Radar Calibration Motivation Radar equation and measurement Calibration

Radar Calibration • Motivation • Radar equation and measurement • Calibration using a metallic sphere • Calibration using the Sun • Calibration using a standard gain horn • Calibration using polarimetric diversity measurements of rain • Calibration of differential reflectivity (Zdr) Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 1

Impact of Radar Calibration Bias on Rain Rate Algorithms • Biases in radar calibration can have significant impact on fields derived from these measurements. • An example of this is the rain rate. • The algorithm that is used by the National Weather Service (NWS) WSR-88 D is: where R is the rain rate in mm/hr and Z is the reflectivity at horizontal polarization state given in mm 6/m 3 • Example: if there was a calibration bias of – 2 d. B in radar system and the measured reflectivity was 40 d. B. The rain rate would be calculated as 12. 2 mm/hr when the actual rain rate would be 16. 95 mm/hr • In the case of severe weather, radar measurement accuracy is critical in providing accurate warning to the public. Lecture notes on radar calibration Percentage of error in R due to bias errors in Z V. Chandrasekar, 8 Nov 2005 2

Impact of Radar Calibration Bias on Rain Rate Algorithms • Rain rate can also be estimated using polarimetric radar measurements • A rain rate algorithm using polarimetric measurements of differential reflectivity (Zdr) and horizontal reflectivity (Zh) is given as where R is the rain rate in mm/hr and Zh is the reflectivity at linear horizontal polarization state given in mm 6/m 3 and Zdr is differential reflectivity Lecture notes on radar calibration Contours of fraction of error in R due to bias errors in Z and Zdr V. Chandrasekar, 8 Nov 2005 3

• A radar is a complex system consisting of many components such as transmitters, receivers, amplifiers, filters, microwave components, etc. • A radar system has to many components to be able to characterize every component. • For this reason it is conventional to evaluate and characterize the system as a whole. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 4

Radar equation for distributed targets • Assumed a rectangular pulse is transmitted, the received power ( Pr) at range r 0 can be written as: Transmitter Receiver • Note that this received power is measured at shifted reference plane for convenience of radar calibration Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 5

Radar equation for distributed targets • The mean power at the receiver can be related to the equivalent reflectivity factor and the radial distance by a radar constant term ( C) • This radar constant is defined as • The radar constant (C) is important in converting the received power measurements to the correct meteorological measurements • Radar calibration involves the evaluation of the parameters in the radar constant Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 6

Filter Loss (lr) • If the transmit waveform is a rectangular pulse of width T 0 then the ratio of the mean power at the output of the receiver to the mean power at the input of the receiver chain can be written as where Wn(r) is the normalized range-weighting function and Gr is the gain of the receiver chain • The finite bandwidth receiver loss, lr, can be calculated by comparing Po to the output power of an infinite bandwidth receiver with the same receiver gain as where lr 1 due to the loss of power associated with the finite bandwidth Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 7

Receiver Gain (Gr) • Important quantity of the weather radar equation • The weather radar equation implicitly assumes a reference plane at the antenna feed horn port for the receiver gain, antenna gain, and transmit power • For calibration purposes the reference plane is generally shifted closer to the input of the receiver Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 8

Receiver Gain (Gr) • Using the shifted reference plane, Gr will be the measured power gain from the shifted reference plane to the receiver output Transmitter Receiver Simplified block diagram of the radar showing the shifted reference plane. • Gr is measured by injecting a continuous wave (CW) signal of known amplitude into the waveguide at the reference plane using a highly stable, standard signal generator and recording the digital output of the receiver (I 2+Q 2) Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 9

Receiver Gain (Gr) • Receiver calibration is done by injecting signal (CW) of known power into directional coupler and output power of receiver are recorded • Receiver gain consists of gains and losses from each component in the receiver chain • By gradually decreasing the power level of the inserted CW signal and recording the digital output of the signal processor, the measurement quality of the receiver’s linearity can be measured and the gain estimated • The uncertainty associated with measurements used to estimate Gr can be evaluated by taking the standard deviation of the measurements to the linear fit • For the CSU-CHILL radar the uncertainty was estimated to be between 0. 14 and 0. 17 d. B Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 10

Receiver Gain (Gr) Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 11

Transmit Power (Pt ) • The transmit power, Pt, is another key quantity of the weather radar equation. • Transmit signal of a weather radar is generally a very high power short pulse on the order of 1 - sec in duration with a peak power around 500 -1000 k. W. • Power level can not be measured directly due to the magnitude of the signal. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 12

Transmit Power (Pt ) Directional Coupler Circulator Transmitter Antenna Receiver Test Set Attenuator Power Sensor Receiver Calibration Path Transmit Power Measurement Path • A directional coupler followed by precision attenuators are usually employed to bring down the transmit signal to a level measurable by a standard power meter • Transmit signal is measured at the same reference plane where the receiver calibration is performed Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 13

Calibration Using a Metallic Sphere • A standard point target makes a good calibration tool because the radar cross section (RCS) is known • A metallic sphere makes a good point target because its RCS can be precisely calculated • A metallic sphere has the same RCS from any viewing angle Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 14

Sphere Calibration Procedure • The radar equation for a metal sphere in the bore-sight of the antenna and in the far-field can be written as where the subscript ‘ms’ represents the metal sphere and lwg is the waveguide loss • Rearranging the terms of the radar equation, gives the antenna gain as where G’ is the antenna gain with waveguide loss factored in Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 15

Sphere Calibration for the CSU-CHILL radar Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 16

Return Signal and IF Filter • Several sweeps were then made during the calibration to ensure that the sphere was located in the boresight of the antenna beam • The rectangular shape with 6 d. B 3 MHz bandwidth IF filter was applied during the sphere calibration. • By using this filter, there is no finite bandwidth loss factor to be considered in received power equation Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 17

Finite Bandwidth Filter Loss (lr) for CSU-CHILL Sphere Calibration • Same filter is used for sphere calibration and precipitation targets Using a rectangular pulse and 1 -MHz filter the filter loss, lr, was, calculated to be 1. 623 d. B. Lecture notes on radar calibration Using the measured transmit pulse and 1 -MHz filter the filter loss, lr, was calculated to be 1. 676 d. B. V. Chandrasekar, 8 Nov 2005 18

Transmit Waveform Measurement and Comparison • The echo from sphere was over sampled at 333 nano-seconds to estimate the transmit waveform • Comparisons of the directly measured transmit pulse and the estimated pulse waveform from the sphere return show good agreement Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 19

Uncertainty in Calibration using a Metallic Sphere Source Error (d. B) Pt measurement 0. 02 Pref measurement 0. 16 ms 0. 02 Root Sum Square (RSS) Error 0. 16 ; a = 15. 25 cm. , a is radius of the sphere • 12 -inch sphere is used, so size parameter is 8. 7 lying in Mie region Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 20

Calibration Using the Sun • The Sun is a useful calibration tool because it can be observed from any point on Earth on a regular basis • The Sun can be treated as a standard noise source whose position at any time WRT a given location on Earth can be precisely calculated • The solar flux incident on the surface of the Earth is generally non-polarized and varies between 100 to 300 solar flux units (SFUs) • A SFU is defined to be 1 x 10 -22 Watts/Hertz/meter 2. • Measurements can be obtained from the Solar Environment Center (SEC) , National Oceanic and Atmospheric Administration (NOAA) in Boulder CO ( http: //www. sec. noaa. gov/) • At 10 cm wavelength the sun is approximately 7% larger than the optical sun Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 21

Scan over the sun Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 22

Antenna gain measurements • The noise source power received by receiver of bandwidth B written as B can be estimated from Power of the Sun Temperature of the Sun Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 23

Antenna Gain Measurement (Cont. ) Effective antenna aperture ; S = Solar flux density Antenna Gain Let Therefore, Antenna gain in log scale is • Note that this antenna gain is the calculated gain before corrections Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 24

Solar Calibration for CSU-CHILL Radar • Power measurements shifted to reference plane Measurements Quantity Value (d. Bm) Psun Ps + P N -103. 10 Phot Ph -101. 47 Pcold Pc -112. 42 Pblue PN -113. 59 ( only H-channel) • Receiver gain H channel = 129. 26 d. B V channel = 129. 42 d. B Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 25

Solar Calibration for CSU-CHILL Radar (Cont. ) • • Solar flux density obtained from the NOAA was The antenna gain can then be calculated as: 117 = SFUs. 38. 61 d. B Gain Corrections Value(d. B) Polarization +3. 0 Beamfilling Distance adjustment +0. 4 +0. 15 = 3. 55 • Polarization correction : Unpolarized signal to single polarized receive antenna state Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 26

Solar Calibration for CSU-CHILL Radar (Cont. ) • The corrected antenna gain can then be given as = 38. 61 + 3. 55 = 42. 16 d. B (H-channel) • Note that the antenna gain for the CSU-CHILL radar based on the solar calibration was includes waveguide and radome losses. • The same procedures give the gain = 42. 23 d. B in V channel. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 27

Solar Calibration for CSU-CHILL Radar (Cont. ) • Antenna Gain estimated weekly using solar calibration in H and V channels from May to September, 2003 Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 28

Calibration Using a Standard Gain Horn • A standard gain horn can be used to calibrate the antenna gain of a radar using the gain-transfer method • Pyramidal standard gain horn – linear polarization in the horizontal and vertical polarization states – highly directive antenna patterns – less susceptible to effects from the surroundings Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 29

Criteria for Positioning Standard Gain Horn 1. Standard gain horn should be placed at far-field (R 2 D 2/ ). For CSUCHILL radar, the set up is about 1200 meters 2. Standard gain horn should be placed in elevated platform to reduce ground clutter. 3. Standard gain horn should be set up in a relatively clear area to avoid multi-path and beam blocking. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 30

Standard Gain Horn Calibration Procedure • Two sets of measurements were made: radar transmitting and standard antenna receiving, and standard antenna transmitting and radar receiving. • These measurements are related by the Friis transmission formula: • The gain of the radar antenna can be calculated by rearranging this equation as: Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 31

Calibration Using Polarimetric Diversity Measurements in Rain • In rainfall polarimetric diversity measurements of horizontal reflectivity (Zh), differential reflectivity (Zdr), and specific differential propagation phase (Kdp) lie in a 3 -dimensional constrained space (Chandrasekar et al. , 1990), (Scarchilli et al. , 1996). • This is to say that there is a self-consistency of polarimetric diversity measurements of rainfall. • Using these self-consistency in rain it is possible to calibrate a radar (Gorgucci et al. , 1999). • Kdp and Zdr are unaffected by absolute calibration errors and can be used to calibrate Zh. • To avoid calibration uncertainty from Zdr measurement errors, Zh-Kdp relation is used for calibration. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 32

Variability of Polarimetric Measurements on DSD Parameter • Simulations were performed to see the effect different rain medium characteristics, DSD parameters, have on polarimetric measurements • Polarimetric radar are measurements are sensitive to the mean shape/size relationship of raindrops, described by slope • Different values were used in the simulation using the Pruppacher and Beard (1970) axis ratio to diameter relation where D is the volume-equivalent diameter, is the slope-size relationship, b and a are the semi-minor and semi-major axis lengths, respectively Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 33

Variability of Polarimetric Measurements on DSD Parameter • Simulations were performed using a Gaussian distribution for the gamma DSD model parameters log(Nw) and D 0, with a uniform distribution for . • A Gaussian distribution was used to more closely simulate a practical DSD distribution based on disdrometer measurements. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 34

Variability of Polarimetric Measurements on DSD Parameter • Two sets of polarimetric measurements were simulated using this DSD parameter distribution and values of 0. 05 and 0. 06. • Power law curves were fitted to the simulated polarimetric measurements as well as disdrometer measurements. • The results of these simulations show a sensitivity to the choice of assumed. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 35

Dual-Polarization Calibration on the CSU-CHILL Radar • Scatter plots of Kdp vs Zh were made from the simulated variables along with Derived Kdp vs Zh • Power law curves were fitted to the scatter points • A calibration bias was estimated by adding a bias to Zh from measurements to match the Derived Kdp to the simulated Kdp curves (Bias boundary =0. 05 and =0. 06) Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 36

Uncertainty in Dual-Polarization Calibration • The dominant factor in the uncertainty of dual-polarization calibration is the characteristics of the rain medium described by the DSD parameters. • The choice of greatly affects the results of the calibration. • Several in-situ and radar observations suggest that values of 0. 05 and 0. 06 are reasonable boundary values. • Using these boundary values a 1 d. B of uncertainty is introduced based on the shift in Z required to move the Kdp curves from one boundary to the other. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 37

Calibration of Differential Reflectivity (Zdr) • Differential reflectivity (Zdr) is the ratio of received power from a horizontally polarized transmit signal to the received power of a vertically polarized signal • Zdr gives information about particle shape and orientation Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 38

Zdr calibration using vertical pointing data • Zdr can be calibrated by observing rain at vertical incidence because Zdr is intrinsically zero for raindrops at vertical incidence. • Necessary to average Zdr measurements taken in rain over 360 in azimuth to avoid the direction dependent bias associated with ground clutter and in the far-field of the antenna. • If Zdr measured by this method is not zero, that value is accounted for the bias of the system. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 39

Zdr calibration using vertical pointing data Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 40

Alternative method of calibrating Zdr • In the absence of rain directly above the radar or if vertical scanning measurements can’t be made it is still possible to calibrate Zdr DRIZZLE REGIONS • In light drizzle raindrops can be assumed to be spherical ( Zdr 0 d. B) • Observations of light drizzle that deviate from zero can be considered a Zdr bias • Sometimes difficult to identify drizzle (low SNR) • Need in-situ verification that the region is actually drizzle (low reflectivity not always drizzle) Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 41

Alternative method of calibrating Zdr ICE REGIONS • Zdr measurements can be made of low density ice particles in the upper regions of storms • Ice regions approximately satisfy polarization plane isotropy and is independent of the antenna’s elevation angle • If ice region satisfies polarization plane isotropy or when the density of hydrometeors is low then Zdr will be near zero • However, small ice crystals can be oriented by in-cloud electric fields and polarization plane isotropy will not hold (Bringi and Chandrasekar, 2001) Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 42

Zdr Calibration for CSU-CHILL Radar • For identified ice regions, scatter plots of Zh vs Zdr were created and a best fit line was fitted to the scatter points to determine a Zdr bias • For vertical looking measurements, Zdr was averaged over 360° in azimuth for each range gate and a line fitted to the plot to determine a bias Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 43

Summary for Calibration • Five calibration methods were described • Conventional calibration methods – Calibration using a metallic sphere – standard gain horn, and – the Sun • Calibration monitoring techniques – Use of test signal and cross polar return power measurement and vertical pointing data to calibrate Zdr – Use of self-consistency of polarimetric measurements in rain – Vertical looking calibrations for Zdr. Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 44

Calibration of Zdr • Agreement gives confidence to using test signal and cross polar measurement monitor the calibration of Zdr. for absence of vertical pointing data. • From the results of the calibrations performed at the CSUCHILL radars, it can be seen that there are several advantages and disadvantages of each calibration method • By conducting calibrations using different methods the level of confidence in the results increases and it may be possible to find problems in certain calibration procedures • Calibration of the radar should be performed regularly • It is recommend that solar calibrations be performed at least three times a month to monitor the calibration of the radar • It is also recommended that sphere calibrations and standard gain horn calibrations be performed at least twice a year Lecture notes on radar calibration V. Chandrasekar, 8 Nov 2005 45