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In the present paper, daily weather data from five weather stations in Iran were used for modeling ET0. The data sample consisted of daily maximum and minimum air temperatures (Tmax and Tmin, respectively), relative humidity (RH), wind speed (SW) at 2 m above land surface, and solar radiation (RS) covering a period of 6 years (from January 2003 to December 2008). The complete information of the studied weather stations as well as the average values of the considered meteorological parameters is given in Table 1. Also, Table 2 sums up the temporal variations of ET0 values in the studied stations. From both tables the spatial and temporal variations of the ET0 values (in terms of global average and standard deviation values) are observed. Due to the absence of experimental measurements, ET0 values calculated according to FAO56-PM equation were considered as the targets for the ANFIS/ANN implementation and evaluation, which is an accepted and very common practice in this situation, in agreement with the FAO recommendation (Allen et al. 1998). The considered input combinations used to feed the ANFIS/ANN models in the present paper are

Table 1

Summary of the studied weather stations (locations and meteorological parameters)

UTM coordinateMeteorological parameters
Stationφ (°N)τ (°E)z (m)Tmean (°C)ΔT (°C)RH (%)SW (m/s)RS (MJ/m2d)ET0 (mm/day)
Bojnurd 37.28 57.16 1,112 13.5 12.9 87.9 2.4 16.7 3.1 
Quazvin 36.15 50.3 1,279.2 14.5 14.4 78.3 1.9 18.3 3.8 
Shiraz 29.32 52.36 1,484 18.4 16 60.1 2.2 20.3 4.1 
Tehran 35.41 51.19 1,190.8 18.6 10 73.8 3.2 15.3 3.4 
Zanjan 36.41 48.29 1,665 11.5 14 63.1 3.2 16.6 3.1 
Average 15.3 13.46 72.64 2.58 17.44 3.5 
Standard deviation 3.11 2.23 11.34 0.59 1.92 0.44 
UTM coordinateMeteorological parameters
Stationφ (°N)τ (°E)z (m)Tmean (°C)ΔT (°C)RH (%)SW (m/s)RS (MJ/m2d)ET0 (mm/day)
Bojnurd 37.28 57.16 1,112 13.5 12.9 87.9 2.4 16.7 3.1 
Quazvin 36.15 50.3 1,279.2 14.5 14.4 78.3 1.9 18.3 3.8 
Shiraz 29.32 52.36 1,484 18.4 16 60.1 2.2 20.3 4.1 
Tehran 35.41 51.19 1,190.8 18.6 10 73.8 3.2 15.3 3.4 
Zanjan 36.41 48.29 1,665 11.5 14 63.1 3.2 16.6 3.1 
Average 15.3 13.46 72.64 2.58 17.44 3.5 
Standard deviation 3.11 2.23 11.34 0.59 1.92 0.44 

φ: latitude; τ: longitude; z: altitude with respect to sea level; Tmean: daily mean air temperature; ΔT: difference between maximum and minimum air temperature; RH: relative humidity; SW: wind speed at 2 m height above ground surface; RS: solar radiation; ET0: daily FAO56-PM evapotranspiration.

Table 2

Temporal variations of ET0 values per test year of each station

BojnurdQuazvinShirazTehranZanjan
Annual ET0 (mm/year) 
2003 1,013.13 1,338.25 1,499.43 1,204.93 1,441.52 
2004 1,134.51 1,341.50 1,526.98 1,220.14 1,437.47 
2005 1,008.16 1,357.14 1,473.85 1,216.15 1,438.52 
2006 1,181.49 1,409.29 1,487.29 1,271.38 1,418.93 
2007 1,120.45 1,331.19 1,466.74 1,231.44 1,351.84 
2008 1,130.24 1,450.56 1,535.58 1,302.59 1,460.82 
Average 1,097.99 1,371.32 1,498.31 1,241.10 1,424.85 
Standard deviation 70.88 47.98 28.03 37.84 38.16 
BojnurdQuazvinShirazTehranZanjan
Annual ET0 (mm/year) 
2003 1,013.13 1,338.25 1,499.43 1,204.93 1,441.52 
2004 1,134.51 1,341.50 1,526.98 1,220.14 1,437.47 
2005 1,008.16 1,357.14 1,473.85 1,216.15 1,438.52 
2006 1,181.49 1,409.29 1,487.29 1,271.38 1,418.93 
2007 1,120.45 1,331.19 1,466.74 1,231.44 1,351.84 
2008 1,130.24 1,450.56 1,535.58 1,302.59 1,460.82 
Average 1,097.99 1,371.32 1,498.31 1,241.10 1,424.85 
Standard deviation 70.88 47.98 28.03 37.84 38.16 
where Ra is the extraterrestrial radiation (mm/day). These inputs are required for the application of the well-known Hargreaves–Samani (Hargreaves & Samani 1985) and Turc (Turc 1961) empirical models, respectively. Input combination (1) was selected because it only requires temperature records. Input combination (2) might allow assessment of the combined effect of RH and RS on ET0 in comparison to (1). It must be pointed out that the higher accuracy of AI methods over their corresponding empirical equations has been widely demonstrated (e.g., Landeras et al. 2008; Shiri et al. 2012, 2013a; Pour Ali Baba et al. 2013). Thus, the mentioned empirical equations will not be assessed in this study.

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