Electromagnetic Waves and Their Propagation Through the Atmosphere

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Electromagnetic Waves and Their Propagation
Through the Atmosphere
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ELECTRIC FIELD
An Electric field exists in the presence of a
charged body
ELECTRIC FIELD INTENSITY (E)
A vector quantity magnitude and direction
(Volts/meter)
MAGNITUDE OF E Proportional to the force acting
on a unit positive charge at a point in the
field DIRECTION OF E The direction that the
force acts
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The Electric Field (E) is represented by drawing
the Electric Displacement Vector (D), which takes
into account the characteristics of the medium
within which the Electric Field exists.
e, the Electric Conductive Capacity or
Permittivity, is related to the ability of a
medium, such as air to store electrical potential
energy.
Vacuum
Air
Ratio
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The Electric Displacement Vector, D, is used to
draw lines of force.
Units of D
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MAGNETIC FIELD
A Magnetic field exists in the presence of a
current
MAGNETIC FIELD INTENSITY (H)
A vector quantity magnitude and direction
(amps/meter)
MAGNITUDE OF H Proportional to the
current DIRECTION OF H The direction that a
compass needle points in a magnetic field
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The Magnetic Field (H) is represented by drawing
the Magnetic Induction Vector (B), which takes
into account the characteristics of the medium
within which the current flows.
m, the Magnetic Inductive Capacity, or
Permeability, is related to the ability of a
medium, such as air, to store magnetic potential
energy.
Vacuum
Air
Ratio
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Magnetic Fields
Magnetic fields associated with moving charges
(electric currents)
I Current
B Magnetic Induction
Magnetic Field Lines are closed loops surrounding
the currents that produce them
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Maxwells Equations for time varying electric
and magnetic fields in free space
Simple interpretation
Divergence of electric field is a function of
charge density
A closed loop of E field lines will exist
when the magnetic field varies with time
Divergence of magnetic field 0 (closed loops)
A closed loop of B field lines will exist in The
presence of a current and/or time varying
electric field
(where ? is the charge density)
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Electromagnetic Waves A solution to Maxwells
Equations
Electric and Magnetic Force Fields
Propagate through a vacuum at the speed of light
Electric and Magnetic Fields propagate as waves
or
where
?, ?, f are coordinates, A is an amplitude
factor, ? is the frequency and ? is an arbitrary
phase
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Electromagnetic waves
Interact with matter in four ways
Reflection
Refraction
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Scattering
Diffraction
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Electromagnetic Waves are characterized by
Wavelength, ? m, cm, mm, mm etc Frequency, ?
s-1, hertz (hz), megahertz (Mhz), gigahertz
(Ghz) where c ??
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Time variations in charge, voltage and current in
a simple Dipole Antenna
Pt. A
Pt. B
wavelength
All energy stored in electric field
All energy stored in magnetic field
Energy is 1) stored in E, B fields, 2) radiated
as EM waves, 3) Dissipated as heat in antenna
Near antenna Energy stored in
induction fields (E, B fields) gtgt energy
radiated (near field) More than a few ? from
antenna Energy radiated gtgt energy
stored in induction fields (far field)
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Polarization of electromagnetic waves
The polarization is specified by the orientation
of the electromagnetic field. The plane
containing the electric field is called the plane
of polarization.
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Electric field will oscillate in the x,y plane
with z as the propagation direction
For a monochromatic wave
where f is the frequency and d is the phase
difference between Exm and Eym and the coordinate
x is parallel to the horizon, y normal to x, and
z in the direction of propagation.
If Eym 0, Electric field oscillates in the x
direction and wave is said to be horizontally
polarized
If Exm 0, Electric field oscillates in the y
direction and wave is said to be vertically
polarized
If Exm Eym, and d p/2 or - p/2, electric
field vector rotates in a circle and wave is
circularly polarized
All other situations E field rotates as an
ellipse
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Propagation of electromagnetic waves in the
atmosphere
Speed of light in a vacuum
Speed of light in air
Refractive index
At sea level n 1.0003 In space n
1.0000
Radio refractivity
At sea level N 300 In space N 0
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The Refractive Index is related to

• Density of air (a function of
• dry air pressure (Pd), temperature (T), vapor
  pressure (e)

2. The polarization of molecules in the air
(molecules that produce their own electric field
in the absence of external forces)
The water molecule consists of three atoms, one O
and two H. Each H donates an electron to the O so
that each H carries one positive charge and the O
carries two negative charges, creating a polar
molecule one side of the molecule is negative
and the other positive.
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Snells law
Where i is the angle of incidence
r is the angle of refraction Vi
is the velocity of light in medium n
Vr is the velocity of light in medium n - Dn
In the atmosphere, n normally decreases
continuously with height Therefore due to
refraction, electromagnetic rays propagating
upward away from a radar will bend
toward the earths surface
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Earth curvature
Electromagnetic ray propagating away from the
radar will rise above the earths surface due to
the earths curvature.
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Ray Path Geometry
Consider the geometry for a ray path in the
Earths atmosphere. Here R is the radius of the
Earth, h0 is the height of the transmitter above
the surface, f0 is the initial launch angle of
the beam, fh is the angle relative to the local
tangent at some point along the beam (at height h
above the surface at great circle distance s from
the transmitter).
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Equation governing the path of a ray in the
earths atmosphere
(1)
where R is the radius of the earth, h is the
height of the beam above the earths surface, and
s is distance along the earths surface.
To simplify this equation we will make three
approximations
1. Large earth approximation
2. Small angle approximation
3. Refractive index 1 in term
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1
1/R
1
X
X
X
Approximate equation for the path of a ray at
small angles relative to the earths surface
(2)
Or, in terms of the elevation angle of the beam
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Spherically Stratified Atmosphere Ray Path
Equation
Integrating (2) yields, (dh/ds)2 2? (1/R
dn/dh) dh constant (3) Since dh/ds f for
small f, (3) can be written as, 1/2(fh2 - f02)
(h - h0)/R n - n0 (h/R n) - (h0/R
n0) Letting M h/R (n-1) x 106, we
have (M - M0)10-6 M is the so-called
modified index of refraction. M has a value of
approximately 300 at sea level.
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Curvature of Ray Paths Relative to the Earth

• If the vertical profile of M is known (say
  through a sounding yielding p, T and q), fh can
  be calculated at any altitude h, that is, the
  angle relative to the local tangent.
• Lets now consider the ray paths relative to the
  Earth. For the case of no atmosphere, or if N is
  constant with height (dN/dh 0), the ray paths
  would be straight lines relative to the curved
  Earth.
• df/ds 1/R dn/dh 1/R
  for n constant with height
• (No atmosphere case?)
• (Flat earth case?)
• For n varying with height,
• df/ds 1/R dn/dh lt
  1/R since dn/dh lt 0
• For the special case where dn/dh -1/R, df/ds
  0. Hence the ray travels around the Earth
  concentric with it, at fixed radius, R h. This
  is the case of a trapped wave. DUCTING

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Curvature of Ray Paths Relative to the Earth
For convenience, it is is easier to introduce a
fictitious Earth radius, 1/R 1/R dn/dh For
typical conditions, dn/dh -1/4 R m-1 Hence R
R/(1 - 1/4) 4/3 R This is the effective Earth
radius model, to allow paths to be treated as
straight lines. Doviak and Zrnic (1993) provide
a complete expression for h vs. r, where r is the
slant range (distance along the ray). h r2
(keR)2 2rkeRsin?1/2 - keR where h is beam
height as slant range r, ? is the elevation angle
of the antenna, and ke is 4/3 (R is the actual
Earth radius).
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Curvature of Ray Paths Relative to the Earth
An additional equation of interest is the
equation that provides the great circle distance
s, from the radar, for the r, h pair (slant
range, beam height), which is s keR
sin-1rcos?/(keR h) We can get even simpler
and consider a the height of the beam at slant
range R and elevation angle ?, h (km) R2/17000
R sin ?
R
h
?
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• 
  

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Non-Standard Refraction

• Non-standard refraction typically occurs with the
  temperature distribution does not follow the
  standard lapse rate (dn/dh ? -1/4 (R)). As a
  result, radar waves may deviate from their
  standard ray paths predicted by the previous
  model. This situation is known as abnormal or
  anomalous propagation (AP).
• Abnormal downward bending -------
  super-refraction
• (most common type of AP)
• Abnormal upward bending -----------
  sub-refraction
• Super-refraction is associated most often with
  cold air at the surface, giving rise to a near
  surface elevated temperature inversion in which
  the T increases with height. Most commonly
  caused by radiational cooling at night, or a cold
  thunderstorm outflow.
• Since T increases with height, n decreases
  (rapidly) with height (dn/dh is strongly
  negative). Since n c/v, v must increase with
  height, causing downward bending of the ray path.

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Non-Standard Refraction
Super-Refraction (most common) dN/dZ lt -79 km-1
and gt -158 km-1
h
h
F0

• Beam is bent downward more than standard
• Situations
• Temperature inversions (warm over cold air
  stable layers)
• Sharp decrease in moisture with height
• And (2) can occur in nocturnal and trade
  inversions, warm air advection (dry),
  thunderstorm outflows, fronts etc.
• Result
• Some increased clutter ranges (side lobes)
• Overestimate of echo top heights (antenna has to
  be tilted higher to achieve same height as
  standard refracted beam)- see figure above
• Most susceptible at low elevation angles (e.g.,
  typically less than 1o)

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Sub-Refraction (not as common) dN/dZ gt 0 km-1
h
h
F0

• Beam is bent upward more than standard
• Situations
• Inverted-V sounding (typical of
  desert/intermountain west and lee-side of
  mountain ranges microburst sounding late
  afternoon and early evening see figure)
• Result
• Underestimate of echo top heights (beam
  intersects top at elevation angles lower than in
  standard refraction case)- see figure above
• Most susceptible at low elevation angles (e.g.,
  typically less than 1o)

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Ducting or Trapping (common) dN/dZ lt -158 km-1

• Beam is severely bent downward and may intersect
  the surface (especially at elevation angles less
  than 0.5o) or propagate long distances at
  relatively fixed heights in an elevated duct.
• Situations
• Strong temperature inversions (surface or
  aloft)
• Strong decreases in moisture with height
• Result
• Markedly Increased clutter ranges at low
  elevation angles
• Range increases to as much as 500 in rare
  instances (useful for tracking surface targets)
• Most susceptible at low elevation angles (e.g.,
  typically less than 1o)
• Elevated ducts can be used as a strategic asset
  for military airborne surveillance and weapons
  control radars. E.g., if a hostile aircraft is
  flying in a ducting layer it could be detected
  a long way away, while its radar cannot detect
  above or below the ducting layer. Conversely,
  friendly aircraft may not want to be located in
  the duct.

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One moral of the whole refraction
story..knowing the exact location of the beam
can be problematic. Remember this when you have
the opportunity to compare the measurements of
two radars supposedly looking at the same storm
volume!
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Inversions withdN/dZ lt -158 km-1lead to
anomalous propagation

• Most common on clear nights during the early
  morning hours. Largely dissipates by midday.
• Common over water, especially in the cold season.
• Radar beam is bent into the ground and returns a
  strong signal to radar.
• Radar echoes are NOT real, there was no
  precipitation occurring in the image at right.

Source Meteorological Service of Canada
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Scanning strategies for scanning radars must take
into account the propagation path of the beam if
certain operational or scientific objectives are
to be addressed. Here, 3 common NWS NEXRAD
Volume Coverage Patters (VCPs) are illustrated.
NEXRADs have a 5-6 minute scan update requirement
for severe weather detection, so they vary their
VCPs and scan rates depending on the weather
situation.
VCP 31 clear air mode
6 min update, slow scan rate
VCP 11 severe weather mode
5 min update, fast scan rate
VCP 21 Wide-spread precip
6 min update, slow scan rate
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Big implication of radar beam height increasing
with range (under normal propagation conditions)
combined with broadening of the radar beam The
radar cannot see the low level structures of
storms, nor resolve their spatial structure as
well as at close ranges. Thus, for purposes of
radar applications such as rainfall estimation,
the uncertainty of the measurements increases
markedly with range.
Storm 1
Storm 2
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Beam Blockage in Complex Terrain

• Beam propagation is a function of the vertical
  refractivity gradient (dN/dz)
• N 77.6(p/T) - 5.6(e/T) 3.75x105(e/T2)
• dN/dz is sensitive to p, T, e
• Thus, changes in the vertical profiles of these
  quantities can change the height of the ray path
  as it propagates away from the radar
• This is especially important in complex terrain,
  because the amount of beam blockage will change
  depending on the vertical refractivity gradient

dN/dZ -40/km
dN/dZ -80/km
)
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Radar Rainfall Climatology - KPBZ
Warm Season
Cold Season
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Mid-Atlantic River Forecast Center (MARFC)
Height of Lowest Unobstructed Sampling Volume
Radar Coverage Map
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West Gulf River Forecast Center (WGRFC)
Height of Lowest Unobstructed Sampling Volume
Radar Coverage Map
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PRECIPITATION MOSAIC
RADAR COVERAGE MAP
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Northwest River Forecast Center (NWRFC)
Warm Season
Cold Season
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Say youd like to site a radar for a research
experiment. In a perfect worldyoud like to be
able to take a swim after work, but AP and beam
blockagemay be a problem. Sidelobes may
intersect the highly reflective ocean creating
sea clutter
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Mountains can be a problem
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Local effects can be a problem too topographic
maps and DEMs can help, but still need to conduct
a site survey to see trees, antennas, buildings,
and overpasses.
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Often times you end up in places like this
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Height of a ray due to earths curvature and
standard atmospheric refraction
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Anomalous Propagation The propagation of a radar
ray along a path other than that associated with
standard atmospheric refraction
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Anomalous propagation occurs when the index of
refraction decreases rapidly with height in the
lowest layers of the atmosphere
Recall that the Refractive Index is related to
n decreases rapidly when T increases with height
and/or e decreases with with height in the lowest
layer
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Effects of anomalous propagation
Note cell towers along Interstates!
Note buildings In Champaign, IL
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Propagation of Electromagnetic Waves
In this section we will discuss the propagation
of EM waves including further discussions on the
index of refraction, Snells Law, and derivation
of equations for the ray path of a radar wave
traveling under various atmospheric conditions.
Since the atmosphere is a non-vacuum, we deal
with wave speeds that are different from the
speed of light, c 2.998 x 108 m/s. As
discussed in the previous section, the wave speed
for a non-vacuum defines the index of refraction,
n c/v where v is the wave speed in the
particular medium. Since c ve0µ0 and v
ve1µ1, we have n2 eµ where e e 1/e0 and µ
µ1 /µ0 Since µ is approximately 1 for most
media considered, n2 e. With egt1, ngt1 and
hence vltc (by a small amount). The general form
of the index of refraction is of the form m
n - ik where k is the absorptivity of the
medium.
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Propagation of Electromagnetic Waves
Index of refraction for the atmosphere governs
the path of radar waves The atmosphere is an
inhomogeneous medium, with variations in
temperature, pressure and water vapor, all of
which contribute to changes in the index of
refraction. Index of refraction for dry air,
or N, the refractivity For dry air, N (n-1)106
K1p/T where P is in mb, T in K, K1 77.6
(K/mb) Substituting from the Ideal Gas Law,
(n-1) 106 K1R? constant x
? Therefore, dn/dz d?/dz
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Propagation of Electromagnetic Waves
Water vapor contribution to the index of
refraction, n Since air molecules essentially
have no permanent dipole moment, N (dry air) does
not vary with frequency. However, this is not
the case for the water vapor molecule, which has
a permanent dipole moment. The degree of
alignment of this dipole moment with the incident
E field vector is frequency dependent. For
microwave frequencies,

N (n-1)106 K3e/T2 - K2e/T where
e is the vapor pressure in mb K2 5.6 K/mb
K3 3.75x105 (K)2/mb Index of refraction may
be found by adding components for both dry air
and water vapor, N K1p/T K3e/T2 - K2e/T
Key question How does N vary with height and
with varying atmospheric conditions?
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Snells Law

• First examine simple refraction in terms of
  Snells Law
• Since p and e decrease exponentially with height,
  n decreases with altitude (these affects offset
  the linear decrease in height for T, for most
  situations). Since n c/v, v increases with
  height and hence the wave is bent downward.
  Snells Law is
• n-?n r
• sin i/sin r vi/vr
  vr
• 
  vi i n
• since vrgt vi it follows that sin r gt sin i and
  hence r gt i
• This is the typical situation for a ray path in
  the atmosphere under conditions where the
  temperature decreases with height.

Curvature of ray path due to n changes,
relative to curvature of Earth is key issue!
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Spherically Stratified Atmosphere Ray Path
Equation

• For dn/dh small, Hartee, Michel and Nicolson
  (1946) derived an exact differential equation for
  a radar ray path in a spherically-stratified
  atmosphere.
• d2h/ds2 - (2/(Rh) 1/n(dn/dh))(dh/ds)2 -(
  (Rh)/R)2 (1/(Rh) 1/n(dn/dh)) 0 (1)
• where d2h/ds2 is the curvature of the ray path.
  Under most conditions, the following assumptions
  can be made
• (dh/ds)2 ltlt 1
• n 1
• h ltlt R
• With these assumptions, (1) reduces to
• d2h/ds2 1/R dn/dh (2)