Range dependent LDR thresholds

To assess in more detail the impact of range, data from the original simulation were divided into 20 km range bins, corresponding to an increase in total beam width of 400 m per bin. The sorted data were used to calculate HR, FAR and the equitable Heidke Skill Score (HSS, appendix B) for non-bright band identification at each range using several different LDR thresholds.

The use of HSS in developing an operational algorithm differs from the ROC curve assessment presented in chapter 4. A simple comparison of hits with false alarms neglects to account for the significant difference in frequency of bright band and non-bright band events, where stratiform bright band occurs over 5 times as often as non-bright band conditions in the Wardon Hill dataset (section 4.2.2). This means that an algorithm that always classified VPRs as “bright band” would have non-zero skill, as it would achieve the correct outcome 84% of the time. The Heidke Skill Score accounts for the lower prior probability of non-bright band precipitation by giving more weight to the correct identification of low probability events. By this measure the “always bright band” classification algorithm would be correctly assessed as having zero skill. The HSS is therefore more likely to be optimised at an objectively “correct” value of LDR (that is, a value with some microphysical significance), and should deliver an algorithm with consistent skill which is not dependent on the relative frequency of events in the underlying climatology.

The best LDR classification threshold as a function of range was chosen to maximise overall HSS, subject to constraints on range dependence. The effect of beam broadening on the measured LDR peak has been shown to be minimal (figure 5.2). This is due to the negligible impact of very low depolarisation from rain and ice phase hydrometeors (section 1.4.3) on an average LDR which includes the much higher melting layer peak. On this basis, the LDR threshold for identifying non-bright band VPRs should be constant with range. However, exceptions to this range independence are likely to occur at short range, where the radar beam width is of order hundreds of metres, so that the beam does not sample the whole of the melting layer. In these cases the measured LDR (and therefore the threshold for non-bright band diagnosis) is expected to be higher, particularly in regime 2.

A constant LDR threshold for non-bright band VPR identification was sought for mea- surements at ranges beyond 41 km, at which a 1o radar beam width exceeds the 700 m melting layer depth assumed in the current UK VPR (Kitchen, 1997). At shorter ranges the threshold should vary with radar beam width, and have a value of -21 dB at zero

Figure 5.5: Heidke Skill Score of LDR thresholds with range, generated via simulation study using 0.5o and 2.0o elevation beams (20-240 km). The black line joins the LDR thresholds with maximum HSS, the zero-range point is the maximum HSS threshold using high resolution LDR peaks (chapter 4), and the shading shows the actual Heidke skill score value. The grey line shows the “fitted” best skill LDR thresholds to be used for operational convective identification.

range from the radar. This zero-range threshold is slightly different from the -20 dB determined in chapter 4, which maximised the difference between HR and FAR rather than the more equitable HSS, which accounts for the relative frequencies of occurrence of bright band and non-bright band VPRs.

Due to the properties of the high resolution profile dataset, very few short range melt- ing layer measurements could be generated using only a simulated 0.5o elevation beam. Unfortunately, data from within 40 km of the radar is particularly needed to inform how the “zero-range threshold” should transform with range into the lower constant threshold for a broadened beam. A 2.0o elevation beam was therefore added to the simulation to provide extra measurements in this region. Since there is no overlap of a 1o radar beam width between these two elevations, simulated melting layer measurements from the same vertical profile occur at different ranges in each scan. The additional 2.0o data at each range bin are therefore independent of those obtained from the 0.5o simulation.

Figure 5.5 shows the combined results from the 0.5o and 2.0o datasets in terms of HSS. The black line shows LDR classification thresholds with the highest HSS at each range, with error bars set at a minimum of ± 0.5 dB, since this was the difference between tested LDR thresholds. At some ranges a number of LDR thresholds showed the same level of skill. In these cases the median of equally skilful thresholds has been plotted, and the error bar range increased to 0.5 dB above and below the maximum and minimum thresholds.

The non-constant behaviour of the measured HSS with range is unexpected. Given the contrast with the behaviour of LDR in isolated cases, this range behaviour is almost cer- tainly an effect of differences in the sampling of different melting layer regimes. Regime

1 melting layer detections, where the melting layer peak is not sampled, will have lower LDR threshold values than regime 2 detections, because the bright band LDR mea- surements will be higher when the peak is sampled. Since regime 2 detections occur with higher frequency at longer ranges (see eg figures 5.2 and 5.3), a slight increase in the “non-bright band” detection threshold would be expected at ranges where regime 2 detections are increasing with respect to regime 1. It is therefore likely that a higher proportion of regime 1 detections at intermediate ranges (50-120 km) explains the lower LDR thresholds required to diagnose non-bright band precipitation in this region. An LDR threshold profile with range was fitted by eye to the HSS dataset and is plotted in figure 5.5. It was decided to vary the LDR threshold linearly in the 0-41 km range bracket, with the linear increase in radar beam width from 0 to 700 m (where the mea- surement samples the entire depth of the melting layer (Kitchen, 1997)). This resulted in thresholds: LDRthresh=    −21−5r/41 r <= 41 km −26 r >41 km (5.1)

where range r is expressed in km and LDR in dB. A melting layer LDR measurement below this threshold is proposed as the new criterion for pixel-by-pixel convective iden- tification in radar PPIs.