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Figure 7. KGE error difference maps between GloFAS v4 and v3 simulations (top row) and cumulative distributions of KGE for both v4 and v3. Using all all points (1st column), using only calibration points for both models without larger reservoir or lake influence (2nd column) and non-calibration points for both models without larger reservoir or lake influence (3rd column).
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Bias
The bias, measured by the absolute value of the 0-centred version of the KGE's bias ratio component (absbiasbias), is very clearly largely contributing to the improved KGE by drastically reduced bias errors in v4 (Figure 8). This . The first row in Figure 8 shows the difference in absvar, the absolute value of bias, as the bias error magnitude difference between v4 and v3. The large impact of the bias is generally the same with all station versions, the stations full list (Figure 8, 1st column), of the calibrated (Figure 8 2nd column) or non-calibrated stations station networks (Figure 8 3rd column). The geographical distribution of the errors is very similar to the KGE's picture in Figure 7, with the tropics in general showing very large bias improvement, often more than halving the bias ratio error of v3 by v4.
The cumulative distributions of the absbias errors of the bias highlight that the bias error is generally getting lower in v4, seemingly everywhere. In fact, the distribution of the actual bias difference values (not shown here) highlight that about 85% of the catchments indeed has lower bias ratio error in v4 than in v3. Figure 7 (2nd row) also highlight that the high median value of 0.43 39 in v3 decreased to only 0.12 05 in v4 (see Figure 7, 2nd row, 1st graph), with -0.22 as the median of the absbias difference values (the graph is not shown here). This confirms that the new v4 model delivers an almost optimal bias in global average sense, and that the improvement in the bias error magnitude (measured by absbias) is a very large -0.22 on the basis of all stations that could be verified. The same bias median values are 0.16 14 to 0.0702 for the calibration stations, with -0.09 as the median of the absbias difference for the calibration stations, while 1.92 to 0.5040, with -0.88 as the median of the absbias differences for the non-calibrated case. This confirms the same picture seen for the KGE, with the calibrated stations showing much smaller improvement in bias than the non-calibrated stations.
Figure 8. Abspbias error difference maps between GloFAS v4 and v3 simulations (top row) and cumulative distributions of abspbias bias for both v4 and v3 (bottom row). Using all all points (1st column), using only calibration points for both models without larger reservoir or lake influence (2nd column) and non-calibration points for both models without larger reservoir or lake influence (3rd column).
Absvar ratio
Variability
The variability, measured by the 0-centred version of the KGE's variability ratio component, shows a quite homogeneous geographical distribution globally (Figure 8, top row). Improvement by v4, i.e. negative var difference, is the overwhelming picture, other than for the non-calibrated stations, which seem more mixed. There is not really any emerging area with a clear cluster of better variability in v3 (i.e. blue dots). It is also clear, that the variability improvement is smaller than the bias improvement seen in Figure 7, there are much less dark red stations in Figure 8 than we had in Figure 7.
The cumulative distributions of var confirm these conclusions. The purple curve (v4) is very clearly more centred on the 0 optimal variability line (centre of the graphs), a little less so with the calibrated stations only, and more with all the stations. However, the non-calibrated stations behave differently, with not too much difference, reflecting the rather mixed picture we saw in the absvar difference map in Figure 8.
The median var value change from -0.10 to -0.03 in v4, with -0.07 as the median of the absvar differences for the all-station case. For the calibration stations the improvement is from -0.06 to -0.02, with -0.04 as the median of the absvar differences, while for the non-calibrated stations it is from -0.24 to -0.15, with -0.05 as the median of the absvar differences. These number also confirm that the variability error improved in v4, but less than the bias errors improved in Figure 7. Moreover, the difference between calibrated and non-calibrated catchments is again less pronounced than it was for the bias case.
Figure 9. Absvar error difference maps between GloFAS v4 and v3 simulations (top row) and cumulative distributions of absvar var for both v4 and v3 (bottom row). Using all all points (1st column), using only calibration points for both models without larger reservoir or lake influence (2nd column) and non-calibration points for both models without larger reservoir or lake influence (3rd column).
Correlation
The variabi