Receiver
Theoretical Values, mV/m
Experimental Values, m/Vm
Electric Field Strength
Table 3. Theoretical and Experimental Values of the Electric Field Strength for the MCO (216 kHz) Radio Signal at AS Receiver
Theoretical Values, mV/m
Experimental Values, m/Vm
Electric Field Strength
4. Theoretical Framework of Ground Wave and Sky Wave
 First, the theoretical amplitude of the ground wave was calculated. For this purpose, the ground wave propagation algorithm GRWAVE [International Telecommunication Union (ITU), 1985] was used. GRWAVE is based on the theory developed by Rotheram [1981a, 1981b]. The theory is concerned with the propagation of the ground wave over a smooth, homogeneous, curved Earth with exponentially decreasing refractive index. The significance of an exponential atmosphere is that it represents the average atmospheric conditions more closely than a linear refractive index variation does [CCIR, 1990f]. Considering the residue series approach, the amplitude of the vertical component of the electric field is given by
where k is the wave number in free space, n is the refractive index of the troposphere, and Ur is the radial component of the Hertz vector U, given by
where r0 is the distance from the center of the Earth, D is the range measured along the Earth's surface between the two terminals which are at the modified heights Ha and Hb, g(2)(S, H) is the outgoing wave height-gain function, and Ψ(2)(Sn, 0) is the excitation factor for the nth mode. The theoretical amplitudes obtained for the CZE and MCO ground wave at the AS receiver are reported in the section named Ground Wave (theoretical values) of Tables 2 and 3, respectively. The computation details are indicated in Appendix A.
 Then, the theoretical amplitude of the sky wave was calculated. For this purpose, the wave hop theory [Knight, 1973; CCIR, 1990c] was considered. According to this theory, the sky wave signal received by an antenna can be considered as a ray starting from the transmitter and reflected one or more times (hops) by the lower ionosphere and by the ground. For distances less than 1000 km, as for the CZE-AS and MCO-AS paths, the sky wave is totally represented by the one-hop wave. Thus the amplitude of the downcoming sky wave received by a short vertical antenna is given by
where EV is the vertical component of the electric field radiated, L is the sky wave path length, ψ is the angle of departure and arrival of the sky wave at the ground relative to the horizontal, R is the ionosphere reflection coefficient, D is the ionosphere focusing factor, Ft is the transmitting antenna factor, and Fr is the receiving antenna factor. The length L as well as the angle ψ in relationship (3) depend only on the ionosphere reflection heights, which can be assumed to be 70 and 90 km, corresponding to daytime and nighttime conditions; on the contrary, the other parameters are also related to the frequency of the wave. At daytime, the R coefficient strongly varies from winter to summer, and thus two different computations of the electric field of the sky wave must be done. The computations are detailed in Appendix A. The theoretical amplitudes at nighttime, at winter daytime, and at summer daytime for the CZE and MCO sky wave at the AS receiver are reported in the section named Sky Wave (theoretical values) of Tables 2 and 3, respectively.
5. Comparison of Theoretical and Experimental Data
 For a correct comparison of the theoretical and experimental data it is necessary to take into account that the amplitude recorded by the receiver is composed of the superimposition of the ground wave and of the sky wave. In principle, such a superimposition is not a simple addition because complex interference processes occur. Nevertheless, at distances greater than 300–400 km, the simple addition could give acceptable results [CCIR, 1990d]. Therefore our basic assumption for the comparison was to use the simple addition of the ground wave and sky wave contributions.
 From the theoretical values reported in Table 2 and taking into account that the receiver has an instrumental zero equal to 0.20 mV/m, the following statements can be made concerning the CZE (270 kHz) radio signal: (1) The ground wave is faint and, alone, cannot be recorded by the receiver; (2) the same consideration applies to the sky wave at summer daytime; and (3) at summer daytime, even the addition of the ground wave and sky wave contributions is less than the instrumental zero. The third item is in a perfect agreement with the mean experimental amplitude at summertime indicated in Table 2. In fact, this value (0.21 mV/m) practically does not represent any signal but only some noise. Looking at the trend in the bottom plot of Figure 3, it is evident that this noise is mainly represented by spikes in the recorded signal. We verified that these spikes are related mainly to summer storms (lightning). At nighttime and at winter daytime, a comparison between the theoretical and experimental values of the sky wave can be made. Subtracting from the values in the section named Electric Field Strength (experimental values) of Table 2, at night and winter daytime, the value 0.08 mV/m that represents the ground wave theoretical intensity, the mean experimental sky wave values were obtained. These values are reported in the section named Sky Wave (experimental values) of Table 2. Looking at the data of Table 2, the ratio between the experimental value and the theoretical one of the sky wave is −0.27 dB at nighttime and −4.8 dB at winter daytime. The first value testified to an excellent agreement, while the second one seems a little large. This discrepancy is mainly related to the fact that the curves for the theoretical computation (Appendix A) related to the winter are valid for “real” winter days, that is, when weather conditions are typical of the winter season [CCIR, 1990c], while the experimental value is calculated on all the winter days (21 December to 21 March). The examination of the winter daytime trend of Figure 3 confirms this statement. In fact, it is evident that the amplitude varies in each winter, and it is larger only in some periods which should represent the “real” winter days. Repeating the experimental estimation of the sky wave amplitude only in these periods, the value of the previous ratio becomes −1.6 dB; that is, a rather good agreement exists.
 From the theoretical values reported in Table 3, the following statements can be made concerning the MCO (216 kHz) radio signal: (1) The ground wave affects the experimental electric field strength of the radio signal; and (2) the sky wave at summer daytime is faint, and its contribution can be neglected. On the basis of the two points above, the recorded signal at summer daytime practically represents the ground wave of the MCO radio signal, and a comparison between the theoretical and experimental value of this wave can be made. From Table 3, the ratio between the experimental and the theoretical value is −0.33 dB; that is, an excellent agreement exists. Then, the theoretical and experimental values of the sky wave, at night and winter daytime, can be compared. At first, the mean experimental values of the sky wave, at night and at winter daytime, were obtained, removing from the values in the section named Electric Field Strength (experimental values) of Table 3 the value 0.54 mV/m that represents the ground wave theoretical intensity. These values are reported in the section named Sky Wave (experimental values) of Table 3. Looking at the data of Table 3, the ratio between the experimental value and the theoretical one at nighttime is +0.03 dB; that is, the agreement is excellent; at winter daytime the ratio value is −6 dB. This value is large enough, and the same consideration regarding the “real” winter days, claimed previously, does not reduce so much the discrepancy. In fact, repeating the experimental estimation of the sky wave amplitude only in the “real” winter periods, the value of the previous ratio becomes −3.2 dB. In this case the influence of the ground wave probably cannot be reduced to a simple addition. It must be noted that this case is the only one (Tables 2 and 3) in which the ground wave and the sky wave have practically equal theoretical values. In any case, the previous results indicate that the assumption of a simple addition of the ground wave and sky wave contributions generally has a good soundness.
6. Solar Activity Effects on the Sky Wave
 Since it is known that solar activity influences the sky wave propagation mode, it is necessary to take into account the sunspots. The physical interpretation of their effect is as follows [CCIR, 1990c]. During a sunspot maximum year, the base of the ionosphere is lower, and the electron density gradient is steeper than during sunspot minimum years. Thus VLF waves which are reflected from this lower layer are more strongly reflected in sunspot maximum years, whereas LF-MF waves, which are reflected above this lower layer, are more strongly absorbed. The maximum in the absorption lies in the frequency range 100–1000 kHz, and the absorption should increase from 100 to 1000 kHz. The sky wave of the radio signals under study should reveal these effects, that is, a reduction of its intensity in sunspot maximum years and a larger reduction of the signal with greater frequency. On the basis of the results presented in section 5, the effect can be investigated only at night and at winter daytime.
 First, the daily number of sunspots from 1996 to 2004 was obtained (National Geophysical Data Center Web site, www.ngdc.noaa.gov, 2005). The trends of the sunspot number from 1996 to 2004 and in the winter periods alone are shown in the top plot of Figure 5. The 4th-order polynomial fitting is superimposed to both the trends, and the presence of a nearly complete solar cycle comes out clearly. Then (1) the experimental amplitude of the sky wave was obtained, at night and at winter daytime, as the difference between each value of the CZE and MCO experimental amplitude and the relative ground wave theoretical value; (2) the mean values during each year (nighttime) and during each winter (daytime) were calculated; and (3) the normalization of these mean values to the pertinent theoretical value of the sky wave was performed. The results for the two radio signals are plotted in Figure 5 as solid squares with the relative 4th-order polynomial fitting superimposed. The existence of decibel values that are always negative at winter daytime is connected mainly with the model defect related to the “real” winter days (section 5). Looking at Figure 5, the normalized amplitude trends of the sky wave at nighttime clearly reveal the opposite of the sunspot trend. In sunspot maximum years, the normalized amplitude has a reduction up to 3.3 dB for 270 kHz (CZE) and up to 2.4 dB for 216 kHz (MCO) with respect to its value during the sunspot minimum years. Concerning the winter daytime, Figure 5 shows for the normalized amplitude of the 270 kHz (CZE) sky wave a behavior similar to the previous ones with a reduction up to 2 dB; on the contrary, for the 216 kHz (MCO) radio signal, the behavior is not well defined. The influence in this case of the ground wave should be taken into account. In section 7, a clear explanation of the previous behavior will come out. It must be specified that the previous decibel estimations were made on the 4th-order polynomial fitting.
7. Solar Activity Effects on the Ground Wave
 Now a possible influence of the solar activity on the ground wave propagation mode has been investigated. For this purpose, the analysis detailed in section 6 has been repeated for the amplitude of the MCO (216 kHz) radio signal at summer daytime. In fact, from section 4 it results that these data practically represent the ground wave. The result is presented in Figure 6. The normalized amplitude trend in Figure 6 reveals a direct similarity with the sunspot trend. In sunspot maximum years, the normalized amplitude has an increase up to 1.5 dB with respect to its value during the sunspot minimum years. Thus the solar activity influences the ground wave propagation mode of the MCO (216 kHz) radio signal, increasing its intensity in the sunspot maximum years and decreasing it in the sunspot minimum years.
 The previous result can clarify the not well-defined trend revealed in section 6 for the 216 kHz (MCO) amplitude at winter daytime. In fact, at this time, an opposite long-term variation produced by the sunspot cycle should act on the amplitude of the ground wave and the sky wave of this radio signal. Therefore a well-defined long-term variation cannot exist in the experimental total amplitude. Then, recalling that the amplitude of the sky wave used in section 6 is obtained by subtracting a constant value from the experimental total amplitude, the previous behavior of the MCO signal at winter daytime is obvious.
 On the basis of our data, the effect of the solar activity on the ground wave propagation of the CZE (270 kHz) radio signal cannot be investigated (section 5). Besides, we cannot specify if the influence of the solar activity on the ground wave propagation mode is a peculiarity related to the MCO-AS path or if it is a general effect. In any case, variations in some of the troposphere parameters which influence the ground wave propagation mode could produce the effect we revealed. Using the GRWAVE algorithm [ITU, 1985], it was found that the most influential troposphere parameter on the amplitude of the ground wave is the refractive index n of the troposphere. Thus, as an example, the amplitude of the ground wave was calculated for the MCO-AS path using the value 1.000630 for the refractive index of the troposphere at the surface of the Earth instead of the standard 1.000315 value used in the computations of Appendix A. The value 0.58 mV/m was obtained for the amplitude of the ground wave instead of the value 0.54 mV/m reported in Table 3, that is, an increase of 0.75 dB that could justify the effect under study. Thus the solar activity could influence the refractive index of the troposphere, increasing its value in the sunspot maximum years and decreasing the value in the sunspot minimum years. Variations in the temperature and/or in the density of the troposphere from the maximum sunspot years to the minimum ones could be responsible for the previous change in the refractive index of the troposphere. If the effect under study is not a general one, the quoted variations could be different on the Earth, being larger only in some zones. One of these zones could exist along the MCO-AS path.
 The experimental estimate of the amplitude of the CZE (270 kHz) and MCO (216 kHz) broadcast signals recorded during 9 years 500–800 km away is in good agreement with the theoretical model concerning the propagation of the ground wave over a smooth, homogeneous, curved Earth with exponentially decreasing refractive index. Similarly, the wave hop theory has given an excellent estimation of the experimental electric field strength of the sky wave at nighttime. At winter daytime, the estimation is good enough only if it is referred to a “real” winter day. No check was possible for the sky wave at summer daytime. Next, the effect of the solar activity (sunspots) on the sky wave propagation mode was confirmed: During a solar cycle, a reduction of the electric field strength in the sunspot maximum years, with a larger effect for the signal with the greater frequency (270 kHz), was clearly revealed. An influence of the solar activity on the MCO ground wave propagation mode was revealed, too. A weak increase of the refractivity of the troposphere in the sunspot maximum years could justify the quoted influence. Further investigations are required to confirm this not well-known effect.
 The influence of solar activity on the LF radio signals over a period of several years (solar cycle) was investigated in this paper. In order to define the influence at shorter periods, the future development of this research will be the investigation of the sunspots and of the sky wave and ground wave using the spectral analysis and filtering processes. The previous two complete analyses will constitute the necessary background for future characterization of anomalies in LF radio propagation.
Appendix A:: Ground Wave and Sky Wave Computation
A1. Ground Wave
 The GRWAVE algorithm with the default values 1.000315 for the refractive index of the troposphere at the surface of the Earth and 7.35 km for the scale height of the troposphere was used. The CZE-AS path and the MCO-AS path were considered as mixed paths (Figure 1) having different values of the permittivity ɛ (15 for the ground and 80 for the sea) and different values of the ground conductivity σ according to the world conductivity maps [CCIR, 1990e].
 The CZE-AS mixed paths are the eastern Europe path, 495 km long and σ = 10−3 S/m; the sea path, 248 km long and σ = 5 S/m; and the Italian path, 75 km long and σ = 3 × 10−3 S/m. The MCO-AS mixed paths are the France path, 35 km long and σ = 3 × 10−4 S/m; the sea path, 231 km long and σ = 5 S/m; and the Italian path, 253 km long and σ = 10−3 S/m.
A2. Sky Wave
 Taking into account that EV 300 mV/m at 1 km, where P is the radiated power in kW, the results are EV = 11619 mV/m for CZE and EV = 11225 mV/m for MCO. The effective frequency is defined as fef = f · cos i(kHz), where f is the transmitted frequency and i is the ionosphere angle of incidence.
 The curves of CCIR [1990c] give the following results: nighttime for CZE, L = 844 km, ψ = 11°, D = 1.18, Ft = Fr = 0.63, fef = 65, and R = 0.13; nighttime for MCO, L = 553 km, ψ = 18°, D = 1.08, Ft = Fr = 0.8, fef = 74, and R = 0.12; daytime for CZE, L = 834 km, ψ = 7.5°, D = 1.2, Ft = Fr = 0.65, fef = 51, and R = 0.029 (winter) and R = 0.0012 (summer); and daytime for MCO, L = 540 km, ψ = 13.5°, D = 1.1, Ft = Fr = 0.76, fef = 67, and R = 0.02 (winter) and R = 0.0007 (summer).
 We want to thank the anonymous reviewers for their helpful suggestions that improved the original version of the manuscript.