Comparison of heuristic and empirical approaches for estimating reference evapotranspiration from limited inputs in Iran

Highlights

• Artificial intelligence and empirical ET₀ models are evaluated.

• Local and regional scenarios were developed and tested.

• GEP outperforms the other applied models in ET₀ estimation.

• Arid regions offer the lowest accuracies among the studied stations.

Abstract

Accurate estimation of reference evapotranspiration (ET₀) values is of crucial importance in hydrology, agriculture and agro-meteorology issues. The present study reports a comprehensive comparison of empirical and semi empirical ET₀ equations with the corresponding Heuristic Data Driven (HDD) models in a wide range of weather stations in Iran. Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS), Support Vector Machine (SVM) and Gene Expression Programming (GEP) techniques are applied for modeling ET₀ values considering different data management scenarios, and compared with corresponding Hargreaves–Samani (HS), Makkink (MK), Priestley–Taylor (PT), and Turc (T) ET₀ models as well as their linear and non-linear calibrated versions along with the regression-based Copais algorithm. The obtained results confirm the superiority of GEP-based models. Further, the HDD models generally outperform the applied empirical models. Among the empirical models, the calibrated HS model found to give the most accurate results in all local and pooled scenarios, followed by the Copais and the calibrated PT models. In both local and pooled applications, the calibrated HS equation should be applied when no training data are available for the use of HDD models. The best results of the models correspond to the humid regions, while the arid regions provide the poorest estimates. This may be attributed to higher ET₀ values associated with these stations and the high advective component of these locations.

Introduction

The average annual precipitation in Iran is about 248 mm leading to arid and semi-arid climate in most regions, with non-uniform spatial and temporal precipitation distribution. During the period of 1996–2011, the freshwater availability has decreased from 2.11 to 1.72 (1000 m³) per capita together with an increasing the irrigation areas [from 7397 to 9413 (1000 ha) for the same period] and a decreasing annual growth rate [from 3.06% to 1.19%] alarming an emerging challenge for water resources management (FAO, 2012, FAO, 2013). Since the main part of water resources in Iran are utilized for agricultural issues (86 km³ per year), accurate information on irrigation water requirements, which is directly linked to crop water requirements (i.e. evapotranspiration, ET) values, is an important challenge for agriculture and water resources planners. Information about ET (the process of water loss to the atmosphere by the combined processes of evaporation and transpiration) values and its trends in different climatic contexts of the country would be used for improving irrigation efficiencies, water reuse and controlled drainage as well as groundwater exploitation. ET can be measured directly using energy balance and water vapor mass flux transfer methodologies or lysimeters. However, these measurements are expensive and time consuming, so their application is limited especially in developing countries. As an alternative, ET can be estimated through calculating reference evapotranspiration (ET₀) using various empirical/semi-empirical models (Doorenbos and Pruitt, 1977). The application of a specific model for ET estimation usually depends on data availability at the studied site. The Penman–Monteith model has been adopted as the reference equation for estimating ET₀ values and calibrating other equations (Allen et al., 1998). Nevertheless, it requires a large number of variables for their application, which is a major limitation.

Use of ET₀ equations with fewer climatic parameters requirements is needed under situations where absence of more complete weather data. However, these equations should be used to calculate ET₀ for any region after evaluating them against either lysimeter measurements or the standard FAO56-PM model (Tabari et al., 2012). In the last decades, several equations have been applied for calculating ET₀ (e.g. Kisi, 2014, Landeras et al., 2008, Pereira and Pruitt, 2004, Tabari et al., 2013, Trajkovic, 2007, Trajkovic, 2010, Trajkovic and Kolakovic, 2009). DehghaniSanij et al. (2004) compared the ET₀ estimates obtained by using the Penman, Penman–Monteith (PM), Wright–Penman, Blaney–Criddle, radiation balance, and Hargreaves models with lysimeter data. The results showed that the PM model gave the most reliable estimates. Lopez-Urrea et al. (2006) investigated the ability of seven different empirical equations for calculating average daily ET₀ in a semiarid climate of Spain and reported that Hargreaves and Samani (1985) model was the most accurate. Trajkovic (2007) employed calibrated Hargreaves equation for estimating ET₀ and he proposed a value of 0.424 instead of the original 0.5 to be used in the adjusted Hargreaves equation for the western Balkan locations. Sabziparvar et al. (2010) examined different pan evaporation-based methods for estimating ET₀ in cold semi-arid and warm-arid climates. They illustrated that the Orang and Snyder method performed better than the other models in cold semi-arid and warm-arid environments, respectively. Tabari (2010) examined the ability of four ET₀ equations with small weather data requirements (Makkink, Turc, Priestley and Taylor, and Hargreaves) in four different climates. He revealed that the Turc model performed better than the other models in estimating ET₀ for cold humid and arid climates. In the humid and semiarid climatic conditions, the Hargreaves equation was found to be the best model. Berengena and Gavilán (2005) compared different ET₀ equations in a highly advective semi-arid environment in Spain. The locally adjusted Penman and ASCE-PM equations found to be the best; followed by the FAO56-PM. Sabziparvar and Tabari (2010) derived spatially distributed maps of ET₀ by using Hargreaves equation for the arid and semi-arid areas of Iran. They indicated that the estimated total monthly ET₀ showed a significant fluctuation during the growing season (April–September) so that the study region experienced the highest and lowest monthly ET₀ values of 250 and 80 mm in July and April, respectively (Tabari et al., 2012).

As an alternative to conventional methods, in recent years, Heuristic Data Driven (HDD) techniques [e.g. Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS), Genetic Programming (GP) and Support Vector Machine (SVM)] have been successfully applied in hydrology and water resources engineering issues, including ET estimations. The complete review of such applications is beyond the scope of the present study and only some relevant literature will be mentioned here. Among others, ANNs have been applied by e.g. Aghajanloo et al., 2013, Huo et al., 2012, Kim and Kim, 2008, Kim et al., 2012, Kim et al., 2013, Kumar et al., 2011, Landeras et al., 2008, Martí and Gasque, 2010, Martí et al., 2010, Martí et al., 2011, RahimiKhoob, 2008a, RahimiKhoob, 2008b, Sudheer et al., 2003, Tabari et al., 2009, Trajkovic et al., 2000, Trajkovic, 2010, Trajkovic and Kolakovic, 2009, Zanetti et al., 2007 for evaporation/evapotranspiration modeling. Further, Aytek, 2009, Dogan, 2009, Kisi, 2006, Kisi and Ozturk, 2007, Kisi et al., 2012, Tabari et al., 2012, Baba et al., 2013, Shiri et al., 2013a applied ANFIS for modeling evapotranspiration. The literature survey showed that the application of GP for modeling evaporation/evapotranspiration is limited, including e.g. Parasuraman et al., 2007, Guven et al., 2008, Shiri et al., 2012, Shiri et al., 2013b. Nevertheless, none of the mentioned studies considers a global comparison between the 4 HDD methods for the same data set. Normally, only one or maximum two approaches are assessed. The objective of the present study is to compare the performance of ANFIS, GEP, ANN and SVM techniques relying on limited inputs in 29 weather stations of Iran, located in different climatic contexts. Their performance is compared with the corresponding existing empirical and semi-empirical ET₀ models relying on the same input combinations. Different types of calibration procedures are evaluated for calibrating the empirical and semi-empirical ET₀ models.