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The variability, measured by the 0-centred version of the KGE's variability ratio component, shows a quite homogeneous geographical distribution globally (Figure 89, 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 78, there are much less dark red stations in Figure 8 9 than we had in Figure 78.
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 89.
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 78. Moreover, the difference between calibrated and non-calibrated catchments is again less pronounced than it was for the bias case.
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Figure 9. Absvar error difference maps between GloFAS v4 and v3 simulations (top row) and cumulative distributions of 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
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The correlation shows a very mixed picture globally, with slightly more positive than negative catchments (Figure 10, top row). The most prominent area with a correlation improvemnt cluster is in central North-America. The mixed picture is similar for all three station selections (in the three columns).
The cumulative distributions confirms that v4 provides only marginal improvement over v3 in correlation. For the high correlations v3 seems to be even very slightly better, while v4 is noticeably better for low to medium correlations. For the calibrated stations this the difference is even less, while for the non-calibrated stations v3 actually seems to be better. It seems the up and downs of the simulations could not really be improved very noticeably by the v4 model.
Regarding the actual correlation values, the median changes from 0.748 to 0.759 in v4, with 0.000 as the median of the correlation differences for the all-station case, i.e. no change on average at all. For the calibration stations, the improvement is from 0.817 to 0.816 (so actually even very slight decrease), with -0.002 as the median of the correlation differences, while for the non-calibrated stations it is from 0.672 to 0.629, with -0.006 as the median of the correlation differences. These number also confirm that the correlation aspect of the river discharge simulation in v4 did improve only marginally when measured using all stations, while the calibration station comparison shows no change at all and the non-calibration comparison shows rather some small deterioration.
Figure 910. Absvar Correlation error difference maps between GloFAS v4 and v3 simulations (top row) and cumulative distributions of var correlation 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).