Report on Polarisation Weather Radar by A. R. Holt & D. H. O. Bebbington

4. Radar Sensing

The radar sensing process is a convolution of propagation along the path from the radar antenna to the resolution volume, backscattering from hydrometeors in the volume, and propagation back along the path from the resolution volume to the radar antenna. These processes are very dependent on the frequency being used. At S-band, the dominant effect in propagation is differential phase shift between vertical and horizontal polarisation. Attenuation is generally small, as is differential attenuation. However, they cannot be ignored if the radar beam is passing through very heavy precipitation, or the path is a long path through significant rain (refs. 38, 39). At these frequencies, scattering by raindrops (but not by hail) is well described by Rayleigh theory (cf ref. 37). As the frequency increases, though differential phase shift increases, attenuation effects increase more rapidly due to the variation of the imaginary part of the refractive index of water with frequency (ref. 40). Moreover, at C-band frequencies and above, Rayleigh theory is no longer sufficient, and Mie theory must be used. Resonance effects can be seen at certain drop sizes (depending on the frequency) (ref. 41). Severe attenuation and differential attenuation effects have been seen at C-band (cf ref. 21).

K_V,H = k₀ + (2π/k₀) ∫f_V,H(D)N(D)dD. (9)

Here D(cm) is the equivolume drop diameter, and f(D) denotes the forward scattering amplitude for drops of diameter D. The integration is over the range of drop diameters, where the maximum diameter is typically 7 or 8mm( drops of 8mm diameter have been seen inwarm rain in Hawaii). Note that f(D) is a complex number quantity, and hence the real part of K determines the phase shift, whilst the imaginary part of K gives the attenuation of the wave. In particular, the attenuation per km, A_V, of a vertically polarised wave is given by

A_V = 8.686 10⁵ Im(K_V) dB (10)

Along the path between a radar antenna and a resolution volume, the radar wave will typically pass through many different rain regions (and maybe through regions containing other hydrometeors such as hail or melting particles). The total phase shift per km of a vertically polarised wave will therefore be

Φ_V = 10⁵ Re(K_V) radians (11)

Along the path being sensed by a radar, there will typically be many different dropsize distributions, each with its own path length. The total attenuation (or phase shift) at a particular resolution volume will therefore be a summation of the individual attenuations (or phase shifts) along each section of the path. Since the attenuation on the return path will be the same as on the outward path, the total effect on the radar return field of the hydrometeors on propagation path will be twice the one-way attenuation or phase shift. The differential attenuation (or phase shift) is the difference between that for horizontal polarisation, and that for vertical polarisation. It is standard to define the differential propagation phase shift, φ_DP, as the two-way difference in phase-shift between horizontal and vertical polarisation, in degrees.

5. 
   Hardware considerations
   

In polarimetric applications the antenna can be a critical component. Since polarimetry depends on the ability of the system to gauge small changes in the vector components of the field, antenna cross-polarization characteristics need to be reduced. The factors in the antenna specification that are important depend to some extent on the type of polarimetric measurement. Some features can be accounted for and corrected by means of a good system calibration, but not all defects can be calibrated out. For an aperture antenna, such as a parabolic dish, the first defect of interest is the primary diffraction sidelobe, which should typically be less than -20 dB with respect in the main lobe, to give adequate suppression over two-way paths. The extent of this lobe depends to a great extent on suitable tapering of the illumination towards the rim of the dish to minimise edge diffraction. This tapering will also help to reduce higher order sidelobes, as the rate of fall-off with order is much improved by the lack of a discontinuity in the illumination, brought about by the edge, and by edge currents. Centred Cassegrain illumination can result in very low extended sidelobes at the expense of raising inner sidelobes due to aperture blockage. One of the impacts of sidelobes is that, as their symmetry is usually considerably inferior to that of the main lobe, (because of the increased sensitivity to manufacturing tolerances and other non-ideal features (such as radomes, supports, etc.) imbalance between sidelobes can give erroneous polarization signatures (refs. D1=44, D2=45.).

In the case of differential reflectivity is is relatively straightforward to align the principal polarizations of the feed system with horizontal and vertical reference planes. For a centre-fed geometry the symmetry planes of a circular parabolic dish naturally obtain. The major potential problems are then likely to lie with the feed support structure. In the case of an offset geometry (usually the offset is in the vertical direction), a vertical symmetry plane will be present. However, there is a lack of symmetry between the currents induced in the upper and lower halves of the reflector and this may have an effect on the polarization purity off axis. The effects of misalignment are equivalent to a bias in hydrometeor canting angle, and are estimated to be small in practice (refs. D2=45, D3=46).

Measurement of circular depolarization requires a higher level of intrinsic cross-polar discrimination than is required for Z_DR measurements, because the co-polar (weak channel) return is usually many decibels below the cross-polar (strong channel) for hydrometeors. At the point where the co-polar difference between linear returns is 0.1 dB the corresponding circular depolarization ratio is roughly –40 dB. The high sensitivity that the CDR technique implies for small deformations in near spherical hydrometeors is potentially undermined by the corresponding sensitivity to small deviations in the engineering of the antenna reflector. Similar arguments apply to measurement of LDR, where the cross-polar components are typically in the range -27 dB to -30 dB. The practical ICPR for systems measuring such parameters should be better than -30 dB.

The requirement for a dual polarization feed is that there be an orthomode transducer (OMT) to a waveguide section capable of supporting both polarizations (ie. two orthogonal modes) and a scalar feed. This can generally be implemented either by means of the choked scalar feed, Potter horn, the corrugated scalar horn (ref. D7=50). All are widely employed in polarimetric radars. The latter operates by satisfying two boundary conditions at once by using a quarter wave depth slots to present a low impedance to tangential H-field as well as E-field on the interior surfaces of the horn. This ensures a close balance between the E-plane response and H-plane response, because the spatial distribution of the fields in the aperture is closely comparable in form, reaching a zero at the same radius. Ideally, the illumination of the aperture should be a Huyghens source (refs. D5=51, D6=49), which the corrugated horn approaches closely when appropriately excited and matched.

An additional advantage of the scalar horn is that the phase centre is well defined, that is, the migration of the phase centre with direction of illumination of the reflector surface is small. This corresponds to the fact that the wavefront is a very close approximation to a spherical surface. Consequently, a good planar wavefront is obtained without the need to correct the reflector surface with respect to a true paraboloid, which would otherwise considerably increase the expense of the reflector.

The equality of field distributions also ensures that the phase centres for each polarization are close to being co-located.

The principle of the orthomode transducer relies on excitation of the orthogonal and independent modes of a circular waveguide section. Linear polarization is obtained by use of a vane which introduces a relative phase delay corresponding to a quarter-wave in the guide. There is little difference in complexity between linear and circular polarization OMTs. The turnstile feed is a design that couples symmetrically displaces waveguide junctions, with non-symmetrically phased shorting waveguide sections to create orthogonally polarized modes according to which junction is fed. Both types of feed are quite frequency sensitive, as the phases introduced are dependent on the lengths of the vanes or shorting sections. Isolation of the order of -50 dB can be obtained over the sorts of narrow fractional bandwidth that usually obtain in current operational radars.

The technical state of the art in weather radar, particularly polarimetric weather radar has lagged behind that in other radar application fields in the last decade or so principally for one reason, namely the high power requirements and the associated large dynamic range required. This has meant in practice that the prevailing power source for weather radars is still the magnetron, although klystron based systems are used operationally, and in a few cases travelling wave tubes are also employed. But, basically, vacuum tube technology is universal. Possibilites for introduction of advanced techniques to weather radar were reviewed in the COST 75 programme (ref. D8=52). One of the obvious candidates considered was that of the phased array. There are (expensive) military systems in which a large number of independent transmit-receive modules are controlled in phase and perhaps also amplitude in order to synthesize a transmit and receive beam. Clearly, in such a system, the total power may requirement may be shared amongst the modules, making the individuak power requirements modest by comparison with those of a vacuum tube design. However the very large number of modules that are required to synthesize a beam with sufficiently small sidelobes makes the cost within the available technology prohibitive for the foreseeable future.