0 40 80 120 160 200
<0 [0-0.2] [0.2-0.4] [0.4-0.6] [0.6-0.8] [0.8-1]
No. of basins
NSE range
C20 C21 C22 C23
Figure 5.12: Cumulative frequency curves for all the basins and their NSE ranges for the four predicted cases ranging from column 20 to column 23 in the supplementary material provided. For better representation baisns withα <1.5 were excluded.
Cumulative frequency curve for the different ranges of NSE values listed from columns 20−23 of the supplementary material provided and no.of basins was shown in figure 5.12. For better representation of these cumulative frequency curves the basins with α <1.5 were discarded. In model testing it was observed that for some of the basins NSE values were exceeded the limit of unacceptable range (for e.g. basins with USGS id 14034470, 13200500, 09268900) which signifies the poor prediction of streamflows. This was mainly attributed by the fact thatα values of all those basins were not exceeding 1.5. But all the equations used to predict streamflow (equations 5.2, 5.3) were derived based on the assumptions thatα≥1.5 [5].
a)
0 40 80 120 160 200
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range b)
0 40 80 120 160
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of basins
PBIAS range No. of basins Vs PBIASrange
Figure 5.13: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) PBIAS, b) RSR. The above values are corresponds to predicted recession flows without using initial discharge and observed recession flows during second half of data with calibratedkvalues from first half of the data. Hero also for better representation baisns withα <1.5 were not considered.
Model evaluation statistics like percent bias (PBIAS), RMSE-observation standard deviation ratio (RSR) were also calculated to check the performance of the model. Column 25−26 of the supplementary material provided shows the biased PBIAS, RSR values of predicted recession flows without using initial discharge, observed streamflows during second half of the validation period.
Figure 5.13 shows the no. of basins and ranges of PBIAS, RSR values. In 48% of the basins the predictions performance rating is very good (PBIAS<±10), in 12% of basins the predictions performance rating is good (±10≤PBIAS<±15), in 16% of the basins the performance rating is satisfactory (±15≤PBIAS<±25) and in 23% of the basins the performance rating is unsatisfactory
(PBIAS >±25). Similarly in terms of RSR in 4% basins performance rating is very good (RSR
< 0.5), in 18% of basins rating is good (0.5 < RSR ≤ 0.6), in 26% of basins performance rating is satisfactory (0.6<RSR ≤0.7) and in rest of basins (52%) of basins prediction is unsatisfactory (RSR>0.7). The above mentioned general performance ratings are recommended for a monthly time step predictions. But our model predictions are in terms of daily time steps, so the above adapted recommended ratings from Moriasi et al (2007). shall be further decreased for daily step prediction which undoubtedly enhances the efficiency our model [18]. Since in literature only the reported NSE, PBIAS values are available, so to check the model performance of individual basin, performance ratings of monthly time steps were considered. All the above mentioned model evaluation statistics (PBIAS, RSR) are calculated only after removing the bias error in the predicted values. Also as our streamflow prediction models are not valid for the basins with α < 1.5, so such basins were discarded in plotting figure 5.13.
Cumulative frequency curves of various model evaluation parameters and their ranges were shown from figures 5.14 to 5.19 for both the cases of prediction.
0 40 80 120 160
[-∞, 0.2] (0.2, 0.4] (0.4,0.6] (0.6,0.8] > 0.8
No. of basins
NSE range
No.of basins Vs NSE range a)
0 40 80 120 160
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of basins
PBIAS range
No. of basins Vs PBIAS range b)
0 40 80 120 160 200
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range c)
Figure 5.14: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) NSE, b) PBIAS, c) RSR. The above values are corresponds to predicted recession flows without using initial discharge and observed recession flows during second half of data with calibrated k values from first half of the data. Here, baisns withα <1.5 were also considered.
0 40 80 120 160
[-∞, 0.2] (0.2, 0.4] (0.4,0.6] (0.6,0.8] > 0.8
No. of basins
NSE range
No.of basins Vs NSE range a)
0 40 80 120 160
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of bains
PBIAS range
No. of basins Vs PBIAS range b)
c)
0 40 80 120 160 200
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range
Figure 5.15: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) NSE, b) PBIAS, c) RSR. The above values are corresponds to predicted recession flows without using initial discharge and observed recession flows during first half of data with calibratedkvalues from the same data. Here, baisns withα <1.5 were also considered.
0 40 80 120 160
[-∞, 0.2] (0.2, 0.4] (0.4,0.6] (0.6,0.8] > 0.8
No. of basins
NSE range
No.of basins Vs NSE range a)
0 40 80 120 160
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of bains
PBIAS range
No. of basins Vs PBIAS range b)
0 40 80 120 160 200
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range c)
Figure 5.16: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) NSE, b) PBIAS, c) RSR. The above values are corresponds to dry weather flow prediction without using the initial discharge by using whole data i.e. total data was used for both the calibration and validation. Here also, baisns withα <1.5 were also considered.
0 40 80 120 160
[-∞, 0.2] (0.2, 0.4] (0.4,0.6] (0.6,0.8] > 0.8
No. of basins
NSE range
No.of basins Vs NSE range a)
0 40 80 120 160 200
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of bains
PBIAS range
No. of basins Vs PBIAS range
b) 0
40 80 120 160 200
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range c)
Figure 5.17: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) NSE, b) PBIAS, c) RSR. The above values are corresponds to predicted recession flows with using initial discharge and observed recession flows during second half of data with calibratedkvalues from first half of the data. Here, baisns withα <1.5 were also considered.
0 40 80 120 160
[-∞, 0.2] (0.2, 0.4] (0.4,0.6] (0.6,0.8] > 0.8
No. of basins
NSE range No.of basins Vs NSE range a)
0 40 80 120 160 200
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of bains
PBIAS range
No. of basins Vs PBIAS range
b) 0
40 80 120 160 200
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range c)
Figure 5.18: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) NSE, b) PBIAS, c) RSR. The above values are corresponds to predicted recession flows with using initial discharge and observed recession flows during first half of data with calibrated k values from the same data. Here, baisns withα <1.5 were also considered.
0 40 80 120 160 200
[-∞, 0.2] (0.2, 0.4] (0.4,0.6] (0.6,0.8] > 0.8
No. of basins
NSE range No.of basins Vs NSE range a)
0 40 80 120 160 200
<±10 (<±10, ±15] (<±15, ±25] >±25
No. of bains
PBIAS range
No. of basins Vs PBIAS range b)
0 40 80 120 160
[0, 0.5] (0.5, 0.6] (0.6,0.7] > 0.7
No .of basins
RSR range
No.of basins Vs RSR range c)
Figure 5.19: Histograms of no.of basins and ranges of model evaluation stastistics interms of a) NSE, b) PBIAS, c) RSR. The above values are corresponds to dry weather flow prediction with using the initial discharge by using whole data i.e. total data was used for both the calibration and validation.
Here also, baisns withα <1.5 were also considered.