Α neural network based prediction method for troposheric ducting over the Hellenic region

Transcription

1 Α neural network based prediction method for troposheric ducting over the Hellenic region THOMAS D. XENOS Assoc Professor Electrical and Computer Eng. Dept. Aristotelion University of Thessaloniki, Thessaloniki, GREECE Abstract:-The prediction of the tropospheric ducting conditions plays an important role in radio wave propagation. The scope of this work is to predict the tropospheric ducting characteristics over the Hellenic region by means of Artificial Neural Networks using data obtained from radio-balloon observations at Hellenicon Airport. It is proved that the tropospheric ducting manifestation can be predicted very accurately. On the other hand the low-altitude duct characteristics are very accurately predicted in all cases, whereas the characteristics of the high-altitude ones are marginally predicted. This can be due to the fact that the frequency of manifestation of the second ones is low. Keywords: Troposphere, Troposheric Ducting, Neural Networks, Radiowave propagation. 1. Introduction Troposphere is the lowest region of the Earth s atmosphere. It extends from the Earth's surface to an altitude of about 10 Km at mid-latitudes, whereas, its highest altitude may extend up to 6 km in the polar region and up to 18 km in the equator zone. The basic parameters describing troposphere are the pressure, the temperature and the relative humidity. The temperature is decreasing with height at a rate of 6.5 o K/Km or faster, down to about o K at an altitude called tropopause. The most important tropospheric parameter concerning radio-wave propagation is the relative humidity, since it affects the refractive index of the medium and consequently its phase velocity, leading to refraction, reflection and scattering phenomena. The refraction index is defined by n= ε r = c / v, where ε r is the tropospheric dielectric constant, c is the speed of light and v is the phase velocity of the electromagnetic wave in the medium. Since n is slightly greater than unity near the earth's surface ( ), the scaled refraction index N, called refractivity, is used; it is defined as [3]: p 5.6e e N= ( n 1) 10 = + (1) 2 T T T where: p is the total pressure in mbar e is the water vapor pressure T is the temperature in o Kelvin. Given the relative humidity (RH %) and temperature, the water vapor pressure e is calculated by the following set of equations [4]: ( T ) x = (2) T e s =. 11 x 6 e (mbars) (3) RH e= e s (4) 100 An electromagnetic ray presents a curvature equal to 1/R with respect to the earth's surface, where R is the earth's radius ( 6370 Km). The curve representing earth s spherical surface for practical reasons can be transformed to a straight line; then the radio-paths can be transformed to cyclic arcs with a curvature equal to 1/R. If the paths already present a curvature 1/p=-dn/dh, then they can be transformed to cyclic arcs with curvature: = (5) p eq p R In the case of linear instead of curvilinear radiowave paths, the equivalent earth's radius R eq is used; then, (5) is transformed to:

2 1 1 1 = (6) R eq R p To study the refraction gradients, the modified refractivity index is used, defined as [5]: h 6 M = ( n 1+ ) 10 = N h (7) a M s derivative with height is equal to or proportional to the expressions of equations (5) and (6). In the present analysis the gradient dm/dh of the modified refractivity index is used in order to compute the refractive conditions. Tropospheric ducting phenomena occur when the condition dm/dh<0 is met. This may happen in two cases; from near the Earth s surface up to a certain height or from a certain height upwards. The scope of this work is to predict the tropospheric ducting phenomena characteristics over the Hellenic region by means of Artificial Neural Networks using data obtained from radio-balloon observations. The prediction of the ducting conditions plays an important role in radio wave propagation design. To our knowledge no similar works for the Hellenic region have been done. 2. Data and Analysis For the calculation of the refractivity indices variations, data from the Hellinikon airport of Athens/Greece (37 o 53'N, 23 o 43'E) were used. The data cover the period from 1991 to The parameters measured are the temperature, relative humidity and height at constant pressure levels. The measured data were provided by the Hellenic National Meteorological Service (HNMS) and come from observations of radio balloons launched twice a day (00.00 and LT). The measured parameter values were classified according to observation hour, day of year and pressure levels. After a preliminary day-by-day statistical process according to the standard deviation of each pressure level, the data were cleared from unrealistic values. Before the calculation of the refractivity indices, interpolation procedures were followed in order to fill missing values, especially at the lower region of the troposphere where the intensity of its variations is higher and also to create smoother curves of the initial parameters. The first interpolation procedure was made in a day-by-day manner according to the reference pressure levels and was the most important and delicate one since it was applied directly to the initial measured data and returned most of the interpolated values, forming smoothed and enriched curves of temperature, relative humidity and height versus pressure. The next interpolation procedure was also applied on a daily basis in order to transform the data according to a reference height, common to the whole dataset. This procedure also enriched the low altitude values and also detected and corrected days where abnormal fluctuations of the original data were present. After the analysis of the data according to the above procedures, the refractivity index N and the modified refractivity index M were calculated using equations (1-4) and (7). Finally an interpolation procedure for M and N with respect to time was followed for each altitude level, in order to fill in missing values that could not be interpolated in the previous steps [7]. The problem of tropospheric duct prediction was solved in two steps; the first predicted the appearance of the tropospheric duct whereas the second the tropospheric duct characteristics. In both cases the available data set was split in two parts; almost 60% of the original data were used for training the N.N. whereas the remaining 40% was used for assessing the validity of the model. To predict the manifestation of tropospheric ducting the neural networks employed presented the following characteristics (Table 1). Training method func- tions One input two hidden-one output linear for the output layer Table 1. Tropospheric duct manifestation problem. N.N. characteristics Training terminated when both the RMS error was minimized and the average of the squared weight sum, the of the N.N. thresholds and of the active N.N. parameters was stabilized. The training procedure has been repeated several times to obtain an optimum solution. The acceptance level was set to either 5% or 10% error. The second problem, i.e. the tropospheric duct characteristics is a far more complicated problem. To begin with, there has to be a differentiation between ducts starting from or near the sea-level and those starting at higher altitudes. The second ones are rarer. Moreover, the characteristics of the daytime ducts (12.00 LT) seem to be different than the night-time ones (00.00 LT) [7]. In both cases several variations of N.N. have been employed. Table 2 and 3 give the N.N. characteristics selected for the LT and LT dataset respectively.

3 Training method func- tions Two hidden, four output layers. linear for the output layer Table 2. Tropospheric duct LT N.N. characteristics. Training method functions Two hidden, six output layers linear for the output layer Table 3. Tropospheric duct LT N.N. characteristics. The training procedure has been repeated several times to obtain an optimum solution. The acceptance level was set to 4m and 5m in altitude and 10m and 12m in width for the LT and LT ducts respectively. To avoid the additional complexity of using different N.N. in studying lowaltitude and high altitude ducts, N.N. with the same characteristics were used in both cases (Tables 2 and 3). Fig 1. Comparison between measured (o) and predicted (.) days with ducts for the years 1991 and Fig 2. Actual (gray) and predicted days (dark gray) for p= Results and discussion Figures 1-3 show the tropospheric duct manifestation prediction results for LT. Fig 3. Prediction percentage accuracy for p=0.05. From figures 1-3 it can be easily derived that even for p=0.05 the prediction accuracy is very high ranging from over 85% to almost 100%. Similar results can be obtained for LT. In fact this proved a far easier problem since the manifestation of tropospheric ducts at midnight can be somehow deterministically predicted [7, 8].

4 Figures 4 and 5 show the probability of successful annual altitude and width prediction of the low- and high-altitude tropospheric ducts within the specified error margins. Fig. 5. Probability of successful annual width prediction of the low- and high-altitude tropospheric ducts within a 4m and 10m error margin respectively. It has to be pointed out the the low-altitude (below 50m) tropospheric ducts are quite common in Greece, whereas the high altitude (over 50 m) ones are very rare. On the other hand their widths range from a few tenths of meters to a maximum of 225 m. The low-altitude duct characteristics (Figs 4 and 5) are very accurately predicted in all cases (in several cases the prediction accuracy reaches 100%), whereas the high altitude ones are marginally predicted. This can be due to the fact that the frequency of manifestation of the second ones is low and consequently the dataset provided for N.N. training is limited. Fig. 4 Probability of successful annual altitude prediction of the low- and high-altitude tropospheric ducts within a 4 m error margin. 4. Conclusions From the results presented, it can be concluded that both the low-altitude and the high-altitude tropospheric ducts show the following tendencies: The low-altitude (below 50m) tropospheric ducts are quite common in Greece, whereas the high altitude (over 50m) tropospheric ducts are very rare. Their widths range from a few tenths of meters to a maximum of 225 m. The low-altitude duct characteristics are very accurately predicted in all cases (in several cases the prediction accuracy reaches 100%), whereas the high altitude ones are marginally predicted. This can be due to the fact that the frequency of appearance of the second ones in the Hellenic region is low. References [1] Anderson, K. D., "Radar detection of lowaltitude targets in a maritime environment", IEEE Trans. Antennas Propagat., 43, , [2] Christophe et al., "Overview of NATO/AC 243/Panel 3 activities concerning radiowave propagation in coastal environments", AGARD Conference Proceedings 567, Propagation Assessment in Coastal Environments, Bremerhafen, Germany September 1994,

5 [3] Flock L. Warren, "Propagation Effects on Satellite Systems at Frequencies Below 10 GHz", NASA reference publication handbook 1108(2), [4] Lear M. William, "Computing Atmospheric Scale Height for Refraction Corrections", NASA Mission Planning and Analysis Division, Lyndon B. Johnson Space Center, [6] Patterson W.L. et al, "Engineer's Refractive Effects Prediction System (EREPS)", Techn. Doc. 2648, Naval Command, Control and Ocean Surveillance Center, [7] Isaakidis S.A., Xenos T.D., Dris N.A., "Tropospheric Ducting Phenomena over the Hellenic Region", International Journal of Communication Systems, Wiley, V17.4, p ,