Research paperApplication of an artificial intelligence technique enhanced with intelligent water drops for monthly reference evapotranspiration estimation
Introduction
An accurate calculation of crop water requirement (ETc) is an essential task for optimizing water consumption, irrigation planning, and increasing water consumption efficiency (Güçlü et al., 2017, Gharbia et al., 2018, Adamala et al., 2019). Its computation for any particular crop is also required in many projects related to water resources, irrigation and drainage, agricultural water management, etc. Direct measurement of this important parameter through the lysimeters is almost difficult, time consuming, and costly. Indirect measurements should be therefore taken into consideration. Practically, reference evapotranspiration (ET0) is firstly computed and it is then converted to the ETc by multiplying the ET0 in crop coefficient (Kumar et al., 2002, Adamala et al., 2019).
Various climatic data including temperature, sunshine hours, wind speed, relative humidity, etc. are the most influential weather parameters on the rate of ET0 (Adamala et al., 2019, Adamala et al., 2014, Mehdizadeh et al., 2017a). It can be therefore said that the evapotranspiration process includes a non-linear and complex nature. Hence, robust tools are needed to capture the ET0 time series. Different approaches can be used to estimate the ET0 comprising of the empirical models, artificial intelligence (AI) techniques, etc. Many empirical equations have been developed, namely the temperature-based, mass transfer-based, and radiation-based. Among them, the popular Penman-Monteith equation, i.e., FAO-56 PM (Allen et al., 1998) is universally accepted as a reference approach to estimate the ET0 and evaluate the performance of other models (Trajkovic, 2009, Valiantzas, 2013, Mossad and Alazba, 2016, Güçlü et al., 2017, Mehdizadeh et al., 2017b). In recent years, the application of AI models has been dramatically expanded to address issues in hydrology and water resources engineering (Gocić et al., 2015, Feng et al., 2016, Güçlü et al., 2017, Adamala et al., 2019, Mehdizadeh and Kozekalani Sales, A., 2018, Mehdizadeh, 2018a, Mehdizadeh, 2020, Mehdizadeh et al., 2017c, Mehdizadeh et al., 2018). In this regard, it can be mentioned to gene expression programming (GEP), support vector regression (SVR), and so on. In fact, the GEP is an advanced form of genetic programming, which is initially proposed by Ferreira (2001). The features of two techniques including genetic programming (GP) and genetic algorithm (GA) are merged in the GEP. SVR is a popular technique for classification, estimation, regression, and pattern recognition (Vapnik et al., 1997). Vapnik et al. (1997) introduced SVR for applying classification in the linear and non-linear data set. Recently, SVR technique is used as a powerful tool for modeling of non-linear systems such as evaporation (Moazenzadeh et al., 2018), evapotranspiration (Mohammadi and Mehdizadeh, 2020), air temperature (Mehdizadeh, 2018b, Aghelpour et al., 2019), and streamflow (Tikhamarine et al., 2019).
In addition to the standalone AI models, the hybrid models can also be developed. Indeed, the aim of implementing the hybrid models is to improve the performance of standalone models when estimating the target parameter (i.e., ET0 in this study). Recently, bio-inspired optimization algorithms have received significant attention to develop the hybrid models in hydrological studies such as estimating the ET0. Literature review shows the ability of optimization algorithms as a boosting tool for predictor models like SVR. Intelligent water drops (IWD) is an evolutionary and population-based algorithm based on the mechanism of water droplets in rivers that encounter many obstacles to reach lakes and oceans, but eventually find their way to their destination. They are inspired. Recently, IWD has tested in different applied engineering fields as an optimizer tool (Kamkar et al., 2010, Alijla et al., 2014, Hendrawan and Murase, 2011, Hoang et al., 2012) and it has also shown well performance in comparison with other nature-inspired optimization algorithms (Shah-Hosseini, 2007, Shah-Hosseini, 2009a, Shah-Hosseini, 2009b).
Here, some of the previous works published in literature on the ET0 modeling are briefly reviewed. The modeling performance of extreme learning machine (ELM) was investigated by Abdullah et al. (2015) for modeling the ET0 of three weather stations located in Iraq. The results illustrated that the ELM provided better results than the feed forward back propagation (FFBP). Kisi (2016) assessed the modeling performance of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS), and M5tree models in modeling the monthly ET0 of two stations in Turkey. Two data analysis approaches were considered, namely the local and external methods. The MARS and M5 tree techniques illustrated superior performances in the local and external conditions, respectively. Mehdizadeh (2018a) applied the MARS and GEP approaches for estimating the daily ET0 at six weather stations in Iran and was found that the MARS performed the best for the whole of the studied stations. Kisi and Alizamir (2018) modeled the daily ET0 time series of the Ankara and Kirikkale, Turkey. They developed a hybrid model via coupling the wavelet (W) with the ELM (i.e., WELM) and then compared its performance with wavelet-artificial neural networks (i.e., WANN), standalone ELM, online sequential ELM, and standalone ANN. It was reported that the proposed WELM performed the best. A new machine learning model was proposed by Fan et al. (2019) named light gradient boosting machine (LGBM) for modeling the daily ET0 of 49 meteorological stations located in China. Its performance was also compared with the M5tree, random forests (RF), and four empirical models. The LGBM was found to be the best model. A comparative study was performed by Saggi and Jain (2019) to assess the performance of deep learning (DL), RF, gradient boosting machine (GBM), and generalized linear model (GLM) in daily ET0 modeling of two stations located in India. It was concluded that the DL showed superiority over the other models used. Huang et al. (2019) evaluated the modeling accuracy of CatBoost, SVM, and RF to estimate the daily ET0 at 12 meteorological stations in China. They reported that the SVM and CatBoost models were the best models under the limited and full access to the climatic data, respectively. The GEP and RF models were employed by Wang et al. (2019) to estimate daily ET0 at 24 weather stations, China. The authors reported the reliable potential of both the mentioned methods. Malik et al. (2019) investigated the applicability of co-active neuro fuzzy inference system (CANFIS) for monthly ET0 prediction of two stations located in India. They concluded that the CANFIS presented reliable ET0 estimates compared to the other applied AI techniques. Tikhamarine et al. (2019) proposed five hybrid models through hybridizing the ANN and five different types of optimization algorithms for modeling the monthly ET0 of two sites in India and Algeria. The hybrid model of ANN coupled with gray wolf optimizer (i.e., ANN-GWO) was found to perform the best. del Cerro et al. (2020) compared the potential of adaptive neuro-fuzzy inference system (ANFIS) and some empirical equations for modeling the daily ET0 of south India and reported the better performance of ANFIS than the empirical models. The daily ET0 time series at southeastern Australia were estimated by Shi et al. (2020) using the RF and empirical models. The RF was found to illustrate better results than the empirical equations used. Ferreira and da Cunha (2020) proposed a novel method including the convolutional neural networks (CNN) for the daily ET0 modeling of 53 locations in Brazil. Its modeling performance was also compared with other techniques, namely RF, XGBoost, and ANN. The results revealed the higher accuracy of proposed CNN than the other models. Tikhamarine et al. (2020) applied three various optimization algorithms to improve the accuracy of SVR in modeling monthly ET0 of three sites at Algeria. Superior performance of the hybrid models than the standalone SVR was reported by the authors. Heddam et al. (2020) proposed two types of ELM including optimally pruned ELM (OPELM) and online sequential ELM (OSELM) to predict daily ET0 of a Mediterranean region located in Algeria. They found out that the OPELM outperformed the OSELM. The overall outcomes of literature review as mentioned above confirmed the reliable potential of AI models to capturing the ET0 time series on various time scales. On the other hand, our literature review illustrated that pre-processing techniques are rarely used by researchers to select the most important climatic inputs in developing the AI-based models. However, pre-processing methods can be a great help in choosing the correct input variables to feed the AI models when estimating the ET0 time series and they can therefore increase the modeling accuracy.
Suitable methods with dependable accuracy are needed to estimate the ET0 due to its importance in the hydrological and climatological studies. The main goals of the present study are therefore as follows: to (1) apply standalone GEP and SVR considering the climatic data and antecedent ET0 data-based scenarios, (2) employ two different pre-processing techniques, namely τ Kendall and entropy for recognizing the most influential climatic parameters to feed the models, (3) propose a novel hybrid model via coupling the SVR and intelligent water drops (IWD), (4) use the empirical equations including the Hargreaves-Samani (H-S) and Priestley-Taylor (P-T) in their original and calibrated versions. To do these, six stations located in Iran were chosen as the study areas. It is worthwhile to note that the application of τ Kendall and entropy pre-processing methods in order to determine most effective climatic parameters on ET0 as well as implementing the hybrid SVR-IWD are the novelties of this work, which have received less attention in previous works on estimating the ET0.
Section snippets
Study area and data used
The present study considered six stations located in Iran as the study areas. Three of the six selected stations (i.e., Arak, Mashhad, Shiraz) include semi-arid climate and the other three ones (i.e., Bandar Abbas, Tehran, Yazd) have the arid climate. It is worthwhile to mention that the climates of the studied stations were determined using the climatic classification proposed by de Martonne (1925). Table 1 tabulates the geographical coordinates of the study locations. Besides, the spatial
Results
In this study, two different scenarios consisting of the climatic data and antecedent ET0 data-based patterns were used for estimating the monthly ET0 time series of the considered stations. To do this, various approaches were employed such as standalone GEP and SVR, hybrid SVR-IWD, and two different empirical models. The performance of all the developed models was evaluated by means of the RMSE, MAE, and R statistical metrics.
Two pre-processing techniques including the τ Kendall and entropy
Discussion
As noted, two pre-processing techniques used in this study including the τ Kendall and entropy introduced different input combinations to estimate the monthly ET0. As is apparent, the air temperature parameters (Tmin, Tmax, T) and solar radiation (Rs) as the effective parameters can affect the ET0 process. The τ Kendall method is a correlation-based pre-processing technique so that it introduces the high-correlated weather parameters with the ET0 as the most influential parameters. It can be
Conclusions
In this study, the monthly ET0 time series of six stations situated in Iran were estimated for the period from 1973 to 2018. To that end, three different methods were used comprising of the standalone models (i.e., GEP and SVR), a novel hybrid model (i.e., SVR−IWD), and empirical models in their original and calibrated versions (i.e., H−S and P−T). The standalone and hybrid models were implemented considering the climatic data and antecedent ET0 data-based scenarios. Additionally, τ Kendall and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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