Prediction of evaporation in arid and semi-arid regions: a comparative study using different machine learning models

Figures & data

Figure 1. Map of the selected study locations in Mosul (Station I) and Baghdad (Station II).

Figure 2. Model structures for: (a) CART; (b) CCNN; (c) SVM.

Table 1. The statistical performance metrics of the applied CART model over the training and testing phases at Station I in Mosul.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	70.81	52.39	.75	.92	.56	.75
M2	53.11	37.42	.85	.96	.68	.85
M3	51.31	35.42	.86	.96	.70	.86
M4	48.35	31.38	.88	.96	.73	.88
M5	33.33	21.68	.94	.98	.82	.94
	Testing phase
M1	67.70	51.34	.71	.92	.53	.80
M2	36.35	30.54	.91	.97	.72	.93
M3	91.89	56.65	.46	.86	.48	.58
M4	58.09	41.43	.78	.94	.62	.86
M5	48.89	37.61	.84	.96	.65	.87

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 2. The statistical performance metrics of the applied CCNN model over the training and testing phases at Station I in Mosul.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	41.67	20.38	.91	.97	.83	.91
M2	23.82	8.58	.97	.99	.92	.97
M3	44.81	29.81	.90	.97	.75	.90
M4	46.15	29.54	.89	.97	.75	.89
M5	45.78	29.71	.89	.97	.75	.89
	Testing phase
M1	91.22	69.43	.48	.87	.36	.62
M2	52.64	40.12	.81	.95	.63	.86
M3	68.05	44.27	.70	.92	.59	.74
M4	68.05	44.27	.70	.92	.59	.74
M5	74.17	42.19	.64	.91	.61	.69

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 3. The statistical performance metrics of the applied GEP model over the training and testing phases at Station I in Mosul.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	70.81	52.39	.75	.92	.56	.75
M2	53.11	37.42	.85	.96	.68	.85
M3	51.31	35.42	.86	.96	.70	.86
M4	48.35	31.38	.88	.96	.73	.88
M5	44.46	28.66	.90	.97	.76	.90
	Testing phase
M1	67.70	51.34	.71	.92	.53	.80
M2	36.35	30.54	.91	.97	.72	.93
M3	91.89	56.65	.46	.86	.48	.58
M4	58.09	41.43	.78	.94	.62	.86
M5	61.03	37.94	.75	.93	.65	.79

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 4. The statistical performance metrics of the applied SVM model over the training and testing phases at Station I in Mosul.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	68.14	47.34	.76	.92	.60	.77
M2	51.01	33.40	.87	.96	.72	.87
M3	51.01	33.40	.87	.96	.72	.87
M4	47.72	31.37	.88	.96	.73	.89
M5	45.23	27.44	.89	.97	.77	.90
	Testing phase
M1	61.15	47.88	.76	.93	.56	.80
M2	35.76	27.71	.91	.97	.74	.92
M3	73.41	40.10	.64	.90	.63	.69
M4	73.41	40.10	.64	.90	.63	.69
M5	58.20	33.77	.77	.94	.69	.79

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 5. The statistical performance metrics of the applied CART model over the training and testing phases at Station II in Baghdad.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	40.11	28.52	.94	.98	.81	.94
M2	44.13	32.13	.93	.98	.79	.93
M3	36.68	25.48	.95	.98	.83	.95
M4	32.95	23.46	.96	.99	.84	.96
M5	31.06	21.27	.96	.99	.86	.96
	Testing phase
M1	86.04	65.10	.72	.92	.55	.74
M2	65.18	46.93	.84	.95	.67	.85
M3	53.76	40.03	.89	.97	.72	.92
M4	51.22	39.10	.90	.97	.73	.92
M5	49.38	36.81	.91	.97	.74	.94

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 6. The statistical performance metrics of the applied CCNN model over the training and testing phases at Station II in Baghdad.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	73.54	56.31	.82	.95	.63	.82
M2	52.19	39.66	.91	.97	.74	.91
M3	46.73	34.53	.93	.98	.77	.93
M4	46.36	34.60	.93	.98	.77	.93
M5	43.37	32.01	.94	.98	.79	.94
	Testing phase
M1	84.29	66.87	.73	.92	.53	.74
M2	57.46	45.78	.87	.96	.68	.89
M3	50.30	37.84	.90	.97	.73	.95
M4	47.49	37.92	.91	.97	.73	.95
M5	37.88	29.63	.94	.98	.79	.96

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 7. The statistical performance metrics of the applied GEP model over the training and testing phases at Station II in Baghdad.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	83.38	65.69	.78	.93	.57	.78
M2	67.89	54.33	.85	.95	.64	.85
M3	67.89	54.33	.85	.95	.64	.85
M4	45.93	33.55	.93	.98	.78	.93
M5	45.94	33.91	.93	.98	.78	.93
	Testing phase
M1	83.45	70.18	.74	.92	.51	.74
M2	64.84	53.94	.84	.95	.62	.89
M3	54.58	43.09	.89	.97	.70	.95
M4	48.10	36.64	.91	.98	.74	.96
M5	36.63	28.80	.94	.98	.80	.95

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Table 8. The statistical performance metrics of the applied SVM model over the training and testing phases at Station II in Baghdad.

Model	Performance metrics
	Training phase
	RMSE	MAE	NSE	WI	LMI	R^2
M1	80.82	59.77	.79	.94	.61	.79
M2	52.86	37.47	.91	.97	.75	.91
M3	52.86	37.47	.91	.97	.75	.91
M4	40.11	28.52	.94	.98	.81	.94
M5	41.34	28.29	.94	.98	.81	.94
	Testing phase
M1	81.74	66.42	.75	.92	.54	.75
M2	55.49	41.22	.88	.97	.71	.89
M3	45.38	34.03	.92	.98	.76	.95
M4	43.78	32.69	.92	.98	.77	.93
M5	32.27	24.75	.96	.99	.82	.97

Note: LMI = Legate and McCabe’s Index; MAE = mean absolute error; NSE = Nash–Sutcliffe coefficient; R² = determination coefficient; RMSE = root mean square error; WI = Willmott’s Index. Bold font denotes lowest RMSE value in each phase.

Figure 7. Taylor diagram visualizations for the performance of the applied predictive models at Station I: (a) CART; (b) CCNN; (c) GEP; (d) SVM.

Figure 8. Taylor diagram visualizations for the performance of the applied predictive models at Station II: (a) CART; (b) CCNN; (c) GEP; (d) SVM.

Figure 9. Time series data visualization between the performance of the applied predictive models (dark blue lines) and the observed evaporation process (black lines) at Station I: (a) CART; (b) CCNN; (c) GEP; (d) SVM.

Figure 10. Time series data visualization between the performance of the applied predictive models (dark blue lines) and the observed evaporation process (black lines) at Station II: (a) CART; (b) CCNN; (c) GEP; (d) SVM.