Estimation of maize evapotranspiration using extreme learning machine and generalized regression neural network on the China Loess Plateau

Population growth and increasing consumption of calorie- and meat-intensive diets are expected to roughly double human food demand by 2050 (Mueller et al. 2012). To meet this increasing food demand in the coming decades, new practices for agricultural water management must be developed, especially in arid and semiarid regions, to boost crop production per amount of water use, i.e., crop water use efficiency (WUE). As the only term that appears in both water balance and surface energy balance equations (Xu & Singh 2005), evapotranspiration (ET) is not only the basis of a deep understanding of ecological and hydrological processes, but also an important indicator to evaluate WUE in agriculture. About half the lands on Earth are short of water (Newman et al. 2006), and more than 90% of water used in agriculture is lost by ET (Rana & Katerji 2000; Ding et al. 2013). Therefore, accurate estimation of ET is of importance to regional agricultural water management aiming at water saving and an increase of WUE (Zhang et al. 2013).

In the past decades, numerous methods, which can be grouped into single-layer (e.g., Penman–Monteith), two-layer (e.g., Shuttleworth–Wallace) and multi-layer (e.g., Clummping) models (Monteith 1965; Shuttleworth & Wallace 1985; Brenner & Incoll 1997), have been proposed for ET estimation since direct measurement of ET is difficult, costly, and not available in many regions (Allen et al. 1998; Ding et al. 2013). The main limitation of these methods developed on a physical basis, however, is their required input data cannot be easily measured, such as aerodynamic resistance and surface resistance (Allen 2000; Ding et al. 2013). To overcome this deficiency, the indirect FAO-56 dual crop coefficient approach was proposed by Allen et al. (1998), which was the product of reference evapotranspiration (ET₀) and crop coefficient (K_c). ET₀ is the evapotranspiration rate of the reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s/m, and an albedo of 0.23, while K_c, the ratio of ET and ET₀, represents the effects of characteristics that distinguish the specific field crops from the reference crop. Compared with the single K_c method, the dual K_c approach makes it possible to better assess the impacts of soil wetting by rain or irrigation, as well as the impacts of keeping part of the soil dry or using mulches for controlling soil evaporation (Zhang et al. 2013), and has been widely applied for ET estimation due to the simplicity and good performances of the approach (Allen 2000; Rousseaux et al. 2009; Liu & Luo 2010; Ferreira et al. 2012; Zhao et al. 2015). Although good performances of this approach have been widely reported, the straightforward adoption of generalized crop coefficients recommended by FAO-56 can lead to errors in the estimation of ET since the dividing of crop growth period and associated crop coefficients are closely related to local climate and crop conditions (Katerji & Rana 2006; Poblete-Echeverría & Ortega-Farias 2013; Zhao et al. 2015). Thus, a modification of the dual K_c approach is needed when applying the method for ET estimation.

In recent years, artificial intelligence (AI) has been successfully implemented in ET₀ estimation. The application of AI in ET₀ modeling was first investigated after 2000 by Kumar et al. (2002), who estimated ET₀ using an artificial neural network (ANN). Since then, efforts towards the estimation of ET₀ using ANN models have been performed (Trajkovic et al. 2003; Kisi 2006; Kim & Kim 2008; Landeras et al. 2008; Traore et al. 2010; Martí et al. 2011a). More recently, many studies have proposed some new AI approaches for ET₀ estimation: Tabari et al. (2012) investigated the performances of support vector machines, adaptive neuro-fuzzy inference system for ET₀ estimation in a semi-arid highland environment in Iran; Shiri et al. (2011, 2012) applied a genetic programming approach for ET₀ and evaporation modeling; Kisi et al. (2012) developed generalized neurofuzzy-based evaporation models in Arizona, USA; Pour Ali Baba et al. (2013) estimated ET₀ using adaptive neuro-fuzzy inference system and ANN for two weather stations in South Korea; Kisi (2013) investigated the applicability of Mamdani and Sugeno fuzzy genetic approaches in modeling ET₀ in Turkey; Shiri et al. (2013) and Martí et al. (2015) used gene expression programming for ET₀ estimation; Kisi (2016) investigated the ability of least square support vector regression, multivariate adaptive regression splines and M5 Model Tree in modeling ET₀ in Turkey; Abdullah et al. (2015) and Feng et al. (2016) examined the capability of extreme learning machine (ELM) for ET₀ estimation in Iraq and Southwest China, respectively. All these studies confirmed good performances of AI approaches for ET₀ estimation worldwide. Differently to ET₀, which is from a reference crop and only affected by meteorological variables, ET for a specific crop is more complicated and affected not only by meteorological variables but also soil properties, crop characteristics, and agronomy management. To the best knowledge of the authors, there are no former studies evaluating the performances of AI approaches for rainfed maize ET estimation considering experimental data as targets.

This study applied two AI approaches, i.e., ELM and generalized regression neural network (GRNN), for maize ET estimation using meteorological and crop data on the China Loess Plateau. The performances of ELM and GRNN were assessed against the modified dual K_c approach for evaluating the newly proposed models considering measured maize ET data from eddy covariance systems in a rainfed cropland as benchmark.

The study was carried out in a rainfed spring maize field at the Experimental Station of Dryland Agriculture and Environment (ESDAE), Ministry of Agriculture, P. R. China, which is located in Shouyang, Shanxi Province, northern P. R. China (37°45′58″N,113°12′9″E, 1,202 m Alt.) during three maize growing seasons (from May 1 to September 28, 2011, May 3 to September 22, 2012, and April 28 to September 25, 2013). The experimental station has a typical continental temperate climate with a mean daily temperature of 7.4 °C, mean annual precipitation of 481 mm and mean annual frost-free days of 140 days. Mean annual precipitation during the growing season of spring maize is about 330 mm. The soil at the experimental station is classified as a cinnamon soil with light clay loam texture and an average bulk density of 1.34 g/cm³. Average volumetric soil water content at field capacity and wilting point were 36.0% and 12.0% to a depth of 1.0 m, respectively. Groundwater is about 150 m below ground surface (Gong et al. 2015).

The maize crop, variety Jingdan-951, was sown in north–south rows with the distance between rows equal to 50 cm and the space between two plants within rows of 30 cm. The maize sowing rate was 66,667 seeds per ha for 3 years. The area of the experiment plots is about 3.0 ha, of which length and width is 200 m and 150 m, respectively, which meets the minimum fetch requirement of eddy covariance system installation (Gong et al. 2015).

Half-hourly meteorological variables were obtained by an automatic weather station (Campbell Scientific Inc., Logan, UT, USA) nearby the experimental plots (Gong et al. 2015). Solar radiation (R_s) was measured with a Silicon Pyranometer (LI200X, LI-COR, Inc., Lincoln, NE, USA) and precipitation (P) was registered with a pluviometer (RGB1, Campbell Scientific Inc.). Wind speed (u₂) and its direction (w) were measured using a cup anemometer and a wind vane (03002-L, R. M. Young Inc., Traverse, MI, USA), respectively. Air temperature (T) and relative humidity (RH) were measured using a Vaisala probe (HMP45C, Vaisala Inc., Tucson, AZ, USA). All variables were monitored at 2 m above the surface and recorded in a data-logger (CR10RX, Campbell Scientific Inc.).

In the center of the experimental plot, latent (LE) and sensible heat (H) fluxes were measured by an open-path eddy covariance system mounted on a tower, which consisted of an open-path infrared gas analyzer (LI-COR Inc., model LI-7500) and a three-dimensional supersonic anemometer (Campbell Scientific Inc., model CSAT3). A temperature and humidity sensor (Campbell Scientific Inc., model HMP45C), a four-way net radiometer (Kipp & Zonen Inc., Delftechpark, The Netherlands, model CNR1), and self-calibrating heat flux sensors (Campbell Scientific Inc., model HFP01) were also used. The sensor height was adjusted to keep the relative height of 0.5 m between sensors and maize canopy constant at interval of 5–7 days. Specific time length depended on the increments of canopy height. The observation site had a wide fetch of at least 50 m in all directions, which allowed us to neglect heat advection in the maize field (Gong et al. 2015). All of the measured meteorological and fluxes data were averaged at daily timescale in the present study.

Two different input combinations were selected to train the GRNN and ELM models. One considered meteorological and crop data as input, the same input data as the modified dual K_c approach, and the other combination considered meteorological data as input to evaluate the capabilities of the ELM and GRNN when only meteorological data are available. Table 1 presents a summary of the input combinations for each model. ELM1 and GRNN1 were fed with meteorological (maximum, minimum, and mean air temperature, maximum, minimum, and mean relative humidity, solar radiation, and wind speed at 2 m height) and crop data (leaf area index and plant height). ELM2 and GRNN2 were fed only with meteorological data since the crop data are not commonly available.

Although k-fold assessment is recommended for assessing the performances of AI models (Martí et al. 2011b, 2015; Shiri et al. 2014a, 2014b, 2015), a simple data set assignment was considered for this study. The k-fold assessment would have involved computational costs that could not be assumed. The considered assessment procedure is a very common practice for AI models' assessment (Shiri et al. 2014c). The data of 2011 and 2012 were used to train the ELM and GRNN models, and data of 2013 were applied to assess the performances of the models. Thus, 293 patterns were available for training, while 150 patterns were used for testing.

T is air temperature, including maximum, minimum, and mean air temperature; RH is relative humidity, including maximum, minimum, and mean relative humidity; R_s is solar radiation; u₂ is wind speed at 2 m height; LAI is leaf area index; h_c is plant height.

Table 2 presents parameters of dual K_c approach for maize ET estimation in 2013. Z_e was 0.1 m in this study, recommended by FAO-56 (Allen et al. 1998). Measured maximum h_c and LAI were 2.97 m and 3.95 m²/m², respectively. REW, TEW, and TAW were calibrated using soil property data, with values of 7, 23, and 181 mm, respectively. Greater TEW and TAW may be due to the fact that the soil in the experimental site was sandy loam, leading to a greater soil water content at field capacity (36.2%). According to Allen & Pereira (2009) and Ding et al. (2013), accurate estimation of canopy cover coefficient could be achieved when κ was 0.7.

Statistical performances of ELM, GRNN, and dual K_c models for maize ET estimation in 2013 are presented in Table 3. Based on the statistical indicators, ELM1 had the best performances for ET estimation, with RMSE of 0.221 mm/d, MAE of 0.203 mm/d, and NS of 0.981, respectively; estimated ET by ELM1 was 364.8 mm, which was 1.3% lower than measured ET. GRNN1 had good performances for ET estimation, too, with RMSE of 0.225 mm/d, MAE of 0.211 mm/d, and NS of 0.981, respectively; estimated ET by GRNN1 was 378.3 mm, which was 2.4% greater than measured ET. The performances of FAO-56 dual K_c approach were poorer than those of ELM1 and GRNN1, but better than those of ELM2 and GRNN2, with RMSE of 0.381 mm/d, MAE of 0.332 mm/d, and NS of 0.871, respectively. Although ELM2 and GRNN2 were not as efficient as ELM1, GRNN1, and dual K_c models, their estimation of ET was acceptable when only meteorological data were available.

Overall, this study found that the ELM and GRNN models can be applied successfully for maize ET estimation. Compared with GRNN, ELM was more efficient. In contrast to traditional FFNN, ELM randomly chooses hidden nodes and analytically determines the output weights, which may result in better performances of ELM. Although good performances of ELM and GRNN were found, they have no physical basis and belong to a class of data-driven black-box approaches (Tabari et al. 2012, 2013). In addition, they cannot partition ET separately into evaporation and transpiration.

The potential of ELM and GRNN for estimation of rainfed maize evapotranspiration was investigated on the China Loess Plateau in this study. A field experiment was conducted during maize growing seasons of 2011–2013 for continuous measurements of maize ET with eddy covariance systems, meteorological variables with automatic weather station, LAI, and h_c. These data were used to train the ELM and GRNN models consisting of two combinations of meteorological and crop parameters. The ELM1 and GRNN1 models whose inputs were meteorological and crop data performed better than the modified dual K_c model, which confirmed the capabilities of ELM and GRNN models for maize ET estimation. Although the ELM2 and GRNN2 models using only meteorological data were not as efficient as ELM1, GRNN1, and dual K_c models, their accuracy for maize ET estimation was acceptable, and could be considered as a tool to estimate maize ET when crop data are insufficient.

We are grateful for the research grants from the National Natural Science Foundation of China (No. 51179194), National Key Technologies R&D Program of China (No. 2015BAD24B01, No. 2012BAD09B01) and Basic Science Research Foundation of China Central Government (BSRF201609). Cordial thanks are extended to the editor and three anonymous reviewers for their valuable comments.