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In order to assess the degree of resolution lost by estimating rainfall using the RegDer method, the ER was aggregated using two methods (i.e., simple aggregation by resampling and a moving average) and the resulting sequences compared to the IER sequence in the time domain. Plots of progressively more aggregated sequences are shown in Figure 5. It can be seen that as aggregation increases, peaks become lower and more spread out and the sequence is effectively smoothed. The coefficient of determination (Rt2) and the correlation (R) between the aggregated sequence and the IER tends to a maximum then decreases as aggregation time increases – ultimately the variation in the sequence would be completely smoothed out. The point at which the maximum value is reached is taken as an estimate of the resolution of the IER. Plots of Rt2 or R values are shown in Figures 6 (aggregation by resampling) and 7 (moving average estimate). Time resolution estimates are shown in Table 1 and compared with the fast time constant (TCq) and the N–S sampling limit.
Table 1

The sampling frequency (hr), time constants (TCq – fast and TCs – slow), SFI (the percentage of the flow taking the slow pathway), the N–S safe sampling limit (hr) and the time resolution of the IER estimated by resampling and moving average methods. Also shown is the frequency domain estimate of the resolution – the cut-off point beyond which the signal carries very little information (illustrated in Figure 8) and can be considered unimportant. The estimated time resolution of the IER sequences is less than the dominant (fast) mode of the catchments and considerably less than the ‘safe’ N–S limit

      Time resolution estimates
 
CatchmentSampling frequency (hr)TCq (hr)TCs (hr)SFIN–S limit (hr)Aggregation by resamplingAggregation by moving averageCut-off point (hr)
Blind Beck 0.25 6.3 22.1 47% 19.9 2.5 h (10 time periods) 2.25 h (9 time periods) 3.8 
Baru 0.083 1.1 18.7 62% 3.4 0.9–1 h (11–12 time periods) 1 h (12 time periods) 1.7 
      Time resolution estimates
 
CatchmentSampling frequency (hr)TCq (hr)TCs (hr)SFIN–S limit (hr)Aggregation by resamplingAggregation by moving averageCut-off point (hr)
Blind Beck 0.25 6.3 22.1 47% 19.9 2.5 h (10 time periods) 2.25 h (9 time periods) 3.8 
Baru 0.083 1.1 18.7 62% 3.4 0.9–1 h (11–12 time periods) 1 h (12 time periods) 1.7 
Figure 5

Comparison of aggregated sequence to the IER sequence for (a) Blind Beck (sampling interval 15 min) and (b) Baru (sampling interval 5 min) at aggregations of 4, 8, 12 and 24 time periods (samples) illustrating how aggregation lowers the peak and spreads the volume of rainfall over a longer time period. The IER sequence is plotted for comparison.

Figure 5

Comparison of aggregated sequence to the IER sequence for (a) Blind Beck (sampling interval 15 min) and (b) Baru (sampling interval 5 min) at aggregations of 4, 8, 12 and 24 time periods (samples) illustrating how aggregation lowers the peak and spreads the volume of rainfall over a longer time period. The IER sequence is plotted for comparison.

Figure 6

Rt2 and R tend to a maximum value as aggregation increases for (a) Blind Beck and (b) Baru. The resolution of the IER is taken to be the point at which the maximum is reached or very little change is apparent. For Blind Beck, this value is reached at 10 periods for both Rt2 and R. The result for Baru is not quite as clear but can be estimated to be 10 periods from R and 11 or 12 from Rt2 although Rt2 continues to increase up to 24 time periods, perhaps due to higher variability of the rainfall.

Figure 6

Rt2 and R tend to a maximum value as aggregation increases for (a) Blind Beck and (b) Baru. The resolution of the IER is taken to be the point at which the maximum is reached or very little change is apparent. For Blind Beck, this value is reached at 10 periods for both Rt2 and R. The result for Baru is not quite as clear but can be estimated to be 10 periods from R and 11 or 12 from Rt2 although Rt2 continues to increase up to 24 time periods, perhaps due to higher variability of the rainfall.

Figure 7

A similar plot to Figure 6 with aggregation by moving average for (a) Blind Beck and (b) Baru. Rather than reaching an asymptotic level, the Rt2 and R values maximise at 9 time periods for Blind Beck and 12 time periods for Baru (determined graphically in Matlab). These values have been used as the estimates of the resolution of the IER and agree well with the estimates made by resampling. Convolution term in the caption is with reference to the method of calculating the moving average.

Figure 7

A similar plot to Figure 6 with aggregation by moving average for (a) Blind Beck and (b) Baru. Rather than reaching an asymptotic level, the Rt2 and R values maximise at 9 time periods for Blind Beck and 12 time periods for Baru (determined graphically in Matlab). These values have been used as the estimates of the resolution of the IER and agree well with the estimates made by resampling. Convolution term in the caption is with reference to the method of calculating the moving average.

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