128
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
Introduction
The calculation of reference crop evapo-
transpiration is a key to intelligent irrigation
systems. Therefore, accurate estimation of
ET
0
becomes important in irrigation schedules for
planning and optimizing the agriculture area.
Numerous methods have been put forward to
estimate
ET
0. Of these, the Penman-Monteith
56 (PM) model has given the best results; it
was officially recommended by the Food and
Agriculture Organization of the United Nations
(FAO) in 1998 (Allen
et al
., 1998). FAO selected
the PMmodel as the standard equation for
ET
0
estimation because it can provide the most ac-
curate results in the world.
ET
0 is also a key
parameter in the design of intelligent irrigation
for field crops. Engineers need to know the ir-
rigation water consumption requirements for
each crop so that they can calculate or estimate
the remaining components of the water balance.
Also, agriculturists need to obtain the specific
water requirements of a crop so that they can
generate a satisfactory yield. It is also necessary
to know whether these specific requirements are
being met with ordinary irrigation.
As described by Kisi (2008) and (Yubin
et al
.,
2014), about 50 measures have been proposed
for estimating evapotranspiration, which can be
sorted into four types: radiation, temperature,
synthetic and evaporating dish. FAO assumed
the ET definition given by Smith, Allen and
Pereira (1997), and adopted the FAO-56 PM as
the sole equation for estimation of
ET
0.
However, the PM model requires a lot of
meteorological data as input, and the calculation
process involves complex and nonlinear regres-
sion among these factors. So, a simpler and
more accurate simulation model needs to seek
ET
0 in the case of lack of meteorological data.
Thus, artificial intelligence algorithms (
e.g
., neu-
ral networks) for reference evapotranspiration
(
ET
0) modeling have been given more attention
in recent decades. Feng and Cui (2015) found
that an ELM model gave better results than
empirical models in the area of central Sichuan.
Kisi (2007) estimated daily ET0 using the ANN
method and compared their calculation results
with the other models. Ozgur Kisiet (2013) pro-
posed a reference evapotranspiration model by
LSSVM. Kisi (2011a) considered daily
ET
0 using
wavelet regression model and compared this
model to other empirical models. Kisi (2011b)
modeled
ET
0 using evolutionary feed-forward
neural networks. Marti, Gonzalez-Altozano and
Gasque (2011) used ANN to estimate daily
ET
0
without local climatic data. Kumar, Raghuwan-
shi and Singh (2011) researched the application
of ANN in estimating evapotranspiration
modeling. Shiri
et al
. (2012) established an
ET
0
simulation model using GEP (gene expression
programming) for Spanish Basque, and found
that the GEP model performed better than the
ANFIS, Hargreaves and Priestley-Taylor mod-
els. Wang, Traore and Kerh (2008), and Traore,
Wang and Kerh (2010) estimated daily
ET
0
using BP-ANN. However, BP-ANN has major
disadvantages, such as its slow speed of training
and difficulty in selecting parameters. In recent
years, new intelligent algorithms have appeared
in the industrial field, such as extreme learning
machines (ELM) and support vector machine,
among others.
In the present study, ELM is proposed as
an alternative to other models for predictive
control. It can randomly choose hidden nodes
and analytically determine the output weights
of SLFNs. However, ELM cannot confirm the
singularity of the output matrix of the hidden
layer, and it also cannot make fine tuning ac-
cording to the characteristics of the data set,
which will affect its efficiency and stability.
The main purpose of this paper is to opti-
mize the ELM approach in the modeling of daily
ET
0 using the original meteorological data. All
previous studies have indicated that intelligent
models can input the factors of FAO-56 PM as
they estimate
ET
0. In fact, these factors will be
another complex computing project by meteoro-
logical raw data, to avoid creating more severe
error during multistage formula calculation.
Also, the manipulation of the inverse of the
