Comparison of the Penman‐Monteith method and regional calibration of the Hargreaves equation for actual evapotranspiration using SWAT-simulated results in the Seolma-cheon basin,South Korea

ABSTRACT

The Hargreaves method provides reference evapotranspiration (ET_o) estimates when only air temperature data are available, although it requires previous local calibration for an acceptable performance. This method was evaluated using the data from 71 meteorological stations in the Seolma-cheon basin (8.48 km²), South Korea, comparing daily estimates against those from the Penman‐Monteith (PM) method, which was used as the standard. To estimate reference ET_o more exactly, considering the climatological characteristics in South Korea, parameter regionalization of the Hargreaves equation is carried out. First, the modified Hargreaves equation is presented after an analysis of the relationship between solar radiation and temperature. Second, parameter (K_ET) optimization of the regional calibration of the Hargreaves equation (RCH) is performed using the PM method and the modified equation at 71 meteorological stations. Next, an application was carried out to evaluate the evapotranspiration methods (PM, original Hargreaves and RCH) in the SWAT (Soil and Water Assessment Tool) model by comparing these with the measured actual evapotranspiration (AET) in the basin. The SWAT model was calibrated using 3 years (2007–2009) of daily streamflow at the watershed outlet and 3 years (2007–2009) of daily AET measured at a mixed forest. The model was validated with 3 years (2010‐2012) of streamflow and AET. RCH will contribute to a better understanding of evapotranspiration of an ungauged watershed in areas where meteorological information is scarce.

EDITOR D. Koutsoyiannis ASSOCIATE EDITOR Not assigned     

Estimating evapotranspiration for a temperate salt marsh,Newcastle, Australia

Evapotranspiration was studied at a salt marsh site in the Hunter River estuary, NSW, Australia, during 1996–8. Estimates of actual evapotranspiration (E_a) were obtained for three sites using the eddy correlation method. These values were compared with results obtained with the Penman and Penman–Monteith equations, and with pan evaporation. The Penman–Monteith method was found to be most reliable in estimating daily and hourly evapotranspiration. Surface resistance values averaging 12 s m^?1 were derived from the eddy correlation estimates. Recent tidal flooding and rainfall were found to decrease surface resistance and increase E_a/E_p ratios. Estimates of evapotranspiration obtained using the Penman–Monteith method were shown to be sensitive to changes in surface resistance, canopy height and the method used to estimate net radiation from incoming solar radiation. These results underline the importance of accurately estimating such parameters based on site‐specific data rather than relying on empirical equations, which are derived primarily for crops and forests. Copyright © 2001 John Wiley & Sons, Ltd.     

Evapotranspiration modelling from climatic data using a neural computing technique

Evapotranspiration is one of the basic components of the hydrologic cycle and essential for estimating irrigation water requirements. This paper investigates the modelling of evapotranspiration using the feed‐forward artificial neural network (ANN) technique with the Levenberg–Marquardt (LM) training algorithm. The LM algorithm has never been used in evapotranspiration estimation before. The LM is used for the optimization of network weights, since this algorithm is more powerful and faster than the conventional gradient descent. Various combinations of daily climatic data, i.e. wind speed, air temperature, relative humidity and solar radiation, from three stations in Los Angeles, USA, are used as inputs to the ANN so as to evaluate the degree of effect of each of these variables on evapotranspiration. A comparison is made between the estimates provided by the ANN and those of the following empirical models: Penman, Hargreaves, Turc. Mean square error, mean absolute error and determination coefficient statistics are used as comparing criteria for the evaluation of the models' performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modelling evapotranspiration process from the available climatic data. The results also indicate that the Hargreaves method provides better performance than the Penman and Turc methods in estimation of the evapotranspiration. The accuracy of the ANN technique in evapotranspiration estimation using nearby station data was also investigated. Copyright © 2007 John Wiley & Sons, Ltd.     

M5 model tree based modelling of reference evapotranspiration

This paper investigates the potential of M5 model tree based regression approach to model daily reference evapotranspiration using climatic data of Davis station maintained by California irrigation Management Information System (CIMIS). Four inputs including solar radiation, average air temperature, average relative humidity, and average wind speed whereas reference evapotranspiration calculated using a relation provided by the CIMIS was used as output. To compare the performance of M5 model tree in predicting the reference evapotranspiration, FAO–56 Penman–Monteith equation and calibrated Hargreaves–Samani relation was used. A comparison of results suggests that M5 model tree approach works well in comparison to both FAO–56 and calibrated Hargreaves–Samani relations. To judge the generalization capability of M5 model tree approach, model created by using the Davis data set was tested with the datasets of four different sites. Results from this part of the study suggest that M5 model tree could successfully be employed in modeling the reference evapotranspiration. Further, sensitivity analysis with M5 model tree approach suggests the suitability of solar radiation, average air temperature, average relative humidity, and average wind speed as input parameters to model the reference evapotranspiration Copyright © 2009 John Wiley & Sons, Ltd.     

Evapotranspiration modelling using support vector machines / Modélisation de l'évapotranspiration à l'aide de ‘support vector machines’

Abstract

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

Development of pan coefficients for estimating evapotranspiration from riparian woody vegetation

The long‐term ‘Millennium Drought’ has put significant pressure on water resources across Australia. In southeastern Australia and in particular the Murray‐Darling Basin, removal of exotic, high‐water‐use Salix trees may provide a means to return water to the environment. This paper describes a simple model to estimate evapotranspiration of two introduced Salix species under non‐water‐limited conditions across seven biogeoclimatic zones in Australia. In this study, Salix evapotranspiration was calculated using the Penman–Monteith model. Field measurements of leaf area index and stomatal conductance for Salix babylonica and Salix fragilis were used to parameterize the models. Each model was validated using extensive field estimates of evapotranspiration from a semi‐arid (S. babylonica, r² = 0.88) and cool temperate (S. fragilis, r² = 0.99) region. Modelled mean annual evapotranspiration showed strong agreement with field measurements, being within 32 and 2 mm year^?1 for S. babylonica and S. fragilis, respectively. Monthly pan coefficients (the ratio of mean evapotranspiration to mean pan evaporation) were developed from 30 years of meteorological data, for 30 key reference sites across Australia for both species using the validated Penman–Monteith models. Open‐water evaporation was estimated from field measurements and was used to develop a simple linear regression model for open‐water evaporation across the 30 reference sites. Differences between modelled evapotranspiration and open‐water evaporation at each site provide an indication of the amount of water that might be returned to the environment from removal of in‐stream Salix species. The monthly pan coefficient method reported has application across riparian environments worldwide where measured evapotranspiration is available for model validation. Copyright © 2013 John Wiley & Sons, Ltd.     

Sensitivity analysis of a Penman–Monteith type equation to estimate reference evapotranspiration in southern Spain

Sensitivity analysis is crucial in assessing the impact of climatic variables on reference evapotranspiration estimations. The sensitivity of the standardized ASCE–Penman–Monteith evapotranspiration equation for daily estimations to climatic variables has not yet been studied in Spain. Andalusia is located in southern Spain where almost 1 million ha are irrigated under quite different conditions; it has a high inter‐annual variability in rainfall. In this study, sensitivity analyses for this equation were carried out for temperature, relative humidity, solar radiation and wind speed data from 87 automatic weather stations, including coastal and inland locations, from 1999 to 2006. Topography and Mediterranean climate characterize the heterogeneous landscape and vegetation of this region. Simulated random and systematic errors have been added to meteorological data to obtain ET₀ deviations and sensitivity coefficients for different time periods. BIAS and SEE (standard error of estimate) have been used to evaluate the effect of both types of errors. The results showed a large degree of daily and seasonal variability, especially for temperature and relative humidity. In general, the effect on ET₀ values of introduced random errors was larger than that of systematic errors. ET₀ overestimations were produced using positive errors in temperature, solar radiation and wind speed data, while these errors in relative humidity resulted in ET₀ underestimations. The sensitivity of ET₀ to the same climatic variables showed significant differences among locations. The geographical distribution of sensitivity coefficients across this region was also studied. As an example, during spring months, ET₀ equation was more sensitive to temperature in stations located along the Guadalquivir Valley. Copyright © 2009 John Wiley & Sons, Ltd.     

Evaluating the use of a gridded climate surface for modelling groundwater recharge in a semi‐arid region (Okanagan Basin,Canada)

Spatially distributed groundwater recharge was simulated for a segment of a semi‐arid valley using three different treatments of meteorological input data and potential evapotranspiration (PET). For the same area, timeframe, land cover characteristics and soil properties, groundwater recharge was estimate using (i) single‐station climate data with monthly PET calculated by the Thornthwaite method; (ii) single‐station climate data with daily PET calculated by the Penman–Monteith method; and (iii) daily gridded climate data with spatially distributed PET calculated using the Penman–Monteith method. For each treatment, the magnitude and distribution of actual evapotranspiration (AET) for summer months compared well with those estimated for a 5‐year crop study, suggesting that the near‐surface hydrological processes were replicated and that subsequent groundwater recharge rates are realistic. However, for winter months, calculated AET was near zero when using the Thornthwaite PET method. Mean annual groundwater recharge varied from ～3·2 to 10·0 mm when PET was calculated by the Thornthwaite method, and from ～1·8 to 7·5 mm when PET was calculated by the Penman–Monteith method. Comparisons of bivariate plots of seasonal recharge rates estimated from single‐station versus gridded surface climate reveal that there is greater variability between the different methods for spring months, which is the season of greatest recharge. Furthermore, these seasonal differences are shown to provide different results when compared to the depth to water table, which could lead to different results of evaporative extinction depth. These findings illustrate potential consequences of using different approaches for representing spatial meteorological input data, which could provide conflicting predictions when modelling the influence of climate change on groundwater recharge. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaporation of grass under non-restricted soil moisture conditions

Abstract

The behaviour of various formulas for evapotranspiration of grass in Nonrestricted soil water conditions is considered. These are the expressions based on the Penman formula, i.e. “old” Penman, Penman-Monteith, Thorn-Oliver and the version recommended more recently by the FAO. Moreover, the Priestley-Taylor and the Makkink formulas are considered, which are radiation-based. Comparisons are made between daily mean values estimated with these formulas and direct measurements. The latter were collected over grass in the period 1979–1982 in the catchment area of the Hupselse Beek (The Netherlands). It was found that if all required input data were measured, the Priestley-Taylor and the “old” Penman formula yielded the best results. The assumption that soil heat flux can be neglected introduces a systematic and a random error of roughly 5%. The empirical estimates for net radiation from sunshine duration, temperature and humidity appear to perform rather poorly. These estimates improved significantly if solar radiation was measured directly. The empirical expression proposed by Slob (unpublished) that requires incoming solar radiation only as input, provided better results than the other more complicated expressions. Moreover, this study reveals that evaporation of unstressed grass is primarily determined by the available energy, i.e. good evaporation estimates can be obtained by using simply λE = 0.86(R_n ? G). The Makkink method appears to be attractive for practical applications. These findings support the use of Makkink's formula for routine calculations of crop-reference evapotranspiration as has been done by the Royal Netherlands Meteorological Institute since 1987.     

Choice between competitive pairs of frequency models for use in hydrology: a review and some new results

Abstract

The potential is investigated of the generalized regression neural networks (GRNN) technique in modelling of reference evapotranspiration (ET₀) obtained using the FAO Penman-Monteith (PM) equation. Various combinations of daily climatic data, namely solar radiation, air temperature, relative humidity and wind speed, are used as inputs to the ANN so as to evaluate the degree of effect of each of these variables on ET₀. In the first part of the study, a comparison is made between the estimates provided by the GRNN and those obtained by the Penman, Hargreaves and Ritchie methods as implemented by the California Irrigation Management System (CIMIS). The empirical models were calibrated using the standard FAO PM ET₀ values. The GRNN estimates are also compared with those of the calibrated models. Mean square error, mean absolute error and determination coefficient statistics are used as comparison criteria for the evaluation of the model performances. The GRNN technique (GRNN 1) whose inputs are solar radiation, air temperature, relative humidity and wind speed, gave mean square errors of 0.058 and 0.032 mm² day^?2, mean absolute errors of 0.184 and 0.127 mm day^?1, and determination coefficients of 0.985 and 0.986 for the Pomona and Santa Monica stations (Los Angeles, USA), respectively. Based on the comparisons, it was found that the GRNN 1 model could be employed successfully in modelling the ET₀ process. The second part of the study investigates the potential of the GRNN and the empirical methods in ET₀ estimation using the nearby station data. Among the models, the calibrated Hargreaves was found to perform better than the others.     

Summer evapotranspiration in western Siberia: a comparison between eddy covariance and Penman method formulations

Evapotranspiration is difficult to quantify because of the many factors and complex processes that influence it. Several empirical methods have been developed over the years to estimate potential evapotranspiration based on easily available parameters. Directly measured data of actual evapotranspiration have been rather sparse in the past and still need to be improved in particular regions like western Siberia. The transition zone between the warm temperate and cold temperate continental climates is very sensitive to climate change, and water stress is an increasingly important issue in these regions with a highly dynamic agricultural activity. So there is a growing need to estimate actual evapotranspiration. Widely usable approximations are needed. In this study, the values of potential evapotranspiration computed with the original version, and eight modifications of the Penman formulation were compared and related to the actual evapotranspiration measured by eddy covariance over a grassland area in western Siberia. The original 1948 and 1963 Penman formulations are best for estimating potential evapotranspiration in the transition zone between the forest steppes and the pre‐taiga. A nearly linear relationship between the potential and actual evapotranspiration was found. A simple modification of the Penman equation (i.e. the multiplication of the result by a factor of 0.47) is suggested for approximating the actual evapotranspiration based on standard meteorological data for the region. The original Penman formulation is most robust and will provide the widest applicability in the future under changing climate and environmental conditions. In this context, it is further recommended not to neglect the ventilation term of the Penman equation, which is often assumed to be negligibly small. A detailed correlation analysis showed that under dry soil conditions, the vegetation largely contributed to the actual evapotranspiration and, in contrast to widely held expectations, that the Penman equation is best adapted to vegetated surfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct and indirect methods to simulate the actual evapotranspiration of an irrigated overhead table grape vineyard under Mediterranean conditions

Two methods, indirect and direct, for simulating the actual evapotranspiration (E) were applied to an irrigated overhead table grape vineyard during summer, situated in the Mediterranean region (south Italy), over two successive years. The first method, indirect but more practical, uses the crop coefficient (K_c) approach and requires determination of the reference evapotranspiration E₀ (FAO (Food and Agriculture Organization) method). This method underestimated on average by 17% the daily values of the actual evapotranspiration E. The analysis in this paper shows that the values of K_c for the table grapes determined by the FAO method seem to not be valid in our experimental conditions. Similar conclusions can be found in the literature for the table grape cultivated under different experimental conditions and using different training systems. The second method, is a direct method for estimating the evapotranspiration. It requires development of a model for the overhead table grape vineyard E, following the Penman–Monteith one‐step approach, and using standard meteorological variables as inputs for the determination of the canopy resistance. This method, which needs a particularly simple calibration, provided a better simulation of the hourly and daily evapotranspiration than the indirect method. In additon, the standard error of the daily values for the direct method ( ± 0 · 41 mm) was about 50% lower than that obtained for the indirect method, also when the indirect method used a locally calibrated coefficient K_c instead of a generic K_c. Both, for practical application and theoretical issues, the advantages and disadvantages linked to the use of each tested method are discussed in detail. Copyright © 2007 John Wiley & Sons, Ltd.     

Blaney-Morin-Nigeria evapotranspiration model

An evapotranspiration model which parallels that proposed earlier by Blaney and Morin has been developed for application in Nigeria. The model, designated as the Blaney-Morin-Nigeria evapotranspiration model, predicts potential evapotranspiration with accuracy and consistency that are better than the Penman model, under Nigerian conditions. It is suggested that the Blaney-Morin evapotranspiration concept may have similar potential elsewhere when given specific form with appropriate constants derived to reflect climatic peculiarities.     

Pan evaporation and potential evapotranspiration trends in South Florida

Declining trends in pan and lake evaporation have been reported. It is important to study this trend in every region to evaluate the validity of the trend and water management implications. Data from nine pan evaporation sites in South Florida were evaluated to see if there is a trend and if the quality of the data is sufficient for such analysis. The conclusion is that pan evaporation measurements are prone to too many sources of errors to be used for trend analysis. This condition is demonstrated in South Florida and in other regions by differences in magnitude and direction between spatially related pan stations and unexplainable observations. Also, potential evapotranspiration (ET_p) was estimated with the Simple (Abtew equation) and the Penman–Monteith method. Both cases indicated no decline in evapotranspiration for the period of analysis. Based on the decline in humidity and the increasing trend in vapor pressure deficit for the short period of analysis, 1992–2009, it appears that South Florida is experiencing increase in evaporation and evapotranspiration at this time assuming no systematic error in the weather stations' observations. Copyright © 2010 John Wiley & Sons, Ltd.     

How do potential evapotranspiration formulas influence hydrological projections?

ABSTRACT

This paper evaluates the sensitivity of hydrological projections to the choice of potential evapotranspiration formulas on two natural sub-catchments, in Canada and Germany. Twenty-four equations, representing a large range of options, are applied for calibration over the whole observation time series and for future conditions. The modelling chain is composed of dynamically downscaled climatic projections and a 20-member (ensemble) hydrological model, along with a snow module. The roots of the sensitivity and its propagation within the hydrological chain are evaluated to show influences on climate change impact conclusions. Results show large differences between the 24 simulated potential evapotranspiration time series. However, these discrepancies only moderately affect the calibration efficiency of hydrological models as a result of adaptation of parameters. Choice of formula influences hydrological projections and climate change conclusions for both catchments in terms of simulated and projected values, and also in the magnitude of changes during important dynamic periods such as spring and autumn high flows and summer low flows. Spread of the hydrological response is lower for the combinational formulas than for temperature-based or radiation-based equations. All the results reveal the importance of testing a large spectrum of potential evapotranspiration formulas in a decision-making context, such as water resources management.     

Fuzzy logic model approaches to daily pan evaporation estimation in western Turkey / Estimation de l’évaporation journalière du bac dans l’Ouest de la Turquie par des modèles à base de logique floue

Abstract

Abstract Evaporation is one of the fundamental elements in the hydrological cycle, which affects the yield of river basins, the capacity of reservoirs, the consumptive use of water by crops and the yield of underground supplies. In general, there are two approaches in the evaporation estimation, namely, direct and indirect. The indirect methods such as the Penman and Priestley-Taylor methods are based on meteorological variables, whereas the direct methods include the class A pan evaporation measurement as well as others such as class GGI-3000 pan and class U pan. The major difficulty in using a class A pan for the direct measurements arises because of the subsequent application of coefficients based on the measurements from a small tank to large bodies of open water. Such difficulties can be accommodated by fuzzy logic reasoning and models as alternative approaches to classical evaporation estimation formulations were applied to Lake Egirdir in the western part of Turkey. This study has three objectives: to develop fuzzy models for daily pan evaporation estimation from measured meteorological data, to compare the fuzzy models with the widely-used Penman method, and finally to evaluate the potential of fuzzy models in such applications. Among the measured meteorological variables used to implement the models of daily pan evaporation prediction are the daily observations of air and water temperatures, sunshine hours, solar radiation, air pressure, relative humidity and wind speed. Comparison of the classical and fuzzy logic models shows a better agreement between the fuzzy model estimations and measurements of daily pan evaporation than the Penman method.     

A simple temperature method for the estimation of evapotranspiration

Accurate estimation of evapotranspiration (ET) is essential in water resources management and hydrological practices. Estimation of ET in areas, where adequate meteorological data are not available, is one of the challenges faced by water resource managers. Hence, a simplified approach, which is less data intensive, is crucial. The FAO‐56 Penman–Monteith (FAO‐56 PM) is a sole global standard method, but it requires numerous weather data for the estimation of reference ET. A new simple temperature method is developed, which uses only maximum temperature data to estimate ET. Ten class I weather stations data were collected from the National Meteorological Agency of Ethiopia. This method was compared with the global standard PM method, the observed Piche evaporimeter data, and the well‐known Hargreaves (HAR) temperature method. The coefficient of determination (R²) of the new method was as high as 0.74, 0.75, and 0.91, when compared with that of PM reference evapotranspiration (ET_o), Piche evaporimeter data, and HAR methods, respectively. The annual average R² over the ten stations when compared with PM, Piche, and HAR methods were 0.65, 0.67, and 0.84, respectively. The Nash–Sutcliff efficiency of the new method compared with that of PM was as high as 0.67. The method was able to estimate daily ET with an average root mean square error and an average absolute mean error of 0.59 and 0.47 mm, respectively, from the PM ET_o method. The method was also tested in dry and wet seasons and found to perform well in both seasons. The average R² of the new method with the HAR method was 0.82 and 0.84 in dry and wet seasons, respectively. During validation, the average R² and Nash–Sutcliff values when compared with Piche evaporation were 0.67 and 0.51, respectively. The method could be used for the estimation of daily ET_o where there are insufficient data. Copyright © 2013 John Wiley & Sons, Ltd.     

QUELQUES EXEMPLES D'APPLICATION DES MESURES DE RAYONNEMENT À LA DÉTERMINATION DE L'ÉVAPO-TRANSPIRATION EN CLIMAT TROPICAL

ABSTRACT

From data obtained at stations set up in Chad, the Central African Republic and Congo-Brazzaville, stretching from the desert to the equatorial zone, it has been possible to compare measurements of evapotranspiration and of evaporation with results obtained by using the energy-balance method. Several difficulties arise in these comparisons since the scale of the measurements (small evaporating surfaces) is generally different from that of the climatic characteristics on which evaporation is dependent.

After proposing a model to resolve this problem and fitting the empirical coefficients of Penman's formula, the author has applied this formula to some results derived for stations in Congo-Brazzaville; the potential evapotranspiration calculated in this way is in good agreement with water balance data.

At these stations the evapotranspiration energy may be a constant percentage of global short-wave radiation.

Finally, the energy-balance method has been used at Brazzaville to measure the actual evapotranspiration over grass during the dry season. The result is that actual and potential evapotranspiration were found to be closely related.

These results indicate the importance of solar readiation in the field of hydrometeorology.     

A simple method using climatic variables to estimate canopy temperature,sensible and latent heat fluxes in a winter wheat field on the North China Plain

Estimation of evapotranspiration from a crop field is of great importance for detecting crop water status and proper irrigation scheduling. The Penman–Monteith equation is widely viewed as the best method to estimate evapotranspiration but it requires canopy resistance, which is very difficult to determine in practice. This paper presents a simple method simplified from the Penman–Monteith equation for estimating canopy temperature (T_c). The proposed method is a biophysically‐sound extended version of that proposed by Todorovic. The estimated canopy temperature is used to calculate sensible heat flux, and then latent heat flux is calculated as the residual of the surface energy balance. An eddy covariance (EC) system and an infrared thermometer (IRT) were installed in an irrigated winter wheat field on the North China Plain in 2004 and 2005, to measure T_c, and sensible and latent heat fluxes were used to test the modified Todorovic model (MTD). The results indicate that the original Todorovic model (TD) severely underestimates T_c and sensible heat flux, and hence severely overestimates the latent heat flux. However, the MTD model has good capability for estimating T_c, and gives acceptable results for latent heat flux at both half‐hourly and daily scales. The MTD model results also agreed well with the evapotranspiration calculated from the measured T_c. Copyright © 2008 John Wiley & Sons, Ltd.     

Validation and calibration of solar radiation equations for estimating daily reference evapotranspiration at cool semi-arid and arid locations

ABSTRACT

In this work, the applicability of 12 solar radiation (R_S) estimation models and their impacts on daily reference evapotranspiration (ET_o) estimates using the Penman‐Monteith FAO-56 (PMF-56) method were tested under cool arid and semi-arid conditions in Iran. The results indicated that the average increase in accuracy of the ET_o estimates by the calibrated R_S models, quantified by the decrease in RMSE, was 2.8% and 6.4% for semi-arid and arid climates, respectively. Mean daily deviations in the estimated ET_o by the calibrated R_S equations in semi-arid climates varied from ?0.283?mm/d^-1 for the Glover‐McCulloch model to 0.080?mm/d for the El-Sebaii model, with an average of ?0.109?mm/d^-1, and in arid climates, they ranged from ?0.522?mm/d^-1 for the Samani model to 0.668?mm/d for the El-Sebaii model, with an average of 0.125?mm/d^-1.

Editor D. Koutsyiannis; Associate editor Not assigned