Atmospheric InstrumentationM. D. Eastin Fundamentals of Radar (Beam) Pulses

Atmospheric Instrumentation M. D. Eastin

Fundamentals of Radar (Beam) Pulses


Outline

Radar Beam Pulses

• Electromagnetic (EM) waves• Basic Characteristics• Application to Radar

• EM Wave Propagation in the Atmosphere• Atmospheric Refraction• Earth Curvature• Combining Refraction and Curvature• Non-standard Refraction• Attenuation

• Radar Returns• Hydrometeor Backscatter


Electromagnetic (EM) WavesBasic Concepts:

• Electromagnetic waves are electric and magnetic pulses that propagate away from theirsource at velocities close to the speed of light (c = 3 x108 m s-1)

• In a vacuum (such as outer space) → EM waves propagate in a straight line• In a medium (such as the atmosphere) → EM waves interact with matter along their path

through four processes depending on the wavelength and type of medium (or matter)

1. Reflection





through four processes depending on the

wavelength and type of medium (or matter)

2. Refraction







3. Scattering







4. Absorption

RadarReflectivity

Radar

Absorption ofradar beam byintense rainfall


Electromagnetic (EM) WavesApplied to Radar:

• The atmosphere is completely transparent to a wide range of EM wavelengths• Radars operate under the basic principle that clear air (nitrogen, oxygen, and water vapor)

exhibit limited transparency to a narrow range of EM wavelengths

• Clear air will refract any EM radiation encountered at these wavelengths• The radar beam path is partially governed by the total refraction experienced by the

transmitted EM pulse as it travels through clear air



• The atmosphere is completely transparent to a wide range of EM wavelengths• Radars operate under the basic principle that hydrometers (water drops and ice crystals)


• Hydrometers will reflect / scatter a portion of EM radiation encountered at such wavelengths• The “return echo” received by a radar is the returned “back scatter” power from an EM

pulse (transmitted at a wavelength known to interact with certain sized hydrometeors) when

the initial pulse interacts with encountered hydrometeors



• The atmosphere is completely transparent to a wide range of EM wavelengths• Radars operate under the basic principle that hydrometers (water drops and ice crystals)


• Intense rainfall will absorb a large portion of EM radiation encountered at these wavelengths• Intense convective cells characterized by high radar reflectivity and heavy rainfall may

absorb (or attenuate) a large fraction of the transmitted EM pulses, preventing the detection of any hydrometeors at greater range and creating an anomalous “rain shadow”


EM Wave Propagation in the AtmosphereBasic Concepts: Role of Earth’s Curvature

• An electromagnetic wave propagating away from its source (a radar antenna) will rise above the Earth’s surface due to the Earth’s curvature


EM Wave Propagation in the AtmosphereBasic Concepts: Refraction

Speed of light in a vacuum (c):

00

1

c

Speed of light in a medium (v):

11

1

v

Refractive Index (n):

11

00

v

cn At sea level: n = 1.0003

In space: n = 1.0000

Slightly slower

where: ε = permittivity (ability to absorb electrical energy)ε0 = 8.850 x 10-12 (in a vacuum)ε1 = 8.876 x 10-12 (at sea level pressure)

μ = permeability (ability to absorb magnetic energy)μ0 = 1.260 x 10-6 (in a vacuum)μ1 = 1.260 x 10-6 (at sea level pressure)


EM Wave Propagation in the AtmosphereRefractive Index in the Atmosphere: Definition for a Single Layer

• Related to: 1. Density of molecules (dry air)2. Polarization of molecules in the air (water vapor)

where: P = pressure of dry air (mb) C1 = 7.76 × 10-5 K mb-1

T = temperature (K) C2 = 5.60 × 10-6 K mb-1

e = water vapor pressure (mb) C3 = 0.375 K2 mb-1

• Through the standard atmosphere the refractive index (n) decreases slowly with height• Through a temperature or moisture inversion the index (n) decreases rapidly with height

23211T

eC

T

eC

T

PCn

The water vapor 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 polarized molecule – one side of the molecule is negative and the other positive.


EM Wave Propagation in the AtmosphereRefractive Index in the Atmosphere: Snell’s Law

• Electromagnetic waves propagating through the standard atmosphere undergo refraction (i.e. they bend like visible light passing through a prism) as they move from one atmosphericlayer to the next (i.e., as atmospheric density changes)

where: θI = angle of incidence (degrees) θR = angle of refraction (degrees) VI = EM wave speed in first medium [ n ] VR = EM wave speed in second medium [ n – Δn ]

• Electromagnetic waves propagating through an inversion undergo severe refraction with angles of refraction potentially greater than 90 degrees

R

I

R

I

V

V

n

nn

sin

sinn - Δn

nθI

θR

VI

VR

M. D. Eastin

Consider the geometry for a wave path in the Earth’s atmosphere. Here R is the radius of the Earth, h0 is the height of the transmitter above the surface, φ0 is the initial launch angle of the beam, φh 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)

EM Wave Propagation in the AtmosphereCombining Refractive Index and Earth’s Curvature:

M. D. Eastin

Combining Refractive Index and Earth’s Curvature:

Exact Differential Equation:

• Valid for an EM wave (radar beam) propagating through a spherically stratified atmosphere:

where: n = refractive index (as defined before)R = radius of Earth (m)h = beam height above the Earth’s surface (m)s = distance along the Earth’s surface (m)

Simplifying the Equation: Three Approximations

1. Large Earth approximation

2. Small angle approximation

3. Refractive index is close to unity

01112

22

2

2

dh

dn

nhRR

hR

ds

dh

dh

dn

nhRds

hd

RhR

tands

dh1tan 1

ds

dh

1n

Atmospheric Instrumentation

EM Wave Propagation in the Atmosphere

Combining Refractive Index and Earth’s Curvature:

A Simplified Equation:

• Apply the three approximations:

• Approximate equation for the path of a beam at small angles relative to the Earth’s surface

Earth curvature term

Atmospheric refraction term

A Final Integrated Equation:

• A complete expression for beam height (h) as a function of slant range (r) from the radar:

where: φ = elevation angle of the antenna (degrees) H0 = antenna height above the surface (m)

M. D. Eastin

01112

22

2

2

dh

dn

nhRR

hR

ds

dh

dh

dn

nhRds

hd XXX1 11 / R

dh

dn

Rds

hd

12

2

Atmospheric Instrumentation

EM Wave Propagation in the Atmosphere

0

2/1222 sin2 HRkRrkRkrh eee

dhdn

Rke

1

1

M. D. EastinAtmospheric Instrumentation

EM Wave Propagation in the AtmosphereCombining Refractive Index and Earth’s Curvature:

• Because the earth curves away from the beam faster than refraction bends it earthward, a beam’s altitude increases with increasing range → standard refraction


EM Wave Propagation in the AtmosphereNon-Standard Refraction:

• Occurs when the environmental temperature profile does not follow the standard lapse rate(i.e., does not decrease with height by roughly 6-10°C/km)

• In such cases, radar beams may significantly deviate from their standard predicted pathsdepending on how environmental lapse rates deviate from the standard

Standard Regular pathke = 4/3

Sub-refraction Abnormal bending upwardske > 4/3

Super-refraction Abnormal bending downwardske < 4/3

Ducting / Trapping Severe bending downwardssuch that the beam may strikethe surfaceke << 4/3


EM Wave Propagation in the AtmosphereNon-Standard Refraction: Sub-refraction

• Beam is bent upward more that standard • Not very common• Greatest impact at low elevation angles

Situations:

• Inverted-V soundings common in deserts and on the leeside of mountains• Most common in the late afternoon and early evening

Impact on Radar Observations:

• Overshoot shallow convection• Underestimate echo tops

Φ0Φ0

hh h’h’


EM Wave Propagation in the AtmosphereNon-Standard Refraction: Super-refraction

• Beam is bent downward more that standard • Most common• Greatest impact at low elevation angles

Situations:

• Temperature inversions• Sharp decrease in moisture with height• Both can occur in relation to nocturnal inversions, warm air advection, fronts, thunderstorm outflows (gust fronts)


• Increased ground clutter• Overestimate echo tops

Φ0Φ0

hhh’h’


EM Wave Propagation in the AtmosphereNon-Standard Refraction: Ducting / Trapping

• Beam is bent downward such that it maintains a constant elevation or strikes the ground• Common• Greatest impact at low elevation angles

Situations:

• Strong temperature inversions• Strong decrease in moisture with height


• Markedly increased ground clutter• Range can increase to over 500 km

• Surface and elevated ducts can be a strategic asset to military surveillance and weapons control radars. For example if a hostile aircraft is flying within a duct, the aircraft could be detected at a long range. In contrast, if a friendly aircraft is flying above a duct, it would be difficult to detect by enemy radar, even at a close range


EM Wave Propagation in the AtmosphereNon-Standard Refraction: Ducting / Trapping

• There is a reason that WSR-88D radars have their lowest elevation angle set at 0.5 degrees• Lower elevation angles would increase the frequency of ducting or trapping

Beam paths for various elevation angles

in the presence of surface based inversions


EM Wave Propagation in the AtmosphereNon-Standard Refraction: Ducting / Trapping – An Example

Real Convection

Ground clutterTall buildings

Grain elevatorsCells phone towers


EM Wave Propagation in the AtmosphereAttenuation:

• Occurs when radar pulsesare absorbed by:

1. Oxygen2. Water vapor3. Ice crystals4. Liquid water drops **5. Wet radome **

• Becomes an increasing concern at smallerwavelengths

3-cm X-band Big concern5-cm C-band Some concern

10-cm S-band No concern

• WSR-88Ds are S-band radarsand rarely experience largeattenuation

XCS


EM Wave Propagation in the AtmosphereAttenuation: An Example

dBZ

S-band X-band


Radar ReturnsIndividual Hydrometeors: Basic Idea

• The radar transmits a high-power microwave pulse for a short pulse duration (τ)• The pulse travels at the speed of light in air (c/n) until it reaches a hydrometeor target• A small portion of its power is reflected / scatter back toward the radar by the hydrometeor• The return echo travels at the speed of light in air until it reaches the radar


Radar ReturnsIndividual Hydrometeors: Basic Idea

• Hydrometer range (ri) is determined from the time between pulse transmission and return • The return signal power (Pr) depends on hydrometer size and type• This return power is converted to a radar reflectivity → next lecture• After some time, based on the pulse repetition frequency (fr), a new pulse is transmitted


Summary

Radar Beam Pulses

• Electromagnetic (EM) waves• Basic Characteristics• Application to Radar

• EM Wave Propagation in the Atmosphere• Atmospheric Refraction• Earth Curvature• Combining Refraction and Curvature• Non-standard Refraction• Attenuation

• Radar Returns• Hydrometeor Backscatter


References

Anagnostou, M. N., E. N. Anagnostou, J. Vivkanandan, and F. L. Ogden, 2004: Comparison of raindrop size distributions from X-band and S-band polarimetric observations, Geoscience and Remote Sensing Letters, 4(4), 601-605

Atlas , D., 1990: Radar in Meteorology, American Meteorological Society, 806 pp.

Crum, T. D., R. L. Alberty, and D. W. Burgess, 1993: Recording, archiving, and using WSR-88D data. Bulletin of the American Meteorological Society, 74, 645-653.

Doviak, R. J., and D. S. Zrnic, 1993: Doppler Radar and Weather Observations, Academic Press, 320 pp.

Fabry, F., 2015: Radar Meteorology Principles and Practice, Cambridge University Press, 256 pp.

Reinhart, R. E., 2004: Radar for Meteorologists, Wiley- Blackwell Publishing, 250 pp.

Documents

Atmospheric InstrumentationM. D. Eastin Fundamentals of Radar (Beam) Pulses