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Doppler Radar

Doppler Radar. From Josh Wurman. Doppler Radar. Outline Basic Concepts Doppler Radar Components Phase Shifts and Pulse Trains Maximum Range of Radial Velocity Doppler Dilemma Doppler Spectra of Weather Targets. Basic Concepts. Doppler Shift:

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Doppler Radar

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  1. Doppler Radar From Josh Wurman M. D. Eastin

  2. Doppler Radar • Outline • Basic Concepts • Doppler Radar Components • Phase Shifts and Pulse Trains • Maximum Range of Radial Velocity • Doppler Dilemma • Doppler Spectra of Weather Targets M. D. Eastin

  3. Basic Concepts • Doppler Shift: • A frequency shift in electromagnetic waves due to the motion of scatters • toward or away from the observer • Analogy: The Doppler shift for sound waves is the change in frequency one • detects as race cars or airplanes approach and then recede from • a stationary observer • Doppler Radar: • A radar that can determine the frequency shift through measurement of the phase change • that occurs in electromagnetic waves during a series of pulses M. D. Eastin

  4. Basic Concepts • Doppler Shift from a Single Radar Pulse: • Recall the electric field of a transmitted wave: • (1) • The returned electric field at some later time: • (2) • Time it took to travel to and from the object(s): • (3) • Substituting: • (4) M. D. Eastin

  5. Basic Concepts • Doppler Shift from a Single Radar Pulse: • (4) • The received frequency can be determined by taking the time derivative of the quantity • in parentheses and dividing by 2π: • where: vr = Radial velocity of target • fd = Doppler shift • (5) • (6) M. D. Eastin

  6. Basic Concepts • Sign Conventions: • Doppler shift is negative (lower frequency, red shift) for objects • moving away from the radar (positive vr) • Doppler shift is positive (higher frequency, blue shift) for objects • moving toward the radar (negative vr) • These “color” shift conventions are often translated to radar displays: Red: Moving away from radar Blue/Green: Moving toward radar M. D. Eastin

  7. Basic Concepts • Component of Motion: • The observed radial velocity is the component of three-dimensional air motion that • is along the radar beam • In essence, the Doppler radar only measures one component of the full wind field M. D. Eastin

  8. Basic Concepts • Magnitude of a Doppler Shift: • These frequency shifts are very small: Thus Doppler radars must employ very stable • transmitters and receivers in order to detect Doppler shifts with high accuracy • (i.e. resolve vr to within 1 m/s or less) M. D. Eastin

  9. Doppler Radar Components • Block Diagram: • STALO generates local frequency (fL) • COHO generates a known phase (fC) • Mixer combines fC with fL to get • transmitted frequency (fT) • Klystron amplifies • Antenna transmits • Frequency of received echo is the • transmitted (fT) plus Doppler shift (fD) • Receiver uses STALO signal to • remove local frequency • Signal amplified • Phase detector use COHO signal to • estimate the Doppler shift from the • original phase M. D. Eastin

  10. Doppler Radar Components • Block Diagram: • Amplitude of Doppler signal: • Phase of the Doppler signal: M. D. Eastin

  11. Pulse Shifts and Pulse Trains • Why Emphasis is on Phase and not Frequency? • Typical period of a Doppler shift cycle → 1/fD → 1 millisecond • Typical pulse duration → τ → 1 microsecond • Problem: • Only a very small fraction of an entire Doppler shift cycle is contained in a single return • Method to Overcome: • Transmit a “rapid-fire” train of pulses • Each pulse will return a slightly different phase (φ1, φ2, φ3, φ4, …) • The multiple phase shifts are then used to reconstruct, or estimate, the Doppler shift cycle • (see next slide) • The Doppler frequency (i.e. radial velocity, vr) can then be estimated from the mean • difference between successive phases returned by the train of pulses • (see the slide after next) M. D. Eastin

  12. Pulse Shifts and Pulse Trains Reconstructing the Doppler shift cycle from multiple phase shifts: Dots correspond to the measured samples of phase φ from a “train” composed of 16 pulse returns M. D. Eastin

  13. Pulse Shifts and Pulse Trains • Relating Phase Shifts to Radial Velocity: • Consider a single target moving radially along the radar beam • Distance target moves in one pulse period (Tr): • (7) • Corresponding phase shift between two successive pulses is equal to the • the fraction of a wavelength traversed between two consecutive pulses: • (8) • Solving for radial velocity: • (9) • In practice, the radial velocity must be determined from the mean phase shift • from all successive pulses in the train M. D. Eastin

  14. Pulse Shifts and Pulse Trains • Problem: No Unique Solution • More than one Doppler frequency (i.e. radial velocity) will fit a finite sample of phase values • In essence a determined radial velocity is not unique • However, the possible radial velocities are multiples of a common value determined • by the radar transmission characterisiics (see next slide…) M. D. Eastin

  15. Maximum Range of Radial Velocity • What is the maximum possible radial velocity before ambiguity occurs? • We need at least two measurements per wavelength to determine phase • Thus, the phase change between successive pulses must be less than half a wavelength: • Starting with (9): • Re-arranging and applying the criteria above: • (10) • Solving for radial velocity in the extreme case [right side of (10)]: • (11) • where: F = sampling rate (or the PRF for the pulse period) M. D. Eastin

  16. Maximum Range of Radial Velocity • Nyquist velocity (vr-max): • Represents the maximum (or minimum) radial velocity a Doppler radar can measure • unambiguously • True radial velocities larger (or smaller) than this value will be “folded” back into the • unambiguous range → multiple folds can occur Unambiguous Velocity Range -10 -10 -10 -5 -5 -5 0 0 0 5 5 5 10 10 10 -30 -20 -10 Actual Radial Velocity 0 10 20 30 M. D. Eastin

  17. Maximum Range of Radial Velocity Folded Radial Velocities: Folded Velocities M. D. Eastin

  18. Maximum Range of Radial Velocity Can you find the folded velocities in this image? M. D. Eastin

  19. Doppler Dilemma • Maximizing your Nyquist Velocity : • Table shows that Doppler radars capable of measuring a large range of radial velocities • unambiguously have long wavelengths and large PRFs • Problem: • Recall that in order for radars to maximize their range, a small PRF is required Which do we choose? They are inversely related M. D. Eastin

  20. Doppler Dilemma Maximizing your Nyquist Velocity : M. D. Eastin

  21. Doppler Dilemma • How to Circumvent the Dilemma: Alternating PRFs • Radar transmits burst of pulses at alternating low and high frequencies • Lower PRF for reflectivity with higher PRF for radial velocities • This technique is regularly used by the NEXRAD radars • The result → Doppler winds are determined out to 120 km range • → Reflectivity determined out to 240 km range Measure reflectivity Measure velocity M. D. Eastin

  22. Doppler Spectra of Weather Targets • Variability in Vr: • Despite small time periods between each pulse in a train, changes in air motions and • the drop size distribution within the contributing volume will occur • As before, we need to account for this variability • Reasons for Variability: • 1. Wind shear (especially in the vertical) • 2. Turbulence • 3. Differential fall velocity (more relevant at large elevation angles) • 4. Antenna rotation • 5. Curvature of microwave wave fronts (e.g. Gaussian main lobe) M. D. Eastin

  23. Doppler Spectra of Weather Targets • Variability in Vr: Result • A series of pulses will measure a spectrum of velocities (or Doppler frequencies) M. D. Eastin

  24. Doppler Spectra of Weather Targets • Variability in Vr: First Three Moments • Zero Order • Average returned power from pulse train • Area under the curve (see previous slide) • Related to equivalent radar reflectivity factor Ze M. D. Eastin

  25. Doppler Spectra of Weather Targets • Variability in Vr: First Three Moments • First Order • Mean radial velocity • Associated with peak in the power spectrum (see previous slide) • Reflectivity weighted (i.e. large drops have greater influence on mean radial velocity) M. D. Eastin

  26. Doppler Spectra of Weather Targets • Variability in Vr: First Three Moments • Second Order • Spectral width • Associated with the variation in observed radial velocities (see previous slide) • Influenced by turbulence and wind shear M. D. Eastin

  27. Doppler Spectra of Weather Targets • Example: • Vertically pointing Doppler radar • with a large beam width (8 degs) • during a spring storm Snowflakes Freezing Level Ground Clutter Small Raindrops M. D. Eastin

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