Specific differential phase shift as a rainfall estimator

As shown in Section 2.4.3 specific differential phase is an often used estimator for rainfall intensity due to its reduced sensitivity to the DSD when compared to reflectivity. It is also insensitive to hail and graupel (as they have a circular effective cross section) and is used to measure the liquid rainfall content of echoes which contain a mixture of ice and liquid rainfall. The signal processor of the mobile radar generates KDP using Fourier

transformation of the measured phase shift, which can be used to assess the performance of KDP in the first instance, given there are several alternative methodologies for the

calculation ofKDP (Schneebeli and Berne, 2012; Wang and Chandrasekar, 2009; Ryzhkov

and Zrnic, 1996, for example). One feature of all proposed methodologies is the difficultly of accurately calculating low values of KDP due to measurement noise in the phase

shift, which leads to KDP being utilised more at higher rainfall rates. To examine this

uncertainty two rainfall accumulations have been generated here, one which uses R(KDP)

whenever possible, only utilising R(ZC) whenKDP is not estimated and a second which

below 0.5 deg/km and/or when R(ZC) is below 5 mm/hr, it uses R(KDP) when R(ZC) is

greater than 10 mm/hr and the weighted average of R(ZC) and R(KDP) when the rainfall

rate is between 5 and 10 mm/hr where the weighting for R(KDP) varies linearly from 0

at 5 mm/hr to 1 at 10 mm/hr. Through the process the X-band R(KDP) relationship

from Ryzhkov et al. (2014) is used, where the rainfall coefficient is 16.9 and the exponent is 0.801.

Figure 7.16 shows the total rainfall accumulations out to 150 km range for each of these methods, with the large difference being a result of overestimation of rainfall by R(KDP)

at low rainfall rates where the estimation uncertainty has the greatest effect on rainfall rates. Taking a true rainfall rate of 2 mm/hr, the equivalentKDP would be 0.07 deg/km,

which when the measurement accuracy is no better than 0.2 deg/km is not accurately recordable, with rainfall estimates in the range 0 to 6 mm/hr being probable at these intensities. When the rainfall rate is more intense the measurement uncertainty no longer dominates the estimates, and with thresholding the performance of R(KDP) is much more

reliable as seen in Panel B.

Figure 7.16: Total rainfall accumulation for the COPE field campaign as measured by

the NCAS mobile weather radar at an elevation of 0.5◦when using R(KDP) as the rainfall

estimator. Panel A shows the accumulation when using R(KDP) whenever possible while

B shows the accumulation when selectively using R(KDP) at only moderate to heavy

rainfall intensities. Each panel is a 300 km square centred on the radar and contains the accumulation from 1131 valid scans across the field campaign.

Chapter 7. Radar QPE 151

This improvement is observed in the correlations between radar accumulations and the rain gauges, with R2 increasing from -0.04 to 0.26 and the gradient reducing from 1.68 to 0.70. The results for the second method are within the same range as the other approaches explored so far, showing no benefit to using KDP over the other methods. However

previous research has indicated R(KDP) to be beneficial during periods of intense rainfall,

and a closer look at its performance in this situation is required.

7.3.2.1 Performance in intense rainfall

The following example shows the benefit of using R(KDP) during periods of intense rain-

fall by focusing on a period of convective rainfall on 2 August 2013, where a line of convective cells developed along a convergence line running along the peninsula. This example has previously been seen in Figure 7.13 where the problem of attenuation cor- rection for both reflectivity and differential reflectivity was examined and Figure 7.17 repeats the rainfall estimates from corrected reflectivity alongside the rainfall estimate obtained solely from using R(KDP) for this radial. During the first 15 km of the shown

radial there is generally good agreement between the two estimates but the previous ob- servations about estimation errors in lighter rainfall are shown between 10.5 and 13 km where R(KDP) estimates zero rainfall despite the reflectivity signature and between 13

and 19 km where R(KDP) is estimating 6 mm/hr compared to reflectivity estimates of

under 2 mm/hr. During the most intense period of rainfall, between 27 and 35 km the general trend of the two estimates is similar, but the R(KDP) has a much smoother pro-

file and a lower peak rainfall intensity. One reason for this is the contamination of the reflectivity estimates with ice phase hydrometeors which lead to higher reflectivity being observed than would be generated solely from the liquid water content of the precipita- tion while another reason is the smoothing required to generate acceptable estimates of KDP from the noisy data, as smoothing always leads to a reduction in peak intensity.

The R(KDP) lies within the uncertainty bounds of the reflectivity estimates due to the

significant amount of attenuation occurring in this example, and given R(KDP) provides

a rainfall measurement which is not affected by attenuation it can be used to exam- ine the value of α used in this study in these cases, with good agreement seen between the R(KDP) and the R(ZC) whenα=0.27 dBZ/degree in the region beyond the rainfall

Figure 7.17: Rainfall estimates using R(KDP) compared to R(ZC). Data shown is

taken from the 2013-08-02 17:51UTC radar volume at an azimuth of 86◦and elevation of 0.5◦. Rainfall estimates from the radar calculatedKDP is shown by the solid red line,

with the solid black line showing rainfall from the horizontal reflectivity corrected with anαof 0.27 dBZ/deg (solid black line). The gray lines show the rainfall when correcting

using anαof 0.14 and 0.35 dBZ/deg (bottom and top respectively)

This example, and others from the field campaign, indicate that R(KDP) adds useful

information to rainfall estimates in these higher intensity cases but the overly smooth profile of KDP, particularly in convective cells and the difficulty in obtaining reliable

estimates of low values ofKDP indicates an alternative estimation ofKDP will be required

to obtain more accurate rainfall accumulations in the future. Alternative estimation techniques exist which adapt the length of the filtering window applied to the data depending on the reflectivity observed at that point, which gives higher spatial resolution within the region of peak rainfall intensity leading to higher maximum intensities in convective cells (Wang and Chandrasekar, 2009; Matrosov et al., 2006; Brandes et al., 2001). Given this is likely to provide more accurate rainfall estimates in these regions a more sophisticated estimation should be explored for the mobile X-band radar in the future.