A minimalistic approach for evapotranspiration estimation using the Prophet model

Figures & data

Table 1. General information of meteorological stations and basic statistical parameters of the meteorological variables for the study period (1980–2017) for four stations located in the southern part of Japan. SD: standard deviation.

Station name	Latitude		Longitude		Altitude (m a.s.l.)	Koppen climate classification
Aso San	32º52.8´N		131º04.4´E		1592	Dfb
Kumamoto	32º 48.8´N		130º 42.4´E		38	Dfa
Miyazaki	31º 52.6´N		131º 26.9´E		6	Cfa
Oita	33º 28.7´N		131º 44.2´E		5	Cfa
	Station: Aso San
	Tavg	Tmin	Tmax	Sh (h)	Wind	Rh	ETo
Statistical parameters	(ºC)	(ºC)	(ºC)	Sh (h)	(km/d)	(%)	(mm/month)
Mean	9.84	6.69	13.5	4.34	397.04	81.59	65.1
SD	7.77	8.09	7.74	1.19	43.32	6.08	27.19
Kurtosis	–1.35	–1.37	–1.26	–0.07	0.39	–0.1	–1.07
Skewness	–0.13	–0.03	–0.21	0.07	0.08	–0.22	0
Minimum	–5.6	–8.6	–2.7	1.2	268	62	18.91
Maximum	22.1	19.3	26.4	8.5	553	96	141.05
	Station: Kumamoto
Mean	16.93	12.48	21.98	5.53	183.55	70.69	93.38
SD	7.87	8.29	7.77	1.25	26.99	5.19	38.95
Kurtosis	–1.36	–1.39	–1.31	–0.31	–0.12	–0.1	–1.11
Skewness	–0.04	0.06	–0.11	0.15	0.33	0.24	0.17
Minimum	2.7	–1.6	7.2	1.8	121	57	35.03
Maximum	29.6	26	35.2	9.3	268	87	181.66
	Station: Miyazaki
Mean	17.62	13.45	22.25	5.85	258.98	73.29	97.07
SD	7.05	7.69	6.53	1.31	36.25	6.47	31.99
Kurtosis	–1.34	–1.37	–1.28	0.16	–0.05	–0.52	–0.55
Skewness	–0.02	0.01	–0.01	–0.22	0.33	–0.29	0.5
Minimum	4.8	–0.2	10.4	1.96	172.8	56	45.36
Maximum	29.8	25.9	34.7	9.73	380.16	90	192.51
	Station: Oita
Mean	16.43	12.48	20.78	5.53	223.03	69.59	93.63
SD	7.4	7.74	7.36	1.23	29.01	6.89	32.56
Kurtosis	–1.34	–1.37	–1.27	0.26	–0.36	–0.69	–0.7
Skewness	0.03	0.09	0.02	0.31	0.04	0.05	0.43
Minimum	3.7	–0.6	7.3	2.43	138.24	53	43.96
Maximum	29.3	25.6	34.6	10.05	293.76	88	185.07

Figure 1. Location of meteorological stations used in this study in Kyushu Islands in the southern part of Japan.

Table 2. Input variables for Prophet, SVR models and empirical formulas.

Models	Input Variables	Input variables for Empirical formulas
SVR-1 and P-1	Tavg	Thornthwaite method
SVR-2 and P-2	Tmax	-
SVR-3 and P-3	Tmin	-
SVR-4 and P-4	Rh	-
SVR-5 and P-5	U2	-
SVR-6 and P-6	Sh	-
SVR-7 and P-7	Tmin and Tmax	Hargreaves method
SVR-8 and P-8	Tmin, Tmax and Rh	-
SVR-9 and P-9	Tmin, Tmax and Sh	-
SVR-10 and P-10	Tmin, Tmax and U2	-
SVR-11 and P-11	Tmin,Tmax,U2 and Rh	-
SVR-12 and P-12	Tmin,Tmax,U2, Rh and Sh	Penman-Monteith FAO-56 method

Table 3. Comparison between SVR and Prophet model with sole input of climatic variable for the test period.

Station	SVR						Prophet
	Model	RMSE (mm)	RSR	NSE	R^2	KGE	Model	RMSE (mm)	RSR	NSE	R^2	KGE
Aso San	SVR-1	13.26	0.47	0.78	0.79	0.87	P-1	10.83	0.38	0.85	0.88	0.87
	SVR-2	13.51	0.48	0.77	0.78	0.86	P-2	9.09	0.32	0.89	0.91	0.92
	SVR-3	13.92	0.49	0.75	0.76	0.82	P-3	11.66	0.41	0.83	0.87	0.86
	SVR-4	23.98	0.85	0.27	0.29	0.24	P-4	4.9	0.17	0.97	0.97	0.97
	SVR-5	25.77	0.91	0.16	0.20	0.06	P-5	11.67	0.41	0.83	0.88	0.86
	SVR-6	22.56	0.80	0.35	0.38	0.40	P-6	7.22	0.26	0.93	0.97	0.91
Kumamoto	SVR-1	13.86	0.35	0.87	0.88	0.92	P-1	17.62	0.45	0.80	0.92	0.85
	SVR-2	15.96	0.41	0.83	0.85	0.90	P-2	13.93	0.35	0.87	0.94	0.89
	SVR-3	15.96	0.41	0.83	0.85	0.90	P-3	20.17	0.51	0.73	0.91	0.82
	SVR-4	38.70	0.98	0.02	0.03	−0.16	P-4	7.64	0.19	0.96	0.96	0.98
	SVR-5	33.43	0.85	0.27	0.29	0.25	P-5	14.88	0.38	0.85	0.93	0.88
	SVR-6	29.10	0.74	0.45	0.45	0.51	P-6	7.59	0.19	0.96	0.98	0.95
Miyazaki	SVR-1	14.96	0.45	0.79	0.82	0.89	P-1	15.59	0.47	0.78	0.85	0.86
	SVR-2	13.84	0.42	0.82	0.83	0.89	P-2	13.64	0.41	0.83	0.89	0.88
	SVR-3	16.35	0.49	0.75	0.78	0.87	P-3	16.51	0.5	0.75	0.84	0.84
	SVR-4	31.53	0.95	0.08	0.11	0.13	P-4	8.2	0.25	0.94	0.94	0.97
	SVR-5	32.52	0.98	0.02	0.02	−0.19	P-5	12.16	0.37	0.86	0.88	0.87
	SVR-6	28.26	0.85	0.26	0.29	0.24	P-6	8.21	0.25	0.94	0.96	0.92
Oita	SVR-1	14.84	0.43	0.81	0.82	0.89	P-1	14.55	0.42	0.82	0.87	0.85
	SVR-2	13.46	0.39	0.84	0.85	0.90	P-2	12.41	0.36	0.87	0.91	0.89
	SVR-3	17.10	0.50	0.75	0.77	0.87	P-3	16.03	0.47	0.78	0.86	0.83
	SVR-4	32.76	0.95	0.08	0.12	0.20	P-4	8.5	0.25	0.94	0.95	0.95
	SVR-5	30.74	0.89	0.19	0.22	0.24	P-5	15.24	0.44	0.80	0.88	0.86
	SVR-6	25.12	0.73	0.46	0.46	0.52	P-6	7.64	0.22	0.95	0.98	0.91

Figure 2. Comparison of observed and estimated ETo by different models (SVR-1, P-1 and Thornthwaite) with Tavg as input parameters for the test period.

Figure 3. Correlation coefficient between ET_o and climatic variables for the test period.

Table 4. Comparison between SVR and Prophet model with multiple input of climatic variables for the test period.

Station	SVR						Prophet
	Model	RMSE (mm)	RSR	NSE	R^2	KGE	Model	RMSE (mm)	RSR	NSE	R^2	KGE
Aso San	SVR-7	9.33	0.33	0.89	0.94	0.90	P-7	6.61	0.23	0.94	0.95	0.97
	SVR-8	4.25	0.15	0.98	0.98	0.97	P-8	4.56	0.16	0.97	0.98	0.96
	SVR-9	5.74	0.20	0.96	0.96	0.96	P-9	4.81	0.17	0.97	0.98	0.96
	SVR-10	8.65	0.31	0.90	0.93	0.93	P-10	6.64	0.23	0.94	0.95	0.97
	SVR-11	4.16	0.15	0.98	0.98	0.98	P-11	4.63	0.16	0.97	0.98	0.96
	SVR-12	3.04	0.11	0.99	0.99	0.99	P-12	3.32	0.12	0.99	0.99	0.98
Kumamoto	SVR-7	9.50	0.94	0.94	0.94	0.96	P-7	9.76	0.25	0.94	0.96	0.93
	SVR-8	7.77	0.96	0.96	0.96	0.97	P-8	6.37	0.16	0.97	0.98	0.96
	SVR-9	9.00	0.95	0.95	0.95	0.94	P-9	5.4	0.14	0.98	0.98	0.98
	SVR-10	8.31	0.21	0.95	0.96	0.96	P-10	6.68	0.17	0.97	0.97	0.97
	SVR-11	7.94	0.2	0.96	0.96	0.96	P-11	6.91	0.18	0.97	0.99	0.94
	SVR-12	6.63	0.17	0.97	0.97	0.97	P-12	3.86	0.1	0.99	0.99	0.97
Miyazaki	SVR-7	11.86	0.36	0.87	0.87	0.91	P-7	11.4	0.34	0.88	0.94	0.91
	SVR-8	8.23	0.25	0.94	0.94	0.96	P-8	4.99	0.15	0.98	0.98	0.97
	SVR-9	9.94	0.30	0.91	0.93	0.86	P-9	7.11	0.21	0.95	0.97	0.94
	SVR-10	12.57	0.38	0.85	0.89	0.87	P-10	7.47	0.23	0.95	0.96	0.94
	SVR-11	8.05	0.24	0.94	0.94	0.92	P-11	4.79	0.14	0.98	0.98	0.98
	SVR-12	6.59	0.2	0.96	0.97	0.94	P-12	3.12	0.09	0.99	0.99	0.99
Oita	SVR-7	8.14	0.24	0.94	0.94	0.95	P-7	13.06	0.38	0.85	0.90	0.91
	SVR-8	8.14	0.24	0.94	0.94	0.95	P-8	7.22	0.21	0.96	0.98	0.94
	SVR-9	6.34	0.18	0.97	0.97	0.95	P-9	6.9	0.2	0.96	0.98	0.93
	SVR-10	8.13	0.24	0.94	0.94	0.93	P-10	10.56	0.31	0.90	0.93	0.93
	SVR-11	8.19	0.24	0.94	0.94	0.95	P-11	6.08	0.18	0.97	0.98	0.96
	SVR-12	5.74	0.17	0.97	0.97	0.98	P-12	3.91	0.11	0.99	0.99	0.98

Figure 4. Comparison of observed and estimated ETo by different models (SVR-7, P-7 and Hargreaves) with Tmin and Tmax as input parameters for the test period.

Figure 5. Comparison of accuracy of models with different input combinations for the test period.

Figure 6. Comparison of observed and estimated ETo by the best models (SVR-12 and P-12) for the test period.

Figure 7. Comparison of accuracy of SVR (SVR-1 to SVR-12) and Prophet (P-1 to P-12) models with 12 different input combinations for the test period.