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Five statistical indices were taken to quantify the agreement between the observed and predicted non-dimensional static and dynamic scour depths for long- and short-impinging jets. The statistical values are listed in Tables 5–8. It can be noticed that the performance of the equation proposed by Aderibigbe & Rajaratnam (1996) for the estimation of non-dimensional static scour depth under long-impinging jets (Table 5) is found to be the best among all the statistical indicators, i.e., RMSE, MAE, MAPE, NSE, and KGE. These results are in line with the graphical analysis. The Equation (11) proposed by Chen et al. (2022) gives the second-highest agreements between observed and computed data. The NSE value of these two equations was greater than 0.5, indicating that the performance of the predicted values is satisfactory.

Table 5

Statistical analysis of static scour depth under long-impinging jet

S. No.	Author's	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	0.046	0.721	0.037	0.222	0.862
2.	Ansari et al. (2003)	0.076	0.238	0.058	0.253	0.520
3.	Chakravarti et al. (2014)	0.104	−0.425	0.081	0.343	0.276
4.	Amin et al. (2021)	0.072	0.324	0.055	0.260	0.600
5.	Shakya et al. (2022)	0.075	0.267	0.064	0.311	0.655
6.	Chen et al. (2022)	0.051	0.652	0.042	0.218	0.790

S. No.	Author's	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	0.046	0.721	0.037	0.222	0.862
2.	Ansari et al. (2003)	0.076	0.238	0.058	0.253	0.520
3.	Chakravarti et al. (2014)	0.104	−0.425	0.081	0.343	0.276
4.	Amin et al. (2021)	0.072	0.324	0.055	0.260	0.600
5.	Shakya et al. (2022)	0.075	0.267	0.064	0.311	0.655
6.	Chen et al. (2022)	0.051	0.652	0.042	0.218	0.790

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Table 6

Statistical analysis of static scour depth under short-impinging jet

S. No.	Authors	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	0.988	−0.250	0.616	0.4133	−0.0214
2.	Ansari et al. (2003)	0.848	0.078	0.472	0.2783	0.1119
3.	Chakravarti et al. (2014)	0.769	0.242	0.4109	0.2450	0.1888
4.	Amin et al. (2021)	0.178	0.959	0.1343	0.1374	0.9791
5.	Shakya et al. (2022)	0.302	0.882	0.1609	0.1291	0.7787
6.	Chen et al. (2022)	1.042	−0.390	0.6832	0.4896	−0.0691

S. No.	Authors	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	0.988	−0.250	0.616	0.4133	−0.0214
2.	Ansari et al. (2003)	0.848	0.078	0.472	0.2783	0.1119
3.	Chakravarti et al. (2014)	0.769	0.242	0.4109	0.2450	0.1888
4.	Amin et al. (2021)	0.178	0.959	0.1343	0.1374	0.9791
5.	Shakya et al. (2022)	0.302	0.882	0.1609	0.1291	0.7787
6.	Chen et al. (2022)	1.042	−0.390	0.6832	0.4896	−0.0691

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Table 7

Statistical analysis of dynamic scour depth under long-impinging jet

S. No.	Authors	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	0.84	−0.426	0.673	0.700	0.362
2.	Chakravarti et al. (2014)	1.762	−5.273	1.192	1.113	−0.896
3.	Amin et al. (2021)	2.428	−10.908	1.493	1.057	−1.867
4.	Kartal & Emiroglu (2021)	0.692	0.032	0.536	0.584	0.497
5.	Chen et al. (2022)	0.609	0.248	0.425	0.389	0.553

S. No.	Authors	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	0.84	−0.426	0.673	0.700	0.362
2.	Chakravarti et al. (2014)	1.762	−5.273	1.192	1.113	−0.896
3.	Amin et al. (2021)	2.428	−10.908	1.493	1.057	−1.867
4.	Kartal & Emiroglu (2021)	0.692	0.032	0.536	0.584	0.497
5.	Chen et al. (2022)	0.609	0.248	0.425	0.389	0.553

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Table 8

Statistical analysis of dynamic scour depth under short-impinging jet

S. No.	Authors	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	62.79	−466.9	28.976	4.337	−19.79
2.	Chakravarti et al. (2014)	2.89	0.0069	2.454	0.944	0.256
3.	Amin et al. (2021)	3.309	−0.299	2.099	0.749	0.320
4.	Kartal & Emiroglu (2021)	3.106	−0.145	2.136	0.576	0.105
5.	Chen et al. (2022)	2.660	0.160	1.560	0.301	0.182

S. No.	Authors	RMSE	NSE	MAE	MAPE	KGE
1.	Aderibigbe & Rajaratnam (1996)	62.79	−466.9	28.976	4.337	−19.79
2.	Chakravarti et al. (2014)	2.89	0.0069	2.454	0.944	0.256
3.	Amin et al. (2021)	3.309	−0.299	2.099	0.749	0.320
4.	Kartal & Emiroglu (2021)	3.106	−0.145	2.136	0.576	0.105
5.	Chen et al. (2022)	2.660	0.160	1.560	0.301	0.182

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