Martin Hagen Institut für Physik der Atmosphäre DLR Oberpfaffenhofen Introduction to Meteorological Radars COPS Summer School 2007

Martin Hagen, COPS Summer School, Content of Lecture History Electromagnetic waves, technique Basics of scattering Radar equation Estimation of precipitation Doppler radar and estimation of wind fields Polarimetric radar

Martin Hagen, COPS Summer School, Introduction RADARRadio Detection and Ranging Radar in meteorology Application of Radar systems (Weather Radar) in Meteorology. The weather radar is the only remote sensing system which can observe clouds and precipitation with high temporal (minutes) and spatial (kilometer) resolution.

Martin Hagen, COPS Summer School, “Radar weather” is precipitation

Martin Hagen, COPS Summer School, Application of Weather Radar  synoptic meteorology -position, extend, and life-cycle of precipitation systems like fronts, thunderstorms,... -tracking of structures  nowcasting -position of precipitation and severe weather  hydrology -measurement of rain fall -forecasting of floods  aviation meteorology -height of zero-degree level -position and intensity of turbulence -top heights of thunderstorms

Martin Hagen, COPS Summer School, Application of weather radar  climatology -distribution of precipitation -damages by storms

Martin Hagen, COPS Summer School, Application of weather radar  research -micro-physics and dynamics of clouds and precipitation -boundary meteorology -development of operational applications -assimilation of radar data into numerical models

Martin Hagen, COPS Summer School, History of Radar and Radar Meteorology Basics work by Faraday and Maxwell (=> Maxwell Equations; 1865) relating electrical and magnetic fields. First transmission of electrical signals: Heinrich Hertz (1886). First „ Radar “ for the detection of boats (Hülsmeyer, 1904). Development of radar systems during WW II in Germany, Great- Britain, USA, and Canada. 1942/43 spurious echoes where identified as precipitation ‘ s operational weather radars 1980 ‘ s networking of weather radars

Martin Hagen, COPS Summer School, Radar networks

Fundamentals of Meteorological Radars

Martin Hagen, COPS Summer School, Weather radars FZK Karlsruhe DWD Berlin DLR Ober- pfaffenhofen DWD Feldberg

Martin Hagen, COPS Summer School, Electromagnetic Waves Fundamental are the Equations compiled by Maxwell (1865) relating the electric and magnetic fields: A changing electrical field causes a changing magnetic field A changing magnetic field causes a changing electrical field Both vector fields are perpendicular to each other and perpendicular to the propagation vector E: electrical field vector H: magnetic field vector

Martin Hagen, COPS Summer School, An electromagnetic field can be described by the amplitude and frequency of the oscillation f =frequency, unit: 1/s, Hz =wave length, unit: m c = speed of light m/s in vacuum Frequency bands for radars (IEEE Standard): Frequency (GHz) Wave length (cm) Band WVKaKKuXCSL Weather radars use:X-Band: 10 GHz (3 cm) C-Band: 5.6 GHz (5.4 cm) S-Band: 3 GHz (10 cm) L-Band: 1.3 GHz (23 cm)

Martin Hagen, COPS Summer School, Techniques of a Weather Radar Basic parts of a radar: –Transmitter (magnetron, klystron), 50 – 1200 kW, 1 µ s pulse –Antenna, 1 – 10 m diameter –Receiver (analog – digital) –T/R limiter –Radar control –Signal processor –Display

Martin Hagen, COPS Summer School, Antenna Reflector antenna other forms of antennas –(phased) array (patch) antenna –slotted wave guide

Martin Hagen, COPS Summer School, Radar Beam Radar beam should be narrow for high spatial resolution, about 1° for weather radars. Power density in the main lobe. 1 st side lobe at about 2°, power about 0.1% of main lobe. Beam width (half power width;  0 or  3 dB ; one way) is the angle at which the power is half the power of the center.

Martin Hagen, COPS Summer School, Radar Display Horizontal panorama display: (PPI = plan position indicator) Measurements at different azimuth angles with a constant elevation. 1 – 6 rotations per minute. Vertical cross-section display: (RHI = range height indicator) measurements at constant azimuth but with different elevation angles.

Martin Hagen, COPS Summer School, Radar Display Several PPI ’ s at different elevations are combined to a volume scan. Products: –CAPPI (constant altitude PPI) –MaxCAPPI –Echo top –3D-Display –arbitrary cross-sections

Martin Hagen, COPS Summer School, Echo TopMaxCAPPI

Martin Hagen, COPS Summer School, Beam Propagation in the Atmosphere In the standard atmosphere the radar beam is bend towards the ground due to the vertical gradient of the index of refraction. Height of the radar beam Hheight of beam rrange R’apparent earth radius 8483 km  elevation H 0 height of radar tower

Martin Hagen, COPS Summer School, Radar Equation for Point Targets Relation between transmitted power and received signal The transmitter power is emitted isentropic, at a point a power density S is observed: Using a transmit antenna with the gain g, a point target with the area Aσ will receive the power:

Martin Hagen, COPS Summer School, Radar Equation for Point Targets At the target an oscillation will induced. The target is transmitting isentropic without absorption of energy. The radar with an antenna area Ae receives the power: Using A e = g / 4  gives: or with σ the backscatter cross-section

Martin Hagen, COPS Summer School, Radar Equation for Volume Targets Meteorological targets like precipitation fill the radar beam (normally). Backscatter cross sections add therefore: The volume ish depth of volume (pulse length)  0 and θ 0 beam width Radar equation for volume targets (  0 = θ 0 ) pulse volume beam width

Martin Hagen, COPS Summer School, Backscatter Cross-Section The backscatter cross-section is an apparent cross-section which scatters back the incoming wave. Can be solved analytically for spheres (G. Mie, 1908) or ellipsoids (R. Gans, 1912). Spheres large with respect to wave length D/λ > 10 “optical range” with geometric backscatter cross-section, Spheres small with respect to the wave length D/λ < 1/10 “Rayleigh scatter” C-Band: D < 5 mm

Martin Hagen, COPS Summer School, Mie Scatter In between: Mie-scatter Mie- or resonance region Resonances at the sphere surface (perimeter = πD). Mie and Rayleigh scatter is only valid for spherical particles like raindrops, graupel, hail,... But not for ice particles like needles or snow aggregates

Martin Hagen, COPS Summer School, Radar Reflectivity: since most meteorological targets are within the Rayleigh region Temperatureλ = 10 cmλ = 3 cm |K| 2 20°C for water 10°C °C |K| 2 for ice, independent ρ = 1 g/cm 3 Radar Reflectivity

Martin Hagen, COPS Summer School, Radar Reflectivity Factor Radar reflectivity factor Radar reflectivity (  )radar reflectivity factor (z) z is independent of wave length and refractive index When radar people talk about “reflectivity” they mean normally “radar reflectivity factor”

Martin Hagen, COPS Summer School, Radar Constant P r is measured, of interest is the property “backscatter cross-section” of the meteorological target, which can be expressed in z assuming Rayleigh scatter and water particles c: radar constant

Martin Hagen, COPS Summer School, Radar Reflectivity Factor Radar reflectivity factor can have a huge range thunderstorm: mm 6 m -3 cumulus cloud: 0.01 mm 6 m -3 Electrical engineers use logarithmic ratios to work with large numbers: v = (p 1 /p 2 )V = 10 log 10 (p 1 /p 2 ) unit dB ("dezi Bel") Radar meteorologists use Radar reflectivity factor relative to 1 mm 6 m -3 = 70 dBZ = -20 dBZ

Martin Hagen, COPS Summer School, If received signal power is duplicated, reflectivity is 3 dB higher (not dBZ !!) Small numbers changes in reflectivity can result in large differences of rain fall rate: if 50 dBZ correspond to 50 mm/h, then 53 dBZ can correspond to 100 mm/h from R. Rinehart: Radar for Meteorologists

Rain Measurements by Radar

Martin Hagen, COPS Summer School, Radar Observations of Precipitation stratiform precipitationrain showers, thunderstorms PPI: 120 km range

Martin Hagen, COPS Summer School, Rain Drop Size Distribution Rain drop size distribution: number of raindrops per volume and diameter interval N(D) mm -1 m -3 can be variable from event to event simple parameterizations are used to represent the distribution Diameter (mm) Drop size distributions (10 min average)

Martin Hagen, COPS Summer School, Rain Drop Size Distribution A common rain drop size distribution (RDSD) is the Gamma RDSD N 0 concentration at D = 0 Λ slope of RDSD D 0 median diameter μ Dispersion Termed as an exponential RDSD with µ = 0 “Marshall – Palmer distribution” with N 0 = 8000 mm- 1 m -3 Λ = 4.1 R mm -1

Martin Hagen, COPS Summer School, Rain Drop Size Distribution Rain fall rate as a function of N(D) Reflectivity factor as function of N(D) Same rain fall rate but different reflectivity since z  D 6 but R  D 3.7

Martin Hagen, COPS Summer School, Rain Fall Rate and Radar Reflectivity Factor Common used in radar meteorology are empirical relations between reflectivity factor and rain rate. z in mm -6 m -3 R in mm/h Coefficients a and b are estimated from measurements: radar and rain gauge RDSD measurements with disdrometers

Martin Hagen, COPS Summer School, Common z-R Relations A summary in Battan (1973) gives 69 different z-R relations for different climates and precipitation types (stratiform/ convective). Marshall-Palmer relation z = 200 R 1.6 Relations for Southern Germany warm air advection z = 104 R 1.34 cold air advection z = 249 R 1.42 weak press. gradient z = 227 R 1.37 thunderstorm z = 311 R 1.38 Operational z-R relations Germanyz = 256 R 1.42 Switzerland z = 316 R 1.5 Austriaz = 200 R 1.6

Martin Hagen, COPS Summer School, Coefficient b can be assumed to be 1.5, high temporal variations of a Measurements in Locarno during MAP – SOP (1999)

Martin Hagen, COPS Summer School, Rain Observations Accumulated precipitation from radar measurements Is this realistic ??

Martin Hagen, COPS Summer School, Rain Observation by Radar Weather radars allow for precipitation observations with high spatial and temporal resolution. But, rain observation by radar is affected by different processes.

Martin Hagen, COPS Summer School, Beam Blockage and Beam Filling If only a part of the radar beam is filled by precipitation reflectivity is lower since the scattering volume is smaller than the measurement volume. - at the edges of precipitation - behind ground obstacles

Martin Hagen, COPS Summer School, Ground Clutter The radar pulse is also reflected by ground targets within the radar beam or its side lobes. Reflectivity of ground clutter can be very high. Filtering by - clutter masks - signal characteristics high variance of precipitation low variance of clutter Will fail if clutter is moving !

Martin Hagen, COPS Summer School, Vertical Profile and Melting Layer Stratiform rain is normally formed from melting snow flakes. Convective rain forms from frozen drops or graupel (hail). The melting layer is about 500 m thick and located below the 0° C isotherm. Due to the enhanced reflectivity the melting layer is also called “bright band”. Ice particles grow to snow aggregates melting snow has higher reflect. melting particles collapse to drops

Martin Hagen, COPS Summer School, Vertical Profile of Reflectivity (VPR) Only at short ranges the weather radar can observe the precipitation close to ground. At far distances only the upper levels of precipitation can be observed. Measurements in snow will underestimate the precipitation at the surface. Measurements in the melting layer will overestimate the precipitation at the surface.

Martin Hagen, COPS Summer School, Vertical Profile of Reflectivity

Martin Hagen, COPS Summer School, Operational Rain Products Operational rain products Automatic calibration with signal generator or using the sun as known noise source Usage of sophisticated ground clutter filter Correction of VPR by measured or climatological reflectivity profiles Automatic adaptation of z-R relation by gauge or disdrometer measurements at surface  swiss daily precipitation amount looks reasonable

Doppler Velocity

Martin Hagen, COPS Summer School, Doppler Velocity The Doppler effect (Christian Doppler, ) describes the observed change in frequency if there is a relative motion between: - signal source and(propagation speed of signal with speed c) - observer(relative motion with speed v) example sound: v =  20 m/s, f 0 = 5 kHz, c = 300 m/s => f = 5  kHz example radar: v =  20 m/s, f 0 = 5 GHz, c = 3  10 8 m/s => f = 5  GHz

Martin Hagen, COPS Summer School, Doppler Velocity Motion of an object with speed v by a distance Δr during the time Δt (between two measurements) results in a change of the phase by Δ . angular velocity Doppler frequency This method is termed as “pulse-pair processing”.

Martin Hagen, COPS Summer School, Doppler Velocity Other way to get the Doppler frequency: Transformation of the time series of phase differences (  -  0 ) with a Fourier transform into frequency space. The fundamental oscillation is the Doppler frequency.

Martin Hagen, COPS Summer School, Doppler Velocity The Doppler velocity is the mean – weighted by reflectivity – velocity of all particles in the measurement volume. Only a motion along the radar beam (“radial”) can cause a phase change. v r = v  cos(  ) measurement volume beam width

Martin Hagen, COPS Summer School, Maximum Doppler Velocity The maximum unambiguous Doppler velocity is given by the sampling interval  the pulse repetition frequency (PRF). The observed phase angles are not ambiguous. φ = -90°equalφ = 270° v = -½ v max equalv = +1½ v max

Martin Hagen, COPS Summer School, Maximum Doppler Velocity Maximum Doppler velocity v max : unambiguous velocity, Nyquist velocity, aliasing velocity Only in the Nyquist interval it is possible to estimate the Doppler velocity without ambiguity. v = v r + 2 n v a n = , -2, -1, 0, 1, 2,  n aliasing factor. 0 v a Doppler velocity -v a -3 v a -2 v a -v a 0v a 2 v a 3 v a Target velocity -2 v a -3 v a 2 v a

Martin Hagen, COPS Summer School, Maximum Range The PRF can not increased arbitrarily since first the pulse has to return to the radar before the next one is emitted. maximum range “Doppler dilemma” r maximum range

Martin Hagen, COPS Summer School, Maximum Doppler Velocity Automatic unfolding techniques - dual / triple PRF to increase v max - image processing algorithms to remove foldings - pulse coding to increase r max

Martin Hagen, COPS Summer School, Interpretation of Doppler Velocity Constant Wind Field Zero velocity is perpendicular to wind flow, maximum Doppler velocity indicated direction of flow and speed. towardsaway Velocity negative Doppler velocity: towards radar positive Doppler velocity: away from radar

Martin Hagen, COPS Summer School, Interpretation of Doppler Velocity Rotation and Convergence Area A: Rotation: Zero speed (corrected for advection) parallel to radar beam. Area B: Convergence: Zero speed (corrected for advection) perpendicular to radar beam.

Martin Hagen, COPS Summer School, Cold Front

Martin Hagen, COPS Summer School, Squall Line

Martin Hagen, COPS Summer School, Velocity Azimuth Display (VAD)

Martin Hagen, COPS Summer School, Velocity Azimuth Display (VAD)

Martin Hagen, COPS Summer School,

Martin Hagen, COPS Summer School, Wind Profiles IMK Karlsruhe

Martin Hagen, COPS Summer School, Uniform Wind Technique Data from a segment of a circle, averaged in an area of about 20° x 20 km Size of area: -  v r /  has to be estimated accurate - wind field should be constant in area

Martin Hagen, COPS Summer School, Operational Uniform Wind Technique

Polarimetric Weather Radar

Martin Hagen, COPS Summer School, Polarimetric Weather Radar Polarimetric Products: reflectivity horizontal and vertical depolarization ratio differential reflectivity propagation phase correlation coefficient Rain Graupel Hail linear circular elliptic polarizations

Martin Hagen, COPS Summer School, Rain drops falling with their terminal velocity are oblate due to the air flow from below. Observations in a vertical wind tunnel (Univ. Mainz): Shape of Falling Rain Drops

Martin Hagen, COPS Summer School, Rain Drop Shapes Various studies in wind tunnels or observations in free atmosphere

Martin Hagen, COPS Summer School, Differential Reflectivity (Z DR ) Indication for oblate particles falling horizontally orientated Reflectivity Z HH Differential Reflectivity ZDR

Martin Hagen, COPS Summer School, Rain Rate Estimation with Polarimetric Radar Problem with classic z-R relation due to RDSD. Different RDSD can give different rain rate at same reflectivity. Differential reflectivity indicates contribution of large (oblate) rain drops. diameter (mm) diameter (mm)

Martin Hagen, COPS Summer School, Estimation of Rain Fall Rate Additional parameter ZDR gives additional information. z – R relation versus z – ZDR – R relation However, high precision for data is required.

Martin Hagen, COPS Summer School, Linear Depolarization Ratio (LDR) Indication for oblate particles falling irregular or canted

Martin Hagen, COPS Summer School, Classification of Hydrometeors Different ranges of ZDR and LDR can be used to identify hydrometeors. Additional information are reflectivity and the height of the 0° isotherm (Höller et al., 1994). Boundaries are for C-band. A complete classification requires correction of attenuation and multiple- scattering.

Martin Hagen, COPS Summer School, Hydrometeor Classification

Martin Hagen, COPS Summer School, Classification using Fuzzi Logic (Vivekanandan, 1999) Additional parameter correlation coefficient ρ HV (0) and spezific differential phase K DP. Gives more detailed classification. “Fuzzi Logic“ is used to find the most probable hydrometeor class.

Martin Hagen, COPS Summer School, Reflectivity Differential Reflectivity Classification

Martin Hagen, COPS Summer School, Verification of Hydrometeor Classification

Martin Hagen, COPS Summer School, Thunderstorm development in the Alpine Foreland

Martin Hagen, COPS Summer School, F0-Microburst 20. June 2002 Rain Graupel Hail 1542 UTC PPI Z 1542 UTC PPI V 1542 UTC PPI Hyd

Martin Hagen, COPS Summer School, Summary Only a small part of radar meteorology has been covered. Weather radar is a powerful tool to understand microphysics and dynamics in the atmosphere high temporal and spatial resolution Radar data are used for meteorological applications like nowcasting and for hydrological purpose. Research offers new tools to improve data quality and opens new technology for advanced systems.

Martin Hagen, COPS Summer School,

Martin Hagen, COPS Summer School, announcement Open position for PhD thesis in radar meteorology “polarimetric rain fall rate estimation” Institut für Physik der Atmosphäre DLR Oberpfaffenhofen Weßling, Germany 3 years starting this year contact: