A study of rain attenuation on terrestrial paths at millimetric wavelengths in South Africa.

In this thesis, the ITU-R global forecasting techniques for predicting the cumulative distribution of rain attenuation on land links are studied using a five-year rain rate data for twelve different geographical locations in the Republic of South Africa. A comparative study is done on these available rain attenuation modes; The ITU-R model, Crane Global model, and the Moupfouma models at different frequencies and propagation path lengths based on the actual I-minute integration time rain rate exceedances at 0.01% of the time averaged over a 5-year period for each geographic location . Rainfall Forecasting and Modeling Calculation of Specific Rainfall on Terrestrial Line of Sight Links 64 5.1.1 Results and discussion of the different locations 65 5.2 Estimation of road attenuation using different existing models on the available ones.

Appendix A: Calculation of Specific Rainfall Damping 103 Appendix B: Estimation of Road Damping Using Different Existing Models on the.

LIST OF TABLES

The Atmosphere

The Troposphere
Effect of the Troposphere on Terrestrial Radio Paths

Our environment consists of the land (lithosphere), the water (hydrosphere), the air (atmosphere) and the living things (biosphere) around us [7]. The atmosphere is divided into different layers according to the variability of the temperature gradient with height. The air pressure at the top of the troposphere is only 10% of that at sea level [11].

Scattering due to irregularities in the upper layers of the troposphere, which allows signals to reach very long distances (several kilometers) and can be used to provide tropospheric links.

Fig. 1.1 Generalized vertical distribution of temperature and Pressure up to 110 km [8]

Nature of Precipitation

Effects of Hydrometeors on Microwave Propagation

Change in the ray path shape that ceases to be a straight line and becomes curved, in response to the changes in the refractive index along the path;. Creation of privileged directions for wave propagation (channels) that enable signals to reach distances much greater than would be possible without atmosphere;. Considerable fluctuations in the amplitude of the received signal due to the existence of several signal paths, each with its own time delay, which interfere with each other.

Types of Rain

South Africa Climate and Physical Features

The southern parts of the country border the Indian Ocean and the Atlantic Ocean. One of the greenest and best clay areas in the country is KwaZulu-Natal, which comprises only 7.6% of the country and is the second most populous province. Between the mountains and the humid subtropical coast are savanna grasslands, and here and along the coast there are also areas of native forest.

The fertility of the soil and relatively good rainfall (more than 1000 mm per year) make agriculture crucial to the economy.

Fig 1.2 Map of South Africa and neighbouring countries [15]

Seasonal Variability of South Africa Rainfall

The winter rainfall area is a relatively small area along the west and south-west coasts of the Cape and has a Mediterranean-type rainfall regime with striking winter maxima. In the summer rain zone covering most of the rest of the country, light orographic rains are common along the windward slopes of the eastern slope. In most of the summer rainfall area, intense convective storms, accompanied by thunder, lightning, sudden showers, and often hail, are the source of most rainfall.

Between the winter and summer rain areas lies a transition area where rain comes in all seasons - i.e. neither in winter nor in summer is more than 60 percent of the annual total recorded.

Justification for the Dissertation

It can be seen that rainfall in South Africa is unreliable and unpredictable across the country. This means that a solid database of propagation measurements must be made as close as possible to the target geographic area of operations. However, most of the measurements in the databases were made in temperate areas of the Northern Hemisphere [23].

The purpose of this dissertation is to obtain sufficient measurements of propagation for different geographical locations in the Republic of South Africa (as shown in Figure 1.2) over several years, which can then be used to classify the country into different climatic rainfall zones.

Aims and Objectives of the Study

This is achieved through the five years of rain rate measurements for twelve different geographical locations in South Africa provided by the South African Weather Service to predict the rain rate and rain attenuation on country roads in South Africa. To determine the cumulative distributions of the invasion rate for different geographical locations in South Africa. To classify South Africa into different climatic rainfall zones based on the available data and measurements.

To estimate the attenuation of the ram path exceeded 0.01% of the time for different climate zones in South Africa using different existing models.

Chapter Summary

Propagation in a Lossless Dielectric Medium
Propagation in a Low-loss Dielectric medium

To determine the rain rate exceedance for 0.01% of the time for each location. To calculate specific rain attenuation for different locations based on available rain data. The effect of rain on terrestrial radio paths and existing rain attenuation models as applied to this research center are also reviewed in reasonable depth.

Maxwell's equations provide the starting point for research into the propagation of electromagnetic waves through the propagation medium [24].

Free Space Loss

Tropospheric Loss

If the rate of refractive index decrease with height is sufficiently large and extends over a sufficient height interval and horizontal extent, it can give rise to atmospheric channels that conduct radio energy beyond the normal horizon. Over a large horizontal area, the refractive index suddenly decreases with height, this can lead to partial reflection of radio energy. On line-of-sight paths, these refractive index fluctuations can cause significant scintillation (rapid fading), which is greater in magnitude for longer or higher frequency [12].

There may also be reflected rays (or more than one) from layers of abrupt change in refractive index with height.

Fig 2.1 Tropospheric effects of cloud and precipitation on radiowave propagation [12]

Propagation Loss' Factors

Atmospheric Gaseous Losses
Rain Losses
Clouds and Fog Losses
Obstacle Losses

6A reduction in the amplitude (field strength) of a radio wave caused by an irreversible conversion of energy from the radio wave to matter in the propagation path. 7A process by which the energy of a radio wave is dispersed in direction due to interaction with inhomogeneities in propagation. Scattering by the very small liquid water droplets that make up liquid water mists near the Earth's surface and liquid water clouds higher in the atmosphere can cause significant attenuation at the higher frequencies.

Clouds in the most active parts of mid-latitude thunderstorms can have liquid water contents above 5 gI m3• The heights of liquid water in the atmosphere can range from 0 km above the ground (a fog) to 6 km above the ground in strong updrafts in convective clouds.

Fig 2.2 gives the specific attenuationS due to absorption of oxygen and water vapour near the surface of the earth as a function of frequency

Building Material Losses
Foliage Losses
Absorption and Scattering Effects
Excess Attenuation Due to Rainfall
Specific Attenuation
Rain Attenuation Prediction Methods

Prediction of Long-term Rainfall Attenuation Statistics
Moupfouma Model
The Crane Attenuation Models

Chapter Summary
Global Studies on Radioclimatological Modeling
African Scenario
Asian Scenario
European Scenario
South America Scenario
North America Scenario
Chapter Summary
Rain Rate Statistics Measurement in South Africa
Effect of Integration Time on Rain Rate Statistics
Comparison of Rain Rate Statistics for Different Geographical Locations
Cumulative Distribution of Rain Intensities for Different Geographical Locations
Determination of South Africa Rain Climatic Zones
Chapter Summary
Computation of Specific Rain Attenuation on Terrestrial Line-of-Sight Links

Results and Discussion from the Various Locations

Estimation of Path Attenuation Using Different Existing Models on the A vailable Local Rain Data

Results and Discussion of the Existing Models on the Available Local Data

Prediction of Rain Attenuation Model for South Africa from Measurements

Signal Attenuation Measurements in Durban for the Various Months
Rain Attenuation Modeling in Durban at 19.5 GHz from Measurements
Discussion for Rain Attenuation Measurements

Statistical Analysis of the Rain Attenuation Models Predicted from the Measurements in Durban
Application of Rain Attenuation Predictions
Chapter Summary
Conclusion
Recommendation for Future Work

Step 1: Get the R001 rain rate that is exceeded 0.01% of the time (with an integration time of 1 minute). This model provides a prediction of attenuation or integrated path velocity given an equally likely value of rain rate [2]. The following chapter focuses on the various works done by different authors on the prediction of precipitation rate and attenuation in different parts of the world.

Moupfouma [44], developed two more general global models using two parameters, one of which was easily exceeding the rain rate for 0.01% of the time. In the range 0.1–1% of the year, the distribution function for the hourly observations gives a good estimate of the distribution function for the mean rain rate at minute I. The available measured instantaneous rain rate distributions were then pooled (combined) for each of the climatic regions.

The annual 1-minute integration time rain rate statistics at 0.0 I% exceedance of time for each site within the same climatic regions are compared. FigAA The variation in annual rainfall intensity (mm/h) exceeded 0.01% of the time for South Africa (temperate and inland temperate regions). This difference is almost close to that of Richards Bay, which is located in the coastal savannah.

Using actual local rain rate data from these locations, the rain amount exceeded 0.01% of the time was determined from the cumulative distributions of their precipitation amounts for a one-minute integration time (see Chapter 4). Also, the ITU-R [38] mean Ro.ol values for rainfall for 0.01% of the time were exceeded with a one minute integration time of the mean year for South Africa, to calculate the specific attenuation for these locations . From the earlier sections in this chapter, it appears that the specific rain attenuation (reduction per unit length) predicted for each geographic location based on the average point rain rate statistics exceeded 0.01% of the time with an integration time of 1 minute may be is not too high. sufficient for estimating the attenuation along a radio link path [2], [28].

In addition, there is a non-uniformity of rain along the path of the radio link and a non-linear dependence of the specific attenuation due to rain. The attenuation behavior due to rain in the month of October in Durban at 19.5 GHz is shown in Fig. Therefore, the damping recorded at these high rain rates reflects a corresponding reduction in effective path length.

Table 2.1 Frequency dependent coefficients for estimating specific attenuation [36]

APPENDICES

A1.5 Specific rain attenuation for horizontal and vertical polarization in U1undi; takes rain rate exceeded for 0.01% of the time. B2.2 Rainfall prediction models for terrestrial line-of-sight links for Cape Town for frequencies 20 GHz and 30 GHz. B2.3 Rain attenuation prediction models for ground line-of-sight links for Brandvlei for frequencies 20 GHz and 30 GHz.

B2.4 Rain attenuation prediction models for terrestrial line-of-sight links for Pretoria for the 20 GHz and 30 GHz frequencies. B2.5 Rain attenuation prediction models for terrestrial line-of-sight links to Durban for the 20 GHz and 30 GHz frequencies. B2.6 Rain attenuation prediction models for terrestrial line-of-sight links to Ladysmith for the frequencies 10 GHz, 20 GHz, 30 GHz and 40 GHz.

B2.7 Rain attenuation prediction models for terrestrial line-of-sight links for Newcastle for frequencies 10 GHz, 20 GHz, 30 GHz and 40 GHz. B2.8 Prediction models for rain attenuation for terrestrial line-of-sight connections for Vryheid for frequencies 10 GHz, 20 GHz, 30 GHz and 40 GHz. B2.9 Rain attenuation prediction models for terrestrial lines of sight for Pietermaritzburg for frequencies 10 GHz, 20 GHz, 30 GHz and 40 GHz.

B2.10 Rain attenuation prediction models for line-of-sight terrestrial links for Ulundi for frequencies 10 GHz, 20 GHz, 30 GHz and 40 GHz. B2.11 Rain attenuation prediction models for line-of-sight terrestrial links for East London for frequencies 10 GHz, 20 GHz, 30 GHz and 40 GHz.