1. Polarimetric Weather Radar
Gordon Ariho

2. Outline Introduction Weather Radar Polarimetric Weather Radar
Scope
Weather Radar
Polarimetric Weather Radar
Operation
Case Study
POLDIRAD
Analysis: Benefits of Polarimetric Weather Radar
Rain Rate estimates
Errors
Conclusion

3. Introduction
Weather is a key aspect of most (if not all) human activities and therefore having good weather estimations can help in managing and planning several activities like games, trips, flights, evacuations (in case of severe weather) etc.
It should be noted that weather radars don’t forecast weather! However, when there is a cloud or precipitation fall, radars can be used to estimate precipitation rates.

4. Scope
The scope of this presentation is to expound on polarimetric weather radar and how it enhances weather estimations.
Polarimetric weather radar switches polarization of the waveform for example between horizontal and vertical polarization, either between individual pulses or groups of pulses.
This type of radar is can be useful in classifying the atmospheric constituents (rate, size, shape, type (rain, snow etc.)).

5. Weather Radar Weather radars help the meteorological offices to:
Locate precipitation
Estimate precipitation:
rain, snow, hail etc.)
Estimate precipitation characteristics :
shape, speed, size, etc.

6. Weather Radar
Weather radars have the same basic principle of operation like Primary Surveillance Radars (PSR) but:
Weather targets are usually much larger and fluid in nature than PSR targets
The velocities encountered with weather constituents are usually slower than in the PSR case
Atmospheric constituents are considered to be clutter within a PSR system whereas it’s the primary concern of weather radars.
In either application, the terrain clutter must be filtered out.

7. Weather Radar
Idealized H and V waves shown propagating along the beam and two quasi cylindrical resolution volumes, and time series traces I and Q of the echoes from the two resolution volumes for the H or V wave. Each trace is a sequence of echo samples (dots) spaced by mTs. Also shown are the Doppler spectra of echo samples from the two volumes for one polarization
Source: R J Doviak, R D Palmer,

8. Weather Radar
Weather radars are usually pulsed radars and the returned signal is processed to determine an estimate of the precipitation rate.
With Doppler capability, the frequency shift due to the motion of atmospheric constituents (cloud and precipitation) can be used to determine wind speed.
Frequency selection for weather radars must take into account the interaction with cloud and precipitation particles at that frequency. Lower frequencies are generally not suited for weather radar applications because they just ‘see’ through the clouds..
Thus 10 cm (S-band) radar is preferred but is more expensive than a 5 cm C-band system. 3 cm X-band radar is used only for short-range units, and 1 cm Ka-band weather radar is used only for research on small-particle phenomena such as drizzle and fog.

9. Weather Radar
S band radars operate on a wavelength of 8-15 cm and a frequency of 2-4 GHz and are not easily attenuated. This makes them useful for near and far range weather observation. The National Weather Service (NWS) uses S band radars on a wavelength of just over 10 cm. The drawback to this band of radar is that it requires a large antenna dish (can exceed 25 feet in size ) and a large motor to power it.
C band radars operate on a wavelength of 4-8 cm and a frequency of 4-8 GHz and the dish size does not need to be very large. The signal is more easily attenuated, so this type of radar is best used for short range weather observation. The frequency allows C band radars to create a smaller beam width using a smaller dish and also do not require as much power as an S band radar.

10. Weather Radar
Apart from Doppler shift, we have backscattering and propagation effects:
Backscattering deals with each individual atmospheric constituent particle and how it reflects a portion of the transmitted power back towards the radar. This portion of backscattered power is a function of size, shape and ice density of each cloud and precipitation particle.
Propagation effect on the other hand is concerned with how the cloud or precipitation particles as a whole work to modify the power and phase of the transmitted signal.

11. Weather Radar
There are uncertainties in radar estimates of atmospheric constituents due to the dynamic nature of how the particles change:
shape (e.g. sphere to mushroom head),
size,
density,
physical states (e.g. from ice to water)
mixture (e.g. rain and snow, or snow and ice).
These are further complicated by the non-linear relationship between backscattered power and particle size.
Polarimetric radars attempt to address these problems and improve estimation accuracy.

12. Polarimetric Weather Radar
Polarimetric radars (dual-polarization radars), transmit radio wave pulses that have both horizontal and vertical orientations.
The horizontal pulses essentially give a measure of the horizontal dimension of cloud (cloud water and cloud ice) and precipitation (snow, ice pellets, hail, and rain) particles
The vertical pulses essentially give a measure of the vertical dimension.
Since the power returned to the radar is a complicated function of each particles size, shape, and ice density, this additional information results in improved estimates of rain and snow rates, better detection of large hail location in summer storms, and improved identification of rain/snow transition regions in winter storms.

13. Polarimetric Weather Radar
It should be noted that the Doppler feature relates to cloud motion and polarimetry to precipitation type and rate
Ordinary weather radars measure the backscattered power received from the radar's horizontal pulses (i.e. horizontal reflectivity).
Polarimetric Weather Radars compare the backscattered power received from both horizontal and vertical pulses in different ways for example ratios or correlations, to estimate the size, shape, and ice density of cloud and precipitation particles.

14. Operation Polarimetric Weather Radars measure :
Differential reflectivity: ratio between the horizontal and vertical received power and is a good indicator of drop shape which in turn gives a good estimate of average drop size.
The correlation coefficient: between the reflected horizontal and vertical received power and it’s a good indicator of regions where there is a mixture of precipitation types, such as rain and snow.
The linear depolarization ratio: ratio between the vertical component and the horizontal component of the backscattered waveform that is more specifically either the ratio of a vertical received power from a horizontal pulse or a horizontal received power from a vertical pulse and it is a good indicator of regions where a mixture of precipitation types occur.
The specific differential phase: a comparison of the received phase difference measurement between the horizontal and vertical pulses and is a "propagation effect" that is a very good estimator of rain rate.

15. Operation
Due to the added information on the cloud and precipitation particle size, shape and ice density, polarimetric weather radars can offer:
Refined estimates of precipitation rates.
Precipitation size (e.g. for hail) and type (hail or snow or ice or rain) discrimination.
Classification of precipitation type in winter storms.
Detection of electrically active storms.
Detection of aircraft icing conditions.
“Ice in flight is bad news. It destroys the smooth flow of air, increasing drag while decreasing the ability of the airfoil to create lift. It can roll or pitch uncontrollably, and recovery might be impossible.” … The AOPA Air Safety Foundation

16. Operation
Mathematical models are being developed to use weights on the polarimetric variables’ relevance in classifying each cloud (cloud water and cloud ice) and precipitation (snow, ice pellets, hail, and rain) particle type.
A composite weight analysis of each variable can be used to classify the dominant particle type for each portion of the cloud and hence improve predictions from short-term computer forecast models.

17. Operation
The horizontal and vertical linear polarization is usually implemented by a simultaneous-transmit simultaneous-receive (STSR) configuration
Another design switches from pulse-to-pulse the H and V transmissions but has simultaneous H and V reception, this is called alternate transmit simultaneous receive (ATSR). ATSR is able to measure cross polar signals but these are weak compared to co-polar signals. Therefore high powered transmitters would be required for ATSR mode and this has favored adoption of the STSR mode.
(Pierre CB)

18. Operation
Block diagram for a single V channel (i.e., vertical polarized waves are transmitted) of a homodyne polarimetric Doppler radar. For STSR mode, the transmitted pulse would be split between H (not shown here) and V channels after the amplifier transmitter and sent to two transmit/receive (T/R) switches and a dual-polarimetric antenna. Upon receive, the H and V channels would have separate electronics to receive the signals independently.

19. Operation
Assuming no propagation effects, the backscattered electric field can be described by the following equation:
where Eh ,Ev are the electric field components in the h, v direction, the superscripts i and b correspond to the incident and backscattered fields, respectively, and shv is the complex backscattering matrix element corresponding to vertical transmission and horizontal reception. The other elements of the backscattering matrix follow accordingly.

20. Operation
The co-polar backscattering matrix elements (shh and svv) are derived from the complex echo signals with horizontal and vertical polarizations. Consequently, the horizontal and vertical reflectivity factors are obtained as:
Where average backscattered cross-section per unit volume e.g
The density of scatterers is and 𝐾w is the complex dielectric factor for water
The cross polar backscattering matrix elements are orders (1 or 2) of magnitude weaker than the co-polar (ATSR mode)

21. Operation
For spherical hydrometeors 〈 |shh|2 〉=〈 |svv|2 〉like the smallest drops, however for the larger drops, ice crystals, hail stones, etc., these polarimetric parameters change drastically hence providing more data about the shape of the hydrometeors. The differential reflectivity, ZDR is used to quantify this variation by taking the logarithm of the ratio of 𝑍h and 𝑍v to produce:
Typically, shh is larger than svv for drops distorted by drag forces as shown in Figure (next slide), usual values of ZDR for rain varies from 0 to +4 dB. While for snow, ice crystals usually have large aspect ratios, so ZDR varies from +1 to +6 dB, depending on crystal orientation

22. Operation
(Pruppacher and Beard, 1970)

23. Case Study : POLDIRAD
POLDIRAD is a polarimetric weather radar developed for research tasks of the DLR Institute of High Frequency Technology for highly accurate measurement of precipitation fields.
It’s a Doppler C-band system with polarization agility for transmitting, dual-channel receiving, and has real time processing and display.
For real time display the choice has to be two of the following: reflectivity factor, differential reflectivity, depolarization ratio, Doppler velocities, and Doppler spectral widths for both receiving channels. These can be displayed either on a PPI scope or on an RHI scope.
POLDIRAD has elliptical circular polarization and alternative linear horizontal and vertical polarization with the option to receive cross-polarized echo signals.
The rest of the technical details are summarized in table below and more details can be found at:

24. POLDIRAD Technical specifications
System
Frequency
C-Band, GHz = 5,45 cm wavelength
Maximum range
300 km
Number of range bins
452
Samples per range bin
32, 64, 12
Antenna
Diameter
ca. 5 m
Beam width
1° horizontal and vertical
Gain
ca. 44,5 dB
Sidelobe isolation
< -32 dB
Cross-polarization isolation
< -28 dB
Position
DLR Oberpfaffenhofen (25 km southwest of Munich)
Height above sea-level
602,5 m
Latitude
48° 05' 12" North
Longitude
11° 16' 45" East
Transmitter
Peak power
400 kW
Pulse repetition frequency
variable from 160 to 2400 Hz
Pulse length
2 µs, 1 µs and 0.5 µs
Loss from transmitter to antenna
ca. 2,5 dB
Receiver
Number of channels 2
Receiver response
linear (dynamics ca. 40 dB) logarithmic (dynamics ca. 80 dB)
Polarization network
Polarizations
variable (linear, circular, elliptic)
Switching time
8 µs
This radar has been used to investigate and distinguish snow, graupel, hail and rain in addition to different types of thunderstorms, frontal systems and squall lines.

25. Analysis
Rain rate, R can be derived either by retrieving the drop size distribution (DSD) or using empirical relations. Using DSD, the rain rate can be calculated as:
Empirical relations include:
The NEXRAD R(Z):
Estimation based on Z and ZDR:
Estimation based on KDP (specific differential phase):
A comparison (simulated) of rain rates estimated with and without polarimetric radar (C-band) was done using MATLAB.

26. Analysis For this iteration, ZDR was ranging from .7 to about 3.5 dB.
(crude simulation! Yet to be refined)

27. Polarimetric algorithms
Ryzhkov,
S. Giangrande
and T. Schuur
List of different polarimetric algorithms used for rainfall estimation

28. Errors of the radar estimates
Table: Mean biases, standard deviations, and RMS errors of the radar estimates of one hour rain totals (in mm) and areal mean rain rates
(in mm h-1) for different radar rainfall algorithms.
We see improvement with estimates using polarimetric parameters
Ryzhkov,
S. Giangrande
and T. Schuur

29. Conclusion
R(Z) algorithm i.e without the input of polarimetric parameters can lead to over estimation of rain rates as shown by studies (Ryzhkov, S. Giangrande and T. Schuur)
Improvements are realized when polarimetric parameters are included for R(Z,ZDR) and even better estimates are obtained with R(ZDR,KDP)
However studies show that these estimation algorithms perform better for particular applications and rain intensity.

30. Conclusion