Estimating Reference Crop Evapotranspiration Research Articles

Improved Hargreaves Model Based on Multiple Intelligent Optimization Algorithms to Estimate Reference Crop Evapotranspiration in Humid Areas of Southwest China

Reference crop evapotranspiration (ET0) is an important indicator for precise regulation of crop water content, irrigation forecast formulation, and regional water resources management. The Hargreaves model (HG) is currently recognized as the simplest and most effective ET0 estimation model. To further improve the prediction accuracy of the HG model, this study is based on the data of 98 meteorological stations in southwest China (1961–2019), using artificial bee colony (ABC), differential evolution (DE) and particle swarm optimization (PSO) algorithms to calibrate the HG model globally. The standard ET0 value was calculated by FAO-56 Penman–Monteith (PM) model. We compare the calculation accuracy of 3 calibrated HG models and 4 empirical models commonly used (Hargreaves, Priestley–Taylor, Imark–Allen and Jensen–Hais). The main outcomes demonstrated that on a daily scale, the calibrated HG models (R2 range 0.74–0.98) are more accurate than 4 empirical models (R2 range 0.55–0.84), and ET0-PSO-HG has the best accuracy, followed by ET0-ABC-HG and ET0-DE-HG, with average R2 of 0.83, 0.82 and 0.80, average RRMSE of 0.23 mm/d, 0.25 mm/d and 0.26 mm/d, average MAE of 0.52 mm/d, 0.53 mm/d and 0.57 mm/d, and average GPI of 0.17, 0.05, and 0.04, respectively; on a monthly scale, ET0-PSO-HG also has the highest accuracy, followed by ET0-ABC-HG and ET0-DE-HG, with median R2 of 0.96, 0.95 and 0.94, median RRMSE of 0.16 mm/d, 0.17 mm/d and 0.18 mm/d respectively, median MAE of 0.46 mm/d, 0.50 mm/d, and 0.55 mm/d, median GPI of 1.12, 0.44 and 0.34, respectively. The calibrated HG models (relative error of less than 10.31%) are also better than the four empirical models (relative error greater than 16.60%). Overall, the PSO-HG model has the most accurate ET0 estimation on daily and monthly scales, and it can be suggested as the preferred model to predict ET0 in humid regions in southwest China regions.

Assessing the Robustness of Pan Evaporation Models for Estimating Reference Crop Evapotranspiration during Recalibration at Local Conditions

A classic method for assessing the reference crop evapotranspiration (ETo) is the pan evaporation (Epan) method that uses Epan measurements and pan coefficient (kp) models, which can be functions of relative humidity (RH), wind speed (u2), and temperature (T). The aim of this study is to present a methodology for evaluating the robustness of regression coefficients associated to climate parameters (RH, u2, and T) in pan method models during recalibration at local conditions. Two years of daily data from April to October (warm season) of meteorological parameters, Epan measurements from class A pan evaporimeter and ETo estimated by ASCE-standardized method for the climatic conditions of Thessaloniki (Greece, semi-arid environment), were used. The regression coefficients of six general nonlinear (NLR) regression Epan models were analyzed through recalibration using a technique called “random cross-validation nonlinear regression RCV-NLR” that produced 1000 random splits of the initial dataset into calibration and validation sets using a constant proportion (70% and 30%, respectively). The variance of the regression coefficients was analyzed based on the 95% interval of the highest posterior density distribution. NLR models that included coefficients with a 95% HPD interval that fluctuates in both positive and negative values were considered nonrobust. The machine-learning technique of random forests (RF) was also used to build a RF model that includes Epan, u2, RH, and T parameters. This model was used as a benchmark for evaluating the predictive accuracy of NLR models but, also, for assessing the relative importance of the predictor climate variables if they were all included in one NLR model. The findings of this study indicated that locally calibrated NLR functions that use only the Epan parameter presented better results, while the inclusion of additional climate parameters was redundant and led to underfitting.

Neuro-fuzzy estimation of reference crop evapotranspiration by neuro fuzzy logic based on weather conditions

Reference evapotranspiration (ET0) is considered and one of the most valuable parameter for hydrological, climatological investigation and water resources management as well. In this article the evapotranspiration was determined with the simplified equation of Makkink. There is need for precise approximation of the reference crop evapotranspiration in order to determine the water requirement in irrigated agriculture. However ET0 estimation is very difficult to achieve due to too many input parameters. Therefore the primary objective of the research was to establish regression models of the ET0 in regard to several input weather parameters. The regression models will be created by input/output data pairs. The main aim is to achieve predictive capable models for the ET0. Also according to the regression models precision one can determine the input parameters influence on the ET0. Hence one king of ranking process will be performed in order to select which factors have the most influence on the ET0. The repression models will be created by neuro fuzzy logic procedure since the procedure could handle high nonlinearity between input and output data pairs. According to the results Global radiation has the strongest influence on the ET0. Combination of Daily average temperature and Global radiation is the optimal combination for the ET0 estimation.

Estimating reference crop evapotranspiration under limited climate data in West Texas

Study regionWest Texas, USA Study focusEstimation of crop reference evapotranspiration (ETo) is essential for many aspects of water resources planning and management such as irrigation scheduling. Available widely used methods for calculating ETo include American Society of Civil Engineers’ Standardized Reference Evapotranspiration and Food and Agriculture Organization’s Penman-Monteith equations (FAO-ETo). These methods use complete climate datasets to estimate daily ETo, whereas simple evapotranspiration models based on radiation and temperature use limited climate data. In this study, daily ETo estimated using the temperature based Hargreaves-Samani (HS) equation were compared and evaluated with those estimated using the standard FAO-ETo at different stations of West Texas Mesonet. New hydrological insights for the regionThe results showed that the HS equation with original coefficients underestimated daily ETo values as compared to FAO-ETo data. New coefficients of the globally, monthly and regionally calibrated HS equation against FAO-ETo data were derived and proposed for more accurate daily ETo estimates in West Texas. Based on the results of global, monthly and regional calibration scenarios, ETo estimated by the calibrated and validated HS equation using fitted month-specific coefficients showed better agreement with FAO-ETo both within and outside the calibration region. No significant improvement in ETo estimation was observed for the HS equation using interpolated coefficients derived from station-specific calibrated coefficients as compared with commonly calibrated coefficients derived based on datasets of all selected meteorological stations in West Texas.

Comparing of Generalized Linear Models, Random Forest and Gradient Boosting Trees in Estimation of Reference Crop Evapotranspiration (Case Study: The Sistan Plain)

Comparing of Generalized Linear Models, Random Forest and Gradient Boosting Trees in Estimation of Reference Crop Evapotranspiration (Case Study: The Sistan Plain)

Performance evaluation of solar radiation equations for estimating reference evapotranspiration (ETo) in a humid tropical environment

Abstract Solar radiation (Rs) is an essential input for estimating reference crop evapotranspiration, ETo. An accurate estimate of ETo is the first step involved in determining water demand of field crops. The objective of this study was to assess the accuracy of fifteen empirical solar radiations (Rs) models and determine its effects on ETo estimates for three sites in humid tropical environment (Abakaliki, Nsukka, and Awka). Meteorological data from the archives of NASA (from 1983 to 2005) was used to derive empirical constants (calibration) for the different models at each location while data from 2006 to 2015 was used for validation. The results showed an overall improvement when comparing measured Rs with Rs determined using original constants and Rs using the new constants. After calibration, the Swartman–Ogunlade (R2 = 0.97) and Chen 2 models (RMSE = 0.665 MJ∙m−2∙day−1) performed best while Chen 1 (R2 = 0.66) and Bristow–Campbell models (RMSE = 1.58 MJ∙m−2∙day−1) performed least in estimating Rs in Abakaliki. At the Nsukka station, Swartman–Ogunlade (R2 = 0.96) and Adeala models (RMSE = 0.785 MJ∙m−2∙day−1) performed best while Hargreaves–Samani (R2 = 0.64) and Chen 1 models (RMSE = 1.96 MJ∙m−2∙day−1) performed least in estimating Rs. Chen 2 (R2 = 0.98) and Swartman–Ogunlade models (RMSE = 0.43 MJ∙m−2∙day−1) performed best while Hargreaves–Samani (R2 = 0.68) and Chen 1 models (RMSE = 1.64 MJ∙m−2∙day−1) performed least in estimating Rs in Awka. For estimating ETo, Adeala (R2 =0.98) and Swartman–Ogunlade models (RMSE = 0.064 MJ∙m−2∙day−1) performed best at the Awka station and Swartman–Ogunlade (R2 = 0.98) and Chen 2 models (RMSE = 0.43 MJ∙m−2∙day−1) performed best at Abakaliki while Angstrom–Prescott–Page (R2 = 0.96) and El-Sebaii models (RMSE = 0.0908 mm∙day−1) performed best at the Nsukka station.

A distributed interval nonlinear multiobjective programming approach for optimal irrigation water management in an arid area

Considering the uncertainties in agricultural system and spatiotemporal variability in evapotranspiration and precipitation, a distributed interval nonlinear multiobjective programming (DINMP) model was developed for optimal allocation of limited irrigation water resources in the middle reaches of Heihe River basin. The meteorological data from meteorological stations were used to estimate reference crop evapotranspiration (ET0) through FAO56 Penman-Monteith (PM) equation, and then the remote sensing MOD16/PET data were fitted by linear regression model according to the FAO56 PM results. The 95% confidence interval was used to further improve the accuracy of the fitting results. Thus, satellite-based potential evapotranspiration (PET) and ground-based ET0 estimation were integrated to not only reflect the spatial and temporal variability but also guarantee the accuracy of the ET0. In the terms of precipitation, spatial interpolation was used to spatial information of precipitation. Based on these spatiotemporal data, a DINMP with three objectives, including maximizing economic benefits and water saving as well as minimizing water shortage of critical growth periods, was formulated, and further solved by fuzzy coordination method. The optimal allocation scheme improves the irrigation water productivity by [0.50, 0.66] kg/m3, and decreases net irrigation water allocation by [0.33, 1.01] ×108 m3. These results show that DINMP can not only consider the uncertainties and multiple objectives in agricultural water management, but also improve the spatial resolution of optimal water allocation strategies. The framework of this study can provide a reference for agricultural water managers in similar areas to obtain more reasonable water allocation schemes.

Estimation of crop evapotranspiration through spatial distributed crop coefficient in a semi-arid environment

Accurate and reliable estimation of reference crop evapotranspiration (ETo) is important due to its critical role in determining crop water requirement in irrigated agriculture. The aim of the paper was to estimate the evapotranspiration (ETc) using spatially distributed crop coefficient (Kc) and open access earth observing datasets in a semi-arid environment. We have estimated the actual evapotranspiration (ETc) based on spatially distributed crop coefficient (Kc) using following models namely Surface Energy Balance Algorithm for Land (SEBAL), Makkink model, Hargreaves and Samani model, Camargo method and Jensen-Haise model. Further, these models estimates were compared with Penman-Monteith estimate.Comparative evaluation of models was performed through statistical tests, and it was found that the Makkink model performed satisfactory compared with standard Penman-Monteith model estimate (R2 = 0.88). Leaf area index (LAI) and the Kc was in strong (second order polynomial) relationship (R2 = 0.98). The analysis also shows distributed actual evapotranspiration based on Makkink model has good agreement with actual evapotranspiration from Penman-Monteith with R2 of 0.84, respectively, for the study area. The finding suggests that the Makkink model estimates ETo are very close to the universally accepted Penman-Monteith model based ETo.

How Ångström–Prescott Coefficients Alter the Estimation of Agricultural Water Demand in South Korea

The Food and Agriculture Organization (FAO) Penman–Monteith equation, recognized as the standard method for the estimation of reference crop evapotranspiration (ET0), requires many meteorological inputs. The Ångström–Prescott (A-P) formula containing parameters (i.e., a and b) is recommended to determine global solar radiation, one of the essential meteorological inputs, but may result in a considerable difference in ET0 estimation. This study explored the effects of A-P coefficients not only on the estimation of ET0, but also on the irrigation water requirement (IWR) and design water requirement (DWR) for paddy rice cultivation, which is the largest consumer of agricultural water in South Korea. We compared and analyzed the estimates of ET0, IWR, and DWR using the recommended (a = 0.25 and b = 0.5) and locally calibrated A-P coefficients in 16 locations of South Korea. The estimation of ET0 using the recommended A-P coefficients produced significant overestimation. The overestimation ranged from 3.8% to 14.0% across the 16 locations as compared to the estimates using the locally calibrated A-P coefficients, and the average overestimation was 10.0%. The overestimation of ET0 corresponded to a variation of 1.7% to 7.2% in the overestimation of the mean annual IWR, and the average overestimation of the IWR was 5.1%. On average, the overestimation was slightly reduced to 4.8% in DWR estimation, since the effect of A-P coefficients on the IWR estimation decreased as the IWR increased. This study demonstrates how the use of A-P coefficients can alter the estimation of ET0, IWR, and DWR in South Korea, which underscores the importance of their proper consideration in agricultural water management.

Estimating reference crop evapotranspiration with elevation based on an improved HS model

Abstract Estimation of ET0 in high-elevation (above sea level, ASL) areas of Tibet presents unique challenges: scarcity of monitoring stations, short-time coverage of meteorological data, low-oxygen and low-pressure environment, and strong solar radiation. In this study, altitude factors and modified temperature constants are utilized to improve the Hargreaves (HS) model based on 30-year daily meteorological data from 20 typical sites in Tibet. The improved model, Hargreaves-Elevation (HS-E) improved model, could provide better results at different time scales. Negative ET0 values were unavoidable in the HS model when applied to high-elevation areas. However, the HS-E model solved this problem and improved the accuracy of estimated ET0. In particular, the HS-E model performs better when the time scale becomes larger. Therefore, the HS-E model is highly recommended to estimate ET0 in high-elevation areas where the meteorological data are scarce, for example, in Tibet above 2,000 m.

The Uncertainty of Penman‐Monteith Method and the Energy Balance Closure Problem

AbstractThe Penman‐Monteith (PM) method is considered the most accurate method for estimating reference crop evapotranspiration (ET0). However, the method has obvious flaws in energy balance closure. In this study, the changing trends between latent heat flux of ET0 (LEp) and surface net radiation (Rn) in China were analyzed based on observational data from 800 meteorological stations. The results showed that the multiyear average ratio of LEp/Rn was highest in the warm temperate zone and was lowest in the subfrigid zone of the Tibetan Plateau. Correspondingly, the values of LEp/Rn in these areas were ranged from 1.138 to 0.647. At the site scale, there were 61, 178, and 170 meteorological stations with daily average LEp/Rn values >1 during three periods (from January to April, May to August, and September to December, respectively). The ratio of LEp/Rn showed an obvious surface energy imbalance, and it was extremely obvious in northern China. Meanwhile, it is found that there was also great uncertainty of the ET0, which estimated based on the calculated and measured net radiation. In general, the uncertainty of ET0 was ranged from −0.955 to 1.028 mm/day and the average value of uncertainty was 0.154 mm/day. The uncertainty also showed obviously temporal variation, which was lower during April to October, but was higher in other times. The main cause of the energy balance closure problem was the overestimation of the aerodynamic component of ET0. In view of such situation, this study suggested the two ways to estimate ET0 for different regions.

HYDRUS (2d/3d) simulation of water flow through sandy loam soil under potato cultivation in Southern Manitoba

The HYDRUS (2D/3D) modeling tool was used to simulate water flow through subsurface-drained sandy loam soil under potato (Solanum tuberosum) cultivation in Southern Manitoba. The model was used to simulate water flow through a 2-D model domain of dimensions, 15 m width × 2.5 m depth. The model was calibrated and validated with field data measured during the growing season of year 2011 at the Hespler Farms, Winkler, Manitoba. Field measurements, including soil water content and watertable depth, for two test plots under subsurface free drainage were used for the calibration and validation. Weather data were also obtained to estimate reference crop evapotranspiration, which was used as input data in the model. Based on the reference crop evapotranspiration, and crop coefficient of the potato crop, the actual crop evapotranspiration was estimated and compared to the simulated actual crop evapotranspiration results. The results showed that the model was able to account for 50% to 78% of the variation in the estimated actual crop evapotranspiration. With respect to water flow through the soil, the observed soil water content and the simulated soil water content were compared using graphical and quantitative analysis. Based on the coefficient of determination (R2), the model accounted for 68% to 89% variation in the observed data. The intercept of the regression line varied from 0.01 to 0.08, and the slope, 0.75 to 0.99. The Nash–Sutcliffe modeling efficiency coefficient (NSE) varied from 0.62-0.89, the Percent bias (PBIAS) values varied from -1.99% to 1.16%. The root mean square error-observations standard deviation ratio (RSR) values varied from 0.33 to 0.61. The values for the evaluation parameters show that the model was able to simulate the water flow through the soil profile reasonably well.

Estimation of reference evapotranspiration using Aquacrop model for agro-climatic conditions of Madhya Pradesh

Accurate estimation of evapotranspiration is necessary step for better management and allocation of water resources. The United Nations Food and Agriculture Organization (FAO) adopted the Penman Moneith method as a global standard to estimate reference crop evapotranspiration (ETo). The study aimed to estimate FAO P-M reference evapotranspiration for different district of five agro climatic zones of Madhya Pradesh state by using Aquacrop model. Daily weather data including maximum and minimum temperature, precipitation, relative humidity, wind speed and solar radiation were collected for the period of 1979 to 2013 which were used as input data in Aquacrop. Several statistical parameters were used for characterizing the spatial and temporal variability of ETo. The average monthly ETo was found maximum in month of May (10.67 mm day-1) in all district of different agro climatic zones for the average period considered for the study and also for each years, whereas average minimum ETo was estimated in month of December (3.23 mm day-1) in Kymore Plateau and August (2.44 mm day-1) in Satpura Plateau. The mean daily reference evapotranspiration ranges from 4 mm day-1 to 10 mm day-1 for all districts. From the statistical analysis it was found that spatial variability of ETo lower than the temporal variability. It means the bigger differentiation of ETo in the years than in the space.

English

A number of methods have been developed to estimate reference crop evapotranspiration (ETo), but most of the reliable methods are complex and parameter rich models and therefore difficult to apply in data scarce regions. This study was conducted to determine suitable simple ETo methods in Cape Coast by comparing estimated ETo values of three indirect-measurement methods: Hamon, Hargreaves, Blaney Criddle; and two direct-measurement methods: Class A pan and Piche evaporimeter with the Food and Agriculture Organization (FAO) Penman-Monteith equation (FAO56-PM) estimated ETo values. All the methods underestimated ETo values obtained by the FAO56-PM method. However, the estimated ETo values by the Hamon, Hargreaves, and Blaney-Criddle are strongly correlated (R = 0.89, 0.87 and 0.81 respectively), while the Class A pan and Piche evaporimeter methods are weakly correlated (R= 0.37 and 0.31, respectively) with the FAO56-PM method. All but the Piche evaporimeter methods appeared suitable for estimating ETo in the study area. The Class A pan, though weakly correlated with the FAO56-PM method, was also suitable because it had the least mean absolute error (MAE; 0.26 mm day-1) and mean absolute percentage error (MAPE; 6.5%) among the other methods and its ETo curve was closer to the FAO56-PM’s. Key words: Reference crop evapotranspiration, Cape Coast, Food and Agriculture Organization (FAO) Penman-Monteith equation, direct-measurement method.

The best alternative for estimating reference crop evapotranspiration in different sub-regions of mainland China

Reference crop evapotranspiration (ETo) is a critically important parameter for climatological, hydrological and agricultural management. The FAO56 Penman-Monteith (PM) equation has been recommended as the standardized ETo (ETo,s) equation, but it has a high requirements of climatic data. There is a practical need for finding a best alternative method to estimate ETo in the regions where full climatic data are lacking. A comprehensive comparison for the spatiotemporal variations, relative errors, standard deviations and Nash-Sutcliffe efficacy coefficients of monthly or annual ETo,s and ETo,i (i = 1, 2, …, 10) values estimated by 10 selected methods (i.e., Irmak et al., Makkink, Priestley-Taylor, Hargreaves-Samani, Droogers-Allen, Berti et al., Doorenbos-Pruitt, Wright and Valiantzas, respectively) using data at 552 sites over 1961–2013 in mainland China. The method proposed by Berti et al. (2014) was selected as the best alternative of FAO56-PM because it was simple in computation process, only utilized temperature data, had generally good accuracy in describing spatiotemporal characteristics of ETo,s in different sub-regions and mainland China, and correlated linearly to the FAO56-PM method very well. The parameters of the linear correlations between ETo of the two methods are calibrated for each site with the smallest determination of coefficient being 0.87.

Evaluation and Recalibration of Empirical Constant for Estimation of Reference Crop Evapotranspiration against the Modified Penman Method

The major demand in our country is irrigation demand. Looking to the low irrigation potential and small water resources, it is felt necessary to see that water must be used economically and efficiently. This may be achieved by using latest methods of determination of water requirements for crops and applying the proper water management practices. Evapotranspiration (ET) is a basic for calculation of water requirement for crops. The various popular empirical equations for reference crop evapotranspiration (ETr) belong to three categories namely, Temperature, Radiation based methods and Combined methods. The above methods are site specific; hence it is necessary to recalibrate the coefficients for applying them in India. In the present paper, the standard combined method namely FAO modified Penman method was used to recalibrate the constants in temperature based (TB) methods and it can also be used to determine the ETr for the selected station. Four TB evapotranspiration models namely Blaney-Criddle, Romanenko, Kharrufa, and, Thronthwaite methods are recalibrated and the constant in each method are redefined for the data from Lekkur station, Cuddalore district in India. The result shows that, large error existed when ETr has been calculated with original constants. Hence regression equations were developed to minimise these variations in magnitude. It was found that out of four methods the Blaney-Criddle method suits better for the selected region.

Comparison of 16 models for reference crop evapotranspiration against weighing lysimeter measurement

Accurate estimation of reference crop evapotranspiration (ET0) is important due to its crucial role in determining crop water requirement in irrigated agriculture. Though a great number of models have been developed, their rigorous evaluation with measurements is still lacking, leading to confusion and arbitrariness in model selection. In this paper daily estimates of 16 ET0 models, including five combination-, six radiation and five temperature-based ones, were compared with weighing lysimeter measurements during crop growing season (April through October) in 2012 at a semiarid site in China. Daily ET0 was measured by two weighing lysimeters (area 1.3m×1.3m, depth 2.3m) located in a fescue grass (Festuca arundinacea Schreb) plot (100m×100m) surrounded by a 167ha crop, winter wheat rotated with summer maize. We found the models were ranked decreasingly as: FAO-ppp-17 Penman>1963 Penman>FAO-24 Blaney-Criddle (BC)>1996 Kimberly Penman>FAO-24 radiation>FAO-56 Penman-Monteith (PM)>FAO-24 Penman>Turc>DeBruin-Keijman>Jensen-Haise>Priestley-Taylor>Hargreaves>Makkink>Hamon>Blaney- Criddle>Mcloud on basis of RMSE (root mean square error). Overall, the combination models performed best with RMSE ranging from 0.93 to 1.32mmd−1, followed by the radiation models with RMSE from 1.28 to 1.79mmd−1, and the temperature models with RMSE from 1.09 to 2.48mmd−1. The best combination model (FAO-ppp-17 Penman) was respectively 29% and 17% more accurate than the best radiation (FAO-24 radiation) and temperature (FAO-24 BC) models. Better performance of the combination and radiation models resulted because they explicitly contain the dominant factors influencing ET0. All models tended to overestimate under low evaporative demand while underestimating the measured values under high demand, but on average the combination and radiation methods underestimated by 0.46mmd−1 and 0.60mmd−1, respectively, whereas the temperature method overestimated by 0.21mmd−1. All combination and radiation models, and the Hargreaves and FAO-24 BC in temperature method showed robust structure. To improve them future efforts should be on local calibration, but for temperature models showing structure failure focus should be on its optimization. The coefficients of commonly used models were calibrated and related to meteorological variables. Particularly, those of the Priestley-Taylor, Makkink, Turc and the Hamon were enhanced, while those of the Hargreaves and BC were decreased. In climate similar to the current site in China we suggest continued use of the older Penman equations for combination method and the FAO-24 radiation or Turc for radiation method. Meanwhile, two questions need to be addressed in future studies: i) adoption of the FAO-56 PM equation as the sole standard for computing ET0 and the proper value for surface resistance; and ii) the effectiveness of the later modifications to the original wind function in the Penman equation.

Evaluation of pan coefficient for estimating reference crop evapotranspiration in Solapur station, Maharashtra

Evaluation of pan coefficient for estimating reference crop evapotranspiration in Solapur station, Maharashtra

Comment on the Reference to Makkink Potential Evaporation Equation

The Makkink evaporation equation has been applied worldwide to estimate potential evaporation based on measured or estimated radiation, and mean atmospheric temperature. The general form of the Makkink equation is similar to the well-known Priestley and Taylor (1972) evaporation, although Makkink proposed the equation nearly 2 decades earlier. The writers have examined 51 references that refer directly or through a secondary source to the Makkink equation, yet every reference the writers have sighted refers to Makkink (1957b) as the relevant reference. This reference is incorrect, as the Makkink equation is not mentioned therein. After an exhaustive library search and pursing other avenues through colleagues, the writers are convinced the correct reference is Makkink (1957a). de bruin (1981) cites Makkink (1960) in a discussion of methods to estimate reference crop evapotranspiration. Makkink (1957a) is written in the international language Esperanto, and researchers can use the Google Translate function to translate. The Makkink equation, as reported in Makkink (1957a), is

Use of average data of 181 synoptic stations for estimation of reference crop evapotranspiration by temperature-based methods

Evapotranspiration has a highlighted role in agricultural and forest meteorology researches, hydrological cycle, irrigation scheduling, and water resources management. There are many models to estimate the evapotranspiration including mass transfer, radiation, temperature, and pan evaporation-based models. This study aims to compare temperature-based models to detect the best model under different weather conditions. For this purpose, weather data were gathered from 181 synoptic stations in 31 provinces of Iran. The evapotranspiration was estimated using 11 temperature-based models and was compared with the FAO Penman-Monteith model. The results showed that the Modified Hargreaves-Samani models estimate the evapotranspiration better than other models in the most provinces of Iran (25 provinces). However, the values of R2 were less than 0.98 for 15 provinces of Iran. Therefore, the models were calibrated and preciseness of estimation was increased. However, the estimation was improved only in 14 provinces. The new temperature-based models estimated the evapotranspiration in the eastern (RK, NK, SB, and KE) provinces of Iran (with a various temperature range 14–20 °C) better than other provinces. The best precise methods were the Modified Hargreaves-Samani 1 method for AL (before calibration) and the Modified Hargreaves-Samani 3 method for KE (after calibration). Finally, a list of the best performance of each model has been presented to use other regions and next researches according to values of mean, maximum, and minimum temperature, elevation, minimum and mean relative humidity, sunshine, precipitation, and wind speed. The results are also useful for selecting the best model when we must apply temperature-based models because of type of available data.