A new VLF/LF atmospheric noise model



[1] Atmospheric noise, originating essentially from lightning discharges, is the main disturbance of VLF/LF telecommunications. This paper characterizes atmospheric noise in the 10–80 kHz range and proposes a new model: very accurate low-frequency noise model (VALERIE). This model uses a new approach, which combines noise measurements with lightning data. The noise statistics were obtained from several years of measurements taken by the Délégation Générale de l'Armement (DGA)/Centre Technique des Systèmes Naval (CTSN) (Toulon, France) and the Space and Naval Warfare Systems (SPAWAR) (San Diego, California). Lightning data were provided by recent satellite observations made by NASA. A comparison of VALERIE predictions with measurements by cross validation showed an increase in accuracy compared to the current International Telecommunication Union (Geneva) model and a decreased average deviation. The model has been validated for the Atlantic area but may be extended as new measurements are collected.

1. Introduction

[2] Atmospheric noise is the main disturbance in the 10–80 kHz radio frequency range. The knowledge of its characteristics is a key factor in the calculation of signal-to-noise ratio to improve the prediction of communication coverage in low-frequency communications. The existing atmospheric noise model of the International Telecommunication Union (ITU) [2003], based on measurements made in the 1960s, showed a lack of accuracy mainly with regard to time and geographical variations [Sailors, 1993; Portala, 2001; Fieve, 2005]. In 1997, the Centre Technique des Systèmes Navals (CTSN, France) started a series of worldwide measurements to improve noise characterization and to detect the weaknesses of the current noise model. The end goal of the CTSN was to make a new noise model based on long-term noise statistics. A collaboration between the CTSN and the Space and Naval Warfare Systems Center (SPAWAR) was established to increase the amount of noise statistics and the world coverage of measuring stations. Since the noise originates in lightning discharges, very soon it became essential to also take into account the spatial distribution of lightning. For this purpose, lightning data from the NASA Global Hydrology and Climate Center, Huntsville, Alabama, were integrated into the CTSN database to establish an empirical relationship between lightning occurrence and noise level. The calculation of the global link between lightning activity and noise measurement corresponds to a new approach in noise modeling.

[3] This paper summarizes the results of the statistical analysis of noise in different variation domains. It explains the construction method of the new noise model. A comparison of the prediction by the new very accurate low-frequency noise model (VALERIE) with the measurements (cross validation) and the existing ITU model is presented.

2. Noise Measurements

[4] In order to improve knowledge of noise characteristics in the low-frequency domain, CTSN deployed a worldwide network of measurement stations. The total network was made up of seven measuring stations: five around the Atlantic Ocean, one on the Mediterranean coast, and one in the Indian Ocean (Figure 1).

Figure 1.

Atmospheric noise measurement network.

[5] At each station the measurement was obtained through two whip antennas of different effective height, whose signals were combined to obtain a total dynamic range of 120 dB. This high range was necessary to measure atmospheric noise, which is characteristically very impulsive. The antennas were regularly calibrated with a ferrite core magnetic antenna. The signal was filtered between 10 and 80 kHz and sampled at 200 kHz through a Digital Signal Processing (DSP) card that processed the signal. To extract the noise parameters, a 200 Hz bandwidth Fourier transform was applied to the signal, previously weighted with a Blackman-Harris window.

[6] Output parameters were collected every hour and included different statistical parameters at specified narrowband frequencies, such as average and root-mean-square noise levels (Eavg (equation (1)) and Erms (equation (2)), noise impulsivity (Vd) (equation (3)), and noise amplitude probability distribution (APD) (equation (4)), respectively):

equation image
equation image
equation image
equation image

E(t) represents the signal received on the antenna in V/m. The T period considered at CTSN is 4 min. The noise parameters and the bandwidth considered were identical to those used in the actual noise model of ITU [2003] and are described by Spaulding and Washburn [1985]. These are chosen for the direct comparison of measurements with the ITU noise model.

[7] Raw measurements (time domain data) were also regularly recorded in order to allow new postprocessing. The DSP card was linked to a GPS antenna for precise dating of measurements.

[8] A data exchange collaboration was established between CTSN and SPAWAR for noise measurements. The characteristics of the SPAWAR network and its measurement system are described by Tomko and Hepner [2001].

[9] Data from both CTSN and SPAWAR networks were integrated at CTSN into a single noise database and sorted to exclude man-made signals and noise from atmospheric noise measurements. This step was essential to obtain correct data: It includes a primary standard check of noise levels sorting out mainly nonworking periods. It was followed by a new method consisting of excluding measurements whose impulsivity Vd is lower than 2 dB. This is because man-made noise is mostly of a sinusoidal kind and as such induces close to zero impulsivity, whereas atmospheric noise is characteristically very impulsive and its Vd is rarely lower than 3 dB.

3. Noise Characteristics

[10] The long-term statistics of the data collected by both CTSN and SPAWAR networks produced a precise description of noise characteristics. These statistics were separated into different domains that corresponded to noise variation domains such as yearly (in relation to the solar cycle), monthly and daily variations, frequency dependence, and spatial distribution. The noise observations presented in this section are summarized in Table 1, but detailed information is given by Fieve [2005]. Data set covers from 1997 up to 2005: all measurements stations were considered except St.-Pierre Island (56°W–47°N, east Canadian coast) and Toulon (6°E–43°N, France), where artificial noise surpassed atmospheric noise. The first item that had to be checked in order to build a statistical model was the yearly variation of the noise. The measurements showed that atmospheric noise in this frequency domain was relatively constant over the years and the global variation of the monthly median for each year did not exceed an average of ±1.5 dB (Table 2 and Figures 2 and 3) . This confirmed that a statistical model was the right approach. The low variation of noise over the years can be explained by a large integration of noise due to the long distance of propagation in those frequencies. This can be confirmed by the fact that the yearly variation coefficient increases with the frequency when the propagation coverage, and as such the surface of the integration area, decreases. Thus, even if the location and intensity of the sources of noise (lightning) differ from one year to another, the integration of the noise induced by long-range propagation largely smoothes out those differences.

Figure 2.

Example of the yearly variation of the median atmospheric noise level on Martinique Island.

Figure 3.

Example of the yearly variation of the median impulsivity Vd level on Martinique Island.

Table 1. Summary of the Characteristics of Noise and Its Consequences on the Noise Model
Variation ParameterInfluenceRange of ImportanceConsequences for the ModelTaken Into Account in the Model
Time domain    
   Solar cyclenegligible over the period considered, has to be evaluated on a longer period<1.5 dBno need of a solar cycle influenceno
   Yearnegligible<1.5 dBstatistic modeling logical, based on the probability distribution averaged over the yearsno
   Monthessential, importance varies with the climatefrom 3 to 23 dBmodeling of the variations based on measurement statisticsyes
   Dayimportant, depends on the frequency but similar on all sitesfrom 3 to 15 dBmodeling of the variations based on measurement statisticsyes
Frequency domainessentialdecrease of ∼30 dB over 10–80 kHzmodeling of the variations based on measurement statisticsyes
Spatial domainessentialUp to 25 dBspatial sampling not sufficient, necessity of another source of datayes
Decileslow, depends on sites and frequency<±6 dBtime validity of the results to be calculatedyes
Time domain    
   Yearnegligible<1.0 dBstatistic modeling logicalno
   Monthlow for VLF, higher for LFup to 6 dBmodeling of the variations based on measurement statisticsyes
   Daylowup to 3 dBmodeling of the variations based on measurement statisticsyes
Frequency domaindepends on the distance to source of noise: decreases with the frequency in a quiet period, unstable in a stormy periodup to 3 dBmodeling difficult, modeling of the variations based on measurement statisticsyes
Spatial domainimportant∼5 dBmodeling of the variations based on measurement statisticsyes
Decileslow<3 dBtime validity of the results to be calculatedyes
Table 2. Yearly Variations of Atmospheric Radio Noise
SitesVLF Yearly Variability, dBLF Yearly Variability, dB

[11] The question as to whether the solar cycle had an impact on the variations of the noise level was also raised. The solar cycle period is 11 years on average, during which the amount of electromagnetic field generated by the sun varies in significant proportions. When reaching the Earth, the solar electromagnetic field is directed mainly toward the poles because of the shield effect of the geomagnetic field. It then represents natural noise, which can, during periods of high solar activity, disturb telecommunications in a wide range of frequencies essentially in the polar areas. This natural noise through its propagation in the ionospheric channel could significantly increase the natural noise level. However, the fact that variations in solar field intensity have an important impact on ionospheric properties and modify the VLF/LF propagation conditions is of greater importance to atmospheric noise. Nevertheless, no correlation between solar flux and noise level variations was recorded over the measurement period (Figures 4 and 5) . Overall, the absence of the impact of the solar cycle on noise levels has to be confirmed over a longer period of measurements.

Figure 4.

Comparison of the variation levels of atmospheric noise (crosses) and solar radio flux 10.7 cm (NOAA) (circles), Martinique.

Figure 5.

Comparison of the variation levels of atmospheric noise (crosses) and solar radio flux 10.7 cm (NOAA) (circles), French Guyana.

[12] However, atmospheric noise shows strong seasonal dependence, which can be explained by the origin of the noise: lightning discharges. New thunderstorm data [Christian, 1999; Christian et al., 1999] confirmed the fact that lightning occurs when the temperature increases and is mostly a summer phenomenon. This is consequently observed with atmospheric noise. Noise variations throughout the year depend on regional weather variations (Table 3 and Figure 6): Around the equator the noise level is approximately the same all year round (Ascension and Guyana stations, variations of the monthly median through the year are lower than 3 dB), at higher latitude the variations increase, the highest were observed in Florida (variations of the monthly median up to 23 dB) where atmospheric conditions change a lot between summer and winter. However, at higher latitudes, taking Fairbanks, Alaska, as an example, the variations decrease again (variations of the monthly median up to 16 dB).

Figure 6.

Atmospheric noise monthly variations.

Table 3. Span of the Monthly Variations of Atmospheric Radio Noisea
17 kHz50 kHz
1200 LT0000 LT1200 LT0000 LT
  • a

    In units of dB.


[13] Diurnal dependence is of lesser importance but should not be neglected. The changes in level due to diurnal variations are between 3 dB (lower part of the frequency range) and 15 dB (higher part of the frequency range). The variation is similar at all stations and is due to two factors: the influence of the propagation and the distribution of thunderstorms during the day (Figures 7 and 8) . The former was characterized by a lower level of noise during daytime (propagation range decreases) compared to nighttime, the second showed a peak of intensity around 1500 LT, which corresponds to a peak in local lightning activity.

Figure 7.

Schematic trends of the diurnal variations of the atmospheric noise.

Figure 8.

Example of the diurnal variations of atmospheric noise at different frequencies, Ascension Island.

[14] As mentioned above, noise characteristics varied with frequency (Figures 8 and 9) . The noise level peaked at 10 kHz and decreased regularly with increasing frequency, up to 80 kHz, of about 30 dB (more pronounced between 10 and 20 kHz). The decrease was higher during daytime than nighttime, which resulted in a higher difference in noise level between night and day (lower level of noise during the day) at LF frequencies (>30 kHz).

Figure 9.

Example of frequency variations at Martinique for the summer season 2003. The measures are obtained via narrowband Erms levels and the spectra from a fast Fourier transform realized by postprocessing of raw data. Two modelings are shown: linear and spline interpolation.

[15] Another important parameter to take into account when considering atmospheric noise levels is the geographical position. The differences observed between the medians of the different measurement sites rose to 25 dB (Figure 6). When observing the distribution of lightning (NASA Optical Transient Detector (OTD) lightning maps available via the Global Hydrology Resource Center, Alabama), the source of noise, over the globe, two main points are to be observed. Lightning is globally more intense as one get closer to the equator; this is due to the link between high temperatures and the occurrence of lightning. However, other parts of the world, outside the equator (Florida, Madagascar, and northern India), also show favorable atmospheric conditions for the build up of thunderstorms, usually when air masses with different properties meet. The second point is the low level of lightning activity over the ocean. Some exceptions can also be observed here, particularly in the northwest of the Atlantic Ocean. The geographical distribution of lightning therefore shows a complex structure confirmed in the spatial distribution of the noise.

[16] A key point in evaluating the possibility of modeling the geographical distribution of the noise was to estimate its spatial coherence. The correlation (equations (5) and (6)) of the impulsivity and the noise level between different sites at the same time and date was calculated:

equation image
equation image

where Rxy is the correlation number, Nx is the number of elements considered, equation image is the average of the x elements, and σx is the standard deviation of the x elements.

[17] The results, presented in Figure 10, showed that a correlation only appeared between the closest sites, Toulon and Lannion, 980 km apart, as well as Martinique and Guyana, 1500 km apart. The correlation was higher for very low frequencies (<30 kHz) at nighttime when the propagation conditions increased the coherence area, which was consistent. Between Dakar and Guyana, 4500 km apart, no noise variation correlation was observed. From this, one can conclude that the measurement sites were too far apart to interpolate the noise level directly from the measurements, even when the modeling area was limited to the Atlantic area. All the previous observations were then included in the building of a new atmospheric noise model presented in section 4.

Figure 10.

Correlation of noise variations versus distance between the measurement sites.

[18] Some observations were also made on the impulsivity parameter, the voltage deviation Vd, that had previously been remarked [Chrissan and Fraser-Smith, 2000]. The Vd impulsivity levels cannot be systematically correlated with lightning distribution or with noise levels. It appeared that a high number of lightning streaks tend to lower the impulsivity level. This can be explained by the fact that the different impulses overlap each other and as such reduce the impulsivity of the signal [Fieve et al., 2004]. Very stormy areas present a lower Vd than areas in which medium activity is observed. So Vd levels cannot be directly extrapolated from lightning storm distribution.

4. Noise Model

[19] The new model is based on the interpolation of the collected data in the time and frequency domain. The main issue was to establish the spatial distribution of noise, the number of measurement sites being insufficient.

[20] The time and frequency domain interpolation was done using spline interpolation functions applied to the data. The thin plate spline functions allow the creation of smoothing interpolation for ungridded bivariate data so that the resulting function coincides with the measurement points. The probability distribution of the root-mean-square average Erms (noise energy) established from the measurements was examined. It was interpolated with the following samplings: one point per hour and per month in the time domain and 6 (CTSN measurements) to 10 (SPAWAR measurements) points in the frequency domain.

[21] The spatial distribution had to be treated apart. The distance of atmospheric noise coherence was estimated as being smaller than 4000 km. The distance from the measurement sites to the middle of the Atlantic Ocean being larger than the coherence distance, the number of measurement sites was insufficient to interpolate noise levels between them. The only means of estimating the noise far from the measurement sites was to consider its source: the lightning discharges. The purpose was to produce a global method combining noise measurement and lightning distribution.

[22] The spatial distribution of lightning obtained from NASA satellites is available from the database of the Global Hydrology Resource Center, Alabama [Christian, 1999; Christian et al., 1999; Blakeslee et al., 1999]. Lightning data from the OTD satellite were examined for the main part as they cover a wider part of the globe. The measurements of the satellites represent only a sample of the lightning actually occurring, since the satellite only passes over an area about two times a day. However, about 10 years of lightning measurements (Lightning Imaging Sensor and OTD satellites) were available which was enough to establish statistical information on lightning, including the average distribution of lightning through the day. Four different parameters were used to define lightning intensity: areas, groups, flashes, and events. A flash represents an approximate lightning streak; an event is the smallest light activity detected by the sensor of the satellite; a lightning streak actually contains multiple discharges that all contribute to the generation of electromagnetic noise. Flashes were examined in this study for the distribution of lightning.

[23] From average maps of lightning intensity for each hour of the day and each month, the propagation of the field generated by lightning was globally evaluated and compared to the noise statistics for the same period in order to establish a link between lightning and atmospheric noise. For this purpose, individual flashes were grouped into blocks of 10° longitude to 10° latitude, which was sufficient considering the coherence area of atmospheric noise. A coefficient, representing the lightning intensity of each block, was obtained for every month and every hour. The energy received at one given point of the globe depends on the distance of the different lightning blocks from this point. A global estimation of the propagation attenuation with distance was made, based initially on the known VLF/LF propagation characteristics [Bérenger, 2002, 2003]. A comparison between noise level at different stations and global lightning intensity propagated to the point in question gave a coefficient of the dependence between these two phenomena, and the propagation parameters were adjusted until lightning intensity and noise level were closely correlated at different sites (Figure 11). The propagation conditions were dependent on the frequency and the period of day. The operation was then repeated to calculate the propagation parameters for the different conditions encountered. The coefficients obtained were not strictly identical at the different sites (differ in a 10% span); these differences represent the normal variations in propagation or lightning conditions over the globe. Thus, instead of calculating the coefficient average to apply the same value on the whole globe, a geometrical interpolation (Shepard's inverse distance [Shepard, 1968]) was used to take geographical differences into account and to stay as close as possible to existing measurements. Once the relation between lightning intensity and noise generation was established, the noise level could be calculated for the different parts of the world from the lightning maps (Figures 12, 13, and 14).

Figure 11.

Lightning attenuation function with distance.

Figure 12.

VALERIE VLF/LF atmospheric noise model.

Figure 13.

Erms noise median level map, June, 1200 UT, 20 kHz.

Figure 14.

Vd noise impulsivity median level map, June, 1200 UT, 20 kHz.

5. Results

[24] The method described above could only be validated through a comparison of noise predictions with new measurements or through cross validation followed by an evaluation of the increase in accuracy obtained compared with the current ITU noise reference model [ITU, 2003]. Table 4 shows the results of the cross validation. This consists of eliminating a measurement site from the model and comparing the predictions obtained at this location with the measurements collected. It appeared that the error logically increased as the station became more isolated. The error obtained was, however, always lower than or similar to that of the ITU model.

Table 4. Comparison of VALERIE Model and ITU Model Predictions With Median Measurements, Absolute Value of Average Error, and Deviationa
Cross ValidationSDNoise ModelSD
17 kHz50 kHz17 kHz50 kHz17 kHz50 kHz17 kHz50 kHz
  • a

    In units of dB.

Ascension, UK
Dakar, Senegal
Martinique, France

[25] A comparison of the VALERIE noise model prediction was made with new measurements from Toulon, France (Table 5). As mentioned in section 3, most of the measurements made at this site could not be used, since artificial noise was present on the site. However, a series of measurements carried out in order to find new measurement sites in the Toulon area, free of artificial noise, provided 2 months of real atmospheric noise data. The noise levels could be compared to the new model (VALERIE) and to the ITU model. This comparison showed particularly good results in the low frequency (error < 2 dB). At high frequency the accuracy obtained was lower (error ∼8 dB) but still improved compared with the accuracy of the actual model.

Table 5. Comparison of VALERIE Model and ITU Model Predictions With Measurements Realized in Toulon, France, July and August 2003, Absolute Value of Average Error and Deviationa
 Model Prediction Error
17 kHz50 kHz17 kHz50 kHz
  • a

    In units of dB.

July 20031.96.39.410.5
August 20031.29.911.515.0

6. Conclusion

[26] This paper presents VALERIE, a new VLF/LF atmospheric noise model, whose accuracy is improved compared with the ITU's [2003] current reference model. It is based on both worldwide noise measurements and lightning statistics data and proposes a global approach to both these phenomena in order to predict atmospheric radio noise. This global approach is justified by the large integration area due to the long distance of propagation in the VLF/LF frequency range. The accuracy of the model, as low as ±5 dB around the actual measured values, could be estimated by cross validation. The VALERIE model gives the probability distribution of this noise and an estimation of the impulsivity for the 10–80 kHz frequency range.

[27] VALERIE is limited, for the moment, to the Atlantic area but could be extended as soon as more data are available to validate the model in other parts of the world. The model is also built to integrate a real-time lightning detection system in the future, which CTSN plans to add to the measurement stations.


[28] This work could not have been done without the support and assistance of the Délégation Générale de l'Armement (DGA), French Ministry of Defense. Part of the noise data were provided by the Space and Naval Warfare (SPAWAR) Systems Center, San Diego, California, under a data exchange cooperation agreement. Lightning data were provided by the NASA Optical Transient Detector (OTD) and the Lightning Imaging Sensor instrument teams via the Global Hydrology Resource Center at the Global Hydrology and Climate Center, Huntsville, Alabama.