Signal strength variations at 2 GHz for three sea paths in the British Channel Islands: 1

detailed discussion and propagation modelling 2

3

S.D. Gunashekar1, E.M. Warrington1, D.R. Siddle1 and P. Valtr2 4

5

1 Department of Engineering, University of Leicester, Leicester, LE1 7RH, UK. 6

2 Department of Electromagnetic Field, Czech Technical University in Prague, Technická 2, 166 27 7

Prague 6, Czech Republic 8

9

10

Abstract 11

Signal strength measurements at 2 GHz have recently been made on three over-sea paths in the 12

British Channel This paper focuses on explaining the propagation characteristics during periods of 13

normal reception and periods of enhanced signal strength with particular emphasis on a 48.5 km 14

transhorizon path between Jersey and Alderney path. Evaporation ducting and diffraction appear to 15

be the dominant propagation mechanisms at most times. The influence of the evaporation duct 16

during periods of normal propagation has been confirmed by modelling the over-sea propagation 17

conditions using Paulus-Jeske evaporation duct refractivity profiles as input to the parabolic 18

equation method. During periods of enhanced propagation, which occur approximately 8% of the 19

time on the longest path (48.5 km), the presence of additional higher-level ducting/super-refractive 20

structures has been verified and their influence has been modelled with reasonable success. 21

22

1. Introduction 23

Signal strength measurements at 2 GHz have recently been made on three over-sea paths in the 24

British Channel Islands (see Table 1 for transmitter and receiver locations). A summary of these 25

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measurements are presented in the companion to this paper [Siddle et al., 2007], together with a 26

statistical analysis of the received signal strength variations and a comparison with predicted values 27

made using current ITU-R Recommendations. The antenna heights were such that the ends of the 28

two longest links were beyond the optical horizon, and for the shortest link the ends were within the 29

optical horizon for most of the time. A large tidal range is prevalent in the Channel Islands (up to 30

10 m in Guernsey on a spring tide), and consequently the obscuration due to the bulge of the earth 31

varies significantly within the tidal cycle. 32

In order to correlate the varying signal strengths with different weather processes, meteorological 33

data were obtained from a number of sites around the Channel Islands (see Table 2). Hourly, sea-34

level meteorological data were available from the Channel Light Vessel (CLV) anchored in the 35

English Channel to the northwest of all three radio paths. The distance of the CLV to the midpoint 36

of the Jersey-Alderney link is approximately 70 km, and the nominal height at which observations 37

are made at this station is 5.0 m above mean sea level. Higher altitude weather data were obtained 38

from the airports on Jersey, Alderney and Guernsey with heights of 84.0, 88.7, and 102.0 metres 39

above mean sea level respectively. Data from the Maison St. Louis Observatory in St. Helier, 40

Jersey (54.0 m above mean sea level) and from a privately owned weather station in La petit Val, 41

Alderney (10.7 m above mean sea level) were also employed. 42

This paper focuses on explaining the propagation characteristics during periods of normal reception 43

and periods of enhanced signal strength (ESS) with particular emphasis on the 48.5 km transhorizon 44

Jersey to Alderney path (signal strengths that exceed a threshold calculated assuming free space 45

loss along the path are classified as enhanced signals). 46

2. Signal Strength Variations and the Estimated Evaporation Duct Height 47

The correlation between the computed Paulus-Jeske (P-J) evaporation duct heights [Paulus, 1985] 48

and the corresponding hourly signal strengths measured at the Alderney high antenna is shown in 49

Figure 1 together with the ESS threshold and diffraction threshold (assuming mean antenna heights 50

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above sea level for the upper antennas) calculated assuming standard atmospheric conditions. 51

Hourly measurements of air temperature, sea temperature, relative humidity and wind speed made 52

at the CLV were employed in calculating the duct heights according to the P-J formulation. Ideally, 53

the meteorological measurements would have been made close to the midpoint of the propagation 54

paths, however such data were not available and the CLV was the closest available source. Since 55

the CLV was somewhat displaced from the paths of interest, horizontal homogeneity was (by 56

necessity) assumed. 57

To illustrate the effect of the tide, the data have been divided into four parts: cases when the tide 58

height (assumed to be the average of the heights at Jersey and Alderney) between the transmitter 59

and receiver is less than -2 m relative to its mean value, cases when the tide height lies between -60

2 m and 0 m, cases when the tide height lies between 0 m and 2 m, and cases when the tide height 61

between the transmitter and receiver exceeds 2 m. Best-fit lines for each tidal range are also 62

indicated in the figure. The majority of the data lie between the free space and diffraction threshold 63

values indicating that the evaporation duct is able to increase the received signal strength at 64

Alderney well beyond the diffraction level. However, the enhancement in signal strength provided 65

by the evaporation duct is not sufficient to exceed the free space threshold. Additionally, the 66

distribution of data corroborates the observation made in the companion paper [Siddle et al., 2007] 67

that during periods of normal reception, stronger signals are received when tide heights are low and 68

vice versa. 69

At most times during periods of non-ESS, the measured signal strengths increase with duct height, 70

an observation consistent with reports made by various authors [SPAWAR, 2004; Hitney et al., 71

1985; Hitney and Veith, 1990]. Considering only the non-ESS data, the signal strength at the 72

Alderney high antenna increases at the rate of 0.61 dB per metre increase in duct height. For the 73

Guernsey and Sark high antennas, the corresponding values are 0.59 dB/m and 0.25 dB/m 74

respectively. 75

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For the cases of ESS, there is no definite correlation between measured signal strength and 76

calculated evaporation duct height, suggesting either the existence of additional propagation 77

mechanism(s) during these periods, or that under these conditions the estimate of the duct height is 78

incorrect. The inverse relationship between tide height and signal strength is no longer evident, and 79

in general the calculated evaporation duct heights during periods of ESS appear to be less than the 80

duct heights during periods of normal reception (for all valid data, the mean of the P-J evaporation 81

duct height is 8.3 m, reducing to 6.0 m for times when ESS signals are observed at Alderney). 82

It is important to note that the P-J method of estimating evaporation duct heights is an open ocean 83

model [Paulus, 1985; Hitney and Veith, 1990; Babin et al, 1997] that works reasonably well for 84

conditions of atmospheric instability (mostly prevalent in the open ocean) where the air is colder 85

than the sea. During stable periods, when the air temperature exceeds the sea temperature, the P-J 86

method incorporates a temperature correction (on the assumption that an error has been made 87

during measurement) that results in an under-estimation of the evaporation duct height [Paulus, 88

1985]. Whilst it may be true that stable conditions are uncommon in the open ocean [Paulus, 1985; 89

Babin et al, 1997], it is likely that these will occur more often in coastal regions that are particularly 90

prone to land-induced effects such as advection of warm air over a cooler sea surface. This is 91

another reason for the departure from the general trend of higher duct heights corresponding to 92

higher signal strengths during periods of ESS (Figure 1), as these occur primarily when stable 93

atmospheric conditions are prevalent. 94

3. Modeling Periods of Normal Reception with the Parabolic Wave Equation Method 95

With the advent of powerful computers, the computationally intensive parabolic equation (PE) 96

method [Dockery, 1988; Craig and Levy, 1991; Barrios, 1994; Levy, 2000] has become an efficient 97

and practical tool for tropospheric radiowave propagation calculations (see, for example, studies of 98

the effects of tropospheric ducting on the performance of UHF radio links presented by Slingsby 99

[2001] and Sirkova and Mikhalev [2004]). In this section, the propagation conditions during 100

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periods of normal reception in the Channel Islands have been modelled using the PE method. In 101

particular, the split-step parabolic wave equation [Dockery, 1988; Kuttler and Dockery, 1991] that 102

implements impedance-boundary conditions [Dockery and Kuttler, 1996] was utilised for field 103

strength calculations. Predictions for short periods of time (in summer and winter) were also made 104

using the radiowave propagation assessment tool, AREPS [SPAWAR, 2004] that makes use of a 105

hybrid model incorporating the split-step PE method as a sub-model [SPAWAR, 2004]. The results 106

for a few weeks of test cases indicate that the propagation loss values calculated with the PE 107

method and with AREPS are within 1-2 dB of each other. 108

Modified refractivity profiles based on the Paulus-Jeske method [Paulus, 1985] were generated for 109

each hourly reading and utilised as inputs to the PE model. A typical modified refractivity-height 110

profile (for 7 December 2003 at 18:00 UT) illustrating the presence of an evaporation duct is shown 111

in Figure 2 (left frame). For this particular case (air temperature: 7.8°C, sea temperature: 12.9°C, 112

dew point temperature: 2.6°C and wind speed: 14.3 m/s), the evaporation duct height is 14.7 m 113

while the transmitter and receiver heights above sea level are 13.8 m and 11.1 m respectively. For 114

the purpose of illustration, also shown in Figure 2 (right frame) is the height vs. range ray-trace plot 115

for the evaporation duct profile and transmitter specified above (produced in AREPS [SPAWAR, 116

2004]). Trapping of some of the direct and reflected rays between the earth’s surface and the top of 117

the evaporation duct at 14.7 m is evident and consequently propagation occurs for extended ranges 118

within the trapping layer. There is good agreement between the measured signal strength of 119

-86.6 dBm and the predicted signal strength of -88.1 dBm. 120

3.1 Illustrative Examples 121

During a distinctive cold weather period (4-10 December 2003) when normal reception occurs, 122

there is very good agreement between the measured and the PE-predicted signal strengths at the 123

Alderney high antenna (Figure 3). This behaviour was also apparent for the Guernsey and Sark 124

measurements, and for both the high and low antennas. In contrast, for a typical period of signal 125

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enhancement during late summer (12-18 September 2003), there is little correlation between the 126

observations and the PE-predicted values (Figure 4). The predicted signal strengths in this case 127

simply indicate the regular oscillation in received power caused by the tides. 128

3.2 Analysis with Complete Signal Strength Data Set 129

A scatter plot of the measured signal strengths and the PE-predicted signal strengths for all the valid 130

hourly data at the Alderney high antenna is shown in Figure 5 (left frame). The overall correlation 131

for these of data is poor (correlation coefficient = 0.17), however there appears to be a definite 132

correlation between the observed and predicted signal strengths particularly for cases of normal 133

reception. A clearer depiction of this correlation can be seen in the right frame of Figure 5 in which 134

all cases of enhanced signal strength have been removed. The correlation coefficient for these data 135

is 0.45. 136

Every tropospheric duct has a maximum wavelength that it can support, depending upon the 137

geometry and the change in refractivity across the duct. The maximum cut-off wavelength, λmax, 138

provides a general indication of the radio-wave trapping capability of a duct, and is given in 139

Equation 1 [Turton et al, 1988; Brooks et al, 1999]. 140

λmax

= 23

k t δM (1) 141

where t is the duct thickness (m), δM the modified refractivity change across the duct (M-units), 142

and k = 3.77 x 10-3 for a surface-based duct or 5.66 x 10-3 for an elevated duct. 143

It is noteworthy that when only those cases of non-enhanced signal strengths are used in which the 144

corresponding evaporation duct cut-off wavelengths exceed 15 cm, the correlation coefficient 145

between the PE-predicted and measured signal strengths at the Alderney upper antenna increases to 146

0.66. 147

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Thus, even though the cut-off wavelength is simply a rough indication of the trapping capability of 148

an evaporation duct, it can still be used to show that when the likelihood of 2 GHz radio waves 149

getting trapped within a duct is maximized, the evaporation duct does becomes the dominant 150

propagation phenomenon. (For a detailed discussion of the concept of maximum cut-off wavelength 151

for evaporation ducts, the reader is directed to the works of Hall [1979] and Turton et al [1988].) 152

Finally, it is also interesting to note that when the Paulus-Jeske evaporation profiles are used in the 153

PE model, none of the predicted signal strengths exceed the value of the free space threshold. 154

Further evidence of the correspondence between the measured and PE-predicted signal strengths 155

can be obtained from Figures 6 and 7. The cumulative frequency distribution curves for three sets of 156

data with reference to the Alderney high antenna are shown in Figure 6. These data sets are (a) all 157

measured signal strength, (b) only non-enhanced measured signal strength and (c) PE-predicted 158

signal strength (using P-J evaporation duct profiles). The mean hourly signal strengths for the two 159

years of data (for the same three signal strength data sets) are presented in Figure 7. In both figures, 160

the change in shape of the distributions for that of all measured data and for just non-enhanced 161

signal strength data is very significant. The PE-predicted signals provide a much-improved estimate 162

of the measured signal strengths during periods of normal reception. 163

Given that only the effect of the evaporation duct has been accounted for in these cases, this 164

suggests that (a) the evaporation duct is responsible for propagation during periods of normal 165

reception (i.e. cold weather periods) and (b) the evaporation duct refractivity profiles assumed 166

within the PE predictions during periods of enhanced reception are insufficient to model the 167

propagation, at least as it impacts on our paths/antenna heights. The latter conclusion points towards 168

the existence of propagation mechanism(s) other than the evaporation duct which are responsible 169

for the occurrence of enhanced signal strengths and that are not being taken into account in the 170

prediction scheme. 171

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4. Explanation of Enhancements Using Meteorological Data from Higher Levels in the 172

Troposphere 173

4.1 Estimation of Refractivity Lapse Rate 174

Hourly weather data from the meteorological stations listed in Table 2 were closely analysed in 175

order to corroborate the existence of higher-level ducting/super-refractive structures during periods 176

of enhanced signal strength. The refractivity lapse rate, dN/dh (in N-units/km), in approximately the 177

first 100 m of the troposphere was estimated for two years of data. This was achieved by finding the 178

slope of the best-fit line through points on the refractivity vs. height plot for hourly data from the 179

various sites noted above. The mean refractivity gradient was calculated to be approximately 180

-71 N-units/km, showing that on average the conditions in the lowest part of troposphere are very 181

close to being super-refractive. It should be noted that a number of conclusions that are arrived at in 182

this section are based on estimations of the refractivity at different locations. Ideally, co-located 183

refractivity measurements at different altitudes midway between the transmitter and receiver path 184

are required. 185

Monthly curves of the mean value of dN/dh between the earth’s surface and a height of 1 km 186

derived from historical radiosonde data are presented in ITU-R Recommendation P.453 [ITU-R, 187

2003]. For the region around the English Channel, this gradient varies between -40 and -50 N-units 188

in the 1 km layer. The departure from these standard values of dN/dh is to be expected since we are 189

dealing with the lowest 100 m of the troposphere in a marine environment. Further statistics in 190

ITU-R Recommendation P.453 indicate that the refractivity gradient in the lowest 100 m above the 191

surface of the earth is less than -100 N-units/km for small percentages of time. Additionally, more 192

recent data extracted from ITU-R databases [ITU-R, 2003] indicates that the refractivity gradient 193

exceeded for 50% of the time in the lowest 65 m of the region is about -55 N-units/km. 194

Of 8340 valid Alderney high antenna signal strength and dN/dh data, 730 (8.8%) correspond to 195

cases of enhanced signal strength. The occurrence statistics of the four types of refractive conditions 196

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(ducting, super-refraction, normal and sub-refraction) and the corresponding percentages of 197

occurrence of enhanced signal strength at the Alderney high antenna are listed in Table 3. The most 198

important result that may be derived from this table is that 664 out of 730 (91%) cases of signal 199

strength enhancements occur during ducting or super-refractive atmospheric conditions, thus 200

underlining the significance of these non-standard modes of propagation in the context of long-201

range UHF propagation. Also, despite the fact that ducting or super-refraction occurs almost 40% 202

of the time, ESS events are recorded only 8.8% of the time. This would suggest that although 203

ducting and super-refraction are primarily responsible for the occurrence of enhanced signal 204

strengths on transhorizon over-sea paths, they do not necessarily always result in ESS (though the 205

likelihood of ESS reception increases). Nevertheless, these anomalous effects do allow radio signals 206

(enhanced or non-enhanced) to reach distant receivers that under normal atmospheric conditions 207

would not propagate beyond the horizon. 208

As expected, there are very few cases of enhanced signal strengths during periods of sub-refraction. 209

Furthermore, as Figure 8 illustrates, practically all the ducting events occur in the spring and 210

summer months. Thus, by simply utilising the long-term refractivity lapse rate as an indicator, we 211

can get a reasonably clear verification of the different atmospheric conditions encountered in the 212

lowest region of the troposphere during long-range UHF propagation over the sea. 213

4.2 Identification of Potential Higher-Level Trapping Layers in the Troposphere 214

During the spring and summer months, the sea temperature at the CLV is lower than the air 215

temperatures measured at all sites including the CLV, indicative of a stable atmosphere. This 216

confirms that a stable atmosphere correlates well with the occurrence of enhanced signals, and the 217

extent of the stability is not just restricted to the lowest few metres above the surface of the sea. In 218

contrast, during autumn and winter, the average sea temperature well exceeds all the air temperature 219

readings, indicating a highly unstable atmosphere during these periods. 220

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In addition, there are also inversions in modified refractivity taking place (that is, a decrease in M 221

with height instead of the normal increase in M). Inversions in modified refractivity are an 222

indication of potential ducting layers [Hitney et al., 1985]. In particular, these inversions appear to 223

occur between the heights of the Alderney and Guernsey airports during the spring and summer 224

months. 225

In order to identify the reasons for these M-inversions, the monthly occurrence frequency of 226

temperature inversions between Alderney (88.7 m) and Guernsey (102.0 m) and the monthly 227

average of the relative humidity difference between these two heights are shown in the top and 228

bottom frames, respectively of Figure 9. The former parameter has been quantified by determining 229

the rate of incidence of the temperature at the Guernsey Airport altitude exceeding the temperature 230

at the Alderney Airport altitude by more than 1ºC. Under normal circumstances, air temperature and 231

water vapour pressure in the troposphere decrease with altitude. However, a temperature inversion 232

and/or rapid lapse rates in the water vapour pressure between two layers of air can result in the 233

occurrence of very high refractivity lapse rates (i.e. dN/dh ≤ -157 N-units/km or dM/dh ≤ 0 234

M-units/km). Together, or in isolation, these two effects will result in the occurrence of 235

tropospheric ducting layers. 236

A definite seasonal pattern is evident from both plots. The occurrence frequency of temperature 237

inversions taking place between the heights of the Alderney and Guernsey airports increases 238

substantially during summer and spring (March to August) while reaching a minimum in the 239

autumn and winter months (September to February). The difference in relative humidity also rises 240

during the spring and summer months, indicating a faster-than-normal RH lapse rate between the 241

heights of 88.7 m and 102.0 m. Thus, the plots verify that the two key processes that result in 242

ducting in the troposphere (manifested in M-inversions) are taking place. 243

The monthly percentage occurrence of strong M-inversions between the altitudes of the Alderney 244

and Guernsey airports are presented in the bottom frame of Figure 10; that is, the occurrence 245

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frequency of MGuernsey - MAlderney being less than -5 M-units. This translates to an equivalent 246

refractivity lapse rate of approximately -533 N-units/km, indicating extreme ducting conditions. For 247

comparison, the monthly occurrence frequencies of ESS cases on the Jersey-Alderney radio path 248

(both high and low antennas) are also shown in the top frame of Figure 10. Clearly, both plots 249

follow very similar seasonal patterns with the respective occurrence percentages reaching 250

comparable values. 251

As mentioned previously, during the spring and summer months there is a definite change in the 252

physical properties of the air at higher altitudes relative to that at the surface. The CLV M (5.0 m 253

above mean sea level) is normally well below the value of M at the Jersey Airport (i.e. 84.0 m 254

above mean sea level). Figure 11 shows the number of monthly occurrences of M-inversions 255

between the surface (i.e. the CLV) and the altitude of the Jersey Airport. Specifically, the graph 256

illustrates the number of cases per month when the surface modified refractivity exceeds the 257

modified refractivity at an altitude of 84.0 m. Over the two years of measurement, it is estimated 258

that there are 937 cases of such inversions in modified refractivity, of which approximately 40% 259

coincide with the occurrence of enhanced signal strengths at Alderney. The monthly variation in 260

this figure is very similar to the trend exhibited by the monthly ESS occurrence curve presented in 261

top frame of Figure 10, peaking predominantly in the spring and summer months. Almost 61% of 262

these cases of M-inversions occur in the spring and summer periods. If we include September 2003 263

– a month in which a relatively large number of enhanced signals were recorded – the latter figure 264

increases to 83%. A strong correlation therefore exists between the occurrence of ESS signals and 265

very high lapse rates of refractivity taking place aloft in the troposphere throughout the spring/ 266

summer months. 267

Finally, the hourly occurrence frequency of potential trapping layers between the heights of the 268

Guernsey and Alderney airports during periods of enhanced signal strength is depicted in the 269

bottom frame of Figure 12. Once again, for comparison, the diurnal variations in the occurrence of 270

enhanced signals at the Alderney high and low antennas are shown in the top frame (Figure 12). As 271

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with the signal strength, the hourly occurrence frequency of higher-level M-inversions follows the 272

same diurnal trend, with approximately 40% of the inversions occurring between 1500 UT and 273

2000 UT, and comparatively fewer existing in the morning. 274

In the foregoing analysis, due to the lack of meteorological data above an altitude of approximately 275

100 m, the upper limit of these potential ducting layers cannot be specified. Nevertheless, the 276

exceptionally high refractivity lapse rates (resulting in M-inversions) caused by temperature 277

inversions and rapid RH lapse rates between approximately 85.0 m and 100.0 m, provide definitive 278

evidence of the existence of higher-level ducting structures. These higher-altitude ducting layers 279

are most likely resulting in the occurrence of enhanced signal strengths on over-sea UHF paths, 280

primarily during the warm spring and summer periods. 281

4.3 Modeling Periods of Enhanced Signal Strength with the Parabolic Wave Equation Method 282

It has been shown earlier that during periods of normal reception, when the low-level evaporation 283

duct profile was used as input to the parabolic wave equation model, an excellent correlation was 284

achieved between the PE-predicted and measured signal strengths. During periods of enhanced 285

signal strength however, the PE-predictions using the evaporation duct refractivity profile were 286

relatively inaccurate, providing an indication that certain additional higher-level tropospheric 287

phenomena are more dominant at these times. The two preceding sections have focussed on the 288

identification and characterisation of these higher-level ducting/super-refractive layers by utilising 289

refractivity data at different altitudes from nearby weather stations. In this section, an attempt has 290

been made to model the propagation effects during periods of signal strength enhancement, using 291

the limited higher-level refractivity data available to us. 292

Based on the results that have been presented so far indicating the existence of higher-level ducting 293

layers in the troposphere, and in the absence of more detailed meteorological data, refractivity 294

measurements from the various weather stations (listed in Table 2) were combined to provide an 295

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atmospheric profile for the first 100 m to input to the parabolic equation model and AREPS 296

[SPAWAR, 2004]. 297

Figure 13 presents a comparative plot of the PE-predicted signal strength and the measured signal 298

strength at the Alderney high antenna for the same period of enhanced signal strength (12-299

18 September 2003) that was presented in Figure 4. In the case of the higher-level refractivity data 300

simulations (Figure 13), we observe that there is a much better correlation between the measured 301

and predicted signal strengths. Thus, for periods of enhanced signal strength, the correlation 302

between measurements and predictions is better when a higher-level refractivity profile is used than 303

when the low-level evaporation duct profile is used; whereas for periods of normal propagation, the 304

evaporation duct model provides a better correlation. 305

In conclusion it may be said that a seemingly basic scheme that involves the use of refractivity 306

measurements at different altitudes, from sea level up to approximately 100 m, has been applied to 307

the PE-model and AREPS to produce a signal strength profile that agrees reasonably well with the 308

experimental signal strength during phases of enhanced reception. This result provides confirmation 309

of the existence of higher layer ducting stratifications that become dominant (over the low-lying 310

evaporation duct) during periods of ESS propagation over the sea. 311

4.4 Analysis of Upper-Air Radiosonde Data from Nearby Stations 312

Historical as well as current data from nearby radiosonde stations were closely analysed to 313

corroborate the existence of higher-level super-refractive and ducting structures in the English 314

Channel region, particularly when signal strength enhancements are observed at Alderney, 315

Guernsey and Sark. 316

Historical upper-air climatology (contained for example in the AREPS database [SPAWAR, 2004]) 317

from nearby radiosonde stations indicate that surface-based ducts and elevated ducts occur 318

reasonably frequently in the region. Camborne (50.22° N, 5.32° W, altitude: 87 m above mean sea 319

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level) and Brest/Guipavas (48.45° N, 4.42° W, altitude: 103 m above mean sea level) are two such 320

coastal stations in the vicinity of the radio paths in the Channel Islands. In particular, it was noted 321

that surface-based ducts occur more frequently in the months of May to September with less 322

ducting taking place in the autumn and winter months. This occurrence trend of surface-based ducts 323

in this region agrees well with the seasonal pattern of enhanced signal strength incidence along the 324

Channel Island radio links under consideration. Furthermore, it is also interesting to note that the 325

average height of the trapping layers producing the surface-based ducts at Camborne are reasonably 326

close to the approximate height at which trapping layers (caused by temperature inversions and 327

rapid humidity lapse rates) were observed in the upper-air data from various sources in the Channel 328

Islands. 329

High-resolution radiosonde data from two nearby stations were closely analysed for two typical 330

months of normal reception (December 2003) and enhanced signal reception (May 2004). Since 331

there are no radiosonde launch-sites located in the Channel Islands, the closest locations from which 332

high-resolution radiosonde data are available to us are Herstmonceux (50.90° N, 0.32° W, altitude: 333

52 m above mean sea level) and Camborne (50.22° N, 5.32° W, altitude: 87 m above mean sea 334

level), both located very close to the southern coast of UK. Measurements are recorded at 2-second 335

intervals, twice a day (at 1100 UT and 2300 UT) and were obtained from the British Atmospheric 336

Data Centre. 337

The air temperature, pressure and relative humidity (obtained from the air and dew point 338

temperatures) radiosonde measurements from Herstmonceux and Camborne were utilised to 339

produce corresponding values of modified refractivity, M. In order to be sure about the upper 340

extent of these potential ducting structures, weather data was analysed up to approximately twenty 341

height readings. Depending on the case being examined, this roughly corresponds to a maximum 342

altitude of 230-270 m for Herstmonceux and 260-300 m for Camborne. 343

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During December 2003 (when there are no cases of ESS), examination of the radiosonde data 344

reveals that practically all the valid cases have monotonically increasing values of M from the 345

surface value. Very few inversions in modified refractivity are observed, and if at all, are limited to 346

the first two readings (i.e. up to a maximum of 60-75 m for Herstmonceux and 90-100 m for 347

Camborne). There are practically no significant temperature inversions taking place aloft. 348

Hourly ESSs occur at the Alderney high antenna 42% of the time in May 2004. During this month, 349

inspection of the modified refractivity height profiles reveals that there are many more inversions in 350

M compared to December 2003. Furthermore, most of these inversions are accompanied by 351

temperature inversions at the same altitude. Some of the times, a rapid decrease in the relative 352

humidity is also observed. This suggests a correlation between the existence of higher-level 353

trapping layers in the troposphere and the occurrence of ESS events along the over-sea radio links 354

under consideration. 355

It should be noted that despite providing reasonable evidence in support of the existence of higher-356

level trapping and super-refractive structures, the results from the analysis of the high-resolution 357

radiosonde data and the historical upper-air climatology data should be treated with caution: the 358

data that have been studied are from coastal stations that are located some distance away from the 359

over-sea radio paths being investigated; furthermore, since the data are available only twice a day, 360

tangible conclusions about the temporal scope of these higher-level structures cannot be made. 361

Nevertheless, in the absence of more accurate meteorological data, close examination of high-362

resolution radiosonde data from nearby stations does provide some indication of the strong 363

correlation between the occurrence of enhanced signal strengths and the presence of upper-air 364

super-refractive/ducting structures. Furthermore, the higher-level trapping layers are observed 365

reasonably concurrently at different locations around the English Channel region, which strongly 366

indicates (along with the fact that ESSs are observed concurrently at Alderney, Guernsey and Sark) 367

that these are a widespread phenomenon occurring over a large area. 368

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4.5 Analysis of Synoptic Charts 369

Areas of high pressure are often associated with anticyclonic weather [McIntosh and Thom, 1973; 370

McIlveen, 1986] that, in general, are characterised by settled weather and light wind conditions, 371

both of which have been observed in the context of ESS occurrences in the Channel Islands. Dry 372

air from the upper troposphere descends and is heated, sometimes producing an inversion of 373

temperature. Furthermore, anticyclones usually extend over large regions and are slow-moving 374

phenomena. In order to further investigate this, synoptic charts of the region (acquired from the UK 375

Met Office) were closely analysed to identify any distinctive meteorological processes occurring 376

during periods of sustained ESS events. 377

Of the 119 days on which ESS occur, 50 cases of high-pressure centres were noted to be present 378

directly over the English Channel region, and 41 of these 50 events correspond to days on which 379

ESS cases occurred for four hours or longer. Additionally, it was observed that there are 41 days on 380

which high-pressure centres exist over nearby regions in Europe and in the Atlantic. Thus, of all 381

the days on which ESS occurrences are recorded at Alderney, approximately 91 correspond to days 382

(77%) on which high-pressure cells are observed either directly over or close to the Channel Islands 383

region. It is worth mentioning that the presence of high-pressure cells in the region does not always 384

result in the enhancement of signals. In some cases, there is simply a marginal increase in the 385

received power (but not above the free space threshold), while at other times, the anticyclonic 386

weather does not seem to affect the signal at all. 387

It is evident that anticyclonic weather systems (occurring predominantly in the spring and summer 388

months) are a major contributing factor to the occurrence of enhanced signal strengths on over-sea 389

radio paths in the English Channel. It is most likely that the process of subsidence and 390

accompanying advection associated with anticyclones is resulting in the creation of a layer of air at 391

low altitudes within which an inversion in temperature and a strong humidity gradient exists. 392

-16-

Historical data shows that advection ducts frequently form over the English Channel during the 393

summer [Bean and Dutton, 1966]. 394

5. Concluding Remarks 395

This paper describes a series of long-term UHF propagation measurements carried out over three 396

completely over-sea paths in the English Channel ranging from 21.0 km to 48.5 km in length. The 397

measurements and accompanying statistical analyses that have been presented both here and in the 398

companion paper [Siddle et al., 2007] provide a useful addition to the limited statistics related to the 399

low-level propagation of 2 GHz radio waves over long-range sea paths in temperate regions. 400

Evaporation ducting and diffraction appear to be the dominant propagation mechanisms at most 401

times. The influence of the evaporation duct during periods of normal propagation has been 402

confirmed by modelling the over-sea propagation conditions using Paulus-Jeske evaporation duct 403

refractivity profiles (generated using sea surface weather data) as input to the parabolic equation 404

method. 405

Signal strength enhancements have been observed on all three paths subject to investigation, 406

primarily in the late afternoon and evening periods, in the spring and summer months. During 407

periods of enhanced propagation, which occur approximately 8% of the time on the longest path 408

(48.5 km), the presence of additional higher-level ducting/super-refractive structures has been 409

verified and their influence has been modelled with reasonable success. These structures have been 410

characterised by identifying regions of inversions in the estimated modified refractivity profiles and 411

have been shown to be caused by strong lapses of humidity and/or temperature inversions aloft. The 412

higher-level ducting/super-refractive structures follow similar diurnal and seasonal trends as the 413

occurrence of ESS. Finally, analysis of both current and historical data from nearby radiosonde 414

stations also point towards the existence of higher-level trapping structures at comparable altitudes 415

in the region. 416

-17-

Acknowledgements 417

The authors are grateful to Ofcom (formerly the Radiocommunications Agency) for their support of 418

this work, and to Mr. Jon Kay-Mouat (Alderney), St. Peter Port Harbour Authority (Guernsey), 419

Ronez Quarry (Jersey) and Mr. Simon de Carteret (Sark) without whose help, cooperation and 420

agreement it would have been impossible for the measurements to have been made. Additionally, 421

the authors wish to thank Mr. Tim Lillington (Guernsey Airport Meteorological Observatory), Mr. 422

Anthony Pallot (Jersey Airport Meteorological Department) and Mr. Brian Bonnard (Alderney) for 423

providing meteorological data and weather information from the Channel Islands, and Mr. Wayne 424

Patterson (SPAWAR, USA), for his help in using the AREPS software. 425

References 426

Babin, S.M., Young, G.S., and Carton, J.A. (1997), A New Model of the Oceanic Evaporation 427

Duct, Journal of Applied Meteorology, 36(3), 193-204. 428

Barrios, A.E. (1994), A Terrain Parabolic Equation Model for Propagation in the Troposphere, 429

IEEE Transactions on Antennas and Propagation, 42(1), 90-98. 430

Bean, B.R., and E.J. Dutton (1966), Radio Meteorology, U.S. Department of Commerce, National 431

Bureau of Standards Monograph 92. 432

Craig, K.H., and M.F. Levy (1991), Parabolic equation modelling of the effects of multipath and 433

ducting on radar systems, IEE Proceedings – Part F, 138(2), 153-162. 434

Dockery, G.D. (1988), Modeling Electromagnetic Wave Propagation in the Troposphere Using the 435

Parabolic Equation, IEEE Transactions on Antennas and Propagation, 36(10), 1464-1470. 436

Dockery, G.D. and J. R. Kuttler (1996), An Improved-Boundary Algorithm for Fourier Split-Step 437

Solutions of the Parabolic Wave Equation, IEEE Transactions on Antennas and Propagation, 438

44(12), 1592-1599. 439

Hall, M.P.M. (1979), Effects of the Troposphere on Radio Communication, Institution of Electrical 440

Engineers. 441

-18-

Hitney, H.V., J.H. Richter, R.A. Pappert, K.D. Anderson, and G.B. Baumgartner Jr. (1985), 442

Tropospheric Radio Propagation Assessment, Proceedings of the IEEE, 73(2), 265-283. 443

Hitney, H.V., and R. Veith (1990), Statistical Assessment of Evaporation Duct Propagation, IEEE 444

Transactions on Antennas and Propagation, 38(6), 794-799. 445

ITU-R (2003), ITU-R Recommendation P.453, The radio refractive index: its formula and 446

refractivity data, International Telecommunication Union. 447

Kuttler, J.R., and G.D. Dockery (1991), Theoretical description of the parabolic 448

approximation / Fourier split-step method of representing electromagnetic propagation in the 449

troposphere, Radio Science, 26(2), 381-393. 450

Levy, M.F. (2000), Parabolic Equation Methods for Electromagnetic Wave Propagation, IEE 451

Electromagnetic Wave Series 45. 452

McIlveen. J.F.R. (1986), Basic Meteorology – a physical outline, Van Nostrand Reinhold (UK) Co. 453

Ltd. 454

McIntosh, D.H., and A.S. Thom (1973), Essentials of Meteorology, Wykeham Publications 455

(London) Ltd. 456

Paulus, R.A. (1985), Practical Application of an Evaporation Duct Model, Radio Science, 20(4), 457

887-896. 458

Siddle, D.R., E.M. Warrington and S.D. Gunashekar (2007), Signal strength variations at 2 GHz for 459

three sea paths in the British Channel Islands: observations and statistical analysis, Radio 460

Science (ibid). 461

Sirkova, I. and M. Mikhalev (2004), Parabolic-Equation-Based Study of Ducting Effects on 462

Microwave Propagation, Microwave and Optical Technology Letters, 42(5), 390-394. 463

Slingsby, P.L. (1991), Modelling Tropospheric Ducting Effects on VHF/UHF Propagation, IEEE 464

Transactions on Broadcasting, 37(2), 25-34. 465

-19-

Space and Naval Warfare Systems Command (SPAWAR) (2004), Atmospheric Propagation 466

Branch, San Diego, U.S.A., User’s Manual (UM) for Advanced Refractive Effects Prediction 467

System (AREPS). 468

Turton, J.D., D.A. Bennetts and S.F.G. Farmer (1988), “An introduction to radio ducting,” 469

Meteorological Magazine, 117, pp. 245-254. 470

471 472

-20-

472

Table 1: Geographical positions and altitudes (above mean sea level) of the transmitting and 473

receiving antennas. 474 475 476

477

478

479

480

481

482

483

484

Table 2: Geographical positions and altitudes of weather stations in the Channel Islands 485

Latitude

Longitude

Altitude above

mean sea level

Channel Light Vessel 49° 54’ N 02° 54’ W 5.0 m

La Petit Val, Alderney 49° 43’ N 02° 13’ W 10.7 m

Maison St. Louis Observatory,

St. Helier, Jersey

49° 12’ N 02° 06’ W 54.0 m

Jersey Airport 49° 13’ N 02° 12’ W 84.0 m

Alderney Airport 49° 42’ N 02° 13’ W 88.7 m

Guernsey Airport 49° 26’ N 02° 36’ W 102.0 m

486

Table 3: Occurrence statistics of the four major types of refractive conditions and the 487 corresponding percentages of occurrence of enhanced signal strength at the 488 Alderney high antenna (August 2003 to August 2005) 489

Jersey (Transmitter)

Alderney (Receiver)

Guernsey (Receiver)

Sark (Receiver)

Latitude

49° 16’ N

49° 43’ N

49° 27’ N

49° 26’ N

Longitude

02° 10’ W

02° 10’ W

02° 31’ W

02° 21’ W High antenna

17.5 m

13.0 m

14.0 m

13.0 m

Low antenna

14.5 m

10.0 m

10.0 m

10.0 m

Atmospheric

condition

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

Ducting/Trapping dN/dh ≤ -157 dM/dh ≤ 0 734 391 (53.6%)

Super-refraction -79 ≥ dN/dh > -157 78 ≥ dM/dh > 0 2565 273 (37.4%)

Normal 0 ≥ dN/dh > -79 157 ≥ dM/dh > 78 4602 59 (8.1%)

Sub-refraction dN/dh > 0 dM/dh > 157 439 7 (0.9%)

Total 8340 730 (8.8%)

-21-

490

491 492 493 494 495 496 497 498 499 500 501

502

Figure 1: Scatter plot of the Paulus-Jeske evaporation duct heights and the measured signal strengths at the Alderney high antenna with the data characterised according to four distinct tidal ranges

Mea

sure

d si

gnal

stre

ngth

at t

he A

lder

ney

high

ant

enna

(dB

m)

P-J evaporation duct height (m)

-22-

502 503

504

Figure 2: Sample modified refractivity vs. height profile for an evaporation duct (Paulus-Jeske) on 07 December 2003 at 18:00 UT (using weather data from the Channel Light Vessel) (left frame) and the corresponding height vs. range ray-trace plot with the transmitter placed at 13.8 m (right frame)

Evaporation duct height = 14.7 mTransmitter height = 13.8 m

-23-

504 505

506

Figure 3: Comparison between the hourly measured signal strength and the PE-predicted signal strength (using P-J evaporation duct profiles) at the Alderney high antenna during a period of normal reception in winter (4-10 December 2003)

Free space threshold

Hig

h a

nte

nn

a si

gnal

str

engt

h a

t A

lder

ney

(dB

m)

-24-

506

Figure 4: Comparison between the hourly measured signal strength and the PE-predicted signal strength (using the P-J evaporation duct profile) at the Alderney high antenna during a period of signal enhancement in summer (12-18 September 2003)

Hig

h a

nte

nn

a si

gnal

str

engt

h a

t A

lder

ney

(dB

m)

Free space threshold

-25-

506 507

508

Figure 5: Scatter plots showing the correlation between the measured signal strength and the predicted signal strength (using the PE model with P-J evaporation duct profiles as input) for all data (left frame) and for non-ESS data only (right frame)

-26-

508 509 510

511

Figure 7: Graph depicting the hourly means for three sets of signal strength data at Alderney (high antenna): (a) all measured signals (b) only non-enhanced measured signals and (c) PE-predicted signals (using P-J evaporation duct profiles)

Figure 6: Cumulative frequency distribution curves for three sets of signal strength data at Alderney (high antenna): (a) all measured signals (b) only non-enhanced measured signals and (c) PE-predicted signals (using P-J evaporation duct profiles)

Perc

enta

ge e

xcee

ding

sig

nal s

tren

gth

(%)

-27-

511 512 513

514

Figure 8: Graph illustrating the seasonal distribution of ducting events in the Channel Islands (i.e. dN/dh ≤ -157 N-units/km), using refractivity data from nearby meteorological stations

dN/d

h (N

-uni

ts/k

m)

-28-

514 515

516

Figure 9: Monthly plots of the percentage occurrence of temperature inversions between the heights of the Guernsey (102.0 m) and Alderney (88.7 m) airports (top frame) and the average relative humidity difference between these two heights (bottom frame) from August 2003 to August 2005

Mon

thly

ave

rage

of

(Ald

erne

y R

H –

Gue

rnse

y R

H) (

%)

Month

Month

Occ

urre

nce

frequ

ency

of

(Gue

rnse

y Ta

ir –

Ald

erne

y Ta

ir) >

1°C

(%)

-29-

516 517

518

Figure 10: Monthly plots of the percentage occurrence of enhanced signal strengths at the Alderney high and low antennas (top frame) and the corresponding occurrence frequency of modified refractivity inversions between the heights of the Guernsey (102.0 m) and Alderney (88.7 m) airports (bottom frame) from August 2003 to August 2005

-30-

518 519

520

Figure 11: The number of occurrences of M-inversions per month between the heights of the CLV (5.0 m) and the Jersey airport (84.0 m) (August 2003 to August 2005)

Month

Num

ber o

f occ

urre

nce

of M

-inve

rsio

ns b

etw

een

the

CLV

(5.0

m) a

nd J

erse

y A

irpor

t (84

.0 m

)

-31-

520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571

Figure 12: Graph illustrating the diurnal variation in the occurrence of enhanced signal strengths at the Alderney high and low antennas (top frame) and the corresponding occurrence frequency of modified refractivity inversions between the heights of Guernsey (102.0 m) and Alderney airports (88.7 m)

-32-

572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600

601

Figure 13: Comparison between the hourly measured signal strength and the PE-predicted signal strength (using higher-level refractivity data) at the Alderney high antenna during a period of signal enhancement in summer (12-18 September 2003)

Free space threshold