139
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
•
30.37 and 33.50% error, respectively. For Xi’an,
the ELM, LSSVM, and Hargreaves were ranked
the second best, followed Priestley-Taylor and,
finally, Mc Cloud.
In short, for the different cities, the ISO-ELM
performed better than the other models, and the
other models had different degrees to adapt to
the application.
Conclusion
The improved sequential extreme learning ma-
chine (IOS-ELM) is designed and applied for
simulation of daily reference evapotranspiration
through different manipulation of the inverse of
the matrix and using the regularization factor
and online learning method at the same time
Experimental results demonstrated that the
IOS-ELM can learn faster and achieve better
performance than traditional ELM.
First, the IOS-ELM model effectively over-
comes the defects of traditional ELM, such as
slow training speed, difficult parameter deci-
sions, difficulty in setting the singularity and
effect of data samples.
Second, the potential of the ISO-ELM
technique for the estimation of reference
evapotranspiration was investigated for four
areas in Shaanxi of China; particularly, eight
meteorological data were used as inputs.
Third, it was demonstrated that intelligent
algorithm models (IOS-ELM, ELM, and LSSVM)
are widely applicable to different areas, but
Table 7. Performance statistics of the models in the validation period.
Models
Total ET0(mm)
Relative error (%)
Yulin Ankang Hanzhong Xi’an
Yulin Ankang Hanzhong
Xi’an
Observed
5 039
4 661
4 307
3 134
-
-
-
-
ISO-ELM
5 279
4 650
4 306
3 117
4.76
0.23
0.02
0.54
ELM
5 274
4 636
4 413
3 207
4.66
0.54
2.46
2.33
LSSVM
5 488
4 639
4 408
3 226
8.91
0.47
2.35
2.94
Hargreaves
3 003
3 362
3 080
3 276
40.40
27.87
28.49
4.53
Mc Cloud
1 784
3 672
2 999
2 436
64.60
21.22
30.37
22.27
Priestley-Taylor
2 844
3 051
2 864
2 727
43.56
34.54
33.50
12.99
empirical models were limited to specific re-
gions and required modification.
Fourth, in the different meteorological data
combinations for
ET
0 estimation, as long as
there was a temperature-related parameter
calculation, the calculation accuracy of
ET
0 was
over 94%, and
T
max was especially effective.
These accurate calculations can be a valuable
reference for the development of intelligent ir-
rigation in water decision-making systems.
Acknowledgments
This work was supported by the National High Technology
Research and Development Program of China (863 Program)
under Grant Nos. 2011AA100509-01.
Notation
The following symbols are used in this paper:
ET
0 = reference evapotranspiration (mm day
-1
).
D
= slope of the saturation vapor pressure
function (kPaC
-1
).
Rn
= net radiation (MJ m
-2
day
-1
).
G
= soil heat flux density (MJ m
-2
day
-1
).
c
= psychometric constant (kPa C
-1
).
T
= mean air temperature (°C).
U2 = average24-h wind speed at 2 m height
(ms
-1
).
Rs
= solar radiation (MJ m
-2
day
-1
).
es
= the saturation vapor pressure (kPa).
ea
= the actual vapor pressure (kPa).
