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<br />where the summations are over all pairs for the entire storm event for the various choices of radar <br /> <br />estimates from the nine surrounding polar bins. Up until now, the. discussion has assumed a rain <br /> <br />rate threshold in the PPS algorithm corresponding to 51 dBZ, but three other thresholds ranging <br /> <br />from 49 to 55 dBZ have also been examined and are included in the table for comparison and <br /> <br />later discussion in section 6, <br /> <br />Focusing on the case using a 51 dBZ rain rate cap (third row in Table I), it is clear that <br /> <br />the choice of which of the nine radar estimates to pair with the gauge observation can have a <br /> <br />potentially large impact on the sample bias and therefore ultimately on the computed bias <br /> <br />estimate from the Kalman filter. For this particular convective rainfall event, if the radar <br /> <br />estimate centered on the gauge (column 4) or the 9-bin average (column 5) was chosen to form <br /> <br />the gauge-radar pairs (both are very similar), the resulting bias estimates from the Kalman filter <br /> <br />might have been much lower than the near-unity biases in Fig. 6a, perhaps closer to 0.6 as shown <br /> <br />in the table, indicating a significant radar overestimation relative to the gauges, Smaller bias <br /> <br />estimates coming from the Adjustment algorithm would have reduced the radar overestimation; <br /> <br />however, the algorithm-computed hourly bias estimates in Fig. 6a were no lower than 0.96. <br /> <br />Even though lower values would have been desirable, at least a bias of 0,96 closely matches the <br /> <br />storm-total sample bias of 0.903 if using the current algorithm's logic for choosing gauge-radar <br /> <br />pairs (Table I, column 2, row 3), so the Kalman filter appears to be working fme. <br />However. one could ask whether the current method of forming the gauge-radar pairs <br />realistically captures the true, unknown bias that the Adjustment algorithm is trying to estimate. <br /> <br />Clearly the sample biases shown in columns 2 and 3 for 51 dBZ (0.903 and 0.906) are <br /> <br />significantly different that those in columns 4 or 5 (0.614 or 0.637) and would have a significant <br /> <br />13 <br />