Neural networks with artificial bee colony algorithm for modeling daily reference evapotranspiration

The study investigates the ability of artificial neural networks (ANN) with artificial bee colony (ABC) algorithm in daily reference evapotranspiration (ET₀) modeling. The daily climatic data, solar radiation, air temperature, relative humidity, and wind speed from two stations, Pomona and Santa Monica, in Los Angeles, USA, are used as inputs to the ANN–ABC model so as to estimate ET₀ obtained using the FAO-56 Penman–Monteith (PM) equation. In the first part of the study, the accuracy of ANN–ABC models is compared with those of the ANN models trained with Levenberg–Marquardt (LM) and standard back-propagation (SBP) algorithms and those of the following empirical models: The California Irrigation Management System (CIMIS) Penman, Hargreaves, and Ritchie methods. The mean square error (MSE), mean absolute error (MAE) and determination coefficient (R²) statistics are used for evaluating the accuracy of the models. Based on the comparison results, the ANN–ABC and ANN–LM models are found to be superior alternative to the ANN–SBP models. In the second part of the study, the potential of the ANN–ABC, ANN–LM, and ANN–SBP models in estimation ET₀ using nearby station data is investigated.     

Evapotranspiration modeling using a wavelet regression model

The present study proposes a simple wavelet regression (WR) approach for modeling reference evapotranspiration (ET₀). The WR model was improved combining two methods: discrete wavelet transform (DWT) and a linear regression model. The accuracy of the WR models was compared with that of the single linear regression (LR) models. The daily climatic data from three stations in central California are used as inputs to the WR models to estimate ET₀ obtained using the FAO-56 Penman–Monteith equation. The comparison of these results revealed that the WR models could increase the forecast accuracy of the LR models. A comparison is also made between the estimates provided by the WR models and those of the following empirical models: CIMIS Penman, Hargreaves, Ritchie and Turc. Based on a comparison of these results, the WR models were found to perform better than the empirical models in daily ET₀ modeling.     

Reference evapotranspiration based on Class A pan evaporation via wavelet regression technique

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.     

Ancillary data supply strategies for improvement of temperature-based ETo ANN models

The development of new and more precise models for reference evapotranspiration (ET_o) estimation from minimum climatic data is mandatory, since the application of existing methods that provide acceptable results is limited to those places where large amounts of reliable climatic data are available. The performance quality of empirical equations and their local calibrations is to be questioned in a large variety of climatic contexts. As an alternative to traditional techniques, artificial neural networks (ANNs) are highly appropriate for the modelling of non-linear processes, which is the case of evapotranspiration. Nevertheless, temperature-based ANN models do not always provide accurate enough ET_o estimations and their performance depends highly on the specific relationships temperature-ET_o of the studied continental context. This paper describes the performance improvement of temperature-based ANN models through the consideration of exogenous ET_o records as ancillary inputs in different continental contexts of the autonomous Valencia region, on the Spanish Mediterranean coast. The influence on the model performance of the number of considered ancillary stations and the corresponding number of training patterns is also analysed. Finally, this performance is compared with existing empirical and ANN temperature-based models. The proposed models can be used with high accuracy not only for infilling purposes, but also for estimating ET_o outside the training station. Concerning models which demand scant climatic inputs, the proposed model provides performances with lower associated errors than the currently existing temperature-based models, which only consider local data. The local performance of the model presents 0.084 of average absolute relative error (AARE). The external performance of the model presents 0.1072 of AARE.     

Artificial neural network estimation of reference evapotranspiration from pan evaporation in a semi-arid environment

The objective of this study was to test an artificial neural network (ANN) for converting pan evaporation data (E _p) to estimate reference evapotranspiration (ET₀) as a function of the maximum and minimum air temperature. The conventional method that uses Pan coefficient (K _p) as a factor to convert E _p to ET₀, is also considered for the comparison. The ANN has been evaluated under semi-arid conditions in Safiabad Agricultural Research Center (SARC) in the southwest of Iran, comparing daily estimates against those from the FAO-56 Penman–Monteith equation (PM), which was used as standard. The comparison shows that, the conventional method underestimated ET₀ obtained by the PM method. The ANN method gave better estimates than the conventional method that requires wind speed and humidity data.     

Applicability of support vector machines and adaptive neurofuzzy inference system for modeling potato crop evapotranspiration

Estimation of crop evapotranspiration (ET_C) for certain crops such as potato is very important for irrigation planning, irrigation scheduling and irrigation systems management. The primary focus of this study was to investigate the accuracy of the adaptive neurofuzzy inference system (ANFIS) and support vector machines (SVM) for potato ET_C estimation when lysimeter measurements or the complete weather data for applying the FAO method are not available. The estimates of the ANFIS and SVM models were compared with the empirical equations of Blaney–Criddle, Makkink, Turc, Priestley–Taylor, Hargreaves and Ritchie. The performances of the different SVM and ANFIS models were evaluated by comparing the corresponding values of root mean square error (RMSE), mean absolute error (MAE) and correlation coefficient (r). The drawn conclusions confirmed that the SVM and ANFIS models could provide more accurate ET_C estimates than the empirical equations. Overall, the minimum RMSE (0.042 mm/day) and MAE (0.031 mm/day) values and the maximum r value (0.98) were obtained using the SVM model with mean air temperature, relative humidity, solar radiation, sunshine hours and wind speed as inputs.     

Water requirements of maize in the middle Heihe River basin, China

As part of an intercomparison study on crop evapotranspiration (ET_c), six methods for estimating ET_c have been applied to maize field in the middle Heihe River basin, China. The ET_c was estimated by the soil water balance and Bowen ratio-energy balance methods while the Priestley-Taylor, Penman, Penman-Monteith and Hargreaves methods were used for estimating the reference evapotranspiration (ET₀). The results showed that the trend of ET_c was very similar, while the differences were significant among the different methods. The variations of ET_c were closely related to the LAI as well as to the meteorological features. The ET_c for the Bowen ratio-energy balance, Penman, Penman-Monteith, soil water balance, Priestley-Taylor and Hargreaves methods totaled 777.75, 693.13, 618.34, 615.67, 560.31 and 552.07 mm, respectively, with the daily mean values for 5.26, 4.68, 4.18, 4.16, 3.79 and 3.73 mm day⁻¹. The Penman-Monteith method provided fairly good estimation of ET_o as compared with the Priestley-Taylor, Penman, Hargreaves methods. By contrast with the Penman-Monteith method, the Bowen ratio-energy balance and Penman methods were 25.8% and 12.0% higher, while the Priestley-Taylor and Hargreaves methods were 9.4% and 10.7% lower, respectively. Therefore, the Hargreaves and Priestley-Taylor methods were the alternative ET_c methods in arid regions of Northwest China.     

Comparing Penman–Monteith and Priestley–Taylor approaches as reference-evapotranspiration inputs for modeling maize water-use under Mediterranean conditions

A comparison between experimental and simulated data, considering the Priestley–Taylor (PT) and Penman–Monteith (PM) reference-evapotranspiration (ET₀) approaches was carried out. Experimental data, obtained from an irrigation assessment, conducted during the 1995 and 1996 maize growth-seasons at Zaragoza, Spain, was compared to the mechanistic-model SWAP simulation-results, considering each of the ET₀ calculation approaches in the model input. Soil hydraulic properties, meteorological data, seeding and harvest dates, crop water management and other experimental data were used as SWAP input. As corresponding to the windy and dry conditions found in many Mediterranean landplanes, PT-ET₀ values were significantly lower than PM-ET₀ calculations. Furthermore, simulated actual evapotranspirations considering the PT approach (PT-ET_c) were lower than those found in the simulations that consider the PM approach (PM-ET_c). Correspondingly, simulated drainage flux and soil water contents were higher when the PT-ET₀ approach was used. The correlation coefficients between simulated and measured actual maize evapotranspirations and soil water contents were statistically significant, but the same for both ET₀ calculation approaches. Mean and median differences between actual and simulated maize water-use were not statistically different from zero for both considered ET₀ calculation approaches. Experimental data variability was significantly higher than simulated variability. The comparisons among the evaluated irrigation options, made with the experimental water-use data, lead almost to the same conclusions than those achieved from the simulated maize water-use. Considering PM-ET_c rather than PT-ET_c yields no statistical difference in the modeling-based conclusions. According to the obtained results, the PT approach could be used under Mediterranean conditions for comparative assessments aimed to support irrigation decision-making.     

Reference evapotranspiration estimation without local climatic data

The Penman–Monteith equation for reference evapotranspiration (ET_o) estimation cannot be applied in many situations, because climatic records are totally or partially not available or reliable. In these cases, empirical equations that rely on few climatic variables are necessary. Nevertheless, the uncertainty associated with empirical model estimations is often high. Thus, the improvement of methods relying on few climatic inputs as well as the development of emergency estimation tools that demand no local climatic records turns into a task of great relevance. The present study describes different approaches based on multiple linear regression, simple regression and artificial neural networks (ANNs) to deal with ET_o estimation exclusively from exogenous records from secondary stations. This cross-station approach is based on a continental characterization of the study region, which enables the selection and hierarchization of the most suitable ancillary data supplier stations. This procedure is compared with different traditional and cross-station approaches, including methodologies that also consider local temperature inputs. The proposed methods are also evaluated as gap infilling procedures and compared with a simple methodology, the window averaging. The artificial neural network and the multiple linear regression approaches present very similar performance accuracies, considerably higher than simple regression and traditional temperature-based approaches. The proposed input combinations allow similar performance accuracies as ANN models relying on exogenous ET_o records and local temperature measurements. The cross-station multiple linear regression procedure is recommended due to its higher simplicity.     

A wind-based qualitative calibration of the Hargreaves ET0 estimation equation in semiarid regions

This study evaluates the Hargreaves (HARG) equation for estimation of monthly ET₀ under the semiarid conditions of the middle Ebro River Valley (NE Spain). First, the Hargreaves equation was compared against measured lysimeter ET₀ values at Zaragoza for the period May 1997–October 2000. The average of estimated values was only 5.6% above the average of measured values. Later, the Hargreaves equation was compared against the FAO Penman–Monteith equation for monthly ET₀ estimation at nine locations. These locations can be grouped as non-windy (Alcañiz, Daroca and Tamarite) and windy (Almudévar, Ejea, Gallocanta, Monflorite, Sariñena and Zaragoza). Simple linear regression and error analysis statistics suggest that agreement between the two estimation methods was quite good for the windy locations. Average errors ranged between 2 and 5% for Almudévar, Ejea, Sariñena and Zaragoza, and between 7 and 10% for Gallocanta and Monflorite where some underestimation was observed. However, the agreement between the Hargreaves and FAO Penman–Monteith equations was lower for the non-windy locations. In this case, the Hargreaves equation overestimated ET₀ and average errors varied between 14 and 20%. According to these results, it is proposed that, under the semiarid conditions of this study, no local calibration would be required for windy locations (those where monthly average windspeeds above 2.0 m s⁻¹ are frequent), while a value of 0.0020 instead of the original 0.0023 should be used in the Hargreaves equation for non-windy locations. Further research should be undertaken to evaluate whether these results can be extended to other semiarid regions of the world.     

Comparative study of Hargreaves’s and artificial neural network’s methodologies in estimating reference evapotranspiration in a semiarid environment

The Penman–Monteith equation (PM) is widely recommended because of its detailed theoretical base. This method is recommended by FAO as the sole method to calculate reference evapotranspiration (ET_o) and for evaluating other methods. However, the detailed climatological data required by the Penman–Monteith equation are not often available especially in developing nations. Hargreaves equation (HG) has been successfully used in some locations for estimating ET_o where sufficient data were not available to use PM method. The HG equation requires only maximum and minimum air temperature data that are usually available at most weather stations worldwide. Another method used to estimate ET_o is the artificial neural network (ANN). Artificial neural networks (ANNs) are effective tools to model nonlinear systems and require fewer inputs. The objective of this study was to compare HG and ANN methods for estimating ET_o only on the basis of the temperature data. The 12 weather stations selected for this study are located in Khuzestan plain (southwest of Iran). The HG method mostly underestimated or overestimated ET_o obtained by the PM method. The ANN method predicted ET_o better than HG method at all sites.     

An analysis of the tendency of reference evapotranspiration estimates and other climate variables during the last 45 years in Southern Spain

Climate change will have important implications in the agriculture of semi-arid regions, such as Southern Spain, where the expected warmer and drier conditions might augment crop water demand. To evaluate these effects, a data set consisting of observed daily values of air temperature, relative humidity, sunshine duration and wind speed from eight weather stations in Andalusia and covering the period 1960-2005 was used for estimating reference evapotranspiration (ET_o). ET_o was calculated using five methods: the more complex Penman-Monteith FAO-56 (PM) equation, considered as a reference in this study, and four alternative methods with fewer data requirements, Hargreaves, Blaney-Criddle, Radiation and Priestley-Taylor. These methods were compared to PM with respect to ET_o average values and trends. The non-parametric Mann-Kendall test was used to evaluate annual and seasonal trends in the main climate variables and ET_o.Due to increases in air temperature and solar radiation, and decreases in relative humidity, statistically significant increases in PM-ET_o were detected (up to 3.5 mm year⁻¹). Although the Hargreaves equation provided the closest average values to PM, this method did not detect any ET_o trend. On the other hand, trends found from Blaney-Criddle and Radiation ET_o values were similar to those obtained from PM. In addition, after a local adjustment, these two methods gave accurate ET_o average values. Therefore, Blaney-Criddle and Radiation methods have shown themselves to be the most accurate approaches for ET_o determination in climate change studies, when available data provided by climate models are limited.     

Estimating reference evapotranspiration with atmometers in a semiarid environment

Reference evapotranspiration (ET₀) estimations require accurate measurements of meteorological variables (solar radiation, air temperature, wind speed, and relative humidity) which are not available in many countries of the world. Alternative approaches are the use of Class A pan evaporimeters and atmometers, which have several advantages compared to meteorological stations: they are simple, inexpensive and provide a visual interpretation of ET₀. The objectives of the study were to compare the evaporation from atmometers (ET_gage) with the evapotranspiration estimated by the FAO-56 Penman-Monteith equation (ET_0PM) and to evaluate the variability between three modified atmometers of a commercial model. Comparison between daily ET_gage measured by the atmometer and ET_0PM showed a good correlation. However, ET_gage underestimated ET_0PM by approximately 9%. Differences between ET_gage and ET_0PM ranged from −2.4 to 2.2 mm d⁻¹ while the mean bias error was −0.41 mm d⁻¹. Underestimations occurred more frequently on days with low maximum temperatures and high wind speeds. On the contrary, atmometer overestimations occurred on days with high maximum temperatures and low wind speeds. Estimates of ET₀ using the atmometer appeared to be more accurate under non-windy conditions and moderate temperatures as well as under windy conditions and high temperatures. Atmometers 2 and 3 overestimated the evaporated water by atmometer 1 with a maximum variability of cumulative water losses of 4.5%. A temperature-based calibration was performed to improve the atmometer accuracy, using maximum temperature as an independent variable, with good results.     

Crop coefficient of sesame in a semi-arid region of I.R. Iran

Crop coefficient of sesame is necessary for the water requirement estimation in irrigation water planning and management. This study has been initiated to determine the crop coefficient (K_c) of sesame in a semi-arid climate. The relationships between K_c and ET_p/E_p (pan evaporation) and leaf area index (LAI), growing degree-day (GDD) and days after sowing (DAS), were also investigated. The seasonal ET_p for sesame in the study area with a 5 month growth period was 910 m. The mid-season and late-season K_c values for sesame were 1.08 and 0.64, respectively. These values are somewhat lower and higher than those for other oil seed crops. The K_c value for the initial stage was close to that obtained by the procedure proposed by Allen et al. [Allen, R.G., Smith, M., Pereira, L.S., Pruitt, W.O., 1997. Proposed revision to the FAO procedure for estimating evapotranspiration. In: The Second Iranian Congress on Soil and Water Issues, 15–17 February 1997. Tehran, I.R. of Iran, pp. 1–18]. The ratio of ET_p/E_p varied between 0.49–1.0 from the beginning to the middle of the growing season which is a sign of mild local advection in the region. The maximum ratios of ET_p/ET₀ and ET_p/E_p occurred at a LAI of 3.0. Furthermore, third-order polynomials were presented to predict the K_c values from days after sowing (DAS), percent days after sowing (%DAS) and growing degree-day (GDD).     

Lysimetric determination of muskmelon crop coefficients cultivated under plastic mulches

A trial was carried out at the lysimeter station in southern Italy on muskmelon crop cultivated with and without plastic mulch during spring–summer in 2001 and 2003. The objective of the experiment was to verify the reliability of the crop evapotranspiration (ET_c) estimate by means of the most recent update of the FAO Irrigation and Drainage Paper 56, in comparison with ET_c directly measured by two mechanical weighing lysimeters.Crop coefficients (K_c) were determined during different development stages based on lysimetric measures of ET_c and of the reference evapotranspiration (ET₀) estimated through the Penman Monteith and the Hargreaves methods. On melon crop cultivated without plastic mulch, corrected crop coefficients (K_c) following the last FAO Irrigation and Drainage Paper 56 procedures were well correlated with those measured from lysimeter and were as reliable as the ET_c estimate. In contrast, values of K_c proposed by FAO Irrigation and Drainage Paper 56 for crops grown with plastic mulch were meaningfully lowers than those measured from lysimeter, loading to an underestimation of water consumption. On muskmelon, cultivated with and without plastic mulch, it is necessary to adapt development phase duration, suggested by the FAO Irrigation and Drainage Paper 56, to the real phenology of the employed cultivar. An adaptation of the phenology to the real duration of the single phases is essential to avoid error in the estimate of ET_c.     

Comparative analysis of 31 reference evapotranspiration methods under humid conditions

Evaluation of simple reference evapotranspiration (ET_o) methods has received considerable attention in developing countries where the weather data needed to estimate ET_o by the Penman–Monteith FAO 56 (PMF-56) model are often incomplete and/or not available. In this study, eight pan evaporation-based, seven temperature-based, four radiation-based and ten mass transfer-based methods were evaluated against the PMF-56 model in the humid climate of Iran, and the best and worst methods were selected from each group. In addition, two radiation-based methods for estimating ET_o were derived using air temperature and solar radiation data based on the PMF-56 model as a reference. Among pan evaporation-based and temperature-based methods, the Snyder and Blaney–Criddle methods yielded the best ET_o estimates. The ET_o values obtained from the radiation-based equations developed here were better than those estimated by existing radiation-based methods. The Romanenko equation was the best model in estimating ET_o among the mass transfer-based methods. Cross-comparison of the 31 tested methods showed that the five best methods as compared with the PMF-56 model were: the two radiation-based equations developed here, the temperature-based Blaney–Criddle and Hargreves-M4 equations and the Snyder pan evaporation-based equation.     

Temporal and spatial variations of evapotranspiration for spring wheat in the Shiyang river basin in northwest China

The methods for estimating temporal and spatial variation of crop evapotranspiration are useful tools for irrigation scheduling and regional water allocation. The purpose of this study was to develop a method for mapping spatial distribution of crop evapotranspiration and analyze the temporal and spatial variation of spring wheat evapotranspiration in the Shiyang river basin in Northwest China in the last 50 years. DEM-based methods were employed to estimate the spatial distribution of spring wheat evapotranspiration (ET_c). Reference crop evapotranspiration (ET₀) was calculated with the Penman–Monteith equation using meteorological data measured from eight stations in the basin. Crop coefficient (K_c) was determined from measured evapotranspiration in spring wheat season in the region. The results showed that ET_c gradually increased in the upper reaches of the basin in the last 50 years, while the middle reaches showed a significant decreasing trend, and in other regions, no significant trend was found. These changes can be attributed to expansion of irrigation areas and climate change. The multiple regression analysis between ET_c and altitude, latitude, and aspect were carried out for eight weather stations and the relationships were used to map ET_c for the basin. The spatial variations of ET_c were analyzed for three typical growing seasons based their precipitation. Results showed that long-term average ET_c over cultivated land was increasing from 270 mm in southwest mountainous area to 591 mm in northeast oasis of the basin, and the relative error between the estimated ET_c in spring wheat growing season by reference evapotranspiration (ET₀) and crop coefficient (K_c), and the interpolated ET_c was within 11.1%.     

Forecasting and optimizing furrow irrigation management decision variables

Furrow irrigation can be better managed if the management decision variables (irrigation time and amount; inflow rate and cutoff) can be determined ahead of time. In this study, these decision variables were forecast and optimized using 1 day ahead grass reference crop evapotranspiration (ET₀) forecasts, based on the ARMA (1,1) time-series model, with a seasonal furrow irrigation model for both homogeneous and heterogeneous infiltration conditions. Heterogeneity in infiltration characteristics was restricted to variations along the furrow length as opposed to variations between furrows. The results obtained were compared with their counterparts using the observed ET₀ for the same period during the 1992 cropping season. Seasonal performance (application efficiency, inflow, runoff and deep percolation volumes) and economic return to water (yield benefits minus seasonal water related and labor costs) were affected by infiltration conditions, while irrigation requirement and bean yield were unchanged. In a given infiltration case, seasonal performance, irrigation schedules, bean yield and economic return to water were comparable (lower than 4% difference) for the two ET₀ conditions. For each ET₀ condition, individual irrigation events resulted in different irrigation designs (inflow rate and cutoff time) except inflow rates with heterogeneous infiltration. Differences in inflow volume were less than 2% and 5%, respectively, for homogeneous infiltration and heterogeneous infiltration. For the conditions studied, furrow irrigation management decision variables can be forecast and optimized to better manage the irrigation system, because irrigation performance was the same for both (forecast and observed) ET₀ cases. Received: 9 October 1999     

Evapotranspiration and water use of full and deficit irrigated cotton in the Mediterranean environment in northern Syria

Cotton (Gossypium hirsutum L.) is the most important industrial and summer cash crop in Syria and many other countries in the arid areas but there are concerns about future production levels, given the high water requirements and the decline in water availability. Most farmers in Syria aim to maximize yield per unit of land regardless of the quantity of water applied. Water losses can be reduced and water productivity (yield per unit of water consumed) improved by applying deficit irrigation, but this requires a better understanding of crop response to various levels of water stress. This paper presents results from a 3-year study (2004-2006) conducted in northern Syria to quantify cotton yield response to different levels of water and fertilizer. The experiment included four irrigation levels and three levels of nitrogen (N) fertilizer under drip irrigation. The overall mean cotton (lint plus seed, or lintseed) yield was 2502 kg ha⁻¹, ranging from 1520 kg ha⁻¹ under 40% irrigation to 3460 kg ha⁻¹ under 100% irrigation. Mean water productivity (WP_ET) was 0.36 kg lintseed per m³ of crop actual evapotranspiration (ET_c), ranging from 0.32 kg m⁻³ under 40% irrigation to 0.39 kg m⁻³ under the 100% treatment. Results suggest that deficit irrigation does not improve biological water productivity of drip-irrigated cotton. Water and fertilizer levels (especially the former) have significant effects on yield, crop growth and WP_ET. Water, but not N level, has a highly significant effect on crop ET_c. The study provides production functions relating cotton yield to ET_c as well as soil water content at planting. These functions are useful for irrigation optimization and for forecasting the impact of water rationing and drought on regional water budgets and agricultural economies. The WP_ET values obtained in this study compare well with those reported from the southwestern USA, Argentina and other developed cotton producing regions. Most importantly, these WP_ET values are double the current values in Syria, suggesting that improved irrigation water and system management can improve WP_ET, and thus enhance conservation and sustainability in this water-scarce region.     

An evaluation of two hourly reference evapotranspiration equations for semiarid conditions

The methodology proposed by the Food and Agriculture Organization (FAO) (Doorenbos, J., Pruitt, W.O., 1977. Crop water requirements. FAO irrigation and drainage. Paper No. 24. FAO, Rome) and updated by Allen et al. (Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO irrigation and drainage. Paper No. 56. FAO, Rome) for calculating crop water requirements is the most extended and accepted method worldwide. This method requires the prior calculation of reference evapotranspiration (ET_o). This study evaluates the FAO-56 and American Society of Civil Engineers (ASCE) Penman–Monteith (PM) equations for estimation of hourly ET_o under the semiarid conditions of the province of Albacete (Spain). The FAO-56 and ASCE equations (hourly time step) were compared against measured lysimeter ET_o values at Albacete for 13 days during the period of April–October 2002 and 16 days during April–October 2003. The average of estimated FAO-56 Penman–Monteith ET_o values was equal to the average of measured values. However, the average of estimated ASCE Penman–Monteith values was 4% higher than the average of measured lysimeter ET_o values. This method overestimated measured lysimeter ET_o values by 0.45 mm h⁻¹.Simple linear regression and error analysis statistics suggest that agreement between both estimation methods and the lysimeter was quite good for the province of Albacete.In this paper, the FAO-56 Penman–Monteith equation for calculating hourly ET_o values was more accurate than the ASCE Penman–Monteith method under semiarid weather conditions in Albacete.