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This study presents an extreme learning machine (ELM) approach, for estimating monthly reference evapotranspiration (ET0) in two weather stations in Serbia (Nis and Belgrade stations), for a 31-year period (1980–2010). The data set including minimum and maximum air temperatures, actual vapour pressure, wind speed and sunshine hours was employed for modelling ET0 using the adjusted Hargreaves (ET0,AHARG), Priestley–Taylor (ET0,PT) and Turc (ET0,T) equations. The reliability of the computational model was accessed based on simulation results and using five statistical tests including mean absolute percentage error (MAPE), mean absolute deviation (MAD), root-mean-square error (RMSE), Pearson correlation coefficient (r) and coefficient of determination (R2). The validity of ELM modelled ET0 are compared with the FAO-56 Penman–Monteith equation (ET0,PM) which is used as the reference model. For the Belgrade and Nis stations, the ET0,AHARG ELM model with MAPE = 9.353 and 10.299%, MAD = 0.142 and 0.151 mm/day, RMSE = 0.180 and 0.192 mm/day, r = 0.994 and 0.992, R2 = 0.988 and 0.984 in testing period, was found to be superior in modelling monthly ET0 than the other models, respectively.

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... The popularity of machine learning in recent years can be attributed to the incorporation of probability and statistics into the algorithm that deals with traditional fixed rule-based models, which require manual input [27]. Machine learning models, in general, are black boxes in nature, but several studies conducted have shown their consistent reliability and accuracy in ETo estimation applications compared to other established empirical models [15,22,23,[28][29][30]. Among these machine learning models, the Support Vector Machine (SVM) and Extreme Learning Machine (ELM) have generally exhibited better prediction accuracy in ETo estimations in various studies worldwide, such as in India [31], China [32,33], and Spain [34]. ...

... There are different kernel functions that can be applied for the transformation of data suitable for finding linear decision boundaries for different non-linearly separable data sets. The commonly used Radial Basis Function (RBF) non-linear kernel function was used in this study due to its better performance in ETo and estimations compared with other kernel functions [22,29], which is expressed as: ...

... ELM has a more favorable general capability with faster learning speed; it does not require too much human intervention and can run much faster than the conventional algorithms. ELM is an efficient algorithm with numerous advantages such as ease of use, quick learning speed, higher performance, and suitability for many nonlinear activation and kernel functions [29,57,58]. The basic theory of ELM can be given as follows: ...

The need for accurate estimates of reference crop evapotranspiration (ETo) is important in irrigation planning and design, irrigation scheduling, reservoir management among other applications. ETo can be accurately determined using the internationally accepted FAO Penman–Monteith (FAO-56 PM) equation. However, this requires numerous observed data, including solar radiation, air temperature, relative humidity, and wind speed, which in most cases are unavailable, particularly in developing countries such as the Philippines. This study developed models based on Support Vector Machines (SVMs) and Extreme Learning Machines (ELMs) for the estimation of daily ETo using different input combinations of meteorological data in Region IV-A, Philippines. The performance of machine learning models was compared with the different established alternative empirical models for ETo. The results show that the SVM and ELM models, with at least Tmax, Tmin, and Rs as inputs, provide the best daily ETo estimates. The accuracy of machine learning models was also found to be superior compared to the empirical models given with same input requirements. In general, SVM and ELM models showed similar modeling performance, although the former showed lower run time than the latter

... For instance, the Jensen-Haise model used local meteorological data from the western United States to build the dimensionless energy equation for determining ETo, but its applicability in other locations is limited (Dong et al., 2021;Gao et al., 2021). ML models effectively reach the optimal solution by continuously adjusting the input weights and biases of the models throughout algorithm execution, which has the benefits of good stability, robustness, fast learning, and good generalization performance (Dong et al., 2021;Gao et al., 2021;Gocic et al., 2016;Malik et al., 2021;Wu et al., 2021). The daily ETo estimation accuracy of the ELM models was more accurate than that of the empirical models, and similar results have been reported in research conducted in various climate regions (Chia et al., 2021;Saggi et al., 2022;Tejada et al., 2022;Wu et al., 2021;Zhao et al., 2022;Zhu et al., 2020). ...

... In comparison to ELM, the improved ELM based on biological heuristic algorithms had better global convergence and merit-seeking capacity, hence avoiding local convergence and generating suboptimal solutions, thereby significantly enhancing the accuracy and efficiency of the models (Gocic et al., 2016;Huang et al., 2006;Kumar et al., 2016). In this study, combining biological heuristic algorithms (GWO, MFO, PSO, and WOA) with ELM increased the estimation accuracy of ELM models, which was supported by many other studies (Gao et al., 2021;Mokari et al., 2022;Wu et al., 2021;Zhao et al., 2022;Zhu et al., 2020). ...

Due to frequent drought events, increased water demand for agricultural production and limited, accurate estimation of reference evapotranspiration (ETo) is necessary for developing crop irrigation schemes and rational allocation of regional water resources. The extreme learning machine (ELM) was optimized using four biological heuristic algorithms, namely, Grey Wolf Optimizer (GWO-ELM), Moth-Flame Optimization (MFO-ELM), Particle Swarm Optimization (PSO-ELM), Whale Optimization Algorithm (WOA-ELM), and besides three types of empirical models (temperature-, radiation-, and mass transfer-based), and Penman model (P-M) were also applied to estimate the daily ETo in the Hetao irrigation district (HID). The results demonstrated that GWO-ELM obtained the highest estimation accuracy (R2 = 0.945–0.955; RRMSE = 14.52–15.29%; MAE = 0.124–0.141 mm d⁻¹, and NSE = 0.942–0.952) at all stations when using mass transfer combination (Tmax, Tmin, RH, u2) as models input, and the GWO-ELM hybrid model outperformed other models. Herein, the biogenic heuristic algorithm can effectively enhance the ELM performance in ETo estimation, it was strongly recommended for estimating daily ETo in the HID using the hybrid GWO-ELM model and mass transfer combination as input. The optimized hybrid algorithms, especially GWO-ELM, can accurately estimate daily ETo with limited meteorological data, which can provide scientific guidance for the development of precision agriculture in the HID.
Abbreviations: ANN: artificial neural network; BP: back propagation neural network; CMA: China Meteorological Administration; D-T: Dalton; EL: elevation; ELM: extreme learning machine; ETo: reference evapotranspiration; GEP: gene expression programming; GP: genetic programming; GWO: gray wolf optimization; H-S: Hargreaves-Samani; MFO: moth flame optimization; ML: machine learning; P-M model: FAO-56 Penman-Monteith (P-M) model; P-T: Priestley-Taylor; PSO: particle swarm optimization; RF: random forest; R-O: Rohwer; SVM: support vector machine; SVR: support vector regression; WOA: whale optimization algorithm

... In recent years, the extreme leaning machine (ELM) model has attracted a wide range of scholars' interests for its light and simple structure, high efficiency and stability. It has been applied in simulating many kinds of natural phenomena Deo et al., 2016), including ET 0 (Gocic et al., 2016;Fan et al., 2018;Kumar et al., 2016;Feng et al., 2016Feng et al., , 2017b. Abdullah et al. (2015) firstly introduced the ELM model for estimating ET 0 . ...

... Abdullah et al. (2015) firstly introduced the ELM model for estimating ET 0 . Gocic et al. (2016) verified the excellent performance of the ELM model in Nis and Belgrade of Serbia. Patil and Deka (2016) assessed the suitability of the ELM, artificial neutral networks (ANN) and empirical models under three input combinations in the Thar Desert, India. ...

Accurate and fast estimation of reference evapotranspiration (ET0) is important in determining crop water requirements, designing irrigation schedule, planning and managing agricultural water resources, especially when limited meteorological data are available. This study proposed a novel kernel extreme learning machine model coupled with the K-means clustering and firefly algorithms (Kmeans-FFA-KELM) with 5, 10, 15, 20, 25, 30 and 40 data subsets for estimating monthly mean daily ET0 in parallel computation in the Poyang Lake basin of South China with pooled temperature data from 26 weather stations. Two input combinations, i.e. (1) mean temperature (Tavg) and extraterrestrial radiation (Ra), (2) maximum and minimum temperatures (Tmax and Tmin) and Ra, were considered. Meteorological data during 1966–2000 were used to train the models, while those for the period 2001–2015 were used for model testing. The results showed that the prediction accuracy of selected machine learning models with Tmax, Tmin and Ra was improved by 7.0–15.5% in terms of RMSE compared to that with Tavg and Ra during testing. The FFA-KELM model slightly outperformed the adaptive network based fuzzy inference system (ANFIS) model, both of which were superior to the random forest (RF) and M5 prime model tree (M5P) models, followed by the Hargreaves and Thornthwaite models. The RMSE values of Kmeans-FFA-KELM models with more than 20 subsets were decreased by 0.7–3.5% compared with those of the FFA-KELM models. The Kmeans-FFA-KELM model with 25 subsets (FFA-KELM-25) outperformed the FFA-KELM model in summer and in the count of absolute errors greater than 0.9 mm d⁻¹. The computational time of Kmeans-FFA-KELM models first decreased and then increased with the increase of the subset number. The parallel FFA-KELM-25 model (0.5–0.7 s) significantly reduced the computational time, which was 10–13 times faster than the sequential Kmeans-FFA-KELM model (7.0–7.4 s), and 1185–1603 times faster than the FFA-KELM model (802.2–830.0 s). This study provides a new and fast modeling method for processing large datasets in agricultural and water resources studies on a regional scale.

... In the last decade, advances in computation have led to the introduction of Machine Learning (ML) methodologies in the reference evapotranspiration calculation, proving its high accuracy results by using different approaches. Several ML models have been studied such as Multilayer Perceptron (MLP) (Jahanbani and El-Shafie, 2011;Kumar et al., 2002;Martí et al., 2010;Wang et al., 2008), Support Vector Machine (SVM) (Fan et al., 2018;Ferreira et al., 2019;Guo et al., 2011;Kisi, 2013;Shrestha and Shukla, 2015;Tabari et al., 2012;Wen et al., 2015), Decision Tree (DT) and ensemble learning models (Fan et al., 2018;Feng et al., 2017a;Kisi and Kilic, 2016;Pal and Deswal, 2009;Rahimikhoob, 2014), Extreme Learning Machine (ELM) (Abdullah et al., 2015;Fan et al., 2018;Feng et al., 2017b;foGocic et al., 2016), Generalized Regression Neural Network (GRNN) (Feng et al., 2017a(Feng et al., , 2017bKim and Kim, 2008;Kisi, 2006;Ladlani et al., 2012), Convolutional Neural Networks (CNN) (Ferreira and da Cunha, 2020), and another techniques such as Gene Expression Programming (GEP) (Shiri et al., 2012;Shiri et al., 2014) and Adaptive Neuro Fuzzy Inference System (ANFIS) (Karimaldini et al., 2012;Keshtegar et al., 2018;Shiri et al., 2012;Shiri et al., 2014;Tabari et al., 2012). ...

... Even if the number of neurons is less than the number of inputs, the hidden node parameters of ELM should not be tuned throughout training, being able to learn distinct samples with good results (Abdullah et al., 2015;Feng et al., 2017b;foGocic et al., 2016). ...

The estimation of Reference Evapotranspiration (ET0) is crucial to estimate crop water requirements, especially in developing countries and areas with scarce water resources. In these regions, the impossibility of collecting all the required data to compute FAO-56 Penman-Monteith equation (FAO56-PM) make scientists search new methodologies to accurately estimate ET0 with the minimum number of climatic parameters. In this work, several neural network approaches have been evaluated for estimating ET0 using datasets from five weather stations located in Southern Spain (semiarid region of Andalusia). The assessment of statistical performance (Root Mean Square Error -RMSE-, Mean Bias Error -MBE-, coefficient of determination -R2- and Nash-Sutcliffe model efficiency coefficient -NSE-) of models namely Multilayer perceptron (MLP), Generalized Regression Neural Network (GRNN), Extreme Learning Machine (ELM), Support Vector Machines (SVM), Random Forest (RF) and XGBoost were carried out using different input variables configurations. Only temperature-based data were used as inputs; the calculation of new variables called EnergyT (the integral of the half hourly temperature values of a day) and Hourmin (the difference in hours between time sunset and the time when the maximum temperature occurs) had promising results for the most humid stations. The good results obtained with EnergyT when it is used as an input of the system demonstrated that the information contained on it gives detailed characterization of the daily thermic behavior at each location, resulting in a more efficient model than those using only daily maximum, minimum temperature and extraterrestrial radiation values. In general, the modelling results showed that no model firmly outperformed the others, although MLP and ELM were commonly the models that gave the best performances for all sites: mean values of R2 >0.89, mean values of NSE >0.88, mean values of RMSE <0.67 mm/day and mean values of MBE ranging from -0.17 to 0.30 mm/day. Therefore, EnergyT and Hourmin can be used to estimate ET0 more accurately in stations where data acquisition is limited, like in developing countries or at low-cost weather stations that cannot collect all the required meteorological variables used in FAO56-PM. Overall, the use of ELM is recommended due to its high performance in terms of efficiency (NSE) for all the configurations and for all locations, especially using EnergyT as an input variable.

... For the direct methods, the time series method and artificial computational or neural networks (ANNs or CNNs) (Feng et al., 2017a;Landeras et al., 2009;Yassin et al., 2016) are the two primary procedures utilized to forecast ET 0 based on current and historical weather data. In recent years, many studies have addressed ET 0 estimation using machine learning methods, such as extreme learning machines (ELMs) (Abdullah et al., 2015;Kisi and Alizamir, 2018;Gocic et al., 2016), support vector machines (SVMs) (Fan et al., 2018;Ferreira et al., 2019) and support vector regression (SVR) (Granata, 2019). As for the indirect methods, the future weather variables are forecasted and used in empirical or analytical models such as Hargreaves-Samani (Hargreaves and Samani, 1985), the Blaney-Criddle equations (Blaney and Criddle, 1962) and the FAO-56 PM (Allen et al., 1998) models to forecast ET 0 . ...

... Evapotranspiration (ET), a key parameter in the hydrological cycle, plays an important role in agricultural water management in precision agriculture (Gocic et al. 2016;Feng et al. 2017a;Jovic et al. 2018). The lysimeter and eddy covariance systems help accurately measure ET (Allen et al. 2011;Mehdizadeh 2018;Tang et al. 2018), but their applications are limited as they are costly and time-consuming. ...

Obtaining accurate data on reference crop evapotranspiration (ET0) is important for agricultural water management. A novel Gaussian exponential model (GEM) was developed in this study to predict ET0 with limited climatic data. The GEM was further compared with the M5 model tree (M5T), extreme learning machine (ELM), and boosted trees (BT) model under local and regional scenarios. Daily meteorological data during 1997–2016 from four stations in Northeast China were used to develop and validate the model. The results showed that the models considering solar radiation and relative humidity demonstrated considerably higher accuracy than those using other inputs. The GEM demonstrated higher accuracy among the four machine learning models for different stations. The accuracy of GEM under local scenarios was higher than that under regional scenarios with the root mean square error (RMSE) reducing by 0.025–0.046 mm/d, relative root mean square error (RRMSE) reducing by 0.879–2.022%, coefficient of efficiency (Ens) increasing by 0.008–0.026, the coefficients of determination (R2) increasing by 0.008–0.026, and mean absolute error (MAE) reducing by 0.015–0.033 mm/d. The GEM considering solar radiation had the highest accuracy with the global performance indicator (GPI) of 1.876. It can also be seen from the Taylor diagrams that the GEM has the the lowest standard deviation and mean square error and the highest correlation coefficient with the standard values. In general, the GEM considering solar radiation had the lowest error and the highest consistency and could be recommended for ET0 simulation for Northeast China.

... They were able to reproduce more 418 accurate ETo estimates than the conventional empirical Hargreaves model. A similar study419 was conducted by Gocic et al.[45] over two weather stations in Serbia.[46] compared the 420 supervised learning approaches Regression Tree (RT), Bagging, RF, and SVM while predicting actual ET. ...

Machine learning (ML), as an artificial intelligence tool, has acquired significant progress in data-driven research in Earth sciences. Land Surface Models (LSMs) are important components of the climate models, which help to capture the water, energy, and momentum exchange between the land surface and the atmosphere, providing lower boundary conditions to the atmospheric models. The objectives of this review paper are to highlight the areas of improvement in land modeling using ML and discuss the crucial ML techniques in detail. Literature searches were conducted using the relevant key words to obtain an extensive list of articles. The bibliographic lists of these articles were also considered. To date, ML-based techniques have been able to upgrade the performance of LSMs and reduce uncertainties by improving evapotranspiration and heat fluxes estimation, parameter optimization, better crop yield prediction, and model benchmarking. Widely used ML techniques used for these purposes include Artificial Neural Networks and Random Forests. We conclude that further improvements in land modeling are possible in terms of high-resolution data preparation, parameter calibration, uncertainty reduction, efficient model performance, and data assimilation using ML. In addition to the traditional techniques, convolutional neural networks, long short-term memory, and other deep learning methods can be implemented.

... The highest R 2 yielded by the ELM model was 0.991 in Iraq and the corresponding value was 0.985 by the ANN model. For the same purpose, Gocic et al. [34] evaluated the performance of ELM for predicting ET 0 , as well as three empirical models in Nis and Belgrade stations of Serbia. Their results confirmed that ELM was a stable and reliable model. ...

... In [80], Dou et al. used four different machine learning approaches in different terrestrial ecosystems for ET estimation. ANN, support vector machine (SVM), extreme learning machine (ELM) [81], and adaptive neuro-fuzzy inference system (ANFIS) [78,[82][83][84][85][86] were compared with each other on estimating ET. In [87], Torres-Rua et al. built a narrowband and broadband emissivities model for UAV thermal imagery using a deep learning (DL) model. ...

Estimating evapotranspiration (ET) has been one of the most critical research areas in agriculture because of water scarcity, the growing population, and climate change. The accurate estimation and mapping of ET are necessary for crop water management. Traditionally, researchers use water balance, soil moisture, weighing lysimeters, or an energy balance approach, such as Bowen ratio or eddy covariance towers to estimate ET. However, these ET methods are point-specific or area-weighted measurements and cannot be extended to a large scale. With the advent of satellite technology, remote sensing images became able to provide spatially distributed measurements. However, the spatial resolution of multispectral satellite images is in the range of meters, tens of meters, or hundreds of meters, which is often not enough for crops with clumped canopy structures, such as trees and vines. Unmanned aerial vehicles (UAVs) can mitigate these spatial and temporal limitations. Lightweight cameras and sensors can be mounted on the UAVs and take high-resolution images. Unlike satellite imagery, the spatial resolution of the UAV images can be at the centimeter-level. UAVs can also fly on-demand, which provides high temporal imagery. In this study, the authors examined different UAV-based approaches of ET estimation at first. Models and algorithms, such as mapping evapotranspiration at high resolution with internalized calibration (METRIC), the two-source energy balance (TSEB) model, and machine learning (ML) are analyzed and discussed herein. Second, challenges and opportunities for UAVs in ET estimation are also discussed, such as uncooled thermal camera calibration, UAV image collection, and image processing. Then, the authors share views on ET estimation with UAVs for future research and draw conclusive remarks.

... In most studies, the machine learning models increased the precision of calculating ET o using temperature data (Wen et al., 2015;Gocic et al.,2016;Torres et al.,2011). However, in this study, we found that temperature-based LSTM, DNN, and SVM models did not improve the accuracy for estimating ET o because the R 2 and RMSE values of them were almost the same statistically. ...

... First, Abdullah et al. (2015) used ELM to forecast ET o at three Iraqi stations and concluded that the ELM model is highly efficient and computerized at high generalization speeds [70,71]. Ever since, the ELM for ET o predictions has been used by many studies in different climate environments [72][73][74]. To the best of the authors' knowledge, all models presented in the literature were established to simulate the evapotranspiration using a single model for each location or case study. ...

Reference evapotranspiration ETo is one of the most significant factors in the hydrological cycle since it has a great influence on water resource planning and management, agriculture and irrigation management, and other processes in the hydrological sector. In this study, an efficient and local predictive model was established to forecast the monthly mean ETo t over Turkey based on the data collected from 35 locations. For this purpose, twenty input combinations including hydrological and geographical parameters were introduced to three different approaches called multiple linear regression MLR, random forest RF, and extreme learning machine ELM. Moreover, in this study, large investigation was done, involving the establishment of 60 models and their assessment using ten statistical measures. The outcome of this study revealed that the ELM approach achieved high accurate estimation in accordance with the Penman–Monteith formula as compared to other models such as MLR and RF. Moreover, among the 10 statistical measures, the uncertainty at 95% U95 indicator showed an excellent ability to select the best and most efficient forecast model. The superiority of ELM in the prediction of mean monthly ETo over MLR and RF approaches is illustrated in the reduction of the U95 parameter to 49.02% and 34.07% for RF and MLR models, respectively. Furthermore, it is possible to develop a local predictive model with the help of computer to estimate the ETo using the simplest and cheapest meteorological and geographical variables with acceptable accuracy.

... However, the Blaney-Criddle formula used in the initial construction of the Nagler-2009 model and the Glenn-2015 model is a temperature-dominated method. Studies indicated that the Penman-Monteith method outperformed other ET 0 models [60] and has been regarded as the standard model for ET 0 computation and the calibration of other empirical ET 0 models [61][62][63]. To sum up, ET 0 estimated using the Penman-Monteith equation is a better characterization for the meteorological conditions in these ERSETMs. ...

Accurate estimates of evapotranspiration (ET) are essential for the conservation of ecosystems and sustainable management of water resources in arid and semiarid regions. Over the last two decades, several empirical remotely sensed ET models (ERSETMs) had been developed and extensively used for regional-scale ET estimation in arid and semiarid ecosystems. These ERSETMs were constructed by combining datasets from different sites and relating measured daily ET to corresponding meteorological data and vegetation indices at the site scale. Then, regional-scale ET on a pixel basis can be estimated, using the established ERSETMs. The estimation accuracy of these ERSETMs at the site scale plays a fundamental and crucial role in regional-scale ET estimation. Recent studies have revealed that ET estimates from some of these models have significant uncertainties at different spatiotemporal scales. However, little information is available on the performance of these ERSETMs at the site scale. In this study, we compared eight ERSETMs, using ET measurements from 2013 to 2018 for two typical eddy covariance sites (Tamarix site and Populus site) in an arid riparian ecosystem of Northwestern China, intending to provide a guide for the selection of these models. Results showed that the Nagler-2013 model and the Yuan-2016 model outperformed the other models. There were substantial differences in the ET estimation of the eight ERSETMs at daily, monthly, and seasonal scales. The mean ET of the growing season from 2013 to 2018 ranged from 465.93 to 519.65 mm for the Tamarix site and from 386.22 to 437.05 mm for the Populus site, respectively. The differences in model structures and characterization of both meteorological conditions and vegetation factors were the primary sources of different model performance. Our findings provide useful information for choosing models and obtaining accurate ET estimation in arid regions.

... ANN and SVM were developed to simulate and predict daily ET by Dou and Yang (2018) with the extreme learning machine (ELM) and adaptive neuro-fuzzy inference system (ANFIS) algorithms. These are two state-of-the-art machine learning algorithms that have been extensively used in hydrological time series modelling and forecasting (Gocic et al. 2016;Alizadeh et al. 2017). Dou and Yang (2018) investigated the feasibility and effectiveness of using ELM and ANFIS to model and estimate daily ET with flux tower observations in different types of ecosystems. ...

The remote sensing (RS) technique is less cost- and labour- intensive than ground-based surveys for diverse applications in agriculture. Machine learning (ML), a branch of artificial intelligence (AI), provides an effective approach to construct a model for regression and classification of a multivariate and non-linear system. Without being explicitly programmed, machine learning models learn from training data, i.e., past experience. Machine learning, when applied to remotely sensed data, has the potential to evolve a real-time farm-specific management system to reinforce farmers' ability to make appropriate decisions. Recently, the use of machine learning techniques combined with RS data has reshaped precision agriculture in many ways, such as crop identification, yield prediction and crop water stress assessment, with better accuracy than conventional RS methods. As agriculture accounts for approximately 70% of the worldwide water withdrawals, it must be used in the most efficient way to obtain maximum yields and food production. The use of water management and irrigation based on plant water stress have been demonstrated to not only save water but also increase yield. To date, RS and ML-based results have encouraged farmers and decision-makers to adopt this technology to meet global food demands. This phenomenon has led to the much-needed interest of researchers in using ML to improve agriculture outcomes. However, the use of ML for the potential evaluation of water stress continues to be unexplored and the existing methods can still be greatly improved. This study aims to present an overall review of the widely used methods for crop water stress monitoring using remote sensing and machine learning and focuses on future directions for researchers.

... Among the ELM's three layers (e.g., input layer, hidden layer, and output layer), the hidden layer does not need to be tuned. ELM randomly selects the input weights, and then analytically determines the output weights of SLFNNs (Abdullah et al., 2015;Gocic et al., 2016;Huang et al., 2006;Patil and Deka, 2016). ...

One of the major components of the hydrological cycle, reference evapotranspiration (ET0) represents the maximum amount of water transferred from the land surface to the atmosphere. Vital to quantifying crop water needs, accurate predictions of ET0 are particularly critical in arid regions, where they allow for informed water resources management adjustments through changes to agricultural irrigation rates and scheduling. Drawing upon 84 meteorological stations in northwest China, spatiotemporal variations in present-day ET0 were investigated. Support vector regression (SVR), Extreme learning machine (ELM), and Multivariate adaptive regression spline (MARS) — three machine learning (ML) techniques — served to establish relationships between historical ET0 and the Coordinated Regional Climate Downscaling Experiment – East Asia (CORDEX-EA), drawn from the output data sets of each of three regional climate models (RCM): Weather Research and Forecasting (WRF), Regional Climate Model version 4.0 (RegCM4) and the Mesoscale Model version 5 (MM5). The ML-RCM combinations were calibrated and validated with separate batches (66:34, respectively) of historical ET0 data, and their respective performance and level of uncertainty were assessed statistically. In the historical period (1960–2017) ET0 declined by −0.15, −0.75, and − 0.42 mm y⁻¹ in north Xinjiang, south Xinjiang, and Qinghai region, respectively, and increased in the Hexi Corridor by 0.5 mm y⁻¹. For all four regions, the MARS-WRF and MARS-MM5 combinations performed well and showed greater predictive accuracy than either ELM-WRF or ELM-MM5 combinations. Performances in predicting future (2035–2050) ET0 from CORDEX-EA outputs based on regional climate predictions RCP 4.5 and RCP 8.5 scenarios, depended to a greater extent on the RCM outputs that were selected, rather than the modeling methods. Future ET0 predicted from RCMs generally exhibit increasing trends, and more significantly under the RCP 8.5 scenario. The representation and characterization ability of RCMs to future climate change is crucial for future ET0 projection. Uncertainty analysis, achieved by employing multiple RCMs to predict future ET0, is highly recommended. Knowledge of trends in future ET0 can help guide the management of agricultural irrigation in oases and support decision-makers engaged in water resources management in the future.

... The fast iteration of ELM is due to the fact that only the number of hidden layer nodes have to be tuned and this in turn reduces the risk of overfitting. Their work was followed up by Gocic et al. [64], where they trained the ELM using empirical models with lesser input parameters. In their study, it was found that the ELM trained with the HS model was more superior to those that were trained with the PT model and the Turc model. ...

Difficulties are faced when formulating hydrological processes, including that of evapotranspiration (ET). Conventional empirical methods for formulating these possess some shortcomings. The artificial intelligence approach emerges as the best possible solution to map the relationships between climatic parameters and ET, even with limited knowledge of the interactions between variables. This review presents the state-of-the-art application of artificial intelligence models in ET estimation, along with different types and sources of data. This paper discovers the most significant climatic parameters for different climate patterns. The characteristics of the basic artificial intelligence models are also explored in this review. To overcome the pitfalls of the individual models, hybrid models which use techniques such as data fusion and ensemble modeling, data decomposition as well as remote sensing-based hybridization, are introduced. In particular, the principles and applications of the hybridization techniques, as well as their combinations with basic models, are explained. The review covers most of the related and excellent papers published from 2011 to 2019 to keep its relevancy in terms of time frame and field of study. Guidelines for the future prospects of ET estimation in research are advocated. It is anticipated that such work could contribute to the development of agriculture-based economy.

... This type of models can generally be classified into three categories: Penman-Monteith (PM) or Priestley-Taylor models (Cleugh et al., 2007;Leuning et al., 2008;Mu et al., 2007;Mu et al., 2011;Peng et al., 2019;Yao et al., 2015;Zhang et al., 2010), surface energy balance models (Bastiaanssen et al., 1998;Li, Kustas, et al., 2019;McCabe & Wood, 2006;Norman et al., 1995;Qiu, 1996;Qiu et al., 1996;Wang et al., 2016), and empirical vegetation index-land surface temperature triangle/trapezoidal models (Carlson & Petropoulos, 2019;Jiang & Islam, 1999;Long & Singh, 2012;Yang & Shang, 2013;Zhu et al., 2017). The second group of models include statistical models, which can be empirical or semi-empirical model (Jung et al., 2009;Jung et al., 2010;Tramontana et al., 2016;Wang et al., 2007) or based on machine learning (ML) techniques (Alemohammad et al., 2017;Feng et al., 2017;Gocic et al., 2016;Granata, 2019;Jung et al., 2009;Tang et al., 2018). These statistical models can be more easily applied, especially at the global scale, but can behave poorly outside of their calibration range and predict climate anomalies, such as extremes (Tramontana et al., 2016). ...

Estimating ecosystem evapotranspiration (ET) is important to understanding the global water cycle and to study land‐atmosphere interactions. We developed a physics constrained machine learning (ML) model (hybrid model) to estimate latent heat flux (LE), which conserves the surface energy budget. By comparing model predictions with observations at 82 eddy covariance tower sites, our hybrid model shows similar performance to the pure ML model in terms of mean metrics (e.g., mean absolute percent errors) but, importantly, the hybrid model conserves the surface energy balance, while the pure ML model does not. A second key result is that the hybrid model extrapolates much better than the pure ML model, emphasizing the benefits of combining physics with ML for increased generalizations. The hybrid model allows inferring the structural dependence of ET and surface resistance (rs), and we find that vegetation height and soil moisture are the main regulators of ET and rs.

... 8 Since the estimation of the compressive strength of noslump concrete could be challenging task it is suitable to use computational intelligence techniques. [9][10][11][12] In this study is performed ranking procedure of the most influential parameters for compressive strength of no-slump concrete prediction by neuro-fuzzy logic. 13 This type of concrete has slump in range of 0 and 25 mm and it is known as dry cast concrete. ...

Concrete with low or zero slump is known as no‐slump concrete. The main purpose of the no‐slump concrete is prefabrication. Determination of compressive strength of the no‐clump concrete could be difficult task because of many input variables. These variables represent constituents of the no‐slump concrete, mixture proportion, complication etc. The no‐slump concrete is very sensitive according to the inputs variation and therefore estimation of the compressive strength as the main output factor could be challenging task. Therefore in this study the main aim was to determine influence of the input variables on the compressive strength of the no‐slump concrete. The ranking procedure will be done based on regression models. The regression models will be created by adaptive neuro‐fuzzy inference system. According to the results silica fume has the strongest influence on the compressive strength prediction of no‐slump concrete. The obtained results could be useful in improvement of compressive strength of no‐slump concrete.

... Although actual evapotranspiration (ETa)gives maximum precision of ET (Abdullah & Malek, 2016;Benli et al., 2006;Cruz-Blanco et al., 2014;Djaman et al., 2016;Shiri et al., 2013), this method is known for its complexity. Number of methods have been developed for estimating ET such as bowen ratio energy balance system (Malek & Bingham, 1993;Spittlehouse & Black, 1980;Todd et al., 2000), eddy covariance flux partitioning (Amazirh et al., 2017;Anderson et al., 2017;Wang & Wang, 2017), empirical models (Allen et al., 1998;Irmak et al., 2003;Makkink, 1957;Penman, 1948;Thornthwaite, 1948;Valiantzas, 2013a;Xu & Singh, 2000), Extreme Learning Machines (Abdullah et al., 2015;Feng et al., 2016;Feng et al., 2017;Gocic et al., 2016;Taormina & Chau, 2015;Torres et al., 2011) and artificial neural network (Adamala et al., 2014;Antonopoulos & Antonopoulos, 2017;Falamarzi et al., 2014;Kumar et al, 2002;Wandera et al., 2017;Yassin et al., 2016). Every method has its own pros and cons and yet empirical model method seems to be the easiest way in computing ETp since it only requires meteorological data. ...

The search for an accurate evapotranspiration (ET) continues when the world has responsibility to cope with the water scarcity issue, population outgrown and uncertain change of weather. Measuring actual evapotranspiration (ETa) can be tedious and requires a lot of time and cost. Therefore, numbersof empirical ETmodels have been developed to overcome this problem. The Valiantzas' modelsare quite familiar to the hydrologist community as it has been developed based on Penman evaporation equation. This paper presents the evaluation on the selected six Valiantzas' models by comparing to Food and Agricultural Organization Penman-Montieth (FAO-PM) empirical model in estimating ET in the Peninsular Malaysia. Seventeen meteorological stations around Peninsular Malaysia with data gathered from 1987 till 2003 were tested. The performance for each model was evaluated by root mean square error (RMSE), coefficient of determination (R 2), percentage error (PE) and mean bias error (MBE). All the six models showed good agreement to FAO-PM with R 2 > 0.90. The PETval2 model which gave R 2 of 0.97 was the best performer with the lowest RMSE, PE and MBE of 0.26, 5.5% and 0.14,respectively. The good and sensible performance on the ET estimation displayed by Valiantzas' model may promise an accurate method for calculation on the water management for irrigation and catchment studies.

... In addition, compared to the estimates made with all inputs, the predictions made with four inputs (without net radiation) are more successful, albeit with a slight difference. Gocic et al. (2016) calculated monthly reference evapotranspiration by using ELM and compared their results with different empirical equations for a 31-year period. Minimum and maximum air temperatures, actual vapor pressure, wind speed and sunshine duration were used as inputs while the empirical equation results as the output. ...

Determination of surface energy balance depends on the energy exchange between land and atmosphere. Thus, crop, soil and meteorological factors are crucial, particularly in agricultural fields. Evapotranspiration is derived from latent heat component of surface energy balance and is a key factor to clarify the energy transfer mechanism. Development of the methods and technologies for the aim of determining and measuring of evapotranspiration have been one of the main focus points for researchers. However, the direct measurement systems are not common because of economic reasons. This situation causes that different methods are used to estimate evapotranspiration, particularly in locations where no measurements are made. Thus, in this study, non-linear techniques were applied to make accurate estimations of evapotranspiration over the winter wheat canopy located in the field of Atatürk Soil Water and Agricultural Meteorology Research Institute Directorate, Kırklareli, Turkey. This is the first attempt in the literature which consist of the comparison of different machine learning methods in the evapotranspiration values obtained by the Bowen Ratio Energy Balance system. In order to accomplish this aim, support-vector machine, Adaptive neuro fuzzy inference system and Artificial neural network models have been evaluated for different input combinations. The results revealed that even with only global solar radiation data taken as an input, a high prediction accuracy can be achieved. These results are particularly advantageous in cases where the measurement of meteorological variables is limited. With the results of this study, progress can be made in the efficient use and management of water resources based on the input parameters of evapotranspiration especially for regions with limited data.

... In addition, when working with input data at low temporal resolution, any sensor failure at the weather station could lead a large number of missing data, which could hamper the accuracy of hourly ET o , and hence, ET and drought predictions. Therefore, ML models are being increasingly applied to extract patterns and insights from the everincreasing stream of spatial and temporal data for ET o predictions (Gocic, Petković, Shamshirband, & Kamsin, 2016;Antonopoulos & Antonopoulos, 2017;Mehdizadeh, Behmanesh, & Khalili, 2017;Wu, Zhou, Ma, Fan, & Zhang, 2019). The daily ET o prediction is a regressiontype problem aiming at forecasting continuous-response values from multivariate input sequences and feedback, and hence, require supervised ML methods. ...

Due to their enhanced predictive capabilities, noninterpretable machine learning (ML) models (e.g. deep learning) have recently gained a growing interest in analyzing and modeling earth & planetary science data. However, noninterpretable ML models are often treated as “black boxes” by end-users, which could limit their applicability in critical decision making processes. In this paper, we compare the predictive capabilities of three interpretable ML models with three noninterpretable ML models to answer the overarching question: Is it essential to use noninterpretable ML models for enhanced model predictions from hydro-climatological datasets? The ML model development and comparative analysis are performed using measured climate data and synthetic reference crop evapotranspiration (ETo) data, with varying levels of missing values, from five weather stations across the karstic Edwards aquifer region in semi-arid south-central Texas. Our analysis reveals that interpretable tree-based ensemble models produce comparable results as noninterpretable deep learning models on structured hydro-climatological datasets. We show that the tree-based ensemble model is also capable of imputing varying levels of missing climate data at the weather stations, employing the newly developed sequential transfer-learning technique. We applied an explainable machine learning (eXML) framework to quantify the global order of importance of hydro-climatic (predictor) variables on ETo, while highlighting the local dependencies and interactions amongst the predictors and ETo. The eXML framework also revealed the inflection points of the climate variables at which the transition from low to high daily ETo rates occur. The ancillary explainability of ML models are expected to increase users’ confidence and support any future decision-making process in water resource management.

... However, machine learning models are likely to solve similar issues due to not requiring any assumptions (Rezaie-Balf et al., 2017;Wang et al., 2017;Wu et al., 2020). Current machine learning models include multilayer perceptron (Traore et al., 2016), long short-term memory (Majhi et al., 2019), radial basis function neural networks , multilayer artificial neural networks (Keskin and Terzi, 2006;Jain et al., 2008;Wu et al., 2020), extreme learning machine (Abdullah et al., 2015;Feng et al., 2016;Gocic et al., 2016;Wu et al., 2020;Zhu et al., 2020), genetic programming (Shiri et al., 2012), self-organizing map neural networks (Malik et al., 2018), support vector machine (SVM) (Wen et al., 2015), and random forest . As the structure and parameters of machine learning models also affect computing accuracy (Gocić et al., 2015;Wang et al., 2019;Wu et al., 2020), machine learning models hybridized with swarm intelligence algorithms (e.g., the whale optimization algorithm, genetic algorithm, particle swarm optimization algorithm, firefly algorithm, and quantum-performed particle swarm optimization algorithm) are often used to overcome these shortcomings, allowing them to be the best choice for estimating ET (Gocić et al., 2015;Petković et al., 2016;Yin et al., 2017;Moazenzadeh et al., 2018;Wu et al., 2020;Zhu et al., 2020). ...

Evapotranspiration (ET) plays a vital role in the water cycle and energy cycle and serves as an important linkage between ecological and hydrological processes. Accurate estimation of ET based on data-driven methods is of great theoretical and practical significance for exploring soil evaporation, plant transpiration and the regional hydrological balance. Most existing estimation approaches were proposed based on multiple meteorological variables. This study proposed a novel hybrid estimation approach to estimate the monthly ET using only historical ET time series in the southeastern margins of the Tengger Desert, China. The approach consisted of three sections including data preprocessing, parameter optimization and estimation. The model evaluation demonstrated that the hybrid model based on the variational mode decomposition (VMD) method, grey wolf optimizer (GWO) algorithm and support vector machine (SVM) model achieved superior computational performance compared to the performance of other methods. The Nash–Sutcliffe coefficient of efficiency (NSCE) increased from 0.8588 to 0.8754 and the mean absolute percentage error (MAPE) decreased from 28.42% to 23.22% in the testing stage. Thus, we suggest that the hybrid VMD-GWO-SVM model will be the best choice for estimating ET in the absence of regional meteorological monitoring.

... Different machine learning algorithms have been reported in the literature to model the process of predicting the ET 0 values, e.g., support vector machine algorithm (SVM) [17][18][19] and least square support vector machine [20,21] have been applied to model ET 0 process. Genetic programming has also been used in the mathematical formulation of ET 0 value prediction [22][23][24] by many researchers, the suitability of extreme learning machine (ELM) is used to estimate ET 0 values [7,25,26], treebased models such as M5 model tree [27,28], random forest [29][30][31], and extreme gradient boosting (XGBoost) [19,27,32] have also been explored for the same. Also, the process of predicting evapotranspiration has been analyzed with artificial neural networks (ANNs) [33][34][35] and an adaptive neuro-fuzzy inference system (ANFIS) [36,37]. ...

Reference evapotranspiration (ET 0) plays an undeniably important role in irrigation management. Thus, accurate estimation of ET 0 is necessary to avoid over or under irrigation to increase agricultural productivity and manage water resources effectively. Due to the limited availability of climate datasets in developing countries, the estimation of ET 0 remains the biggest challenge. This study presents two-hybrid deep neural network models for the estimation of reference evapotranspiration: Convolution-Long Short Term Memory (Conv-LSTM), which performs the convolution operation in LSTM cells and Convolution Neural Network-LSTM (CNN-LSTM) that uses the convolution layer for feature extraction of input data and then extracted features are fed to LSTM layers. The study also focuses on climate data scarcity conditions, and thus, different input combinations of climate parameters have been used to investigate the minimum required parameters to model the ET 0 process. The climate dataset of two stations of India: Ludhiana and Amritsar, is adopted to develop proposed models. It includes daily maximum temperature (T max), minimum temperature (T min), wind speed measured at the height of 2 m (U 2), solar radiation (R s), relative humidity (Rh), vapor pressure (Vp), and sunshine hours (Ssh) data from the period 2003 to 2015 of Ludhiana station and 2000 to 2016 of Amritsar station. Several performance measures are used to assess the precision of the model and to perform sensitivity analysis. Temperature and radiation are observed as the prime data inputs required to estimate ET 0 values. The proposed hybrid models are then compared with existing temperature and radiation-based empirical models such as Hargreaves, Makkink, and Ritchie. The comparison reveals that CNN-LSTM and Conv-LSTM outperform these existing models. Also, Conv-LSTM performs best among all for the estimation of ET 0.

... Different machine learning algorithms have been reported in the literature to model the process of predicting the ET 0 values, e.g., support vector machine algorithm (SVM) [17][18][19] and least square support vector machine [20,21] have been applied to model ET 0 process. Genetic programming has also been used in the mathematical formulation of ET 0 value prediction [22][23][24] by many researchers, the suitability of extreme learning machine (ELM) is used to estimate ET 0 values [7,25,26], treebased models such as M5 model tree [27,28], random forest [29][30][31], and extreme gradient boosting (XGBoost) [19,27,32] have also been explored for the same. Also, the process of predicting evapotranspiration has been analyzed with artificial neural networks (ANNs) [33][34][35] and an adaptive neuro-fuzzy inference system (ANFIS) [36,37]. ...

Smart agriculture aims to improve the quality and quantity of crops by efficiently managing available resources. One of the main components of smart agriculture is precision irrigation which applies the required amount of water at the right time to crops. Crop evapotranspiration (ETc) prediction can contribute to managing the irrigation strategies effectively. Although several methods have been introduced for estimating ETc values, these methods are still associated with various challenges and limitations (high cost, time-consuming, and meteorological data unavailability). The current study is motivated by the desire to create deep learning (DL) based models capable of estimating ETc reliably to eliminate the above-mentioned limitations and forecast future ETc values for adaptation strategies. In this paper, two-hybrid DL models, i.e., Convolution Neural Network-eXtreme Gradient Boosting (CNN-XGB) and Convolution Neural Network-Support Vector Regression (CNN-SVR) are proposed to estimate daily ETc values of wheat and rice crops. Further, limited climate data (minimum temperature (Tmin), maximum temperature (Tmax), mean temperature (Tmean) and solar radiation (Rs)) is used for the prediction of ETc values to handle data-scarce situations. Also, the future climate data obtained using two emission scenarios: Representative Concentration Pathways (RCP) 4.5 and RCP 8.5 for the time period 2023–2033, are used to project changes in ETc. The results demonstrate that the proposed hybrid models provide satisfactory performance with the Nash–SutcliffeEfficiency (NSE) = 0.95 and 0.976 for rice and wheat ETc values, respectively. The simulation of future data reveals the increase in Tmin by 7.03%, 7.33%, and Tmax by 10.5%, 11.5% for RCP 4.5 and RCP 8.5 respectively. Also, an increase in ETc of rice crop has been reported by 20%–22% while increment of wheat ETc has been noticed by 3%–4%. Thus, the proposed approach efficiently estimates ETc of wheat and rice crops using limited climate data and could assist water resource managers in achieving agricultural water sustainability.

... The empirical model has great limitations in solving nonlinear problems. Gocic et al.[42] applied 20 years of meteorological data on Serbia to build an ET O model based on ELM and a variety of empirical formulas, and the results showed that the estimation accuracy of ELM was better than that of the empirical model. However, the selection of kernel functions and parameter settings in the ELM model is not optimal, which causes some errors in the model results. ...

The accurate estimation of reference crop evapotranspiration (ETO) plays an important role in guiding regional water resource management and crop water content research. In order to improve the accuracy of ETO prediction in regions with missing data, this study used the partial correlation analysis method to select factors that have a large impact on ETO as input combinations to construct ETO estimation models for typical stations in semi-arid regions of China. A biological heuristic optimization algorithm (Golden Eagle optimization algorithm (GEO) and Sparrow optimization algorithm (SSA)) and Extreme Learning Machine model (ELM) were combined to improve the estimation accuracy. The results showed that Ra was the primary factor affecting the ETO model, with an importance range of 0.187–0.566. Compared with the independent ELM model, the hybrid model has higher accuracy and stability. The estimated value of the SSA-ELM model under five-factor input condition (Ra, RH, Tmax, Tmin, U2) is closest to the standard value calculated by FAO56 PM: RMSE = 0.067–0.085, R2 = 0.998–0.999, MAE = 0.050–0.066 and NSE = 0.998–0.999. In general, the combination of a partial correlation analysis algorithm and a hybrid model can be used to estimate ETO with high accuracy under the condition of reducing input factors. Use of the first five factors extracted from the partial correlation analysis algorithm as input to build an ETO estimation model based on SSA-ELM in China’s semi-arid regions is recommended, which can also provide a reference for ETO estimation in similar regions.

... A comparison of ET+F values obtained by common IO methods during the rice observation period in 2017 is shown in Figure 4. Intuitively, the results of the two methods fit well. In this analysis, the difference in ET+F values between the IO method and the common method was determined by statistical measures, including the coefficient of determination (R 2 ), mean bias error (MBE), root mean square error (RMSE), relative root mean square error (RRMSE) and index of agreement (d) [28,33] (Table 1). The validation results showed a satisfactory correlation between the two methods calculated (ET+F), with ...

A Beijing paddy field, along with in-situ experiments, was used to validate and refine the in-situ observation (IO) method to describe nonpoint source pollution (NPS) in paddy fields. Based on synchronous observed rainfall, water depth, and water quality data at two locations (1# (near inlet) and 2# (near outlet)) with large elevation differences, the evapotranspiration and infiltration loss (ET+F), runoff depth and NPS pollution load were calculated according to IO, and a common method was used to calculate ET+F. Then, the results of the different methods and locations were compared and analyzed. The results showed that 1# observation point was located at a lower position compared with 2# observation point. According to 1# observation point, there were 5 days of dry field in the drying period, which was consistent with the actual drying period, and there was a dry period of 9 days based on 2# observation point. The ET+F estimated by IO fit well with the calculated values. In the experiment, 6 overflows and 1 drainage event were identified from the observed data at locations 1# and 2#. The relative deviation of the NPS pollution of total nitrogen (TN), total phosphorus (TP), chemical oxygen demand (COD), nitrate-nitrogen (NO3−-N) and ammonia nitrogen (NH4+-N) was between 0.6% and 2.0%. The water level gauge location had little influence on IO but mostly affected the water depth observations during the field drying period. The mareographs should be installed in low-lying paddy field areas to monitor water depth variation throughout the whole rice-growing season.

... Recent years, machine learning models have been increasingly used for estimating a variety of meteorological parameters, such as solar radiation (Hassan et al., 2017;Ibrahim and Khatib, 2017;Mousavi et al., 2017;Fan et al., 2018a;Feng et al., 2019;Qiu et al., 2022b), T a (Zou et al., 2017;Li et al., 2020), RH in greenhouses (Zou et al., 2017), wind speed (Memarzadeh and Keynia, 2020;Rodrigues Moreno et al., 2020;Xiang et al., 2020), and pan evaporation (Kisi, 2015;Deo et al., 2016;Lu et al., 2018), as well as for estimating ET 0 (Abdullah et al., 2015;Gocic et al., 2016;Huang et al., 2019;Saggi and Jain, 2019;Wu et al., 2019a), and vegetation/crop evapotranspiration (Shrestha and Shukla, 2015;Yao et al., 2017;Tang et al., 2018;Yamaç and Todorovic, 2020). However, studies on estimation of daily and monthly e a by using machine learning models are rarely reported. ...

Information of actual vapour pressure (ea) is frequently required in many disciplines. However, psychrometric data required to calculate ea are often not readily available. Hence, it is of great importance to develop models to estimate ea when psychrometric data are unavailable. Here, five machine learning models were developed for estimating ea, viz. extreme gradient boosting (XGBoost), extreme learning machine (ELM), kernel-based nonlinear extension of Arps decline (KNEA), multiple adaptive regression splines (MARS), and support vector machine (SVM) models. Their performance was also compared to a dynamic model proposed recently, which estimates ea by adjusting dew point temperature from minimum temperature (Tmin) with dynamic correction factor. Three input combinations using only temperature data (i.e. Tmin and mean temperature (Tmean)) were considered in the machine learning models. The meteorological data collected from 1,188 stations across six climate zones were used to develop and assess the models. The overall results revealed that the dynamic and machine learning models offered satisfactory ea estimates spanning from hyper arid to humid climates. However, the accuracy of the dynamic model was lower than all machine learning algorithms using either only Tmin or combinations of Tmean and Tmin in all climate zones. The machine learning models using Tmean and Tmin were superior to those using only Tmean or Tmin. There were comparable performances among the ELM, KNEA, MARS, and SVM models with various input variables; however, the XGBoost model incorporating Tmean and Tmin produced the best accuracy. The computational demand was least for the ELM model, followed by the XGBoost model. Considering the accuracy and computational demand, the XGBoost model is recommended for predicting daily and monthly ea from hyper arid to humid climates when historical data are prior known. When there are no historical data, we recommend using the global XGBoost model incorporating Tmean, Tmin, and aridity index for estimating daily and monthly ea from arid to humid regions, and using the dynamic model in hyper-arid regions.

... Different machine learning algorithms have been reported in the literature to model the process of predicting the ET 0 values, e.g., support vector machine algorithm (SVM) [17][18][19] and least square support vector machine [20,21] have been applied to model ET 0 process. Genetic programming has also been used in the mathematical formulation of ET 0 value prediction [22][23][24] by many researchers, the suitability of extreme learning machine (ELM) is used to estimate ET 0 values [7,25,26], treebased models such as M5 model tree [27,28], random forest [29][30][31], and extreme gradient boosting (XGBoost) [19,27,32] have also been explored for the same. Also, the process of predicting evapotranspiration has been analyzed with artificial neural networks (ANNs) [33][34][35] and an adaptive neuro-fuzzy inference system (ANFIS) [36,37]. ...

Reference evapotranspiration (ET0) plays an undeniably important role in irrigation management. Thus, accurate estimation of ET0 is necessary to avoid over or under irrigation to increase agricultural productivity and manage water resources effectively. Due to the limited availability of climate datasets in developing countries, the estimation of ET0 remains the biggest challenge. This study presents two-hybrid deep neural network models for the estimation of reference evapotranspiration: Convolution—Long Short Term Memory (Conv-LSTM), which performs the convolution operation in LSTM cells and Convolution Neural Network—LSTM (CNN-LSTM) that uses the convolution layer for feature extraction of input data and then extracted features are fed to LSTM layers. The study also focuses on climate data scarcity conditions, and thus, different input combinations of climate parameters have been used to investigate the minimum required parameters to model the ET0 process. The climate dataset of two stations of India: Ludhiana and Amritsar, is adopted to develop proposed models. It includes daily maximum temperature (Tmax), minimum temperature (Tmin), wind speed measured at the height of 2 m (U2), solar radiation (Rs), relative humidity (Rh), vapor pressure (Vp), and sunshine hours (Ssh) data from the period 2003 to 2015 of Ludhiana station and 2000 to 2016 of Amritsar station. Several performance measures are used to assess the precision of the model and to perform sensitivity analysis. Temperature and radiation are observed as the prime data inputs required to estimate ET0 values. The proposed hybrid models are then compared with existing temperature and radiation-based empirical models such as Hargreaves, Makkink, and Ritchie. The comparison reveals that CNN-LSTM and Conv-LSTM outperform these existing models. Also, Conv-LSTM performs best among all for the estimation of ET0.

... Alternatively, machine learning (ML) models have shown their capability to be used as powerful tools to estimate ET 0 since they do not require any specific knowledge of internal variables (Wang et al. 2017). Several ML models including artificial neural networks (ANN), support vector machine (SVM), random forest (RF), extreme learning machine (ELM), and genetic programming (GP) have been investigated by various researchers to estimate ET 0 (Fan et al. 2018;Feng et al. 2017aFeng et al. , 2017bGocic et al. 2016;Traore et al. 2016;Wen et al. 2015;Yin et al. 2017). Among these models, the SVM and ELM models have showed the best estimation accuracies compared to the other ML models (Abdullah et al. 2015;Fan et al. 2018;Feng et al. 2017b;Patil and Deka 2016;Yin et al. 2017Yin et al. , 2016. ...

Reference evapotranspiration (ET0) is a major factor for water resource management. Although the FAO Penman-Monteith model is the highly recommended for estimating ET0, its requirement of a complete climatic variables has made the application of this model complicated. The objective of this study was to investigate the potential of four machine learning (ML) models including Extreme Learning Machine (ELM), Genetic Programming (GP), Random Forest (RF), and Support Vector Regression (SVR) for estimating daily ET0 with limited climatic data using a 10-fold cross-validation method across different climate zones in New Mexico. Four input scenarios including S1 (Tmax (maximum air temperature), Tmin (minimum air temperature), RHave (average relative humidity), U2 (wind speed at 2 m height), RS (total solar radiation)) (Tmax, Tmin, RHave, U2, RS), S2 (Tmax, Tmin, U2, RS), S3 (Tmax, Tmin, RS), and S4 (Tave, RS) were considered using climatic data during the 2009-2019 period from six selected weather stations across different climate zones. The results showed that the estimated daily ET0 differed significantly following ML model types and input scenarios across different climate zones. The ML models under S1 scenario showed the best estimation accuracy during the testing stage in climate zones 1 and 5 (RMSE and MAE < 0.5 mm d-1). The ML models under S3 and S4 scenarios were found to be more preferred at climate zones 1,5, and 8 (RMSE and MAE < 1 mm d-1). The estimation accuracy of ML models was decreased with lack of RHave, U2 data in input scenarios although the ML models based on S4 scenario (only Tave and Rs) showed acceptable ET0 estimations particularly in the climate zone 5 (0.5 mm d-1 < RMSE <0.6 mm d-1). The SVR and ELM were the best ML models for all input scenarios in the studied climate zones where these models showed the best stabilities in the testing stages.

The accurate estimation of reference crop evapotranspiration (ET0) is of great significance to improve agricultural water use efficiency and optimize regional water resources management. At present, the applicability evaluation system of ET0 models is still lacking in several climate regions in China, leading to the confusion in application of the ET0 model in some specific regions. In this study, the daily meteorological data of 84 representative stations in four climate regions of China during the past 30 years (1991–2019) were selected to evaluate the ET0 simulation results of twelve empirical models (four temperature models, five radiation models, and three hybrid models) on the daily scale, and the optimal models suitable for each climate region were screened. Whale optimization algorithm (WOA) was used to optimize the optimal model to improve the simulation accuracy, and the ET0 results were compared with those predicted by extreme learning machine (ELM). The results showed that the estimation accuracy of the hybrid model was the best throughout China, followed by the radiation model, and the temperature model was relatively poor, with R² ranges of 0.77–0.88, 0.60–0.86, and 0.58–0.82, respectively. Among the temperature-based models, Hargreaves-Samani and Improve Baier-Robertson model had the highest accuracy, with R² of 0.80 and 0.79. Among the radiation-based models, Priestley-Taylor and Jensen-Haise models had the best accuracy, with R² of 0.82 and 0.79. Among the hybrid models, Penman model had the highest accuracy, with R² of 0.84. The accuracy of Hargreaves-Samani and Improve Baier-Robertson model in SMZ climate region was higher than TCZ, TMZ, and MPZ, and the accuracy of Jensen-Haise model in TCZ was the highest. The estimation accuracy of Priestley-Taylor and Penman models was similar in SMZ, TCZ, TMZ and MPZ. Using WOA to optimize the optimal temperature, radiation, and hybrid models, the prediction accuracy was improved by 12.05 %, 11.06 %, and 10.46 %, which were higher than the result of ELM model, with R² of 0.90, 0.91, 0.95 and 0.90, respectively. Therefore, it is recommended to adopt WOA to optimize the empirical model to estimate the ET0 all over China.

Acceptable estimation of reference Evapotranspiration (ET0) values by the Penman-Monteith FAO (PM FAO) equation requires accurate solar radiation (Rs) data. Rs values could be estimated using the Angstrom's radiation model. The aim of this study was to determine the as and bs coefficient (as Angstrom's parameters) for the Ardabil plain as an arid and cold region. Angstrom's radiation model and PM FAO equation were calibrated for the study area, by optimizing the as and bs parameter using Generalized Reduced Gradient (GRG) method. Measured Rsdata were collected from the Ardabil Synoptic Station and measured ET0 data were determined using three lysimeters that were installed at the Hangar Research Station. Calibrated results showed that optimized as and bs values were 0.117 and 0.384, respectively. Compared to the original models, errors including RMSE, AE and RE values were decreased and fitted parameters including R 2 and regression line slope (m) were improved in the calibrated models. The GMER values for the original models showed that Angstrom's radiation model overestimated the Rs values and PM FAO equation underestimated the ET0 values. Locally calibrated models estimated Rs and ET0 values better than the original one. Nash-Sutcliffe efficiency coefficient (NSE) values proved that Rs and ET0 estimation by the original models were not satisfactory, but were acceptable in the case of the calibrated models. However, calibration of Angstrom's radiation model and PM FAO equation is necessary for each region.

Evapotranspiration (ET) is a critical component in global water cycle and links terrestrial water, carbon and energy cycles. Accurate estimate of terrestrial ET is important for hydrological, meteorological, and agricultural research and applications, such as quantifying surface energy and water budgets, weather forecasting, and scheduling of irrigation. However, direct measurement of global terrestrial ET is not feasible. Here, we first gave a retrospective introduction to the basic theory and recent developments of state-of-the-art approaches for estimating global terrestrial ET, including remote sensing-based physical models, machine learning algorithms and land surface models (LSMs). Then, we utilized six remote sensing-based models (including four physical models and two machine learning algorithms) and fourteen LSMs to analyze the spatial and temporal variations in global terrestrial ET. The results showed that the mean annual global terrestrial ET ranged from 50.7 × 103 km³ yr−1（454 mm yr−1）to 75.7 × 103 km³ yr−1 (6977 mm yr−1), with the average being 65.5 × 103 km³ yr−1 (588 mm yr−1), during 1982–2011. LSMs had significant uncertainty in the ET magnitude in tropical regions especially the Amazon Basin, while remote sensing-based ET products showed larger inter-model range in arid and semi-arid regions than LSMs. LSMs and remote sensing-based physical models presented much larger inter-annual variability (IAV) of ET than machine learning algorithms in southwestern U.S. and the Southern Hemisphere, particularly in Australia. LSMs suggested stronger control of precipitation on ET IAV than remote sensing-based models. The ensemble remote sensing-based physical models and machine-learning algorithm suggested significant increasing trends in global terrestrial ET at the rate of 0.62 mm yr−2 (p −2, respectively. In contrast, the ensemble mean of LSMs showed no statistically significant change (0.23 mm yr−2, p > 0.05), even though most of the individual LSMs reproduced the increasing trend. Moreover, all models suggested a positive effect of vegetation greening on ET intensification. Spatially, all methods showed that ET significantly increased in western and southern Africa, western India and northeastern Australia, but decreased severely in southwestern U.S., southern South America and Mongolia. Discrepancies in ET trend mainly appeared in tropical regions like the Amazon Basin. The ensemble means of the three ET categories showed generally good consistency, however, considerable uncertainties still exist in both the temporal and spatial variations in global ET estimates. The uncertainties were induced by multiple factors, including parameterization of land processes, meteorological forcing, lack of in situ measurements, remote sensing acquisition and scaling effects. Improvements in the representation of water stress and canopy dynamics are essentially needed to reduce uncertainty in LSM-simulated ET. Utilization of latest satellite sensors and deep learning methods, theoretical advancements in nonequilibrium thermodynamics, and application of integrated methods that fuse different ET estimates or relevant key biophysical variables will improve the accuracy of remote sensing-based models.

The precise estimation of reference evapotranspiration (ET0) is crucial for the planning and management of water resources and agricultural production. In this study, the applicability of the Hargreaves Samani (HS), artificial neural network (ANN), multiple linear regression (MLR) and extreme learning machine (ELM) models were evaluated to estimate ET0 based on temperature data from the Verde Grande River basin, southeastern Brazil. These models were evaluated in two scenarios: local and pooled. In the local scenario, training, calibration and validation of the models were performed separately at each station. In the pooled scenario, meteorological data from all stations were grouped for training and calibration and then separately tested at each station. The ET0 values estimated by the Penman-Monteith model (FAO-56 PM) were considered the target data. All the developed models were evaluated by cluster analysis and the following performance indices: relative root mean square error (RRMSE), Pearson correlation coefficient (r) and Nash-Sutcliffe coefficient (NS). In both scenarios evaluated, local and pooled, the results revealed the superiority of the artificial intelligence methods (ANN and ELM) and the MLR model compared to the original and adjusted HS models. In the local scenario, the ANN (with r of 0.751, NS of 0.687 and RRMSE of 0.112), ELM (with r of 0.747, NS of 0.672 and RRMSE of 0.116) and MLR (with r of 0.743, NS of 0.665 and RRMSE of 0.068) models presented the best performance, in addition to being grouped in the same cluster. Similar to the observations from the local scenario, the ANN (with r of 0.718, NS of 0.555 and RRMSE of 0.165), ELM (with r of 0.724, NS of 0.601 and RRMSE of 0.151) and MLR (with r of 0.731, NS of 0.550 and RRMSE of 0.091) models presented the best performance in the pooled scenario and were grouped in the same cluster. The locally trained models presented higher precision than the models generated with pooled data; however, the models generated in the pooled scenario could be used to estimate ET0 in cases of unavailability of local meteorological data. Although the MLR, ANN and ELM models, based on temperature data, are appropriate alternatives to accurately estimate ET0 in the Verde Grande River basin, southeastern Brazil, the MLR model presents the advantage of the use of explicit algebraic equations, facilitating its application.

The present investigation was carried out in the experimental farm of AICRP on IFS, College of Agriculture, Indore during Kharif seasons of 2013-14 and 2014-15. The main focus of this research was to establish the biophysical model i.e. Decision Support System for Agrotechnology Transfer (DSSAT) for crop yield forecast for Malwa Agroclimatic zone of western Madhya Pradesh for soybean variety JS-335.

HVAC systems provide satisfactory indoor environments, but they usually consume large amounts of energy in order to achieve an acceptable thermal comfort level and indoor air quality (IAQ). Balancing thermal comfort, IAQ, and energy consumption is thus a challenging task. However, the main problem faced in such research is that it is inefficient to conduct traditional experiments or numerical simulation to obtain the optimal air supply parameters from a large number of variables. Therefore, the aim of this study is to develop a rapid prediction and optimization framework of IAQ, occupant comfort, and energy consumption. Firstly, Building Information Modeling (BIM) technology and Computational Fluid Dynamics (CFD) simulations are used to create the database containing indoor velocity, temperature and CO2 concentration for different distributions of occupants and ventilation parameters. Next, the extreme learning machine (ELM) model optimized by the grey wolf optimizer (GWO) algorithm is developed to predict the thermal comfort level and CO2 concentration, and the input parameters of the prediction models are interpolated to generate more cases. Finally, the satisfied air supply parameters for various optimization objectives are determined by combining the predicted PMV value and CO2 concentration with the energy consumption analysis. The results of the comprehensive analysis showed that the average concentration of CO2 after optimization is reduced and the |PMV|avg is reduced to less than 0.5, which is within acceptable limits. In addition, 14.34% energy saving is achieved in the illustrative example.

Pores are inevitably produced during the production of glass fiber reinforced polymers (GFRP). Quantitative characterization of porosity is a most important aspect of performance evaluation of GFRP. Herein, we present a novel strategy for porosity detection of GFRP based on the interaction mechanism between terahertz (THz) wave and porous GFRP (porosity: 0.29%–4.01%; pore size: about 20–600 μm). By using the transmission and absorption spectra of GFRP, a porosity prediction model is established by combining the supervised learning approach of support vector regression (SVR) and ensemble methods, which can predict the porosity of unknown test samples with a coefficient of determination R² = 0.976 and root mean square error RMSE = 0.174%. Conversely, THz transmission and absorption spectra for porous GFRP are successfully reconstructed by SVR and the ensemble methods. The results indicate that THz spectroscopy in combination with SVR and the ensemble methods is robust and accurate in porosity analysis and could play a significant role in industrial applications where nondestructive on-line detection of porosity in polymer composites is desirable.

Evapotranspiration (ET) is the crucial parameter of agricultural irrigation and the hydrological cycle. To obtain the optimal estimation model of ET with film-mulching for spring maize, the extreme learning machine model (ELM) optimized by sparrow search algorithm (SSA) was built. The ET results were compared with four machine learning models, including artificial bee colony algorithm optimized ELM model (ABC-ELM), particle swarm algorithm optimized ELM model (PSO-ELM), genetic algorithm optimized ELM model (GA-ELM), ELM model, and two empirical models, including the modified Shuttleworth-Wallace model (SW) and Priestley-Taylor model (PT). We evaluated the accuracy of different models using the root mean square error (RMSE), coefficient of determination (R²), mean absolute error (MAE), coefficient of efficiency (Ens) and GPI. The results showed that the SSA-ELM models show high accuracy under different input combinations in different growth periods. Throughout the growing season of spring maize, the slope of the fitting equation of the SSA-ELM9 model was 0.895. The RMSE, R², Ens, MAE and GPI were 0.433 mm/d, 0.895, 0.895, 0.342 mm/d and 1.382, respectively. The SSA-ELM models showed the highest accuracy for ET estimation of spring maize in different growth periods, followed by PSO-ELM, ABC-ELM and GA-ELM models. The accuracy of the SSA-ELM models was better than that of the SW PT models. Therefore, the SSA-ELM model can estimate spring maize ET with film mulching.

Evapotranspiration (ET) is a critical element of the hydrological cycle, and its proper assessment is essential for irrigation scheduling, agricultural and hydro-meteorological studies, and water budget estimation. It is computed for most applications as a product of reference crop evapotranspiration (ET 0 ) and crop coefficient, notably using the well-known two-step method. Accurate predictions of reference evapotranspiration (ET 0 ) using limited meteorological inputs are critical in data-constrained circumstances, and the preferred FAO-56 Penman-Monteith (PM) equation cannot be used. To overcome the complexity of calculation, the present study is focused on developing a Random Forest-based ET 0 model to estimate the crop ET for the semi-arid region of northwest India. The RF-based model was developed by focusing on the readily available data at the farm level. For comparative study Hargreaves–Samani model was also modified and used to estimate the ET 0 . Further, ET 0 was also estimated using existing models like Hargreaves–Samani model and the Modified Panman model. The models' calibration and validation were done using meteorological data collected from the weather station of Punjab Agricultural University for 21 years (2090 − 2010) and nine years (2011–2019), respectively, and the PM FAO-56 model was taken as a standard model. The developed RF-based model's mean absolute error and root-mean-square deviation were found to be better than the other models, and it was obtained as 0.95 mm/d and 1.32, respectively, with an r ² value of 0.92. The developed RF-based model was used to predict the ET 0 , and further, predicted ET0 values were used for irrigation scheduling of two growing seasons (2020–2021) of maize and wheat crops. The result of the field experiment also shows that there was no significant yield reduction in the crop. Hence, This developed study model can be used for the irrigation in the semiarid region of the Punjab India as well as other part of world. Also, it can be used as a replacement FAO-56 model.

Accurate prediction of reference evapotranspiration (ETo) is pivotal to the determination of crop water requirement and irrigation scheduling in agriculture as well as water resources management in hydrology. In the present study, the particle swarm optimization (PSO) algorithm was utilized to optimally determine the parameters of the extreme learning machine (ELM) model, and a novel hybrid PSO-ELM model was thus proposed for estimating daily ETo in the arid region of Northwest China with limited input data. The PSO-ELM model was compared with the original ELM, artificial neural networks (ANN) and random forests (RF) models as along with six empirical models (including radiation-, temperature- and mass transfer-based empirical models). Three input combinations were utilized to develop the data-driven models, which corresponded to the radiation-, temperature- and mass transfer-based models, respectively. The results indicated that machine learning models provided more accurate ETo estimates, compared with the corresponding empirical models with the same inputs. The hybrid PSO-ELM model exhibited better performance than the other models for daily ETo estimation as indicated by the statistical results. Although radiation-based machine learning models outperformed temperature- and mass transfer-based machine learning models, the temperature-based PSO-ELM model obtained reasonable results when only air temperature data were available, which was considered as a promising model for forecasting future ETo with temperature data. Overall, the PSO-ELM model was superior to the other machine learning and empirical models, which was thus recommended to predict daily ETo with limited inputs in the arid region of Northwest China.

Evapotranspiration (ET) is critical in linking global water, carbon and energy cycles. However, direct measurement of global terrestrial ET is not feasible. Here, we first reviewed the basic theory and state-of-the-art approaches for estimating global terrestrial ET, including remote-sensing-based physical models, machine-learning algorithms and land surface models (LSMs). We then utilized 4 remote-sensing-based physical models, 2 machine-learning algorithms and 14 LSMs to analyze the spatial and temporal variations in global terrestrial ET. The results showed that the ensemble means of annual global terrestrial ET estimated by these three categories of approaches agreed well, with values ranging from 589.6 mm yr−1 (6.56×104 km3 yr−1) to 617.1 mm yr−1 (6.87×104 km3 yr−1). For the period from 1982 to 2011, both the ensembles of remote-sensing-based physical models and machine-learning algorithms suggested increasing trends in global terrestrial ET (0.62 mm yr−2 with a significance level of p0.05), although many of the individual LSMs reproduced an increasing trend. Nevertheless, all 20 models used in this study showed that anthropogenic Earth greening had a positive role in increasing terrestrial ET. The concurrent small interannual variability, i.e., relative stability, found in all estimates of global terrestrial ET, suggests that a potential planetary boundary exists in regulating global terrestrial ET, with the value of this boundary being around 600 mm yr−1. Uncertainties among approaches were identified in specific regions, particularly in the Amazon Basin and arid/semiarid regions. Improvements in parameterizing water stress and canopy dynamics, the utilization of new available satellite retrievals and deep-learning methods, and model–data fusion will advance our predictive understanding of global terrestrial ET.

Accurate short-term forecasts of daily reference evapotranspiration (ET0) are essential for real-time irrigation scheduling. Many models rely on current and historical temperature data to estimate daily ET0. However, easily accessible temperature forecasts are relatively less reported in short-term ET0 forecasting. Furthermore, the accuracy of ET0 forecasting from different models varies locally and also across regions. We used five temperature-dependent models to forecast daily ET0 for a 7-day horizon in the North China Plain (NCP): the McCloud (MC), Hargreaves-Samani (HS), Blaney-Criddle (BC), Thornthwaite (TH), and reduced-set Penman–Monteith (RPM) models. Daily meteorological data collected between 1 January 2000 and 31 December 2014 at 17 weather stations in NCP to calibrate and validate the five ET0 models against the ASCE Penman–Monteith (ASCE-PM). Forecast temperatures for up to 7 d ahead for 1 January 2015–19 June 2021 were input to the five calibrated models to forecast ET0. The performance of the five models improved for forecasts at all stations after calibration. The calibrated RPM is the preferred choice for forecasting ET0 in NCP. In descending order of preference, the remaining models were ranked as HS, TH, BC, and MC. Sensitivity analysis showed that a change in maximum temperature influenced the accuracy of ET0 forecasting by the five models, especially RPM, HS, and TH, more than other variables. Meanwhile, the calibrated RPM and HS equations were better than the other models, and thus, these two equations were recommended for short-term ET0 forecasting in NCP.

The exact evaluation of Extreme Learning Machine (ELM) compactness is difficult due to the randomness in hidden layer nodes number, weight and bias values. To overcome this randomness, and other problems such as resultant overfitting and large variance, a selective weighted voting ensemble model based on regularized ELM is investigated. It can strongly enhance the overall performance including accuracy, variance and time consumption. Efficient Prediction Sum of Squares (PRESS) criteria that utilizing Singular Value Decomposition (SVD) is proposed to address the slow execution. Furthermore, an ensemble pruning approach based on the eigenvalues for the input weight matrix is developed. In this work, the ensemble base classifiers weights are calculated based on the same PRESS error metric used for the solutions of the output weight vector (β) in RELM, thus, it can reduce computational cost and space requirement. Different state-of-the-art learning approaches and various well-known facial expressions faces and object recognition benchmark datasets were examined in this work.

Accurate prediction of reference crop evapotranspiration (ET0) is important for regional water resources management and optimal design of agricultural irrigation system. In this study, three hybrid models (PSO-ELM, GA-ELM and ABC-ELM) integrating the extreme learning machine model (ELM) with three biological heuristic algorithms, i.e., PSO, GA and ABC, were proposed for predicting daily ET0 based on daily meteorological data from 2000 to 2019 at twelve representative stations in different climatic zones of China. The performances of the three hybrid ELM models were further compared with the standalone ELM model and three empirical models (Hargreaves, Priestley-Talor and Makkink models). The results showed that the hybrid ELM models (R² =0.973-0.999) all performed better than the standalone ELM model (R²=0.955-0.989) in four climatic regions in China. The estimation accuracy of the empirical models was relatively lower, with R² of 0.822-0.887 and RMSE of 0.381-1.951 mm/d. The R² values of PSO-ELM, GA-ELM and ABC-ELM models were 0.993, 0.986 and 0.981 and the RMSE values were 0.266 mm/d, 0.306 mm/d and 0.404 mm/d, respectively, indicating that the PSO-ELM model had the best performance. When setting Tmax, Tmin and RH as the model inputs, the PSO-ELM model presented better performance in the temperate continental zone (TCZ), subtropical monsoon region (SMZ) and temperate monsoon zone (TMZ) climate zones, with R² of 0.892, 0866 and 0.870 and RMSE of 0.773 mm/d, 0.597 mm/d and 0.832 mm/d, respectively. The PSO-ELM model also performed in the mountain plateau region (MPZ) when only Tmax and Tmin data were available, with R² of 0.808 and RMSE of 0.651mm/d. All the three biological heuristic algorithms effectively improved the performance of the ELM model. Particularly, the PSO-ELM was recommended as a promising model realizing the high-precision estimation of daily ET0 with fewer meteorological parameters in different climatic zones of China.

As the standard method to compute reference evapotranspiration (ET0), Penman-Monteith (PM) method requires eight meteorological input variables, which makes it difficult to apply in data scarce regions. To overcome this problem, a hybrid bi-directional long short-term memory (Bi-LSTM) model was developed to forecast short-term (1–7-day lead time) daily ET0. The model was trained, validated and tested using three meteorological variables for the period of 2006–2018 at selected three meteorological stations located in the semi-arid region of central Ningxia, China. The performance of the hybrid Bi-LSTM model to forecast short-term daily ET0 was evaluated against daily ET0 calculated by the Penman-Monteith method using the statistical metrics namely, mean absolute error (MAE), root mean square error (RMSE), Pearson's correlation coefficient (R) and Nash-Sutcliffe efficiency (NSE). The results showed that the hybrid Bi-LSTM model with a combination of three meteorological inputs (maximum temperature, minimum temperature and sunshine duration) provides the best forecast performance for short-term daily ET0 at the selected meteorological stations. When averaged across stations, the statistical performance at different forecast lead time were as follows; 1-day lead time: RMSE = 0.159 mm day−1, MAE = 0.039 mm day−1, R = 0.992, NSE = 0.988; 4-day lead time: RMSE = 0.247 mm day−1, MAE = 0.075 mm day−1, R = 0.972, NSE = 0.985 and 7-day lead time: RMSE = 0.323 mm day−1, MAE = 0.089 mm day−1, R = 0.943, NSE = 0.982. Moreover, the hybrid Bi-LSTM model consistently improved the forecast performance of short-term daily ET0 compared to the adjusted Hargreaves-Samani (HS) method and the general Bi-LSTM model. The hybrid Bi-LSTM model developed in this study is currently integrated into the modern intelligent irrigation system of 30 ha of Lycium barbarum plantation in central Ningxia in China, a region with limited meteorological data. It is recommended however that the hybrid Bi-LSTM should be evaluated across a wide range of climatic conditions in different regions of the world.

Accurate estimation of reference evapotranspiration (ET0) is of utmost importance for hydrological balance, global change and water resource management. However, caused by the insufficient meteorological data and indefinite input combination, uncertainties may exist in the simplified artificial intelligence (AI) models. Thus, determination the uncertainty is significant for accurate ET0 results. In this study, the validity of 29 combination scenarios of maximum and minimum temperature, wind speed, relative humidity, solar radiation, sunshine duration, and atmospheric pressure was examined by applying the artificial neural network (ANN), support vector regression (SVR), and extreme learning machine (ELM) models for the arid Altay Prefecture. Performances of the models were evaluated against the Penman-Monteith equation by coefficient of correlation (R), root mean squared error (RMSE), mean absolute error (MAE), and Nash-Sutcliffe efficiency (NS) in testing period. The Monte Carlo (MC) technique was firstly performed to analyze the sensitivity of the meteorological parameters and the uncertainty of the AI models. The results confirmed the indispensable role of temperature and the predominant function of the aerodynamic part in evapotranspiration process. An input pattern, which is able to reveal the physical mechanism of AI models in ET0 estimation, was proposed innovatively. Both the SVR and ELM models are highly recommended for ET0 estimation due to the comparable simulating ability and lower uncertainty. The findings help to understand the implied intrinsic mechanism of evapotranspiration in AI models and can be regarded as a breakthrough in ET0 modeling.

For developing countries, scarcity of climatic data is the biggest challenge, and model development with limited meteorological input is of critical importance. In this study, five data intelligent and hybrid metaheuristic machine learning algorithms, namely additive regression (AR), AR-bagging, AR-random subspace (AR-RSS), AR-M5P, and AR-REPTree, were applied to predict monthly mean daily reference evapotranspiration (ET 0). For this purpose, climatic data of two meteorological stations located in the semi-arid region of Pakistan were used from the period 1987 to 2016. The climatic dataset includes maximum and minimum temperature (T max , T min), average relative humidity (RH avg), average wind speed (U x), and sunshine hours (n). Sensitivity analysis through regression methods was applied to determine effective input climatic parameters for ET 0 modeling. The results of performed regression analysis on all input parameters proved that T min , RH Avg , U x , and n were identified as the most influential input parameters at the studied station. From the results, it was revealed that all the selected models predicted ET 0 at both stations with greater precision. The AR-REPTree model was located furthest and the AR-M5P model was located nearest to the observed point based on the performing indices at both the selected meteorological stations. The study concluded that under the aforementioned methodological framework, the AR-M5P model can yield higher accuracy in predicting ET 0 values, as compared to other selected algorithms.

Climate change is leading to changing patterns of precipitation and increasingly extreme global weather. There is an urgent need to synthesize our current knowledge on climate risks to water security, which in turn is fundamental for achieving sustainable water management. Climate Risk and Sustainable Water Management discusses hydrological extremes, climate variability, climate impact assessment, risk analysis, and hydrological modelling. It provides a comprehensive interdisciplinary exploration of climate risks to water security, helping to guide sustainable water management in a changing and uncertain future. The relevant theory is accessibly explained using examples throughout, helping readers to apply the knowledge learned to their own situations and challenges. This textbook is especially valuable to students of hydrology, resource management, climate change, and geography, as well as a reference textbook for researchers, civil and environmental engineers, and water management professionals concerned with water-related hazards, water cycles, and climate change.

Even though research shows that aggregate stability and mean weight diameter (MWD) are critical components of soil health, it is not routinely measured. An alternative approach to the physical measurement is to calculate these values based on routinely measured soil parameters. Therefore, the objective was to compare two artificial intelligence (AI) based machine learning approaches i.e. support vector machine (SVM) and artificial neural network (ANN) models in prediction of soil wet aggregate stability (quantified by MWD). Soil samples (120) from the Indo‐Gangetic Alluvium major soil group, that are characterized as Ustifluvents were used in the study. These samples were analyzed for sand, silt, clay; bulk density (BD), organic carbon (OC), and mean weight diameter (MWD). The correlation coefficient (r) was highest in case of SVM model with a percentage increase of 16.92 and 2.70 when compared with MLR and ANN respectively. The SVM and ANN models showed 6.36% and 2.12% decrease in RMSE in training dataset while a 14.28% decrease was found for SVM in testing dataset when compared to the multi‐linear regression (MLR) model. Results showed that ANN with two neurons (building blocks of ANN) in hidden layer had better performance in predicting MWD than MLR, whereas the radial basis kernel function based SVM was found to be best for training and testing data of MWD. Soil texture, OC and BD can be used to predict soil structural stability effectively using SVM. However, additional work is needed to confirm these findings with other soils. This article is protected by copyright. All rights reserved

The Food and Agriculture Organization of the United Nations (FAO) estimates that population growth will reach 11.2 billion by the year 2100, which will contribute to food and agricultural product demand, making irrigation optimization essential. In this context is highlighted the evapotranspiration parameter is determined by the FAOPM method. However, a precise measurement of this parameter requires several climatic parameters that can not be available in rural areas, in which, a promise solution belongs in approaches that use just a few climatic parameters which can be obtained by satellites and weather stations combined with machine learning models. In this research, the MLP (Multilayer perceptron) e SVM (Support Vector Machines) models were used to model the reference evapotranspiration with satellite and weather stations data under two approaches: the local approach where the models are trained and tested on the training location, and the regional approach where the models trained on the training location were applied on a test location. These approaches were applied in two experiments: the first on a temperate climate zone, and the second on a tropical climate zone. The results indicate that the MLP model stood out when compared with the SVM model in all tests realized, in which, the models trained with the climatic parameters of temperature and radiation obtained the metrics of R2 of 0.6568, RMSE of 0.1103, and MAE de 0.0882 for the temperate climatic zone experiment and metrics R2 of 0.7391, RMSE 0.1266, and MAE of 0.1063 for the tropical climate zone experiment on the first approach which demonstrates the potential of using only these parameters to model de evapotranspiration. For the second approach, the MLP model could be applied to the tropical climate zone in which the metrics R2 of 0.7158, RMSE of 0.1592, and MAE of 0.1428 were obtained. Yet the result obtained by the models applied on the temperate climate zone was inconclusive which indicates that for the conditions of this location the models can’t be applied with the second approach.

Extreme learning machine (ELM) has gained increasing interest from various research fields recently. In this review, we aim to report the current state of the theoretical research and practical advances on this subject. We first give an overview of ELM from the theoretical perspective, including the interpolation theory, universal approximation capability, and generalization ability. Then we focus on the various improvements made to ELM which further improve its stability, sparsity and accuracy under general or specific conditions. Apart from classification and regression, ELM has recently been extended for clustering, feature selection, representational learning and many other learning tasks. These newly emerging algorithms greatly expand the applications of ELM. From implementation aspect, hardware implementation and parallel computation techniques have substantially sped up the training of ELM, making it feasible for big data processing and real-time reasoning. Due to its remarkable efficiency, simplicity, and impressive generalization performance, ELM have been applied in a variety of domains, such as biomedical engineering, computer vision, system identification, control and robotics, etc. In this review, we try to provide a comprehensive view of these advances in ELM together with its future perspectives.

Monthly mean reference evapotranspiration (ET
0
) is estimated using adaptive network based fuzzy inference system (ANFIS) and artificial neural network (ANN) models. Various combinations of long-term average monthly climatic data of wind speed, air temperature, relative humidity, and solar radiation, recorded at stations in Turkey, are used as inputs to the ANFIS and ANN models so as to calculate ET
0
given by the FAO-56 PM (Penman-Monteith) equation. First, a comparison is made among the estimates provided by the ANFIS and ANN models and those by the empirical methods of Hargreaves and Ritchie. Next, the empirical models are calibrated using the ET
0
values given by FAO-56 PM, and the estimates by the ANFIS and ANN techniques are compared with those of the calibrated models. Mean square error, mean absolute error, and determination coefficient statistics are used as comparison criteria for evaluation of performances of all the models considered. Based on these evaluations, it is found that the ANFIS and ANN schemes can be employed successfully in modeling the monthly mean ET
0
, because both approaches yield better estimates than the classical methods, and yet ANFIS being slightly more successful than ANN.

Evaporation is a major component of the hydrological cycle. It is an important aspect of water resource engineering and management, and in estimating the water budget of irrigation schemes. The current work presents the application of adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) approaches for modeling daily pan evaporation using daily climatic parameters. The neuro-fuzzy and neural network models are trained and tested using the data of three weather stations from different geographical positions in the U.S. State of Illinois. Daily meteorological variables such as air temperature, solar radiation, wind speed, relative humidity, surface soil temperature and total rainfall for three years (August 2005 to September 2008) were used for training and testing the employed models. Statistic parameters such as the coefficient of determination (R 2), the root mean squared error (RMSE), the variance accounted for (VAF), the adjusted coefficient of efficiency (E 1) and the adjusted index of agreement (d 1) are used to evaluate the performance of the applied techniques. The results obtained show the feasibility of the ANFIS and ANN evaporation modeling from the available climatic parameters, especially when limited climatic parameters are used.

An accurate and simple Reference Evapotranspiration (ETo) numerical model eases to use for supporting irrigation planning and its effective management is highly desired in Sahelian regions. This paper investigates the performance ability of the Gene-expression Programming (GEP) for modeling ETo using decadal climatic data from a Sahelian country; Burkina Faso. For the study; important data are collected from six synoptic meteorological stations located in different regions; Gaoua, Pô, Boromo, Ouahigouya, Bogandé and Dori. The climatic data combinations are used as inputs to develop the GEP models at regional-specific data basis for estimating ETo. GEP performances are evaluated with the root mean square error (RMSE), and coefficient of correlation (R) between estimated and targeted Penman-Monteith FAO56 set as the true reference values. Obviously; from the statistical viewpoint; GEP computing technique has showed a good ability for providing numerical models on a regional data basis. The performances of GEP based on temperatures data are quite good able to substitute empirical equations at regional level to some extent. It is found that the models with wind velocity yield high accuracies by causing radical improve of the performances with R2 (0.925-0.961) and RMSE (0.131-0.272 mm day-1); while relative humidity may cause only (R2 = 0.801-0.933 and RMSE = 0.370-0.578 mm day-1). Statistically; GEP is an effectual modeling tool for computing successfully evapotranspiration in Sahel.

Accurate estimation of reference evapotranspiration (ET0) is important for water resources engineering. Therefore, a large number of empirical or semi-empirical equations have been
developed for assessing ET0 from numerous meteorological data. However, records of such weather variables are often incomplete or not always available
for many locations, which is a shortcoming of these complex models. Therefore, practical and simpler methods are required
for estimating the ET0. In this study, the efficiency of a wavelet regression (WR) model in estimating reference evapotranspiration based on only
Class A pan evaporation is examined. The results of the WR model are compared with those of three pan-based equations, namely
the FAO-24 pan, Snyder ET0 and Ghare ET0 equations and their calibrated versions. Daily Class A pan evaporation data from the Fresno and Bakersfield stations of the
United States Environmental Protection Agency in California, USA, are used in the study. The WR model estimates are compared
against those of the FAO-56 Penman–Monteith equation. Results showed that the WR model is capable of accurately predicting
the ET0 values as a product of pan evaporation data.

This study investigates the accuracy of support vector machines (SVM), which are regression procedures, in modelling reference evapotranspiration (ET0). The daily meteorological data, solar radiation, air temperature, relative humidity and wind speed from three stations, Windsor, Oakville and Santa Rosa, in central California, USA, are used as inputs to the support vector machines to reproduce ET0 obtained using the FAO-56 Penman-Monteith equation. A comparison is made between the estimates provided by the SVM and those of the following empirical models: the California Irrigation Management System (CIMIS) Penman, Hargreaves, Ritchie and Turc methods. The SVM results were also compared with an artificial neural networks method. Root mean-squared errors, mean-absolute errors, and determination coefficient statistics are used as comparing criteria for the evaluation of the models' performances. The comparison results reveal that the support vector machines could be employed successfully in modelling the ET0 process.

According to conventional neural network theories, single-hidden-layer feedforward networks (SLFNs) with additive or radial basis function (RBF) hidden nodes are universal approximators when all the parameters of the networks are allowed adjustable. However, as observed in most neural network implementations, tuning all the parameters of the networks may cause learning complicated and inefficient, and it may be difficult to train networks with nondifferential activation functions such as threshold networks. Unlike conventional neural network theories, this paper proves in an incremental constructive method that in order to let SLFNs work as universal approximators, one may simply randomly choose hidden nodes and then only need to adjust the output weights linking the hidden layer and the output layer. In such SLFNs implementations, the activation functions for additive nodes can be any bounded nonconstant piecewise continuous functions g : R --> R and the activation functions for RBF nodes can be any integrable piecewise continuous functions g : R --> R and integral of R g(x)dx not equal to 0. The proposed incremental method is efficient not only for SFLNs with continuous (including nondifferentiable) activation functions but also for SLFNs with piecewise continuous (such as threshold) activation functions. Compared to other popular methods such a new network is fully automatic and users need not intervene the learning process by manually tuning control parameters.

This paper presents a mathematical analysis of the effect of
limited precision analog hardware for weight adaptation to be used in
on-chip learning feedforward neural networks. Easy-to-read equations and
simple worst-case estimations for the maximum tolerable imprecision are
presented. As an application of the analysis, a worst-case estimation on
the minimum size of the weight storage capacitors is presented

It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: (1) the slow gradient-based learning algorithms are extensively used to train neural networks, and (2) all the parameters of the networks are tuned iteratively by using such learning algorithms. Unlike these conventional implementations, this paper proposes a new learning algorithm called extreme learning machine (ELM) for single-hidden layer feedforward neural networks (SLFNs) which randomly chooses hidden nodes and analytically determines the output weights of SLFNs. In theory, this algorithm tends to provide good generalization performance at extremely fast learning speed. The experimental results based on a few artificial and real benchmark function approximation and classification problems including very large complex applications show that the new algorithm can produce good generalization performance in most cases and can learn thousands of times faster than conventional popular learning algorithms for feedforward neural networks.1

Reference evapotranspiration (ET0) is an essential component in hydrological ecological processes and agricultural water management. Accurate estimation of ET0 is of importance in improving irrigation efficiency, water reuse and irrigation scheduling. FAO-56 Penman-Monteith (P-M) model is recommended as the standard model to estimate ET0. Nevertheless, its application is limited due to the lack of required meteorological data. In this study, trained extreme learning machine (ELM), backpropagation neural networks optimized by genetic algorithm (GANN) and wavelet neural networks (WNN) models were developed to estimate ET0, and the performances of ELM, GANN, WNN, two temperature-based (Hargreaves and modified Hargreaves) and three radiation-based (Makkink, Priestley-Taylor and Ritchie) ET0 models in estimating ET0 were evaluated in a humid area of Southwest China. Results indicated that among the new proposed models, ELM and GANN models were much better than WNN model, and the temperature-based ELM and GANN models had better performance than Hargreaves and modified Hargreaves models, radiation-based ELM and GANN models had higher precision than Makkink, Priestley-Taylor and Ritchie models. Both radiation-based ELM (RMSE ranging 0.312∼0.332 mm d-1, Ens ranging 0.918∼0.931, MAE ranging 0.260∼0.300 mm d-1) and GANN models (RMSE ranging 0.300∼0.333 mm d-1, Ens ranging 0.916∼0.941, MAE ranging 0.2580∼0.303mm d-1) could estimate ET0 at an acceptable accuracy level, and are highly recommended for estimating ET0 without adequate meteorological data.

New reference evapotranspiration formulas based on simplifications of Penman’s equation were developed applicable to humid areas, where wind speed and/or relative humidity data are missing. The new formulas were obtained by empirical calibration adjustments using meteorological data obtained from the humid locations of the CLIMWAT global data base. The performance of the new derived formulas was tested under various climatic conditions using data set monthly and daily data obtained from 16 weather stations at humid locations of California, Florida, and Greece. Comparisons indicated that the suggested formulas performed better than other empirical methods not requiring wind and/or humidity data for the majority of humid locations.

The adaptive neuro-fuzzy inference system (ANFIS) is applied for selection of the most influential reference evapotranspiration (ET0) parameters. This procedure is typically called variable selection. It is identical to finding a subset of the full set of recorded variables that illustrates good predictive abilities. The full weather datasets for seven meteorological parameters were obtained from twelve weather stations in Serbia during the period 1980–2010. The monthly ET0 data are obtained by the Penman–Monteith method, which is proposed by Food and Agriculture Organization of the United Nations as the standard method for the estimation of ET0. As the performance evaluation criteria of the ANFIS models the following statistical indicators were used: the root mean squared error (RMSE), Pearson correlation coefficient (r) and coefficient of determination (R2). Sunshine hours are the most influential single parameter for ET0 estimation (RMSE = 0.4398 mm/day). The obtained results indicate that among the input variables sunshine hours, actual vapor pressure and minimum air temperature, are the most influential for ET0 estimation. The maximum relative humidity and maximum air temperature are the most influential optimal combination of two parameters (RMSE = 0.2583 mm/day).

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

The evapotranspiration crop coefficients (Kc) that are used to estimate actual evapotranspiration (ETa) using a two-step approach (i.e., Kc×reference ET) for limited irrigated and rainfed maize are extremely rare. The effects of full and limited irrigation and rainfed practices on maize ETa and soil water dynamics were quantified. Grass- and alfalfa-based crop coefficients (Kco and Kcr) were developed for full- and limited-irrigation settings as well as for rainfed conditions. Four irrigation regimes [fully irrigated treatment (FIT), 75% FIT, 60% FIT, 50% FIT] and rainfed treatments were implemented. In general, depletion in available soil water increased with the decrease in irrigation regime from FIT to rainfed treatment. Maize ETa increased with irrigation amounts and ranged from 481 mm for the rainfed treatment to 620 mm for the FIT in 2009 and from 579 to 634 mm for the same treatments, respectively, in 2010. Reduction in seasonal ETa relative to FIT were 22, 9, 7, and 2% for the rainfed, 50% FIT, 60% FIT, and 75% FIT, respectively, in 2009. The reductions were 9, 4, 2, and 1% in 2010 for the same treatments. On average, a two-step approach overestimated maize ETa by approximately 26% in 2009 and 17% in 2010. The difference between the two methods ranged from 18% for the FIT to 38% for the rainfed treatment in 2009. The difference in 2010 was smaller owing to a greater amount of precipitation (563 mm in 2010 versus 426 mm in 2009), ranging from 21% for FIT to 12% for the rainfed treatment. One method was not able to effectively account for the impact of water-limiting and rainfed conditions on Kc when estimating ETa, resulting in considerable error in 2009. A new set of maize Kco and Kcr values under rainfed, limited, and fully irrigated settings were developed as a function of the thermal unit and days after emergence. The midseason average Kco values were 1.26, 1.20, 1.11, 1.08, and 1.10 for the FIT, 75% FIT, 60% FIT, 50% FIT, and rainfed treatments, respectively. The midseason average Kcr values were 1.05, 1.00, 0.97, 0.95, and 0.92 for the same treatments, respectively. In general, more water limitation and crop water stress resulted in lower midseason Kc values, and there was a gradual decrease in the peak Kco and Kcr values from FIT toward the rainfed treatment. The new set of Kco and Kcr equations can be beneficial for estimating maize water use for in-season irrigation management under full- and limited-irrigation settings as well as estimating evaporative losses under rainfed conditions for the locations that have similar soil, crop, climate, and management conditions of this study.

Accurate estimation of reference evapotranspiration (ET0) is needed for planning and managing water resources and agricultural production. The FAO-56 Penman–Monteith equation is used to determinate ET0 based on the data collected during the period 1980–2010 in Serbia. In order to forecast ET0, four soft computing methods were analyzed: genetic programming (GP), support vector machine-firefly algorithm (SVM-FFA), artificial neural network (ANN), and support vector machine–wavelet (SVM–Wavelet). The reliability of these computational models was analyzed based on simulation results and using five statistical tests including Pearson correlation coefficient, coefficient of determination, root-mean-square error, absolute percentage error, and mean absolute error. The end-point result indicates that SVM–Wavelet is the best methodology for ET0 prediction, whereas SVM–Wavelet and SVM-FFA models have higher correlation coefficient as compared to ANN and GP computational methods.

This study compares two different adaptive neuro-fuzzy inference systems, adaptive neuro-fuzzy inference system (ANFIS) with grid partition (GP) method and ANFIS with subtractive clustering (SC) method, in modeling daily reference evapotranspiration (ET 0 ). Daily climatic data including air temperature, solar radiation, relative humidity and wind speed from Adana Station, Turkey were used as inputs to the fuzzy models to estimate daily ET 0 values obtained using FAO 56 Penman Monteith (PM) method. In the first part of the study, the effect of each climatic variable on FAO 56 PM ET 0 was investigated by using fuzzy models. Wind speed was found to be the most effective variable in modeling ET 0 . In the second part of the study, the effect of missing data on training, validation and test accuracy of the neuro-fuzzy models was examined. It was found that the ANFIS-GP model was not affected by missing data while the test accuracy of the ANFIS-SC model slightly decreases by increasing missing data’s percent. In the third part of the study, the effect of training data length on training, validation and test accuracy of the ANFIS models was investigated. It was found that training data length did not significantly affect the accuracy of ANFIS models in modeling daily ET 0 . ANFIS-SC model was found to be more sensitive to the training data length than the ANFIS-GP model. In the fourth part of the study, both ANFIS models were compared with the following empirical models and their calibrated versions; Valiantzas’ equations, Turc, Hargreaves and Ritchie. Comparison results indicated that the three-and four-input ANFIS models performed better than the corresponding empirical equations in modeling ET 0 while the calibrated two-parameter Ritchie and Valiantzas’ equations were found to be better than the two-input ANFIS models.

This paper proposes a novel short-term load forecasting (STLF) method based on wavelet transform, extreme learning machine (ELM) and modified artificial bee colony (MABC) algorithm. The wavelet transform is used to decompose the load series for capturing the complicated features at different frequencies. Each component of the load series is then separately forecasted by a hybrid model of ELM and MABC (ELM-MABC). The global search technique MABC is developed to find the best parameters of input weights and hidden biases for ELM. Compared to the conventional neuro-evolution method, ELM-MABC can improve the learning accuracy with fewer iteration steps. The proposed method is tested on two datasets: ISO New England data and North American electric utility data. Numerical testing shows that the proposed method can obtain superior results as compared to other standard and state-of-the-art methods.

In this paper, we present one dynamic model hypothesis to perform fish trajectory tracking in the fish ethology research and develop the relevant mathematical criterion on the basis of the Extreme Learning Machine (ELM). It is shown that the proposed scheme can conduct the non-linear and non Gaussian tracking process by multiple historical cues and current predictions – the state vector motion, the color distribution and the appearance recognition, all of which can be extracted from the single-hidden layer feedforward neural network (SLFN) at diverse levels with ELM. The strategy of the hierarchical hybrid ELM ensemble then combines the individual SLFN of the tracking cues for the performance improvements. The simulation results have shown the excellent performance in both robustness and accuracy of the developed approach.

This study investigates the applicability of Mamdani and Sugeno fuzzy genetic approaches in modeling
reference evapotranspiration (ET0). The daily air temperature, solar radiation, relative humidity and wind
speed data from Adana and Antalya stations, Turkey, were used as inputs to the fuzzy genetic models for
estimating ET0 obtained using the standard FAO-56 Penman–Monteith equation. Comparison of two dif-
ferent fuzzy genetic methods indicated that the Sugeno fuzzy genetic (SFG) method was faster and had a
better accuracy than theMamdani fuzzy genetic (MFG)method in modeling daily ET0. SGF and MFGmod-
els were also compared with the recently proposed Valiantzas’s equations and following empirical mod-
els: Hargreaves–Samani and Priestley–Taylor methods. Root mean-squared errors (RMSE), mean-absolute
errors (MAE) and determination coefﬁcient (R2
) were used for the evaluation of the models’ perfor-
mances. Results revealed that the SFG and MFG models were performed better than the empirical models
in modeling daily ET0 process. Comparison of the two different fuzzy genetic approaches indicated that
the SFG had a better accuracy than the MFG. For the Adana and Antalya stations, the SFG1 model with
RMSE = 0.219 and 111 mm/day, MAE = 0.097 and 0.080 mm/day and R2
= 0.983 and 0.998 in validation
period was found to be superior in modeling daily ET than the other models, respectively.

The applicability of fuzzy genetic (FG) approach in modeling reference evapotranspiration (ET0) is investigated in this study. Daily solar radiation, air temperature, relative humidity and wind speed data of two stations, Isparta and Antalya, in Mediterranean region of Turkey, are used as inputs to the FG models to estimate ET0 obtained using the FAO-56 Penman–Monteith equation. The FG estimates are compared with those of the artificial neural networks (ANN). Root mean-squared error, mean absolute error and determination coefficient statistics were used as comparison criteria for the evaluation of the models’ accuracies. It was found that the FG models generally performed better than the ANN models in modeling ET0 of Mediterranean region of Turkey.

A comparative study was carried out to evaluate the performance of the advection-aridity (AA) method and the Katerji and Perrier (KP) method to derive time series of actual evapotranspiration (ET). The AA method was formulated as a linear equation which relates actual ET to meteorological data. Meanwhile, the KP method is in a form of a linear equation which relates canopy resistance to meteorological data. Both the AA method and KP method need local calibration. Field work was conducted for the crop of maize and canola grown in the Coleambally Irrigation Area located in southeastern Australia. Results show that with locally calibrated parameters used in each method the AA method performed better than the KP method both for maize and canola crop. Future work will focus on use of the AA method to derive seasonal ET from satellite-based daily ET maps. The findings and methods in this study seem to be useful in deriving ET time series under other climate conditions.