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Correlation coefficients between the input and output variables for Kerman.

Table 6 Correlation coefficients between the input and output variables for Kerman.

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where H is the hidden layer output matrix of SLFN with ith column of H being the ith hidden node’s output with respect to inputs Xiigen « oA its hidden layer. For N arbitrary distinct samples (x;, t;) € R” x R™, x; isn x 1 input vector and t;ism x 1 target vector. If a SLFN with L hid- den nodes can approximate these N samples with zero error then implies that there exist f;, a; and b; such that (Huang et al., 2006a):
where H is the hidden layer output matrix of SLFN with ith column of H being the ith hidden node’s output with respect to inputs Xiigen « oA its hidden layer. For N arbitrary distinct samples (x;, t;) € R” x R™, x; isn x 1 input vector and t;ism x 1 target vector. If a SLFN with L hid- den nodes can approximate these N samples with zero error then implies that there exist f;, a; and b; such that (Huang et al., 2006a):
Descriptive statistics for the input and output variables for Bandar Abbas.
Descriptive statistics for the input and output variables for Bandar Abbas.
Correlation coefficients between the input and output variables for Bandar Abbas.
Correlation coefficients between the input and output variables for Bandar Abbas.
Descriptive statistics for the input and output variables for Kerman.
Descriptive statistics for the input and output variables for Kerman.
Statistical indicators achieved for the ELM and SaE-ELM models in the training and testing phases for Kerman station.
Statistical indicators achieved for the ELM and SaE-ELM models in the training and testing phases for Kerman station.
Fig. 1. Scatter plots of estimated daily soil temperature (ST) by ELM model versus measured values at different depths in the testing phase for Bandar Abbas (Mihalakakou, 2002; Tabari et al., 2011; Talaee, 2014). The sec- ond and third highest correlations with high values were attained for Tyin ANd Tmax, respectively. This also shows that Twin and Tinax play a remarkable role in ST variations. Although corre- lation coefficients of P and Rs; and in particular P are favorable, consideration of three air temperatures (Twin, Tmax and Toyz) seems to be more effective owing to their higher relationships with ST at different depths. This finding is also comparable with the study of (Talaee, 2014). Therefore, to achieve more simplic- ity, only three variables of Tinin, Tmax aNd Tayg are used as input parameters for estimation of ST at all depths in both stations via the developed ELM and SaE-ELM models. For both stations, the highest correlation coefficient at all depths was obtained between ST and Tyg indicating that Tayg is the most influential variable on ST. This verifies that there are strong relationships between Tgyg and ST at different depths. The reason is that both air and soil temperatures are identified based on the energy balance at the ground surface. This finding is totally comparable with those of previous studies
Fig. 1. Scatter plots of estimated daily soil temperature (ST) by ELM model versus measured values at different depths in the testing phase for Bandar Abbas (Mihalakakou, 2002; Tabari et al., 2011; Talaee, 2014). The sec- ond and third highest correlations with high values were attained for Tyin ANd Tmax, respectively. This also shows that Twin and Tinax play a remarkable role in ST variations. Although corre- lation coefficients of P and Rs; and in particular P are favorable, consideration of three air temperatures (Twin, Tmax and Toyz) seems to be more effective owing to their higher relationships with ST at different depths. This finding is also comparable with the study of (Talaee, 2014). Therefore, to achieve more simplic- ity, only three variables of Tinin, Tmax aNd Tayg are used as input parameters for estimation of ST at all depths in both stations via the developed ELM and SaE-ELM models. For both stations, the highest correlation coefficient at all depths was obtained between ST and Tyg indicating that Tayg is the most influential variable on ST. This verifies that there are strong relationships between Tgyg and ST at different depths. The reason is that both air and soil temperatures are identified based on the energy balance at the ground surface. This finding is totally comparable with those of previous studies
Fig. 2. Scatter plots of estimated daily soil temperature (ST) by SaE-ELM model versus measured values at different depths in the testing phase for Bandar Abbas
Fig. 2. Scatter plots of estimated daily soil temperature (ST) by SaE-ELM model versus measured values at different depths in the testing phase for Bandar Abbas
Fig. 3. Scatter plots of estimated daily soil temperature (ST) by ELM model versus measured values at different depths in the testing phase for Kerma:
Fig. 3. Scatter plots of estimated daily soil temperature (ST) by ELM model versus measured values at different depths in the testing phase for Kerma:
Fig. 4. Scatter plots of estimated daily soil temperature (ST) by SaE-ELM model versus measured values at different depths in the testing phase for Kermar
Fig. 4. Scatter plots of estimated daily soil temperature (ST) by SaE-ELM model versus measured values at different depths in the testing phase for Kermar
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