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

2. Atmospheric InstrumentationM. D. Eastin 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

3. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Basic Concepts: Electromagnetic waves are electric and magnetic pulses that propagate away from their source at velocities close to the speed of light (c = 3 × 10 8 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

4. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Basic Concepts: Electromagnetic waves are electric and magnetic pulses that propagate away from their source at velocities close to the speed of light (c = 3 × 10 8 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) 2. Refraction

5. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Basic Concepts: Electromagnetic waves are electric and magnetic pulses that propagate away from their source at velocities close to the speed of light (c = 3 × 10 8 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) 3. Scattering

6. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Basic Concepts: Electromagnetic waves are electric and magnetic pulses that propagate away from their source at velocities close to the speed of light (c = 3 × 10 8 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) 4. Absorption Radar Reflectivity Radar Absorption of radar beam by intense rainfall

7. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Applied 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

8. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Applied to Radar: 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) exhibit limited transparency to a narrow range of EM wavelengths 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

9. Atmospheric InstrumentationM. D. Eastin Electromagnetic (EM) Waves Applied to Radar: 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) exhibit limited transparency to a narrow range of EM wavelengths 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”

10. Atmospheric InstrumentationM. D. Eastin EM Wave Propagation in the Atmosphere Basic 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

11. Atmospheric InstrumentationM. D. Eastin EM Wave Propagation in the Atmosphere Basic Concepts: Refraction Speed of light in a vacuum (c): Speed of light in a medium (v): Refractive Index (n): At sea level: n = 1.0003 In space: n = 1.0000 Slightly slower where: ε = permittivity (ability to absorb electrical energy) ε 0 = 8.850 x 10 -12 (in a vacuum) ε 1 = 8.876 x 10 -12 (at sea level pressure) μ = permeability (ability to absorb magnetic energy) μ 0 = 1.260 x 10 -6 (in a vacuum) μ 1 = 1.260 x 10 -6 (at sea level pressure)

12. Atmospheric InstrumentationM. D. Eastin EM Wave Propagation in the Atmosphere Refractive 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) C 1 =7.76 × 10 -5 K mb -1 T =temperature (K) C 2 =5.60 × 10 -6 K mb -1 e =water vapor pressure (mb) C 3 =0.375 K 2 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 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.

13. Atmospheric InstrumentationM. D. Eastin EM Wave Propagation in the Atmosphere Refractive 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 atmospheric layer to the next (i.e., as atmospheric density changes) where: θ I = angle of incidence (degrees) θ R = angle of refraction (degrees) V I = EM wave speed in first medium [ n ] V R = 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 n - Δn n θIθI θRθR VIVI VRVR

14. M. D. Eastin Consider the geometry for a wave path in the Earth’s atmosphere. Here R is the radius of the Earth, h 0 is the height of the transmitter above the surface, φ 0 is the initial launch angle of the beam, φ h 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 Atmosphere Combining Refractive Index and Earth’s Curvature:

15. 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 Atmospheric Instrumentation EM Wave Propagation in the Atmosphere

16. 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) H 0 =antenna height above the surface (m) M. D. Eastin XXX 111 / R Atmospheric Instrumentation EM Wave Propagation in the Atmosphere

17. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Combining 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

18. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Non-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 paths depending on how environmental lapse rates deviate from the standard StandardRegular path k e = 4/3 Sub-refractionAbnormal bending upwards k e < 4/3 Super-refraction Abnormal bending downwards k e > 4/3 Ducting / TrappingSevere bending downwards such that the beam may strike the surface k e >> 4/3

19. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Non-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 Φ0Φ0 h h h’

20. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Non-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) Impact on Radar Observations: Increased ground clutter Overestimate echo tops Φ0Φ0 Φ0Φ0 h h h’

21. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Non-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 Impact on Radar Observations: 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

22. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Non-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

23. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Non-Standard Refraction: Ducting / Trapping – An Example Real Convection Ground clutter Tall buildings Grain elevators Cells phone towers

24. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Attenuation: Occurs when radar pulses are absorbed by: 1. Oxygen 2. Water vapor 3. Ice crystals 4. Liquid water drops ** 5. Wet radome ** Becomes an increasing concern at smaller wavelengths 3-cm X-bandBig concern 5-cm C-bandSome concern 10-cm S-bandNo concern WSR-88Ds are S-band radars and rarely experience large attenuation XCS

25. M. D. EastinAtmospheric Instrumentation EM Wave Propagation in the Atmosphere Attenuation: An Example dBZ S-bandX-band

26. M. D. EastinAtmospheric Instrumentation Radar Returns Individual 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

27. M. D. EastinAtmospheric Instrumentation Radar Returns Individual Hydrometeors: Basic Idea Hydrometer range (r i ) is determined from the time between pulse transmission and return The return signal power (P r ) 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 (f r ), a new pulse is transmitted

28. Atmospheric InstrumentationM. D. Eastin 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

29. Atmospheric InstrumentationM. D. Eastin 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.