Advances in Applied Agricultural Sciences 2 (2014); 11: 14-27
Assessment of different equations to estimate potential evapotranspiration versus FAO Penman Monteith method
Mohammad Valipour 1*
1 Department of Water Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
This study aims to assess mass transfer-based models versus the FAO Penman-Monteith model to detect the best model using linear regression under different weather conditions. For this purpose, weather data were gathered from 181 synoptic stations in 31 provinces of Iran. The potential evapotranspiration was estimated using 11 mass transfer-based models and was compared with the FAO Penman-Monteith model. The results showed that the Albrecht model estimates the potential evapotranspiration better than other models in the most provinces of Iran (23 provinces). The best values of R2 were 0.9854 and 0.9826 for the Brockamp-Wenner and Albrecht models in Bushehr (BU) and TE provinces, respectively. Finally, a list of the best performance of each model has been presented. The best weather conditions (not only for Iran but also for all countries) to use mass transfer-based equations are 23.6-24.6 MJ/m2/day, 12-26 ℃, 18-30 ℃, 5-21 ℃, and 2.50-3.25 m.s-1 (with the exception of Penman) for solar radiation, mean, maximum, and minimum temperature, and wind speed, respectively. Results are also useful for selecting the best model when researchers must apply temperature-based models on the basis of available data.
Evapotranspiration, FAO Penman Monteith, Humidity, Iran, Linear regression, Mass transfer
High precision measurements of actual evapotranspiration are obtained using lysimeter (Allen et al., 2011; Banihabib et al., 2012; Xu and Chen, 2005; Valipour et al. 2013) or imaging techniques (Allen et al., 2007; Allen et al., 2011; Hart et al., 2009; Rahimi et al., 2014; Tian et al., 2012; Tian et al., 2013), the costs of which are very high. Thus, the FAO Penman-Monteith model (Allen, et al., 1998) has become one modelling approach to estimate the potential evapotranspiration. Although, the FAO Penman-Monteith (FPM) has been applied in various regions of the world (Chiew et al., 1995; Estevez et al., 2009; Ley et al., 2009; Moeletsi et al., 2013; Valipour, 2012; 2013a,b,c), its application requires many parameters which are often difficult to obtain. To this end, experimental models have been developed for estimation of the potential evapotranspiration using limited data. They include mass transfer, radiation, temperature, and pan evaporation-based models. The mass transfer-based model is one of the most widely used models to estimate potential evapotranspiration. The common mass transfer-based models include Papadakis (Papadakis, 1966), Rohwer (Rohwer, 1931), Dalton (Dalton, 1802), Ivanov (Romanenko, 1961), Meyer (Meyer, 1926), Trabert (Trabert, 1896), and WMO (WMO, 1966).
Azhar and Perera (2011) calibrated the Meyer model as well as 9 other (temperature and radiation-based) models under Southeast Australian Conditions successfully. Acheampong (1986) considered the Penman, Thornthwaite, and Papadakis models for the estimation of the potential evapotranspiration for Ghana. Under the varying weather and climatic conditions over the country, the modified Penman method was found to be most suitable for estimating the potential evapotranspiration for Ghana. More examination of the performance resulted in the following rank of preciseness as compared with the FPM estimates: Priestley-Taylor, Makkink, Hargreaves, Blaney-Criddle, and Rohwer (Xu and Singh, 2002). Adjusted Dalton model gives the better estimation of the potential evapotranspiration compared with adjusted Penman-Monteith model for the Kendall subwatershed located in Tucson, Arizona (Rim, 2000). The top six ranked methods obtained for the average as well as for central Saudi Arabia ratings are ranked in the following order of merit: Jensen-Haise, class A pan, Ivanov, adjusted class A pan, Behnke-Maxey, and Stephens-Stewart (Al‐Sha’lan and Salih, 1987). Zhai et al. (2010) calibrated the Hargreaves, Makkink, Turc, Priestley–Taylor, Jensen–Haise, Doorenbos-Pruitt, Abtew, McGuinness-Bordne, Rohwer, and Blaney–Criddle. It can be concluded that calibration can be used to modify the potential evapotranspiration equations with multi-station data to improve the preciseness of the potential evapotranspiration estimates in northwest China. Singh and Xu (1997a) evaluated the Meyer, Dalton, and Rohwer for determining free water evaporation at four climatological stations in north-western Ontario, Canada. The results of comparison showed that all equations were in reasonable agreement with observed evaporation. Jakimavicius et al. (2013) compared the Dalton, Trabert, Meyer, WMO, Mahringer, Thornthwaite, Schendel, Hargreaves-Samani, Irmak, and Kay-Davies models. The study revealed that the Thornthwaite and Schendel gave the most precise assessment in estimating the evaporation from the Curonian Lagoon, Baltic. Bormann (2011) compared the Dalton, Trabert, Meyer, WMO, and Mahringer models with some of other temperature and radiation-based models to analyze climatic change in Germany. He showed significant difference between performances of all models.
In the previous studies, one or more of the mass transfer-based models have been compared with temperature, radiation, or pan evaporation-based models and in the most of the cases, other models (temperature, radiation, or pan evaporation-based models) estimated the potential evapotranspiration better than the mass transfer-based models. Because the previous studies focus on specific (humid, arid, semiarid, etc) weather conditions (that they aren’t suitable for applying the mass transfer-based model) and/or didn’t consider many methods of mass transfer-based models. Moreover, the results of previous studies are not useable for estimation of the potential evapotranspiration in other regions. Because they were recommended for one or more climatic conditions, but a climatic condition contains a wide range of magnitude of each weather parameter (e.g. temperature, relative humidity, wind speed, solar radiation, etc.) and results of each research (for a region with specific weather variations) is not applicable for other regions without determining specified ranges of each weather parameter even if climatic conditions (e.g. humid, arid, semi-arid, temperate, etc.) are identical for both regions. In addition, the governments cannot schedule for irrigation and agricultural water management when the potential evapotranspiration is estimated for a basin, wetland, watershed, or catchment instead a state or province (different parts of them are located at more than one state or province) and/or number of weather station used is low (increasing uncertainity). Since, this study aims to estimate the potential evapotranspiration for 31 provinces of Iran (considering various weather conditions and useful for long-term and macroeconomic policies of governments) using average data of 181synoptic station (decreasing uncertainity) and by 11 mass transfer-based models to determine the best model based on the weather conditions of each province (for which ranges of weather parameters have been determined to use other regions and next researches).
Table 1. Position of all provinces and synoptic stations
Number of Station
Chaharmahal and Bakhtiari (CB)
East Azerbaijan (EA)
Kohgiluyeh and Boyer-Ahmad (KB)
North Khorasan (NK)
Razavi Khorasan (RK)
Sistan and Baluchestan (SB)
South Khorasan (SK)
West Azerbaijan (WA)
Table 2. Model used and parameters applied in each model
Allen et al. (1998)
Brockamp and Wenner (1963)
ETo is the reference crop evapotranspiration (mm/day)
Rn is the net radiation (MJ/m2/day)
G is the soil heat flux (MJ/m2/day)
γ is the psychrometric constant (kPa/℃)
es is the saturation vapour pressure (kPa)
ea is the actual vapour pressure (kPa)
Δ is the slope of the saturation vapour pressure–temperature curve (kPa/℃)
T is the average daily air temperature (℃)
u is the mean daily wind speed at 2 m (m/s)
H is the elevation (m), φ is the latitude (rad)
Tmin is the minimum air temperature (℃)
Tmax is the maximum air temperature (℃)
RH is the average relative humidity (%)
n is the actual duration of sunshine (hr)
Rs is the solar radiation (MJ/m2/day)
ema is the saturation vapour pressure at the monthly mean daily maximum temperature (kPa)
Materials and Methods
In this study, weather information (from 1986 to 2005) has been gathered from 181 synoptic stations of 31 provinces in Iran (without data gaps). Table 1 shows position of each province and number of stations.
In each station, average of weather data in years measured has been considered as value of that weather parameter in each month (e.g. value of relative humidity in July for North Khorasan (NK) is average of 20 data gathered). Finally, average of data in all stations has been considered as value of that weather parameter in each month for provinces with more than one station (e.g. value of relative humidity in July for KH is average of 20×14=280 data gathered). All of the data mentioned have been used to estimate the potential evapotranspiration using 11 mass transfer-based models and were compared with FPM model to determine the best model based on the weather conditions of each province (Table 2).
The best model for each province and the best performance of each model were determined using the coefficient of determination:
In which, i indicates month, ETFPM indicates the potential evapotranspiration calculated for FPM model, and ETm indicates the potential evapotranspiration calculated for mass transfer-based models.
Finally, map of annual average of solar radiation, mean, maximum, and minimum temperature, relative humidity, and wind speed were provided and the best performance of each model based on these values was determined. Furthermore, the map of the best model for each province and the map of the error calculated for each province have been presented.
Results and Discussion
Estimating the potential evapotranspiration for 31 provinces of Iran
Table 3 shows the errors for each model and province. According to the R2-values, each model estimates the potential evapotranspiration for only one or few provinces with very high accuracy. In the other words, preciseness of estimating by mass transfer-based models is very sensitive to variations of the parameters used in each model (Table 2).
Comparison of the best models for each province
Figure 1 compares the potential evapotranspiration using FPM with values estimated using the best method (based on Table 3) for each province.
According to Fig. 1 the Brockamp-Wenner for BU (R2=0.9854) yielded the best the potential evapotranspiration as compared to that from the FPM. However, the Albrecht has been introduced as the best model in the most of provinces (23 provinces). In general, mass transfer-based models are more suitable (R2 more than 0.97) for BU, HO (near the Persian Gulf), SK, KE, SB (south east of Iran) and TE, GI, and ES (south of Iran). However, according to Table 3, variations of the errors (the worst and best R2) for different models are too high in all provinces; e.g. CB (0.839 and 0.9671 for the Penman and Albrecht, respectively), BU (0.8932 and 0.9854 for the Papadakis and Albrecht, respectively), SB (0.8846 and 0.9775 for the Papadakis and WMO, respectively), and HO (0.8083 and 0.9742 for the Ivanov and Albrecht, respectively). These values indicate very different performance of the mass transfer-based models for a specific weather condition in each province. For instance, the Ivanov model estimates the potential evapotranspiration with the least R2 for HO and the greatest R2 for EA than the other models. However, according to Table 2, the Ivanov model is a function of mean temperature and relative humidity, the Papadakis is a function of minimum and maximum temperature and relative humidity, and the other models are a function of mean, minimum, and maximum temperature, relative humidity, and wind speed. In addition, the only difference among the Albrecht, Dalton, Meyer, Rohwer, and WMO models is coefficients used in each model (Table 2) as well as the only difference among the Brockamp-Wenner, Mahringer, and Trabert models is also coefficients used in each model (Table 2). Thus we must use them according to their best weather conditions (with the most accuracy).
Table 3. Error of model calculated for each province
Al. is Albrecht, BW is Brockamp-Wenner, Da. is Dalton, Iv. is Ivanov, Ma. is Mahringer, Me. is Meyer, Pa. is Papadakis, Pe. is Penman, Ro. is Rohwer, and Tr. is Trabert, the underlines show the best value of each method and the bolds show the best value of each province
Distinguishing various regions based on weather conditions
The maps of annual average of the weather parameters have been provided to detect the best conditions (range of weather parameters) that each model estimates the potential evapotranspiration with maximum preciseness (Figs. 2 and 3).
Fig. 2 shows annual average of solar radiation and mean, maximum, and minimum temperature in all 31 provinces of Iran and Fig. 3 shows annual average of relative humidity and wind speed in all 31 provinces of Iran. As shown, value of solar radiation is more than 25.0 MJ.m-2.day-1 for south of Iran, it is from 24.0 to 25.0 MJ.m-2.day-1 for centre of Iran, and it ranges less than 24.0 MJ.m-2.day-1 for north of Iran. The mean temperature is less than 14 ℃ for North West of Iran, it is more than 24 ℃near the Persian Gulf, and it is from 14 to 24 ℃ for the other regions (with the exception of NK and CB). The maximum temperature is more than 28.5 ℃near the Persian Gulf, it is from 25.5 to 27.0 ℃ for desert provinces, it is less than 19.5 ℃ for North West of Iran, and it is from 19.5 to 25.5 ℃ for the other regions. The minimum temperature is more than 17 ℃ near the Persian Gulf, it is less than 7 ℃ for North West of Iran, it is from 11 to 15 near the Caspian Sea, and it is from 7 to 13 ℃ for the other regions (with the exception of CB, NK, KE). The relative humidity is from 65 to 70% near the Persian Gulf (with the exception of KH), it is from 50 to 65% for North West and north east of Iran (with the exception of AR), it is more than 70% near the Caspian Sea, and it is less than 45% for other regions.
Fig. 1. Comparison of evapotranspiration (mm/day) calculated using FAO Penman-Montieth (FPM) with the best model for each province
The wind speed is from 2.50 to 3.50 m.s-1 for south east of Iran and near the Persian Gulf, and it is from 1.25 to 2.75 m.s-1 for the other regions (with the exception of EA, AR, GO, and CB). The mass transfer-based models estimated the potential evapotranspiration in the south (near the Persian Gulf) and south east of Iran (annual relative humidity 65-70% and <35%, respectively) better than other provinces (Fig. 1). Therefore, the provinces of Iran are divided into five categories (at least); (I) the provinces of near the Persian Gulf (KH, BU, and HO), (II) the provinces of near the Caspian Sea (GI, MZ, and GO), (III) the provinces of north east of Iran (WA, EA, AR, and ZA), (IV) CB (due to the difference weather conditions than the near provinces), and (V) the other provinces. These categories are useful for future studies over Iran.
Fig. 2. Average annual variations of solar radiation, mean temperature, maximum temperature, and minimum temperature in Iran
Fig. 3. Average annual variations of relative humidity and wind speed in Iran
Table 5. The best range to use the models based on the results of current study
T is the average daily air temperature (℃), u is the mean daily wind speed at 2 m (m/s), Tmin is the minimum air temperature (℃), Tmax is the maximum air temperature (℃), and RH is the average relative humidity (%)
Fig. 4. The best model for each province and their error
Determining range of weather parameters for the best models
The maps of annual average of weather parameters (Figs. 2 and 3) are useful not only for the mentioned categories but also for determining the range of each parameter for which the best preciseness of the mass transfer-based models is obtained (Table 4).
According to Table 4, the best performance of the Brockamp-Wenner, Mahringer, Meyer, Trabert, and WMO models is in similar weather conditions (T=24-26 ℃, Tmax=28.5-30.0 ℃, Tmin=19-21 ℃, RH=65-70%, and u=3.00-3.25 m.s-1). However, the preciseness of them is different (e.g. 0.9783 and 0.9854 for the WMO and Brockamp-Wenner models, respectively). This underlines the important role of selection of the best model for a specified weather conditions. Furthermore, we can see different ranges in the Albrecht, Dalton, Ivanov, Penman, Rohwer, and Papadakis models (Table 4). Therefore, we can use the mass transfer-based models for other regions (in other countries) based on Table 4 with respect to their errors. The best weather conditions to use mass transfer-based equations are 23.6-24.6 MJ/m2/day, 12-26 ℃, 18-30 ℃, 5-21 ℃, and 2.50-3.25 m.s-1 (with the exception of Penman) for solar radiation, mean, maximum, and minimum temperature, and wind speed, respectively. Results are also useful for selecting the best model when researchers must apply temperature-based models on the basis of available data.
Comparison of the best models with their errors for each province
Figure 4 was plotted to detect the best model for each province versus its error (after calibration).
First, although the Albrecht model is the most useful model for provinces of Iran (23 provinces), but it is not suitable for 2 of the categories (near the Persian Gulf and north east of Iran) and east of Iran (NK, RK, SK, and SB). This confirms that the categories are reliable and these 2 categories need to more attention due to specific weather conditions. Moreover, preciseness of the Albrecht model is less than 0.98 in 18 provinces of Iran. It reveals that the Albrecht model is a general model for estimating the potential evapotranspiration (high application and fair preciseness). Thus, we need to other temperature, radiation, and pan evaporation-based models to estimate the potential evapotranspiration in these 18 provinces. For instance, values of solar radiation is more than 25.0 MJ.m-2.day-1 for FA and KB, hence the radiation-based models may be useful for these provinces (Bakhtiari et al., 2010; Fooladmand, 2008; Fooladmand, 2011; Sepaskhah 1999). It reveals that only if we use the mass transfer-based models for suitable (based on Table 4) and specific (based on Figs. 2 and 3) weather conditions, the highest preciseness of estimating will be obtained.
In this study, 11 mass transfer-based models were used to estimate the potential evapotranspiration in 31 provinces of Iran.
The preciseness of estimating by mass transfer-based models is very sensitive to variations of the parameters used in each model.
The best values of R2 were 0.9854 and 0.9826 for the Brockamp-Wenner and Albrecht models in BU and TE provinces, respectively.
The provinces of Iran are divided into five categories (at least); the provinces of near the Persian Gulf (KH, BU, and HO), the provinces of near the Caspian Sea (GI, MZ, and GO), the provinces of north east of Iran (WA, EA, AR, and ZA), CB (due to the difference weather conditions than the near provinces), and the other provinces. These categories are useful for future studies over Iran.
We can use the mass transfer-based models for other regions (in other countries) based on ranges of each weather parameters for the best models with respect to their errors.
Only if we use the mass transfer-based models for suitable and specific weather conditions (based on weather conditions and the categories), the highest preciseness of estimating will be obtained.
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