Daily reference evapotranspiration modeling by using genetic programming approach in the Basque Country (Northern Spain)

Summary

Evapotranspiration, as a major component of the hydrological cycle, is of importance for water resources management and development, as well as for estimating the water budget of irrigation schemes. This study presents a Gene Expression Programming (GEP) approach, for estimating daily reference evapotranspiration (ET₀) in four weather stations in Basque Country (Northern Spain), for a 5-year period (1999–2003). The data set comprising air temperature, relative humidity, wind speed and solar radiation was employed for modeling ET₀ using FAO-56 Penman Monteith equation as the reference. The GEP results were compared with the Adaptive Neuro-Fuzzy Inference System (ANFIS), Priestley–Taylor and Hargreaves–Samani models. Based on the comparisons, the GEP was found to perform better than the ANFIS, Priestley–Taylor and Hargreaves–Samani models. The ANFIS model is ranked as the second best model.

Introduction

Evapotranspiration (ET) is the process of water loss to the atmosphere by the combined processes of evaporation and transpiration. Accurate assessment of evapotranspiration is needed for computation of crop water requirement, irrigation scheduling, water resources management and planning, water allocation and determination of the water budget, especially under arid conditions where water resources are scarce and fresh water is a limited resource. Therefore, reliable estimation of evapotranspiration is of great importance. Water requirement should be adjusted by taking into account the climatic conditions. Several attempts stated the needs for accurate estimation of ET in order to predict crop water requirement (Allen, 1996, Chiew et al., 1995). There are some mathematical models which apply measured climatic variables as independent variables for ET estimation (e.g., Thornthwaite, 1948, Blaney and Criddle, 1950, Turc, 1961, Jensen and Haise, 1963, Priestley and Taylor, 1972, Makkink, 1957, Hargreaves and Samani, 1985, and FAO-56 Penman Monteith (Allen et al., 1998)).

The term reference ET (ET₀) was introduced by the United Nations Food and Agriculture Organization (FAO) as a methodology for computing crop evapotranspiration (Doorenbos and Pruitt, 1977), because the interdependence of the factors affecting the ET makes the study of the evaporative demand of the atmosphere regardless of crop type, its stage of development and its management difficult. The reference evapotranspiration represents the evapotranspiration from a hypothesized reference crop (height 0.12 m, surface resistance 70 s m⁻¹ and albedo 0.23) (Allen et al., 1998).

In the recent past, the adapted FAO-56 Penman Monteith equation [which will be referred to as FAO56-PM in short] has been adopted as a reference equation for estimating the reference evapotranspiration (ET₀) and calibrating other ET₀ equations (Allen et al., 1998). The Penman–Monteith equation has two important advantages (Landeras et al., 2008): (i) it can be applied in a great variety of environments and climate scenarios without local calibration and (ii) it has been validated using lysimeters under a wide range of climatic conditions. On the other hand, the need for large number of climatic variables (e.g., air temperature, relative humidity, solar radiation and wind speed) is a major disadvantage of the FAO56-PM equation. Many stations are equipped with sensors for air temperature detection, but, the presence of sensors necessary for the detection of the remaining parameters is not so habitual and the data quality provided by them is sometimes poor (Droogers and Allen, 2002).

In the recent years, Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Genetic Programming (GP) methods have been applied in hydrology and water resources engineering issues. Recent experiments have reported that ANN may offer some promising results in hydrology and water resources engineering (Tahir, 1998, ASCE, 2000, Odhiambo et al., 2001, Kumar et al., 2002, Sudheer et al., 2003, Trajkovic, 2005, Maier and Dany, 2000, Supharatid, 2003, Kisi, 2004a, Kisi, 2004b, Kisi, 2005, Kisi, 2006a, Kisi, 2006b, Kisi, 2007, Kisi, 2009, Landeras et al., 2008, Jain et al., 2004).

Kisi (2006c) investigated the ability of ANFIS technique to improve the accuracy of daily evaporation estimation. Based on his results, the ANFIS computing technique could be used successfully in modeling evaporation process from the available climatic data. Kisi and Ozturk (2007) used the ANFIS computing technique for evapotranspiration estimation. Aytek (2009) modeled evapotranspiration using a co-active ANFIS. Moghaddamnia et al. (2009) applied ANN and ANFIS techniques for evaporation estimation in a hot and dry climate in Iran. Shiri et al., 2011a, Shiri et al., 2011b compared ANFIS to ANN to estimate daily pan evaporation values from climatic data and found ANFIS to be better than ANN. Shiri et al. (2011) used ANFIS for predicting short term operational water levels.

Khu et al. (2001) applied GP to real-time runoff forecasting for the Orgeval Catchment in France and compared the results with observations and with results obtained by using conventional methods. Their comparisons indicate GP to be of acceptable accuracy. Drecourt, 1999, Savic et al., 1999, Babovic and Keijzer, 2002, Muttil and Liong, 2001, Liong et al., 2002 and Aytek and Alp (2008) applied GP to rainfall–runoff modeling. Giustolisi (2004) determined the Chezy resistance coefficient using GP. Aytek and Kisi (2008) applied GP to transport streams with suspended sediment, and found it to be better than conventional rating curve and multi-linear regression techniques. Harris et al. (2003) used GP to predict velocity in compound channels with vegetated flood plains. Rabunal et al. (2007) applied GP and ANNs for the determination of the unit hydrograph of a typical urban basin. Babovic et al., 2001, Babovic et al., 2002 applied GP for modeling risks in water supply. Terzi and Keskin (2005) used the GP approach to estimate evaporation. Shiri and Kisi (2011a) applied artificial intelligence techniques (i.e. ANFIS, ANN and genetic programming) to estimate daily pan evaporation by using available and estimated climatic data in Iran. Shiri and Kisi (2011b) compared GEP to ANFIS for predicting groundwater table depth fluctuations and found GEP to give promising results. Kisi and Shiri (2011) introduced a new wavelet-GP conjunction model for precipitation forecasting.

A review of literature shows that applications of GEP for modeling evapotranspiration are limited. The study of Guven et al. (2008) applied GEP for modeling daily reference evapotranspiration as a function of solar radiation, mean air temperature, wind speed and relative humidity, and compared the performance of this model with other ET₀ equations. Their study demonstrates that a quadruple-input GEP model with the same meteorological requirements of Penman Monteith equation can be applied successfully as an alternative to other empirical ET₀ equations, in North, Central and South California. Nevertheless as it was mentioned above there could be many types of situations with a data lack of any meteorological parameter necessary for the FAO56-PM evapotranspiration estimation. In all these cases, the use of ET₀ alternative equations or ET₀ models with less meteorological inputs is recommended. The development of GEP models with less meteorological requirements than FAO56-PM equation is an almost unexplored task.

The objective of the present study is to demonstrate the applicability of GEP and ANFIS [which will be also referred to as NF in subsequent sections] in modeling daily evapotranspiration. In, this study accuracy of three different GEP models (quadruple-input GEP1 model with solar radiation, mean air temperature, wind speed and relative humidity, double-input GEP2 model with solar radiation and mean air temperature, triple-input GEP3 model with maximum and minimum air temperatures as well as extraterrestrial radiation), has been investigated and compared with corresponding ANFIS1, ANFIS2, ANFIS3, Priestley–Taylor and Hargreaves–Samani models in the Basque Country (Northern Spain). The equation FAO56-PM has been used as the reference. The paper is organized as follows. The next section presents a description of the methods applied in this study. The third section provides the information about the used data, methodological structure and statistical indexes. The applicability of the models on evapotranspiration estimation and the results are examined in the fourth section. Finally, the last section provides conclusions.