Kling–Gupta efficiency,
(23)where Xi is the observed non-dimensional scour depth, Yi is the corresponding computed non-dimensional scour depth, 
, and 
are the averages of the observed and computed non-dimensional scour depth, n is the number of observations, and 
and
are the standard deviation values of the observed and computed data. The ranges of statistical indices are listed below in Table 2.
, and are the averages of the observed and computed non-dimensional scour depth, n is the number of observations, and and are the standard deviation values of the observed and computed data. The ranges of statistical indices are listed below in Table 2. Table 2
Ranges of statistical indices
| Scores | R2 | PBIAS (%) | NSE |
|---|---|---|---|
| Unsatisfactory | R2 < 0.5 | |PBIAS| > 25 | <0.5 |
| Satisfactory | 0.5 < R2 < 0.65 | 15 < |PBIAS| < 25 | 0.5–0.65 |
| Good | 0.65 < R2 < 0.75 | 10 < |PBIAS| < 15 | 0.65–0.75 |
| Very good | 0.75 < R2 < 1 | |PBIAS| < 10 | >0.75 |
| Scores | R2 | PBIAS (%) | NSE |
|---|---|---|---|
| Unsatisfactory | R2 < 0.5 | |PBIAS| > 25 | <0.5 |
| Satisfactory | 0.5 < R2 < 0.65 | 15 < |PBIAS| < 25 | 0.5–0.65 |
| Good | 0.65 < R2 < 0.75 | 10 < |PBIAS| < 15 | 0.65–0.75 |
| Very good | 0.75 < R2 < 1 | |PBIAS| < 10 | >0.75 |
Table 3
Sensitivity and error analysis for 10% increment of the initial parameters
| Scour characteristic | Jet condition | X |  |  | AS | RE | RS |
|---|---|---|---|---|---|---|---|
| Static | Long |  | 2.12 | −0.029 | −0.0138 | −0.12 | −1.24 |
 | 0.055 | −0.031 | −5.69 | −0.13 | −1.33 | ||
| Short |  | 1.924 | −0.092 | −0.0481 | −0.081 | −0.081 | |
 | 0.035 | −0.092 | −2.629 | −0.081 | −0.081 | ||
| Dynamic | Long |  | 6.574 | 1.447 | 0.22 | 1.29 | 12.93 |
 | 0.0074 | 1.1686 | 191.19 | 1.26 | 12.68 | ||
| Short |  | 3.748 | 2.493 | 0.66 | 0.698 | 6.985 | |
 | 0.038 | 2.106 | 65.10 | 0.693 | 6.93 |
| Scour characteristic | Jet condition | X | | | AS | RE | RS |
|---|---|---|---|---|---|---|---|
| Static | Long | | 2.12 | −0.029 | −0.0138 | −0.12 | −1.24 |
| | 0.055 | −0.031 | −5.69 | −0.13 | −1.33 | ||
| Short | | 1.924 | −0.092 | −0.0481 | −0.081 | −0.081 | |
| | 0.035 | −0.092 | −2.629 | −0.081 | −0.081 | ||
| Dynamic | Long | | 6.574 | 1.447 | 0.22 | 1.29 | 12.93 |
| | 0.0074 | 1.1686 | 191.19 | 1.26 | 12.68 | ||
| Short | | 3.748 | 2.493 | 0.66 | 0.698 | 6.985 | |
| | 0.038 | 2.106 | 65.10 | 0.693 | 6.93 |
Table 4
Sensitivity and error analysis for 10% reduction of the initial parameters
| Scour characteristic | Jet condition | X |  |  | AS | RE | RS |
|---|---|---|---|---|---|---|---|
| Static | Long |  | 2.12 | 0.0038 | 0.0018 | 0.016 | 0.163 |
 | 0.055 | 0.008 | 1.4551 | 0.034 | 0.341 | ||
| Short |  | 1.924 | 0.0971 | 0.0505 | 0.085 | 0.858 | |
 | 0.035 | 0.097 | 2.758 | 0.085 | 0.858 | ||
| Dynamic | Long |  | 6.574 | 1.42 | 0.177 | 1.044 | 10.447 |
 | 0.0074 | 1.214 | 163.6 | 1.085 | 10.857 | ||
| Short |  | 3.748 | 2.476 | 0.561 | 0.590 | 5.90 | |
 | 0.0380 | 2.131 | 56.04 | 0.597 | 5.970 |
| Scour characteristic | Jet condition | X | | | AS | RE | RS |
|---|---|---|---|---|---|---|---|
| Static | Long | | 2.12 | 0.0038 | 0.0018 | 0.016 | 0.163 |
| | 0.055 | 0.008 | 1.4551 | 0.034 | 0.341 | ||
| Short | | 1.924 | 0.0971 | 0.0505 | 0.085 | 0.858 | |
| | 0.035 | 0.097 | 2.758 | 0.085 | 0.858 | ||
| Dynamic | Long | | 6.574 | 1.42 | 0.177 | 1.044 | 10.447 |
| | 0.0074 | 1.214 | 163.6 | 1.085 | 10.857 | ||
| Short | | 3.748 | 2.476 | 0.561 | 0.590 | 5.90 | |
| | 0.0380 | 2.131 | 56.04 | 0.597 | 5.970 |