Evaporation process modelling over northern Iran: application of an integrative data-intelligence model with the krill herd optimization algorithm

Figures & data

Figure 1. Map showing location of Iran and the location of the investigated weather stations, Anzali and Astara.

Table 1. Basic statistics of meteorological variables for Anzali station. SD: standard deviation; T: temperature; RH: relative humidity.

Parameter	Tmax	RHmax	RHmin	Rainfall	Wind speed	Sunshine hours	Pan evaporation
	(°C)	(%)	(%)	(mm/d)	(knot)	(h)	(mm/d)
Mean	19.5	92.5	73.1	4.8	6.7	5.3	2.8
SD	8.0	5.8	13.3	13.4	3.3	4.4	2.3
Skewness	–0.06	–2.28	–1.17	4.38	1.47	0.14	0.80
Max	36.0	100.0	100.0	128.9	27.0	13.8	10.1
Min	–0.2	30.0	10.0	0.0	0.0	0.0	0.0

Table 2. Basic statistics of meteorological variables for Astara station.

Parameter	Tmax	Tmin	Tmean	RHmax	RHmin	RHmean	Rainfall	Sunshine hours	Pan evaporation
	(°C)	(°C)	(°C)	(%)	(%)	(%)	(mm/d)	(h)	(mm/d)
Mean	19.6	12.3	15.9	92.6	63.6	78.1	3.4	5.2	2.5
SD	8.7	7.4	7.9	6.1	16.2	10.2	10.1	4.4	2.2
Skewness	–0.05	–0.16	–0.08	–2.16	–0.49	–0.78	5.50	0.21	0.97
Max	36.6	28.0	31.2	100.0	100.0	100.0	122.3	13.5	10.1
Min	–1.6	–7.8	–3.6	51.0	8.0	32.0	0.0	0.0	0.0

Table 3. Gamma test results showing the relative importance of input meteorological variables. Bold indicates best fit. WS: wind speed; SH: sunshine hours; γ: gamma value.

Station	Removed variable	V ratio	Standard error	Slope of the regression line	γ
Anzali	-	0.160	0.0017	0.025	0.040
	Tmax	0.161	0.0008	0.029	0.041
	Tmin	0.155	0.0013	0.043	0.039
	Tmean	0.158	0.0010	0.033	0.039
	RHmax	0.160	0.0016	0.031	0.041
	RHmin	0.162	0.0006	0.024	0.041
	RHmean	0.154	0.0009	0.037	0.038
	Rainfall	0.167	0.0009	0.034	0.042
	WS	0.173	0.0019	0.019	0.043
	SH	0.188	0.0012	0.028	0.047
Astara	-	0.159	0.0006	0.035	0.040
	Tmax	0.161	0.0008	0.042	0.041
	Tmin	0.166	0.0009	0.032	0.042
	Tmean	0.164	0.0013	0.033	0.041
	RHmax	0.173	0.0009	0.019	0.043
	RHmin	0.166	0.0005	0.028	0.041
	RHmean	0.164	0.0012	0.029	0.041
	Rainfall	0.167	0.0014	0.041	0.042
	WS	0.158	0.0012	0.066	0.039
	SH	0.181	0.0010	0.063	0.045

Table 4. Optimal values of MLP, SVM and MLP-KH parameters for Anzali and Astara weather stations.

Parameter	Anzali			Astara
	MLP	SVM	MLP-KH	MLP	SVM	MLP-KH
Learning rate	0.001	–	–	0.001	–	–
Momentum	0.9	–	–	0.9	–	–
Number of initial input variables	9	9	9	9	9	9
Number of final input variables	6	6	6	8	8	8
Number of hidden layers	1	–	1	1	–	1
Number of nodes in hidden layer	17	–	17	11	–	11
Epoch (iteration)	1000	1000	1000	1000	1000	1000
Trade-off parameter, C	–	1.67	–	–	11.48	–
Radial basis function parameter, γ	–	0.1	–	–	1.1	–
Velocity of foraging	–	–	0.02	–	–	0.02
Maximum induced speed	–	–	0.01	–	–	0.01
Computational time (s)	18	24	28	17	23	26

Table 5. Statistical performance indicators for the MLP, SVM and MLP-KH models over the testing phase.

Station	Model	R^2	RMSE (mm/d)	WI	E
Anzali	MLP	0.792	1.088	0.942	0.789
	SVM	0.791	1.096	0.940	0.786
	MLP-KH	0.907	0.725	0.967	0.865
Astara	MLP	0.843	1.197	0.903	0.778
	SVM	0.803	1.290	0.891	0.742
	MLP-KH	0.931	0.855	0.950	0.813

Figure 2. Observed daily pan evaporation versus estimates produced by MLP, SVM and MLP-KH models over the testing phase: (a) Anzali station and (b) Astara station.

Figure 3. (a) Taylor diagram, (b) violin plot and (c) point density distribution to compare MLP, SVM and MLP-KH models with respect to the observed daily pan evaporation over the testing phase – Anzali weather station.

Figure 4. (a) Taylor diagram, (b) violin plot and (c) point density distribution to compare MLP, SVM and MLP-KH models with respect to the observed daily pan evaporation over the testing phase – Astara weather station.

Figure 5. (a) Residuals and (b) their distribution for MLP, SVM and MLP-KH models in estimating daily pan evaporation over the testing phase – Anzali weather station.

Figure 6. (a) Residuals and (b) their distribution for MLP, SVM and MLP-KH models in estimating daily pan evaporation over the testing phase – Astara weather station.