An evaluation of common pan coefficient equations to estimate reference evapotranspiration in a subtropical climate (north of Iran)

Accurate reference evapotranspiration (ET₀) data are essential to water resources project planning and farm irrigation scheduling. Evaporation pans are widely used to estimate reference ET₀. Via the pan coefficient (K _p), ET₀ is estimated from evaporation pan data. Four common K _p equations (Orang in Potential accuracy of the popular non-linear regression equations for estimating pan coefficient values in the original and FAO-24 tables, unpublished report, 1998; Allen and Pruitt in J Irrig Drain Eng 117(5):758–773, 1991; Cuenca in Irrigation system design: an engineering approach, p 133, 1989; Snyder in J Irrig Drain Eng 118(6):977–980, 1992) to calculate daily K _p coefficients to estimate ET₀ were evaluated using a 10-year mean climate dataset for a subtropical climate (north of Iran). Overall results showed that ET₀ calculated using the daily K _p values from Orang (Potential accuracy of the popular non-linear regression equations for estimating pan coefficient values in the original and FAO-24 tables, unpublished report, 1998) provided more accurate daily, monthly, and annual total estimates compared to the others equations.     

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.     

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.     

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.     

Measuring versus estimating net radiation and soil heat flux: Impact on Penman–Monteith reference ET estimates in semiarid regions

The standardized ASCE Penman–Monteith and FAO-56 equations were used to estimate reference evapotranspiration (ET₀) using estimated and measured net radiation (R_n) and soil heat flux (G), based on hourly and daily meteorological data. The estimates were evaluated against lysimeter measurements. The results indicate that using measured or estimated values of R_n and G can have significant effect on the accuracy of the ET₀ estimations, especially when calculations were made on an hourly basis. The FAO-56 version performed very well during the irrigation season on a daily basis. The use of measured R_n and G did not improve ET₀ estimation on a daily basis, therefore, the use of estimated R_n and G appears to be dependable when calculations are based on 24-h weather data. When daily ET₀ was calculated from hourly estimations, the results were different depending on the version used. The ASCE version was more accurate, especially when R_n and G were measured. Therefore, measurement of R_n and G may have potential to improve estimation only when daily ET₀ is calculated from hourly estimations. The PM FAO-56 version was always a little less accurate than the ASCE version. For hourly calculations, using a constant surface resistance (as in FAO-56 version), the PM method underpredicted for high evaporative demand and vice versa. The ASCE version performed better than PM FAO-56 version when R_n and G were measured and estimated. Therefore, ASCE version tended to provide quite accurate values of hourly ET₀, even using estimated values of R_n and G. As conclusion, the methods proposed by FAO-56 for estimating R_n and G tended to produce accurate estimates for daily and hourly ET₀ under semiarid conditions and can be used with some degree of confidence for estimating ET₀. In addition, results suggest that the ASCE standardized equation on an hourly basis improved the accuracy of ET₀ estimation with respect to the FAO-56 version.     

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.     

Evaluation of pan coefficient for reference crop evapotranspiration for semi-arid region

Pan coefficient (K _pan) is the important factor for computation of reference evapotranspiration (ET _o ) from pan evaporation (E _pan). In this paper, the approaches proposed by Cuenca (Irrigation system design: an engineering approach. Prentice-Hall, Englewood Cliffs, 1989), Snyder (J Irrig Drain Eng 118(6):977–980, 1992), Orang (Potential accuracy of the popular non-linear regression equations for estimating pan coefficient values in the original and FAO-24 tables. Unpublished Report, Calif. Dept. of Water Resources, Sacramento, 1998), Raghuwanshi and Wallender (J Irrig Drain Eng 118 (6):977–980, 1998) and Pereira et al. (Agric Water Manage 76:75–82, 1995) were evaluated for a semi-arid region. By comparing with the FAO 56 Penman-Monteith (F-PM) method the Snyder (J Irrig Drain Eng 118(6):977–980, 1992, 1992) approach was best suited for the semi-arid region.     

Evaluation of FAO-56 methodology for estimating reference evapotranspiration using limited climatic data: Application to Tunisia

The Food and Agriculture Organization of the United Nations had improved the version of the Penman–Monteith method (FAO-56 PM) which has recently been proposed as the standard for estimating reference evapotranspiration (ET_o). Unfortunately, some weather variables, especially solar radiation, relative humidity and wind speed, are often missing which could impede the estimation of ET_o with the FAO-56 PM method. To overcome the problem of the availability of climatic parameters, procedures to estimate ET_o with missing climate data are proposed as part of the FAO methodology. Therefore, assessing the accuracy of these procedures for different Tunisian locations is important. The comparison of ET_o estimates using limited data to those computed with full data set revealed that the difference between ET_o obtained from full and limited data set is small considering the 8 locations studied. Both the Mean Bias Error (MBE) and the Root Mean Square Error (RMSE) of the comparison were less than 0.6 and 0.8 with a minimum of −0.4 and 0.2 mm day⁻¹, respectively, leading to small errors in the ET_o estimates. The higher deviations occur when the only available information is minimum and maximum air temperature. These deviations were significantly higher when using the Hargreaves equation to calculate ET_o.     

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.     

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.     

Estimation of banana (Musa sp.) plant transpiration using a standard 20 cm pan in a greenhouse

An experiment was carried out in a naturally ventilated greenhouse to study the relationship between banana (Musa sp.) plant transpiration (Tr) measured with load cells, reference crop evapotranspiration (ET_o) calculated with five widely used models (i.e. the Priestley-Taylor, FAO radiation, Hargreaves, FAO Penman and FAO Penman-Monteith models) and pan evaporation (E_pan) measured with a standard Chinese 20 cm pan. Microclimatic conditions were measured inside the greenhouse. Results show that vapor pressure deficit and air temperature had good linear correlations to banana Tr with R² of 0.67 and 0.62, respectively. Among the five models tested, banana Tr and ET_o calculated with the FAO-Penman model yielded the highest determination coefficient (R² = 0.67), followed by the FAO-PM model (R²=0.63), the FAO radiation model (R²=0.52), the Hargreaves model (R²=0.49) and the Priestley-Taylor model (R²=0.47). Banana transpiration Tr vs. E_pan yielded an R² of 0.83, which is higher than the five models tested. In conclusion, the 20 cm pan can be useful for estimating banana Tr in greenhouses.     

Estimation of crop evapotranspiration of irrigation command area using remote sensing and GIS

This paper describes the use of satellite-based remote sensing (RS) data and geographic information system (GIS) tools for estimating seasonal crop evapotranspiration in Mahi Right Bank Canal (MRBC) command area of Gujarat, India. Crop coefficients (K_c) for various major crops grown in MRBC were estimated, empirically, from the RS derived soil adjusted vegetation index (SAVI) values. A reference crop evapotranspiration (ET₀) map was generated from point meteorological observations. The K_c and ET₀ maps were combined to generate seasonal crop evapotranspiration (ET_crop) map which highlighted spatial variation in ET_crop ranging from more than 600 mm for healthy tobacco crops to less than 150 mm for very poor wheat crops.     

Evapotranspiration predictions: a comparison among GLEAMS,Opus, PRZM-2, and RZWQM models in a humid and thermic climate

Environmental fate models are increasingly used to evaluate potential impacts of agrochemicals on water quality to aid in decision making. However, errors in predicting processes like evapotranspiration (ET), which is rarely measured during model validation studies, can significantly affect predictions of chemical fate and transport. This study compared approaches and predictions for ET by GLEAMS, Opus, PRZM-2, and RZWQM and determined effects of the predicted ET on simulations of other hydrology components. The ET was investigated for 2 years of various fallow–corn growing seasons under sprinkler irrigation. The comparison included annual cumulative daily potential ET (ET_p), actual ET, and partitioning of total ET between soil evaporation (E_s) and crop transpiration (E_t). When measured pan evaporation was used for calculating ET_p (the pan evaporation method), Opus, PRZM-2, and RZWQM predicted 74, 65, and 59%, respectively, of the 10-year average ET reported for a nearby site. When the energy-balance equations were used for calculating ET_p (the combination methods), GLEAMS, Opus, PRZM-2, and RZWQM predicted 84, 105, 60, and 72% of the reported ET, respectively. The pan evaporation method predicted a similar amount of ET to the combination methods for bare soil, but predicted less ET when both E_s and E_t occurred. RZWQM reasonably predicted partitioning of ET to E_s, while GLEAMS and Opus over-predicted this partitioning. A close correlation between soil water storage in the root zone and ET suggests that accurate soil water content predictions were fundamental to ET predictions. ©     

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%.     

Least squares support vector machine for modeling daily reference evapotranspiration

The accuracy of a least square support vector machine (LSSVM) in modeling of reference evapotranspiration (ET₀) was examined in this study. The daily weather data, solar radiation, air temperature, relative humidity and wind speed of two stations, Glendale and Oxnard, in southern district of California, were used as inputs to the LSSVM models to estimate ET₀ obtained using the FAO-56 Penman–Monteith equation. In the first part of the study, LSSVM estimates were compared with those of the following empirical models: Priestley–Taylor, Hargreaves and Ritchie methods. The comparison results indicated that the LSSVM performed better than the empirical models. In the second part of the study, the LSSVM results were compared with those of the conventional feed-forward artificial neural networks (ANN). It was found that the LSSVM models were superior to the ANN in modeling ET₀ process.     

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.     

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.     

Estimation of reference evapotranspiration for southern region of Saudi Arabia

The reference crop evapotranspiration (ET_r) for four areas in Saudi Arabia was estimated using five different methods: FAO-Penman, Jensen-Haise, Blaney & Criddle, pan evaporation, and calibrated FAO-Penman under local conditions (Penman_-SA). Comparison was also made between the estimated ET_r and the measured ET_r of alfalfa grown in lysimeters in the Riyadh area. Regression analysis revealed that estimated ET_r values were highly correlated with measured ET_r values. In addition, linear regression relationships between ET_r values estimated by the Penman_-SA method and other methods were determined. The results of this study indicated that the calibrated Penman_-SA method can be transferred successfully to other locations, and this method could be used for the estimation of ET_r values in all areas in the southern region of Saudi Arabia. Received: 16 January 1998     

Evapotranspiration and responses to irrigation of broccoli

In cold, semi-arid areas, the options for crop diversification are limited by climate and by the water supply available. Growing irrigated crops outside the main season is not easy, because of climatic and market constraints. We carried out an experiment in Albacete, Central Spain, to measure the water use (evapotranspiration, ET) of broccoli (Brassica oleracea L. var. italica Plenck) planted in late summer and harvested at the end of fall. A weighing lysimeter was used to measure the seasonal ET under sprinkler irrigation. Consumptive use reached 359 mm for a period of 109 days after transplanting. The crop coefficient (K_c) for broccoli was obtained and compared to the standard recommendations for normal planting dates. Dual crop coefficient computations of the lysimeter ET data indicated that evaporation represented 31% of seasonal ET. An analysis of the variation in daily K_c values at a time of full cover suggested that the use of a grass lysimeter as a reference ET (ET_o) was superior to using the ASCE Penman-Monteith (ASCE PM) equation at hourly time steps, which in turn caused less variability in K_c than when using the FAO-56 Penman-Monteith (FAO-56 PM) equation at daily time steps for the ET_o calculation. An additional experiment aimed at evaluating the yield response to applied irrigation water by the drip method (seven treatments, from 59 to 108% of ET_c) generated a production function that gave maximum yields of near 12 t ha⁻¹ at an irrigation level of 345 mm, and a water use efficiency of 3.37 kg m⁻³. It is concluded that growing broccoli in the fall season is a viable alternative for crop diversification, as the lower yields obtained here may be more than compensated for by the higher produce prices in autumn, at a time of the year where irrigation water demand for other crops is very low.     

An evaluation of common evapotranspiration equations

A comparison is made between the Pruitt and Doorenbos version of an hourly Penman-type equation, the Food and Agriculture Organization (FAO) hourly Penman-Monteith equation, and an independent measure of reference evapotranspiration (ET₀) from lysimeter data. Reducing the canopy resistance improved the hourly FAO Penman-Monteith estimates. Daytime soil heat flux density is estimated as 10% of net radiation in the FAO hourly Penman-Monteith equation; however, the measured soil heat flux density under grass that was never shorter than 0.10 m in this study was between 3% and 5% of net radiation. The daytime totals of hourly ET₀ from the hourly Penman-Monteith and Pruitt-Doorenbos equations and ET₀ from the 24-h FAO Penman-Monteith equation were computed using data from five Italian and five Californian stations. A comparison showed that all of the equations gave acceptable results. The Pruitt-Doorenbos equation may slightly over-estimate ET₀ in conditions of summertime cold air advection. Received: 18 November 1998