132
Zhang
et al
.,
Improved online sequential extreme learning machine for simulation of daily reference evapotranspiration
Tecnología y Ciencias del Agua
, vol. VIII, núm. 2, marzo-abril de 2017, pp. 127-140
•
ISSN 2007-2422
Where
c
=
H
0
T
T
0
,
M
=
H
0
T
H
0
,
g
+
= {
g
∈
R
N
0 ×
N
0
},
g
is a positive definite symmetric matrix.
Step (3) Set
K
= 0; then, present the (
K
+ 1)th
chunk of new observations:
K
+
1
=
x
i
,
t
i
(
)
{
}
N
j
j
=
1
i
=
K
j
=
1
N
j
K
+
1
where
N
K
+1
is the number of observations in the
(
K
+ 1)th chunk.
Step (4) Calculate the partially hidden layer
output matrix
H
K
+1
for the (
K
+ 1)th chunk of
data
K
+
1
, as shown in (17):
H
K
+
1
=
g w
1
x
1
+
b
1
(
)
g w
N
~
x
1
+
b
N
~
(
)
g w
1
x
N
K
+
1
+
b
1
(
)
g w
N
~
x
N
+
b
N
~
(
)
N
K
+
1
N
~
(13)
Step (5) According to step (1), calculate the
output weight
b
K
+ 1
.
Step (6) Set
k
=
k
+ 1. Go to Step (3).
Application and results
IOS -ELM model under lack of data
The original eight meteorological parameters
chose and combined with a different pattern
in this section, which was taken as input
values. Meanwhile, the calculation of FAO
56 Penman-Montieth was put as the output
value. By this method, the IOS-ELM model
is established. However, it needs to further
consider the effectiveness of the combination
pattern among the eight meteorological data.
Therefore, the correlation between
ET
0 and the
data was analyzed. In this way, ISO-ELM can
choose reasonable meteorological parameters to
complete the forecast even if there is a lack of
meteorological data. This is shown in table 4.
It can be clearly seen from table 2 that the
ET
0 outperformed all eight meteorological pa-
rameters in terms of correlation. Although the
data set is not similar for different cities, the cor-
relation behaved in the same way.
T
max
is closely
correlated with evapotranspiration for each city,
followed by the average temperature, minimum
temperature, the actual sunshine time and wind
speed. The influence of the latitude and altitude
were so small that they were negligible. Finally,
the humidity is negative.
The simulation accuracy of the IOS-ELM
model was discussed by referring to table 2
under lack of meteorological data. It should
be noted that the latitude and altitude were
eliminated because they had virtually no effect
on the results. Taking Yulin city as an example,
the first 10-year (1971-1999) span of data was
used to train the models. Then, using different
combinations, the error was analyzed, as well
as the correlation coefficient and effectiveness
of the prediction. This is shown in table 3.
The ISO-ELM model was applied by com-
paring the different parameters shown in table
3. It is immediately noticeable that the predic-
tion results were the same for eight-parameter
and six-parameter inputs. That is because the
latitude and altitude almost have no effect on
the prediction for the same station. Secondly,
the temperature had the largest influence on
the prediction, particularly the maximum tem-
perature. As long as the temperature is one of
Table 2. Correlation of data and
ET
0.
Uh
T
RH
m
T
min
T
max
n
φ
Z
Yulin
0.20
0.88
-0.36
0.79
0.92
0.50
-2e-15
NaN
Ankang
0.15
0.85
-0.34
0.71
0.93
0.70
-7e-16
Hanzhong
0.21
0.85
-0.48
0.73
0.93
0.69
4e-15
Xi’an
0.30
0.80
-0.43
0.72
0.85
0.66
1e-16
