Analysis of climatic trend - University of Wales, Newport
Reliable Broadband Satellite-integrated Network Design through Propagation and Networking Solutions
By
Sahena Begum
Submitted in partial fulfilment for the degree of Doctor of Philosophy
[pic]
University of Glamorgan
May, 2009
Acknowledgements:
May I take this opportunity to express my gratitude to my Director of Studies, Dr. Ifiok Otung, for his scholastic guidance, constant support and care throughout the years. I sincerely appreciate the valuable time and close attention he has given me during the course of this study. If it were not his vision and expertise, this endurance would have been prolonged. I also wish to thank Prof. Khalid Al-Begain, my second supervisor.
I would like to thank all my colleagues at the University for their time and company.
My heartiest thanks to my friends back home, here and abroad for their love, support and encouragement.
My special “Thank You” to all my family for their love.
Abstract:
Satellites will play an indispensable role in the deployment of commercial networks to meet an increasing demand for supporting multimedia services at high data rates. Next generation satellite systems, operating at high frequency bands offer large bandwidth and are able to provide broadband services. To interface satellite links with existing terrestrial networks for providing communication access to a variety of users directly, several performance issues need to be addressed. Current thesis presents a technically viable satellite-integrated network model that is efficient in carrying broadband services to users over a wide scattered area.
Accurate prediction of attenuation level is necessary for a reliable network model to operate with required service availability. Long term rainfall data has been analysed to characterise attenuation level at a selected region such as Dhaka. It is shown that rainfall is highly seasonal and attenuation level is quite high during monsoon. However, the seasonal behaviour of rainfall can be exploited to improve the link availability. Radar and rain gauge measurements at Sparsholt are also used to find rain cell size distribution, which is an important factor in site diversity implementation to combat severe rain fade. It is found that convective rain cell has extension in the region of 10 km.
The network model is designed with dimensioning the effective bandwidth to support a number of users over the satellite link by taking into account the multimedia traffic characteristics. Concatenated coding, a robust coding scheme is implemented to improve the link quality at a level required to deliver broadband services. The ITU-T performance objectives of 7.5×10[pic] for CLR and 1.4×10[pic] for CER over satellite links are met at a required Eb/No of 2.95 dB and 2.88 dB respectively. Different enhancement mechanisms for optimum TCP performance are implemented to combat the large propagation delay associated with a satellite link. It is revealed through the simulation that TCP performance over a satellite link is as efficient as terrestrial links with these enhancement mechanisms.
Finally, the overall performance of the designed network is evaluated through link budget analysis and simulation. An innovative downlink power control strategy has been implemented to maintain the link during the rainiest months. The interference level due to high power satellite transmission in the designed system is also calculated to protect other existing communication links sharing the same frequency bands.
A feasible broadband network designed with characterising propagation as well as networking issues will efficiently deliver broadband communication services to a large population promptly and in a cost-effective manner. Such a network solution will be in the realm of current R & D towards broadband satellite networks.
Table of Contents
Acknowledgements ii
Abstract iii
Table of Contents iv
List of Figures vii
List of Tables ix
Acronyms and abbreviations x
1 Introduction 1
1.1 Introduction: 2
1.2 Research Motivation: 4
1.3 Overview - contents of thesis: 7
1.4 Summary of novel contribution: 11
2 Radio Wave Propagation 14
2.1 Introduction: 15
2.2 Earth’s atmosphere: 17
2.3 Interaction mechanism: 18
2.3.1 Absorption- 19
2.3.2 Scattering- 19
2.3.3 Refraction- 19
2.3.4 Diffraction- 19
2.3.5 Multipath- 19
2.3.6 Scintillation- 20
2.3.7 Fading- 20
2.3.8 Frequency Dispersion- 20
2.4 Propagation factors (above 3 GHz): 20
2.4.1 Gaseous attenuation- 21
2.4.2 Hydrometeor attenuation- 21
2.4.3 Depolarisation- 21
2.4.4 Radio noise- 22
2.4.5 Angle of arrival variations- 22
2.4.6 Bandwidth coherence- 22
2.4.7 Antenna gain degradation- 23
2.4.8 Tropospheric scintillation- 23
2.5 Propagation factors (up to 3 GHz): 23
2.5.1 Ionospheric scintillation- 24
2.5.2 Polarisation rotation- 24
2.5.3 Group delay- 24
2.5.4 Multipath fading and scintillation- 25
2.6 Propagation impairments in an earth-space link: 25
2.6.1 Free space attenuation- 25
2.6.2 Phenomenon associated with refractive index- 26
2.6.3 Attenuation by atmospheric gases- 26
2.6.4 Hydrometeor attenuation- 27
2.6.5 Fog and cloud attenuation – 27
2.6.6 Rain attenuation- 28
2.7 Conclusions: 34
3 Characterisation of Rain Attenuation in Bangladesh 36
3.1 Introduction: 37
3.2 Rainfall characterisation: 38
3.2.1 Seasonal precipitation trends: 38
3.2.2 Annual precipitation trend (Dhaka): 41
3.3 Annual and monthly rainfall distribution: 45
3.4 Rain rate distribution: 49
3.4.1 Seasonal variations in rain rate distribution: 54
3.5 Rain attenuation: 56
3.6 Risk estimation in rain attenuation prediction: 62
3.7 Conclusions: 66
4 Rain Cell Size Distribution 70
4.1 Introduction: 71
4.2 Rain cell translation velocity: 73
4.3 Wind field from Doppler analysis: 76
4.4 Comparison of cell translation speed, Doppler speed and wind speed: 79
4.5 Rain cell size distribution: 81
4.6 Conclusions: 85
5 Traffic Analysis and Network Design 89
5.1 Introduction: 90
5.2 Telecommunication infrastructure in Bangladesh: 90
5.3 Dimensioning traffic path: 93
5.3.1 Traffic load or intensity: 94
5.3.2 Grade of Service (GoS): 96
5.3.3 Traffic model: 97
5.3.3.1 Capacity by Erlang B traffic model: 98
5.3.3.2 Capacity by Erlang C traffic model: 99
5.4 Characteristics of Ethernet data: 101
5.4.1 Self-similarity: 101
5.4.2 Properties of self-similarity: 102
5.4.3 The Hurst parameter- The measure of self-similarity: 105
5.5 Dimensioning Ethernet traffic by Closed-Queuing Network (CQN) model: ……………………………………………………………………………105
5.6 Satellite-integrated Network model: 109
5.7 Conclusions: 111
6 Performance of ATM over Satellite Links 115
6.1 Introduction: 116
6.2 ATM layer and QoS parameters: 118
6.3 Concatenated coding with Reed-Solomon and convolution coding: 121
6.4 Parameters affected by coding scheme in satellite-integrated networks: 124
6.5 Performance of ATM with concatenated coding scheme: 126
6.6 Performance of TCP in terms of segment error ratio with concatenated coding scheme: 128
6.7 Conclusions: 130
7 TCP/IP Performance Evaluation over Satellite Links 134
7.1 Introduction: 135
7.2 TCP overview: 136
7.2.1 TCP vanilla or Tahoe: 137
7.2.2 TCP Reno: 138
7.2.3 TCP New Reno: 139
7.2.4 SACK: 140
7.3 TCP throughput: 140
7.4 Enhancing TCP over satellite channels: 142
7.4.1 Path MTU discovery: 142
7.4.2 TCP window scaling: 142
7.4.3 Selective Acknowledgements: 144
7.4.4 Forward error correction: 144
7.4.5 Split TCP connections: 145
7.4.6 Multiple data connections (XFTP): 146
7.5 MATLAB simulation environment for TCP protocol: 146
7.6 Variation of TCP throughput with propagation delay: 151
7.7 TCP (Reno) throughput performance over satellite link: 152
7.8 Conclusions: 162
8 Link Budget Analysis and Simulation 166
8.1 Introduction: 167
8.2 Link budget set up: 168
8.3 Link budget analysis: 169
8.4 Time series simulation: 174
8.5 Conclusions: 179
9 Conclusions and Further Work 181
9.1 Conclusions: 182
9.2 Future prospects: 186
Appendix-A 187
Appendix-B 191
Appendix-C 195
List of Figures
Figure 1.1: Comparison of predicted attenuation by SAM and ITU-R model (using ITU-R rain rate for both models) 5
Figure 1.2: Block diagram of thesis layout 8
Figure 2.1: Schematic representation of the propagation of a transverse electromagnetic wave 15
Figure 2.2: Atmospheric layers 17
Figure 3.1: Rain gauge stations over Bangladesh 39
Figure 3.2: Seasonal rainfall trend in different stations over Bangladesh (1961-2003) 40
Figure 3.3: Annual rainfall time series in Dhaka (1961-2003) 41
Figure 3.4: Annual rainfall trend in Dhaka (a) 1961-1969 (b) 1970-1975 (c) 1976-81 (d) 1982-88 (e) 1989-94 (f) 1995-03 42
Figure 3.5: Power spectral density of annual rainfall in Dhaka (1961-2003) 43
Figure 3.6: Annual rainfall distribution in Dhaka 46
Figure 3.7: Rainfall distribution for the month July in Dhaka 47
Figure 3.8: Rainfall distribution for the month January in Dhaka 48
Figure 3.9: Measured annual rainfall statistics in comparison with predicted rain rate by Rice-Holmberg model for Sparsholt, UK and Surabaya, Indonesia 50
Figure 3.10: Rain rates for different stations (Bangladesh) by Rice-Holmberg model 53
Figure 3.11: Seasonal variations of rainfall rates by Rice-Holmberg model in Dhaka 55
Figure 3.12: Predicted rain attenuation using R-H and ITU rain rate for Dhaka 57
Figure 3.13: Approximation of attenuation reduction factor using Sparsholt data 58
Figure 3.14: Comparison of predicted attenuation applying reduction factor (Dhaka) 60
Figure 3.15: Attenuation for various levels of availabilities as a function of the month 62
Figure 3.16: Rain attenuation risk estimation for Bangladesh 64
Figure 3.17: Rain attenuation variability from three standard deviations bound for Bangladesh 65
Figure 4.1: PPI of reflectivity field, dBz (colorbar on right) on 23 March,2004 73
Figure 4.2: Identified rain cell on PPI on 23 March, 2004 (a) Cell in the previous scan; (b) Correlated cell in the next scan 75
Figure 4.3: Motion vector on an azimuth plane 77
Figure 4.4: Doppler velocity from event on 23 March, 2004 at a range 58 km 78
Figure 4.5: Comparison of wind speed, Doppler wind speed and cell translation speed 80
Figure 4.6: Cumulative distribution of rain cell sizes obtained from rain gauge data 83
Figure 4.7: Cumulative distribution of rain cell sizes obtained from radar observation 84
Figure 5.1: Microwave coverage of Bangladesh (source-BTTB annual report, 2001) 91
Figure 5.2: Traffic flow model 94
Figure 5.3: Closed-queueing network (CQN) model 106
Figure 5.4: A satellite-integrated network model 110
Figure 6.1: An ATM cell 118
Figure 6.2: ATM HEC operation at receiver 120
Figure 6.3: Block diagram of a concatenated coding scheme 121
Figure 6.4: Array representation of symbol interleaver 123
Figure 6.5: Performance of concatenated coding scheme on AWGN channels 123
Figure 6.6: CLR and CER vs. Eb /No (filled circles are extrapolated values) 127
Figure 6.7: TCP Segment Error Ratio vs. Eb /No (filled circles are extrapolated values) 129
Figure 7.1: The chronology of slow start and congestion avoidance algorithm of TCP 147
Figure 7.2: Illustration of RTT calculation 148
Figure 7.3: Comparison of results from MATLAB with experiment 150
Figure 7.4: TCP throughput at different propagation delay 151
Figure 7.5: Throughput for different file sizes without loss (Maximum TCP window 64 Kbytes) 152
Figure 7.6: Window dynamics for file size of 200 Kbytes (Maximum TCP window 64 Kbytes) 153
Figure 7.7: Window dynamics for file size of 10 Mbytes (Maximum TCP window 64 Kbytes) 154
Figure 7.8: Throughput for a 10 Mbytes file transfer for different TCP window sizes (without loss) 155
Figure 7.9: Throughput for a 10 Mbytes file transfer for different TCP window sizes (with loss and without loss) 156
Figure 7.10: Throughput for a 10 Mbytes file transfer for different TCP window sizes with large segment size (no loss) 157
Figure 7.11: Throughput for a 100 Mbytes file transfer for different TCP window sizes with large segment size (no loss) 158
Figure 7.12: Comparison of percentages of throughput with different window sizes over terrestrial and satellite links 159
Figure 7.13: Comparison of percentages of throughput with different window sizes and file sizes over satellite links 160
Figure 7.14: Comparison of percentages of throughput over satellite links with loss and without loss 161
Figure 8.1: Comparison of Attenuation level for Sparsholt and Dhaka 174
Figure 8.2: Attenuation time series for Sparsholt and Dhaka 175
Figure 8.3: Instantaneous link behaviour with rain event for Dhaka (Zonal beam) 176
Figure 8.4: Instantaneous link behaviour with rain event for Dhaka (Spot beam) 177
List of Tables
Table 2.1: Propagation concerns for satellite communication systems 33
Table 3.1: Statistical parameters for different periods of Annual rainfall in Dhaka 43
Table 3.2: Comparison of ITU-R and R-H derived rain rates against measurement at Sparsholt (UK) 51
Table 3.3: Comparison of ITU-R and R-H derived rain rates against measurement at Surabaya (Indonesia) 51
Table 3.4: Rice-Holmberg parameters for different stations in Bangladesh 52
Table 3.5: Comparison of the 0.01% rain rates of ITU-R and R-H computations 54
Table 4.1: Statistics of rain cells from rain gauge and radar data 82
Table 5.1: Telecommunication indicator 2007 92
Table 5.2: Traffic model characteristics 97
Table 6.1: Effects of bit errors on ATM cell 119
Table 6.2: ATM performance objectives for satellites (class 1 services) 128
Table 8.1: Earth stations parameters 168
Table 8.2: Satellite parameters 169
Table 8.3: Most significant link budget parameters (clear air) for zonal beam 170
Table 8.4: Most significant link budget parameters (under rain) for zonal beam 171
Table 8.5: Most significant link budget parameters (under rain) for spot beam 172
Acronyms and abbreviations
4G – Fourth-Generation Wireless
4KSS – 4K Slow Start
AAL – ATM Adaptation Layer
ACK – Acknowledgements
ARQ – Automatic Repeat Request
ATM – Asynchronous Transfer Mode
AWGN – Additive White Gaussian Noise
BDP – Bandwidth Delay Product
BER – Bit Error Ratio
B-ISDN – Broadband- Integrated Service Digital Network
BPSK – Binary Phase Shift Keying
BSS – Broadcasting Satellite Service
BTTB – Bangladesh Telegraph and Telephone Board
CAMRa – Chilbolton Advanced Meteorological Radar
CBR – Constant Bit Rate
CER – Cell Error Ratio
CLR – Cell Loss Ratio
CMR – Cell Misinsertion Rate
CQN – Closed Queuing Network
CTD – Cell Transfer Delay
DSL – Digital Subscriber Line
DSD – Drop Size Distribution
EIRP – Effective Isotropically Radiated Power
ENSO – El-Nino Southern Oscillation
FEC – Forward Error Correction
FFT – Fast Fourier Transform
FS – Fixed Service
FSS – Fixed Satellite Service
ftp – file transfer protocol
GEO – Geostationary Earth Orbit
GoS – Grade of Service
HEC – Header Error Control
http – hyper text transfer protocol
ICT – Information and Communication Technology
IETF – Internet Engineering Task Force
IP – Internet Protocol
IS – Infinite Server
IT – Information Technology
ITU-R – International Telecommunication Union- Radio Recommendation
LAN – Local Area Network
MTU – Maximum Transmission Unit
PAWS – Protection Against Wrapped Sequence
PCM – Pulse-code Modulation
PER – Packet Error Ratio
PD – Propagation Delay
PS – Processor Sharing
QoS – Quality of Service
QPSK – Quaternary Phase Shift Keying
RCVWND – Receive Window
RFC – Request for Comments
R-H – Rice- Holmberg
RS – Reed-Solomon
RTO – Retransmission Time-out
RTT – Round Trip Time
RTTM – Round Trip Time Measurement
SACK – Selective Acknowledgements
SAM – Simple Attenuation Model
SECR – Severely Errored Cell Ratio
SER – Segment Errror Ratio
SMTP – Simple Mail Transfer Protocol
ssthresh – slow start threshold
TCP – Transmission Control Protocol
TDM – Time Division Multiplex
TDMA – Time Division Multiple Access
TRMM – Tropical Rainfall Measuring Mission
UDP – User Datagram Protocol
UMTS – Universal Mobile Telecommunication Systems
VHF – Very High Frequency
VSAT – Very Small Aperture Terminal
WAN – Wide Area Network
WiMAX – Worldwide Inter-operability for Microwave Access
www – world wide web
CHAPTER 1
Introduction
1 Introduction:
Satellites form an essential part of telecommunications systems worldwide, carrying large amounts of data and telephone traffic in addition to television signals from its inception. Satellites have the advantage of offering a number of exclusive features not readily available by other means of communication [1] [2]
• Minimum extra transportation cost associated with the “last-mile”
• Cost effectiveness on thin routes.
• Satellites can be used in remote areas as gap fillers and in areas where terrestrial coverage is inadequate or unreliable to off-load traffic
• More robustness to meteorological conditions
• Scalable architecture i.e. a new user can join a satellite communication system by acquiring the necessary tools
Optical fibre systems tend to concentrate around developed areas giving further impetus for growth to an already developed region whereas satellites give an equal coverage to all regions because of their inherent broadcasting capability. Thus for example, the advantages of broadband could reach the remotest regions instantly using a satellite system whereas it is likely to be a long time before optical fibre links to the region can be economically justified.
In recent years the increased demand for electronic connectivity across the globe has been driving newer technologies such as Universal Mobile Telecommunication Systems (UMTS), Worldwide Interoperability for Microwave Access (WiMAX), fourth-generation wireless (4G) etc to meet the requirements of multimedia communications. Due to its unique broadcasting capability and large global coverage, satellite systems will play a significant role in tandem with these newer technologies, either on its own or as a complementary means of communication. In this context, the next generation satellite systems often termed “broadband satellite networks”, “multimedia satellite networks” or “satellite-fibre networks” are being envisaged to support various data communication services such as private intranet, digital video broadcasting and internet.
Many of the applications under the broadband umbrella are Transmission Control Protocol/Internet Protocol (TCP/IP) based high availability services that require higher speed and higher quality of data transmissions with more efficiency and reliability than existing services such as voice, broadcasting etc. Higher frequency bands such as Ku-band (14/12 GHz) and Ka-band (30/20 GHz) proved attractive to provide these services although these bands are more susceptible to rain fading [3]. TCP protocol does not perform efficiently in a satellite environment due to errors induced and large propagation delay imposed by the channel. Thus providing broadband services at required availability and optimum fidelity require newer solution at the corresponding layer of the protocol stack or cross-layer protocol optimisation [4]. Interoperating satellite communication networks with terrestrial networks where the major technologies are Internet Protocol (IP) and Asynchronous Transfer Mode (ATM) require propagation as well as networking solutions which are technically challenging to meet the different Quality of Service (QoS) requirements at relevant layers. Numerous mitigation techniques have been investigated for the efficient transport of ATM and TCP/IP applications over the satellite network at different functional layers and these are often inter-related [2] [4].
In this thesis the main goal was to design a reliable satellite-integrated network by finding suitable solution to combat inherent characteristics of satellite link such as fading and the large propagation delay to deliver the broadband traffic at the required QoS. A tropical region such as Bangladesh has been chosen to realise the satellite-integrated network, where rainfall level is generally high and where most of the city areas have well developed communication networks whereas rural areas are cut-off from the mainstream communication infrastructure. A feasible broadband network will allow multimedia services to a large population promptly and in a cost-effective manner, especially for users separated by long distances, including rural areas and remote islands.
2 Research Motivation:
Following the challenging issues outlined above of the satellite-integrated network, prime consideration for the system design was given to improving the rain attenuation prediction model based on local meteorological measurements, and optimising the satellite link quality as well as TCP/IP performance evaluation in delivering broadband services at the desired quality to end users.
Accurate prediction of the rain attenuation level is crucial in the system design procedure such as choice of services at the selected frequency and service availability. There are several rain attenuation prediction models [5] [6] [7] [8] available to quantify the rain attenuation level, which were developed for different climatic conditions. Figure 1.1 shows the predicted attenuation by Simple Attenuation Model (SAM) and International Telecommunication Union (ITU-R) model using ITU-R rain rate for Bangladesh at 18.7 GHz frequency band and 46.10 path elevation angle. As can be seen, SAM predicts significantly different attenuation level compared to ITU-R model, which is usually applied for benchmarking the attenuation level for commercially designed systems. For a more reliable prediction, a novel rain attenuation prediction model has been developed over the region based on the local meteorological measurements.
[pic]
Figure 1.1: Comparison of predicted attenuation by SAM and ITU-R model (using ITU-R rain rate for both models)
As the rain structure in the slant path is directly related to rain rate, rainfall volume and local climate [9], the statistical knowledge of the structure of rain is important in site diversity implementation. Rain gauge records and radar data for a large number of years are used to find the rain cell size distribution over Sparsholt, UK, a temperate climate. Convective rain cells extend over more limited regions in tropical regions, a typical cell size ranging from 2-5 km and often lasting for only 10- 20 minutes [10] [11]. The information of intense rain cell extension over UK could still be applicable over Bangladesh in setting-up the diversity stations as the simultaneous occurrence of rain within this close proximity will be very low.
A critical point in designing a satellite-integrated network is to dimension the required bandwidth to carry the multimedia traffic. Different traffic models are analysed and Closed Queuing Network Model (CQN) is applied to calculate the bandwidth for multimedia traffic.
Different error control schemes can be found in the research literature to carry efficiently either the ATM or TCP/IP traffic over the error prone satellite links [2] [12]. A robust concatenated coding scheme has been implemented which is efficient in delivering the QoS parameters at ATM layer as well as in reducing the Packet Error Ratio (PER) at TCP layer required for optimum TCP performance.
The above concatenated coding scheme presents TCP with a more reliable satellite channel. Nevertheless, TCP performance is still degraded as its feedback triggered algorithm suffers severely due to a large propagation delay. To address these deficiencies and optimise TCP performance on the designed satellite network, selected parameters such as window scaling and Path MTU (Maximum Transmission Unit) discovery have been tuned which are currently standardised by Internet Engineering Task Force (IETF) [13].
The interest in extending broadband services over satellite links have triggered a wide spectrum of research topics concerning different protocol layers- application, transport, data link and physical link. In conjunction with protocol layers, different performance attributes such as router buffer size, queuing discipline, link quality and network availability have also been addressed for satellite-multimedia networks. However, the vast majority of studies concentrated on protocol performance. This thesis presents several novel approaches namely improving the system availability and link quality, dimensioning the required capacity of the link to carry the traffic and tuning the TCP parameters for optimum network performance. The novel network is constructed with the optimised parameters to deliver high availability broadband services at the required quality.
3 Overview - contents of thesis:
Following the introductory chapter the thesis is divided into two major sections, namely Propagation and Networking, containing different items of work undertaken in the research leading to a reliable satellite-integrated network. The initial design starts with addressing physical layer performance analysis and characterising rain attenuation level over the region, which is the primary parameter affecting network availability. A robust coding scheme is implemented at the physical layer to optimise the QoS parameters at ATM layer. End-to-end performance enhancement technique was addressed at the TCP layer for efficient data transfer in the network. System level analysis of the network was then performed by incorporating individual parameters from different layers. The structure of the thesis is depicted in Figure 1.2.
Figure 1.2: Block diagram of thesis layout
Chapter 2 looks into the fundamentals of radio wave propagation to provide a general understanding of the topics before attempting to develop a solution. The Earth’s atmosphere, interaction mechanism, propagation factors and different propagation impairments are all described. A detailed derivation of rain attenuation computation method is presented, rain being the biggest obstacle to the design of earth-space communication links at Ku-band frequencies and above.
Chapter 3 describes the characterisation of rain attenuation over Bangladesh, the main propagation topic undertaken in the research, using 40 years of rainfall data. This will be incorporated in the link budget analysis to work out the availability of the network. The analyses include periodicity of annual rainfall, rainfall distribution, seasonal variation of rainfall etc which are vital to be considered in improving the system availability.
Chapter 4 discusses the rain cell size distribution derived from long term rain gauge and radar measurements at Sparsholt, UK. By tracking the rain cell in consecutive radar scans, cell translation velocity was obtained, which was then applied in the synthetic storm technique to find the cell size distribution.
Chapter 5 presents a novel satellite-integrated network based on dimensioning the effective bandwidth. Different conventional traffic models are investigated detailing their application for different types of traffic. Based on the characteristics of multimedia traffic, CQN model was chosen for calculating the required bandwidth.
Chapter 6 provides the error control mechanisms to improve the link quality at a desired BER required to deliver ATM QoS parameters as well as to reduce PER for optimum TCP performance. Concatenated coding scheme with Reed Solomon (RS) outer code and ½ rate convolution inner code with block interleaving of depth five in between is implemented to improve the link quality.
Chapter 7 summarises the two performance enhancing mechanisms standardised by IETF that can be deployed end-to-end, namely window scaling and Path MTU discovery. The algorithms of TCP Reno are implemented in MATLAB to analyse the impact of performance enhancing schemes.
Chapter 8 gives the link budgets, methodology and final results of the simulation scenario. Seasonal variability of rainfall, spot beam configuration and attenuation time series generated from Sparsholt event are incorporated in the link budget analysis and simulation.
Chapter 9 finally concludes the thesis summarising the work as a whole and highlights directions that could lead to further research in the relevant area.
4 Summary of novel contribution:
The novel contribution of the thesis is summarised as follows-
• An improved rain attenuation prediction model. This work was published in Radio Science [14].
• Rain cell size distribution in the UK. This work was published in EuCAP2006 [15] and in Radio Science [16].
• Determination of cell translation velocity by tracking intense rain cells in successive radar PPI (Plan Position Indicator) scans.
• Novel satellite-integrated network with effective link bandwidth.
• Optimisation of ATM QoS parameters and TCP Segment Error Ratio (SER) with concatenated coding scheme. The last two works will be submitted to International Journal of Satellite Communications and Networking [17] for publication.
• Optimisation of TCP throughput over satellite links.
References:
1. M. Riccharia, Satellite Communication Systems, McMillan, 1995.
2. A. Jamalipour, M. Marchese, H. S. Cruickshank, J. Neale and S. N. Verma,
“Guest Editorial- Broadband IP Networks via Satellites- Part 1, IEEE Journal
On selected Areas in Communication, Vol. 22, No. 2, 2004, pp. 213-217.
3. D. Panagopoulos, M. Arapoglou and P.G. Cottis, “Satellite Communications at Ku, Ka and V bands, Propagation Impairments and Mitigation Techniques”, IEEE Communications Surveys and Tutorials, Vol.6, No. 3, Third Quarter 2004.
4. G. Giambene and S. Kota, “Cross-layer Protocol Optimization for Satellite Com-
munications Networks: A Survey”, International Journal of Satellite
Communication, 24, 2006, pp. 323-314.
5. ITU-R, “Propagation data and prediction methods required for the design of Earth-space telecommunication systems”, Rec. ITU-R P.618-8, 2003.
6. W.L. Stutzman and W.K. Dishman, “A Simple Model for The Estimation of
Rain-induced Attenuation along Earth-to-Space Paths at Millimeter
Wavelengths”, Radio Science, Vol. 17, 1982, pp. 1465-1475.
7. M. J. Leitao and P. A. Watson, “Method for Prediction of Attenuation on Earth-
space Links based on Radar Measurements of the Physical Structure of Rainfall”,
IEE proceedings, Vol.133, No.4, July 1986, pp. 429-440.
8. R. K. Crane, “Prediction of Attenuation by Rain”, IEEE Transactions on
Communications, Vol. Com-28, No.9, September 1980, pp. 1717-1733.
9. G.H. Bryant, I. Adimula, C. Riva and G. Brussaard, “Rain Attenuation Statistics
from Rain Cell Diameters and Heights”, International Journal of Satellite
Communication, 19, 2001, pp. 263-283.
10. H. E. Green, “Propagation Impairments on Ka-Band SATCOM Links in
Tropical And Equatorial regions”, IEEE Antennas and Propagation Magazine,
Vol. 46, No. 2, 2004, pp.31-45.
11. Q. W. Pan and G. H. Bryant, “Results of 12 GHz Propagation Measurements in
Lae (PNG)”, Electronics Letter, 28, 1992, pp. 2022-2024.
12. I. F. Akyildiz and S. Jeong, “Satellite ATM Networks: A Survey”, IEEE Com-
Munications Magazine, July 1997, pp. 30-43.
13. M. Allman, D. Glover, J. Griner, K. Scott, J. Touch and D. Tran, “Ongoing TCP
Research Related to Satellites”, RFC 2760, 1998.
14. S. Begum and I. E. Otung, “Characterisation of Rain Attenuation in
Bangladesh and Application to Satellite Link Design”, Radio Science, Vol. 43,
RS1008, doi:10.1029/2007RS003634, 20008.
15. S. Begum, C. Nagaraja and I. E. Otung, “Analysis of Rain Cell Size Distribution
for Application in Site Diversity”, European Conference on Antennas and
Propagation, Nice, France, 6-10 November, 2006.
16. S. Begum and I. E. Otung, “Rain Cell Size Distribution Inferred from Rain
Gauge and Radar Data in the UK”, Radio Science, Vol. 44,
RS2015, doi:10.1029/2008RS003984, 20009.
17. S. Begum and I. E. Otung, “Design and Performance Analysis of a Satellite-,
integrated Network”, International Journal of Satellite Communications and
Networking, submitted, 2009.
CHAPTER 2
Radio Wave Propagation
1 Introduction:
An electromagnetic wave, referred to as a radio wave at radio frequencies, is characterised by variations of its electric and magnetic fields (Figure 2.1). The oscillating motion of the field intensities vibrating at a particular point in space at a frequency f excites similar vibrations at neighbouring points and the wave is said to travel or to propagate. Mathematically,
S = E×H (2.1)
where S is the Poynting vector representing the direction of propagation and power per unit area of the wave.
[pic]
Figure 2.1: Schematic representation of the propagation of a transverse electromagnetic wave
The wavelength λ of the electromagnetic wave is the spatial separation of two successive oscillations, which is the distance the wave travels during one cycle of oscillation. Number of oscillations per unit time is termed as the frequency of the electromagnetic wave. The frequency and the wavelength in free space are related by
λ = c/f
where c is the propagation or phase velocity of light in vacuum given as
c = [pic], εo is the permittivity which is 10[pic]/36 π Farad per metre
μo is the permeability which is 4π × 10[pic]Henry per metre
resulting c = 3×10[pic]m/s.
A radio signal will be degraded depending on frequency, temperature, pressure and water vapour concentration while propagating through the earth’s atmosphere. It is important to characterise the signal interaction with the atmosphere at different frequencies to calculate attenuation level to design the communication link [1].
This chapter presents the earth’s atmosphere, interaction mechanism of radio waves with the atmosphere and propagation factors. Different propagation impairments in an earth-space link are also presented with detailed description of rain attenuation in particular which is the main impairment factor that needs to be considered in this thesis to design an earth-space communication link.
2 Earth’s atmosphere:
A signal travelling between an earth station and a satellite must pass through the earth atmosphere which is divided into categories as in Figure 2.2. The troposphere is the region of the atmosphere adjacent to the earth and extending upwards to about 10 km. It is in this region the clouds are formed. The ionosphere extends from about 50 km to roughly 2000 km above the surface. Due to the radiations from the sun, the ionosphere takes on a stratified character called the D, E and F layers. The radiations are mainly ultraviolet rays, γ rays and cosmic particles such as electrons and protons.
[pic]
Figure 2.2: Atmospheric layers
The D layer is found occasionally at a height of 50 to 100 km in the daytime and is of little importance. The E layer is a relatively permanent layer at about 100 km. During the day the ionic density in this layer is strongest and may almost vanish at night due to the recombination of ions. The F layer is also more or less permanent at about 300 km. In the daytime, it divides into the F[pic] and F[pic]layers and is subject to erratic variations. Apart from seasonal variations, sun-spot activity causes further magnetic storms and consequent radio fadeouts [1].
It is the ionised layers high up in the ionised atmosphere and the moist, turbulent layers way down in the lower reaches of the neutral atmosphere which are the principal factors in radio wave propagation. The various regions in the ionosphere act as reflectors or absorbers to radio waves at frequencies below about 30 MHz, and space communications is not possible. As the frequency is increased, the reflection properties of the E and F layers are reduced and the signal will propagate through. Radio waves above about 30 MHz will propagate through the ionosphere with degradation of varying degrees depending on the frequency, geographic location and time of the day. As the frequency of the wave increases, ionospheric effects become less significant and above about 3 GHz the ionosphere is essentially transparent to space communications [1] [2].
3 Interaction mechanism:
The interactions of the radio wave with the atmosphere occur through the following mechanism [1] [3] [4]:
1 Absorption-
Absorption is a reduction in the amplitude of a radio wave caused by an irreversible transfer of energy from the radio wave to matter in the propagation path.
2 Scattering-
Scattering is a process in which the energy of a radio wave is dispersed in direction due to interaction with inhomogeneities in the propagation medium.
3 Refraction-
This is a change in the direction of propagation of a radio wave resulting from the spatial variation of refractive index of the medium.
4 Diffraction-
A change in the direction of propagation of a radio wave resulting from the presence of an obstacle, a restricted aperture, or other object in the medium is referred to as a diffraction. This phenomenon can be explained by physical optics rather than geometrical optics.
5 Multipath-
The propagation condition that results in a transmitted radio wave reaching the receiving antenna by two or more propagation paths is called multipath. This effect can arise due to refractive index irregularities in the troposphere or ionosphere, or from structural and terrain scattering on the earth’s surface.
6 Scintillation-
Owing to the presence of irregularities inside the medium, an electromagnetic wave undergoes rapid variations in its amplitude, phase and directions of arrival. These variations are called scintillations and are characterised by their depth, period and speed of variation.
7 Fading-
Fading is the variation of the amplitude of a radio wave caused by changes in the transmission path with time. The terms fading and scintillation are often used interchangeably; however, fading is usually used to describe slower time variations, on the order of seconds or minutes, while scintillation refers to more rapid variations, on the order of fractions of a second in duration.
8 Frequency Dispersion-
Frequency dispersion is a change in the frequency and phase components across the bandwidth of a radio wave, caused by a dispersive medium. A dispersive medium is one whose constitutive components (permittivity, permeability and conductivity) depend on frequency (temporal dispersion) or wave direction (spatial dispersion).
4 Propagation factors (above 3 GHz):
Generally, radio waves with frequency 3 GHz and above are affected through the following propagation factors primarily produced in the troposphere [1] [2] [3]:
1 Gaseous attenuation-
Gaseous attenuation is an absorption process that results in a reduction in signal amplitude caused mainly by oxygen and water vapour. Gaseous attenuation increases with increasing frequency and is dependent on atmospheric temperature, pressure and humidity.
2 Hydrometeor attenuation-
Condensation of atmospheric water vapour gives rise to hydrometeors such as rain, clouds, fog, snow, ice which attenuate radio waves through absorptive and scattering effects. Rain attenuation is the dominant impairment in the space communication systems operating at 10 GHz and above. Cloud and fog attenuations are much less severe than rain attenuation; however, they must be considered in link design, particularly for frequencies above 15 GHz. Dry snow and ice particle attenuation is usually so low that it is unobservable on space communications link operating below 30 GHz.
3 Depolarisation-
Depolarisation is a phenomenon whereby all or part of a radio wave emitted with a given polarisation no longer has any determined polarisation after propagation. Rain and ice depolarisation can be a problem in the frequency bands above about 12 GHz, particularly for “frequency reuse” communication links which employ dual independent orthogonal polarised channels in the same frequency band to increase channel capacity. Depolarisation caused by multipath propagation is generally limited to very low elevation angle space communication and is dependent on the polarisation characteristics of the receiving antenna.
4 Radio noise-
Radio noise is the presence of undesired signals or power in the frequency band of a communication link generated by natural or man-made sources. It can degrade the noise characteristics of receiver systems and affect antenna design or system performance. Atmospheric gases (oxygen, water vapour), rain, clouds and surface emissions are all natural noise sources and effective in the frequency range of 1 GHz and above. Man-made sources include- other space or terrestrial communication links, electrical equipment and radar systems. Extraterrestrial cosmic noise must only be considered for frequencies below about 1 GHz,.
5 Angle of arrival variations-
Angle of arrival variations are a refraction process caused by refractive index changes in the transmission path. It is only observable with large aperture antennas (10 metres or more) and at frequencies well above 10 GHz. The angle of arrival change results in an apparent shift in the location of satellite position and can be compensated for by re-pointing the antenna.
6 Bandwidth coherence-
Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered "flat", or in other words the approximate maximum bandwidth or frequency interval over which two frequencies of a signal are likely to experience comparable or correlated amplitude fading. If the multipath time delay spread equals D seconds, then the coherence bandwidth Wc in hertz is given approximately by the equation: Wc = 1/2πD. The coherence bandwidth for typical space communication frequencies is one or more gigahertz, and is not expected to be a severe problem.
7 Antenna gain degradation-
Amplitude and phase fluctuations induced by the atmosphere can produce perturbations across the antenna aperture, resulting in a reduction of total power available at the antenna feed. The resulting effect is termed as antenna gain degradation. This effect can be produced by intense rain; however it is observable with very large aperture antennas at frequencies above about 30 GHz and for very long path lengths through the rain, i.e. low elevation angles.
8 Tropospheric scintillation-
Refractive index irregularities due to high humidity gradients and temperature inversion layers in the first few kilometres of altitude cause tropospheric scintillation. The effects are seasonally dependent, vary day to day, and with local climate.
5 Propagation factors (up to 3 GHz):
The major propagation factors which affect space communication at frequencies above ionospheric penetration frequency and up to about 3 GHz are as follows:
1 Ionospheric scintillation-
Ionospheric scintillation is produced by electron density irregularities near the altitude of maximum electron density, the F region, at approximately 200-400 km in altitude. These conditions are most prevalent in the equatorial regions at high latitude location and during periods of high sunspot activity. Ionospheric scintillations have been observed at frequencies from 20 MHz through 6 GHz, with the bulk of data being amplitude scintillation observations in the VHF (30-300 MHz) bands. Scintillations can be very severe in the frequency bands below 300 MHz and often are the limiting factor for reliable communications system performance in the VHF bands.
2 Polarisation rotation-
In the presence of earth’s magnetic field, the ionosphere exhibits birefringence, splitting the incident wave into ordinary and extraordinary components. Since these waves propagate with different phase velocities, the resultant plane of polarisation of the combined wave rotates as it propagates. This effect is known as Faraday rotation.
3 Group delay-
Due to the presence of free electrons in the propagation path the propagation time from satellite to the Earth is longer than the time calculated in free space. The wave propagates with a group velocity lower than the speed of light in vacuum. The resulting delay, known as the group delay or group propagation time, induces an error in the estimation of the distance from the satellite. The effect can be extremely critical for radio-navigation or satellite ranging links which require an accurate knowledge of range and propagation time for reliable performance. Group delay will be about 25 microseconds at 100 MHz for an earth-space path at a 30 degree elevation angle and is approximately proportional to the reciprocal of the frequency squared.
4 Multipath fading and scintillation-
Multipath fading and scintillation are the variations in the amplitude and phase of a radio wave, caused by terrain and surface roughness conditions. This problem is important in terrestrial communications and must also be considered for earth-space transmissions at low elevation angles, and for VHF mobile satellite links.
6 Propagation impairments in an earth-space link:
Besides free space attenuation, propagation impairments on earth-space links mainly involve effect of irregularities of refractive index inside the troposphere and the ionosphere, absorption due to atmospheric gases, namely oxygen and water vapour, and attenuation caused by hydrometeors like clouds, rain, fog, snow and ice [1] [5].
1 Free space attenuation-
Radio waves experience transmission loss due to the dispersion of energy which takes place as the wave travels away from the transmitter. This free space attenuation A0 is given by
A[pic]= 20log[pic]([pic]) dB (2.2)
where λ is the wavelength and d is the distance travelled between the transmitter and receiver.
2 Phenomenon associated with refractive index-
The refractive index of the media (troposphere, ionosphere etc.) varies along the direction of propagation of a radio wave. Accordingly, an electromagnetic wave will follow a curvilinear trajectory and the wave is said to be refracted. The curvature of the trajectory is proportional to the refractivity gradient. From this phenomenon originate a number of different other effects such as lengthening of the path, changes in the propagation velocity or the angle of arrival, scintillation etc.
3 Attenuation by atmospheric gases-
The transmission attenuation caused by atmospheric gases results from the molecular resonance of oxygen and water vapour. An oxygen molecule has a single permanent magnetic moment. At certain frequencies, its coupling with the magnetic field of an incident electromagnetic wave causes resonance absorption. In particular, at frequencies around 60 GHz a coupling occurs between the intrinsic moment of the electron, its spin and the rotational energy of the molecule, generating a series of absorption lines quite close to each other in the spectrum. These absorption lines come to merge, thus forming a single and broad absorption band. The water vapour molecule behaves like an electric dipole. The interaction of such a molecule with an incident wave disorientates the molecule by generating an additional internal potential energy. The maximum attenuation reached in the band around 22 GHz is due to the resonance of the water molecule which starts to rotate while absorbing a high proportion of the incident electromagnetic energy.
For evaluating the attenuation due to atmospheric gases it is required to take into account the contribution of all the absorption lines of oxygen and water vapour and the continuous spectrum of the absorption due to water and ice. There are several models [6][7][8] to find the attenuation level by atmospheric gases. As a numerical application of the ITU-R model, the specific attenuation due to atmospheric gases in the case of an average atmosphere (7.5 g/m[pic]) was found to be equal to approximately 0.2 dB/km and 15 dB/km at 20 and 60 GHz respectively [2].
4 Hydrometeor attenuation-
Hydrometeor refers to the condensed form of water vapour such as rain, hail, ice, fog, cloud or snow etc. Hydrometeors attenuate the signal in two ways: the energy absorption by Joule effect and the wave diffusion induced by the particles.
5 Fog and cloud attenuation –
Attenuation due to clouds and fog is determined on the basis of the total water content per unit volume. The liquid water concentration is typically equal to approximately 0.05 g/m[pic] inside a moderate fog (visibility of the order of 300 m) and of 0.5 g/m[pic]inside a thick fog (visibility of the order of 50 m). In the case of clouds and fogs consisting entirely of very small droplets with diameter less than 0.01 cm on average, the Rayleigh approximation is valid at frequencies lower than 200 GHz. Attenuation can therefore be expressed as a function of the total water content per unit volume (g/m[pic]). Under these assumptions, the specific attenuation in clouds or fogs is
[pic] (dB/km)
where γ[pic] is the specific attenuation inside the cloud in dB/km, K[pic] is the specific attenuation in dB/km per g/m[pic] and M is the concentration of liquid water in clouds or in fog in g/m[pic].
In the case of a moderate fog (0.05 g/m[pic]), the orders of magnitude for attenuation are 0.002 and 0.1 dB/km at the 20 and 60 GHz frequency ranges respectively, while for a thick fog (0.5 g/m[pic]) they reach 0.02 and 1 dB/km respectively.
6 Rain attenuation-
Due to the condensation of water vapour, the diameter of the droplets from which cloud forms increases, either by coalescence or by the absorption of the water vapour around them. With the increase of size, the fall speed also increases and precipitation occurs either in the form of drizzle if the diameter of the droplets lies between 0.1 and 0.5 mm or in the form of rain, if the droplets are of larger dimensions. If the temperature falls below 0[pic]C, hydrometeors occur in solid form (snow or hailstones).
Rain drops both absorb and scatter energy. Rain also causes depolarisation, rapid amplitude and phase fluctuations, antenna gain degradation and bandwidth coherence reduction. The signal loss by rain in an earth-space link is an integral of all the individual increments of attenuation caused by the drops encountered along the path. This is the physical approach to predicting rain attenuation. Prediction of rain attenuation relies more particularly on precipitation intensities (rain rate) expressed in mm/h. Rainfall is highly variable in time and space. In the mid latitudes stratiform rain can span diameters up to several hundreds of kilometres with vertical heights of 4 to 6 km. Convective rains, often associated with thunderstorm events, are of much smaller horizontal extents, usually only several kilometres but can extend to much greater vertical heights because of convective upwelling [6].
The classical development for the determination of the radio wave attenuation due to rain assumes the following:
• The intensity of the wave decays exponentially as it propagates the volume of the rain.
• The water drops are spherical, and
• The contributions of each drop to attenuation are additive and independent of the other.
To determine the specific attenuation let us consider a plane wave of transmitter power P[pic] incident on a volume of uniformly distributed spherical water drops, all of radius ‘r’, extending over length L. The received power P[pic] will be
[pic] (2.3)
where k is the attenuation coefficient for the rain volume, expressed in units of reciprocal length.
The attenuation of the wave is expressed as a positive decibel value given by
[pic]
Converting the log to the base e
[pic]
= 4.343kL (2.4)
The attenuation coefficient k is expressed as
[pic] (2.5)
Where ρ is the drop density i.e. no of drops per unit volume, Q[pic]is the attenuation cross-section of the drop radius r, expressed in units of area, which is the sum of a scattering cross-section Q[pic]and an absorption cross-section Q[pic].
The attenuation cross-section is a function of the drop radius r, the wavelength of the radio wave, and the complex refractive index m of the water drop. That is
[pic]
The drops in a real rain are not all of uniform radius and the attenuation coefficient must be determined by integration over all drop sizes. The size distribution of raindrops represents the number of raindrops with an equivalent radius between r and r+dr per unit volume (m[pic]), and is written in the form n(r)dr. In terms of these, the attenuation coefficient is
[pic] (2.6)
The specific attenuation in decibels per kilometre is, with L = 1 km
[pic] (2.7)
The above equation emphasizes the dependence of rain attenuation on drop size, drop size distribution, rain rate and attenuation cross-section. The first three parameters are characteristics of the rain structure only, and it is through the attenuation cross-section that the frequency and temperature dependence of rain attenuation is included. Considering the type of rain and the rain regime of the region, the drop size distribution have been found to be well approximated by an exponential of the form
[pic]
where N[pic]and Λ are experimentally determined constants, whose values depend on the nature of the rain under consideration. Equation (2.4) can therefore be written as
[pic] (2.8)
where Q[pic] is found by employing the classical scattering theory of Mie for a plane wave radiation upon an absorbing sphere as
[pic]
a[pic] and b[pic] are the Mie scattering coefficients, which are complex functions of m, r and λ.
By introducing the frequency and temperature dependent coefficients which approximately represent the complex behaviour of the complete representation of the specific attenuation in equation (2.3), the relationship between rain rate, as measured on the earth’s surface, and specific attenuation can be approximated by
[pic] (dB/km) (2.9)
The total rain attenuation for an earth-space slant path is thus obtained by integrating the specific attenuation over the total path L
[pic] (2.10)
where the integration is taken over the extent of the rain volume in the direction of propagation [1].
The significant atmospheric impairments encountered by a radio signal along the path between an earth station and a satellite are summarized in Table 2.1 [7].
Table 2.1: Propagation concerns for satellite communication systems
|Propagation impairment |Physical cause |Prime importance |
|Attenuation and sky noise |Atmospheric gases, cloud, rain |Frequencies above about 10 GHz |
|Signal depolarization |Rain, ice crystals |Dual-polarization systems at C and Ku bands |
| | |(depends on system configuration) |
|Refraction, atmospheric multipath |Atmospheric gases |Communication and tracking at low elevation |
| | |angles |
|Signal scintillations |Tropospheric and ionospheric |Tropospheric at frequencies above 10 GHz and|
| |refractivity fluctuations |low-elevation angles; ionospheric at |
| | |frequencies below 10 GHz |
|Reflection multipath, blockage |Earth’s surface, objects on surface |Mobile satellite services |
|Propagation delays, variations |Troposphere, ionosphere |Precise timing and location systems; time |
| | |division multiple access system |
|Intersymbol interference |Ducting, scatter, diffraction |Mainly C band, rain scatter may be |
| | |significant at higher frequencies |
As rain is highly variable in space and time, the value of the total attenuation can be determined only from the knowledge of the characteristics at each point of the path of the raindrops. While measurements of rain attenuation have been realised, either with satellite beacons or with radiometers, these measurements are temporally and spatially scattered and are severely limited as regards frequency. They cannot therefore be readily generalised at all the places around the globe. This has led to the development of several different models based on physical processes and on meteorological data, more particularly on the cumulative distribution of rain intensities, for the evaluation of the link margins to be applied in the deployment of telecommunication systems [2].
7 Conclusions:
Different interaction mechanisms and their effects on radio signal have been discussed and the range of tropospheric and ionospheric effects to be expected on earth-space link operating at different frequencies outlined. The discussion emphasised in greater detail the computation of rain attenuation since rain is the most significant impairment factor at frequencies above 10 GHz.
The next chapter focuses on the work carried out during the course of this research to obtain an improved location-specific estimation of rain attenuation for Bangladesh and other regions of similar climate.
References:
1. L. J. Ippolito, Radiowave Propagation in Satellite Communications,
Van Nostrand Reinhold Company Inc. 1986.
2. H. Sizun, Radiowave Propagation for Telecommunication
Applications, Springer, 2005.
3. J.E. Allnut, Satellite-to-ground Radiowave Propagation, Peter Peregrinus Ltd, 1989.
4. M.P.M. Hall,L.W.Barclay and M.T. Hewit, Propagation of Radio waves, The
Institution of Electrical Engineers, 1996.
5. T. Pratt, C. Bostian and J. E. Allnut, Satellite Communications, John Wiley and
Sons Inc., 2000.
6. H. J. Liebe, G. A. Hufford and M. G. Cotton, “Propagation Modelling of Moist Air and Suspended Water/ice Particles at Frequencies below 1000 GHz”, AGRAD 52nd specialist meeting of the EM wave propagation panel, Palma de Maiorca.
7. Salonen et al., “Study of Propagation Phenomena for Low Availabilities”,
ESA/ESTEC contract 8025/88/NL/PR, Final report.
8. ITU-R, “Attenuation by atmospheric gases”, Rec. ITU-R P.676-7, 2007.
9. L. J. Ippolito, “Radio Propagation for Space Communications System”,
Proceedings of the IEEE, Vol.69, No.6, June 1981, pp. 697-727.
10. D Roddy, Satellite Communiactions, McGraw-Hill, 1989.
CHAPTER 3
Characterisation of Rain Attenuation in Bangladesh
1 Introduction:
For a reliable quantification of rain attenuation in an earth-space link, determination of the temporal, year-to-year variation of rainfall is required as the distribution of rainfall is not uniform over the year. Bangladesh, a tropical region experiences high annual rainfall. Propagation impairments, especially rain attenuation have a significant impact on radio communication links in tropical regions [1]. However, rain is not always present so that propagation impairments have a significant impact only for a certain percentage of the time during a year. The different available empirical models for rain attenuation prediction produce different estimates of the long-term mean fade probability since these models are derived from a few measurement points around the world over limited time periods whereas rain is a natural phenomenon which varies from location-to-location and from year-to-year.
Bangladesh has a tropical monsoon climate, the main seasons being Winter (Nov - Feb), Summer (Mar - Jun) and Monsoon (Jul - Oct). Most of the rainfall occurs during monsoon. To design earth-satellite communication link for a tropical region, modelling of rain fading is central to accurate calculations of signal power budget for links operating above 10 GHz.
This chapter reports on the characterisation of rain attenuation using daily accumulated rainfall data collected over the period 1961 to 2003 from different rain gauge stations of the Bangladesh Meteorological Department. The data were analysed to obtain a reliable mean annual rainfall depth. Eight rain gauge stations were selected in different parts of the country (Figure 3.1). The rain gauges are manual-type 203 mm-diameter gauges used for daily rainfall measurement. Two percent of the rainfall data were missing in four of the selected stations. In this case, missing data gaps were filled by linear interpolation. The Rice-Holmberg model is then applied to find the rain rate distribution from annual rainfall depth. Ten second integrated rainfall data covering a one year period from February 2000 to January 2001 and recorded in Sparsholt, UK by a drop counting rain gauge were employed to validate the cumulative rain rate distribution for Bangladesh derived using the Rice-Holmberg procedure.
Rain attenuation level over the region is predicted using the derived rain rate. An improved rain attenuation prediction model is then devised based on the predicted and measured attenuation at Sparsholt, UK. The uncertainty in predicted attenuation is characterised by an ad hoc model.
2 Rainfall characterisation:
The attenuation and rain rate processes are stochastic with a physical cause and effect relationship between rain rate and attenuation [2]. To characterise the rain attenuation over a certain region, it is worthwhile to examine the pattern and periodicity of rainfall in that region which might reveal any significant geographical as well as seasonal variations within the region.
1 Seasonal precipitation trends:
The seasonal trend of rainfall can be assessed from the monthly precipitation data. For this analysis, the mean monthly precipitation, [pic](mm) for m = 1,2,3,…,12 obtained over N = 43 years of data is determined. Also, the mean annual precipitation [pic] (mm) is calculated for the same data. We can define a ratio
[pic]
Figure 3.1: Rain gauge stations over Bangladesh
(source: hydro.iis.u-tokyo.ac.jp/GAME-T/GAIN-T/map/raingauge_bmd.html)
r[pic] =[pic] (3.1)
which represents the fraction of precipitation during an average year that can be expected in the m[pic] month.
Here, data for 8 stations (Figure 3.1) are analysed. The plot of r[pic] in Figure 3.2 shows that the seasonal precipitation has similar trend for an average year in all parts of the country though some of the stations have higher rainfall than the others. In particular, the south-east part of the country has the highest rainfall, whereas the central part has the lowest rainfall and the northern part has rainfall levels in between.
[pic]
Figure 3.2: Seasonal rainfall trend in different stations over Bangladesh (1961-2003)
2 Annual precipitation trend (Dhaka):
The time series of annual rainfall of Dhaka is plotted for this analysis. From the year 1961 to 1980, the annual rainfall ranges between 1500 mm and 2400 mm. But from 1980 to 2003 the annual rainfall range is much wider, from as high as 3000 mm to as low as 1169 mm (Figure 3.3). A moving average processing with window length 5 years was applied to smooth the annual rainfall time series in order to reveal the long term rainfall trend in Bangladesh. This is shown in Figure 3.3.
[pic]
Figure 3.3: Annual rainfall time series in Dhaka (1961-2003)
It is interesting to observe that the rainfall trend exhibits an oscillatory behaviour superimposed on an overall small positive slope of 0.68 mm/year (Figure 3.3). This means that the annual rainfall is increasing by 0.68 mm per year. However, over smaller interval of 5 to 8 years, the annual rainfall trends vary between positive and negative slopes. More specifically, from 1961 to 1969, the annual rainfall has a negative slope. From 1970 to 1975, the trend has a positive slope. From 1976 to 1981, the trend is negative and from 1982 to 1988, it is positive. From 1989 to 1994 the annual rainfall shows positive trend and from 1994 to 2004, the trend is negative (Figure 3.4).
[pic]
Figure 3.4: Annual rainfall trend in Dhaka (a) 1961-1969 (b) 1970-1975 (c) 1976-81 (d) 1982-88 (e) 1989-94 (f) 1995-03
For these periods we can calculate the mean and variance in order to examine the variability of annual rainfall. As can be seen from the Table 3.1, the mean rainfall over different periods are different over the years with the highest value in the period 1982-1988. The coefficient of variation and the standard deviation are higher in the period of 1989-1994, which are 34.64 and 699.03 respectively. That is the annual rainfall is more variable in that period.
Table 3.1: Statistical parameters for different periods of Annual rainfall in Dhaka
|Parameter |1961-69 |1970-75 |1976-81 |1982-88 |
|.001 |59.51 |102 |77 |32.47 |
|.01 |21.29 |28.7 |29 |1.03 |
|.1 |6.81 |10.7 |10 |7 |
The analysis shows Rice-Holmberg model provide a good estimate of the rain rate distribution in the 0.01-0.1 percent range. However, for smaller percentages of the year, Rice-Holmberg model overestimates the rain rate. This result is consistent with the different studies [9] [10] [11] that averaging affects only the higher rain rates at the smaller percentages of the year.
Table 3.3: Comparison of ITU-R and R-H derived rain rates against measurement at Surabaya (Indonesia)
|% of time |ITU-R |R-H derived |Measured rain rate |% error |
| |rain rate(mm/h) |rain rate(mm/h) |(mm/h) |(Measured Vs R-H) |
|.001 |164.8 |205.9 |175 |17.14 |
|.01 |100.2 |129 |120 |7.5 |
|.1 |37.58 |52.1 |50 |4.2 |
Surabaya, Indonesia has similar climatic conditions to Bangladesh. For Surabaya, the mean annual rainfall depth is 2000 mm and thunderstom ratio is 0.7 [12]. Rain rate distribution was derived using these values in the Rice-Holmberg model (Figure 9). The measured rain rates (based on 1-minute rainfalls) at different time percentages were read from Surayana, 2005 [13]. Again we see from Table 3.3, that the Rice-Holmberg model provides a good estimate of rain rate distribution in the 0.01-0.1 percent range.
The Rice-Holmberg model is therefore applicable to produce the rain rate distribution of a region from its accumulated rainfall data. Different stations were chosen scattered over Bangladesh to find the rain rate distribution by applying Rice-Holmberg model. The parameters of Rice-Holmberg model for the different stations are given in Table 3.4.
Table 3.4: Rice-Holmberg parameters for different stations in Bangladesh
|Parameters |Dhaka |Chittagong |Rangpur |Bogra |Ishurdi |
|Dhaka |23.723 |90.4086 |109.73 |119 |8.45 |
|Chittagong |22.27 |91.82 |128.36 |127.4 |0.75 |
|Rangpur |25.73 |89.23 |95.45 |119.3 |24.99 |
|Bogra |24.85 |89.37 |101.06 |111 |9.84 |
|Ishurdi |24.13 |89.05 |99.15 |104.7 |5.6 |
|Barisal |22.75 |90.33 |113.7 |118 |3.78 |
|CoxsBazar |21.43 |91.93 |125 |137 |9.6 |
|Srimangal |24.3 |91.73 |100.13 |117.5 |17.35 |
Analysis of M shows that the year-to-year annual rainfall M is normally distributed i.e. the long term mean annual rainfall lies within the 95% confidence bounds for the true mean. According to the world map of β [7], the value is 0.5 i.e. 50% rain is of convective type for Bangladesh. However, due to the lack of local measurement, corresponding estimate of the accuracy of β was not obtained.
3 Seasonal variations in rain rate distribution:
Average annual rainfall depth, M partially reflects annual variation in rainfall as long-term data (i.e. at least 11 year period) is used. But within the annual variations there are seasonal as well as diurnal variations. To characterise diurnal variations in rain rate distribution, fine resolution like 1min data are required, which are not available over Bangladesh.
However, from the knowledge of seasonal trend of rainfall, it is expected to have a higher rain rate distribution during monsoon season and a comparatively lower distribution for winter. In Bangladesh, most rainfall occurs during monsoon season. July is the rainiest month, whereas January is the driest month (Figure 3.2).
[pic]
Figure 3.11: Seasonal variations of rainfall rates by Rice-Holmberg model in Dhaka
To compare the rain rate statistics of different months, Rice-Holmberg model is applied to the monthly average by combining 43 years of monthly data such as January, July etc. Figure 3.11 shows the rainfall distributions for the months of January and July. At 0.01% of time rain rate exceeded is 144 mm/h for July compared to only 14.2 mm/h for January. In fact July singularly provides the worst-month statistics in Bangladesh as its rain rate value exceeds that of every other month at all percentage points. To provide a service such as Broadcasting Satellite Service (BSS) at the required availability (usually 1% of the worst month), worst-month statistics has to be considered.
3 Rain attenuation:
On the basis of the rain rate analysis, slant path rain attenuation is predicted using the 18.7 GHz frequency band for a path elevation of 46.1[pic]. The station (Dhaka) location is 23.72[pic]north latitude and 90.41[pic]east longitude at an altitude of 6.5 m above sea level. Rain attenuation statistics is predicted for this slant path using ITU-R model, Rec. 618-8 [14], which employs the rain rate at 0.01% of an average year. At 0.01% of time, the predicted attenuation using ITU rain rate is 37 dB exceeded for 0.01% of an average year. However, using Rice-Holmberg derived rain rate, the exceeded attenuation is 39 dB for the same time percentage (Figure 3.12).
[pic]
Figure 3.12: Predicted rain attenuation using R-H and ITU rain rate for Dhaka
As the empirical models for rain attenuation are derived from a few measurement points around the world over limited time periods, variability is inherent in the estimation of rain attenuation for a particular location. Rain attenuation can vary from location-to-location and from year-to-year. According to the Sparsholt measurement at 18.7 GHz from April 1997 to July 2001, the year-to-year measured attenuation statistics are different though the concurrent year-to-year rain statistics are similar [15]. The year-to-year variation could be due to the way intense rain is distributed along the slant path.
[pic]
Figure 3.13: Approximation of attenuation reduction factor using Sparsholt data
It was important to obtain a measure of how closely the rain attenuation distribution predicted using Rice-Holmberg (R-H) derived rain rates matches with a direct measurement of rain attenuation distribution using a satellite beacon. We determined this measure, referred to as a reduction factor r, at Sparsholt (UK) where both distributions are available, and defined as
r = Predicted attenuation / Measured attenuation
This was found to be well approximated (standard error of 1.55%) by (Figure 3.13)
[pic]
(3.6)
where p is the annual time percentage (0.002 ≤ p ≤0.05).
This factor was then applied to improve the R-H based prediction of rain attenuation in Bangladesh. The assumption made here is that the R-H model performs similarly in both climates. This is a reasonable assumption given that the R-H model has comparable global applicability (e.g. see Figure 9) and has hitherto not been shown to perform significantly differently in any region. As a result we obtain the attenuation distribution in Figure 3.14 (dashed line), which is compared with attenuation distributions predicted using R-H and ITU-R rain rates, and shows lower attenuations (by up to ~18%) at small time percentages (< 0.01%).
It is worth mentioning that at frequencies below around 30 GHz rain type plays a significant role in determining the size of attenuation. For smaller percentages of the year, the attenuation results mainly from thunderstorm rain. It is likely that the ITU-R rain attenuation model (used for the two solid curves of Figure 3.14) somewhat over-estimates the attenuation for Bangladesh at these small percentages of the year. This may be due to the fact that the models for rain drop size distribution (DSD) in tropical regions are quite different from those adopted by ITU-R [16]. An intense rain rate could result in a lower than predicted rain attenuation if the DSD consists of predominantly larger drops. Maitra found that the prevailing DSD in a tropical region can cause significant variation in rain attenuation distribution [17].
[pic]
Figure 3.14: Comparison of predicted attenuation applying reduction factor (Dhaka)
To further check the validity of the above improved attenuation prediction for Bangladesh, comparison was made with measured attenuation values at 12 GHz reported in the literature for a similar climatic region (tropical- monsoon characterised by heavy rainfall), namely Bandung, Indonesia [13]. The measured attenuation at 0.01% of the time was 17 dB, which scales to 35 dB at 18.7 GHz, using the ITU-R frequency scaling procedure [14]. This value is comparable to the 34 dB attenuation predicted for Dhaka by the improved model.
For some specific applications such as BSS, it is often necessary to determine worst month statistics from annual statistics, since an annual distribution may be the only statistics available. To relate worst month and annual statistics, the ITU-R model [18] provides the following expression
[pic] (3.7)
where p[pic] is annual exceedance probability and [pic] is worst month exceedance probability. According to the above relationship, 1% of the worst month value corresponds to 0.3% of the annual value. That is, to determine the margin necessary to maintain an outage no greater than 1% of the worst month, a 0.3% outage of attenuation margin should be read from the available annual distribution plot. Figure 3.14 shows that for the link under consideration this margin would be 9 dB.
Monthly attenuation values were predicted by using 0.01% rain rate for each month calculated as discussed in section 3.1. Figure 3.15 gives a plot of the rain fade margins required to meet various annual availabilities (99 - 99.99%) at each month, assuming the rainfall pattern of that month was characteristic of the whole year. There is clearly a strong seasonal dependence. For example a margin of ~40 dB is required to achieve 99.99% availability during the monsoon months, compared to only ~11 dB in January. Thus year-round operation of high-availability links will not be feasible in Bangladesh at Ku-band frequencies and above without recourse to uneconomic system design and/or sophisticated fade mitigation techniques. However the results of Figure 3.15 indicate that these frequencies can be exploited in Bangladesh to provide high-availability communication links to support non-monsoon seasonal applications such as social or sporting activities.
[pic]
Figure 3.15: Attenuation for various levels of availabilities as a function of the month
4 Risk estimation in rain attenuation prediction:
The occurrence of attenuation by rain is a random process and each single-year distribution function is a sample from that process [2]. Based on the predicted rain rate, rain attenuation is estimated for Dhaka, which reflects the attenuation levels at the required time percentages for the Earth-space link design. But there is always inherent statistical uncertainty in the attenuation prediction due to random behaviour of rain process.
To estimate the risk to be associated with a rain attenuation prediction model, an ad hoc model is applied as by Crane [2]. As an ad hoc procedure for the estimation of the uncertainty associated with an attenuation prediction, the observed deviation from model predictions are used to estimate the distributions of deviations to be expected for a path.
Risk, R, is often computed as the probability of a failure, F[pic] (in prediction), occurring at least once in a period of N years. If the object of an attenuation prediction is the fade margin required to prevent a failure for all but one in N years, then the return period P needed for the calculation of the attenuation cumulative distribution function for design is found from:
R = F[pic]= 1-(1- F[pic])[pic]
F[pic]=1-(1-R)[pic] (3.8)
P=1/ F[pic]
where F[pic] is single year probability of failure. The attenuation for the specified risk, A[pic], is calculated from
A[pic] = A exp(σS[pic]) (3.9)
where A is the attenuation values, σ is the standard deviation relative to a single year probability of failure found from F[pic] by look up in a normal probability table and S[pic] is 0.23 for the year-to-year variation of path attenuation at a single location and 0.29 for the combined year-to-year and location-to-location variations for path attenuation within climate zone [2].
[pic]
Figure 3.16: Rain attenuation risk estimation for Bangladesh
Figure 3.16 shows the upper bound (5%) and lower bound (95%) of rain attenuation obtained by applying an ad hoc model on the predicted rain attenuation after applying reduction factor. According to the graph, median value of the rain attenuation for 0.01% of an average year exceeded is 34 dB. However, 5% of observed years of measurement will have an attenuation in excess of 56 dB at this time percentage, whereas for 95% of observed years the exceeded attenuation will be 21 dB. There is a risk of one failure in N = 5 years of attenuation observation (23 years return period). The predicted rain rate by Rice-Holmberg model is 119 mm/h at 0.01% time. Applying the ad hoc model, the upper bound of rain rate is found to be 186 mm/h and the lower limit is 76 mm/h at the same percentage of time. These rain rates correspond to attenuation of 50 and 30 dB, respectively. The slight difference in the variability is due to the fact that the occurrence of year-to-year rain rate and attenuation is not similar.
[pic]
Figure 3.17: Rain attenuation variability from three standard deviations bound for Bangladesh
In our analysis annual rainfall is normally distributed. Using the mean rainfall at three standard deviations bound, the attenuation is predicted to assess the variability of attenuation (Figure 3.17). According to the graph, the attenuation is 34 dB in the lower bound and 41 dB in the upper bound at 0.01% time. Although the annual rainfall is normally distributed, the rain rate which causes the attenuation is log-normally distributed [2]. As a result, the variability of mean annual rainfall does not reflect the true variability in attenuation.
5 Conclusions:
Accurate prediction of rain attenuation is crucial in the planning of a reliable communication system at any location especially in tropical regions like Bangladesh. The analysis of rainfall pattern reveals that the rainfall has similar pattern in different parts of the country and is highly seasonal. Most of the rainfall occurs during the monsoon (Jul-Oct) period, whereas in winter (Nov-Feb) there is very little rain. Efficient utilisation of satellite communication system resources can be improved by using seasonal information along with annual statistics in the link design process. For example the transmit power of earth station and/or satellite (if on-board processing) can be set at two different levels, one for the rainy months, and a much lower setting for the dry winter months. This would be a simple seasonal link budget approach, as opposed to a more complex fade mitigation strategy through power control which necessitates some provision for monitoring changes in link attenuation.
The Rice-Holmberg model was used to convert local measurement of annual rainfall into rain rate distribution. Based on this R-H derived rain rate, the predicted attenuation was 39 dB at 0.01% time whereas based on ITU-R rain rate, the rain attenuation was 37 dB. By applying the improved rain attenuation model presented, the predicted rain attenuation for Dhaka was found to be 34 dB for the same time percentage.
Typically, power margins of 5-10 dB at C-band and 10-15 dB at Ku, Ka-band can be relatively easily achieved by available power margins (obtained with reasonably sized antennas and with RF transmit power). However, our study suggests that rain attenuation will exceed available power margins for tropical regions like Bangladesh during a significant percentage of the year. Additional methods such as sophisticated fade mitigation strategies, and innovative solutions such as seasonal link budgets or seasonal communication applications need to be considered in order to achieve acceptable link availabilities at affordable costs.
Rain attenuation level together with the seasonal characteristics of rainfall will be incorporated in the link budget analysis of the communication network in chapter 8.
References:
1. G.H. Bryant, I. Adimula, C. Riva and G.Brussard, “Rain Attenuation Statistics
from Rain Cell Diameters and Heights”, International Journal of Satellite
Communications, Vol.19, 2001, pp. 263-283.
2. R. K.Crane, “Estimating Risk for Earth-Satellite Attenuation Prediction”,
Proceedings of the IEEE, Vol.81, No.6, June 1993, pp. 905-913.
3. C. Schuler and M. Chugani, Digital Signal Processing: A Hands-on
approach, McGraw-Hill, New York, 2005.
4. Z. S. Haddad, J. P. Meagher, R. F. Adler, E. A. Smith, I. Eastwood and
S. L. Durden, “Global Variability of Precipitation according to the Tropical
Rainfall Measuring Mission”, Journal of Geophysical Research, Vol. 109, 2004.
5. L. L. Lapin, Probability and statistics for modern engineering, 1990.
6. R. K. Crane, “Prediction of Attenuation by Rain”, IEEE transactions on
communication, Vol. Com-28, No.9, Sept. 1980, pp. 1717-1733.
7. P. L. Rice and N. R. Holmberg, “Cumulative Time Statistics of Surface-
Point Rainfall Rates”, IEEE transactions on communication, Vol. Com-21, No.10,
Oct. 1973, pp. 1131-1136.
8. ITU-R, “Characteristics of precipitation for propagation modelling””, Rec. ITU-R P.837-4, 2003.
9. R. R. Rogers, “Statistical Rainstorm Models: Their Theoretical and Physical
Foundations”, IEEE transactions on Antennas Propagation, Vol. AP-24, 1976,
pp. 547-566.
10. R. K. Crane, “Prediction of the Effects of Rain on Satellite Communication
Systems”, Proceedings IEEE, vol. 65, 1977, pp. 456-474.
11. D. M. A. Jones and A. L. Sims, “Climatology of Instantaneous Rainfall Rates”,
Journal of Applied Meteorology, vol. 17, 1978, 1135-1140.
12. A. Dissanayake, J. Allnutt, and F. Haidara, “A Prediction Model that
Combines Rain Attenuation and Other Propagation Impairments along Earth-
Satellite Paths”, Online Journal of Communications, Issue No. 2, 2002, pp. 1-37.
13. J. Surayana, S. Utoro, K. Tanaka, K. Igarashi, and M. Iida, “Study of
Prediction Models Compared with the Measurement Results of Rainfall Rate and
Ku-band Rain Attenuation at Indonesian Tropical Cities”, ICICS, 2005.
14. ITU-R, “Propagation data and prediction methods required for the design of Earth-space telecommunication systems”, Rec. ITU-R P.618-8, 2003.
15. S. Ventouras, C. L. Wrench, “Measured Slant Path Attenuation and Rainfall
Statistics in Southern England in Relation to ITU-R Predictions”, COST Action
280, 1st International Workshop, July 2002.
16. G. O. Ajayi, and R. L. Olsen, “Modelling of a tropical raindrop size
distribution for microwave and millimetre wave applications”, Radio Science,
Vol. 20, 1985, 193-202.
17. A. Maitra, “Rain Attenuation Modeling From Measurements of Rain Drop
Size Distribution in the Indian Region”, IEEE Antennas and Wireless
Propagation Letters, Vol. 3, 2004, pp. 180-181.
18. ITU-R, “Conversion of annual statistics to worst-month statistics”, Rec. ITU-R P.841-4, 2003.
CHAPTER 4
Rain Cell Size Distribution
1 Introduction:
Knowledge of rain cell size distribution is relevant for the modelling of earth-space propagation in radio communication. To determine the spatial structure of rain cells, long term rain rate time series can be processed by applying the synthetic storm technique assuming some known value of storm translation speed. The underlying hypothesis is that rain patterns move along a line with a constant speed and that advection is the predominant mechanism to account for the spatial variability of rain-rate. The hypothesis holds when a statistical description of rain structure is required, rather than the exact space distribution of rain. Furthermore, as rainfall patterns move over a rain gauge, it is possible to estimate the horizontal extent of rain cells from the duration of various rain rate thresholds as recorded by the rain gauge if a mean advection velocity of rain cells is assumed.
The weather radar is powerful in registering three-dimensional rain (reflectivity) fields in time and space. Since it can provide a way to sample the spatial structure of the rain fields with the spatial continuity, the radar data over a limited period of time (like one rainy season) contain quite complete characterisation of rain structures and types for the covered region [1].
Radar scans send out electromagnetic radiation that strikes hydrometeors in the atmosphere, a part of which reflect back toward the radar. This backscattered energy carries the characteristics of the reflecting bodies such as hydrometeor types, the size of the hydrometeor and absorption qualities of the hydrometeors. Reflectivity fields of precipitation from high resolution scanning radar show structures of various sizes often embedded in each other. Although precipitation intensities are highly variable in space and time they manifest some organisation as higher intensity cores are clustered in features of various scales of cells measuring a few square kilometres most of the time. If a cell is sufficiently long-lived, it is possible to track their movement through successive scans separated in time.
Scanning Doppler radar being coherent can measure the phase of the returning signal, thus enabling the determination of the radial velocity component of the targets. Wind movement is in general three-dimensional and varies over time and space. Complete characterisation of the wind movement requires simultaneous measurements using multiple Doppler radars. However, making some simplifying assumptions about the structure of the observed wind field, a single Doppler radar measurement will suffice to extract the wind field [2].
The main topic of this chapter is the rain cell size distribution obtained from rain gauge and radar data. Reflectivity, dBZ (mm[pic]mm[pic]) and Doppler radial velocity (m/s) available in 300 range gates, each of 300 m length at 0.25 s interval from Chilbolton Advanced Meteorological Radar (CAMRa) situated at Chilbolton (51.1445[pic]N, 1.4370[pic]W), UK were used for 7 events on 26 September, 08 October and 12 May in 2001, 01 July, 22 September and 31 October in 2003 and on 23 March in 2004. The reflectivity data is calibrated and noise free. The unambiguous velocity measured by Chilbolton radar is ±15 m/s and velocity measured beyond these ranges is unfolded [3]. Rain gauge data by a drop counting rain gauge recorded at Sparsholt, 7.8 km from Chilbolton were used for the whole year of 2000, 2003, 2005 and January 2004 to May 2004. Wind measurements at Brize Norton, 63 km from the radar location, were also used for the corresponding periods of radar observation.
2 Rain cell translation velocity:
Radar can provide information on the horizontal structure of storm (rain) cell from PPI measurements of the radar reflectivity factor (Figure 4.1) through constant elevation slices. Different definitions of rain cell are found in the scientific literature with different meanings [4]. In Crane [5] rain cell refers to a volume in which convective phenomena take place. In other approach, a rain cell is considered to be an entity constituted by an area inside of which the rain rate (or the radar reflectivity) is equal to or higher than a specified threshold value. This definition implies that the cell is continuous and that along the contour that bounds it, the rain rate is at the threshold value. The area where rain rate falls below threshold is ignored [6].
[pic]
Figure 4.1: PPI of reflectivity field, dBz (colorbar on right) on 23 March,2004
A rain cell defined by the latter approach can be identified in consecutive PPI scans separated by a fixed time interval. To track the movement of the rain cell a correlation technique is employed, which partitions the reflectivity fields of each scan into blocks and determines by trial and error the displacement of the previous scan that maximises its correlation with the next scan. Dividing this displacement by the inter-scan interval yields the cell translation velocity. Cross-correlation techniques treat the data as a two-dimensional field from which the movement of features may be inferred [7] [8] [9] [10].
A correct match of each cell to its corresponding appearance in a subsequent scan is complicated by the physical changes that rain cells exhibit between radar scans. For example a rain cell might decay, grow, merge or split between observations. Moreover, a rain cell might move independently in directions that differ from that of the whole radar image. The movement of a rain cell can be either a propagation, whereby a portion of the cell movement arises from growth on new echoes, or a translation, which is the motion of the cell centroid not resulting from propagation [11].
To identify a rain cell within the precipitation areas, a threshold reflectivity value of 35 dBZ was used [6]. When tracking a previous rain cell (at time t1) based on a current scan (at time t2), difficulties arise as new cells can appear and existing cells can split, merge or disappear. There are five possible scenarios [12]:
1. A cell at t2 has no predecessor at t1, which means a new cell came into existence.
2. A cell at t1 has no successor at t2, which means an existing cell disappeared.
3. A cell at t1 has exactly one successor at t2. This is cell translation.
4. A cell at t1 has more than one successor at t2 (i.e. the cell split into several parts).
5. A cell at t2 has more than one predecessor at t1 (i.e. several cells merged into one).
The above correlation analysis was performed only to find cell translation, ignoring cell growth and cell decay (Appendix-A). A frame is taken centred at peak intensity around an identified cell in the previous image (at time t1). The choice of the size of this frame is guided by two considerations: A frame that is too small in size will contain too few data points for the correlation coefficients to be stable, whereas a frame that is too large will only give a general mean flow on a broad spatial scale. In our study, a 5 km×5 km frame size, partitioned into 25×25 blocks, was considered a good compromise in reliably tracking a cell. Each block was assigned a value of zero if its reflectivity fell below threshold and a value of 1 otherwise. The search for maximum correlation (i.e. approximate match) between a frame from the previous scan and a neighbourhood in the current scan extends from zero displacement up to an excursion limit set by a maximum translation speed of 30 m/s.
[pic]
Figure 4.2: Identified rain cell on PPI on 23 March, 2004 (a) Cell in the previous scan; (b) Correlated cell in the next scan
As an example, Figure 4.2 shows two successive scans of a rain event on 23 March 2004 featuring isolated and intense rain cells (maximum reflectivity 51 dBZ). The time difference between the successive scans is from 2 min 15 s to 3 min. The block at the centre of a frame in the LHS scan (at time say t1) is marked, and has co-ordinates say (x1, y1). At a later time t2 corresponding to the RHS scan, the location of this block will be at point (x2, y2) within the RHS scan which gives the highest correlation between the frames centred at (x1, y1) and (x2, y2). The translation speed v and direction of motion ( (counter-clockwise from East) are then obtained as
[pic] (4.1)
Translation speeds and directions were similarly computed for all other events.
3 Wind field from Doppler analysis:
Browning and Wexler [13] showed that if a wind field varies almost linearly then the velocity components of a wind field can be approximated by a Taylor series expansion limited to first derivatives. In this way, the velocity field inside an observed domain is described by the sum of the value at the centre and the gradient terms. As the radar senses only radial velocity, the tangential component can be determined by analysing measured radial velocity values at various points along a circle corresponding to different azimuth β and range r values within a scan as in Figure 4.3. Under these assumptions, the radial velocity V[pic](β) can be seen as a periodic function with base period 2π (Appendix-B) that can be written in the form of a Fourier series expansion [2]:
[pic]
Figure 4.3: Motion vector on an azimuth plane
[pic] (4.2)
The first three coefficients are given by,
[pic] (4.3)
[pic] (4.4)
[pic] (4.5)
where, u[pic]and v[pic]are the horizontal components of velocity, α is the elevation angle.
[pic]
Figure 4.4: Doppler velocity from event on 23 March, 2004 at a range 58 km
However, if there is no scatterer at a particular point on the circle or the scatterer motion at this point is perpendicular to the radar beam, then the radial velocity will be zero. Such points were filled by cubic interpolation. The data was smoothed (Figure 4.4) using an ideal low pass filter of cut-off 50 cycles/deg and an FFT was applied to obtain the coefficients that yielded the horizontal wind speed as
[pic] (4.6)
The horizontal divergence is given by
[pic] (4.7)
The average vertical velocity can be calculated from the continuity equation:
[pic] (4.8)
Integrating between levels z and z[pic]
[pic] (4.9)
Considering vertical velocity, wa at surface (level z[pic]) to be zero then vertical velocity at any level z will be
[pic] (4.10)
Vertical motion at top of any layer is proportional to layer mean divergence. If divergence is negative, then vertical motion is positive, which implies rising motion i.e. updraft. If divergence is positive, then vertical motion is negative, which implies sinking motion i.e. downdraft. The vertical velocity ranges from 5 ~ 26 cm/s in the events studied. The detail analysis of vertical velocity is not presented for brevity.
4 Comparison of cell translation speed, Doppler speed and wind speed:
Figure 4.5 shows comparisons of the radar Doppler-derived wind speed, the correlation-based storm translation speed, and the ground measured wind speed at Brize Norton for corresponding events or observation intervals (numbered from 1 to 14 along the x-axis). Rain cells are expected to move with the wind speed at 700 mb pressure level at 2 to 3 km above ground [14]. The wind speed measured at ground level was increased by a factor of 1.5 to account for the variation of wind speed with height above ground [15].
[pic]
Figure 4.5: Comparison of wind speed, Doppler wind speed and cell translation speed
Although the computed translation speed of rain cells shows broad agreement with elevated wind speed, their detail variation is different. The differences could be due to the fact that although rain cell movement is driven by winds, the rain cell pattern observed on the ground at a given region may reflect the speed and direction of the generating precipitation at a higher altitude [16]. There is however a considerable difference between cell translation speed and Doppler derived wind speed. It is worth noting that the Doppler method described above gives a reliable measure of only the radial velocity component of a large rain volume, and the steps employed to derive horizontal translation speed from this radial measurement assumes a linear flow field which is not the case in localized convective events.
5 Rain cell size distribution:
Rain gauges provide a record of the amount of rainfall over time, or rain rate time series, at different locations. Since rain is a moving entity, this time series can be converted into a spatial series by employing some known value of rain translation speed. This is the so called synthetic storm technique [17]. Rain rate measurements at 10 s integration time were converted into 1-min rain rate time series before determining the event durations for threshold rain rates from 5 to 50 mm/h. Multiplying these durations by the average rain cell translation speed of 10.1 m/s yielded an equivalent distance span and hence size of the corresponding rain cell.
Rain cell sizes were also deduced from radar measurements comprising 66 PPI scans in 7 rain events within a 100 km range of Hampshire. The radar reflectivity field z (dBZ) was converted into rain rate R (mm/h) through the relation z = 200R[pic], which assumes a Marshall-Palmer rain drop size distribution. The “contour” and “polyarea” functions of MATLAB have been tested and found to be very accurate in obtaining the vertices and area of a polygon. So, these functions were employed to compute the area of rain cells of defined thresholds, and this area was then converted to cell size (i.e. diameter) in km by equating with a circular shaped region.
The numbers of rain cells of various rain rate thresholds obtained using rain gauge data are much lower than the numbers from radar data (Table 4.1). This is because the rain-gauge-based estimate employs the average rain rate in 10 s intervals at a single location whereas radar captures instantaneous rain rate values at multiple locations. The radar measurement employed covered one rain event in summer, four events in autumn and two in spring, and may therefore not have sufficient seasonal variety for the results to be reliably representative of an average year. The rain gauge data on the
Table 4.1: Statistics of rain cells from rain gauge and radar data
|Rain rate threshold |No. of cell from Rain gauge |No. of cell from Radar |
|≥ 5 mm/h |6432 |9719 |
|≥ 10 mm/h |4066 |5033 |
|≥ 20 mm/h |217 |3448 |
|≥ 30 mm/h |130 |2493 |
other hand covered all seasons of a 3-year period. The smallest cell size determined using rain gauge data was 0.61 km, so cells of size less than 0.61 km were not considered in the radar data analysis.
[pic]
Figure 4.6: Cumulative distribution of rain cell sizes obtained from rain gauge data
Figures 4.6 and 4.7 show the cumulative distributions of rain cell sizes derived from rain gauge and radar measurements respectively, for rain rate thresholds from 5 to 50 mm/h. The lower rain rate cells (of thresholds 5 to 10 mm/h) extend up to 65 km in diameter for results derived from rain gauge measurements using the synthetic storm technique. Intense rain cells (thresholds ( 20 mm/h) on the other hand have extensions around 5 to 10 km, which is in agreement with the results found in earlier studies [14] [17]. It can be seen that the two methods yield comparable results for intense rain cells, whereas there is considerable difference for the lower rate cells where radar observations show cell sizes up to 25 km. The families of curves for intense cells are similar in overall appearance to those reported by Yau and Rogers [14]. It should be noted that the accuracy of the synthetic storm technique depends on
[pic]
Figure 4.7: Cumulative distribution of rain cell sizes obtained from radar observation
the use of correct values of storm translation speed for the different rain patterns. In our analysis, the same translation speed determined for the intense rain cells associated with highly mobile convective rain was applied to the lower rate cells of stratiform rain. This is likely to have resulted in overestimation of the spatial extent of weaker rain cells. Rain rates lower than 5 mm/h were not considered since the assumption of a circular cell shape no longer holds, as revealed by the radar observations. Very intense rain cells above 50 mm/h appeared on the radar scans as small dots whose areas could not be reliably computed, so rain intensities above 50 mm/h were excluded from the analysis. Furthermore, the sample size of intense rain cells observed using both rain gauge and radar was quite small (between 2 and 6) making their distributions unstable [17]. In particular, distributions below 0.02% were not possible, and cell sizes indicated in Figures 4.6 & 4.7 at small percentages ( ................
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