Comparative analysis of classification techniques and input-output patterns for monthly rainfall prediction

Figures & data

Figure 1. Geographical location of karkheh basin and selected rainfall stations.

Figure 2. Rainfall time series in the rain gauge stations of Sarab Seyed Ali, Kaka Reza, Afrine (kashkan) and Pol Dokhtar.

Table 1. Characteristics of selected synoptic stations in the Karkhe basin.

Row	Station name	Height	Longitude	Latitude	Row	Station name	Height	Longitude	Latitude
1	Abdolkhan	40	48.38	31.83	18	Kaka Reza	1530	48.25	33.71
2	Afrine (Kashkan)	800	47.87	33.31	19	Kanal Varayene	1759	48.4	34.08
3	Aghajan Bolaghi	1802	48.05	34.85	20	Kashenbele Lak	46.64	34.29	1500
4	Baba Pir Ali	1917	48.35	34.63	21	Kheir Abad	1770	48.57	34.47
5	Badr Gard	1274	46.75	33.95	22	Murmuri	485	47.72	32.75
6	Baskele Boorim	1460	46.48	33.94	23	Noor Abad	1780	47.95	34.06
7	Cham Anjir	1140	48.22	33.43	24	Pay Pol	125	48.13	32.4
8	Cham Gaz	385	47.82	32.95	25	Pihan	1820	48.87	34.13
9	Dare Tang Alashtar	1720	48.25	33.91	26	Pol Chehr	1280	47.43	34.34
10	Dartoot	1110	46.68	33.74	27	Pol Dokhtar	700	47.77	33.15
11	Dehno (Herood)	1800	48.75	33.5	28	Pol Zal	335	48.08	32.82
12	Doab Merk	1310	46.79	34.55	29	Ravansar	1343	46.65	34.7
13	Eslam Abad	1349	46.52	34.11	30	Sarab Seyed Ali	1520	48.2	33.78
14	Firoozan	1503	48.12	34.35	31	Sarabi	1925	48.48	34.53
15	Halilan (Simereh)	1000	47.23	33.73	32	Tang Siab	880	47.2	33.38
16	Heidar Abad	1290	47.45	34.43	33	Vargach	703	46.84	33.56
17	Jelogir	370	47.83	32.93	34	Vesaj	1650	48.22	34.32

Table 2. Types of kernel functions (Ren, Hu, & Miao, 2016).

Kernel	Formula	Optimization Parameter(s)
Linear	$\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}}.{\mathrm{x}}_{\mathrm{j}}\right)={\mathrm{x}}_{\mathrm{i}}\ast {\mathrm{x}}_{\mathrm{j}}$	-
Polynomial	$\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}}.{\mathrm{x}}_{\mathrm{j}}\right)={\left(\mathit{\gamma }\left({\mathrm{x}}_{\mathrm{i}}\ast {\mathrm{x}}_{\mathrm{j}}\right)+\mathrm{C}\right)}^{\mathrm{d}}$	$\mathit{\gamma }.\mathrm{C}.\mathrm{d}$
Hyperbolic tangent	$\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}}.{\mathrm{x}}_{\mathrm{j}}\right)=\tanh \left(\mathit{\gamma }{\mathrm{x}}_{\mathrm{i}}\ast {\mathrm{x}}_{\mathrm{j}}+\mathrm{C}\right)$	$\mathit{\gamma }.\mathrm{C}$
RBF	$\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}}.{\mathrm{x}}_{\mathrm{j}}\right)=\exp \left(-\mathit{\gamma }{\left|{\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{j}}\right|}^2\right)$	$\mathit{\gamma }$

Figure 3. The general structure of the SA algorithm.

Figure 4. Flow structure of SVM-SA model (Bashar, Nozari, Marofi, Mohamadi, & Ahadiiman, 2023).

Figure 5. Structure of four machine learning systems: SISO, SIMO, MISO and MIMO.

Figure 6. The framework of study identification and selection process.

Figure 7. Comparison of observed and predicted rainfall in the validation stage by Monte Carlo and Thomas Fiering models at Sarabi rain gauge station.

Table 3. The results related to the prediction of rainfall in the 10 studied rain gauge stations using the Monte Carlo and Thomas Fiering methods.

Station		Validation step
Row	Name	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	0.17	51.75	1.31	−0.03
2	Baba Pir Ali	0.23	38.34	1.19	0.11
3	Cham Anjir	0.23	48.75	1.31	−0.25
4	Cham Gaz	0.21	56.58	1.45	−0.27
5	Kaka Reza	0.16	66.35	1.47	−0.28
6	Kheir Abad	0.22	39.78	1.24	0.05
7	Pol Dokhtar	0.27	42.74	1.21	−0.01
8	Sarab Seyed Ali	0.22	50.66	1.24	−0.01
9	Sarabi	0.32	42.06	1.23	−0.03
10	Tang Siab	0.21	44.54	1.65	−0.58

Figure 8. Comparison of observed and predicted rainfall in the calibration and validation stage using SIMO method and with the help of SVM-SA model in Sarabi rain gauge station.

Table 4. Results related to rainfall predicting in 10 studied rain gauge stations by SIMO method and with the help of SVM-SA.

Station		Calibration step				Validation step
Row	Name	R^2	RMSE (mm)	SE	NSE	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	0.61	30.47	0.74	0.61	0.49	36.46	0.92	0.49
2	Baba Pir Ali	0.81	20.64	0.54	0.80	0.44	27.48	0.85	0.33
3	Cham Anjir	0.65	27.66	0.7	0.65	0.44	33.04	0.89	0.43
4	Cham Gaz	0.71	28.8	0.71	0.71	0.51	35.31	0.91	0.50
5	Kaka Reza	0.68	31.71	0.67	0.68	0.53	40.98	0.91	0.51
6	Kheir Abad	0.73	17.86	0.59	0.73	0.38	32.3	1.01	0.37
7	Pol Dokhtar	0.63	26.45	0.79	0.63	0.5	30.3	0.86	0.49
8	Sarab Seyed Ali	0.64	31.12	0.72	0.64	0.54	34.47	0.85	0.53
9	Sarabi	0.9	13.21	0.36	0.89	0.58	27.05	0.79	0.57
10	Tang Siab	0.64	26.44	0.75	0.63	0.45	26.44	0.98	0.44

Figure 9. Comparison of observed and predicted rainfall in the calibration and validation stage using MIMO method and with the help of SVM-SA model in Sarabi rain gauge station.

Table 5. Results related to rainfall predicting in 10 studied rain gauge stations by MIMO method and with the help of SVM-SA.

Station name			Calibration step				Validation step
Row	Dependent	Independent	R^2	RMSE (mm)	SE	NSE	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	Pol Dokhtar	0.95	11.06	0.27	0.95	0.80	23.8	0.61	0.79
2	Baba Pir Ali	Sarabi	0.92	12.05	0.34	0.92	0.77	20.32	0.55	0.77
3	Cham Anjir	Dehno	0.91	13.48	0.36	0.91	0.63	27.8	0.71	0.63
4	Cham Gaz	Jelogir	0.96	10.61	0.24	0.96	0.8	21.56	0.6	0.80
5	Kaka Reza	Sarab Seyed Ali	0.90	18.59	0.40	0.90	0.75	27.66	0.57	0.75
6	Kheir Abad	Sarabi	0.98	5.72	0.19	0.97	0.73	22	0.64	0.64
7	Pol Dokhtar	Afrine (Kashkan)	0.95	10.28	0.3	0.94	0.83	17.99	0.59	0.82
8	Sarab Seyed Ali	Kaka Reza	0.88	18.38	0.43	0.88	0.73	25.45	0.58	0.73
9	Sarabi	Kheir Abad	0.99	4.29	0.12	0.99	0.58	27.38	0.69	0.58
10	Tang Siab	Afrine (Kashkan)	0.90	13.86	0.42	0.89	0.84	16.56	0.49	0.84

Figure 10. Comparison of observed and predicted rainfall in the calibration and validation stage using SISO method and with the help of SVM-SA model in Sarabi rain gauge station.

Table 6. Results related to rainfall prediction in 10 studied rain gauge stations by the SISO method and with the help of SVM-SA.

Station name			Calibration step				Validation step
Row	Dependent	Independent	R^2	RMSE (mm)	SE	NSE	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	Pol Dokhtar	0.91	14.94	0.36	0.91	0.91	16.5	0.42	0.90
2	Baba Pir Ali	Sarabi	0.83	17.65	0.5	0.83	0.89	14.34	0.39	0.89
3	Cham Anjir	Dehno	0.77	21.32	0.57	0.77	0.74	23.42	0.6	0.74
4	Cham Gaz	Jelogir	0.88	19.23	0.44	0.88	0.8	21.85	0.6	0.79
5	Kaka Reza	Sarab Seyed Ali	0.78	27.05	0.58	0.78	0.84	22.67	0.46	0.83
6	Kheir Abad	Sarabi	0.93	9.58	0.31	0.93	0.89	12.5	0.36	0.88
7	Pol Dokhtar	Afrine (Kashkan)	0.9	13.96	0.4	0.90	0.87	16.88	0.55	0.84
8	Sarab Seyed Ali	Kaka Reza	0.78	24.54	0.57	0.78	0.85	18.88	0.43	0.85
9	Sarabi	Kheir Abad	0.93	10.61	0.3	0.93	0.92	12.04	0.3	0.92
10	Tang Siab	Afrine (Kashkan)	0.83	17.5	0.52	0.83	0.82	17.35	0.51	0.82

Figure 11. Comparison of observed and predicted rainfall in the calibration and validation stage using SISO method and with the help of LR model in Sarabi rain gauge station.

Table 7. Results related to rainfall predicting in 10 studied rain gauge stations by SISO method and with the help of LR.

	Station name		Calibration step				Validation step
Row	Dependent	Independent	R^2	RMSE (mm)	SE	NSE	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	Pol Dokhtar	0.9	15.65	0.38	0.90	0.91	16.42	0.42	0.90
2	Baba Pir Ali	Sarabi	0.83	17.65	0.5	0.83	0.89	14.33	0.39	0.89
3	Cham Anjir	Dehno	0.74	22.68	0.6	0.74	0.75	22.91	0.59	0.75
4	Cham Gaz	Jelogir	0.86	20.85	0.48	0.86	0.79	22.02	0.61	0.79
5	Kaka Reza	Sarab Seyed Ali	0.77	27.47	0.59	0.77	0.84	22.72	0.46	0.83
6	Kheir Abad	Sarabi	0.93	9.57	0.31	0.93	0.92	10.39	0.3	0.92
7	Pol Dokhtar	Afrine (Kashkan)	0.9	13.96	0.4	0.90	0.91	13.41	0.44	0.90
8	Sarab Seyed Ali	Kaka Reza	0.77	25.15	0.58	0.77	0.84	19.5	0.45	0.84
9	Sarabi	Kheir Abad	0.93	10.78	0.31	0.93	0.92	11.81	0.3	0.92
10	Tang Siab	Afrine (Kashkan)	0.83	17.56	0.53	0.83	0.82	17.45	0.51	0.82

Figure 12. Comparison of observed and predicted rainfall in the calibration and validation stage using the MISO method and with the help of the SVM-SA model at the Sarabi rain gauge station.

Table 8. The results related to rainfall predicting in 10 studied rain gauge stations using the MISO method and with the help of SVM-SA.

	Station name			Calibration step				Validation step
Row	Dependent	Independent	Independent	R^2	RMSE (mm)	SE	NSE	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	Pol Dokhtar	Tang Siab	0.92	14.2	0.34	0.92	0.90	14.5	0.39	0.90
2	Baba Pir Ali	Sarabi	Kheir Abad	0.83	17.68	0.50	0.83	0.86	15.85	0.41	0.92
3	Cham Anjir	Kaka Reza	Sarab Seyed Ali	0.86	18.04	0.45	0.86	0.81	17.94	0.54	0.79
4	Cham Gaz	Jelogir	Pol Zal	0.94	13.74	0.31	0.94	0.92	17.33	0.39	0.91
5	Kaka Reza	Cham Anjir	Dehno	0.82	23.83	0.51	0.78	0.67	28.22	0.7	0.74
6	Kheir Abad	Baba Pir Ali	Sarabi	0.93	8.93	0.31	0.93	0.92	10.12	0.29	0.92
7	Pol dokhtar	Afrine (Kashkan)	Tang Siab	0.92	12.34	0.36	0.92	0.88	14.06	0.45	0.88
8	Sarab Seyed Ali	Cham Anjir	Kaka Reza	0.87	18.5	0.43	0.87	0.87	16.48	0.41	0.86
9	Sarabi	Baba Pir Ali	Kheir Abad	0.94	9.63	0.28	0.94	0.93	11.05	0.28	0.93
10	Tang Siab	Pol Dokhtar	Afrine (Kashkan)	0.84	16.81	0.50	0.86	0.82	17.27	0.54	0.82

Figure 13. Comparison of observed and predicted rainfall in the calibration and validation stage using the MISO method and with the help of the MLR model at the Sarabi rain gauge station.

Table 9. The results related to rainfall predicting in the 10 studied rain gauge stations using the MISO method and with the help of MLR.

	Station name			Calibration step				Validation step
Row	Dependent	Independent	Independent	R^2	RMSE (mm)	SE	NSE	R^2	RMSE (mm)	SE	NSE
1	Afrine (Kashkan)	Pol Dokhtar	Tang Siab	0.92	14.2	0.34	0.92	0.90	14.5	0.39	0.90
2	Baba Pir Ali	Sarabi	Kheir Abad	0.83	17.68	0.50	0.83	0.86	15.85	0.41	0.92
3	Cham Anjir	Kaka Reza	Sarab Seyed Ali	0.86	18.04	0.45	0.85	0.81	17.94	0.54	0.80
4	Cham Gaz	Jelogir	Pol Zal	0.94	13.74	0.31	0.90	0.92	17.33	0.39	0.88
5	Kaka Reza	Cham Anjir	Dehno	0.82	23.83	0.51	0.73	0.67	28.22	0.7	0.72
6	Kheir Abad	Baba Pir Ali	Sarabi	0.93	8.93	0.31	0.93	0.92	10.12	0.29	0.96
7	Pol dokhtar	Afrine (Kashkan)	Tang Siab	0.92	12.34	0.36	0.92	0.88	14.06	0.45	0.88
8	Sarab Seyed Ali	Cham Anjir	Kaka Reza	0.87	18.5	0.43	0.87	0.87	16.48	0.41	0.92
9	Sarabi	Baba Pir Ali	Kheir Abad	0.94	9.63	0.28	0.93	0.93	11.05	0.28	0.94
10	Tang Siab	Pol Dokhtar	Afrine (Kashkan)	0.84	16.81	0.50	0.84	0.82	17.27	0.54	0.83

Table 10. Average indicators related to monthly rainfall prediction in the studied rain gauge stations.

Method	Model	Ave SE	Std SE
Classic	Monte Carlo/Thomas Firing	1.29	0.23
SIMO	SVM-SA	0.99	0.25
MIMO	SVM-SA	0.70	0.18
SISO	SVM-SA	0.54	0.17
	LR	0.52	0.16
MISO	SVM-SA	0.54	0.18
	MLR	0.53	0.17

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