Elsevier

Agricultural Water Management

Volume 188, 1 July 2017, Pages 101-114
Agricultural Water Management

Research Paper
Evaluation of FAO56-PM, empirical, semi-empirical and gene expression programming approaches for estimating daily reference evapotranspiration in hyper-arid regions of Iran

https://doi.org/10.1016/j.agwat.2017.04.009Get rights and content

Highlights

  • Modeling daily ETo using different models are reported here.

  • Models were fed using original and estimated meteorological data.

  • Gene expression programming was compared with the empirical models.

  • Gene expression programming was superior in all studied cases.

Abstract

Accurate estimation of the reference evapotranspiration (ETo) is needed in water resources planning and management, irrigation scheduling and efficient agricultural water management. The FAO56-PM combination model is usually applied as a benchmark model for calculating ETo and calibrating other ETo models. However, the need for large amount of meteorological variables is a major drawback of this model, especially in case of data scarcity. Therefore, application of ETo models relying on fewer meteorological parameters, as well as calculating ETo using estimated meteorological variables is recommended in literature. The present paper aims at assessing the performances of different ETo models using the recorded and estimated meteorological parameters and comparing the results with the corresponding gene expression programming (GEP) models (based on the same input parameters of the employed ETo models) in hyper-arid regions. Daily meteorological parameters from 5 hyper-arid locations of Iran (covering a period of 12 years) were used. The commonly used Hargreaves (HG), Priestley-Taylor (PT), Turc (Tr) and Kimberly-Penman (KP, for alfalfa reference crop) were established and calibrated using both the recorded and estimated solar radiation, relative humidity, and wind speed data. The obtained results revealed that the GEP models outperform the corresponding empirical and semi-empirical models in all three studied categorizes (temperature/humidity-, radiation-, and combination-based approaches). The results also showed that the calibrated PT (original) and Tr (with estimated relative humidity) models gave the most accurate results among the related groups.

Introduction

Accurate assessment of evapotranspiration (ET) is needed for computation of crop water requirement, water resources management, and determination of the water budget, especially under arid conditions where water resources are scarce and fresh water is a limited resource (Allen et al., 1998). Knowledge of the ET is also essential for analyzing water balances at the land surface which is important to calculate the drainage requirements for preventing water logging and removing enough water from the root zone to enhance the crop production (Ridder and Boonstra, 1994). Nevertheless, continuous simulation hydrological models generally require (at least the minimum) inputs of rainfall amount as well as ET (Kay and Davies, 2008). Therefore, reliable estimation of evapotranspiration is of great importance. The term reference ET (ETo) 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 irrespective of crop type, its stage of development and its management difficult. The reference evapotranspiration represents the evapotranspiration from a hypothesized reference crop [grass] (height 0.12 m, surface resistance 70 s m−1 and albedo 0.23) (Allen et al., 1998). There are mainly five ETo computing model categories, e.g. water budget, mass transfer, combination-, temperature-, and radiation-based methods (Xu and Singh, 2002), from which, application of a specific model depends on data availability at each site. In the recent past, the Penman-Monteith ETo model adopted by FAO (FAO56-PM model) has been applied as the standard model for estimating ETo and calibrating other empirical and semi-empirical ETo models (Droogers and Allen, 2002). The model has been commonly used by agronomists, irrigation engineers and other scientists as the standard ETo model (e.g., Alexandris et al., 2006, Cai et al., 2007, Tabari et al., 2013). Despite its capability for application in a great variety of environments and climate scenarios without local calibration, the FAO56-PM model needs large number of climatic variables (e.g. air temperature, relative humidity, solar radiation and wind speed). Such meteorological variables are often incomplete in many weather stations, especially in developing regions. The Kimberly-Penman model (Wright and Jensen, 1972) (KP) is also utilized to compute the alfalfa-reference ET (ETr) which uses the same input parameters of the benchmark FAO56-PM model. The ETr values computed by the KP model should be adjusted to provide estimates of ETo to enable the comparisons between KP and FAO56-PM models (Irmak et al., 2003). In the contrary, there are some empirical and semi-empirical ETo models which use limited meteorological data. Among others, Hargreaves-Samani (Hargreaves and Samani, 1985) (HG), Priestley-Taylor (Priestley and Taylor, 1972) (PT), and Turc (Turc, 1961) (Tr) models have attracted more attention worldwide. In the case of the absence of the necessary parameters of FAO56-PM model, HG model can be applied to compute ETo values as recommended by Allen et al. (1998). Since the model needs only the temperature records of the station as well as the extraterrestrial radiation values (which can be calculated using the station’s latitude and the day of year), it can be used in wide variety of the locations with available temperature data. PT and Tr models can be applied when the temperature and solar radiation data are available. Nevertheless, establishing FAO56-PM and radiation-based models through using estimated (ancillary) data has been proposed in literature. Tabari et al. (2013) compared various ETo models in a humid condition of Northern parts of Iran and concluded that the radiation-based models are the best among other studied models, followed by the temperature-based and pan evaporation-based models. DehghaniSanij et al. (2004) assessed different temperature-based, radiation-based and combination-based ETo models in a semi-arid environment of Iran. The obtained results revealed the FAO56-PM superiority in simulating lysimeter data. Zhao et al. (2004) utilized FAO56-PM as the benchmark model and evaluated different ETo models (including HG) in a semi-arid region of China and found that the HG was the best ETo model in the studied region. Nandagiri and Kovoor (2006) evaluated the performances of various ETo methods in the major climate regimes of India and founded the HG as the best model in simulating benchmark FAO56-PM ETo values among other applied methodologies. Jabloun and Sahli (2008) compared ETo estimates provided through using limited data to those computed with full data set in Tunisia and revealed that the difference between ETo obtained from full and limited data set is small in the studied region. Sabziparvar and Tabari (2010) evaluated the performances of the Makkink, PT, and HG models against the standard FAO56-PM model in eastern arid and semiarid regions of Iran. The obtained results showed the superiority of HG model. Sabziparvar et al. (2010) evaluated various pan evaporation-based ETo models in cold semi-arid and warm arid climates of Iran. Tabari (2010) evaluated Makkink, Tr, PT and HG models for ETo estimation in four different climatic contexts and found that the Tr model was the best model of FAO56-PM ETo estimation in cold humid and arid climates, while the HG was the optimal model in warm humid and semi-arid regions. Rahimikhoob et al. (2012) tested the performance and characteristic behavior of four ETo models in a subtropical climate and revealed the need for a local calibration of the empirical and semi-empirical ETo models. From the literature review it might be stated that in general, no one model is the best for all climatic contexts and scenarios.

As an alternative to the empirical and semi-empirical ETo models, heuristic data driven models [e.g. gene expression programming, GEP] has been widely employed in the recent years. According to Ferreira (2001), the advantages of GEP are: (i) the chromosomes are simple entities: linear, compact, relatively small, easy to manipulate genetically (replicate, mutate, recombine, etc); (ii) the expression trees are exclusively the expression of their respective chromosomes; they are entities upon which selection acts, and according to fitness, they are selected to reproduce with modification. The genetic programming models (i.e., GEP) are superior to other heuristic models in giving explicit formulations for the studied problem which shows the relationships between the input and target parameters. Moreover, in the GEP approaches there is no predefined function to be considered (GEP randomly creates formed functions and selects the one that best fits the experimental results). Also, there is no restriction in the complexity and structure of the randomly formed functions (Guven et al., 2008). Genetic programming (i.e. GEP) is less sensitive to the number of inputs (i.e. different data columns used) as it is to the information content in the data used. The goal of data design is to maximize the relevance of the data regarding the ability to have predicative value for the desired output while minimizing the redundancy between various data inputs (i.e. the data columns). Minimizing the redundancy is important because collecting unproductive data wastes resources and an excessive number of data inputs can degrade model accuracy. This involves collecting data over a range of conditions; much like one would do using a design of experiment approach. Hence, the genetic programming approach can be used with any number of years of data, provided the information content in the data set is sufficient to evolve a generalized formulation (Deschaine, 2014). Different applications of heuristic data driven models in water resources engineering have been reported by researchers. In ETo modeling context, Landeras et al. (2008) compared neural networks and different empirical and semi-empirical ETo models in the humid region of Basque County, Spain. Pour Ali Baba et al. (2013) tested various neural networks and neuro-fuzzy models for estimating daily ETo using the both recorded and estimated solar radiation data. Falamarzi et al. (2014) developed wavelet-based neural networks models to forecast daily ETo using temperature and wind speed data. Kisi (2016) applied three different heuristic regression approaches for ETo estimation in Turkey. Traore et al. (2016) applied neural networks technique for forecasting near future ETo values using restricted climate information. Feng et al. (2016) employed different neural networks models for ETo estimating in humid regions of Southwest China. Yassin et al. (2016) compared GEP with neural networks in estimating daily ETo values under arid conditions and concluded that the neural networks −based ETo models were slightly better than GEP-based models. Also, Guven and Kisi (2011), Guven et al. (2008), Shiri and Kisi (2011), Shiri et al., 2012, Shiri et al., 2013, Shiri et al., 2014a, Shiri et al., 2014b, Shiri et al., 2015 and Kisi (2016) have applied GEP for ETo modeling using different data management scenarios and climatic contexts. Genetic programming has the advantage where the structure and constants for a solution are evolved simultaneously. This increases the degrees of freedom over other function fitting methods, such as regression and other methods which use a prescribed mathematical structure, including parameter estimation of fixed physically based models. Combining physically based models with subject matter expertise and site specific data has been demonstrated to produce higher quality representations over methods that solely rely on a single approach (Deschaine, 2014). The present study aims at presenting GEP models (which have been fed with the original and the estimated meteorological parameters) for estimating daily ETo values in a hyper-arid region of Iran and comparing with the corresponding empirical and semi-empirical ETo models (utilizing the same original and estimated meteorological parameters).

Section snippets

Used data

Daily meteorological data from five weather stations in dry region of Iran were used in the present research. Table 1 summarizes the positions of the studied stations. The annual precipitation value of the studied stations is generally less than 300 mm. Among the studied cases, Bushehr is a coastal station with the lowest altitude (9 m). Data samples consisted of daily values of air temperature (TA) [including maximum (Tmax), mean (Tmean) and minimum (Tmin) air temperature values], relative

Implementation and evaluation of empirical and semi–empirical models

The ratio [Kr] between the ETr (estimated by KP variants) and ETo (obtained by FAO565-PM model) is a measure for adjusting ETr values to be comparable to FAO56-PM ETo calculations. The Kr values of different KP variants for the whole study period are presented in Fig. 1. The range of Kr values is from 0.913 to 1.404, with an average of 1.158. However, some greater values have been observed for summer season during this period. Jensen et al. (1990) used an approximate value of 1.15 for Kr.

Conclusions

A modeling study is reported here to estimate daily ETo using meteorological data by utilizing empirical and heuristic data driven (GEP) approaches. The obtained results revealed that GEP surpasses the other applied empirical and semi empirical ETo models in all cases. While the specific models evolved on this data may not be directly transferrable to other locations with different meteorological situations (since they are site specific) the process presented in this paper is general and is

Acknowledgments

Dr. Larry M. Deschaine, PE an Optimization and Machine Learning Subject Matter Expert with HydroGeoLogic, Inc. Reston, VA USA (www.hgl.com) provided technical insight and review of specific questions to support the theoretical and application aspects of machine leaning to this study.

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