Signal strength measurements at 2 GHz have recently been made on three over-sea paths in the British Channel Islands. This paper focuses on explaining the propagation characteristics during periods of normal reception and periods of enhanced signal strength with particular emphasis on a 48.5 km transhorizon path between Jersey and Alderney. Evaporation ducting and diffraction appear to be the dominant propagation mechanisms at most times. The influence of the evaporation duct during periods of normal propagation has been confirmed by modeling the over-sea propagation conditions using Paulus-Jeske evaporation duct refractivity profiles as input to the parabolic equation method. During periods of enhanced propagation, which occur approximately 8% of the time on the longest path (48.5 km), the presence of additional higher-altitude ducting/super-refractive structures has been verified and their influence has been modeled with reasonable success.
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 Signal strength measurements at 2 GHz have recently been made on three over-sea paths in the British Channel Islands (see Table 1 and Figure 1 for transmitter and receiver locations). A summary of these measurements are presented in the companion to this paper [Siddle et al., 2007], together with a statistical analysis of the received signal strength variations and a comparison with predicted values made using current ITU-R Recommendations. The antenna heights were such that the ends of the two longest links were beyond the optical horizon, and for the shortest link the ends were within the optical horizon for most of the time. A large tidal range is prevalent in the Channel Islands (up to 10 m in Guernsey on a spring tide), and consequently the obscuration due to the bulge of the earth varies significantly within the tidal cycle.
Table 1. Geographical Positions and Altitudes (Above Mean Sea Level) of the Transmitting and Receiving Antennas
 In order to correlate the varying signal strengths with different weather processes, meteorological data were obtained from a number of sites around the Channel Islands (see Table 2). Hourly, sea-level meteorological data were available from the Channel Light Vessel (CLV) anchored in the English Channel to the northwest of all three radio paths. The distance of the CLV to the midpoint of the Jersey-Alderney link is approximately 70 km, and the nominal height at which observations are made at this station is 5.0 m above mean sea level. Higher altitude weather data were obtained from the airports on Jersey, Alderney and Guernsey with heights of 84.0, 88.7, and 102.0 metres above mean sea level respectively. Data from the Maison St. Louis Observatory in St. Helier, Jersey (54.0 m above mean sea level) and from a privately owned weather station in La Petit Val, Alderney (10.7 m above mean sea level) were also employed.
Table 2. Geographical Positions and Altitudes of Weather Stations in the Channel Islands
Altitude Above Mean Sea Level
Channel Light Vessel
La Petit Val, Alderney
Maison St. Louis Observatory, St. Helier, Jersey
 This paper focuses on explaining the propagation characteristics during periods of normal reception and periods of enhanced signal strength (ESS) with particular emphasis on the 48.5 km transhorizon Jersey to Alderney path (signal strengths that exceed a threshold calculated assuming free space loss along the path are classified as enhanced signals).
2. Signal Strength Variations and the Estimated Evaporation Duct Height
 The correlation between the computed Paulus-Jeske (P-J) evaporation duct heights [Paulus, 1985] and the corresponding hourly signal strengths measured at the Alderney high antenna is shown in Figure 2 (upper frame) together with the ESS threshold and diffraction threshold (assuming mean antenna heights above sea level for the upper antennas) calculated assuming standard atmospheric conditions. Hourly measurements of air temperature, sea temperature, relative humidity and wind speed made at the CLV were employed in calculating the duct heights according to the P-J formulation. Ideally, the meteorological measurements would have been made close to the midpoint of the propagation paths, however such data were not available and the CLV was the closest available source. Since the CLV was somewhat displaced from the paths of interest, horizontal homogeneity was (by necessity) assumed.
 To illustrate the effect of the tide, the data have been divided into four parts (Figure 2, lower frame): cases when the tide height (assumed to be the average of the heights at Jersey and Alderney) between the transmitter and receiver is less than −2 m relative to its mean value, cases when the tide height lies between −2 m and 0 m, cases when the tide height lies between 0 m and 2 m, and cases when the tide height between the transmitter and receiver exceeds 2 m. Best-fit lines for each tidal range have been plotted in the lower frame of Figure 2.
 In the upper frame of figure 2, the majority of the data lie between the free space and diffraction threshold values indicating that the evaporation duct is able to increase the received signal strength at Alderney well beyond the diffraction level. However, the enhancement in signal strength provided by the evaporation duct is not sufficient to exceed the free space threshold. Additionally, the distribution of data in the lower frame of Figure 2 corroborates the observation made in the companion paper [Siddle et al., 2007] that during periods of normal reception, stronger signals are received when tide heights are low and vice versa.
 At most times during periods of non-ESS, the measured signal strengths increase with duct height, an observation consistent with reports made by various authors [SPAWAR, 2004; Hitney et al., 1985; Hitney and Veith, 1990]. Considering only the non-ESS data, the signal strength at the Alderney high antenna increases at the rate of 0.61 dB per metre increase in duct height. For the Guernsey and Sark high antennas, the corresponding values are 0.59 dB/m and 0.25 dB/m respectively.
 For the cases of ESS (Figure 2, upper frame), there is no definite correlation between measured signal strength and calculated evaporation duct height, suggesting either the existence of additional propagation mechanism(s) during these periods, or that under these conditions the estimate of the duct height is incorrect. The inverse relationship between tide height and signal strength is no longer evident, and in general the calculated evaporation duct heights during periods of ESS appear to be less than the duct heights during periods of normal reception (for all valid data, the mean of the P-J evaporation duct height is 8.3 m, reducing to 6.0 m for times when ESS signals are observed at Alderney).
 It is important to note that the P-J method of estimating evaporation duct heights is an open ocean model [Paulus, 1985; Hitney and Veith, 1990; Babin et al., 1997] that works reasonably well for conditions of atmospheric instability (mostly prevalent in the open ocean) where the air is colder than the sea. During stable periods, when the air temperature exceeds the sea temperature, the P-J method incorporates a temperature correction (on the assumption that an error has been made during measurement) that results in an under-estimation of the evaporation duct height [Paulus, 1985]. Whilst it may be true that stable conditions are uncommon in the open ocean [Paulus, 1985; Babin et al., 1997], it is likely that these will occur more often in coastal regions that are particularly prone to land-induced effects such as advection of warm air over a cooler sea surface. This is another reason for the departure from the general trend of higher duct heights corresponding to higher signal strengths during periods of ESS (Figure 2, upper frame), as these occur primarily when stable atmospheric conditions are prevalent.
3. Modeling Periods of Normal Reception With the Parabolic Wave Equation Method
 With the advent of powerful computers, the computationally intensive parabolic equation (PE) method [Dockery, 1988; Craig and Levy, 1991; Barrios, 1994; Levy, 2000] has become an efficient and practical tool for tropospheric radiowave propagation calculations (see, for example, studies of the effects of tropospheric ducting on the performance of UHF radio links presented by Slingsby  and Sirkova and Mikhalev ). In this section, the propagation conditions during periods of normal reception in the Channel Islands have been modeled using the PE method. In particular, the split-step parabolic wave equation [Dockery, 1988; Kuttler and Dockery, 1991] that implements impedance-boundary conditions [Dockery and Kuttler, 1996] was utilised for field strength calculations. Predictions for short periods of time (in summer and winter) were also made using the radiowave propagation assessment tool, AREPS [SPAWAR, 2004] that makes use of a hybrid model incorporating the split-step PE method as a sub-model [SPAWAR, 2004]. The results for a few weeks of test cases indicate that the propagation loss values calculated with the PE method and with AREPS are within 1–2 dB of each other.
 Modified refractivity, M profiles based on the Paulus-Jeske method [Paulus, 1985] were generated for each hourly reading and utilised as inputs to the PE model. A typical modified refractivity-height profile (for 07 December 2003 at 18:00 UT) illustrating the presence of an evaporation duct is shown in Figure 3. For this particular case (air temperature: 7.8°C, sea temperature: 12.9°C, dew point temperature: 2.6°C and wind speed: 14.3 m/s), the evaporation duct height is 14.7 m while the transmitter and receiver heights above sea level are 13.8 m and 11.1 m respectively. For the purpose of illustration, shown in Figure 4 is the height vs. range ray-trace plot for the evaporation duct profile and transmitter specified above (produced in AREPS [SPAWAR, 2004]). Trapping of some of the direct and reflected rays between the earth's surface and the top of the evaporation duct at 14.7 m is evident and consequently propagation occurs for extended ranges within the trapping layer. There is good agreement between the measured signal strength of −86.6 dBm and the predicted signal strength of −88.1 dBm.
3.1. Illustrative Examples
 During a distinctive cold weather period (04–10 December 2003) when normal reception occurs, there is very good agreement between the measured and the PE-predicted signal strengths at the Alderney high antenna (Figure 5). This behaviour was also apparent for the Guernsey and Sark measurements, and for both the high and low antennas. In contrast, for a typical period of signal enhancement during late summer (12–18 September 2003), there is little correlation between the observations and the PE-predicted values (Figure 6). The predicted signal strengths in this case simply indicate the regular oscillation in received power caused by the tides.
3.2. Analysis With Complete Signal Strength Data Set
 A scatterplot of the measured signal strengths and the PE-predicted signal strengths for all the valid hourly data at the Alderney high antenna is shown in Figure 7 (upper frame). The overall correlation for these data is poor (correlation coefficient = 0.17) and the standard deviation between the observations and predictions is approximately 12 dB. However there appears to be a definite correlation between the observed and predicted signal strengths particularly for cases of normal reception. A clearer depiction of this correlation can be seen in the lower frame of Figure 7 in which all cases of enhanced signal strength have been removed. The correlation coefficient for these data is 0.45, and the standard deviation between the measured and predicted signal strengths reduces to 7.4 dB.
 Every tropospheric duct has a maximum wavelength that it can support, depending upon the geometry and the change in refractivity across the duct. The maximum cut-off wavelength, λmax, provides a general indication of the radio-wave trapping capability of a duct, and is given in equation (1) [Turton et al., 1988; Brooks et al., 1999].
where t is the duct thickness (m), δM the modified refractivity change across the duct (M-units), and k = 3.77 × 10−3 for a surface-based duct or 5.66 × 10−3 for an elevated duct.
 It is noteworthy that when only those cases of nonenhanced signal strengths are used in which the corresponding evaporation duct cut-off wavelengths exceed 15 cm, the correlation coefficient between the PE-predicted and measured signal strengths at the Alderney upper antenna increases to 0.66.
 Thus, even though the cut-off wavelength is simply a rough indication of the trapping capability of an evaporation duct, it can still be used to show that when the likelihood of 2 GHz radio waves getting trapped within a duct is maximized, the evaporation duct does becomes the dominant propagation phenomenon. (For a detailed discussion of the concept of maximum cut-off wavelength for evaporation ducts, the reader is directed to the works of Hall  and Turton et al. .) Finally, it is also interesting to note that when the Paulus-Jeske evaporation profiles are used in the PE model, none of the predicted signal strengths exceed the value of the free space threshold.
 Further evidence of the correspondence between the measured and PE-predicted signal strengths can be obtained from Figures 8 and 9. The cumulative frequency distribution curves for three sets of data with reference to the Alderney high antenna are shown in Figure 8. These data sets are (a) all measured signal strength, (b) only nonenhanced measured signal strength and (c) PE-predicted signal strength (using P-J evaporation duct profiles). The mean hourly signal strengths for the two years of data (for the same three signal strength data sets) are presented in Figure 9. In both figures, the change in shape of the distributions for that of all measured data and for just nonenhanced signal strength data is very significant. The PE-predicted signals provide a much-improved estimate of the measured signal strengths during periods of normal reception.
 Given that only the effect of the evaporation duct has been accounted for in these cases, this suggests that (a) the evaporation duct is responsible for propagation during periods of normal reception (i.e. cold weather periods) and (b) the evaporation duct refractivity profiles assumed within the PE predictions during periods of enhanced reception are insufficient to model the propagation, at least as it impacts on our paths/antenna heights. The latter conclusion points towards the existence of propagation mechanism(s) other than the evaporation duct which are responsible for the occurrence of enhanced signal strengths and that are not being taken into account in the prediction scheme.
4. Explanation of Enhancements Using Meteorological Data From Higher Levels in the Troposphere
4.1. Estimation of Refractivity Lapse Rate
 Hourly weather data (air temperature, pressure and relative humidity) from fixed weather sensors located at the meteorological stations listed in Table 2 were closely analysed in order to corroborate the existence of higher-altitude ducting/super-refractive structures during periods of enhanced signal strength. The refractivity lapse rate, dN/dh (in N-units/km), in approximately the first 100 m of the troposphere was estimated for two years of data. This was achieved by finding the slope of the best-fit line through points on the refractivity vs. height plot for hourly data from the various sites noted above. The mean refractivity gradient was calculated to be approximately −71 N-units/km, showing that on average the conditions in the lowest part of troposphere are very close to being super-refractive. It should be noted that a number of conclusions that are arrived at in this section are based on estimations of the refractivity at different locations. Ideally, co-located refractivity measurements at different altitudes midway between the transmitter and receiver path are required.
 Monthly curves of the mean value of dN/dh between the earth's surface and a height of 1 km derived from historical radiosonde data are presented in ITU-R Recommendation P.453 [ITU-R, 2003]. For the region around the English Channel, this gradient varies between −40 and −50 N-units in the 1 km layer. The departure from these standard values of dN/dh is to be expected since we are dealing with the lowest 100 m of the troposphere in a marine environment. Further statistics in ITU-R Recommendation P.453 indicate that the refractivity gradient in the lowest 100 m above the surface of the earth is less than −100 N-units/km for small percentages of time. Additionally, more recent data extracted from ITU-R databases [ITU-R, 2003] indicates that the refractivity gradient exceeded for 50% of the time in the lowest 65 m of the region is about −55 N-units/km.
 Of 8340 valid Alderney high antenna signal strength and dN/dh data, 730 (8.8%) correspond to cases of enhanced signal strength. The occurrence statistics of the four types of refractive conditions (ducting, super-refraction, normal and sub-refraction) and the corresponding percentages of occurrence of enhanced signal strength at the Alderney high antenna are listed in Table 3. The most important result that may be derived from this table is that 664 out of 730 (91%) cases of signal strength enhancements occur during ducting or super-refractive atmospheric conditions, thus underlining the significance of these nonstandard modes of propagation in the context of long-range UHF propagation. Also, despite the fact that ducting or super-refraction occurs almost 40% of the time, ESS events are recorded only 8.8% of the time. This would suggest that although ducting and super-refraction are primarily responsible for the occurrence of enhanced signal strengths on transhorizon over-sea paths, they do not necessarily always result in ESS (though the likelihood of ESS reception increases). Nevertheless, these anomalous effects do allow radio signals (enhanced or nonenhanced) to reach distant receivers that under normal atmospheric conditions would not propagate beyond the horizon.
Table 3. Occurrence Statistics of the Four Major Types of Refractive Conditions and the Corresponding Occurrence Frequencies of Enhanced Signal Strength at the Alderney High Antenna (August 2003 to August 2005)
Refractivity Gradient, dN/dh(N-Units/km)
Modified Refractivity Gradient, dM/dh(M-Units/km)
Number of Occurrences
Number of Corresponding Occurrences of ESS at the Alderney High Antenna
dN/dh ≤ −157
dM/dh ≤ 0
−79 ≥ dN/dh > −157
78 ≥ dM/dh > 0
0 ≥ dN/dh > −79
157 ≥ dM/dh > 78
dN/dh > 0
dM/dh > 157
 As expected, there are very few cases of enhanced signal strengths during periods of sub-refraction. Furthermore, as Figure 10 illustrates, practically all the ducting events occur in the spring and summer months. Thus, by simply utilising the long-term refractivity lapse rate as an indicator, we can get a reasonably clear verification of the different atmospheric conditions encountered in the lowest region of the troposphere during long-range UHF propagation over the sea.
4.2. Identification of Potential Higher-Altitude Trapping Layers in the Troposphere
 During the spring and summer months, the sea temperature at the CLV is lower than the air temperatures measured at all sites including the CLV, indicative of a stable atmosphere. This confirms that a stable atmosphere correlates well with the occurrence of enhanced signals, and the extent of the stability is not just restricted to the lowest few metres above the surface of the sea. In contrast, during autumn and winter, the average sea temperature well exceeds all the air temperature readings, indicating a highly unstable atmosphere during these periods.
 In addition, there are also inversions in modified refractivity taking place (that is, a decrease in M with height instead of the normal increase in M). Inversions in modified refractivity are an indication of potential ducting layers [Hitney et al., 1985]. In particular, these inversions appear to occur between the heights of the Alderney and Guernsey airports during the spring and summer months.
 In order to identify the reasons for these M-inversions, the monthly occurrence frequency of temperature inversions between Alderney (88.7 m) and Guernsey (102.0 m) and the monthly average of the relative humidity difference between these two heights are shown in the upper and lower frames, respectively of Figure 11. The former parameter has been quantified by determining the rate of incidence of the temperature at the Guernsey Airport altitude exceeding the temperature at the Alderney Airport altitude by more than 1°C. Under normal circumstances, air temperature and water vapour pressure in the troposphere decrease with altitude. However, a temperature inversion and/or rapid lapse rates in the water vapour pressure between two layers of air can result in the occurrence of very high refractivity lapse rates (i.e. dN/dh ≤ −157 N-units/km or dM/dh ≤ 0 M-units/km). Together, or in isolation, these two effects will result in the occurrence of tropospheric ducting layers.
 A definite seasonal pattern is evident from both plots. The occurrence frequency of temperature inversions taking place between the heights of the Alderney and Guernsey airports increases substantially during summer and spring (March to August) while reaching a minimum in the autumn and winter months (September to February). The difference in relative humidity also rises during the spring and summer months, indicating a faster-than-normal RH lapse rate between the heights of 88.7 m and 102.0 m. Thus, the plots verify that the two key processes that result in ducting in the troposphere (manifested in M-inversions) are taking place.
 The monthly occurrence frequency of strong M-inversions between the altitudes of the Alderney and Guernsey airports are presented in the lower frame of Figure 12; that is, the occurrence frequency of MGuernsey − MAlderney being less than −5 M-units. This translates to an equivalent refractivity lapse rate of approximately −533 N-units/km, indicating extreme ducting conditions. For comparison, the monthly occurrence frequencies of ESS cases on the Jersey-Alderney radio path (both high and low antennas) are also shown in the upper frame of Figure 12. Clearly, both plots follow very similar seasonal patterns with the respective occurrence percentages reaching comparable values.
 As mentioned previously, during the spring and summer months there is a definite change in the physical properties of the air at higher altitudes relative to that at the surface. The CLV M (5.0 m above mean sea level) is normally well below the value of M at the Jersey Airport (i.e. 84.0 m above mean sea level). Figure 13 shows the number of monthly occurrences of M-inversions between the surface (i.e. the CLV) and the altitude of the Jersey Airport. Specifically, the graph illustrates the number of cases per month when the surface modified refractivity exceeds the modified refractivity at an altitude of 84.0 m. Over the two years of measurement, it is estimated that there are 937 cases of such inversions in modified refractivity, of which approximately 40% coincide with the occurrence of enhanced signal strengths at Alderney. The monthly variation in this figure is very similar to the trend exhibited by the monthly ESS occurrence curve presented in the upper frame of Figure 12, peaking predominantly in the spring and summer months. Almost 61% of these cases of M-inversions occur in the spring and summer periods. If we include September 2003 – a month in which a relatively large number of enhanced signals were recorded – the latter figure increases to 83%. A strong correlation therefore exists between the occurrence of ESS signals and very high lapse rates of refractivity taking place aloft in the troposphere throughout the spring/summer months.
 Finally, the hourly occurrence frequency of potential trapping layers between the heights of the Guernsey and Alderney airports during periods of enhanced signal strength is depicted in the lower frame of Figure 14. Once again, for comparison, the diurnal variations in the occurrence of enhanced signals at the Alderney high and low antennas are shown in the upper frame (Figure 14). As with the signal strength, the hourly occurrence frequency of higher-altitude M-inversions follows the same diurnal trend, with approximately 40% of the inversions occurring between 1500 UT and 2000 UT, and comparatively fewer existing in the morning.
 In the foregoing analysis, due to the lack of meteorological data above an altitude of approximately 100 m, the upper limit of these potential ducting layers cannot be specified. Nevertheless, the exceptionally high refractivity lapse rates (resulting in M-inversions) caused by temperature inversions and rapid RH lapse rates between approximately 85.0 m and 100.0 m, provide definitive evidence of the existence of higher-altitude ducting structures. These higher-altitude ducting layers are most likely resulting in the occurrence of enhanced signal strengths on over-sea UHF paths, primarily during the warm spring and summer periods.
4.3. Modeling Periods of Enhanced Signal Strength With the Parabolic Wave Equation Method
 It has been shown earlier that during periods of normal reception, when the low-level evaporation duct profile was used as input to the parabolic wave equation model, an excellent correlation was achieved between the PE-predicted and measured signal strengths (Figure 5). During periods of enhanced signal strength however, the PE-predictions using the evaporation duct refractivity profile were relatively inaccurate (Figure 6), providing an indication that certain additional higher-altitude tropospheric phenomena are more dominant at these times. The two preceding sections have focussed on the identification and characterisation of these higher-altitude ducting/super-refractive layers by utilising refractivity data at different altitudes from nearby weather stations. In this section, an attempt has been made to model the propagation effects during periods of signal strength enhancement, using the limited higher-altitude refractivity data available to us.
 Based on the results that have been presented so far indicating the existence of higher-altitude ducting layers in the troposphere, and in the absence of more detailed meteorological data, refractivity measurements from the various weather stations (listed in Table 2) were combined to provide an atmospheric profile for the first 100 m to input to the parabolic equation model and AREPS [SPAWAR, 2004].
Figure 15 presents a comparative plot of the PE-predicted signal strength and the measured signal strength at the Alderney high antenna for the same period of enhanced signal strength (12–18 September 2003) that was presented in Figure 6. In the case of the higher-altitude refractivity data simulations (Figure 15), we observe that there is a much better correlation between the measured and predicted signal strengths. Thus, for periods of enhanced signal strength, the correlation between measurements and predictions is better when a higher-altitude refractivity profile is used than when the low-altitude evaporation duct profile is used; whereas for periods of normal propagation, the evaporation duct model provides a better correlation.
 In conclusion it may be said that a seemingly basic scheme that involves the use of refractivity measurements at different altitudes, from sea level up to approximately 100 m, has been applied to the PE-model and AREPS to produce a signal strength profile that agrees reasonably well with the experimental signal strength during phases of enhanced reception. This result provides confirmation of the existence of higher layer ducting stratifications that become dominant (over the low-lying evaporation duct) during periods of ESS propagation over the sea.
4.4. Analysis of Upper-Air Radiosonde Data From Nearby Stations
 Historical as well as current data from nearby radiosonde stations were closely analysed to corroborate the existence of higher-altitude super-refractive and ducting structures in the English Channel region, particularly when signal strength enhancements are observed at Alderney, Guernsey and Sark.
 Historical upper-air climatology (contained for example in the AREPS database [SPAWAR, 2004]) from nearby radiosonde stations indicate that surface-based ducts and elevated ducts occur reasonably frequently in the region. Camborne (50.22°N, 5.32°W, altitude: 87 m above mean sea level) and Brest/Guipavas (48.45°N, 4.42°W, altitude: 103 m above mean sea level) are two such coastal stations in the vicinity of the radio paths in the Channel Islands. In particular, it was noted that surface-based ducts occur more frequently in the months of May to September with less ducting taking place in the autumn and winter months. This occurrence trend of surface-based ducts in this region agrees well with the seasonal pattern of enhanced signal strength incidence along the Channel Island radio links under consideration. Furthermore, it is also interesting to note that the average height of the trapping layers producing the surface-based ducts at Camborne are reasonably close to the approximate height at which trapping layers (caused by temperature inversions and rapid humidity lapse rates) were observed in the upper-air data from various sources in the Channel Islands.
 High-resolution radiosonde data from two nearby stations were closely analysed for two typical months of normal reception (December 2003) and enhanced signal reception (May 2004). Since there are no radiosonde launch-sites located in the Channel Islands, the closest locations from which high-resolution radiosonde data are available to us are Herstmonceux (50.90°N, 0.32°W, altitude: 52 m above mean sea level) and Camborne (50.22°N, 5.32°W, altitude: 87 m above mean sea level), both located very close to the southern coast of UK. Measurements are recorded at 2-second intervals, twice a day (at 1100 UT and 2300 UT) and were obtained from the British Atmospheric Data Centre.
 The air temperature, pressure and relative humidity (obtained from the air and dew point temperatures) radiosonde measurements from Herstmonceux and Camborne were utilised to produce corresponding values of modified refractivity, M. In order to be sure about the upper extent of these potential ducting structures, weather data was analysed up to approximately twenty height readings. Depending on the case being examined, this roughly corresponds to a maximum altitude of 230–270 m for Herstmonceux and 260–300 m for Camborne.
 During December 2003 (when there are no cases of ESS), examination of the radiosonde data reveals that practically all the valid cases have monotonically increasing values of M from the surface value. Very few inversions in modified refractivity are observed, and if at all, are limited to the first two readings (i.e. up to a maximum of 60–75 m for Herstmonceux and 90–100 m for Camborne). There are practically no significant temperature inversions taking place aloft.
 Hourly ESSs occur at the Alderney high antenna 42% of the time in May 2004. During this month, inspection of the modified refractivity height profiles reveals that there are many more inversions in M compared to December 2003. Furthermore, most of these inversions are accompanied by temperature inversions at the same altitude. Some of the times, a rapid decrease in the relative humidity is also observed. This suggests a correlation between the existence of higher-altitude trapping layers in the troposphere and the occurrence of ESS events along the over-sea radio links under consideration.
 It should be noted that despite providing reasonable evidence in support of the existence of higher-altitude trapping and super-refractive structures, the results from the analysis of the high-resolution radiosonde data and the historical upper-air climatology data should be treated with caution: the data that have been studied are from coastal stations that are located some distance away from the over-sea radio paths being investigated; furthermore, since the data are available only twice a day, tangible conclusions about the temporal scope of these higher-altitude structures cannot be made. Nevertheless, in the absence of more accurate meteorological data, close examination of high-resolution radiosonde data from nearby stations does provide some indication of the strong correlation between the occurrence of enhanced signal strengths and the presence of upper-air super-refractive/ducting structures. Furthermore, the higher-altitude trapping layers are observed reasonably concurrently at different locations around the English Channel region, which strongly indicates (along with the fact that ESSs are observed concurrently at Alderney, Guernsey and Sark) that these are a widespread phenomenon occurring over a large area.
4.5. Analysis of Synoptic Charts
 Areas of high pressure are often associated with anticyclonic weather [McIntosh and Thom, 1973; McIlveen, 1986] that, in general, are characterised by settled weather and light wind conditions, both of which have been observed in the context of ESS occurrences in the Channel Islands. Dry air from the upper troposphere descends and is heated, sometimes producing an inversion of temperature. Furthermore, anticyclones usually extend over large regions and are slow-moving phenomena. In order to further investigate this, synoptic charts of the region (acquired from the UK Met Office) were closely analysed to identify any distinctive meteorological processes occurring during periods of sustained ESS events.
 Of the 119 days on which ESS occur, 50 cases of high-pressure centres were noted to be present directly over the English Channel region, and 41 of these 50 events correspond to days on which ESS cases occurred for four hours or longer. Additionally, it was observed that there are 41 days on which high-pressure centres exist over nearby regions in Europe and in the Atlantic. Thus, of all the days on which ESS occurrences are recorded at Alderney, approximately 91 correspond to days (77%) on which high-pressure cells are observed either directly over or close to the Channel Islands region. It is worth mentioning that the presence of high-pressure cells in the region does not always result in the enhancement of signals. In some cases, there is simply a marginal increase in the received power (but not above the free space threshold), while at other times, the anticyclonic weather does not seem to affect the signal at all.
 It is evident that anticyclonic weather systems (occurring predominantly in the spring and summer months) are a major contributing factor to the occurrence of enhanced signal strengths on over-sea radio paths in the English Channel. It is most likely that the process of subsidence and accompanying advection associated with anticyclones is resulting in the creation of a layer of air at low altitudes within which an inversion in temperature and a strong humidity gradient exists. Historical data shows that advection ducts frequently form over the English Channel during the summer [Bean and Dutton, 1966].
5. Concluding Remarks
 This paper describes a series of long-term UHF propagation measurements carried out over three completely over-sea paths in the English Channel ranging from 21.0 km to 48.5 km in length. The measurements and accompanying statistical analyses that have been presented both here and in the companion paper [Siddle et al., 2007] provide a useful addition to the limited statistics related to the low-altitude propagation of 2 GHz radio waves over long-range sea paths in temperate regions.
 Evaporation ducting and diffraction appear to be the dominant propagation mechanisms at most times. The influence of the evaporation duct during periods of normal propagation has been confirmed by modeling the over-sea propagation conditions using Paulus-Jeske evaporation duct refractivity profiles (generated using sea surface weather data) as input to the parabolic equation method.
 Signal strength enhancements have been observed on all three paths subject to investigation, primarily in the late afternoon and evening periods, in the spring and summer months. During periods of enhanced propagation, which occur approximately 8% of the time on the longest path (48.5 km), the presence of additional higher-altitude ducting/super-refractive structures has been verified and their influence has been modeled with reasonable success. These structures have been characterised by identifying regions of inversions in the estimated modified refractivity profiles and have been shown to be caused by strong lapses of humidity and/or temperature inversions aloft. The higher-altitude ducting/super-refractive structures follow similar diurnal and seasonal trends as the occurrence of ESS. Finally, analysis of both current and historical data from nearby radiosonde stations also point towards the existence of higher-altitude trapping structures at comparable altitudes in the region.
 The authors are grateful to Ofcom (formerly the Radiocommunications Agency) for their support of this work, and to Jon Kay-Mouat (Alderney), St. Peter Port Harbour Authority (Guernsey), Ronez Quarry (Jersey) and Simon de Carteret (Sark) without whose help, cooperation and agreement it would have been impossible for the measurements to have been made. Additionally, the authors wish to thank Tim Lillington (Guernsey Airport Meteorological Observatory), Anthony Pallot (Jersey Airport Meteorological Department) and Brian Bonnard (Alderney) for providing meteorological data and weather information from the Channel Islands, and Wayne Patterson (SPAWAR, USA), for his help in using the AREPS software.