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

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 Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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) Radar Meteorology M. D. Eastin

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) Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

Transmitted Frequency 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) Transmitted Frequency X-band C-band S-band Radial Velocity 9.37 GHz 5.62 GHz 3.0 GHz 1 m/s 62.5 Hz 37.5 Hz 20.0 Hz 10 m/s 625 Hz 375 Hz 200 Hz 50 m/s 3125 Hz 1875 Hz 1000 Hz Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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

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) Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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…) Radar Meteorology M. D. Eastin

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) Radar Meteorology M. D. Eastin

Unambiguous Velocity Range Actual Radial Velocity 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 -10 10 -5 5 Unambiguous Velocity Range -20 -30 20 30 Actual Radial Velocity Radar Meteorology M. D. Eastin

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

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

They are inversely related 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 Wavelength Radar PRF (s-1) (cm) 200 500 1000 2000 3 1.5 3.75 7.5 15.0 5 2.5 6.25 12.5 25.0 10 5.0 50.0 Which do we choose? They are inversely related Radar Meteorology M. D. Eastin

Doppler Dilemma Maximizing your Nyquist Velocity : Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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) Radar Meteorology M. D. Eastin

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

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 Radar Meteorology M. D. Eastin

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) Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin

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 Radar Meteorology M. D. Eastin