Modeling reference evapotranspiration using extreme learning machine and generalized regression neural network only with temperature data

doi:10.1016/j.compag.2017.01.027

Computers and Electronics in Agriculture

Volume 136, 15 April 2017, Pages 71-78

https://doi.org/10.1016/j.compag.2017.01.027 Get rights and content

Highlights

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ELM, GRNN and Hargreaves were applied to estimate daily ET₀ only using temperature data.
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Local and pooled data management scenarios were developed/calibrated and tested.
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ELM performed better than GRNN, Hargreaves and calibrated Hargreaves for local scenario.
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GRNN provided the most accurate results among the considered models for pooled scenario.

Abstract

Accurate estimation of reference evapotranspiration (ET₀) is essential to agricultural water management. The present study developed two artificial intelligence models for daily ET₀ estimation only with temperature data, including extreme learning machine (ELM) and generalized regression neural network (GRNN) in 6 meteorological stations of Sichuan basin, southwest China, and compared the proposed ELM and GRNN with the corresponding temperature-based Hargreaves (HG) model and its calibrated version considering FAO-56 Penman-Monteith ET₀ as benchmark. Two data management scenarios were evaluated for estimation of ET₀: (1) the models were trained/calibrated and tested using the local data of each station; and (2) the models were trained/calibrated using the pooled data from all the stations and tested in each station. In the first scenario, the results showed that the temperature-based ELM model provided the better estimation than the GRNN, HG and calibrated HG models, with average relative root mean square error (RRMSE) of 0.198, mean absolute error (MAE) of 0.267 mm/d and Nash-Sutcliffe coefficient (NS) of 0.891, respectively. In the second scenario, GRNN model provided the most accurate results among the considered models, with average RRMSE of 0.194, MAE of 0.263 mm/d and NS of 0.895, respectively. Both of the temperature-based GRNN and ELM performed much better than the HG and calibrated HG models for the two scenarios, and the temperature-based GRNN and ELM models are appropriate alternatives for accurate estimation of ET₀ for Sichuan basin of southwest China, which is very helpful for farmers or irrigation system operators to improve their irrigation scheduling.

Introduction

As the only term that appears in both water balance and surface energy balance equation (Xu and Singh, 2005), evapotranspiration (ET) is of importance for ecological and hydrological processes, and plays a key role in designing and operating irrigation projects (Abdullah et al., 2015). Its accurate estimation provides valuable information for computation of crop water requirement, development of irrigation scheduling, management of water resources and determination of the water budget (Shiri et al., 2012).

ET can be measured directly by experimental techniques, e.g. eddy covariance systems, lysimeters and Bowen ratio energy balance (Zhang et al., 2013, Kool et al., 2014, Martí et al., 2015), but these methods are complex, costly and not available in many regions (Allen et al., 1998, Ding et al., 2013). Therefore, development of mathematical models for ET estimation is highly needed, which usually relies on reference evapotranspiration (ET₀). The FAO-56 Penman-Monteith (PM) model is recommended as the sole standard method for estimating ET₀ and validating other models (Allen et al., 1998), which requires a number of meteorological variables, including maximum and minimum air temperature, solar radiation, relative humidity and wind speed. However, these meteorological inputs are not commonly available or unreliable, especially in developing countries (Droogers and Allen, 2002, Almorox et al., 2015). According to Shih (1984) and Traore et al. (2010), an ideal method for estimating of ET₀ should be selected based on minimal input data variables without affecting the accuracy of estimation. Thus temperature-based Hargreaves (HG) model is an alternative due to its simplicity and high accuracy (Jensen et al., 1997), and can be applied for future estimation of ET₀ using the temperature forecasts (Luo et al., 2014). Allen et al. (1998) recommended the HG model as PM alternative method for ET₀ estimation when the data set of PM model required are not fully available. Almorox et al. (2015) assessed 11 representative temperature-based methods for estimating ET₀, HG model provided the most accurate global average performance in arid, semiarid, temperate, cold and polar climates. But the model usually underestimates ET₀ under high wind conditions (wind speed > 3 m/s) and overestimates under conditions of high relative humidity or at low evapotranspiration rates (Allen et al., 1998, Droogers and Allen, 2002, Xu and Singh, 2002), so a local calibration of HG model is very necessary.

In the last years, artificial intelligence (AI) models have been successfully applied to estimate ET₀ with limited meteorological data. The implementation of AI models in ET₀ estimation was first investigated by Kumar et al. (2002) using artificial neural network (ANN). Later, AAN in modeling ET₀ received much attention from researchers (Trajkovic et al., 2003, Kisi, 2006, Kisi, 2008, Zanetti et al., 2007, Kim and Kim, 2008, Landeras et al., 2008, Traore et al., 2010, Martí et al., 2011). Kumar et al. (2011) discussed ANN architecture, development, selection of training algorithm and performance criteria for ET₀ estimation. However, ANN requires many data for training, and is easily getting stuck in a local minimum. Some new AI models have been proposed for ET₀ estimation, e.g. support vector machines (Kisi and Cimen, 2009, Tabari et al., 2012), adaptive neuro-fuzzy inference system (Tabari et al., 2012, Pour Ali Baba et al., 2013, Shiri et al., 2011, Shiri et al., 2014), generalized neurofuzzy models (Kisi et al., 2012), M5 Model Tree (Kisi, 2016), fuzzy genetic approaches (Kisi and Cengiz, 2013, Kisi, 2013), gene expression programming (Shiri et al., 2014, Martí et al., 2015), and extreme learning machine (ELM) (Abdullah et al., 2015, Patil and Deka, 2016, Feng et al., 2016a).

Sichuan basin is one of the major agricultural regions in China, but seasonal drought happens frequently in this area. Scarcity of water and growing demand for food supplies emphasize on developing improved methods for crop-water estimation (Patil and Deka, 2016). Moreover, real-time irrigation management and water resources allocation is highly need in China for development of precision agriculture. Accurate estimation of ET₀ is crucial to enhance precision irrigation level and increase water use efficiency. The present study aims to investigate the ability of ELM and generalized regression neural network (GRNN) for ET₀ estimation only with temperature inputs, considering two data management scenarios (I) the models were trained and tested using the local data of each station; and (II) the models were trained using the pooled data from all the stations and tested in each station. Further, the ELM and GRNN models were compared against to the well-known empirical Hargreaves models.

Section snippets

Study area and data set

The study area is located in Sichuan basin, with an area of about 0.26 million km², a population of 90 million. The well-known Dujiangyan Irrigation Project is located in the centre of Sichuan basin, supplying irrigation water for 0.7 million hm² irrigated farmland. The study area has a warm and humid climate, with mean annual air temperature of 17.4 °C and mean annual relative humidity of 79.5%. The meteorological stations and the statistical properties of climatic variables are shown in Table 1.

Local implementation of the models

The performance of the ELM, GRNN, HG and calibrated HG models during the test period is given in Fig. 2. From the general trend of RRMSE, MAE and NS, as presented in Fig. 2, the temperature-based ELM model had the best performances, with RRMSE ranging 0.167–0.222, MAE ranging 0.228–0.315 mm/d and NS ranging 0.844–0.933, respectively. The ELM model performed best at station 6 (Liangping) while the model performed poorest at station 2 (Mianyang). The performance of temperature-based GRNN model

Conclusion

The present study investigated the applicability of temperature-based ELM and GRNN models for daily ET₀ estimation in Sichuan basin, southwest China. In the first part of the present study, the ELM, GRNN and HG models were trained/calibrated separately at each station, and tested at each station considering FAO-56 PM ET₀ as the benchmark. In the second part, the ELM, GRNN and HG models were trained/calibrated using the pooled data of the stations and were tested separately at each station.

The

Acknowledgments

We thank the National Climatic Centre of the China Meteorological Administration for providing the climate database used in this study. This work is finantially supported by National Key Technologies R&D Program of China (No. 2015BAD24B01) and the National Key Research and Development Program of China (2016YFC0400206). Cordial thanks are extended to the editor and two anonymous reviewers for their valuable comments.

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¹: These authors contributed equally to this work.

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Original papersModeling reference evapotranspiration using extreme learning machine and generalized regression neural network only with temperature data

Highlights

Abstract

Introduction

Section snippets

Study area and data set

Local implementation of the models

Conclusion

Acknowledgments

J. Hydrol.

J. Hydrol.

Agric. Water Manage.

J. Hydrol.

Agric. Water Manage.

Comput. Electron. Agr.

Neurocomputing

J. Hydrol.

J. Hydrol.

Agric. Water Manage.

Agric. For. Meteorol.

Agric. Water Manage.

Agric. Water Manage.

Agric. Water Manage.

Comput. Electron. Agr.

J. Hydrol.

Comput. Electron. Agr.

Comput. Electron. Agr.

J. Hydrol.

Agric. Water Manage.

J. Hydrol.

Estimating reference evapotranspiration under inaccurate data conditions

Irrig. Drain. Syst.

Estimation of maize evapotranspiration using extreme learning machine and generalized regression neural network on the china loess plateau

Hydrol. Res.

Original papers
Modeling reference evapotranspiration using extreme learning machine and generalized regression neural network only with temperature data