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THE UNIVERSITY OF HULL
Development of a Heterogeneous Microwave Network, Fade Simulation Tool
Applicable to Networks that Span Europe
being a Thesis submitted for the Degree of
Doctor of Philosophy in Electronic Engineering
in the University of Hull
by
HAFIZ BASARUDIN
(MEng.)
(HND, British Malaysian Institute)
January, 2012
ACKNOWLEDGEMENTS
First and foremost, my utmost gratitude to Dr. K. S. Paulson, my supervisor, whose
sincerity, guidance and encouragement I will never forget and has helped me to finish
this work. I would also like to extend my gratitude to others including Mr. N. G.
Riley, Dr. Franklin Mung'au, the department and Graduate School. I would also like
to acknowledge the support of the British Atmospheric Data Centre and the National
Oceanic and Atmospheric Administration, Physical Science Division for providing
the critical datasets for this research. Last but not least, my sincere gratitude to my
family and friends who helped me a lot in finishing this project through continuous
encouragement and support during my study.
i
ABSTRACT
Radio communication systems operating at microwave frequencies are strongly
attenuated by hydrometeors such as rain and wet snow (sleet). Hydrometeor
attenuation dominates the dynamic fading of most types of radio links operating
above 10 GHz, especially high capacity, fixed, terrestrial and EarthSpace links. The
International Telecommunication Unions – Radio Section (ITUR) provides a set of
internationally recognized models to predict annual fade distributions for a wide
variety of individual radio link. However, these models are not sufficient for the
design and optimisation of networks, even as simple as two links. There are
considerable potential gains to be achieved from the optimized design of realtime or
predictive Dynamic Resource Management systems. The development of these
systems requires a joint channel simulation tool applicable to arbitrary, heterogeneous
networks. This thesis describes the development of a network fade simulation tool,
known as GINSIM, which can simulate joint dynamic fade timeseries on
heterogeneous networks of arbitrary geometry, spanning Europe.
GINSIM uses as input meteorological and topological data from a variety of sources
and numerically calculates the joint effects on fading on all links in a specified
network. ITUR models are used to transform rain rate into specific attenuation and to
estimate the specific attenuation amplification due to nonliquid hydrometeors. The
resulting simulation tool has been verified against ITUR models of average annual
fade distributions, fade slope and fade duration distributions, in the southern UK.
Validation has also been performed against measured terrestrial and Earthspace link
data, acquired in the Southern UK and Scotland.
ii
CONTENTS
Acknowledgement
i
Abstract
ii
Contents
iii
List of Figures and Tables
vii
Notation
x
Glossary of Terms
xii
CHAPTER 1 INTRODUCTION .................................................................................. 1
1.1 Brief description of GINSIM............................................................................... 6
1.2 Aims and objectives............................................................................................. 8
1.3 Thesis outline....................................................................................................... 8
CHAPTER 2 MICROWAVE FADE MECHANISMS .............................................. 10
2.1 Formation Cloud and Rainfall ........................................................................... 10
2.2 EarthSpace Radio Communication System...................................................... 13
2.3 Absorption by Atmospheric Gasses ................................................................. 14
2.4 Rain Parameters, Scattering and Attenuation .................................................... 16
2.4.1 Rain Scattering ....................................................................................... 17
2.4.2 Raindrop Size Distribution (DSD) ......................................................... 18
2.4.3 Rain Drop Shape and Canting Angle ..................................................... 21
2.4.4 Rain rate ................................................................................................. 23
2.4.5 Specific Attenuation of rain ................................................................... 25
2.4.6 Rain Attenuation .................................................................................... 26
2.5 Sleet Attenuation ............................................................................................... 29
iii
2.6 Cloud Attenuation.............................................................................................. 32
Chapter 2 summary.................................................................................................. 33
CHAPTER 3 METEOROLOGICAL MEASUREMENTS ........................................ 34
3.1 Rainfall Measurements ...................................................................................... 34
3.1.1 Rain gauge.............................................................................................. 36
3.1.2 Weather radar ......................................................................................... 38
3.1.3 Meteorological Satellites........................................................................ 43
3.2 Meteorological Measurement Datasets ............................................................. 46
3.2.1 Chilbolton DropCounting and TippingBucket Rain Gauge ................ 47
3.2.2 Chilbolton Advance Weather Radar (CAMRa) ..................................... 47
3.2.3 Nimrod and OPERA............................................................................... 48
3.2.4 MultiSensor Precipitation Estimate (MPE) .......................................... 50
3.2.5 NCEP/NCAR Reanalysis datasets ......................................................... 51
3.2.6 Shuttle Radar Topography Mission (SRTM).......................................... 52
Chapter 3 Summary ................................................................................................. 54
CHAPTER 4 NETWORK FADE SIMULATION .................................................... 56
4.1 General Procedures for Network Fade Simulation............................................ 56
4.2 Different approaches for Network Fade Simulation.......................................... 61
4.2.1 Rain Cell models .................................................................................... 61
4.2.2 Statistical Rain Rate Variation Models ................................................. 64
4.2.3 Downscaling NWP or Meteorological Data........................................... 66
4.2.3a SISTAR .................................................................................... 66
4.2.3b SATCOM ................................................................................. 67
4.2.3c Hull Rain Fade Network Simulator (HRFNS) and GINSIM ... 68
4.3 Downscaling and network simulation processes for GINSIM .......................... 69
iv
4.3.1 Disaggregation ....................................................................................... 71
4.3.2 Interpolation ........................................................................................... 72
4.3.3 Extrapolation into Low Rain Rate Regions............................................ 73
4.3.4 Advection ............................................................................................... 74
4.3.5 Transforming to Specific Attenuation Fields and Pseudointegration .. 74
4.3.6 Rain Height model ................................................................................. 75
Chapter 4 Summary ................................................................................................. 80
CHAPTER 5 VALIDATION WITH ITUR MODELS ............................................. 81
5.0 Experimental setup ............................................................................................ 81
5.1 Validation of Rain Rate Distribution................................................................. 82
5.2 Validation of First Order Statistics for Annual Hydrometeor Fade .................. 84
5.3 Validation of Second Order Statistics for Hydrometeor Fade........................... 87
5.3.1 Fade Duration......................................................................................... 87
5.3.2 Fade Slope .............................................................................................. 89
Chapter 5 Summary ................................................................................................. 93
CHAPTER 6 VALIDATION WITH MEASURED TERRESTRIAL AND EARTHSPACE LINKS............................................................................................................ 94
6.1 Measurement data.............................................................................................. 94
6.2 Comparison of simulated and measured fade data ............................................ 96
6.2.1 Distributions and Joint Distributions of Fade ........................................ 96
6.2.2 Distributions of Fade at different spatial and temporal scales ............... 98
6.2.3 Site Diversity Comparison ................................................................... 102
6.2.4 Validation of Autocovariance ............................................................. 106
Chapter 6 Summary ............................................................................................... 109
CHAPTER 7 CONCLUSIONS AND FUTURE OUTLOOK .................................. 110
v
7.1 Assumptions, Limitations and Recommendations .......................................... 111
7.1.1 Disaggregation ..................................................................................... 111
7.1.2 Advection ............................................................................................. 111
7.1.3 Specific Attenuation............................................................................. 112
7.1.4 Rain Height model ............................................................................... 113
7.2 Comparison with other Network Fade Simulation Tools ................................ 114
7.3 Future Works and Recommendations.............................................................. 115
7.3.1 Downscaling Attenuation TimeSeries ................................................ 115
7.3.2 Other Atmospheric Fade Effects .......................................................... 116
7.3.3 Nowcasting .......................................................................................... 116
7.3.4 Global Applications and Different Climate Regions ........................... 117
7.3.5 Climate Change .................................................................................... 118
7.4 Future Outlooks ............................................................................................... 118
REFERENCES AND BIBLIOGRAPHY ................................................................. 119
APPENDIX A: DISAGGREGATION...................................................................... 133
APPENDIX B: INTERPOLATION.......................................................................... 135
vi
LIST OF FIGURES AND TABLES
Figure 1.1: Block diagram of the GINSIM
Figure 2.1: Convective and stratiform cloud formation.
Figure 2.2: Rain formation within a cloud from Usman (2005)
Figure 2.3: A geometry path for an EarthSpace link.
Figure 2.4: Specific attenuation due to Atmospheric gasses from Rec. ITUR 6768
(2009)
Figure 2.5: Energy scattering pattern of Rayleigh and Mie.
Figure 2.6: Ulbrich Gamma DSD model with m variation. D0 is assumed to be 0.1 cm
and N0 is 80000 cm1m3.
Figure 2.7: Evolution of Rain drops with radius lengths in mm.
Figure 2.8: Rain rate annual distribution for Chilbolton from Rec. ITUR P.8375
(2007)
Figure 2.9: Specific Attenuation of 20 and 30 mm/hr for different frequencies from
Rec. ITUR P.8383 (2005)
Figure 2.10: Annual Rain Attenuation distribution from Rec. ITUR P.53013 (2009)
Figure 2.11: Sleet fade multiplication factor for specific attenuation of rain from Rec.
ITUR P.53013 (2009)
Figure 3.1: Basic diagram of an echosounding system for radar.
Figure 3.2: Internal working of a Nimrod rain radar.
Table 3.3: Operating Bands for Radar with its relevant frequency and wavelength.
Figure 3.4: Weather satellites from various countries and agencies.
Figure 3.5: Nimrod rain map covering the whole UK and part of Europe.
Figure 3.6: OPERA rain maps covering most of Europe.
Figure 3.7: Geo potential Heights of 1000 mBar pressure level.
Figure 3.8: SRTM topographical map of the southern UK.
Figure 4.1 Sample images of rain fields produced by MultiEXCELL.
Figure 4.2: Example simulation of a stratiform event type of precipitation.
Figure 4.3: Before and after the disaggregation process of a rain rate field.
vii
Figure 4.4: Basic diagram of the interpolation process.
Figure 4.5: Diagram of a radio link (red) superimposed on a matrix with rain rates.
Figure 4.6: General diagram to calculate ZDI for rain height.
Figure 4.7: ZDI heights in a year (30 year average)
Figure 4.8: General diagram of the implementation of BaconTjelta sleet model for a
slant path.
Figure 5.1: Comparisons of rain rate exceedance distributions derived from direct
measurement and from Nimrod data over the three calendar years 2004 to 2006.
Figure 5.2: Annual rain exceedance distributions for the original and downscaled
Nimrodderived rain fields for the three calendar years 2004 to 2006.
Figure 5.3: Distributions of annual hydrometeor fade for 38 GHz, terrestrial links of
length 5 km and 8 km, as predicted by Rec. ITUR P.53013 (2009) and produced by
simulation. Distributions are illustrated with and without allowing for extra fading
due to wet snow.
Figure 5.4: Annual distributions of hydrometeor fade for a Ka band uplink to a
geostationary satellite from a Chilbolton ground station. Comparisons are between
Rec. ITUR 61810 (2009) and the simulation result over the three calendar years
2004 to 2006.
Figure 5.5: Illustrations of Fade Duration and Fade Slope
Figure 5.6: Comparison of annual fade duration statistics from the Rec. ITUR
P.16231 (2005) model and from simulation.
Figure 5.7: Comparison of annual fade duration statistics from Rec. ITUR P.16231
(2005) model and simulation for the three years 2004 to 2006 at 11 dB threshold
level.
Figure 5.8: Comparison of annual fade slope statistics from Rec. ITUR P.16231
(2005) model and simulated Nimrod data at 1, 3 and 10 dB threshold levels
Figure 5.9: Annual fade slope distribution at 0.01% fade level, for a Ku band
geostationary EarthSpace link, as predicted by Rec. ITU P.16231 (2005) and
determined from three years of simulation.
Figure 6.1: Geometry of the measured radio links in south of UK
viii
Figure 6.2: Average annual fade distribution for the GBS EarthSpace link to
Sparsholt and terrestrial link (South Wonston  Sparsholt), both measured and
simulated, from April 2004 – March 2005.
Figure 6.3: Joint fade exceedance statistics for the EarthSpace and terrestrial links
from April 2004 – March 2005.
Figure 6.4: Average annual fade distribution for terrestrial link (South Wonston Sparsholt) with 1 km scale to 125 meters from April 2004 – March 2005.
Figure 6.5: Average annual fade distribution for EarthSpace link (Sparsholt) with 1
km scale to 125 meters from April 2004 – March 2005.
Figure 6.6: Average annual fade distribution for terrestrial link in Sparsholt from 5
min to 18.75 seconds (April 2004 – March 2005).
Figure 6.7: Average annual fade distribution for EarthSpace link in Sparsholt from 5
min to 18.75 seconds (April 2004 – March 2005).
Figure 6.8: Annual single and joint statistics for Chilbolton and Sparsholt from April
2004 – March 2005.
Figure 6.9: Annual single and joint statistics between Dundee and Sparsholt from
April 2004 – March 2005.
Figure 6.10: Diversity Gain for two EarthSpace links in Sparsholt and Chilbolton,
April 2004 – March 2005.
Figure 6.11: Diversity Gain for two EarthSpace links in Sparsholt and Dundee, April
2004 – March 2005.
Figure 6.12: Autocovariance of the measured measured terrestrial link fade timeseries compared to the GINSIM prediction.
Figure 6.13: Autocovariance function statistics of the measured EarthSpace link fade
timeseries compared to the GINSIM prediction.
Figure 6.14: Autocovariance function statistics of the measured EarthSpace link fade
timeseries compared to the GINSIM prediction.
Figure 7.1: Vector wind (m/s) at 700 mBar pressure level.
ix
NOTATION
a and b
Parameters of the ZR relationship equation
A
Attenuation level in dB
A0.01
Attenuation exceed for 0.01% of the time in dB
b and a
major and minor axis length of the water drop
C
(1) Coefficient formed by merging of all constant parameters in the
radar equation. (2) Autocovariance
d
Path length
D
Drop diameter
D0
Drop mean diameter
Dx and Dt
Spatial and temporal decorrelation distances
E
Expected value
f
Frequency in Hz
fB
3 dB cut off frequency of the low pass filter (Hz)
G
Antenna gain
h
Pulse length
k and
Frequency and polarization dependent coefficients
Kl
Specific attenuation coefficient ((dB/km)/(g/m3))
m
Order of gamma distribution
M
Liquid water density in the cloud or fog (g/m3).
N(D)
Drop size distribution
N0
Drop concentration at D = 0
N”( f )
Imaginary part of the frequency dependent complex refractivity
Pr
Received power
Pt
Transmitted power
Pr
Averaged received power for precipitation illuminated by the radar
r
(1) Path reduction factor, (2) Distance between the radar and target
R
Rain rate in mm/hr
x
R0.01%
Rain rate exceeded for 0.01% of the time in mm/hr
R0.001%
Rain rate exceeded for 0.001% of the time in mm/hr
T
Temperature
z
Altitude
Z
Radar reflectivity in dBZ
ZV and ZH
Radar reflectivity of a vertically and horizontally polarised pulse
Lapse rate in units of temperature divided by units of altitude
R
Specific attenuation of rain in dB/km
c
Specific attenuation within the cloud in dB/km
Slope of the drop size distribution
h
Altitude relative to the rain height in metres
V
Volume illuminated at any instant
x and t
Spatial and temporal sampling
(h)
Sleet fade multiplication factor for specific attenuation of rain
Wavelength
(f)
Dielectric permittivity of water
Backscattering cross section of the target
Standard deviation of the conditional fade slope
and
Vertical and horizontal beam widths of an antenna
Fade slope in dB/s
xi
GLOSSARY OF TERMS
2D

Twodimensional
3D

Threedimensional
4G

Fourth generation
ACM

Adaptive Coding and Modulation
ARMD

Assymetric Random Midpoint Displacement
CAMRa

Chilbolton Advanced Meteorological Radar
CEOS

Committee on Earth Observation Satellites
CFARR

Chilbolton Facility for Atmospheric and Radio Research
dB

Decibels
DNM

Dynamic Network Management
DRM

Dynamic Resource Management
DSD

Drop Size Distribution
DVBRCS

Digital Video Broadcasting  Return Channel via Satellite
DVBS2

Digital Video Broadcasting  Satellite  Second Generation
ECMWF

European Centre for MediumRange Weather Forecasts
EUMETNET 
European Meteorological Network Services
EUMETSAT 
European Organisation for the Exploitation of Meteorological
Satellites
EHF

Extremely High Frequency
EXCELL

Exponential CELL
FBfs

Fractional Brownian Fields
FMTs

Fade Mitigation Techniques
GBS

Global Broadcast Service
GHz

Giga Hertz
GINs

Global Integrated Networks
GOES

Geostationary Operational Environmental Satellite
HAPs

High Altitude Platforms
HRFNS

Hull Rain Fade Network Simulator
xii
HYCELL

HYbrid CELL
ICAO

International Civil Aviation Organization
IPTV

Internet Protocol television
IR

Infrared
ISA

International Standard Atmosphere
ITUR

International Telecommunication UnionRadio Section
JAXA

Japan Aerospace Exploration Agency
LAS

Local Average Subdivision
LEO

Low Earth Orbit
LMS

Land Mobile Satellite
MESO

Multicommunity Environmental Storm Observatory
MIMO

Multipleinput and multipleoutput
MPE

MultiSensor Precipitation Estimate
MPEF

Meteorological Product Extraction Facility
NASA

National Aeronautics and Space Administration
NCAR

National Center for Atmospheric Research
NCEP

National Centers for Environmental Prediction
NEXRAD

NextGeneration Radar
NGA

National GeospatialIntelligence Agency
NOAA

National Oceanic and Atmospheric Administration
NWP

Numerical Weather Prediction
OFDM

Orthogonal frequencydivision multiplexing
PSD

Physical Science Division
SATNEx

SATellite Network of EXperts
SHF

Super High Frequency
SISTAR

SImulator of the SpaceTime behaviour of the Attenuation due
to Rain
SRTM

Shuttle Radar Topography Mission
SSM/I

Special Sensor Microwave/Imager
THz

Tera Hertz
xiii
TRMM

Tropical Rainfall Measuring Mission
UAS

Unmanned Airborne Systems
UAVs

Unmanned Aerial Vehicles
UM

Unified Model
VHF

Very High Frequency
ZDI

Zero Degree Isotherm
xiv
CHAPTER 1 INTRODUCTION
Modern telecommunications systems use a wide variety of channels e.g. copper,
fibreoptic and airlinks. Wireless links are often faster and cheaper to set up as they
do not require the disruption of installing a wire or fibre along the route. They also
yield greater flexibility and mobility compared to fixed cables. Airlinks also allow
communications with, or via, elevated platforms such as satellites, airplanes, High
Altitude Platforms (HAPs) and other places to which it would be impossible to install
a physical connection. A large proportion of all communications is carried by radio
waves along airlinks. High capacity Super High Frequency (SHF) and Extremely
High Frequency(EHF) radio links are integral to the backbone networks of all
developed countries, and are even more important in developing countries with less
legacy wired network. Communications via elevated platforms require both an uplink
and downlink and so are, at a minimum, networks of at least two links. Currently
there are no internationally recognized models to predict the performance of networks
of two or more links.
High capacity communications systems require higher operating frequencies to
provide the bandwidth. High capacity radio systems currently use the millimetre and
microwave frequencies in the higher SHF and EHF bands. These links can be broadly
characterised as terrestrial if both transmitter and receiver are near the ground or
EarthSpace if one end is on a satellite. Intermediate categories exist where one end
of the link is a High Altitude Platforms (HAPs) or an aircraft. Terrestrial links
between fixed ground stations and copperfibre networks form the backbone of
telecommunications systems. However, satellite communications are increasingly
important for both broadcast systems and as parts of Global Integrated Networks
(GINs).
This is an attraction in developing countries that can rollout telecommunications
infrastructure quickly and cheaply. Mobile phone communications can be made
1
rapidly available in large cities using a base stations networked by microwave links.
In remote places, broadband can be delivered via satellite. Apart from the sudden
broadening in the services provided by the satellite, many private and government
organizations, especially in United States and Europe, have made massive
investments in the development of satellite communication systems based on the
WTEC panel report on Global Satellite Communications Technology and Systems
(www.wtec.org/pdf/satcom2.pdf). Furthermore, there is a market shift where business
and consumers are more directly in contact with satellite service providers.
Although microwave links are cheaper and quicker to deploy than fixed wired
services, the signals that travel between transmitter and receiver must propagate
through the surrounding environment or channel. During propagation signals can be
distorted or attenuated by a wide range of mechanisms (Chris Haslett, 2008; Crane,
1996). Other signals are received as interference to the wanted signal. When present
in the channel, rain and other hydrometeors (sleet, fog, and cloud) will scatter and
absorb radio waves. The specific attenuation due to hydrometeors is highly frequency
dependent. For frequencies below 5 GHz, hydrometeor attenuation is small compared
to signal impairment caused by other causes, for example multipath or ducting.
Therefore, attenuation due to rain and other hydrometeors is not part of the system
design and planning for communications between mobile base stations and handsets.
However, the higher capacity links joining peripheral base stations to the wired
network operate at higher frequencies and their availability is limited by hydrometeor
fading. For most links operating above 10 GHz, hydrometeor fade is the dominant
and limiting fade mechanism (Zhang, 2008; Chris Haslett, 2008; Crane, 1996).
National telecommunications regulators typically license fixed terrestrial links to
operate at a power level aimed to yield a specific average annual availability; 99.99%
for most links and 99.999% for critical links (Trevor Manning, 2009). A base power
level is calculated given typical clearsky path attenuation, calculated using
diffraction models and knowledge of the path elevation profile, and estimated
2
interference from other systems. In addition, a fade margin is calculated from models
of the hydrometeor fade that would be expected for 0.01% or 0.001% of an average
year. The International Telecommunication UnionRadio Section (ITUR) maintains a
set of models for predicting average annual distributions of fade, with a oneminute
integration time, on individual, terrestrial and EarthSpace links. These models are
adequate for the regulation and coordination of terrestrial links and can be used to
assign a fixed fade margin and estimate link budgets for EarthSpace links. The ITUR also provides models of fade duration and fade slope for a tensecond integration
time, principally used in the design of Fade Mitigation Techniques (FMTs). However,
these ITUR models are not sufficient for the design and optimisation of networks of
radio links, even as simple as two links in route diverse or multihop configuration,
which require a joint channel model with a temporal resolution of onesecond or
shorter.
The recently completed SATNEx (SATellite Network of EXperts) II (IST 027393)
European Network of Excellence, and the ongoing IC0802 COST Action, have
identified the urgent need for joint channel models for Global Integrated Networks
(GINs) utilising terrestrial, satellite, unmanned airborne systems (UAS) and HAPs
radio links in the Very High Frequency (VHF) to W bands. In particular, these models
are necessary for the design and optimisation of proposed Land Mobile Satellite
(LMS) systems at Ka and Ku bands and higher EHF frequencies (currently at L, S
and Cband but quickly reaching capacity), see W. Zhuang (1997). Recent projects by
the French space agency CNES (SWIMAX and SDMB) have identified these as the
future for broadband and broadcast systems to mobile receivers in trains, planes and
road vehicles. A draft report by the Electronic Communications Committee of CEPT
(European Conference of Postal and Telecommunications Administrations) stresses
the importance of proposed consumer systems delivering broadband, (Internet
Protocol television) IPTV and multimedia applications to users, direct from satellite
at Ka and Ku bands, (www.erodocdb.dk/docs/doc98/official/pdf/ECCRep152.pdf).
These services will need to coexist with terrestrial services. Of particular concern is
3
the performance of the terrestrial networks linking ground stations to content
providers, in conjunction with the satellite uplinks. These systems require adaptive
FMTs and Dynamic Resource Management (DRM), see Callaghan (2008). Based on
work reported in COST 255 and 280, various adaptation techniques have been
included in standards Digital Video Broadcasting  Satellite  Second Generation
(DVBS2) and Digital Video Broadcasting  Return Channel via Satellite (DVBRCS)
such as uplink power control, reconfigurable antenna systems, and adaptive coding
and modulation (ACM). All these dynamic adaptation techniques require simulation
on channel models during their development and evaluation. The most important fade
mechanisms for EHF on terrestrial or slant paths are scattering by rain and cloud
droplets, absorption by atmospheric gases and scintillation. These fade mechanisms
exhibit complex spatial and temporal correlations, due to their dependence upon the
weather. Furthermore, it is necessary to be able to model a very wide range of scales
i.e. from a radio beam Fresnel diameter to the width of a continent and from onesecond fade variation to the lifetime of a large weather system.
Joint channel simulators are vital for the design, evaluation and optimisation of these
proposed systems. It is essential that sufficient diversity exists in terrestrial networks
to ensure ground stations have access to content and that ground station diversity
ensures content can be communicated to satellites. This will require meteorological
nowcasting to predict link outage and to dynamically reconfigure networks. The
development of fourth generation (4G) direct broadcast to mobile from satellites
techniques, such as multipleinput and multipleoutput (MIMO) Orthogonal
frequencydivision multiplexing (OFDM), will require adaptation to differential fade
along alternate paths, see Liolis et al. (2007). There is likely to be considerable
advantage in the application of ACM techniques developed for satellite
communications to terrestrial networks. However, joint channel models are required
to quantify the benefits on terrestrial networks.
System designers and radio planners face a common problem in forecasting or
4
predicting the effects of rain and other hydrometeors on telecommunication systems.
Current existing models offer limited prediction of joint rain fade distribution on
microwave links. At the moment, most designers rely on existing models such as
from the ITUR to predict statistics of hydrometeors events for an average year or
average worst month.
A known method to generate simultaneous fade timeseries for a heterogeneous
networks of SHF and EHF radio links is to generate finescale, spatialtemporal
weather fields and then to simulate the effects on each radio link Zhang (2008). The
weather fields have come from a range of sources i.e. measured radar data, Numerical
Weather Prediction (NWP) or stochastic simulations constrained by measured
statistics.
One of the earliest systems was developed in Italy and is known as EXCELL; see
(Bosisio and Riva, 1998; Paraboni et al., 2002). However, the EXCELL system
assumes unrealistically smooth spatialtemporal variation of rain rate and its scope
and resolution are poorly defined. The Hull Rain Fade Network Simulator (HRFNS),
Paulson and Zhang (2009), is based on the downscaling of radar data, but is only
applicable over squares of size 50 km in the southern UK. The University of Bath
EHF SATCOM system, Hodges et al. (2003), combines numerical weather models
with radar data to model satellite channels and is valid across the UK. It includes rain
and cloud fade mechanisms as well as scintillation and absorption by atmospheric
gases. Rain fields derived purely from statistical models of rain rate or log rain rate
variation have been employed to model EarthSpace and terrestrial links (Callaghan,
2004; Gremont and Fillip, 2004). A new simulation tool is currently being developed
by ONERA in France called SISTAR. The ONERA system utilises ERA40 historical
NWP data from European Centre for Mid Range Weather Forecast (ECMWF) and is
applicable to satellite links, see Jeannin et al. (2009). However, the input ERA40
data is very coarse and the downscaling techniques employed have not been verified.
More of these will be discussed later in Chapter 4.
5
1.1 Brief description of GINSIM
As discussed in the earlier sections, joint fade timeseries are necessary to evaluate
and optimise the performance of a more complex radio networks and it can only be
acquired through simulation of these links on fine spatial and temporal scale
meteorological fields. This thesis describes the development of GINSIM, a network
fade simulation tool and an extension to the previous HRFNS system. The new
GINSIM is capable of simulating SHF and EHF radio links including terrestrial and
EarthSpace links. Finescale rain fields are generated by numerically downscaling
composite rain images produced by networks of radars. These fields are then
transformed to specific attenuation fields and pseudointegration along the link path
can be performed to obtain the joint fade timeseries. All other fade mechanisms
(other than rain effects) can be added later into the system. The detail procedures of
GINSIM will be explained later in Chapter 4. The following figure describes the
block diagram of GINSIM.
6
Input
Measured
Nimrod rain
maps
Remove Advection
Disaggregation
Loop to obtain
more
measured
Nimrod rain
maps
Introduce rain rates
below
minimum
threshold
Interpolation
Reintroduce
advection
Input
Output
Rain
height
from NOAA
Downscaled
rain maps
Figure 1.1: Block diagram of the GINSIM
7
1.2 Aims and objectives
The main aim of this research is to expand the capability of the previous HRFNS by
adding new fade mechanisms, particularly attenuation due to sleet (wet snow), and
the ability to simulate slant path links such as EarthSpace, EarthHAPs and EarthUAV. Sleet specific attenuation can be calculated using the BaconTjelta sleet model,
see Tjelta et al. (2005). Both the sleet fade calculation and the effective path length of
slant path link rely on rain height parameter which can be extracted from
NCEP/NCAR reanalysis dataset. The old HRFNS was based on rain fields measured
by Chilbolton Advanced Meteorological Radar (CAMRa). The proposed system,
GINSIM utilises rain maps from Nimrod and OPERA to expand the coverage to most
of Europe.
The major objectives of this research:
1. Develop a joint channel rain fade simulation tool, based on algorithms
developed for HRFNS, but using new datasets with European or global
coverage,
2. Incorporate fading by wet snow (sleet),
3. Expand the current system to be able to simulate slant path links,
4. Validate the simulated results with ITUR models,
5. Validate the simulated results with real radio links.
1.3 Thesis outline
The review of research undertaken throughout three years of study has been
documented in this thesis. Chapter 1 provides an introduction, the aims and objectives
and the research overview. Chapter 2 reviews hydrometeors fade mechanisms from
the relevant ITUR models.
Chapter 3 lists meteorological and other measurement datasets, including rain radar
maps from Nimrod/OPERA and NCEP/NCAR reanalysis data, that can could be used
8
in the proposed simulator.
Chapter 4 details the downscaling algorithms applied to the meteorological data,
including the disaggregation and interpolation techniques. Chapter 5 investigates the
validation of downscaled rain radar and simulated radio networks against theoretical
ITUR models. Chapter 6 reports the validation and comparison between simulated
radio networks and real links measurements.
Finally, Chapter 7 summarises and concludes the project. Suggestions of future work
and recommendations are also provided in this chapter.
9
CHAPTER 2 MICROWAVE FADE MECHANISMS
Microwave telecommunication links, including terrestrial and EarthSpace satellite
links operating at EHF band (30300 GHz), offer the large bandwidth and high
capacity required for applications such as multimedia services. The increasing
number of users and the growing complexity of multimedia have driven a demand for
capacity that has pressured regulators to explore higher frequency bands for larger
bandwidth. However, most of the atmospheric fade mechanisms are frequency
dependent, and higher frequencies are usually associated with higher losses. Rain
attenuation is the dominant fade mechanism on fixed links operating above 10 GHz.
Attenuation by other hydrometeors such as cloud, fog and sleet (wet snow),
scintillation due to movement of the atmosphere, absorption by atmospheric gasses,
and multipath effects such as ducting also contribute to fade distributions and may be
the largest fade mechanism in specific circumstances and for short times. This chapter
discusses these fade mechanisms, their effects on radio links and the relevant ITUR
models.
2.1 Formation of Cloud and Rainfall
A wide variety of hydrometeor particles exist in the atmosphere, mainly differing in
shape, size and composition. They are made by complex processes such as ice
nucleation, evaporation and sublimation, condensation, particle breakup and
coalescence. Clouds exists in many forms including convective (Cumulus type of
clouds), uniformly distributed layer (stratus) and thin layer clouds (cirrus) which can
be located at altitudes above 5 km. Generally, clouds are formed in the troposphere
when rising air containing water vapour cools to its dew point (the temperature at
which the air becomes saturated). Water vapour condenses and freezes onto existing
dust, salt and ice particles. Ice crystals within the cloud can fall into warmer layers
and melt to become water droplets. These water droplets then will be large and dense
enough and fall as rain drops.
10
Clouds are usually formed in a convective or stratiform type. Convective clouds are
usually smaller, typically from hundreds of metres to several kilometres across and
are often associated with thunderstorms. Convective clouds are formed when there
are intense heating from the sun and an abundance of moist air. Stratiform clouds are
typically larger, stably stratified and caused by broader layers of more slowly rising
air. Stratiform cloud could range from 100 to 1000 km across. Figure 2.1 illustrates
the formation for stratiform and convective clouds.
Figure 2.1: Convective and stratiform cloud formation. (The diagram was derived
from www.weatherquestions.com/How_do_clouds_form.htm).
Generally, there are several types of rain events which are usually associated with
cloud types; the convective rain, stratiform or frontal rain and orographic rainfall.
Convective rain is usually heavy, from convective clouds and dominates in tropical
regions. The rainfall rate for convective rain can be as high as 150 mm/hr for
temperature regions and more than 200 mm/hr in tropical regions, for short periods of
time. In the UK, rain event are often assumed to be convective when rain rates
11
exceeding 20 mm/hr last for more than a few minutes. Rainfall from stratiform cloud
is usually light and contains a larger proportion of small raindrops. However,
stratiform rain has larger coverage area in contrast to convective rain events, typically
hundreds of kilometres across. Orographic rainfall is formed when a parcel of air
containing water vapour collides with a mountain and is forced upwards. Orographic
rain can lead to significantly different microclimates around large geographic features
but is not important for most areas of the UK.
For temperate regions, the Bergeron process is the leading rainfall generating
mechanism (Usman, 2005). The Bergeron process, also known as the ice crystal
process, forms precipitation in cold clouds by the growth of ice crystals. Supercooled
water droplets, as cold as 40°C, evaporate and the vapour sublimes onto ice crystals,
making larger crystals. Water droplets can also collide with ice crystals and freeze.
These ice crystals will melt into water droplets as they fall into warmer levels. This
region is called melting layer and it is related to a radio term known as the rain height.
In radar meteorology the melting layer is known as the bright band as it produces a
strong return echo. The height of the melting later is strongly affected by temperature
profile or lapse rate through the atmosphere and can vary depending on seasons and
regions. Typically, the melting layer is at its maximum height during summer.
Collision and coalescence processes are more important in rainfall formation in the
tropical region. Cloud droplets which are carried by air currents will collide with
other droplets forming larger drops until they become large enough to form raindrops.
Not all droplets fall as rain since some evaporate before they reach the ground
(Usman, 2005). Figure 2.2 illustrates the processes leading to the formation of rain
within a cloud.
12
Figure 2.2: Rain formation within a cloud from Usman (2005)
2.2 EarthSpace Radio Communication System
Radio communications with satellites may use high frequencies as the path through
the attenuating troposphere is often short. Due to the elevation of the link,
interference is often less of a problem than with terrestrial links. In most of the
commercial
EarthSpace telecommunications, the satellites are located in
geostationary orbit above the equator where the angular velocity of the satellite is
equal to the rotation of Earth. The large orbit radius (approximately 36,000
kilometres) allows large areal coverage, without the ongoing expense of building and
maintaining terrestrial networks. Except for at high latitudes, EarthSpace links do not
require ‘path clearance’ like the terrestrial link to check if the signal will be blocked
by tall obstacles (hills, mountains, buildings) since the Earth station only need point
directly to the satellite. The most important parameter when dealing with
hydrometeor fades on EarthSpace links is the rain height. The zero degree isotherm
(ZDI) height (the altitude where the temperature is zero degrees Celsius) is closely
related to rain height. Figure 2.3 illustrates the path geometry for an EarthSpace link.
13
Figure 2.3: A geometry path for an EarthSpace link.
For a stratified, rainy atmosphere the EarthSpace path passes through three regions.
Near the ground, rain will consist entirely of liquid particles and the specific
attenuation will be close to that predicted by Rec. ITUR P.8383 (2005). Higher, in
the melting layer, mixed phase particles will exist leading to specific attenuations
many times that associated with rain rate of the equivalent intensity. Above the
melting layer, all hydrometeors will be frozen and the specific attenuation at EHF
frequencies is close to zero. The melting layer straddles the ZDI as supercooled
water particles exist above this level and partially melted mixed phase particles exist
below. Rec. ITUR P.61810 (2009) includes the effects of the melting layer by
assuming rain exists up to an altitude known as the rain height, assumed in Rec. ITUR P.8393 (2001) to be 360 m above the ZDI. Rain height can vary from near the
ground level to 5 km depending on seasons and regions.
2.3 Absorption by Atmospheric Gasses
Water vapour and oxygen molecules in the atmosphere have resonant frequencies at
which they strongly absorb radio waves, causing high attenuation. Absorption by
atmospheric gasses depends upon the temperature and partial pressure of these gasses.
Therefore their spatial and temporal variation is rather gradual. Rec. ITUR 6768
(2009) provides procedures to calculate losses due to absorption for radio waves as
shown in Figure 2.4. Specific attenuation has been calculated using the model in Rec.
14
ITUR P.6768 (2009) for frequencies from 1 to 350 GHz using parameters for a
standard atmosphere i.e. a temperature of 20 Celsius, pressure 1013 hPa, and water
vapour density of 7.5 g/m3. Rec. ITUR P.6768 (2009) writes the specific attenuation
due to absorption by atmospheric gasses is written as:
o w 0.1820 f N " ( f ) dB/km
(2.1)
where o and w are specific attenuations for dry air and water vapour respectively, f
is the frequency in GHz and N”( f ) is the imaginary part of the frequency dependent
complex refractivity.
Figure 2.4: Specific attenuation due to Atmospheric gasses from Rec. ITUR 6768
(2009)
For most links the average and dynamic fading caused by atmospheric gasses is
insignificant. For instance, for a radio link operating at 10 GHz, the total specific
attenuation due to absorption is approximately 0.01 dB/km. On the other hand, the
specific attenuation rises steadily beyond 20 GHz and at resonance peaks, for
15
example the oxygen line at 60 GHz, can reach values between 16 and 17 dB/km.
Peaks of absorption within communications frequencies occur at approximately 22
GHz (for water vapour) and 60GHz (for oxygen). The frequency regions between
these absorption peaks are called atmospheric windows. The frequencies in demand
for use in long distance telecommunications and radar system design are in the
window regions. Bands close to absorption peaks are available for adhoc, unlicensed
use due to the short reuse distance. As the frequency windows become congested,
radio designers are forced to consider higher frequencies. Beyond 60GHz, the
absorption loss for oxygen is decreasing but the absorption for water vapour steadily
increases and becomes more complicated with stronger water vapour lines occurring
at 183, 325 and 380 GHz (Liebe, 1989). For radio links operating at frequencies at
beyond 350 GHz, the atmospheric absorption loss can be more significant than rain
fading, Paulson (2005). For instance, specific attenuation for atmospheric absorption
can be at 1000 dB/km at 1THz. Low margin systems operating close to absorption
lines can experience slow variation in fade margin due to changes in temperature and
pressure and this can lead to outages at lower rain rates than would be otherwise
expected.
2.4 Rain Parameters, Scattering and Attenuation
Scattering and absorption by rain and other hydrometeors (wet snow, hail) is the
dynamic fade mechanism leading to the largest prolonged fading on most millimetric
telecommunications links. Attenuation due to rain is negligible at frequencies below 5
GHz. However, above 10 GHz, losses due to rain can cause outages and it is the
factor that limits availability of these links. Scattering by rain can increase
interference by scattering unwanted signal into a receiver, as well as reduce the power
of the wanted signal. Raindrops have a similar size to the millimetre radio wavelength
in the EHF band. For instance, the wavelength for 38 GHz radio signal is around 8
mm while the diameters for raindrops are usually from 1 or few mm to 10 mm
(Usman, 2005). Specific attenuation of rain on microwave links depends on various
16
parameters including the rain drop size distribution (DSD), raindrop shape and rain
rate.
2.4.1 Rain Scattering
Rain drops scatter and absorb the incident radio wave energy. Rayleigh scattering is
an approximate theory that describes scattering when the hydrometeor particle is
much smaller than the wavelength of the radio wave. According to Rayleigh
scattering, the energy of the incident radio wave is scattered with a radiation pattern
similar to that of a dipole and the amount of energy that is scattered is proportional to
D3/λ, where D is the diameter of the particle and is the wavelength. If the
hydrometeor particles are of a similar size to the wavelength then the more
complicated Mie scattering model is used. Mie scattering is only applicable to
spherical objects and so becomes increasingly inaccurate for larger rain drops and is
not applicable to most sleet particles. Mie scattering predicts larger peaks in the
forward and backwards scattering directions than Rayleigh scattering. The Rayleigh
scattering model can be used for most cases of rain scattering effects on microwave
links. Figure 2.5 illustrates the radiation pattern predicted by Rayleigh and Mie
scattering models.
Figure 2.5: Energy scattering pattern of Rayleigh and Mie.
17
2.4.2 Raindrop Size Distribution (DSD)
The distribution of different sizes of raindrop has been studied and modeled since the
beginning of 1940s, (Law and Parson, 1943; Marshall and Palmer, 1948). Initially a
crude measurement of DSD was performed using flour pallet or bloating paper
methods. Since then, more advance equipment has been designed and built for DSD
measurement, such as the well known drop impact disdrometer by Joss & Waldvogel
(1977). A disdrometer with impact sensor served as a basis for drop sizing
instruments where vertical momentum of an impacting drop is transformed into an
electrical pulse whose amplitude is a function of the drop diameter. One such example
of a disdrometer is the Distromet Joss Waldvogel Impact Disdrometer RD69,
installed at Chilbolton and Sparsholt and operated by the Chilbolton Facility for
Atmospheric and Radio Research (CFARR). Recently, an optical disdrometer,
(Lempio G. E. et al., 2007) was presented where the main working principles for such
equipment is the light extinction of precipitation particles passing through a
cylindrical sensitive volume of 120 mm length and 22 mm diameter. The electronic
signal caused by a precipitation particle is proportional to its crosssectional area.
The DSD, N(D)dD is the number of raindrops per unit volume where the diameter of
the equivalent volume spherical drop is between D and D+dD. The DSD is related to
rain rate by the fallspeed as a function of D. The shape of the DSD is often assumed
to be exponential (Marshall and Palmer, 1948, Waldvogel, 1974) or a Gamma
function (Ulbrich, 1983). Both distributions have exponential large drop tails but
differ in the proportion of small drops. Some of the variation in the size of the small
drop distribution is due to systematic measurement errors associated with the
instruments used to measure the distribution. The uncertainty in the number of large
drops is always large due to the low numbers measured leading to large sampling
uncertainty.
The exponential distribution DSD from Marshall and Palmer is given by:
18
N ( D) N 0 exp(D)
(2.2)
where N 0 is a MarshallPalmer scale parameter and found to be approximately 8000
mm1m3. The value of is given by:
4.1R 0.21
(2.3)
where R is rainfall rate in mm/hr.
It is usually assumed that for sufficiently large sample volumes, exponential DSD
models are adequate. As the sample volume becomes small, usually for ground based
instruments and short integration times, then the Gamma distribution often provides a
better fit. The Gammatype distribution is known to adequately model the DSD
variation and is given by:
N ( D) N 0 D m exp(D)
(2.4)
is given by:
3.67 m
D0
(2.5)
where D0 is the mean diameter.
The value of m, the order of the Gamma distribution varies within a range of 1 to 10.
From the equation above, when m is 0, the distribution is a MarshallPalmer type
exponential distribution. When m is increases, the number of drop concentration
decreases and when m is decreases, the number of drop concentration increases as
shown in Figure 2.6. Note that for positive m the concentration of small drops goes to
19
zero as drop diameter goes to zero. The values of m can be related to a particular rain
event type. Values of m correspond to convective (0 ≤ m ≤ 1), stratiform (m > 2) and
orographic (m < 0) (Usman, 2005).
Figure 2.6: Ulbrich Gamma DSD model with m variation. D0 is assumed to be 0.1 cm
and N0 is 80000 cm1m3.
For the same rain rate, variation in the DSD can lead to variation in the predicted
microwave specific attenuation by a factor of two, more or less than the average
value. At higher EHF frequencies, this uncertainty grows due to the increasing
importance of smaller drops. At millimetric frequencies, the uncertainty is large due
to variation in the number of large drops. Rayleigh scattering predicts a scattering
crosssection proportional to the diameter raised to the sixth power. At frequencies
for which Rayleigh scattering is appropriate, a single 10 mm drop scatters as much as
a million 1 mm drops while having only a thousandth of the water volume. As the
first Fresnel zone for many links is of the order of a metre across, specific attenuation
is expected to vary along the link around the ITUR value associated with the rain
20
rate. However, the uncertainty in link fade due to this variation is expected to be
reduced by integration of specific attenuation along the link path. Because of this,
using the specific attenuation predicted by Rec. ITUR P.8383 (2005) is expected to
be adequate in most cases.
2.4.3 Rain Drop Shape and Canting Angle
Small rain drops around 1 mm in diameter are spherical due to surface tension.
However, shapes and sizes of larger raindrops gradually change due to hydrodynamic
forces experienced when they are descending in free fall, as illustrated in Figure 2.7.
The diagram was based on Usman (2005) evolution of rain drops and sizes.
Figure 2.7: Evolution of rain drops with radius lengths in mm.
The distribution of raindrop sizes reflects the very complicated collision, breakup
and evaporation processes occurring in the air column. The combination of water
circulation within the drop, and drag due to air flowing around the drop as it falls,
tends to flatten the base of larger raindrops turning them into oblate spheroids. As the
raindrop diameter further increases, the base becomes concave (Zhang, 2008). When
the radius increases to 5 mm or more, the drop balloons and breaksup into a random
number of smaller drops. The entire evolution process will start again for new small
raindrops. Convective rain event such as thunderstorms generally have a wider range
of raindrop sizes compared to the stratiform type of rain event.
For scattering calculations, it is common to view the shape of rain drop as oblate
21
spheroids. One of the earliest studies of the shapes of raindrops was performed by
Pruppacher and Beard (1970). The experiment was performed by observing water
drops suspended in a vertical wind tunnel. They have shown that water drops falling
at terminal velocity were deformed into approximate oblate spheroids. They have
discovered that water drops with diameters in the range 1 to 4 mm have a linear
correlation between the axial ratios and drop size leading to the following equation:
b
1.03 0.62D
a
(2.6)
where b and a are major and minor axis length of the water drop respectively and D is
the diameter of the volume equivalent spherical drop. This expression is only known
to work for diameters larger than 1 mm, (Usman, 2005). Equation (2.6) was later
theoretically verified by the numerical evaluation of the balance of forces acting on a
drop falling under gravity, (Pruppacher and Pitter, 1971). The rain drop shape model
of PruppacherPitter is a well known and accepted model by scientific communities
for the calculation of microwave attenuation by rain. Several other models were
suggested later to refine the linear expression of PruppacherPitter including Morrison
and Cross (1971), Beard and Chuang (1987) and Goddard and Cherry (1984).
Linearly polarized radio waves propagating through a rain event suffer phase shift
and differential attenuation due to the verticalhorizontal asymmetry of the nonspherical large raindrops. However, for a given fade depth, differential attenuation
and phase shift decrease as frequency is increased because the more spherical smaller
rain drops make a larger contribution to the total attenuation (Barclay, 2003).
Rain drops are known to be canting if the rain drop axis symmetry is not vertical.
This is commonly caused by vertical wind shear near the ground. Canting angles
affect radio links by transferring some energy between horizontally and vertically
polarized waves. The fading effect due to canting angle is considered insignificant in
22
contrast to variation in drop size (Usman, 2005).
2.4.4 Rain rate
Specific attenuation can be calculated from the DSD and a drop shape model.
However, the disdrometers required to measure DSD are still relatively rare and
instruments to measure drop shape are even less common. Specific attenuation is
more commonly associated with rain rate as this is a parameter that is widely
measured and much is known of its statistics. Rain rate, or rain intensity, is measured
in units of millimetres per hour (mm/hr)
and vast databases of rain rate
measurements exists spanning hundreds of years and many thousands of locations.
Specific attenuation is usually modeled as a powerlaw function of rain rate. This
simple powerlaw combines all the complications of the scattering fields produced by
all the drops of different shapes and their arrangement in space. Although rain rate is
the most common parameter used for estimating specific attenuation, it is far from the
best. Rain kinetic energy is much closer to specific attenuation, in terms of DSD
moments, and can be measured by many instruments. Similarly, the transformation of
radar reflectivity into a rain rate and then into a specific attenuation is effectively a
frequency scaling and the derived specific attenuation may be more accurate than the
intermediate rain rate.
The most important meteorological statistic when planning a radio system is the
rainfall rate exceeded for 0.01% or 0.001% of the time, R0.01% and R0.001%. These rain
rates are highly geographical dependent. For temperate regions, R0.01% can be around
30 mm/hr while for arid regions it is only few mm/hr. For tropical regions that
experience monsoon seasons, the R0.01% can be as large as 150 mm/hr. Normally, radio
engineers will design a terrestrial fixed link to have 99.99% availability in an average
year, and to fail when it experiences rain rates higher than R0.01% .
Several procedures exist to estimate the statistics of rain rate in a particular region.
Empirically, rain rate statistics can be directly measured using a rain gauge and/or
23
rain radar. A rain gauge is a device utilised by hydrologists and meteorologists to
quantify the amount of liquid precipitation over a set period of time. Rain radar is a
type of weather radar that can be used to locate and estimate precipitation or rain.
Statistics of rain rate can also be found in Rec. ITUR P.8375 (2007), or in the
Global Crane model (Crane, 1996). Rain parameters are known to exhibit long term
correlations and large yeartoyear variability. Anecdotally, ten years of rain data is
required to estimate the average annual rain rate exceeded 0.01% of the time to the
precision needed for radio planning. The Rec. ITUR P.8375 (2007) model provides
the annual distribution of rainfall rate with an integration time of 1 minute for the
entire globe, derived from numerical weather prediction, but recommends the use of
locally measured rain rates if available. Figure 2.8 illustrates an example of a rain rate
distribution from Rec. ITUR P.8375 (2007), which shows the 0.01% of the
exceeded level is around 25 mm/hr at Chilbolton, UK, at approximately 53 degrees
north in latitude.
Figure 2.8 Rain rate annual distribution for Chilbolton from Rec. ITUR P.8375
(2007)
24
2.4.5 Specific Attenuation of rain
Rec. ITUR P.8383 (2005) provides the international recognized model to calculate
specific attenuation of rain from the rain rate. The specific attenuation, R (dB/km) is
obtained from the rain rate R (mm/hr) using the power law relationship:
R kR
(2.7)
where k and are frequency and polarization dependent coefficients. The coefficients
can be determined using the following equations:
log f b
10
j
log10 k a j exp
cj
j 1
4
2
m log f c
k
10
k
log f b 2
10
j
a j exp
m log f c
10
c
j
j 1
(2.8)
5
(2.9)
where f is the frequency in the range 1 to 1000 GHz. Values for the constants required
to calculate k and are provided by Rec. ITUR P.8383 (2005). Specific attenuation
increases with frequency and rain rate as illustrated in Figure 2.9.
25
Figure 2.9: Specific Attenuation of 20 and 30 mm/hr for different frequencies from
Rec. ITUR P.8383 (2005)
2.4.6 Rain Attenuation
Rain attenuation is defined as signal loss in dB at the receiver due to rain events.
Calculation of rain attenuation for a microwave link requires integration of the
specific attenuation along the link’s path. Annual statistics of rain attenuation can be
determined empirically by monitoring links. However, along with equipment effects,
fading mechanisms other than rain scatter such as absorption by atmospheric gasses,
scintillation,
multipath,
scattering
by
water
drops
on
the
antenna
and
interference/noise, will be present in the measurement and therefore it may not be
impossible to identify just the fading due to rain. When planning a link,
well
established models, such as the Rec. ITUR P.53013 (2009) for terrestrial links and
Rec. ITUR P.61810 (2009) for EarthSpace links, can be used to predict the average
annual distribution of oneminute fading due to rain and other processes.
26
Rec. ITUR P.53013 (2009) predicts the rain attenuation that will be exceeded for
0.01% of an average year from R0.01% and link parameters using the following steps:
1. Estimate R0.01% using Rec. ITUR P.8375 (2007) or from locally measured
data.
2. Determine the associated specific attenuation R exceeded for 0.01% of the
time using Rec. ITUR P.8383 (2005).
3. Determine the effective path length, deff = r×d using the following equations
from Rec. ITUR P.53013 (2009):
r
1
1 d / d0
(2.10)
Where d is the actual length of a radio link in kilometres and r is the path
reduction factor.
This term is necessary to translate the point specific
attenuation into a path averaged value.
For rain rate 100 mm/h:
d0 35 e–0.015 R0.01
(2.11)
For rain rate 100 mm/hr, the R0.01 value will be 100 mm/hr.
4. Finally, multiply the effective path length with the specific attenuation to
estimate the rain attenuation at 0.01% exceeded level, A0.01
A0.01 R deff R dr
dB
(2.12)
Figure 2.10 demonstrates the annual rain fade statistics calculated using Rec. ITUR
P.53013 (2009) for a R0.01% rain rate of 30 mm/hr and for terrestrial 38 GHz links of
various lengths. Longer paths experience more rain attenuation as more of the link
experiences fading.
27
Figure 2.10: Annual Rain Attenuation distribution from Rec. ITUR P.53013 (2009)
Similarly, rain attenuation distributions can be derived from Crane’s model. Unlike
the ITUR models which utilises the path reduction factor, Crane takes into account
the variation of rain rates along a horizontal path. There are three versions of Crane’s
model. The first version was the Global Crane model developed in 1980. In 1982,
Crane developed a 2component Crane model that used a path integrated technique.
Crane further refined his model in 1989 to include spatial correlation and statistical
variations of rain within a cell. All of these models are included in his book, (Crane,
1996). However, there are some disputes in terms of reliability and performance
between ITUR and Crane’s models. William Myer (1999) concluded that it is not
clear which model is better than the other especially at higher rain rates. Both the
ITUR and Crane’s models use differently globally defined rainfall zones or rain rate
maps.
The calculation of rain attenuation for EarthSpace link using Rec. ITUR P.61810
(2009) is similar. EarthSpace links experience rain fading from the ground station up
28
to an altitude known as the rain height. Rec. ITUR P.8393 (2001) assumes that the
average annual rain height is 360 m above the average annual zerodegree isotherm
(ZDI) height. Both horizontal and vertical path reduction factors are introduced to
account for the spatial variability of specific attenuation.
When a melting layer exists, an EarthSpace link will pass through it, albeit for a
relative short distance. This is in contrast to terrestrial links, which only pass through
the melting layer when the ZDI is near the ground, but then often the whole link is in
the melting layer. The effects of the melting layer on EarthSpace links is introduced
by the 360 m offset between the ZDI and the rain height. Currently there are no
models for shorter slant paths that may terminate within the melting layer, such as
links between ground and Unmanned Aerial Vehicles (UAVs).
.
2.5 Sleet Attenuation
Sleet particles are a mixture of ice, liquid water and air. In a stratified atmosphere,
they can exist from about 500 m above the ZDI to approximately 1000 m below. In
convective events they can exists throughout the rain column. It has been established
that sleet or wet snow attenuates radio waves many times more than rain of the
equivalent intensity, see (Tjelta et al, 2005).
There are many reports of outages on terrestrial links due to sleet or wet snow in the
past 50 years. Takada and Nakamura published a report in 1966 where an
experimental, 14.6 km radio link operating at 11 GHz experienced six times higher
attenuation due to sleet than would be expected for the same precipitation rate of
liquid water, (Takada and Nakamura, 1966). Link monitoring experiments carried out
by Rutherford Appleton Laboratory identified sleet as the major cause of unexpected
outages on links in both the southern UK, (Thurai and Woodroffe, 1997), and in
Scotland, (Walden et al, 2003).
Currently, the most reliable model to predict average annual excess attenuation due to
29
sleet on terrestrial links is the BaconTjelta sleet model (Tjelta et al, 2005) which
utilizes global maps and apriori information to calculate the quantity of sleet and
establish a mean specific attenuation profile to acquire excess fade in the melting
layer region. The model assumes a Gaussian distribution of rain heights and a fixed
formula for the melting layer excess specific attenuation as a function of the position
in the melting layer.
Excess attenuation due to sleet will vary with altitude relative to the rain height as
illustrated in Figure 2.11. The sleet multiplication factor is the specific attenuation
due to sleet divided by the specific attenuation due to the equivalent rain rate. On
average, sleet will cause a maximum attenuation about 3.6 times higher than the
specific attenuation due to the equivalent rain rate, approximately 300 m below the
rain height. At altitudes more than a kilometre below the rain height, the
multiplication factor approaches 1 as most particles have then melted into water. For
heights that are closer to the rain height, the multiplication factor approaches zero as
most particles are ice which has a very low specific attenuation.
30
Figure 2.11: Sleet fade multiplication factor for specific attenuation of rain from Rec.
ITUR P.53013 (2009)
Equation 2.13 is the model of the sleet multiplication factor provided by Rec. ITUR
P.53013 (2009):
0
2
4 1 e h / 70
(h)
2 2
2
1 1 e ( h / 600) 4 1 e h / 70 1
1
0 h
1200 h 0
(2.13)
h 1200
where (h) is the multiplication factor and h is the altitude relative to the rain
height in metres.
31
2.6 Cloud Attenuation
Rain events are usually associated with cloud although cloud has a larger spatial
coverage. Cloud consists of water or ice particles with a diameter generally less than
0.01 cm and can occur across a wide range of altitudes and in a wide variety of
shapes. Cloud attenuations are usually small, typically a few dB for Earthspace links
operating below 100 GHz. However, cloud attenuation can be crucial at higher EHF
frequencies since cloud particles are an order of magnitude smaller than rain drops.
Cloud is not as dynamic as rain in space and time and often they are present when it is
not raining. However, this will still be detrimental for satellite links since the duration
of the cloud in an area will be longer than rain events, hence the period of cloud
attenuation will be longer than rain fade. The different types of clouds including
cumulus, cumunolimbus, stratus and nimbostratus have variable cloud liquid water
content and fade which further complicates the problem of predicting cloud fade
(Dissanayake et al, 2001). Rec. ITUR P.8404 (2009) provides guidelines to model
and calculate cloud attenuation. According to the ITU recommendations, the Rayleigh
approximation is applicable for frequencies below 200 GHz. Like fog, it is usual to
link cloud specific attenuation to the volumetric liquid water content. The specific
attenuation within a cloud can be written as:
c Kl M
dB/km
(2.14)
where:
c :
specific attenuation (dB/km) within the cloud,
Kl :
specific attenuation coefficient ((dB/km)/(g/m3)) and
M :
liquid water density in the cloud or fog (g/m3).
The coefficient Kl may be derived from a mathematical model based on Rayleigh
scattering, which uses a doubleDebye model for the dielectric permittivity ( f ) of
water and it is valid for frequencies up to 1 THz.
32
Chapter 2 summary
Microwave links suffer fading due to a range of mechanisms including absorption by
atmospheric gasses and scattering by hydrometeors such as cloud drops, sleet and
rain. Scattering by sleet and rain generally cause the largest protracted fades for radio
links operating above 10 GHz, and limit the availability of these links. The specific
attenuation of a hydrometeorfilled atmosphere may be related to the equivalent rain
rate. The internationally recognised model Rec. ITUR P.8383 (2005) links rain rate
to an average specific attenuation. In practice, specific attenuations vary considerably
around the Rec. ITUR P.8383 (2005) value to variation in particle phase, drop size
distributions, drop shapes and canting angles. In later chapters I introduce a rain fade
simulation method for heterogeneous networks where the hydrometeor fade
experienced by a link is estimated by pseudointegration of the specific attenuation
along the link path. The Rec. ITUR P.8383 (2005) value is used, multiplied by the
Rec. ITUR P.53013 (2009) sleet multiplication factor. It is expected that averaging
of specific attenuation along the link, and over many events, will yield the correct
longterm statistics of hydrometeor fading.
33
CHAPTER 3 METEOROLOGICAL MEASUREMENTS
A range of meteorological input data is necessary for the simulator. At millimetre
wave frequencies, terrestrial links are short, from 10 km down to a few hundred
metres, but rain specific attenuation is high and so finescale spatialtemporal rain
fields are vital. For the simulation of slant paths it is necessary to produce fields of
rain and possibly cloud density, at a range of altitudes. The previous HRFNS system
used Chilbolton Radar Interference Experiment (CRIE) rain maps as coarsescale
input data, but these data is only cover a 52 o arc with a range of 60 km, centered on
Chilbolton in the southern UK. The proposed simulator requires measurement
datasets that can cover a large part of Europe or are global as part of the development
for network simulator applicable at global scale, and so a new source of input data is
needed. This chapter catalogues the datasets relevant for GINSIM and discusses the
techniques used for parameter estimation. Meteorological datasets other than rainfall
that can be useful for GINSIM and these will also be discussed.
At a minimum, three parameter datasets are required for the GINSIM development:
topography, rain height and rain field. This will be described on section 4.3 in
Chapter 4. These parameters should be provided on a sufficiently fine sampling
interval to allow for numerical downscaling to the scales required for channel
simulation. Topography is timeinvariant and available from several sources. Rain
height needs to be deduced from zero degree isotherm height. This varies slowly in
space and can be provided by several NWP model databases. Rain fields are the most
difficult parameter due to their spatial and temporal variability. Additionally, rain
parameters are notoriously difficult to estimate remotely.
3.1 Rainfall Measurements
Forecasting or estimating spatial and temporal distributions of rain events remains
one of the most challenges issue for meteorological services. A range of instruments
34
exist to measure rainfall including rain gauges, weather radars, aircraft and satellites.
Rain gauges provide direct measurement of rainfall rates but lack spatial coverage
due to the small collection area for each rain gauge and low gauge densities. Rain
gauges are completely absent in some areas such as over the sea where analysts have
to use weather radars or measurements from satellites to estimate rainfall rates. Rain
gauges are usually used as “ground truth” in order to compare, calibrate and verify
other remote measurement techniques such as from radars and satellites.
Meteorological radars utilise an echosounding system to estimate hydrometeor
parameters. Polar or crosspolar radar reflectivity can be related to parameters of the
dropsizedistribution and derived parameters such as rain rate. Rain radars can
provide wide spatial coverage and high spatial and temporal resolution. However, the
surfacebased weather radars only cover some parts of the world (Western Europe,
Japan and North America). In addition, many effects such as ground clutter, variation
of raindrop size distribution and bright band reflections may lead to inaccurate rain
parameter estimation.
Measuring weather parameters, including rainfall rate, from sensors on board
satellites is becoming increasingly important as this method can yield global coverage
relatively economically. Satellite observations suffer a fundamental limitation as they
observe weather from above. Often parameters near the ground, such as rain rate,
need to be estimated from measurements of cloud top parameters. These estimates
may suffer very large prediction uncertainties and some have low temporal and
spatial resolutions. Weather satellites are usually fitted with radiometers that can
measure emissions from the Earth’s surfaces and cloud tops. Increasingly weather
satellites have been equipped with rainfall radars, i.e. the Tropical Rainfall Measuring
Mission (TRMM). Other satellites such as the National Oceanic and Atmospheric
Administration (NOAA)’s Geostationary Operational Environmental Satellite
(GOES) rely on measuring the infrared (IR) visible radiation emission from Earth to
estimate rainfall rate, (Scofield and Kuligowski, 2003).
35
3.1.1 Rain Gauges
A rain gauge is a device mainly used by hydrologists or meteorologists to estimate the
amount of precipitation over a set period of time. The use of rain gauges can be dated
back to ancient Greece. The Egyptian nilometer provided a timeseries of the size of
Nile inundations spanning 5000 years (www.waterhistory.org/histories/cairo/). The
world’s first standardize rain gauge was invented in 1890 by George James Symons,
one of the members of British meteorological society.
Rain gauges are still considered to be the most dependable tool to accurately estimate
rainfall intensity in a particular location and are often used as point measurements.
The calculation of rainfall rate using standard rain gauges is performed by dividing
the volume of water collected by the area of catchment area (commonly a funnel) and
the collection period. Gauges may be heated to melt snow collected in the funnel. A
range of methods exists to automatically measure the volume of collected water
including weighing, drop counting or tipping bucket mechanisms. Over the last
decade, wide ranges of optical devices have come to dominate the market.
Tipping bucket rain gauges operate by using a funnel to collect and direct the
collected rainfall to a seesaw like container. The lever tips when the amount of water
collected reaches the preset volume, sending an electrical signal for recording, and
dumps all the collected water. Drop counting gauges perform in a similar fashion.
Precipitation is collected in a sump that over flows producing equilsized drops.
These drops are detected optically. Since tipping bucket and drop counting rain gauge
physically measure the collected precipitation in small quanta, they may produce
errors in extremes of rain rate. They suffer the same problems of funnel collection
efficiency as manual gauges.
Weighing rain gauges operate by measuring the changes of the collected water’s
mass. A major advantage is the ability to measure the accumulation of nonliquid
36
hydrometeors e.g. hail and snow. They may also provide a more accurate reading of
intense rain events compared to tipping bucket or drop counting rain gauges.
Rain gauges have many limitations and require constant maintenance. Rain gauge
funnels distort the wind field in their vicinity and this can change the amount of
precipitation at the point of measurement. This is a particular problem when
measuring light rain in high winds. Ice that collects in the funnel, either ice that falls
as hydrometeors or due to freezing of the funnel, can block the funnel and cause no
rain to be detected for long periods. When this ice melts, all the collected water can
suddenly flow into the measurement container or system. Heating the funnel reduces
this problem but also causes evaporation in the funnel and reduces the accuracy of
light rain measurements. Obtaining rain data, especially during intense storms can be
difficult due to wind extremes. Birds often sit on the funnel edge and defecate into the
funnel causing blockages. Spiders and insects may build nests in the funnel or
measurement system, also causing blockages. Dust, pollen and soil can also block
systems. Additionally, it is difficult to find suitable sites for rain gauges, particularly
in urban areas. These sites need to be secure from interference by people and other
animals. They also need to be in open areas where the microclimate is not effected by
nearby buildings or trees.
Even though rain gauge provides direct rainfall rate measurement, compared to radar
which estimate rainfall rate by relating precipitation to some remotely sensed
quantity, a single rain gauge has poor spatial coverage and only indicates rainfall
intensity at a small local area. Smith et al. (1994, 1996) have shown that rain radar
can performs better than a network of rain gauges in terms of depicting the intensity
and spatial extent of heavy precipitation. Rain radars avoid some of the problems
associated with wind extremes and the mechanical limitation of automatic rain gauges
during heavy precipitation events, (Groisman and Legates, 1994) and (Peck, 1997).
37
3.1.2 Weather Radar
Radar (Radio Detection and Ranging) was first developed in United Kingdom in
1935 by a meteorologist named Robert WatsonWatt. At first, radar was not intended
to observe precipitation echoes but to detect aircraft. At that time, weather echoes
detected by radars were treated as unwanted signals or noise. Shortly after the world
war two, scientists become more interested in studying weather phenomenon.
Radar operates as an echosounding system where it transmits and receives the
returned echo as illustrated in Figure 3.1.
Figure 3.1: Basic diagram of an echosounding system for radar.
The radar transmits pulses of electromagnetic waves in a narrow beam for a very
short period of time: Chilbolton’s CAMRa radar has a pulse length of 0.5
microseconds. Some of the transmitted energy is reflected back to the radar when the
transmitted beam collides with atmospheric precipitation. The radar collects the
reflected energy until reflections are too small to measure before transmitting a new
pulse. For radars operated by the UK Meteorological Office, the reading or listening
time of the reflected energy is usually around 3300 microseconds. Figure 3.2
illustrates the internal working of Nimrod rain radar.
38
Figure 3.2: Internal working of a Nimrod rain radar. (Courtesy of UK Meteorological
Office)
Typically, the beam width of modern radars is around 1o. The distance from the radar
to precipitation or other targets can be derived from the time taken for pulses to travel
back and forth between radar and the targets. The reflected energy collected by the
radar antenna is much weaker than the transmitted pulses mainly due to freespace
loss, atmospheric scatterings and absorptions. The equation for reflected power
collected by the radar, (Skolnik, 2002), is given by:
Pr
Pt G 2 2
(4 ) 3 r 4
(3.1)
39
Pr is the received power, Pt is the transmitted power, G represents antenna gain, is
the wavelength,
is the backscattering cross section of the target and r is the
distance between the radar and target. Based from the equation in (1), all the constant
parameters of the radar equation can be merged into a coefficient C:
Pr
CZ
r2
(3.2)
where Pr is the averaged received power for precipitation illuminated by the radar
and Z is the radar reflectivity usually expressed in dBZ: dBZ 10 log(Z ) . Equation
(3.2) shows that the received power Pr from a volume of precipitation is inversely
proportional to r2 (Patra, 2001) due to the increasing spread of the radar beam. The
conversion of radar reflectivity Z to precipitation rate R in mm/hr can be made using a
ZR relationship, Z aR b , where a and b are parameters that can be obtained using
regression analysis. Numerous ZR relationships exist for different rain types, radars
and climate regions. Battan (1973) has listed 69 different ZR relationships derived
from different climate regions by several researchers. Some of the variation in ZR
relationships is due to the mix of rain types and DSD in the region of the radar
(Cluckie and RicoRamirez, 2004). A well known ZR relationship equation is derived
from the MarshallPalmer DSD formula:
Z 200 R 1.6
(3.3)
The UK’s Meteorological Office’s Nimrod radars use this equation to estimate
precipitation rate, (Harrison et al., 2000). A formula to relate
was given by Usman (2005) and Patra (2001):
40
D
6
and rain rate R
Z
1
V
D
6
aRb 200R1.6
(3.4)
v
h
V (r )(r )
2 2 2
(3.5)
where V is the volume illuminated at any instant, D is the diameter of the water
droplet, h is the pulse length, and represent vertical and horizontal beam widths
of an antenna.
The most conventional form of radar is the single polarised radar which transmits and
receives pulses using the same linearly polarised antenna, either horizontally or
vertically polarisation. More advance radars such as dual polarised and Doppler
radars can extract more or different measurement parameters.
Doppler radar is commonly used to obtain information on the direction and speed of
falling hydrometeors. Doppler radar operates by measuring the Fourier power
spectrum of the reflected energy. The Doppler effect increases the frequency of the
reflected energy when the scatterer is moving towards the radar. Similarly, targets
moving away from the radar reflect at a lower frequency. The power spectrum may
be interpreted as the radial velocity mix within the sample volume.
Dual polarisation radars measure the horizontal and vertical polarised components of
reflected radio waves. Typically, rain drops are either spherical for small drops or
oblate spheroid for large drops (Pruppacher and Pitter, 1971). Large rain drops tend to
have larger horizontal crosssection area than vertical and their radar reflectivity of
horizontally polarised waves tends to be higher than for vertically polarised. The
difference in polar reflectivity allows the radar to estimate the mixture or large and
small drops. A ratio of reflected horizontal and vertical power in decibels, known as
the differential reflectivity, may be written:
41
Z DR 10 log(
ZH
)
ZV
(3.6)
where ZV and ZH are the reflectivity of a vertically and horizontally polarised pulse.
Larger positive values of ZDR indicate the presence of large oblate raindrops and are
associated with heavy rain.
Radars can operate in different frequency bands, depending on the application. Table
3.3 shows the different frequency bands with its wavelength and application based
from Multicommunity Environmental Storm Observatory (MESO)’s website
(w8lrk.org/article/RadarTutorial.pdf) and from Usman (2005).
.
Frequency (GHz)
Wavelength (cm)
Band
Application
30
1
K
Cloud
10
3
X
Precipitation
6
5
C
Precipitation
3
10
S
Precipitation
1
30
L
Precipitation
Table 3.3: Operating Bands for Radar with its relevant frequency and wavelength.
Raindrops have typical diameters from 1 to 10 mm.
The wavelengths used to
measure rain are a tradeoff between getting sufficient reflection from the raindrops
and the loss of reflected power due to absorption and scattering by other particles.
Most of the current weather radars utilise SBand with a frequency of 3GHz to
estimate precipitation. However, over the last decade, the use of CBand and XBand
has become increasingly important for weather radars to estimate precipitation.
Higher frequency bands for radar have more precise rainfall estimation but may suffer
larger atmospheric attenuations (Usman, 2005). Radars operating at KBand are
highly sensitive to extremely small or light precipitation and thus can be used to
estimate cloud density.
42
The deployment of weather radar to estimate precipitation addresses the lack of
spatial coverage when using a rain gauge network. Furthermore, radar provides
rainfall information in nearreal time whereas it may take some time to collect data
from a gauge network. However, the translation from radarmeasured reflectivity into
rainfall rate can be challenging and may produce estimation errors due to various
reasons including reflection from nonliquid hydrometeors and nonmeteorological
factors such as beam block, ground clutter and spurious echoes. Differences in
calibration between radars also lead to estimation error where a difference of 1 dBZ
in calibration can lead to 17% difference in rain rate, (Hunter, 1996). Precipitation
located at extreme long range from radar may not be fully representative of the actual
rainfall near the surface due to Earth’s curvature and the increasing elevation of beam
with the distance from radar. At long ranges the radar beam may be above the
precipitation or rainfall may evaporate at lower levels beneath the radar beam, and so
precipitation is underestimated or often undetected, (Hunter, 1996; Kitchen and
Jackson, 1993; Smith et al., 1996). In addition, bright band (melting layer) effects
may lead to overestimation of rainfall rates when the radar beam reflects off the
melting layer, (Kitchen and Jackson, 1993; Smith et al., 1996). Furthermore, the
relationship between radar reflectivity and rain rate can vary widely and the use of
simple ZR relationships, Z aR b may lead to estimation errors up to 100 %,
(Usman, 2005).
Various methodologies have been suggested and employed to address these issues
including vertical profile adjustment, comparing with the previous or adjacent radar
scans to find radar faults and verification with other sources of measurements such as
rain gauges or even communications links.
3.1.3 Meteorological Satellites
Meteorological or weather satellites are equipped with passive or active sensors to
detect radiation emission from Earth’s surface and atmosphere while orbiting at low
43
Earth orbit or polar orbit (Nimbus) and at geostationary orbit (GOES, METEOSAT).
These satellites can be uses to measure or estimate various meteorological fields
including cloud and precipitation. Generally, rainfall rate estimation from satellite can
be divided into two categories, infrared (IR) and microwavebased precipitation
estimates. Both of these measurements have a very indirect relation between surface
precipitation and the measured satellite signal.
The IRbased satellites, such as NOAA’s GOES, estimate rainfall rate by measuring
the radiance or brightness temperatures of the cloudtop in the infrared (IR) frequency
spectrum from geostationary orbit in which the temperature of the cloud top is related
to cloudtop height for optically thick clouds below the tropopause. This relationship
assumes that the cloud height is related to cloud thickness and colder clouds are more
likely to produce precipitation than warmer clouds. This method may only work for
convective events where cloud top parameters are more closely related to surface
rainfall, but will be problematic for warm top stratiform clouds (where surface rain
rates are often underestimated because of the relatively warm cloud tops) and for nonprecipitation cirrus clouds since they have low brightness temperature, (Scofield and
Kuligowski, 2003). Even if this method could work with convective clouds, the
amount of precipitation produced is strongly dependent on the stage in the life cycle
of the convective event. Despite of this, IRbased satellites usually provide high
spatial and temporal resolution data. For example, GOES and METEOSAT both yield
4 km spatial resolution rainfall rates, every 15 minutes for GOES and 30 minutes for
METEOSAT.
The use of microwavebased satellite measurements is a more direct method to
estimate rainfall rates than IRbased measurements. These instruments estimate
rainfall rate by measuring the absorption of microwave radiation by liquid water or on
the scattering by ice particles within the microwave spectrum, (Scofield and
Kuligowski, 2003). However, it is usual for microwave instruments to have poorer
spatial resolution than its IRbased counterpart. Resolution is typically insufficient to
44
determine small scale precipitation events. Furthermore, the long revisit times of the
Low Earth Orbit (LEO) satellites that carry these instruments lead to significant
sampling errors for accumulated rainfall estimation (Ebert et. al, 1998).
Estimation of rainfall rates from satellites offer considerable advantages over radar
and rain gauge networks since it can provide crucial rainfall information in regions
where data from radar and rain gauges are not available, such as over oceans. In
addition, they do not have the spatial inconsistencies that radars have such as changes
in radar beam height and the different calibrations between radars. However, the
relationship between satellitemeasured radiance and surface rainfall rates is less
robust than the relationship between ground based radar reflectivity and rainfall rates.
Therefore, rainfall estimation results from these satellites must not be considered as a
replacement for radars and rain gauges but as a complement, (Scofield and
Kuligowski, 2003). Both the IR and microwavebased satellite instruments can be
combined (known as blending) to expand their applications and increase accuracy.
One such example algorithm is the Multisensor Precipitation Estimate (MPE). The
MPE regularly uses rain gauge or radars for validation purposes. Recent weather
satellite systems, such as the Tropical Rainfall Measuring Mission or TRMM, have
been equipped with precipitation radar (Scofield and Kuligowski, 2003; Usman,
2005). Systems such as the TRMM radar are a new alternative to IR and microwavebased satellite precipitation estimation.
TRMM is a joint venture between National Aeronautics and Space Administration
(NASA) and Japan Aerospace Exploration Agency (JAXA) and it is the first weather
satellite utilising precipitation radar to estimate rainfall in the tropical regions The
TRMM satellite is equipped with multiple sensors and instruments including TRMM
Microwave Imager (TMI), precipitation radar, visible and infrared sensors, and a
lightning detector. The TRMM satellite is able to provide vertical profiles of rain and
snow from the surface up to 12 miles in height and offers average rainfall over 5 o x 5o
(for low resolution) and 0.5o x 0.5o (for high resolution) areas with a monthly rainfall
45
rate. The TRMM project is highly ambitious since it offers rainfall estimation over a
large coverage area. However even the high resolution data are not adequate for radio
propagation simulation (Usman, 2005) due to the low temporal resolution. With the
improving sensor technology and algorithms, satellite borne rainfall radars, such as
those used by TRMM, may soon be able to provide the finer resolutions necessary for
radio network simulation. Figure 3.4 illustrates the wide variety of weather satellites
operated by different agencies/countries and in different orbits including the
geostationary and polar orbit.
Figure 3.4: Weather satellites from various countries and agencies. (Taken from Earth
Observation Handbook by Committee on Earth Observation Satellites (CEOS),
www.eohandbook.com/eohb05/ceos/part2_6.html)
3.2 Meteorological Measurement Datasets
This section discusses the range of meteorological measurement datasets that are
produced by different measurement sources including rain gauge, weather radar and
46
satellite. Some of these datasets can be applied to or assist GINSIM and this will be
explained later in the following sections.
3.2.1 Chilbolton DropCounting and TippingBucket Rain Gauge
British Atmospheric Data Centre (BADC) archives the Chilbolton dropcounting and
tippingbucket rain gauge data. The dropcounting gauges were developed by the staff
at Chilbolton Observatory (www.stfc.ac.uk/chilbolton). Tippingbucket gauges are
common, the UK Environment Agency operates a network of 1300 such gauges, but
they offer poor rain rate resolution compared to dropcounting gauges. The dropcounting rain gauge collects the rainwater in the 150 cm2 funnel which channels
water into a sump that produces equilsized drops. These drops are counted as they
pass through an optical sensor and the number observed in each 10 second period is
recorded. Each drop corresponds to an accumulation of 0.004 mm, compared to 0.2
mm per tip for a standard Environment Agency tippingbucket gauge. For this
research, the rain gauge data was used not as a part of the GINSIM’s main operations
but for verification with the results. The rain gauges operate routinely at Chilbolton
Observatory, UK (51.1445°N, 1.4370°W) and Sparsholt, UK (51.0879°N,
1.3914°W).
3.2.2 Chilbolton Advance Weather Radar (CAMRa)
The Chilbolton Advance Meteorological Radar (CAMRa) operated by Rutherford
Appleton Laboratory and located at Chilbolton Observatory in Hampshire in the
southern UK, is the largest fully steerable meteorological radar in the world. CAMRa
operates at 3 GHz and its large antenna offers an extremely narrow beam resulting in
increased resolution: at 100 km from the radar, the resolution of a 0.25 degree beam
width is 400 metres. CAMRa has dual polarization capability which makes it possible
to determine the shape and orientation of cloud and precipitation particles,
(Chilbolton Radar Website, www.stfc.ac.uk/Chilbolton/24821.aspx).
47
The CAMRa weather radar was used in the Chilbolton Radar Interference Experiment
(CRIE) which operated for two years 19871989 to measure rain over the Southern
UK. The CRIE was designed mainly for examination and development of rain scatter
interference models as part of the COST 210 project (COST 210, 1991). This dataset
provides rain information with a very high spatial resolution, 300 m diameter voxels,
and temporal sampling time, 10 minute return time. However, the experiment
operated on a 9 day out of 27 duty cycle and only provides information for the area
around Chilbolton. The previous HRFNS, (Zhang, 2008) is based on these data. The
downscaling algorithms developed for this dataset are applicable over spatial and
temporal scales up to tens of kilometres and minutes.
3.2.3 Nimrod and OPERA
The UK Meteorological Office operates the Nimrod network of 15 CBand rain
radars operating at 5.4 GHz. Composite measurements of instantaneous rain rate over
1, 2 and 5 km voxels, spanning UK and neighboring European countries including
northern of France, are produced with a 5 or 15 minute sample period. These data
span 1999 to the present, with the higher resolutions (1km spatial resolution)
available since 2004. Currently, the British Atmospheric Data Centre (BADC)
archives singlesite and composite Nimrod rain maps. Figure 3.5 shows a typical
composite Nimrod rain map.
48
Figure 3.5: Nimrod rain map covering the whole UK and part of Europe. (Courtesy of
BADC)
Each Nimrod site has a computer system that can perform aerial elevation control and
digital signal processing. These raw data then sent to Radarnet IV Central Processing
at Exeter for various corrections and calibrations, including correction for attenuation
by intervening rain, correction to range attenuation, elimination of ground clutter,
conversion of radar reflectivity to rainfall rates and conversion from raw polar cells to
National Grid Cartesian Cell. Rain gauges are used as ground truth as part of the main
quality checking method for Nimrod’s rainfall rate scans.
Each rain radar vertically scans the area between four to eight low elevation angles
(commonly between 0.5 and 4 degrees depending on the surrounding hills) every 5
minutes to ensure the best rainfall rates estimation on the surface. The radars provide
scans with ranges up to approximately 75 km (for 1 and 2 km spatial resolution) and
255 km (for 5 km resolution).
The European Meteorological Network Services (EUMETNET) is currently
managing OPERA, a project that aims to integrate Nimrod with a large number of
continental European radars into a network that will provide these data spanning
Europe. Limited OPERA composite data is now available for research purposes.
OPERA data was to be generally available from 2011 but has suffered delays due to
49
difficulties maintaining consistency across national boundaries. Figure 3.6 shows a
typical OPERA composite rain map over Europe.
Figure 3.6: OPERA rain maps covering most of Europe. (Courtesy of EUMETNET)
3.2.4 MultiSensor Precipitation Estimate (MPE)
Although Nimrod and OPERA data will provide a basis for UK and European
network simulation, the development of a global simulation tool requires consistent
data with a global span. This is far more likely to be achieved by satellite Earth
observation systems than by combining national radar networks. The European
Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) is an
intergovernmental organisation that operates a constellation of METEOSAT Earth
observation satellites and publishes a wide range of derived datasets. The MPE
dataset yields global rain rates integrated across 3 km pixels with a 5 minute sample
period. Cloud information is provided with 9 km pixels and hourly sampling. The
50
EUMETSAT’s MPE integrates the IR channel data from METEOSAT satellites and
Special Sensor Microwave/Imager (SSM/I) microwave data from USDMP satellites
in the reprocessing branch of its Meteorological Product Extraction Facility (MPEF)
to estimate precipitation rate.
3.2.5 NCEP/NCAR Reanalysis datasets
The NCEP/NCAR Reanalysis datasets provides various parameters (including geopotential height, air temperature, vector wind) of the Earth’s atmosphere over a global
2.5o grid at 6 hour intervals from 1948 to the present, calculated at 17 pressure levels
ranging from 1000 mBar to 10 mBar. The global grid has 73 latitudes and 144
longitudes. Reanalysis datasets are produced by assimilating climate observations
taken from various sources including satellites, ships, weather radars and ground
stations and using the same climate model throughout the entire reanalysis period.
The product is a joint collaboration between National Centers for Environmental
Prediction (NCEP) and the National Center for Atmospheric Research (NCAR). The
data is available from NOAA’s Earth System Research Laboratory and NCEP. Figure
3.7 demonstrates the global map of geo potential heights for 1000 mBar pressure
level, extracted from NCEP/NCAR Reanalysis I data that are archived by NOAA’s
Physical Science Division (PSD) (www.esrl.noaa.gov/psd).
51
Figure 3.7: Geo potential Heights of 1000 mBar pressure level. (Courtesy of NOAA)
The NCEP/NCAR Reanalysis I data provide information (specifically the geopotential height and air temperature as a function of pressure levels) that allows the
estimation of rain height. This is important when calculating the fade experienced by
slant paths and for the implementation of the BaconTjelta sleet model for terrestrial
microwave links.
3.2.6 Shuttle Radar Topography Mission (SRTM)
The Shuttle Radar Topography Mission (SRTM) is an international research effort
spearheaded by the National GeospatialIntelligence Agency (NGA) and NASA in
obtaining digital elevation models on a nearglobal scale to generate the most
complete highresolution digital topographic database of Earth to date.
SRTM consisted of a specially modified radar system that flew onboard the Space
Shuttle Endeavour during an 11day mission in February of 2000, completing 176
52
orbits. A key SRTM technology was radar interferometry, which compared two radar
images or signals taken at slightly different angles. This mission used singlepass
interferometry, which acquired two signals at the same time by using two different
radar antennas. An antenna located on board the space shuttle collected one dataset
and the other dataset was collected by an antenna located at the end of a 60metres
mast that extended from the shuttle. Differences between the two signals allowed for
the calculation of surface elevation. The elevation models derived from the SRTM
data are used in Geographic Information Systems or other application software. The
spatial resolution for the SRTM datasets is 1 arcsecond, approximately 30 metres, for
area within United States of America and 3 arcsecond, approximately 90 metres, for
the rest of the world. Figure 3.8 illustrates a sample image of SRTM in the southern
UK, extracted from Consortium for Spatial Information’s website (www.cgiarcsi.org)
which archives SRTM’s global topography map with 90 metres spatial resolution.
Each of the pixels in this data contains specific information on height in metres above
sea level.
Figure 3.8: SRTM topographical map of the southern UK.
53
The variations of the Earth’s surface height constraint the melting layer height and the
altitude of ground stations. The SRTM can be incorporated into the GINSIM
simulator to increase its accuracy in calculating sleet attenuation in the melting layer
for both terrestrial and EarthSpace links. It is possible to use this map to produce a
path profile of wanted and interference paths. For microwave links, the map can be
used to check that the wanted path has adequate clearance. It will be desirable for
interference path to be obstructed by terrain features. Rec. ITUR P.45214 (2009)
uses path profiles generated by the terrain map in order to estimate the likely strength
of any interfering signal.
Chapter 3 Summary
There exists a range of estimated precipitation datasets derived from measurements of
ground based and space instruments. Rain gauges are often used as “ground truth”
since they measure rainfall directly, but with poor spatial coverage. Rain gauges are
often used for verification or calibration of indirect rainfall estimates. Rainfall
estimation from satellites offer wider coverage than ground based radars but their
measurements are less reliable and require further developments before they can truly
replace radars. Currently, weather radar provides sufficient spatial and temporal
resolution, suitable for GINSIM development for radio network simulation across
Europe, even though it faces some challenges including spurious echoes, beam block,
different calibration with adjacent radars and the variable relationship between radar
reflectivity and the actual precipitation. Nonetheless, rain radars are still reliable and
widely used by meteorologists and even as part of verification process for satellitebased precipitation estimation such as MPE. In addition, radar has finer spatial and
temporal resolutions than measurements from weather satellites.
Nimrod/OPERA rain maps have been identified as suitable inputs for GINSIM.
Although Nimrod uses single polarisation radar, unlike the dual polarisation CAMRa,
54
its wider coverage of the whole UK (Nimrod) and most of Europe (OPERA) give
them a significant advantage for GINSIM. NCEP/NCAR Reanalysis I data provide
crucial information to calculate rain height for slant path and the integration of
BaconTjelta sleet model. Furthermore, the global coverage and easy access for
NCEP/NCAR Reanalysis I data make it ideal for GINSIM development.
55
CHAPTER 4 NETWORK FADE SIMULATION
As discussed earlier in Chapter 1 and 2, microwave links including terrestrial and
EarthSpace links operating above 10 GHz, experience losses or fade due to
absorption and scattering by liquid and mixedphase hydrometeors in the atmosphere
(rain, sleet, fog, wet snow and cloud). Hydrometeor fade exhibits complex spatial and
temporal correlations, due to its dependence upon the atmospheric circulations. The
Radio Section of the International Telecommunication Union (ITUR) archives a
large number of propagation models in the P recommendations. These models are
generally utilised for predicting average annual, oneminute, fade distributions for
individual EarthSpace and terrestrial links. Second order statistics including fade
duration and slope are also provided in the ITUR models. These models are
sufficient to determine fixed fade margins for those individual links but are of little
use in the design and optimisation of Fade Mitigation Techniques (FMTs) and
Dynamic Network Management (DNM) of a more complex radio networks. For these
tasks it is necessary to have models capable of predicting joint channel timeseries of
fade, often at a time resolution considerable shorter than oneminute.
One of the known methods of producing joint hydrometeor fade timeseries with
correct auto and crosscovariance is to simulate the fade on link networks
superimposed on specific attenuation fields derived from realistic hydrometeor fields.
This method has been used by Bosisio and Riva (1998), Hodges et al. (2003),
Callaghan (2004), Gremont and Filip (2004), Paulson and Zhang (2009) and Jeannin
et al. (2009). The variety of systems indicates that the network fade simulation is an
active area of research. This chapter focuses on the principles of network fade
simulation tools, development of Hull’s GINSIM and descriptions of other tools.
4.1 General Procedures for Network Fade Simulation
Network fade simulation tools provide the joint hydrometeor fade timeseries for a
56
heterogeneous network of EHF radio links by producing finescale, spatial  temporal
hydrometeor fields and then overlaying radio networks to simulate the effects on any
number of individual links. In general, network fade simulation involves some or all
of the following processes:
1) Produce or obtain the coarse scale meteorological data
2) Downscale the coarse scale data to scales similar to Fresnel zones
3) Transform the downscaled fields into specific attenuation fields.
4) Perform pseudointegration of all specific attenuations along the radio link’s
path to obtain timeseries of attenuations.
5) Downscale the attenuation timeseries.
6) Add other fade mechanisms to produce total attenuation.
Rain fields are the most dynamic of meteorological events and exhibit considerable
variation in both time and space. Measuring rain intensity fields has fundamental
difficulties and is prone to both systematic and random errors whether measurement
is performed by networks of gauges or radar, either hosted on the ground or on
satellites.
The fade experienced by a radio link is determined by the scattering and absorption
within a volume roughly defined by the first Fresnel zone. Meteorological scatterers,
such as hydrometeors (raindrops, ice pellets, hail, and complex mixedphase
particles) exhibit considerable spatial and temporal variation. Typically, smaller
integration volumes yield more extremes of parameter variation i.e. oneminute rain
rates are typically less smoothed that hourly rain rates. For channel fade simulators to
yield variation with the correct distribution and variation, they need to be based on
parameter fields with integration volumes similar in size to Fresnel zone diameters.
These scales are typically tens to hundreds of metres, depending upon the frequency
and path length. The following equation described the calculation for the radius of the
first Fresnel zone:
57
r 8.657
D
f
(4.1)
where r is the radius in meters, D is the total distance in kilometers, f is the frequency
operation of the link in gigahertz
Currently there exist no meteorological databases of measured rain fields with the
required spatial and temporal resolutions suitable for radio network simulation. Rain
gauges can provide point rain rates recorded with integration times as short as 10
seconds. However, rain gauges are usually widely separated. Radars can provide
instantaneous measurement of rain rates over large areas, albeit with the added
complication of estimating rain parameters from radar reflectivity. It is generally
uneconomic to operate rain gauge networks to provide similar spatial coverage and
resolution to that provided by radars. Weather radars hosted on satellites can offer
global coverage but often provide low spatial resolution and may have irregular
temporal sampling. The rain rate estimated provided by satellite based radars suffer
the same problems as estimates derived from ground based radars with the added
complication that surface rain rates are estimated from above the weather system.
Numerical Weather Prediction and reanalysis datasets (with assimilated data from a
wide range of meteorological measurements) provide wider coverage than radars and
rain gauges but they are based on global grids with extremely low spatial and
temporal resolution.
Rain fields with high resolutions can be obtained using numerical methods to
stochastically introduce finerscale variation into the coarsescale datasets. These
downscaling processes rely upon statistical models for parameter variation valid over
the range from coarse to finescale. The downscaling of meteorological fields is an
active area of research as indicated with numerous simulators by different
researchers. Downscaling relies upon constraining statistics of variation that span the
range of scales from coarse to fine. A range of statistical models have been proposed
for the variation of rain parameters. Across scales where one physical process
58
dominates there is a possibility of a single simple statistical model. However, over
the range of scales between radio link Fresnel zones and typical radar resolution, it is
likely that more than one process dominates. Various spatial breakpoints between
models have been proposed associated with the scale of rain cells and the spacing
between cells in clusters, see (Veneziano and Bras, 1996). Finescale spatialtemporal
datasets are required not just for statistical model development but also for the
verification of downscaled rain fields. Numerous scaling models, both simple and
multiscaling, have been proposed to describe the spatial and temporal variation of
rain parameters. Over wide scale ranges models generally assume multiscaling
behaviour; see (Lovejoy and Schertzer, 1995). Similar statistics for nonliquid
hydrometeors e.g. snow and wet snow (sleet), have barely been addressed despite the
importance of these particles in microwave scattering, (Tjelta et al., 2005). Once a
priori variation constraining statistics have been identified, numerical downscaling
algorithms may be used to introduce the fine scale variation onto coarse scale,
measured fields.
The combination of spatial and temporal downscaling of meteorological fields
remains an unsolved problem although approximations have been suggested, (Deidda,
2000) and (Paulson and Zhang, 2009). Meteorological measurement can produce
spatialtemporal averages or intermittent samples, and so both disaggregation and
interpolation algorithms are required. For example, radars yield radar reflectivity
averaged over a volume defined by the radar beam width, the scan rate, the
integration time and the range gates; but is also a sample in time as a scanning radar
will only return to that volume once per scan cycle. The downscaling of radar data
requires both the interpolation and disaggregation of measurements and these
processes are fundamentally different.
The transformation of rain rates into specific attenuations can be done using Rec.
ITUR P.8383 (2005). This is an approximation, as specific attenuation is known to
vary by a factor of two or more for the same rain rate due to variations in drop size
59
distribution, (Shkarofski, 1979). However, this variation is assumed to be reduced to
negligible by the averaging effect of pseudointegration along the link path. Fading
due to other nonliquid hydrometeors, such as sleet, can be introduced into network
simulation tools using BaconTjelta sleet model, (Tjelta et al., 2005) and (Tjelta and
Bacon, 2010) if the rain height is known. Rec. ITUR P.53013 (2009) has
incorporated BaconTjelta sleet model in its recommendations to calculate sleet fade.
However, this procedure relies on many assumptions. The method assumes horizontal
stratification of the atmosphere which is generally not true for convective events. The
vertical variation of specific attenuation amplification factor was derived from an
average over a small number of measurements made at a single location. It is likely to
vary by a large factor between individual events.
The pseudointegration of specific attenuation along the path of a radio link is also an
approximation as it ignores the effects of multipath and refraction. Currently it is
unrealistic to downscale the coarse scale meteorological fields to a size of the first
Fresnel zone with 1 second sampling time as such procedure requires astronomically
high computational resources while introducing insignificant amounts of variation.
An alternative method is to downscale the attenuation time series after the fields have
been downscaled to an intermediate scale (larger than Fresnel zones) and the pseudointegration process. This procedure requires less computational resources. However,
the process is still in its infancy and only adhoc methods have been suggested, see
Jeannin et al. (2009). The a priori statistics of temporal attenuation variation, which
need to be conserved by the downscaling process, depend upon many geometric,
climatic and radio parameters and have not been catalogued. Due to the number of
unknowns, the computationally optimal distribution of effort between pre and post
pseudointegration downscaling has not been investigated.
Fading by other meteorological effects may be introduced into simulations.
Absorption by atmospheric gasses, which is determined by temperature, humidity and
pressure, can be introduced into specific attenuation fields using Rec. ITUR P.6768
60
(2009). It has been suggested that turbulence indices could be used to predict
scintillation amplitudes, see Tatarski (1961). Most existing systems do not attempt to
include either of the mechanisms as both are considered insignificant compared to
hydrometeor fade.
4.2 Different approaches for Network Fade Simulation
Taxonomy of network fade simulation tools can be defined by the methods used to
produce the rain fields. Fine scales of rain fields can be produced by statistical models
of rain cell parameters, purely statistical models of spatial temporal rain rate variation
or derived from meteorological radar networks and NWP systems.
4.2.1 Rain Cell models
Fine scale rain fields can be produced by aggregating multiple rain cells. Rain cells
are often defined as regions where the rain rate exceeds a given threshold. Generally,
rain cells have been modeled as circular or elliptical. Rain cell models assume rain
rate variation within the cells to be constant (cylindrical), Gaussian or an
exponentially decline from the centre of the cell. Few parameters are required to
establish raincell profile including radius of the rain cell and the maximum rain
intensity at the center of the cell, see (Paraboni et al., 2002). The constant raincell
profile is frequently used for hydrological modeling purposes, Wheater et al. (2000).
However, models based on constant raincell profiles do not reproduce second order
statistics of rain fade, especially for the covariance of rain fade on two links, Zhang
(2008). Smoother variation of rain rate within a cell could yield better results for
second order statistics. The exponential and Gaussian methods introduce continuous
smooth variation of rain intensity within a cell with the highest rain rate value at the
center point of the cell.
The best known rain cell models are the EXCELL model (Capsoni et al., 1987), the
61
enhanced version of the EXCELL model or MultiEXCELL (Luini and Capsoni, 2011)
and HYCELL model (Féral et al., 2003a&b). EXCELL, and the latter derived
HYCELL, models are based on the joint statistics of parameters describing rain cell
shape and intensity. These joint distributions were derived from databases of rain
radar derived rain fields, (Bosisio and Riva, 1998; Paraboni et al., 2002). The
EXCELL and HYCELL methods claim global application, although there are few
published comparisons with real measurements. This claim relies upon the global
application of rain cell parameter statistics measured in France and Italy.
The EXCELL or (EXponential CELL) was first presented in 1987 by Capsoni
(Capsoni et al., 1987). The model based on the three dimensional SBand
meteorological radar scans for rainfall rates measured at Spino d’Adda near Milan.
The measurements were carried out in 1980 from April to October. In this model, rain
cells were identified when the rain rate exceeded a 5 mm/hr threshold and only with
an area greater than 5 km2 as smaller rain cells would introduce excessive
quantitasation error to the system. The model is based on the distribution of cells;
characterised by an exponential profile of the rain rate. However, the EXCELL
system assumes unrealistically smooth spatial variation of rain rate and its scope and
resolution are poorly defined.
MultiEXCELL, a new rain cell model inspired by EXCELL, offers several
advantages over to its predecessor including the ability to generate complete rain
fields by simulating the natural rain cells' aggregative processes that have been
observed in the rain fields derived by the weather radar at Spino d'Adda.
MultiEXCELL also claims to have global applicability and it also includes a
methodology that utilises ECMWF ERA40 data. Figure 4.1 shows the example of
rain fields produced by the MultiEXCELL model simulating the site diversity of two
EarthSpace links represented by the red arrows, (www.dei.polimi.it).
62
Figure 4.1 Sample images of rain fields produced by MultiEXCELL
The HYCELL or (HYbrid CELL) model was based on rain cells identified from radar
observations in Bordeaux (SouthWestern France, near the ocean) and Karlsruhe
(SouthWestern Germany, in the continental region). HYCELL utilises a hybrid
distribution of the rain rate profile (Exponential and Gaussian distributions). The
HYCELL model uses Gaussian profiles to describe convective type of precipitation
and exponential profiles for stratiform events with low rain rate down to 1 mm/hr.
The model uses elliptical rain cells with major axis, minor axes and the orientation
angle as its parameters. According to the author, the model is well suited for
describing the spatial variability of rain rate at small scales up to few tens of
kilometres. However, the model assumes that rain cells are uniformly distributed over
an area. The rain rate profiles are unrealistically smooth as are the contours. The
authors have even tried to deface the contour lines by introducing noise to the field in
order to produce more realistic rain cell shapes with a similar fractal dimension to
measured rain cells. These models have experienced incremental improvement over
several decades.
63
4.2.2 Statistical Rain Rate Variation Models
Early spatialtemporal rain simulators aimed to reproduce observed statistics such as
point distributions of rain rate, covariance structure and intermittency. The early
simulators were primarily designed for hydrological purposes and for the calibration
of satellite measurements, and so the scales and resolutions are much larger than
Fresnel zones. However, radio engineers and other researchers are now increasingly
more interested in second order statistics describing highresolution rain rate variation
in both time and space, and so researchers are now developing spatialtemporal
statistical models that can produce rain fields with scales near to Fresnel zones. These
models can generate rain fields with more realistic shapes of rain events compared to
EXCELL and HYCELL models. Often these models are divided into those with
exponential correlations, often based on Markov models, and simple or multiscaling
models with powerlaw correlation tails, see (Lovejoy and Schertzer, 1995). One of
the earliest simulation models was developed by Bell (1987). The simulation method
could generate timeseries of rain rates defined on a grid.
A range of spatialtemporal statistical models can be used to generate entirely
synthetic rain rate fields. These models typically assume a specific form for the
autocovariance or spectral density; often exponential or power law. One of these
assumptions, combined with the assumption of stationarity and Gaussian or logNormal distribution, allows rain fields to be generated. Rain fields derived purely
from statistical models of rain rate or log rain rate variation have been employed to
model EarthSpace and terrestrial links (Callaghan, 2004; Gremont and Filip, 2004).
At Rutherford Appleton Laboratory (RAL) and Portsmouth, fully numerical models
developed by Callaghan (2004) have been used produce rain fields based on Voss’s
algorithms (Voss, 1985) to simulate fractional Brownian motion in two dimensional.
The output of this simulator is a monofractal log rain rate field. The method assumes
that log rain rate, where raining, is a stationary, fractional Gaussian process with a
64
Hurst coefficient of 1/3. The assumption that log rain rate is simplescaling leads to
multiscaling rain rate variation. This model was first proposed by Paulson (Paulson,
2002), where it was found to be a good model for temporal variation of rain intensity
derived from optical rain gauge and for spatialtemporal variation of stratiform rain
rate measured using the Chilbolton, CAMRa radar. Figure 4.2 shows the sample
image
of
a
stratiform
type
of
rain
field
produce
by
the
simulator
(www.port.ac.uk/research/telecoms/pdfs/filetodownload,26495,en.pdf).
Figure 4.2: Example simulation of a stratiform event type of precipitation
Gremont and Filip (2004) at the University of Portsmouth have developed a spatialtemporal rain attenuation model and since then has been applied to two dimensional
channel simulation tool to generate joint fade timeseries. The model is based on
generalisation of a stochastic dynamic Maseng Bakken model (Maseng and Bakken,
1981) and has been extended to two arbitrarily correlated satellite links at two
different carrier frequencies. This paper assumed log rain rate fields to be Gaussian
with an exponential or empirical correlation structure. The correlation lag is a linear
65
combination of separation in time and space and is consistent with Taylor’s
hypothesis (Taylor, 1938). Rain specific attenuations along the path are assumed to be
homogeneous up to rain height. The statistical model is capable of producing
consistent first and second order statistics such as the rain attenuation’s power
spectral density, dual location site diversity system, fade slopes, rain attenuation’s
frequency scaling factor and fade duration based on Markov chain. It is claimed that
the proposed model is applicable to metropolitan areas with a 60 km diameter and
with all types of radio networks. It is applicable to the statistical analysis of rain
attenuation and the modeling of site diversity systems. A simulation tool based on this
model has been developed at the University of Portsmouth. The simulator is able to
produce joint fade timeseries for terrestrial and EarthSpace links which can be
crucial for the design of FMTs. Rain advection is assumed to be linear in the
simulation and the notraining regions have been introduced by a thresholding
technique.
4.2.3 Downscaling NWP or Meteorological Data
Several systems are based on the downscaling of NWP or meteorological data to
generate fine scale rain fields. Some of these systems use the same statistical models
of variations as the methods described in the earlier section 4.1.2.
4.2.3a SISTAR
The French aerospace laboratory, ONERA, is also developing a simulation tool called
SISTAR (SImulator of the SpaceTime behaviour of the Attenuation due to Rain) for
EarthSpace links. Its ultimate goal is to produce fine scale rain fields for radio
network simulation with 1 second sampling time and with global applicability. The
system starts with ERA40 historical reanalysis data from ECMWF with global span
but relies upon numerical downscaling of these data from very large grid squares and
integration times, see Jeannin et al. (2009).
66
The ERA40 database yields a large number of parameters including the 6hour rain
accumulations over 2.5o x 2.5o regions and the wind vector at a range of pressure
levels. SISTAR downscales the rain accumulations to 0.01o x 0.01o regions over
periods of 0.1 hours. Disaggregation is achieved by modeling the finescale rain field
as a lognormal process with a given, empirical, double exponential auto covariance.
The disaggregated rain field is advected with the ERA40 wind field at the 700 hPa to
yield timeseries. The fade on slant paths is estimated by pseudointegration of the
specific attenuation associated with the interpolateddissagregatedadvected rain field
along a path from the receiver to the 2o C isotherm (provided by the ERA40
database). The resulting fade timeseries are sampled every 6 minutes (0.1 hours) and
these are stochastically interpolated to yield a 1 Hz sample rate.
The ONERA method is very ambitious and has a number of fundamental limitations.
The distribution of rain rates over each ERA40 pixel is made to be lognormal.
However, Zhang (2008) reported rain rates over regions of a similar size to often have
multimodal distributions due to the mix of event types.
The spatialtemporal disaggregation is performed with a rather adhoc method that
initially yields spatially disaggregated fields of indeterminate temporal accumulation,
and then interpolates between these fields separated by 6hours. No point temporal
autocovariancies imposed. The double exponential spatial autocovariance decays
faster than the powerlaw form consistent with the more accepted simplescaling or
multifractal models of rain rate variation, see Paulson and Zhang (2009). In addition,
the ERA40 datasets spatial and temporal resolutions are too coarse to be downscaled
with the downscaling algorithms developed for HRFNS and GINSIM, and may miss
out many important rain events.
4.2.3b SATCOM
Researchers at the University of Bath, Hodges et al. (2003) have developed the EHF
67
SATCOM system using numerical weather models, forecast data and rain radar data
for deriving attenuation timeseries on fixed satellite and terrestrial links. The system
includes rain and cloud fade mechanisms as well as scintillation and absorption by
atmospheric gases. The performance of this technique depends on the insertion of the
short interval temporal properties (varying typically over 1 second to 15 minutes) that
are statistically independent between stations. This allowed the system to generate
maps of attenuations with spatial resolution of a few kilometres and temporal
resolution of a few seconds. The UK Meteorological Office’s Unified Model (UM)
and Nimrod CBand rain radar network was used to acquire meteorological inputs for
SATCOM, see Hodges et al. (2003). The UM is a NWP model and provides the basis
for the calculation of background fading effects (water vapour absorption,
scintillation and cloud losses). For rain fade, the model uses Nimrod rain radar data as
these have higher spatial and temporal resolutions compared to the current UM
model.
4.2.3c Hull Rain Fade Network Simulator (HRFNS) and GINSIM
The Hull Rain Fade Network Simulator (HRFNS), Paulson and Zhang (2008), is a
heterogeneous network simulation tool capable of producing joint rain fade timeseries for arbitrary networks of terrestrial SHF and EHF links. Over the last three
years, GINSIM has been developed from HRFNS as the application has been
extended to include slant paths including EarthSpace links and links to Unmanned
Airborne Vehicles (UAVs) and High Altitude Platforms (HAPs). Vertical variation of
specific attenuation has been introduced using the BaconTjelta sleet model used in
Rec. ITUR P.53013 (2009), and rain heights derived NOAA NCEP/NCAR
Reanalysis I data, Kalnay et al. (1996).
The rain data used in the development of GINSIM has been obtained from the UK
Meteorological Office Nimrod rain radar network, but the use of equivalent data
produced by the OPERA project (www.knmi.nl/opera) would extend the area over
68
which the system could be used to most of Europe. Nimrod and OPERA composite
rain field images have a 1 km spatial resolution and 5 minutes sample time. The
numerical downscaling processes employed by both GINSIM and HRFNS are
described in detail in Paulson and Zhang (2009) and Zhang (2008).
Paulson (2004) have suggested that the downscaling techniques from the HRFNS can
be applied to input datasets with sample times as long as 20 minutes and spatial
voxels up to 30 km. Nimrod and OPERA derived rain fields have spatial and temporal
resolutions within this range and so are appropriate input data sets for a network
simulator. A simulator based on these datasets would be applicable anywhere in the
UK or Europe respectively.
4.3 Downscaling and network simulation processes for GINSIM
The downscaling techniques developed for the HRFNS and GINSIM produced
numerically enhanced timeseries of rain radar images from the Chilbolton Radar
Interference Experiment (CRIE), measured as part of the European COST 210 project
(1991). Techniques that can preserve a mixture of measured and a priori known
statistics have been implemented for downscaling and interpolating measured rain
fields such as the CRIE. GINSIM downscales a selected region of coarse scale rain
fields from Nimrod and OPERA composite timeseries to produce much finer
resolution spatial and temporal rain fields.
Currently, the simulation processes in GINSIM for radio networks can be summarised
by the following steps (further knowledge on these steps will be explain later in the
relevant subsections in this chapter):
1.
Estimate and remove the advection between consecutive pairs of composite
images.
2.
Disaggregate the coarse scale rain fields.
3.
Interpolate log rain rate into norain regions using Minimum Bending Energy
69
algorithm.
5.
Interpolate scans using ARMD algorithm.
6.
Reintroduce advection.
7.
Transform the downscaled rain rate fields to specific attenuation fields.
8.
Implementing rain height for EarthSpace links and the integration of BaconTjelta sleet model.
9.
Perform pseudointegration of specific attenuation along the path of links.
The simulation of a network involves several steps. First the area spanned by the
network of interest is identified and a coarse, rainmap timeseries for this area is
extracted from Nimrod or OPERA data. Advection of rain events are measured and
removed between two consecutive rain scans. For areas of diameter less than a few
hundred kilometres, advection is usually well modeled as a linear translation. For
larger areas or more complex advection, more complex translations can be used. The
translation is identified by maximization of the crosscovariance between consecutive
composites. For complex advection, crosscovariance is maximised for different subregions and the advection vector is smoothly interpolated between region centres.
Each 2D spatial rain map is disaggregated to smaller integration volumes using a
multiplicative cascade algorithm. Interpolation between scans uses a simplescaling
log rain rate model that requires log rain rates in regions with no rain. These
extremely low rain rates are introduced using Minimum Bending Energy interpolation
algorithms (Zhang, 2008). Then the 3D spatialtemporal data volume between each
consecutive pair of scans is interpolated to finer temporal sampling and the advection
is reintroduced. Once the fine spatialtemporal rain field data is calculated, the
microwave network can be overlaid and the joint fade timeseries calculated by
pseudo integration of the specific attenuation along each link path. The specific
attenuation is calculated using the powerlaw of Rec. ITUR P.8383 (2005) and the
BaconTjelta sleet model that has been incorporated into Rec. ITUR P.53013
(2009). The sleet model introduces a specific attenuation amplification factor that
allows for the mixedphase hydrometeor types in the melting layer. For slant paths,
70
the altitude of each segment of the path is calculated from the link geometry. The
sleet model reduces the specific attenuation to zero when the link altitude is more
than 360 m above the zerodegree isotherm. This altitude is obtained from NOAA
NCEP/NCAR reanalysis data. The fade calculation using this method is equally
applicable to terrestrial, EarthSpace and shorter slant paths such as those to HAPs or
UASs.
4.3.1 Disaggregation
Finerscale spatial variation is introduced into the Nimrod data using a multiplicative
cascade algorithm and constrained by multiscaling exponents measured on CRIE
data and extrapolated from the smallest measured scale i.e. from voxels of diameter
300 m down to 30 m. Lilley et al. (2006) have proposed that the multiscaling
exponents are applicable down to submetre scales. Disaggregation (i.e. refining
existing samples to smaller integration volumes) is achieved using the logPoisson
multiplicative cascade algorithm of Deidda (1999), designed to reproduce measured
multiscaling statistics, Paulson and Zhang (2007). For the GINSIM system, the
Nimrod / OPERA rain fields are disaggregated from 1 km to 125 metres.
According to Zhang (2008), the disaggregation of an instantaneous spatial average
cannot be done in separation from the disaggregation of other samples made near in
time. For instance, two measured radar rain rates separated by only a few seconds
could not be disaggregated independently, since the finescale variation would be
correlated. Therefore, they need to be adequately separated in time. Independent
disaggregation will be acceptable if the spatial integration volume is small relative to
the temporal sampling interval. In general, the disaggregation will be valid as long as
x / Dx t / Dt where x and t are the spatial and temporal sampling
respectively while Dx and Dt are the spatial and temporal decorrelation distances.
Figure 4.3 demonstrates before and aftermath of a Nimrod rain rate field that have
gone through the disaggregation process.
71
Figure 4.3: Before and after the disaggregation process of a rain rate field
4.3.2 Interpolation
The temporal interpolation algorithms are based on an underlying statistical rain
model that assumes spatialtemporal log rain rate fields, when raining, are well
approximated by homogeneous, isotropic, fractional Brownian fields with a Hurst
coefficient of 1/3; (Paulson, 2002; Callaghan, 2004). This model has been derived and
verified over the scales of interest, by analysis of Chilbolton rapid response rain
gauge and CAMRa radar data. The model has been used for the interpolation of rain
gauge data, Paulson (2004). In HRFNS and GINSIM, the interpolation (i.e.
introduction of new samples with the same spatialtemporal averaging at new points
in spacetime) is achieved by ARMD (Assymetric Random Midpoint Displacement)
by Zhang (2008), a variant of the Local Average Subdivision (LAS) algorithm of
Fenton and Vanmarcke (1990). In GINSIM, Nimrod / OPERA rain data are
interpolated to 18.75 seconds from 5 minute sampling time. This is equivalent to
introducing 15 new rain fields between each pair of disaggregated composite images.
Figure 4.4 illustrates the general diagram on interpolated scans produced between two
consecutive measured scans.
72
Figure 4.4: Basic diagram of the interpolation process (time domain)
4.3.3 Extrapolation into Low Rain Rate Regions
Measured log rain rate fields and numerically generated FBfs (Fractional Brownian
Fields) have considerable differences in terms of marginal distribution due to
intermittency of real rain (real rain events are finite in degree and separated by long
intervals without rain and so zero rain rates is always present). Threshold of 0.05
mm/hr has been set to represent no rain rate region but this will inflates rain rates near
the edges of rain events resulting new events being numerically generated in a region
of no rain. Before interpolation, zero rain rates need to be replaced by very low rain
rates that conserve the covariance of log rain rate near the edges of rain events. This
is achieved by using a Minimum Bending Energy interpolation algorithm (Zhang,
2008), constrained by the nonzero rain rates, to replace zerorain rate regions with
very low rain rates. This process creates plausible decay of rain rates at the edges of
rain events. These values are required by the ARMD algorithm use to create new rain
fields between measured fields.
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4.3.4 Advection
Before interpolation between consecutive disaggregated rain fields, advection needs
to be removed. Advection is the movement of the rain fields horizontally by the
ambient wind. The statistical models of rain rate variation used to constrain
interpolation are only applicable to advection less rain fields. Therefore, advection is
removed before interpolation and then reintroduced afterwards.
Zhang (2008) has developed a method to measure and remove advection for CRIE
rain data assuming a linear translation between radar scans and using a concept of
Taylor’s frozen storm hypothesis (Taylor, 1938) . According to Taylor, the temporal
statistics of rain at a fixed location as equivalent to the spatial statistics measured
along a line parallel with advection, assuming that the rain variation is mainly
determined by advection while the evolutionary effects are insignificant, hence
Taylor’s algorithm also known as the frozen storm model. Taylor’s frozen storm
hypothesis assumes that the spatialtemporal rain field may be estimated as a fixed
spatial field moving with a stable velocity. The speed of the rain fields being advected
was calculated by searching the linear displacement that will maximise the correlation
between two successive scans. Currently, GINSIM apply the same method to measure
and remove advection in a small selected area in Nimrod and OPERA rain data.
However, this method is not reliable to be used for larger area i.e. whole of UK since
larger region with such size certainly has multiple advections travelling at different
speeds or directions.
4.3.5 Transforming to Specific Attenuation Fields and Pseudointegration
The downscaled rain rate fields are transformed into specific attenuation fields using
the powerlaw relationship between specific attenuation, R (dB/km) and rain rate R
(mm/hr) in Rec. ITUR P.8383(2003). Radio links can then be overlaid on the
downscaled rain fields to extract points of specific attenuations along the links. Figure
74
4.5 demonstrates the process of overlaying a radio link on a matrix with each pixel
experiencing a specific rain rate. Each rain rate is converted into a specific attenuation
at the frequency of interest, the specific attenuations are interpolated to equilspaced
points along the link path using bilinear interpolation (part of or the extension of
linear interpolation between two variables on a regular grid) or the 2D data
interpolation (the “interp2” function from Matlab). The array of specific attenuations
can be numerically integrated to obtain the total attenuation either through a simple
summation or using a more advance numerical integration method such as Simpson’s
rule.
Figure 4.5: Diagram of a radio link (red) superimposed on a matrix with rain rates
4.3.6 Rain Height model
As discussed earlier in the Chapter 2, rain height (height between the surface and
altitude where all hydrometeors are frozen) is a crucial parameter to simulate slant
paths such as EarthSpace radio links, and implementation of the BaconTjelta sleet
model. The altitude of rain height is strongly determined by the temperature profile or
lapse rate (the rate of decrease of atmospheric temperature with increase in altitude)
in the troposphere region and is given by:
75
dT
dz
(4.2)
Where is the lapse rate in units of temperature divided by units of altitude, T is the
temperature and z is the altitude. The air temperature typically decreases linearly with
the increasing altitude from the surface until it reaches a tropopause line
(approximately 10 km from surface) in the atmosphere. Various average values of
lapse rate exist. Angot performed the earliest known study in 1892, which concluded
that the average value is around 5.5oC/km. Currently, the average global value of
lapse rate defined by the International Civil Aviation Organization (ICAO) as part of
International Standard Atmosphere (ISA) model is 6.5oC/km. However, the actual
lapse rate varies depending on seasons, regions and moisture content of the air. The
average value of the lapse rate is a rough approximation and unsuitable for more
precise studies. Therefore, a more sophisticated method is required to determine rain
height, Christian Roland (2002).
In GINSIM, rain height can be established from NCEP/NCAR Reanalysis I data from
NOAA. As discussed in Chapter 3, the dataset provides various atmospheric
parameters at global grids including geopotential height and temperature for 17
different pressure levels ranging from 1000 to 10 mb. These parameters provide the
basis for a ZDI calculation that can allows the estimation of rain height. Figure 4.6
illustrates the calculation of ZDI based on the reanalysis data from NOAA.
76
Figure 4.6: General diagram to calculate ZDI for rain height
Two parameters are used for the ZDI height calculation, the air temperature and the
geopotential height or altitude, both as a function of pressure level. The ZDI height is
calculated by linear interpolation between the two lowest temperatureheight points
decreasing through zero Celsius with increasing altitude. Diaz et al. (2003) conclude
that the reanalysis data can reliably predict ZDI height, even over mountainous areas,
over the period 1958 to the present. Figure 4.7 shows the average annual ZDI height
variation, calculated at 6hour sample intervals and averaged over 30 years from 1980
till 2009 for the Southern UK. The ZDI is consistent with the average global lapse
rate of 6.5o/km. In winter the ZDI height minimum occurs around 1 km, consistent
with a ground temperature of 6o and constrained by the ground. In summer when the
ground temperatures are typically 20o the ZDI height is around 3 km.
77
Figure 4.7: ZDI heights in a year (30year average)
Average annual rain height assumed to be 360 metres above average annual ZDI
height, by Rec. ITUR P.8393(2001). I assume the same relationship holds for sixhour averages. This is a coarse assumption that will often not be true in practice,
particularly in the presence of convective events. However, it was the most expedient
assumption at the time and a simplification worth investigating. The obtained rain
height can then be used to establish slant paths and for the integration of BaconTjelta
sleet model for all types of radio links. In GINSIM, vertical rain rate variation along
the column from surface to rain height is assumed to be constant, although in reality
this may not be true. However, based on weather radar observations by Goldhirsh and
Katz (1979), on average, the rain intensity did not significantly vary with height
between the surface and the base of the bright band or melting layer. Crane (1996) has
used this evidence to justify his assumption that specific attenuation may be modeled
as being constant from the surface to rain height.
As discussed earlier in Chapter 2, the amplification factor for attenuation by wet
78
snow, relative to the equivalent rain, given by the BaconTjelta sleet model will vary
with height relative to the rain height as shown in Figure 2.11 in chapter 2. Wet snow
can attenuate more than four times more than the equivalent rain. For slant paths,
links are divided into segments with rain rates and different altitudes. These altitudes
can then be used to extract amplification factors for specific attenuation from BaconTjelta sleet model as illustrated in a diagram in Figure 4.8.
Figure 4.8: General diagram of the implementation of BaconTjelta sleet model for a
slant path
The rain height model in GINSIM assumes horizontal stratification of atmosphere
when it is raining which may hold true for stratiform types of precipitation but
certainly not for convective events where the mixed phase hydrometeors may exist in
the entire column of the rain event. This can be problematic for GINSIM to properly
simulate radio links in regions with high occurrence of convective precipitations.
Furthermore, convective events produce more critical attenuations than stratiform
events which can significantly affect the fade distribution statistics.
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Chapter 4 Summary
A known common method of producing joint hydrometeor fade timeseries with
correct auto and crosscovariance, is to simulate the fade on link networks
superimposed on specific attenuation fields derived from realistic hydrometeor fields.
Often, network fade simulators operate by obtaining coarse meteorological data,
numerically downscale to higher resolution, transform the fields to specific
attenuation and perform the pseudointegration along link paths to obtain attenuation
time series. There are generally three different sources of coarsescale rain fields
including the rain cell models, purely statistical models of spatial temporal rain rate
variation and models derived from meteorological radar networks and NWP.
Interpolation and disaggregation algorithms applicable to Nimrod and OPERA rain
composite data have been described. These algorithms have been used to downscale
coarse scale Nimrod / OPERA data from 1 km to 125 metres spatially and 5 minutes
to 18.75 seconds temporally. The Nimrod / OPERA data could be downscaled further
with smaller spatial and temporal scales but that process will require astronomical
computer resources and currently our equipments are unable to do so. Section 6.2.2 in
Chapter 6 describes the effects of different spatial and temporal scales to the annual
fade distribution. In GINSIM, the application has been extended to include slant path
simulation such as EarthSpace links and sleet attenuation calculation. This is done by
using rain height as the parameter that can be calculated using the geopotential
heights and air temperature as functions of pressure levels from NOAA’s
NCEP/NCAR Reanalysis I data.
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CHAPTER 5 VALIDATION WITH ITUR MODELS
The simulation tool can be subjected to a wide range of validation tests. These can be
divided into testing the statistics of the downscaled rain fields and of derived rain fade
timeseries. The whole theme about validation in this chapter and the next chapter is
about testing the simulator whether it can produce the desired final output results that
are consistent with theoretical models and measured links. As the downscaling
process does not aim to reproduce the finescale fields that actually existed during the
simulation interval, only the statistics of rain fields and fade timeseries can be
compared. ITUR provides prediction methods for first order statistics i.e.
distributions of average annual parameters. The ITUR also provides limited models
of second order statistics i.e. fade durations and fade slope. In this chapter, the
simulation output will be compared with the theoretical ITUR models.
5.0 Experimental setup
The following comparisons are based on three calendar years of Nimrod data, 2004 to
2006, spanning a 36 km square region centred on Chilbolton Observatory (51° 8.1’ N,
1° 26.2’ W). These data have been downscaled from a spatial integration area
diameter of 1 km to 125 m. The original 5 minute sampling interval has been
interpolated to 18.75 seconds. The downscaled dataset was used to simulate a range
of terrestrial and EarthSpace links. In this chapter, downscaled Nimrod rain data and
simulated terrestrial and EarthSpace links are compared to the ITUR models
including the rain rate, terrestrial (with and without sleet) and EarthSpace link. The
validation process with ITUR models are divided into two parts, the first order
statistic (annual distribution of rain rate and fade) and the second order statistics (fade
duration and slope). For the first order comparisons, the simulated outputs is
calculated with rain rate of 29 mm/hr at 0.01% and it is expected to be consistent with
the ITUR models especially at higher probability level and probably deviate at
lower exceedance level at 0.001%. For the second order statistics comparisons, the
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simulated outputs are expected to be consistent and with the ITUR models at
different attenuation threshold levels. The word “consistent” in the validation sections
simply means that the output results are in similar shape or patterns and at satisfactory
scale with the models (in Chapter 5) or the measured links (in Chapter 6).
5.1 Validation of Rain Rate Distribution
In this section, three years of downscaled Nimrod rain data centered on Chilbolton are
compared to Rec. ITUR P.8375 (2007) predicted average annual rain rate
distributions. The downscaled data is also compared to the measured Nimrod data and
rain gauge data. Figure 5.1 compares the rain intensity distributions derived from the
Nimrod data, the downscaled data, Rec. ITUR P.8375 (2007) and from Rapid
Response Drop Counting rain gauges, collected from the same years as the Nimrod
data, sited at Chilbolton Observatory and a nearby site at Sparsholt. The Rec. ITUR
P.8375 (2007) distribution is calculated using the 0.01% exceeded rain rate derived
from the downscaled Nimrod data of 29.0 mm/hr. This result demonstrates that the
downscaling
process
produces
rain
fields
with
a
plausible
distribution.
Disaggregation has increased the probability of higher rain rates, as is expected for
smaller integration volumes.
82
Figure 5.1: Comparisons of rain rate exceedance distributions derived from direct
measurement and from Nimrod data over the three calendar years 2004 to 2006
Averaging over the three years of data obscures the yeartoyear variation. Figure 5.2
shows the three years separately and illustrates a factor of two variations in the annual
0.01% exceeded rain rate. The large variations between the three years of measured
Nimrod are consistent with the statistics archived in UK Meteorological Office’s
rainfall accumulation database (www.metoffice.gov.uk/climate/uk/anomacts/) where
there are more rain accumulation was recorded in 2006, particularly in the southern of
UK, compared to 2005 (the least) and 2004. This pattern is reflected in the Nimrod
data, both before and after downscaling.
83
Figure 5.2: Annual rain exceedance distributions for the original and downscaled
Nimrodderived rain fields for the three calendar years 2004 to 2006
5.2 Validation of First Order Statistics for Annual Hydrometeor Fade
A large number of vertically polarised, 38 GHz, zeroelevation, terrestrial links, of
length 5 km and 8 km; have been simulated. For each link length, all possible
positions within the 36 km square orientated northsouth and eastwest (horizontal
and vertical orientations), are simulated and each yields a fade timeseries. With this
technique, thousands of links from all the northsouth and eastwest orientations
within the rain map can be simulated at a time. These links are then averaged to
produce an annual fade distribution for a particular radio link. The links are assumed
to be at an altitude of 600 m, to illustrate the effects of the melting layer, despite the
land surface being at an altitude of 100 m. The hydrometeor fade distributions
illustrated in Figure 5.3 are calculated by averaging over all these link timeseries.
Each fade timeseries can be simulated with and without using BaconTjelta sleet
model (Tjelta et. al., 2005) which has been included in Rec. ITUR P.53013 (2009).
84
When the sleet model is not used, all hydrometeors are as assumed to be liquid rain.
Alternatively, the zerodegree isotherm height can be assimilated from NOAA data
and the effects of mixed phase hydrometeors included. Figure 5.3 illustrates the
distributions of fade, with and without allowing for sleet, calculated by simulation
over the three years. These are compared with the average annual distributions
provided by Rec. ITUR P.53013 (2009), with and without the sleet correction. The
rain rate exceeded 0.01% of the time used in the P.530 model is the 29.0 mm/hr
extracted from the downscaled Nimrod dataset. Figure 5.3 shows very clear
agreement between simulated distributions and ITUR models, both with and without
sleet. The variation is certainly within that expected given the yeartoyear variation
illustrated in Figure 5.2.
Figure 5.3: Distributions of annual hydrometeor fade for 38 GHz, terrestrial links of
length 5 km and 8 km, as predicted by Rec. ITUR P.53013 (2009) and produced by
simulation. Distributions are illustrated with and without allowing for extra fading
due to wet snow.
85
The same simulation process was followed to calculate the hydrometeor fade
distribution for a Ka band uplink to a geostationary satellite. The link uses circular
polarisation at 27.5 GHz and operates at an elevation angle of 28°. Figure 5.4
illustrates the fade distribution calculated over the three year simulation period
compared to the hydrometeor fade prediction of Rec. ITUR P.61810. Given the
yeartoyear variation observed over the three years, the differences between the
distributions at time percentages above 0.01% are within expected bounds. The
observed 0.01% exceeded rain rate is an input parameter into the P.618 model and so
the good agreement at 0.01% is expected. The deviation at lower time percentages
could be an inconsistency between the terrestrial and EarthSpace models P.530 and
P.618, as the terrestrial link distributions were much closer at these time percentages.
Alternatively, the deviation could be due to a feature of the small number of extreme
events that determine the fade at these low time percentages e.g. the events could
have greater rain height that the longterm mean.
Figure 5.4: Annual distributions of hydrometeor fade for a Ka band uplink to a
geostationary satellite from a Chilbolton ground station. Comparisons are between
86
Rec. ITUR 61810 (2009) and the simulation result over the three calendar years
2004 to 2006.
5.3 Validation of Second Order Statistics for Hydrometeor Fade
Optimisation of radio system capacity, quality and reliability require second order
statistics such as fade duration and fade slope as stated in ITU Recommendations
P.16231(2003). These are essential inputs for the design and optimisation of FMTs.
The proposed simulator can produce joint timeseries of fade for arbitrary networks
and so can provide a wide variety of summary statistics.
Figure 5.5: Illustrations of Fade Duration and Fade Slope
5.3.1 Fade Duration
Fade duration is defined as the time period that fade exceeds a given attenuation
threshold. According to the ITU Recommendations P.16231(2003), the distribution
of fade durations yields important information on system outage and unavailability
and is one of the vital parameters which determine the choice of forward error
correction codes and modulation schemes for satellite communication systems.
87
ITU Recommendations P.16231 (2003) provides a prediction model for the average
annual distribution of fade durations for EarthSpace links. The fade duration model
consists of a lognormal distribution for long fades and a powerlaw function for short
fades and is valid for durations longer than one second. Currently, the fade duration
model in the ITUR can only be applied to EarthSpace links operating between 10 to
50 GHz with elevation angles between 5o to 60 o. Figure 5.6 illustrates the simulated
fade duration distributions for a Ka band (27.5 GHz), London to geostationary
satellite link for fade threshold levels of 6, 11 and 21 dB. These correspond to the
Rec. ITUR P.61810 (2009) predicted fades approximately at time exceedances of
0.15%, 0.03% and 0.01% respectively. Figure 5.6 compares the GINSIM simulated
results, for the years 2004, 2005 and 2006; with the P.16231 model predictions.
Figure 5.6: Comparison of annual fade duration statistics from the Rec. ITUR
P.16231 (2005) model and from simulation.
Figure 5.6 describes that the fade durations from the simulated Nimrod data are
88
consistent with the fade durations model from P.16231 including for lower threshold
level (6 dB), middle (11 dB) and the higher level (21dB).
The GINSIM simulated fade duration distribution for a fade threshold of 11 dB for
each calendar year and averaged the three years, are illustrated in Fig. 5.7. The large
year to year variation suggests that the differences between the threeyear simulation
results and the model are not significant.
Figure 5.7: Comparison of annual fade duration statistics from Rec. ITUR P.16231
(2005) model and simulation for the three years 2004 to 2006 at 11 dB threshold
level.
5.3.2 Fade Slope
Fade slope is defined as the rate of change of attenuation with time. Fade slope is
another important parameter when designing FMTs at it constrains the time in which
a system needs to react to increasing fade. Information on the fade slope of the signal
89
can be used for short term prediction of the propagation conditions and the
optimisations of FMTs. The fade slope model in Rec. ITUR P.16231 (2005) is
applicable to satellite links with elevation angles between 10 and 50 degrees and
frequencies from 10 GHz to 30 GHz. The distribution of fade slopes is strongly
dependent upon the fade measurement integration interval. Typically, short
integration intervals yield more extreme fade slopes. The integration interval is
chosen to typical FMT response time and to focus on fade mechanisms with
correlation intervals of this order or longer. An integration interval of 10 s is often
used as this yields the variation due to rain but greatly reduces the effects of
scintillation. Rather than boxcar integration, many systems sample a lowpass
filtered fade timeseries and this can be parameterized by the 3 dB cutoff frequency.
The following equation shows how the fade slope was derived from samples of
attenuation data:
(i )
A(i 1) A(i 1)
2t
dB/s
(5.1)
where A is the attenuation level, i is the sample index and t is the sampling period.
p( / A)
2
(1 (
2 2
))
(5.2)
Equation (5.2) is the conditional fade slope probability density model provided by
Rec. ITUR P.16231 (2005). The only parameter that is required is the standard
deviation of the conditional fade slope, . Equation (5.3) shows how to estimate
.
SF ( f B , t ) A
dB/s
90
(5.3)
Function F gives the dependence on the time interval length and the 3 dB cutoff
frequency of the low pass filter and can be calculated in (5.4):
F ( f B , t )
2 2
(1/ f Bb (2t )b )1 / b
(5.4)
where A is the attenuation level (dB);
f B is the 3 dB cut off frequency of the low pass filter (Hz);
t is the time interval used to calculate the fade slope;
b = 2.3
S is a parameter that depends on elevation angle and climate. For Europe, the average
of S is 0.01;
Figures 5.8 and 5.9 illustrate the fade slope probability density function, conditional
upon the fade level, for the notional Ka band link between London and a
geostationary satellite with 0.02 Hz for f B and the time interval or t is 37.5
seconds. Figure 5.8 shows the conditional fade slope distribution predicted by
GINSIM at fade threshold levels of 1, 3 and 10dB, compared with the Rec. ITUR
P.16231 (2005) fade slope model. The results shows reasonable agreement between
the GINSIM simulation and the P.16231 model at all the tested fade threshold levels.
The low numbers of fade samples at the target fade thresholds yields large uncertainty
in the conditional distributions and sizable fluctuation in the simulated distribution.
However, the simulated and model distributions are very similar in shape, at all fade
levels, and fluctuations in the GINSIM distributions are around means close to the
ITUR model values.
91
Figure 5.8: Comparison of annual fade slope statistics from Rec. ITUR P.16231
(2005) model and simulated Nimrod data at 1, 3 and 10 dB threshold levels
The predicted distribution provided by P.16231, the distributions measured over
three individual years and the average distribution, are compared in Figure 5.9. A
threshold at the 0.01% exceedance levels has been used. The ITUR model is well
within the range of results from the three individual years of GINSIM simulation and
is consistent with the model. The deviation is within that expected given yeartoyear
variation.
92
Figure 5.9: Annual fade slope distribution at approximately 0.01% fade level or 19
dB, for a Ku band geostationary EarthSpace link, as predicted by Rec. ITU P.16231
(2005) and determined from three years of simulation.
Chapter 5 Summary
The GINSIM system has been verified by simulating a variety of notional terrestrial
and EarthSpace links, situated in the southern UK. The simulated distributions of
fade and fade duration and fade slope have been compared to ITUR models and
agreement has been demonstrated, within the limits of the threeyear simulation
period and the expected accuracy of the prediction models. Comparison with ITUR
models is a fairly weak as only average annual distributions are compared. The
system requires further validation of timeseries, in particular with the first and
second order statistics of measured terrestrial and EarthSpace links which will be
shown in the next chapter.
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CHAPTER 6 VALIDATION WITH MEASURED TERRESTRIAL
AND EARTHSPACE LINKS
In the previous chapter, simulation results from GINSIM are compared to ITUR
model predictions, including the annual fade distributions of terrestrial and EarthSpace links and the average annual second order statistics of fade duration and slope.
The simulation results show good agreement with the ITUR models. However,
comparison with the ITUR models is a weak test as the models themselves are only
adequate for the regulation and coordination of radio networks and for assigning fixed
fade margins and offer limited use for the design of fade mitigation techniques
(FMTs) and for the design and optimization of Dynamic Network Management
(DNM) systems. Therefore, further validations of timeseries are required. This
chapter presents comparisons between GINSIM simulations and measured radio link
fade timeseries. Joint fade distributions for pairs of terrestrial and EarthSpace links
and these are compared with measured results from links in the southern UK and
Scotland. The experimental setup, output expectations, the results and discussions are
described further in the following sections.
6.1 Measurement data
All the measured link fade data that will be used for validation were obtained from
the British Atmospheric Data Center (BADC). EarthSpace fading was measured
using a Global Broadcast Service (GBS) beacon operating at 20.7 GHz. Ground
station receivers were operated by Rutherford Appleton Laboratory and had a
dynamic range of approximately 13 dB. Data are available from three ground
receivers, two in the southern UK and one is Scotland. Sparsholt (51°04'N, 01°26'W)
provided data spanning October 2003 to March 2005, Chilbolton (51°08'N, 01°26'W)
provided data from August 2003 to March 2005; while the Scottish data from Dundee
(56.45811°N, 2.98053°W) spans February 2004 to August 2006. The collection and
analyses of these data are described in Callaghan et al. (2008). Figure 6.1 illustrates
94
the geometry or positions of the measured radio links in south of UK.
Figure 6.1: Geometry of the measured radio links in south of UK
Chilbolton and Sparsholt data will be examined to determine the accuracy of
simulated, individual and joint fade distributions. In addition, diversity gain from
simultaneous use of the two ground stations will be simulated and compared to
measured distributions. Fade data is also available from a terrestrial link, Sparsholt to
South Wonston (51.0838°N, 1.3908°W), with length of 5 km operating at 38 GHz
with data starting in October 2002 and ending in March 2005. These data allow joint
distributions of fade on convergent EarthSpace and terrestrial links to be compared
to distributions predicted by the GINSIM.
The resolution of Nimrod data changed in April 2004 and the GINSIM uses the
newer, finer resolution. For this reason, only data collected after April 2004 is used in
the following analyses. Furthermore, it should be noted that the downscaling does not
attempt to reproduce the finescale, spatialtemporal rain field variation that existed at
the time. It produces finescale rain fields that are consistent with an expected
statistical model of spatialtemporal variation. For this reason, direct comparison
between measured and simulated fade timeseries, over the same period of time, have
similar coarse features but the finescale features are not expected to be similar.
95
However, long term first and second order statistics derived from measurements and
simulation should be drawn from the same underlying distributions.
6.2 Comparison of simulated and measured fade data
In this section, measured and simulated, joint fade distributions are compared. The
network examined consists of the terrestrial 38 GHz link and the EarthSpace 20.7
GHz link that converges at Sparsholt. Measured and simulated fade timeseries are
collected for the same oneyear period: April 2004 until the end of March 2005. The
fade data archived on the BADC is relative to a notional clearsky level. The
measured EarthSpace data exhibits Gaussian noise with a standard deviation of
approximately 1 dB and some drift around the 0 dB reference level. For the
comparisons in this section, Gaussian noise with a standard deviation of 1 dB has
been added to the GINSIM simulated fade timeseries and the fade capping effect of
the 13 dB receiver dynamic range has been added.
The simulated outputs are
compared with the measured fade data in terms of annual fade distributions for
terrestrial and EarthSpace links, joint exceedance statistics between terrestrial and
EarthSpace links in Sparsholt, site diversity between two EarthSpace base stations
and auto covariance. The outputs from the simulation are expected to be consistent
(particularly at higher exceedance level) with the measured radio links for annual fade
distributions including the joint distributions and the site diversity comparison. For
auto covariance experiment, the simulated outputs of terrestrial and EarthSpace links
may not be consistent with the measured links due to the presence of scintillation and
multipath on measured links. The following sections contain the results including the
discussions.
6.2.1 Distributions and Joint Distributions of Fade
The joint fade distribution has then been estimated form the joint 2D histogram of
measured and simulated fade data. Figure 6.2 shows fade distributions of the two
links, both measured and simulated, independently. These results agree within
96
expected simulation accuracy. Differences between measured and simulated
distributions can be due to a range of effects. Fading due to fog causes low fade levels
for long periods on the terrestrial link. Both the terrestrial and EarthSpace links are
affected by statistical variation of the specific attenuation – rain rate relationship
which is known to vary by a factor of two for the same rain rate. Fade on the EarthSpace link is also affected by the incidence of convective rain. The simulator assumes
a vertically stratified atmosphere and convective events can cause significantly more
fade than expected. In this case, the limited dynamic range removes extreme fade
events. Before introducing the effects of the limited 13 dB dynamic range of the
receiver, the simulated fade reached 30 dB on the EarthSpace link at 0.001% of time.
This is more plausible than the measured data.
Figure 6.2: Average annual fade distribution for the Global Broadcast Service (GBS)
EarthSpace link to Sparsholt and terrestrial link (South Wonston  Sparsholt), both
measured and simulated, from April 2004 – March 2005.
Figure 6.3 illustrates the 2D, joint fade exceedance statistics for the two links. For
97
exceedance times greater than 0.01% of time, the joint statistics agree very well. At
lower time percentages the contours are very uncertain due to the poor sampling
statistics.
Figure 6.3: Joint fade exceedance statistics for the EarthSpace and terrestrial links
from April 2004 – March 2005.
6.2.2 Distributions of Fade at different spatial and temporal scales
In this section, we test the ability of the simulator to produce annual fade distributions
at different spatial and temporal scales with the same experimental setup in section
6.2.1. The motivation for these comparisons is to study on whether the downscaling
algorithms managed to improve the output results in terms of distributions (especially
dealing with different spatial scales). The comparisons will include various ranges of
spatialtemporal scales from the original spatial and temporal resolutions (1 km and 5
minutes) to the resolutions of the final downscaled data (125 meters and 18.75
seconds) that are used for validations in Chapter 5 and 6. The simulator only
downscaled to these specific spatial and temporal scales due to huge computational
98
resources that are required to maintain smaller spatial and temporal scales of
downscaled data. The Nimrod rain maps are also downscaled at 500 and 250 meters
spatially and 1 min temporally for the comparison purposes. I expect lower fade
distributions for spatial scales that are larger than 125 meters since smaller spatial
integration volume tend to have higher rain rates, see Zhang (2008). For annual fade
distribution comparison at temporal scales, we expect all the distributions to look
similar regardless at any temporal scales since interpolation algorithm is designed to
preserves the distribution statistics, Zhang (2008). The following figures illustrates
the annual fade distribution for terrestrial (Figure 6.4) and for EarthSpace link
(Figure 6.5) at different spatial scales with fixed temporal scale at 18.75 seconds.
Figure 6.4: Average annual fade distribution for terrestrial link (South Wonston Sparsholt) with 1 km scale to 125 meters from April 2004 – March 2005.
99
Figure 6.5: Average annual fade distribution for EarthSpace link (Sparsholt) with 1
km scale to 125 meters from April 2004 – March 2005.
Figure 6.4 and 6.5 illustrate that the downscaling algorithms manage to improve the
distribution results. As expected, the simulated output results becoming more
consistent with the measured link as the spatial scales decreasing from 1 km to 125
meters. The following figures illustrates the annual fade distribution for terrestrial
(Figure 6.6) and for EarthSpace link (Figure 6.7) at different temporal scales with
fixed spatial scale at 125 meters.
100
Figure 6.6: Average annual fade distribution for terrestrial link in Sparsholt from 5
min to 18.75 seconds (April 2004 – March 2005).
Figure 6.7: Average annual fade distribution for EarthSpace link in Sparsholt from 5
101
min to 18.75 seconds (April 2004 – March 2005).
Figure 6.6 and 6.7 illustrates that the distributions are consistent with one another as
expected despite at different temporal scales. Based on the results from Figure 6.4,
6.5, 6.6 and 6.7, we can conclude that the simulator managed to produce results as
expected and improves the distribution results (in the case with the spatial scales).
6.2.3 Site Diversity Comparison
In this section, we test the ability of the simulator to predict site diversity
performance. The two ground stations at Sparsholt and Chilbolton are approximately
8 km apart and so have very similar fade distributions. However, if both ground
stations can be used as a diversity receiver, then the effective fade is the instantaneous
minimum of the fade experienced by the two links. The distribution of instantaneous
minimum fade is important when evaluating the site diversity performance.
Figure 6.8 illustrates the measured and simulated fade distributions for the two EarthSpace links, derived from data spanning April 2004 till end of March 2005, showing
good agreement. Also illustrated are the measured and simulated, minimum joint fade
distributions. These show excellent agreement down to 0.01% of time. Deviation
below this time percentage may be due to the movement of small intense rain events
such as convective events that are not sufficiently described or captured by the 5
minute sample interval of the Nimrod data, or may just reflect large uncertainty due
to low numbers of samples.
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Figure 6.8: Annual single and joint statistics for Chilbolton and Sparsholt from April
2004 – March 2005.
Figure 6.9 illustrates the individual fade distributions, and the instantaneous
minimum fade distribution, for the Sparsholt receiver and the Scottish receiver in
Dundee. The measured and simulated results are in broad agreement. The Dundee
link experiences higher fade levels than the simulation predicts at time percentages
above 0.02% of time, possibly due to the high incidence of light rain that is poorly
determined by Nimrod radars. Due to the large spatial separation between Sparsholt
and Dundee, approximately 500 km, the fade experienced by these links is largely
uncorrelated and so considerable diversity advantage exists.
103
Figure 6.9: Annual single and joint statistics between Dundee and Sparsholt from
April 2004 – March 2005.
Figure 6.10 and 6.11 shows the diversity gain performance, both simulated and
measured, for the Sparsholt and Chilbolton EarthSpace links. According to ITUR
P.618, diversity gain is defined as the difference of attenuation, in dB, between the
single site and joint site for the same percentage of time. The measured and simulated
diversity gains are in excellent agreement.
104
Figure 6.10: Diversity Gain for two EarthSpace links in Sparsholt and Chilbolton,
April 2004 – March 2005.
Figure 6.11: Diversity Gain for two EarthSpace links in Sparsholt and Dundee, April
2004 – March 2005.
105
6.2.4 Validation of Autocovariance
Autocovariance is defined as the covariance of the variable with itself or the variance
of the variable against a timeshifted version of itself. Autocovariance is given by:
C xx (t , t k ) E( X t X )( X t k X )
(6.1)
where E(Y) is the expected value of the random variable Y, X t is the variable at a
time t and X is the mean of the variable. Normalised autocovariance, known as the
autocorrelation is formed by dividing the autocovariance C by the variance 2 . The
autocorrelation is restricted to the closed interval [1,1]. Autocovariance and
autocorrelation are a mathematical tools frequently used in signal processing for
analysing functions or series of values, such as time domain signals. The
autocovariance function of a fade timeseries contains a lot of information on the fade
dynamics and, with other information, can be related to the fade slope and fade
duration statistics. The autocovariance can be used in the development of FMTs. In
this Section, autocovariance functions derived from the measured and simulated fade
timeseries are compared.
As with fade slope and duration, autocovariance is sensitive to sample integration
time, nonstationarity and the presence of noise. To allow direct comparison,
measured fade timeseries are integrated to a sample period of 18.75 seconds, the
same sampling time of the downscaled rain maps from GINSIM. The measured
EarthSpace fade timeseries experience random variation with a standard deviation
of about 1 dB during clearsky conditions; due to a combination of multipath,
interference and equipment noise. In the UK rain occurs for approximately 5% of an
average year and so the autocovariance of the random clearsky variation can
overwhelm rain fade autocovariance, despite the lower fade magnitudes, due to the
much greater period on incidence. To address this, before estimation of covariance
106
both measured and simulated fade timeseries are numerically processed so that any
fades less than 1.5 dB, and all enhancements, are replaced by zero fade. Figures 6.12,
6.13 and 6.14 compare measured and simulated autocovariance functions.
Figure 6.12: Autocovariance of the measured measured terrestrial link fade timeseries compared to the GINSIM prediction.
107
Figure 6.13: Autocovariance function statistics of the measured EarthSpace link fade
timeseries compared to the GINSIM prediction.
Figure 6.14: Autocovariance function statistics of the measured EarthSpace link fade
108
timeseries compared to the GINSIM prediction.
Some systematic variation is to be expected between measured and simulated
autocovariance due to nonhydrometeor fade mechanisms e.g. variation in absorption
by atmospheric gasses, multipath, scintillation etc. Despite this, measured and
simulated results show useful agreement.
Chapter 6 Summary
GINSIM timeseries have been subjected to validation tests by comparison with
measured link data. GINSIM has produced joint fade timeseries with very similar
joint fade distributions to measured results from pairs EarthSpace links and the
combination of an EarthSpace and terrestrial link. Joint fade distributions allow the
performance of multihop and route diverse networks to be predicted. The simulator
has also reproduced measured fade autocovariance for both terrestrial and EarthSpace links. The validation evidence provided in this chapter supports the conclusion
that GINSIM can produce joint hydrometeor fade timeseries with the correct first
and second order statistics. There are several reasons not to expect the simulations to
exactly match measured results. The downscaling of rain fields is a statistical process
that yields different results each time and can produce arbitrarily intense rain cells
with finite probability. Furthermore, the simulator does not currently attempt to model
nonhydrometeor fading mechanisms, which dominate for 95% of the time.
The simulator has only been tested against data acquired in the UK. Further work is
required to verify its performance in other regions. As composite rain radar images
spanning Europe become available from the OPERA project, with consistent quality,
this validation will be performed. In particular, better data position information is
required.
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CHAPTER 7 CONCLUSIONS AND FUTURE OUTLOOK
This thesis is focused on the development of a new network fade simulation tool
called GINSIM. GINSIM is a network fade simulation tool that can produce joint
fade timeseries for arbitrary networks of SHF and EHF radio links, with a temporal
resolution adequate for the development and optimization of dynamic resource
management systems. GINSIM operates by overlaying networks onto specific
attenuation fields derived from the numerical downscaling of recognized databases of
coarsescale meteorological fields, particularly rain rate.
The use of newly available, historical databases of Nimrod (UK coverage) and
OPERA (Europe coverage) composite rain fields have allowed the application area to
be greatly increased so it now spans the UK and, subject to verification, most of
continental Europe, (Paulson and Basarudin, 2011). The OPERA projects produces
composite rain field images with a resolution of 1 km, every 5 minutes, based on a
large number of rain radars operated by European national meteorological agencies.
The downscaling methods developed for the HRFNS, Zhang (2008), have been
adapted to the finer temporal sampling and coarser spatial integration of the Nimrod
and OPERA data compared to CRIE data. Furthermore, more sophisticated
descriptions of advection, applicable over much larger areas, have been developed.
The downscaling of rain fields, both by disaggregation and interpolation, has been
verified by comparison with ITUR models and rain gauge data.
GINSIM is an extension to the HRFNS enabling the simulation of joint fade timeseries for EarthSpace links and shorter slant paths such as those to HAPs and UAVs.
Vertical variation of specific attenuation has been introduced using the BaconTjelta
sleet model combined with the assumption of a stratified atmosphere. The system has
been tested against both ITUR models and measured radio link data. Good
agreement has been found in both the first and second order statistics i.e. average
annual distribution of hydrometeor fade, fade slope and fade duration. Also,
110
predictions of long term autocorrelation and diversity gain have been verified.
Currently GINSIM is one of the most powerful, verified, network fade simulation
tool available. However, GINSIM still requires further enhancement and validation.
The following sections describe the limitations of GINSIM, recommendations for
further development and the future outlook for GINSIM.
7.1 Assumptions, Limitations and Recommendations
7.1.1 Disaggregation
The disaggregation process (Deidda, 1999) was used to refine spatial resolution to
smaller integration volumes. In GINSIM, the coarse scale Nimrod rain maps are
downscaled from 1 km to 125 metres. In the algorithm, each volume within the rain
map is independently downscaled into smaller volumes. Generally, rain rate
measurements made with smaller integration volumes tend to exhibit greater variation
such as high rain rates. The algorithm is designed to reproduce the multiscaling
exponents measured on CRIE data. However, the undressed cascade is also known to
produce nonstationary autocovariance which will not match the autocovariance of
rain fields over scales less than 1 km. One way of addressing this would be to
disaggregate to smaller voxels and then to reaggregate onto a translated grid. Hodges
et al. (2003) suggest filtering the disaggregated field. Both these approaches greatly
reduce the spatial variation in the autocovariance but also change the multifractal
exponents. These problems will only be apparent at scales below 1 km and, except for
very short links, are unlikely to seriously affect the attenuation timeseries produced.
7.1.2 Advection
Use of Nimrod or OPERA data allows more accurate modeling of the advection of
events between rain field measurements due to the fine temporal sampling. This
requires more sophisticated advection transformations for regions larger than
111
approximately 50x50 km2. The HRFNS assumed a linear translation between radar
scans. The advection vector may be estimated by maximising the crosscovariance for
different subregions. Currently the complex advection field is produced by smoothly
interpolating between region centres. The advection of rain events is known to be
highly correlated to the 700 mBar wind vector, Jeannin et al. (2009). This parameter
is commonly provided by NWP databases, albeit on quite coarse grids, and could be
used to constrain or condition the advection field. Fig 7.1 illustrates a 700 mBar wind
vector field from NOAA’s NCEP/NCAR Reanalysis I data.
Figure 7.1: Vector wind (m/s) at 700 mBar pressure level. (Courtesy of NOAA)
7.1.3 Specific Attenuation
One of the major assumptions that are made in GINSIM is the use of the Rec. ITUR
P.8383(2005) model to transform rain rate into specific attenuation, the R relation.
Studies have shown that the specific attenuation can to vary by a factor of two or
112
more either side of the 838 value for the same rain rate. This variation is due to
variations in drop size distribution (DSD). In practice, if the specific attenuation
varied around the ITUR model values along a link path, the pseudointegration to
calculate the total attenuation would greatly reduce the error introduced. Even if this
was not the case, predicted average annual link statistics may well be correct even if
the mean simulated attenuation was quite different from that actually experienced.
There are several approaches that could address this problem. The R relation could
be conditional upon the event type. Different DSD models exist for convective and
stratiform rain and these could be used to derive different R relations. Event type
could be approximately determined from rain rate and event size, as in Capsoni et al
(2009). This classification could also be used in the estimation of rain height.
Alternatively, as Nimrod radars switch to dual polarization, two DSD parameters can
be determined from the radar reflectivity and these can be used to condition the R
relation. Currently it is not clear if this is a problem. Timeseries of measured link
data will need to be compared with many simulations to determine is a significant
bias exists. It is possible that the current simulator will be adequate for many regions
but require adaption in climates with extreme convectivestratiform mixes e.g. in the
tropics.
7.1.4 Rain Height model
Another major assumption is that of a stratified atmosphere. This is used when
calculating the vertical variation of specific attenuation. The current stratified
atmosphere models of specific attenuation variation with altitude are probably
sufficient for stratiform events but absolutely inadequate for convective events.
These events exhibit tall columns of mixed phase hydrometeors which cause extreme
fading due to the long path lengths for slant path links. Rain height for stratiform rain
events usually extend up to 360 m above ZDI. For convective evens the ZDI may not
exist and mixed phase hydrometeors can exist up to altitudes of 10 km due to very
strong updrafts and downdrafts which also prevent the formation of melting layer
113
(Capsoni et. al., 2009). Since the melting layer cannot be formed during a convective
rain event, the BaconTjelta sleet model (Tjelta et. al., 2005) is certainly not
applicable for convective rain. Ultimately, two separate rain height models are needed
to describe the different vertical specific attenuation profiles, one for stratiform and
the other for convective type of precipitations as demonstrated by Capsoni et al.
(2009). The group have develop an improved version of exponential cell (EXCELL)
called SC EXCELL which can distinguish between stratiform and convective rain
events by having two separate physical rain heights, derived from ERA15 database
for each type of rain event (stratiform and convective) to calculate rain attenuation.
The effects of the melting layer in terms of hydrometeor attenuation are also added
into the system. SC EXCELL has shown to perform better than the previous EXCELL
when comparing with radio measurements from DBSG3 database. In addition, SC
EXCELL offers flexibility in terms of modifying some of its input parameters so that
the model can be used for different climate regions. The physical rain height model
for convective precipitation from SC EXCELL could be used for GINSIM when
simulating radio links during convective rain event.
7.2 Comparison with other Network Fade Simulation Tools
As discussed in Chapter 4, there are several ways to develop a network fade
simulation tools which differ in the methods used to produce the fine scale
meteorological fields. Fine scale rain fields can be generated by statistical models of
rain cell parameters, purely statistical models of spatial temporal rain rate variation or
through downscaling coarsescale meteorological measurement data. The three
approaches currently in development each have advantages and disadvantages. Purely
statistical generation of rain fields is computationally fast but limited by lack of
knowledge of rain field statistics at the scales between weather systems and variation
within individual events. There are also concerns that rain field statistics measured at
one location may not translate to other places e.g. between temperate and tropical
regions or between coastal and mountainous regions. The EXCELL and HYCELL
114
rain cell models are capable of producing annual fade distribution and other statistics
but they cannot reproduce timeseries and so are of little use for the design and
optimization of FMTs. The use of NWP or direct observation data, e.g. CRIE, ERA
40, NCEP/NCAR reanalysis or OPERA rain radar data; is limited by the existence of
verified downscaling methods, both disaggregation and interpolation, and the same
uncertainty in constraining variation statistics that limits purely statistical methods
7.3 Future Works and Recommendations
7.3.1 Downscaling Attenuation TimeSeries
The downscaling algorithms in GINSIM could be used to downscale coarsescale rain
rate fields to the very fine scale resolutions consistent with link Fresnel zones and
response times of FMT systems i.e. a few seconds and a few metres. However, for
regions the size of even simple networks, this requires huge computational resources
in terms of processing speed and the space to store data. This problem can be
addressed by numerically downscaling the attenuation timeseries after the pseudointegration process is applied to moderately downscaled meteorological fields, The
ONERA SISTAR system, (Jeannin et al. 2009), operates this way. Such methods
could offer huge computational gain but it is still at its early stage and has not been
properly investigated. The major difficultly is the prediction of the integrationscale
crosscovariance of fade on arbitrary pairs of links. This information is required for
the joint disaggregation of fade timeseries. For links that are widely separated, the
finescale variation of fade can be assumed to be independent. However, for the most
interesting networks i.e. convergent links; this scale dependant crosscovariance is
unknown. Models for the covariance of terrestrial links have been published, e.g.
Paulson et al (2006), but these have not been integrationscale dependant. The
problem has many parameters i.e. radio parameters such as frequencies and
polarizations, network parameters such as geometry, and climate parameters.
However, simple models will need to be developed. The errors introduced by bias in
115
the crosscorrelation model will only effect variation at fineresolution and only for
links in very close proximity. The potential benefits of this scheme seem to greatly
outweight the difficulties.
7.3.2 Other Atmospheric Fade Effects
Currently GINSIM only simulates rain and sleet fade for terrestrial and EarthSpace
links since these are the most dominant hydrometeors fade mechanisms. Further fade
processes can be added to refine the channel models. Absorption by atmospheric
gases is a process that varies slowly in time and space and the fade can be calculated
from local meteorological parameters provided by standard sources. Scintillation
depends upon atmospheric turbulence and system parameters such as antenna
apertures. Once turbulence has been estimated, scintillation timeseries can be added
using the model of Tatarski (1961). Cloud attenuation is another important fade
mechanism and should be taking into account especially when simulating fade for
EarthSpace links at higher frequency band. Cloud data is widely available from
satellite Earth observation sources.
7.3.3 Nowcasting
Network fade simulation tools such as GINSIM could utilise meteorological
nowcasting rainfall products to predict link outage half an hour or an hour into the
future. This information could be used to predicatively reconfigure networks and data
movements. Video streaming is an important application of current and future
networks. Predictive DRM systems could preload network nodes with video data
before a subnetwork becomes isolated by outages. Alternatively, video streams can
be rerouted around outages or to reduce the required capacity of links using dynamic
modulation and coding to mitigate fades. The UK’s Meteorological Office operates a
nowcasting system for rainfall maps (created through extrapolating a sequence of
radar images to produce a very shortrange rainfall forecast) in which can be
116
combined with output from numerical weather prediction models to extend the period
of predictability.
7.3.4 Global Applications and Different Climate Regions
The simulator has only been tested against ITUR models and measured data acquired
in the UK. Further work is required to verify its performance in other regions with
different climates such as the alpine and Mediterranean regions of Europe. As
composite rain radar images spanning Europe become available from the OPERA
project, with consistent quality, this verification will be performed. In particular,
better data position information is required. With the increasing deployment of
weather radars across the world, it is possible to extend the application of a current
simulation tool to a global scale where OPERA could combine with other large rain
radar networks such as NEXRAD (NextGeneration Radar) in the U.S operated by
NOAA. Alternatively, the simulation tool could also be applied to the spaceborne
rain radars, which have wider coverage than ground base rain radars and have
becoming increasing popular, such as the TRMM (Tropical Rainfall Measuring
Mission) by NASA. Recently, China has begun developing their own spaceborne
rain radar and it is expected to be launched in 2016 (Yang et. al., 2010). Currently,
spaceborne rain radars may not have the same quality as the surfacebased rain
radars, see Chapter 3. However, they can still provide data for complex algorithms,
such as the MultiPrecipitation Estimates (MPE), to provide rainfall maps with global
coverage. Over the years, the techniques and algorithms for systems such as MPE are
improving and it may only be a matter of time to have a global rainfall map with
rainfall accuracy and resolutions similar to the current groundbased rain radars.
117
7.3.5 Climate Change
Network fade simulation tool such as GINSIM could be used to investigate the
climate change effects on radio links including terrestrial and EarthSpace links.
Climate change phenomena are usually associated with natural disasters but recently
researchers have begun exploring the effects on radio links. Where propagation
important parameters, such as rain height, rain rate distributions and the mixture of
stratiform and convective events; are reflected in the input data to simulation systems
such as GINSIM, these tools can be used to demonstrate the effects of climate change
on networks. NWP simulations of future climates will also allow the extrapolation of
these effects into the future.
7.4 Future Outlooks
A network fade simulation tool, GINSIM, has been developed and verified. The tool
can currently be applied to networks that span Europe, but have only been verified in
the UK. The methods developed can potentially be used in a global simulation tool
when global meteorological data is available at similar scales to that currently
available in Europe. GINSIM has the potential to augment or replace ITUR models
and provide answers to questions that ITUR models will never address. Applications
include the design and optimization of Dynamic Network Management systems and
managing the introduction of new systems into populated telecommunications bands.
Combining the current system with nowcasting could provide the input data
necessary for predicted DNM.
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APPENDIX A: DISAGGREGATION
A two dimensional spatial multifractal disaggregation method is required for a
network simulator that preserves spatial statistical properties as observed in actual
rainfall. Disaggregation is a process to refine existing sample into smaller spatial
integration volumes. Multifractal cascade method from Deddia (2000) has been
employed for the disaggregation process. The random cascade is created via a
multiplicative process.
Each son rain rate R ij at jth level can be gained by
multiplying the related father at level (j1) by an independent and identical distributed
random variable wi .Therefore R ij wi R j 1 where the scale at the j level is half of
the scale at the level (j1). Collection average or mean of q moments of random
variables R can be related to the statistics of the generator w as following:
R qj R0q w q
j
(A1)
Moment scaling structure function can be established if the information of the rain
rate distribution at the coarsest scale is known. The structure function as shown by
Deddia (1999 and 2000) obeys the scaling law with expected multifractal exponent
ζ(q) depending only on the ensemble averages of the moments of the generator w.
(q) q(2 log 2 w) log 2 w q
(A2)
ζ(q) can be proven as a convex and nonlinear function of the moments q by using the
CauchySchwarz inequality. Hence, the model is appropriate for the generation of
multifractal fields. The selection of probability distribution for the random generator
w characterises the multifractal behaviour and the scale covariance of synthetic
signals. In GINSIM, the logPoisson distribution has been employed. wi = e aβ y,
where y is an i.i.d. or independent and identically distributed sample from a Poisson
133
distribution of mean c.
The qorder moment of the logPoisson distribution is given by:
w q exp[qa c( q 1)]
(A3)
When q=1, then a=c(1β). Conclusively, the expected scaling of synthetic fields can
be assessed:
( q ) 2q c
q( 1) ( q 1)
ln 2
(A4)
where c and β are the parameters for multifractal exponent ζ(q) . Parameters of c and
β must be scaleindependent in order to replicate a scaling regime in synthetic fields.
The parameters c and β from the model can be estimated by solving the minimisation
equation as following:
min [
c,
q
s (q) (q) 2
]
q 1
(A5)
where ζs(q) are the sample multifractal exponents, ζ(q) is the theoretical expectation
as above, q1 is a weight that accounts for the estimation error which is the standard
deviation of ζ(q).
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APPENDIX B: INTERPOLATION
Interpolation is a process to introduce new rain rate measurements where there were
none. In GINSIM, the interpolation is used to introduce new rain rates between
existing scans. Methods for interpolation are based on series of algorithms including
Random Midpoint Displacement algorithm of Voss (1985) and the Local Average
Subdivision algorithm of Fenton and Vanmarcke (1990).
Assume a pair of log rain rate fields to be from a Gaussian fractional Brownian
process:
= ln ( ( +
= ln ( ( ,
Where
,
))
+ ∆ ))
represents the advection vector between scans. A Maximum Likelihood
algorithm is used to estimate the marginal mean L and variance L2 for censored
data, L > Lmin where Lmin is the smallest measurable log rain rate. The set of spatial
sampling points is assumed to be
∆
≡{
∈ ( , )} and let
≡{
≤
≤
+
be the equispaced interpolation times. Then, the discrete interpolation volume
will be
≡ {( , ):
∈ , ∈ }.
The values of the interpolated log rain rate are calculated via a hierarchical algorithm
that introduces fresh samples. These samples are separated by distances that decrease
exponentially with every iteration. Voss’s Random Midpoint Displacement (RMD)
algorithm (1985) was developed to increase the resolution of isotropic FBfs. This
algorithm has been used as a foundation and existing samples are conserved at each
iteration process. The following paragraphs explain the development of an algorithm
for asymmetrically sampled FBfs. The technique is based on the Local Average
Subdivision algorithm by Fenton and Vanmarcke (1990).
The RMD algorithm starts with a FBf that evenly sampled at scale ∆ in each
dimension and produces new samples to generate a FBf sampled at half of the
135
original scale or ∆/2. Assume
∆
= { ; = 1, …
a region of scale ∆ around the interpolate
∆}
to be the log rain rate samples in
at position Y. The new value from the
interpolation process is selected to be:
= ( ∆) +
B1)
∆
where ( ∆ ) is a smoothly interpolated value and
is an independent and identically
distributed (i.i.d.) standard Normal distribution sample. A linear estimator i.e.
( ∆) =
+∑
coefficients
∆
will be implemented for the asymmetric algorithm. The
depend upon the distribution and shape of samples in the scale area
and are selected to fulfil:
(
)=
(
)=
(
)=
,
(B2.1)
(
(0).
) and
(B2.2)
(B2.3)
( ) is the expected value of the product between two log rain rates that are
separated by a distance , with known FBf assumption. It may be obtained from the
( )= ( )−
marginal distribution i.e.
/2. By substituting the equation
in (B1) into the expected value in (B2) and using the independence of
and
produces:
(
)=
+∑
(
)=
+2
(
)=
( ) =∑
∆
+∑
∆
∑
∆
(
+∑
,
∆
) and
∆
∑
(B3.1)
(B3.2)
+
∆
The equations in (B2.1) and (B3.1) indicate that ∑
equations in (B2.2) and (B3.2) yield a further
∆
136
.
(B3.3)
= 1. In addition, the
equations linear in . The value of
the coefficients { } can be extracted via solving the
coefficients { } obtained yield an expression for
∆
∆
∆,
∆
+ 1 linear equations. The
using (B2.3) and (B3.3).
The midpoint interpolation of regularly spaced samples and
∆
∆
taken to be the
= 2 nearest or adjacent neighbours, generated FBfs via Voss’s RMD algorithm
with
=0,
=
∆
and noise variance exponentially decreasing with scale. In
this situation, the calculation for interpolation coefficients is insignificant.
Nevertheless, Nimrod rain data is sampled finer in space than in time in which the
units are decorrelation intervals. The second order moment of the measured rain data
is defined as:
( , ) ≡ ( ( , ) ( + , + ))
= 2 sample units can be determined:
Interpolation scale of
(( + 1)∆
(B4)
, 0) ≅
(0, ∆ )
B5)
where e is a unit vector. In order to produce samples symmetrically distributed in
space and time,
− 1, new, equispaced, log rain rate fields need to be interpolated.
The process can be achieved in m iterations of an asymmetric RMD or ARMD
through equations in (B1), (B2) and (B3). During the first iteration, interpolation
region with diameter ∆ = 2
in sample units are used and the diameter is halved at
each following iteration. For each scale, the interpolation coefficient { } for the
recognised/known
∆
within the interpolation volume or dimension, and the variance
must be established. For interpolation regions located on the boundary of , need
coefficients that are consistent with the asymmetry of
∆,
i.e. the existence of finely
scaled measured rain data on a pair of log rain rate fields (
and
) or the lack of
samples located outside the boundary of . On the other hand, same coefficients can
be applied for all regions that are located away from the boundary.
137