Monthly Reference Evapotranspiration Research Articles

Estimation of Monthly Reference Evapotranspiration with Scarce Information Using Machine Learning in Southwestern Colombia

This research aimed to identify an alternative method to estimate reference evapotranspiration (ETo) with scarce climatological information in southwestern Colombia between 1983-2017 by evaluating and comparing different machine learning techniques. The FAO Penman-Monteith (FAO-PM56) was used as the reference method and four empirical methods (Hargreaves, Thornthwaite, Cenicafé, and Turc) were assessed with five metrics to evaluate the method of best fit to FAO-PM56, root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), Nash-Sutcliffe model efficiency coefficient (NSE), and Pearson correlation coefficient (R). Three models were designed using machine learning techniques to estimate ETo, multiple linear regression (MLR), artificial neural networks (ANN), and autoregressive integrated moving average model (ARIMA). The results showed that the ARIMA-M3 model reported the best performance metrics (RMSE = 4.13 mm month-1, MAE = 3.15 mm month-1, MBE = -0.08 mm month-1, NSE = 0.96 and r = 0.98). However, it restricts in that it can only be used locally and cannot be extrapolated to other climatological stations,because it was calibrated with specific conditions (exogenous variables) and stations,unlike the ANN-M1 model, which only requires training the network for its application. This method will allow estimating ETo in places with scarce information, as vital for water management in places with much uncertainty regarding accessibility and availability.

Estimation of Monthly Reference Evapotranspiration with Scarce Information Using Machine Learning in Southwestern Colombia

This research aimed to identify an alternative method to estimate reference evapotranspiration (ETo) with scarce climatological information in southwestern Colombia between 1983-2017 by evaluating and comparing different machine learning techniques. The FAO Penman-Monteith (FAO-PM56) was used as the reference method and four empirical methods (Hargreaves, Thornthwaite, Cenicafé, and Turc) were assessed with five metrics to evaluate the method of best fit to FAO-PM56, root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), Nash-Sutcliffe model efficiency coefficient (NSE), and Pearson correlation coefficient (R). Three models were designed using machine learning techniques to estimate ETo, multiple linear regression (MLR), artificial neural networks (ANN), and autoregressive integrated moving average model (ARIMA). The results showed that the ARIMA-M3 model reported the best performance metrics (RMSE = 4.13 mm month-1, MAE = 3.15 mm month-1, MBE = -0.08 mm month-1, NSE = 0.96 and r = 0.98). However, it restricts in that it can only be used locally and cannot be extrapolated to other climatological stations,because it was calibrated with specific conditions (exogenous variables) and stations,unlike the ANN-M1 model, which only requires training the network for its application. This method will allow estimating ETo in places with scarce information, as vital for water management in places with much uncertainty regarding accessibility and availability.

Modeling monthly reference evapotranspiration process in Turkey: application of machine learning methods.

In this study, the predictive power of three different machine learning (ML)-based approaches, namely, multi-gene genetic programming (MGGP), M5 model trees (M5Tree), and K-nearest neighbor algorithm (KNN), for long-term monthly reference evapotranspiration (ET0) prediction were investigated. The input data consist of monthly solar radiation (Rs), maximum air temperature (Tmax), and wind speed (Ws) derived from 163 meteorological stations in Turkey. Different input combinations were created and analyzed. The model's performance was evaluated using criteria such as Nash-Sutcliffe efficiency, Kling-Gupta efficiency, relative root mean squared error, mean absolute percentage error, and determination coefficient. Moreover, Taylor, radar, and boxplot diagrams were created. It was determined that the MGGP model outperformed both the M5Tree and the KNN models. The equation obtained from the MGGP model, for the best-performed combination of Rs-Tmax-Ws, was presented. The best weather conditions were obtained as 0.029 to 31.814MJ/m2, - 5.8 to 45.7°C, and 0.140 to 5.086m/s for Rs, Tmax, and Ws, respectively. It was also found that the Rs was the most potent input variable for ET0 estimation while Ws was the weakest.

Evaluation of Empirical and Machine Learning Approaches for Estimating Monthly Reference Evapotranspiration with Limited Meteorological Data in the Jialing River Basin, China.

The accurate estimation of reference evapotranspiration (ET0) is crucial for water resource management and crop water requirements. This study aims to develop an efficient and accurate model to estimate the monthly ET0 in the Jialing River Basin, China. For this purpose, a relevance vector machine, complex extreme learning machine (C-ELM), extremely randomized trees, and four empirical equations were developed. Monthly climatic data including mean air temperature, solar radiation, relative humidity, and wind speed from 1964 to 2014 were used as inputs for modeling. A total comparison was made between all constructed models using four statistical indicators, i.e., the coefficient of determination (R2), Nash efficiency coefficient (NSE), root mean square error (RMSE) and mean absolute error (MAE). The outcome of this study revealed that the Hargreaves equation (R2 = 0.982, NSE = 0.957, RMSE = 7.047 mm month−1, MAE = 5.946 mm month−1) had better performance than the other empirical equations. All machine learning models generally outperformed the studied empirical equations. The C-ELM model (R2 = 0.995, NSE = 0.995, RMSE = 2.517 mm month−1, MAE = 1.966 mm month−1) had the most accurate estimates among all generated models and can be recommended for monthly ET0 estimation in the Jialing River Basin, China.

Development of Monthly Reference Evapotranspiration Machine Learning Models and Mapping of Pakistan—A Comparative Study

Accurate estimation of reference evapotranspiration (ETo) plays a vital role in irrigation and water resource planning. The Penman–Monteith method recommended by the Food and Agriculture Organization (FAO PM56) is widely used and considered a standard to calculate ETo. However, FAO PM56 cannot be used with limited meteorological variables, so it is compulsory to choose an alternative model for ETo estimation, which requires fewer variables. This study built ten machine learning (ML) models based on multi-function, neural network, and tree-based structure against the FAO PM56 method. For this purpose, time series temperature data on a monthly scale are only used to train ML models. The developed ML models were applied to estimate ETo at different test stations and the obtained results were compared with the FAO PM56 method to verify and validate their performance in ETo estimation for the selected stations. In addition, multiple statistical indicators, including root-mean-square error (RMSE), coefficient of determination (R2), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and correlation coefficient (r) were calculated to compare the performance of each ML model on ETo estimation. Among the applied ML models, the ETo tree boost (TB) ML model outperformed the other ML models in estimating ETo in diverse climatic conditions based on statistical indicators (R2, NSE, r, RMSE, and MAE). Moreover, the observed R2, NSE, and r were the highest for the TB ML model, while RMSE and MAE were found to be the lowest at the study sites compared to other applied ML models. Lastly, ETo point data yielded from the TB ML model was used in an interpolation process to create monthly and annual ETo maps. Based on the ETo maps, this study suggests mainly a focus on areas with high ETo values and proper irrigation scheduling of crops to ensure water sustainability.

Comparative analysis of kernel-based versus ANN and deep learning methods in monthly reference evapotranspiration estimation

Abstract. Timely and accurate estimation of reference evapotranspiration (ET0) is indispensable for agricultural water management for efficient water use. This study aims to estimate the amount of ET0 with machine learning approaches by using minimum meteorological parameters in the Corum region, which has an arid and semi-arid climate and is regarded as an important agricultural centre of Turkey. In this context, monthly averages of meteorological variables, i.e. maximum and minimum temperature; sunshine duration; wind speed; and average, maximum, and minimum relative humidity, are used as inputs. Two different kernel-based methods, i.e. Gaussian process regression (GPR) and support vector regression (SVR), together with a Broyden–Fletcher–Goldfarb–Shanno artificial neural network (BFGS-ANN) and long short-term memory (LSTM) models were used to estimate ET0 amounts in 10 different combinations. The results showed that all four methods predicted ET0 amounts with acceptable accuracy and error levels. The BFGS-ANN model showed higher success (R2=0.9781) than the others. In kernel-based GPR and SVR methods, the Pearson VII function-based universal kernel was the most successful (R2=0.9771). Scenario 5, with temperatures including average temperature, maximum and minimum temperature, and sunshine duration as inputs, gave the best results. The second best scenario had only the sunshine duration as the input to the BFGS-ANN, which estimated ET0 having a correlation coefficient of 0.971 (Scenario 8). Conclusively, this study shows the better efficacy of the BFGS in ANNs for enhanced performance of the ANN model in ET0 estimation for drought-prone arid and semi-arid regions.

Application of an artificial intelligence technique enhanced with intelligent water drops for monthly reference evapotranspiration estimation

Reference evapotranspiration (ET0) is one of the most important parameters, which is required in many fields such as hydrological, agricultural, and climatological studies. Therefore, its estimation via reliable and accurate techniques is a necessity. The present study aims to estimate the monthly ET0 time series of six stations located in Iran. To achieve this objective, gene expression programming (GEP) and support vector regression (SVR) were used as standalone models. A novel hybrid model was then introduced through coupling the classical SVR with an optimization algorithm, namely intelligent water drops (IWD) (i.e., SVR−IWD). Two various types of scenarios were considered, including the climatic data- and antecedent ET0 data-based patterns. In the climatic data-based models, the effective climatic parameters were recognized by using two pre-processing techniques consisting of τ Kendall and entropy. It is worthy to mention that developing the hybrid SVR-IWD model as well as utilizing the τ Kendall and entropy approaches to discern the most influential weather parameters on ET0 are the innovations of current research. The results illustrated that the applied pre-processing methods introduced different climatic inputs to feed the models. The overall results of present study revealed that the proposed hybrid SVR-IWD model outperformed the standalone SVR one under both the considered scenarios when estimating the monthly ET0. In addition to the mentioned models, two types of empirical equations were also used including the Hargreaves−Samani (H−S) and Priestley−Taylor (P−T) in their original and calibrated versions. It was concluded that the calibrated versions showed superior performances compared to their original ones.

Comparison of reference evapotranspiration models for the agro-ecological zones of Nigeria

Irrigation practices are best done by estimating the crop water requirement in order to avoid over or under irrigation which may negatively affect crop yields. In this study, weather data (2004-2015) were collected and analyzed. The weather data include; minimum and maximum temperature (°C), relative humidity (%), wind speed (km/day), sunshine (hr/day) and radiation (MJ/m2/day). FAO Penman-Monteith model is a universal standard model used with other five evapotranspiration models such as; Priestley-Taylor model, Thornth-Waite model, Hargreaves model, ASCE-Penman Monteith model and Blaney-Criddle model to compute the mean monthly reference evapotranspiration (ET°) for the six agro-ecological zones of Nigeria. Statistic regressions were performed to examine the relationship of the reference ET° estimates from the five models with the estimates by FAO Penman-Monteith model. The results of the analyses show that the mean monthly average ETo estimates by the FAO Penman-Monteith model, Priestley-Taylor model, Thornth-Waite model, Hargreaves model, ASCE-Penman Monteith model and Blaney-Criddle model across the six weather stations are; 6.48, 7.66, 14.14, 11.16, 5.57, and 3.70 mm/day, respectively. The best predictor is the ASCE-Penman Monteith model which correlated well with the FAO Penman-Monteith model while, the Priestley-Taylor model is the second-best model. Thornth-Waite model and Hargreaves model produced underestimated ET values while, Blaney-Criddle model greatly over-estimated the FAO Penman-Monteith model. Therefore, this study is useful to the precise agricultural water management and regional water resources planning.

Long-term forecast of monthly reference evapotranspiration of the period 2018-2027 using SARIMA and GRNN models (case study: Rasht synoptic station)

سابقه و هدف: تبخیر – تعرق، یک فرایند کلیدی تعادل آب و همچنین یک عنصر مهم از تعادل انرژی است. بنابراین پیش بینی و تخمین تبخیر-تعرق در مدیریت آب زراعی، پیش بینی و نظارت بر خشکسالی و توسعه و بهره برداری از منبع­ های آبی موثر، می ­تواند بسیار با ارزش و کاربردی باشد. هدف از این مطالعه مدل سازی سری زمانی تبخیر-تعرق مرجع در ایستگاه سینوپتیک رشت توسط دو مدل SARIMA و GRNN در دوره 1956-2017، و پیش ­بینی آن برای سال ­های 2018-2027 می ­باشد. مواد و روش­ ها: شهر رشت در منطقه معتدل و مرطوب شمال ایران و در نوار جنوبی دریای خزر واقع است. در این مطالعه از روش تورنت‌وایت اصلاح شده برای برآورد ET0 استفاده شده است که پیشتر به نقل از محققان، در برآورد نرخ تبخیر-تعرق مرجع منطقه‌ی رشت عملکرد مطلوبی بیان کرده ست. میزان تبخیر-تعرق در سال­ های 1956-2017 برآورد شد. دو مدل برای مدل سازی و اعتبارسنجی سری‌‌زمانی ET0 انتخاب گردید. مدل SARIMA از مدل­ های استوکستیک فصلی و مدل GRNN بر پایه‌ی هوش مصنوعی استوار است. ورودی‌های مدل‌ها تا 3 گام زمانی قبل ماهانه و سالانه‌ انتخاب شدند. ماتریس­ های ورودی-هدف، به دو بخش واسنجی (75%) و اعنبارسنجی (25%) تقسیم شدند. تابع ACF نشان دهنده وجود روند فصلی در سری ماهانه ET0، با دوره‌بازگشت 12 بود. با چهار مرتبه تفاضل گیری مشخص شد که بهترین درجه تفاضل گیری مدل SARIMA در مرتبه اول می­ باشد. سایر عملگرهای SARIMA نیز، اعم از اتورگرسیو و میانگین متحرک فصلی و غیر فصلی، توسط سعی و خطا انتخاب شدند. بهینه‌سازی مدل GRNN نیز توسط سعی و خطای پارامتر گستره انجام شد.در این مطالعه معیارهایی همچون RMSE، NS و R برای بررسی خطا و همبستگی خروجی­های مدل استفاده شد. نتایج و بحث: بهترین مدل از الگوی SARIMA، مدل SARIMA(0,0,1)(0,1,1)12 معرفی شد. میزان RMSE و NS برای این مدل به‌ترتیب برابر با 8.89 میلی متر و 0.97 بود. مدل GRNN با اعمال کل ورودی ­ها بهترین نتیجه را نشان داد. مقادیر RMSE و NS در بهترین خروجی GRNN برابر با 9.22 میلی متر و 0.96 محاسبه شد. تفاوت دو مدل در برآورد کمینه‌ها (ماه‌های ژانویه و فوریه) گزارش شد که بنا برآن SARIMA عملکرد بهتری داشت. برای مقایسه‌ این دو مدل از دیاگرام تیلور نیز استفاده شد. دیاگرام تیلور نشان داد دقت SARIMA نه‌تنها در میزان خطا، بلکه در همبستگی و برآورد انحراف معیار مقادیر واقعی، کمی دقیق تر از GRNN عمل نموده است. پس از صحت سنجی مدل­ ها و ارزیابی عملکرد مطلوب آن­ها، بهترین مدل‌های مستخرج از SARIMA و GRNN، بجهت پیش‌بینی نرخ تبخیر-تعرق مرجع 10سال آتی برای (سال ­های 2018-2027) استفاده شدند. نتیجه‌گیری: نتایج پیش‌بینی‌های بیان شده برای سال­ های آینده‌ی رشت، وجود روند صعودی شدید ET0 در سال­های 2018- 2027 را )نسبت به دوره‌ی 1956-2017( نشان داده‌است. این موضوع افزایش سریع‌تر نرخ تبخیر-تعرق مرجع را در سال‌های آتی، برای منطقه مرطوب رشت هشدار می‌دهد. به جهت برنامه‌ریزی منابع آب سطحی و زیرزمینی برای استفاده­ های کشاورزی و زراعی، این مساله بسیار دارای اهمیت بوده و هشداری بسیار جدی برای کشاورزان و مدیران آب در این منطقه خواهد بود.

Quantifying the impact of climate variables on reference evapotranspiration in Pearl River Basin, China

ABSTRACTThe impact of climate variables on monthly reference evapotranspiration (ETo) is a critical issue in water resources management and irrigation planning. The spatio-temporal contribution of climate variables to ETo in the Pearl River Basin (PRB), China, from 1960 to 2016 were calculated based on sensitivity and relative change of each climatic variable. The results show that annual ETo total decreased by 1.64% and diminished in magnitude from the southeast to the northwest. Sunshine duration, wind speed and relative humidity decreased by 15.5%, 7.4%, and 4.0%, respectively, while average temperature increased by 4.25%. The ETo showed a positive sensitivity to all variables except relative humidity, which showed a negative sensitivity. Sunshine duration had the highest contribution of −4.26%, and the overall decrease in ETo was mainly caused by the declines in sunshine duration and wind speed, which offset the positive impact of rises in average temperature and reduction in relative humidity.

Estimation of monthly reference evapotranspiration using novel hybrid machine learning approaches

ABSTRACTIn this research, five hybrid novel machine learning approaches, artificial neural network (ANN)-embedded grey wolf optimizer (ANN-GWO), multi-verse optimizer (ANN-MVO), particle swarm optimizer (ANN-PSO), whale optimization algorithm (ANN-WOA) and ant lion optimizer (ANN-ALO), were applied for modelling monthly reference evapotranspiration (ETo) at Ranichauri (India) and Dar El Beida (Algeria) stations. The estimates yielded by hybrid machine learning models were compared against three models, Valiantzas-1, 2 and 3 based on root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), Pearson correlation coefficient (PCC) and Willmott index (WI). The results of comparison show that the ANN-GWO-1 model with five input variables (Tmin, Tmax, RH, Us, Rs) provides better estimates at both study stations (RMSE = 0.0592/0.0808, NSE = 0.9972/0.9956, PCC = 0.9986/0.9978, and WI = 0.9993/0.9989). Also, the adopted modelling strategy can build a truthful expert intelligent system for estimating the monthly ETo at study stations.

The viability of co-active fuzzy inference system model for monthly reference evapotranspiration estimation: case study of Uttarakhand State

Abstract Reference evapotranspiration (ETo) is a major component of the hydrological cycle linking the irrigation water requirement and planning and management of water resources. In this research, the potential of co-active neuro-fuzzy inference system (CANFIS) was investigated against the multilayer perceptron neural network (MLPNN), radial basis neural network (RBNN), self-organizing map neural network (SOMNN) and multiple linear regression (MLR) to estimate the monthly ETo at Pantnagar and Ranichauri stations, located in the foothills of Indian central Himalayas of Uttarakhand State, India. The significant combination of input variables for implemented techniques was decided by the Gamma test (GT). The results obtained by CANFIS models were compared with MLPNN, RBNN, SOMNN and MLR models based on performance evaluation indicators and visual inspection using line, scatter and Taylor plots for both the stations. The results of comparison revealed that CANFIS-5/CANFIS-9 models (RMSE = 0.0978/0.1394, SI = 0.0261/0.0475, COE = 0.9963/0.9846, PCC = 0.9982/0.9942 and WI = 0.9991/0.9959) with three and five input variables provide superior results for estimating monthly ETo at Pantnagar and Ranichauri stations, respectively. Also, the adopted modelling strategy can build a truthful expert intelligent system for estimating the monthly ETo at the study stations.

Modelling reference evapotranspiration for Megecha catchment by multiple linear regression

Reference evapotranspiration (ETo) is a complex process in the hydrological cycle that influences the quantity of runoff and then the irrigation water requirements. Many methods have been developed to estimate reference evapotranspiration. The reliable reference evapotranspiration methods are parameter rich models but not applicable for data scarce regions. On the other hand, accuracy and reliability of simple reference evapotranspiration models vary widely according to regional climate conditions. Estimation of reference evapotranspiration of specific area is imperative for investigating, planning, designing, and managing irrigation schemes. The objective of the present study is to determine the ETo values using combination Penman–Monteith model and to devise a model used to predict reference evapotranspiration in the Megecha catchment. In this study, the potential of multiple linear regression model using least squares is investigated in modeling of mean monthly reference evapotranspiration obtained using the standard FAO-56 Penman–Monteith equation. Various combinations of daily climatic data, namely solar radiation, air temperature, relative humidity, and wind speed were used as inputs to the model development. Thus, this can give direction to evaluate the degree and effect of each variable on estimated ETo. In line to this, residual analysis, co-efficient of determination and residual error were used as comparison tools for the evaluation of the model performance. The result of the multiple correlation showed that sun hour, wind speed, and maximum temperature were strongly positive correlation with ETOr = 0.82, 0.71, and 0.78, respectively, whereas relative humidity has moderately negative correlation (r = − 0.604). The multiple linear regression model gave residual errors of 0.26 mm/day and co-efficient of determination of 0.92 for the meteorological station considered. Based on the residual analysis results, it was found that the multiple linear regression model followed a linear trend. The input variables of the model were fitting, and this model could be successfully employed in estimating and predicting the monthly reference evapotranspiration in the study area and can be used in similar parts of data sparse regions.

Using gene expression programming in monthly reference evapotranspiration modeling: A case study in Egypt

The Penman-Monteith FAO-56 equation requires the complete climatic records for estimating reference evapotranspiration (ETo). The present study is aimed at developing and evaluating a gene expression programming (GEP) model for estimating mean monthly ETo by using minimal amount of climatic data. The data used in the analysis are collected from 32 weather stations in Egypt through the CLIMWAT database. The results showed that the accuracy of the GEP model significantly improved when either mean relative humidity (RH) or wind speed at 2-m height (u2) was used as additional input variables. The GEP model with the inputs as maximum and minimum air temperature, RH, and u2 showed the lowest root mean square error (0.426 mm d−1 and 0.430 mm d−1) and, the highest coefficient of determination, (0.963 and 0.962) overall index of model performance (0.960 and 0.960), and index of agreement (0.991 and 0.990) for training and testing sets, respectively. Comparing the results of GEP models with other empirical models showed that the GEP technique are more accurate and can be employed successfully in modelling ETo.

Trend of Crop Water Requirement at Akola (Maharashtra), India

Climate change scenario badly affects the agriculture. The present study aimed to characterize the trend in maximum temperature and crop water requirement over a last decade at Akola station (Maharashtra State), because of changing trend in meteorological parameters. Study investigated the trends in temperature and reference evapotranspiration using various statistical parameters like mean, coefficient of variation, coefficient of skewness and coefficient of kurtosis. Monthly maximum air temperature showed slightly decreasing trend over summer season while increasing trend over monsoon and winter season. On the contrary, the monthly reference evapotranspiration showed decreasing linear trend over monsoon and winter season, while increasing trend over summer season. The study concluded that as the monthly reference evapotranspiration showed decreasing linear trend over cropping seasons (i.e. monsoon and winter), the crop water requirement at Akola station shall decrease in future.

Mapping of reference evapotranspiration using geostatistical analysis techniques

Three different interpolation methods (Inverse distance weighting, Ordinary kriging, Simple kriging) were comparatively analyzed to determine the spatial distribution of monthly reference evapotranspiration (ETo) values calculated using the Hargreaves-Samani method (ETo-HG) for ten districts of western Maharashtra. The spatial maps of monthly reference crop evapotranspiration were developed by using GIS interpolation techniques. Simple kriging interpolation technique was found suitable to map average reference crop evapotranspiration (ETo) for all the months except February based on RMSE values. Spatial distribution maps can be used to derive location specific values of ETo required for the estimation of crop water requirement.

Worldwide assessment of the Penman–Monteith temperature approach for the estimation of monthly reference evapotranspiration

When not all the meteorological data needed for estimating reference evapotranspiration ETo are available, a Penman–Monteith temperature (PMT) equation can be adopted using only measured maximum and minimum air temperature data. The performance of the PMT method is evaluated and compared with the Hargreaves–Samani (HS) equation using the measured long-term monthly data of the FAO global climatic dataset New LocClim. The objective is to evaluate the quality of the PMT method for different climates as represented by the Koppen classification calculated on a monthly time scale. Estimated PMT and HS values are compared with FAO-56 Penman–Monteith ETo values through several statistical performance indices. For the full dataset, the approximated PMT expressions using air temperature alone produce better results than the uncalibrated HS method, and the performance of the PMT method is even more improved adopting corrections depending on the climate class for the estimation of the solar radiation, especially in the tropical climate class.

Study of trends in weather parameters at Akola using moving average technique

Climatic parameters (maximum temperature, minimum temperature, wind speed, bright sunshine hours, morning relative humidity, evening relative humidity and open pan evaporation) for 37 years (1971-2007) were collected from Agricultural Meteorological Observatory Dr. PDKV, Akola. Mean monthly climatic data for the period were used to determine reference evapotranspiration (ET 0 ) by FAO-56 Penman-Monteith method. The trends of change of these parameters were analyzed by working out seven years moving average and forming regression equations. The mean monthly maximum air temperature showed slightly decreasing trend for most of the months during the year except February, August and December. Whereas, there was unsteady variation in minimum air temperature and showed linear increasing trend during monsoon period. There was strong variation in wind speed and bright sunshine hours and showed continuous linear decreasing trend. However, mean monthly morning and evening relative humidity showed the linear increasing trend for most of the period of the year. The mean monthly pan evaporation also showed the decreasing trend throughout year. There was major variation in monthly reference evapotranspiration and showed linear decreasing trend for all the months of the year.

Estimation of reference evapotranspiration using multivariate fractional polynomial, Bayesian regression, and robust regression models in three arid environments

The proper evaluation of evapotranspiration is essential in food security investigation, farm management, pollution detection, irrigation scheduling, nutrient flows, carbon balance as well as hydrologic modeling, especially in arid environments. To achieve sustainable development and to ensure water supply, especially in arid environments, irrigation experts need tools to estimate reference evapotranspiration on a large scale. In this study, the monthly reference evapotranspiration was estimated by three different regression models including the multivariate fractional polynomial (MFP), robust regression, and Bayesian regression in Ardestan, Esfahan, and Kashan. The results were compared with Food and Agriculture Organization (FAO)-Penman–Monteith (FAO-PM) to select the best model. The results show that at a monthly scale, all models provided a closer agreement with the calculated values for FAO-PM (R2 > 0.95 and RMSE < 12.07 mm month−1). However, the MFP model gives better estimates than the other two models for estimating reference evapotranspiration at all stations.

Long-term monthly evapotranspiration modeling by several data-driven methods without climatic data

In this study, the ability of four different data-driven methods, multilayer perceptron artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS) with grid partition (GP), ANFIS with subtractive clustering (SC) and gene expression programming (GEP), was investigated in predicting long-term monthly reference evapotranspiration (ET0) by using data from 50 stations in Iran. The periodicity component, station latitude, longitude and altitude values were used as inputs to the applied models to predict the long-term monthly ET0 values. The overall accuracies of the multilayer perceptron ANN, ANFIS-GP and ANFIS-SC models were found to be similar to each other. The GEP model provided the worst estimates. The maximum determination coefficient (R2) values were found to be 0.997, 998 and 0.994 for the ANN, ANFIS-GP and ANFIS-SC models in Karaj station, respectively. The highest R2 value (0.978) of GEP model was found for the Qom station. The minimum R2 values were respectively found as 0.959 and 0.935 for the ANN and ANFIS-GP models in Bandar Abbas station while the ANFIS-SC and GEP models gave the minimum R2 values of 0.937 and 0.677 in the Tabriz and Kerman stations, respectively. The results indicated that the long-term monthly reference evapotranspiration of any site can be successfully estimated by data-driven methods applied in this study without climatic measurements. The interpolated maps of ET0 were also obtained by using the optimal ANFIS-GP model and evaluated in the study. The ET0 maps showed that the highest amounts of reference evapotranspiration occurred in the southern and especially southeastern parts of the Iran.