Data correction

Dual polarisation has also allowed easier implementation of corrections for radar miscal- ibration, beam blockage and attenuation, through the use of the phase shift parameters (Φ_DPand K_DP). All of these corrections work as a result of phase shift being independent of received power, therefore errors which alter the received power do not affect phase shift providing a signal can be retrieved (Vivekanandan et al., 1999; Zrnić and Ryzhkov, 1996).

2.4.2.1 Radar miscalibration

Calibration of radar using the self consistency of dual polarisation variables has been proposed by Gourley et al. (2009) and Vivekanandan et al. (2003) for example. These techniques rely on the principle that reflectivity and differential reflectivity and also differential phase shift are a function of the DSD, and therefore phase measurements can be estimated using power measurements. These can then be compared to measured phase shifts (Scarchilli et al., 1996). In the work of Vivekanandan et al. (2003) KDP

is estimated using Eq. 2.9 and then integrated to calculate a total path phase shift which can be compared to the actual phase shift, the bias between which is a result of miscalibration of reflectivity. Gourley et al. (2009) apply the same approach, but using a variation of Eq. 2.9 and show calibration accuracy of 0.6 dB when using a C-band radar.

KDP = 2.79×10−5Z1.0086ZDR−0.9543 (2.9)

Another approach, proposed by Ryzhkov et al. (2005a), is to directly compared reflectivity and differential reflectivity to specific differential phase, using area-time integrals rather than path integrals. This approach was more suited to the S-band radar used as it allows lower values of K_DP to be used than the path integral approach, and it again showed calibration was possible to within 1 dB.

The main advantage of these techniques is their applicability during normal operating conditions, as they lack the requirement of an external calibration device, and testing procedure, allowing the calibration to be performed regularly without compromising the operational usage or performance of the radar. Therefore ongoing monitoring of the radar calibration is possible without additional costs, which allows easier updating of the calibration, where required.

2.4.2.2 Partial beam blockage

An extension of these approaches is the use of dual polarisation consistency in partial beam blockage correction. In theory, once a radar is well calibrated, any azimuthal differences in self consistency are a result of partial beam blockage and can therefore be used to correct the reflectivity fields accordingly, while it is also possible to apply a simplified approach, where differential reflectivity is not considered (Zhang et al., 2013; Lang et al., 2009). This simplification negates the required correction of differential reflectivity for partial beam blockage, an issue first noted in the literature by Giangrande and Ryzhkov (2005), although correction is still advisable for other uses of differential reflectivity. These approaches all show calibration is possible even in severely blocked sectors (over 90% in the case of Lang et al. (2009)) provided extensive dual polarisation data is available. Another approach recently employed is the use of specific attenuation to quantify partial beam blockage (Diederich et al., 2015a; Ryzhkov et al., 2014), which also allows accurate calibration provided sufficient data is available, with Diederich et al. (2015a) calculating that 19 days of rainfall data may be required to provide a stable correction to within 1 dB.

Chapter 2. Weather radar for hydrology 27

The main advantage of these methods is their ability to account for buildings, vegeta- tion and subtle topographic effects not captured by the traditional digital terrain model approach, and also their independence, as they do not require detailed elevation models which may not be available in some locations. Another advantage is the ability to recal- culate corrections seasonally, which can respond to changes in the local vegetation and new or removed structures. The main disadvantage of these approaches is the amount of data required for stable results, which precludes their use during the initial stages of a deployment.

2.4.2.3 Attenuation

Another application of dual polarisation is the correction of the hydrometeor attenuation particularly prevalent at shorter wavelengths. As discussed in section 2.2.2 attenuation results in a decreasing signal as path integrated rainfall increases, with correction routines relying on estimating the attenuation along the path using empirical relationships or returns from a fixed source. Dual polarisation radars can improve on these corrections as they allow better constraint of the path total attenuation through the use of differential reflectivity (Smyth and Illingworth, 1998a) or differential phase measurements (Schneider et al., 2013; Jameson, 1992, for example). Again these dual polarisation techniques utilise the consistency of dual polarisation measurements, for example Smyth and Illingworth (1998a) constrain attenuation using light drizzle beyond the attenuating rainfall, which should produce an expected differential reflectivity value of between 0 to 0.2 dB. By attributing under measuring in this region to differential attenuation, reflectivity and differential reflectivity can then be corrected, distributing the total attenuation along the path using specific differential phase. They report accuracy of corrections to within 1 dBZ, however the scheme is limited by identifying and observing the correct precipitation beyond the attenuating region, which is not always possible.

Other techniques choose to use differential phase shift to calculate path integrated atten- uation, and then distribute the attenuation using reflectivity measurements. The path integrated attenuation is calculated using DSD coefficients derived from disdrometer mea- surements or scattering simulations. The application of this method varies through the choice of integral path, coefficients and final application, for example Testud et al. (2000) use segments of the radial as the integration path and use attenuation estimation as a

precursor to rainfall estimation using an estimated normalised intercept parameter of the DSD, while Ryzhkov et al. (2014) use the whole radial below the melting layer as the integration path and derive rainfall directly from the specific attenuation calculated during the process. It is also worth noting that these methodologies are sensitive to the presence of hail, where the relationship between phase shift and attenuation is much stronger than in rainfall, the so called “hot-spot" effect, which requires these regions to be treated separately for best results (Ryzhkov et al., 2014, 2013, 2012).

Subject to the accurate estimation of the relationship between specific phase shift and attenuation (the parameterα), the correct treatment of “hot spots" and attenuation not reducing the signal to noise levels, dual polarisation techniques can successfully correct for attenuation. For example, Gu et al. (2011) used simultaneously collected S-band and C-band data to validate successful correction of the C-band data using a variation of the Testud et al. (2000) technique. While most studies use attenuation correction as an intermediary to rainfall estimation, with their results showing the positive impact of attenuation correction, some recent studies have begun to directly estimate rainfall from specific attenuation, which is also showing promising results, particularly when multi radar compositing is required (Diederich et al., 2015b; Ryzhkov et al., 2014; Schneider et al., 2013; Zhu and Cluckie, 2012, for example).