Long-term monthly evapotranspiration modeling by several data-driven methods without climatic data
Introduction
Evapotranspiration (ET) is a process of losing water to the atmosphere via the combined process of evaporation from the soil and transpiration from the plants. In agriculture science especially in arid and semiarid areas, proper prediction of the given crop evapotranspiration (ETc) is important. Therefore, the ability to obtain or estimate evapotranspiration (ET) is of great importance for operating irrigation systems (Karimadldini et al., 2012). ETc can be calculated by multiplying ET0 (reference evapotranspiration) to the crop coefficient (Kc) of the crop.
Several methods and techniques could be applied for calculating or estimating ET including (1) direct, (2) indirect and (3) data-driven methods. Direct measurement method by using lysimeter is the best options for obtaining ET crop and ET0 but is a difficult task because it is time-consuming and needs potential financial and environmental resources. As a result, a large number of indirect methods such as empirical, semi-empirical equations and data driven models have been developed for measuring ET0 from meteorological data (Karimadldini et al., 2012). Some of the indirect ET0 estimation methods can be named as simple pan evaporation-based methods and combination methods such as (Penman, 1963), Penman–Monteith (Monteith, 1965) and etc.
One of the best known indirect method is the Food and Agricultural Organization of the United Nations (FAO) method in which combines the equation of Penman–Monteith modified by Allen in 1998 (FAO-56 PM equation) as a reference equation for ET0 estimation. The FAO-56 Penman–Monteith (PM-56) equation is influenced by several weather parameters including measurement of the maximum and minimum air temperature, maximum and minimum relative air humidity, wind speed and solar radiation. With an exception to the air temperature which is available at most weather stations, the remaining variables are often incomplete or not always available for many locations and even not always reliable (Rahimikhoob, 2010). Regarding the above contexts, there are so many factors affecting ET estimation based on indirect methods, thereafter it is extremely difficult to formulate the ET0 equation that can produce reliable estimates.
The main problem with modeling ET process is its nonlinear dynamic and high complexity, in this respect, using data-driven methods (e.g. ANN, ANFIS, SVM ...) based on soft computing techniques could be considered as proper methods for estimating ET0. These methods are known for their ability in dealing with complex problems, with only sets of available data. In the following, the application of soft computing techniques to evapotranspiration modeling is presented.
Among different soft computing methods, artificial neural networks (ANNs) due to their high ability in the modeling of nonlinear processes such as ET0 are very appropriate tools. In the past decades, ANNs were used to estimate evapotranspiration (Kumar et al., 2002, Sudheer et al., 2003, Trajkovic, 2005, Kim and Kim, 2008, Landeras et al., 2008, Traore et al., 2010). Rahimikhobb (2010) examined the potential for the use of ANNs to estimate ET0 based on air temperature data under humid subtropical conditions on the southern coast of the Caspian Sea. He claimed that the ANN model was superior to indirect empirical equations. A comprehensive and recent review of ANN applications in ET0 modeling can be refereed to Kumar et al. (2011). They showed that the performance of most of the ANN models depends on a few meteorological stations which have recorded weather data for a specific period.
In addition to ANNs, more recently adaptive neuro-fuzzy inference systems (ANFIS) was used to simulate/predict ET0 (Kisi and Ozturk, 2007, Aytek, 2009, Dogan, 2009, Cobaner, 2011, Kisi and Zounemat-Kermani, 2014). ANFIS provides an efficient way of modeling the uncertainty for complicated systems lacking adequate data. Kisi and Ozturk (2007) investigated the capability of the ANFIS in the estimation of ET0 in Los Angeles. The results showed that the ANFIS models could be considered as proper tools in modeling ET0 process. Aytek (2009) applied a coactive neuro-fuzzy inference system (CANFIS) technique for modeling daily ET0, in three stations and compared the results with some empirical formulas. They claimed that CANFIS can be employed as an alternative ET0 model to the existing conventional methods. Cobaner (2011) investigated the potential of grid partition-based fuzzy inference system (G-ANFIS) and subtractive clustering-based fuzzy inference system (S-ANFIS) and ANNs, in modeling of ET0. They found that the S-ANFIS model achieved more accurate results with fewer amounts of iterations as compared to the G-ANFIS and ANN models in modeling ET0 process.
Karimaldini et al. (2012) investigated the potential of the adaptive neuro-fuzzy computing technique (ANFIS) for daily ET0 modeling under arid conditions from limited weather data. The comparison results indicated that by using similar meteorological inputs, the ANFIS models performed better than conventional methods. Tabari et al. (2013) investigated the accuracy of the ANFIS and support vector machines (SVM) for potato ETc estimation. The results confirmed that the SVM models could provide more accurate ETc estimates than the ANFIS and empirical equations. Kisi and Zounemat-Kermani (2014), applied two different types of ANFIS (with grid partition method and ANFIS with subtractive clustering method) in modeling daily ET0. Results indicated that the three-and four-input ANFIS models were superior to the corresponding empirical equations in modeling ET0 while the calibrated two-parameter Ritchie and Valiantzas’ equations were found to be better than the two-input ANFIS models.
Gene-expression programming (GEP) interface is a powerful technique applied in many engineering researches with good generalization ability (Azamathulla et al., 2011, Shiri et al., 2014a, Shiri et al., 2014b, Shiri et al., 2014c, Marti et al., 2015, Kisi and Sanikhani, 2015). It has been observed that related studies in the literature related to the use for ET0 modeling are scare. Guven et al. (2008) presented genetic programming for the estimation of ET0 by using daily atmospheric variables obtained from the California Irrigation Management Information System database. The results of the GEP model were compared to seven conventional models and were found to be in good agreement. Results showed that the GEP model gave a fast and practical method for the estimation of ET0 to obtain accurate results and encourage the use of GEP in other aspects of water engineering studies. In another study, Traore and Guven (2012) investigated the performance ability of the GEP for modeling ET0 using decadal climatic data in Burkina Faso. They claimed that GEP is an effectual modeling tool for successfully computing evapotranspiration. To the knowledge of the writers, there is not any published paper in the literature that compares the ability of ANN, ANFIS with grid partition (ANFIS-GP), ANFIS with subtractive clustering (ANFIS-SC) and GEP in predicting long-term monthly ET0.
The aim of this study is to investigate the accuracy of multilayer perceptron ANN, ANFIS-GP, ANFIS-SC and GEP in predicting long-term monthly ET0 by using data from 50 stations in Iran.
Section snippets
Case study
The study area used in this study lays over the entire region of Iran’s geographical area (25°00′N and 38°39′N latitudes and between 44°00′E and 63°25′E longitudes) of about 1650,000 km2. According to Dinpashoh et al. (2011) generally, Iran is categorized as having arid (BW) and semi-arid (BS) climates based on the Koppen climatic classification (Ahrens, 1998). Precipitation is the main source of water in Iran, which normally amounts to 251 mm or 413 billion cubic meters annually. More than 70%
ANFIS
Neuro-fuzzy systems which are based on the rule-based fuzzy systems uses the capability of neural networks learning algorithm for adapting their rule-base parameters (Zounemat-Kermani and Scholz, 2013). Generally, in ANFIS a six layers multilayer neural network-based fuzzy system is constructed. In this system architecture, the input and output nodes represent the input states (variables) and output response (target), respectively, while in the hidden layers membership functions (MF) and rules
Application and results
Four different data-driven methods, ANN, ANFIS-GP, ANFIS-SC and GEP, were applied for estimating long-term monthly mean ET0. Latitude, longitude, altitude and periodicity component (month of the year) data were used as inputs to the each model. Monthly data of 40 weather stations (40 stations × 12 months = 480 data) were used for training and 10 stations’ data (10 stations × 12 months = 120 data) were used for testing. The stations used for the testing procedure are Mashahd, Bandar abbas, Semnan, Shiraz,
Conclusion
In this study, the accuracy of four different data-driven methods, ANN, ANFIS-GP, ANFIS-SC and GEP, were investigated to predict long-term monthly reference evapotranspiration by using geographical input data. The periodicity component, station altitude, longitude and latitude values were used as inputs to the applied models to estimate the long-term monthly ET0 values. Data from 50 weather stations in Iran were used for training and testing of the models. The data-driven models were compared
Acknowledgement
This study was partly supported by The Turkish Academy of Sciences (TUBA). The first author would like to thank TUBA for their support of this study.
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