The combination of multiple dual polarisation rainfall estimates should lead to a more accurate rainfall product than using any one single approach and new techniques are emerging which have shown this to be possible (Dixon et al., 2015; Cifelli et al., 2011). None of these techniques have as yet made use of rainfall estimates from specific attenua- tion, and given R(Ah) and R(Z(Ah)) were two of the best performing rainfall estimators
when compared to the rain gauges in COPE the following section explores two tech- niques for incorporating these estimates into combined estimators that also use R(ZC),
R(ZC,ZDR) and R(KDP).
7.4.1 Methods of combining radar rainfall estimates
The first technique uses a simple decision tree to select the rainfall estimate which is likely to have the best rainfall estimate with the lowest uncertainty, the process for which is shown in Figure 7.20. The decision tree uses specific differential phase shift where the path maximum phase shift is high, where possible, or when the predicted rainfall rate from the other estimators exceeds 120 mm/hour, it then prefers specific attenuation based rainfall estimates where they are available to the other methods and finally uses differential reflectivity in moderate rainfall where it is valid otherwise reverting to corrected reflectivity. So for each range gate only one method is used, which is likely
to be the most accurate estimate for that particular range gate. A second method is to combine the estimates using a weighted average, where the weight for each rainfall product is a function of factors which determine its accuracy and uncertainty.
Figure 7.20: Flowchart describing the decision tree required to select the most ap- propriate rainfall estimator from the four methods available. Green arrows represent answering yes to each decision (grey box) and orange arrows represent answering no. The selected rainfall options are shown in the orange boxes. For this method a valid R(ZC,ZDR) is obtained in any case where the corrected differential reflectivity is greater
than 0.5 dB, while validKDP requires the radar to have calculatedKDP and it to have
a value greater than 0.5 (deg/km). The maximum ΦDP at a range gate represents the
highest smoothed phase shift up to that point along the radial.
The weighting for each of the dual polarisation rainfall estimates is based on the maximum phase shift along the radial up to that point and the corrected reflectivity, the weighting for R(ZC) is also based on the partial beam blockage correction, while R(ZC,ZDR) also
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uses the corrected differential reflectivity. In the case of R(Z(Ah)) the theoretical reflec-
tivity is used in preference to the corrected reflectivity. Figure 7.21 shows the weights for each of these four variables, with the total weight for each variable at every range gate be- ing the multiplication of each weight calculated at that range gate, and the rainfall being the weighted average of the four rainfall estimates. For example the weighting for R(ZC)
for an echo with a reflectivity of 50 dBZ, a radial maximum phase shift of 40 degrees and a differential reflectivity of 0.4 dB in an unblocked region of the scan (PBB = 0 dBZ) would be 0.325 (1×0.325×1), while for R(ZC,ZDR) it would be 0 (1×0×0), for R(KDP) it
would be 0.75 (1×0.75) and for R(Z(Ah)) it would be 0.5 (0.5×1).
Figure 7.21: Weighting functions to calculate the weighted average rainfall from dual polarisation at each range gate. Each of the dashed lines represents a rainfall estimation method, red is R(KDP), blue is R(ZC,ZDR), black is R(ZC) and green is R(Z(Ah). Each
panel represents a different weighting factor for the rainfall, the top left is corrected reflectivity (Z(Ah) for R(Z(Ah)), the top right is the maximum phase shift along the
radial so far, the bottom left is differential reflectivity and the bottom right is the partial beam blockage correction applied to reflectivity. Total weightings for each rainfall
7.4.2 Results of combining rainfall estimates
Both of the described methods of combining multiple dual polarisation rainfall estimates have been applied to the COPE radar data, with total rainfall accumulations for each at 0.5◦elevation shown in Figure 7.22 with the decision tree method yielding much higher rainfall accumulations than the weighted average method. In the accumulation resulting from the convective line which spans the peninsula to the south of the radar, both meth- ods yield lower rainfall estimates than all of the previous estimates with the exception of selective R(KDP), showing the influence of R(KDP) in these areas of the combined
estimates. Unfortunately, given the location of the rain gauges this effect is not visible within the verification results.
Figure 7.22: Total rainfall accumulation for the COPE field campaign as measured
by the NCAS mobile weather radar at an elevation of 0.5◦when using a combination of rainfall estimators. Panel A shows the accumulation when using rainfall produced with the decision tree method while B shows the accumulation when rainfall is estimated using a weighted average of the available rainfall estimates. Each panel is a 300 km square centred on the radar and contains the accumulation from 1131 valid scans across
the field campaign.
Comparison to rain gauges shows the combined method to have a gradient of 0.82 and a correlation coefficient of 0.31, which is similar to each of the individual methods, and its mean absolute percentage difference is 25% which is bettered only by the theoretical R(Z(Ah)) approach. The weighted method has a much shallower gradient of 0.69 and
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rainfall. The shallower gradient suggests the weightings are biased towards rainfall es- timates which produce lower rainfall intensities and there is future potential to study how changing the combination weightings influences the rainfall estimates provided, but the high correlation between gauges suggests the method is producing consistent rainfall estimates. Removing St Clether and Mary Tavy from the regression analysis improves both estimates, with the decision tree having a gradient of 0.88, a correlation of 0.48 and a MAPD of 21% while the weighted method has a gradient of 0.76, a correlation of 0.65 and a MAPD of 28%.
Figure 7.23: Comparison of rain gauge total rainfall accumulation for the COPE field campaign with rainfall as estimated by the NCAS mobile weather radar at an elevation of 0.5◦using combined rainfall estimates. Each of the panels y-axes shows the rainfall accumulations as taken from the panels of Figure 7.22, A is using the decision tree and B is using the weighted average. Each blue cross represents the total for each of the EA
rain gauge sites. The dashed line in each panel is the one to one line.
While these results indicate combining radar estimates to form a single merged product is viable, they do not suggest they provide more accurate rainfall representations than just using the best single variable rainfall estimate available (R(Z(Ah)), at least for the
rain gauge locations. The previous schemes all combined ice phase estimates in addition to liquid rainfall estimates, which is unnecessary for COPE given the location of the rain gauges and the height of the melting layer during the project and it is in these condi- tions, along with the high intensity convective events hinted at in the widespread total accumulations that combined estimates are likely to have the greatest value. The esti- mates provided here could potentially be improved through adjustment of the weighting
factors, or values used in the decision tree and objectively doing so is an further item for exploration in future work.