1 Introduction

Crop reference evapotranspiration (ET0) is an important element for estimating crop water requirement and an important variable in the agro hydrological system. Accurate and consistent estimate of ET0 in irrigated agriculture is needed for agricultural water management and for using water resources efficiently. Actual crop evapotranspiration can be derived from ET0 by means of proper crop and water stress coefficients (Rana and Katerji 2000; Kite and Droogers 2000). Direct measurement of ET0 is not easy and needs more time and cost. Therefore, in most situations, ET0 is estimated from meteorological parameters. Numerous methods exist to estimate ET0 (e.g. Penman 1948; Blaney and Criddle 1950; Hargreaves and Samani 1985; FAO-56 Penman-Monteith 1998). Among this method FAO-56 PM is considered to be the most appropriate model to predict ET0. The American Society and Civil Engineers (ASCE) recommended the use of the ASCE- Penman- Monteith method, as simplified by FAO Paper No. 56 (Allen et al. 1998), to estimate ET0. Itenfisu et al. (2003) concluded this method provides a consistent basis for objectively assessing the relative performance of ET0 equations over a variety of climates.

Sensitivity analysis is an essential task to determine the expected change in ET0 in response to a known change in meteorological variables. McCuen (1973) was one of the pioneer researchers, who investigated the sensitivity of various evaporation models to change in weather parameters on evaporation rates and the effect of meteorological measurements errors. Several studies have carried out on sensitivity of ET0 to weather parameters (Saxton 1975; Ley et al. 1994; Rana and Katerji 1998; Goyal 2004). But the most of them conducted in a single station and fewer studies on regional and seasonal behavior of the sensitivity of ET0 have been done.

Beven (1979) investigated the sensitivity of estimates of actual crop evapotranspiration (ETa) to errors in input data of the three stations across England and Wales. Beven found that in humid temperate region, the sensitivity of Penman-Monteith estimates of ETa to different input data and parameters is more sensitive to the values of the aerodynamic and canopy resistance parameters that introduce the influence of vegetation type into the predictions.

Singh and Xu (1997) investigated the influence of data errors on evaporation computed by mass transfer-based equation in the State of Vaud in Switzerland. They added 5, 10 and 20 % of systematic and random errors to original data and evaluated the change in evaporation. They found that evaporation is sensitive to vapor pressure gradient, less sensitive to wind speed and most insensitive to air temperature data. Systematic errors in vapor pressure data influenced evaporation inversely to the same magnitude for both monthly and daily time scales. They found that evaporation estimates are more sensitive to random data errors in the monthly time scale. Systematic errors in wind speed and temperature data affect evaporation inversely to the magnitude of about a half and a quarter of the magnitude of the influence of vapor pressure errors, respectively. Systematic errors in vapor pressure data influenced evaporation estimates inversely to more or less the same magnitude.

Goyal (2004) studied the sensitivity of ET0 to change in four climatic parameters (i.e. Tmean, Rn, u2 and ea) within a range of ±20 % in Rajasthan (India). Goyal found that increase in mean air temperature by 20 % (maximum 8 °C) cause ET0 to be increased by 14.8 % in the study area. ET0 found to be less sensitive (11 %) to increase in Rn. Increase in ea (20 %) had a small negative effect (say about −4.3 %) on ET0. Gong et al. (2006) studied the sensitivity of ET0 calculated from the FAO-56 PM to change in climatic variables in the Changjiang (Yangtze River) basin. They found that relative humidity was the most sensitive variable followed by radiation, air temperature and wind speed. Irmak et al. (2006) conducted a sensitivity analysis in the different climatic regions of USA. They used daily time scales and found that ET0 was most sensitive to vapor pressure deficit (VPD) at all regions. In semi-arid regions ET0 was most sensitive following VPD in summer months.

Estevez et al. (2009) conducted the sensitivity analysis to assess the impact of climatic parameters on reference crop evapotranspiration calculated by Penman-Monteith equation in Spain. They selected four climatic variables namely mean air temperature, relative humidity, solar radiation and wind speed from 1996 to 2006. They added random and systematic errors to meteorological data to obtain ET0 deviations. Results indicated that the effect of introduced random errors was larger than that of the systematic errors. They found that using positive errors in RH resulted in ET0 underestimations, but positive errors in the three mentioned variables resulted in ET0 overestimations. Liu et al. (2010) analyzed the sensitivity of ET0 calculated by Penman-Monteith method to meteorological variables in Yellow River basin, China. They used air temperature, solar radiation, relative humidity and wind speed as key climatic parameters for this purpose. They reported that ET0 is sensitive to different variables in different locations of the Yellow River Basin. They also found that in general Rs (Solar Radiation) was the most sensitive variable for ET0 followed by RH, Tmean and wind speed in the basin scale.

Zhang et al. (2010) studied the sensitivity of ET0 obtained from the FAO-56 PM method to change in climatic variables in Shiyang river basin of northwest China. They found that actual vapor pressure, ea, is the most sensitive variable in cool months and in mountainous area, but minimum air temperature, Tmin, is the least sensitive parameter during the year. Dinpashoh (2006) has estimated ET0 for Iran and applied appropriate method for three distinct areas of Iran according to the ratio of precipitation to ET0. Although ET0 values were computed by him based on corrected Tmean for non-ideal condition, but, he did not analyze the sensitivity of ET0 for weather parameters. Bakhtiari and Liaghat (2011) investigated seasonal sensitivity for climatic variables of ASCE Penman-Monteith model in Kerman. Eslamian et al. (2011) studied effects of variation in climatic parameters on evapotranspiration in five area of Iran (including Tehran, Mashhad, Isfahan, Tabriz and Shiraz). Their results showed temperature and relative humidity is the most sensitive parameters in Penman-Montieth method respectively. They did not investigate the effect of Rn (net radiation at crop surface) on ET0.

There is no detailed study on sensitivity of ET0 to key climatic parameters in different scenarios at the selected station of Iran. However, very little information is available on the sensitivity of ET0 in some part of Iran (Eslamian et al. 2011). Also, global warming cause major changes in various meteorological variables. On the other hand, meteorological variables have interaction effect on each other. Therefore, sensitivity analysis of ET0 is essential to better manage the available water resources. These resources in Iran have reduced due to drought in recent years. Therefore, the three main objectives of this study are: (i) to estimate ET0 at the selected station using FAO-56 PM method, (ii) to analyze the sensitivity of ET0 to some key meteorological variables in different scenarios at all stations and (iii) to compare findings of the present study with those of others.

2 Material and Methods

2.1 Study Area

The study area encompasses the whole Iran country. The area of Iran is about 1,650,000 Km2 located approximately between 25°00′ N and 38°39′ N in latitudes and between 44°00′ E and 63°25′ E in longitudes. Due to vast area of Iran, different types of climates can be found. Generally, Iran is categorized as having arid and semi-arid climates based on Köppen climatic classification (Allen et al. 1998). The mean annual precipitation of Iran is about 224 mm. For this study, eight stations namely Abadan, Anzali, Chabahar, Isfahan, Sabzevar, Sanandaj, Tabriz and Zahedan were selected from different types of climates. Figure 1 shows the location of the selected stations in Iran and the details of the selected stations were presented in Table 1. The stations have their own meteorological station.

Fig. 1
figure 1

Study area and location of stations

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Table 1 Details of the selected stations of Iran
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Monthly meteorological data of the selected stations were collected from Islamic Republic of Iran Meteorological Organization (IRIMO) in the period of 1965 to 2005. Quality of data was checked prior to the analyzed and missing data was reconstructed. In this study, mean, maximum and minimum air temperature, relative humidity, wind speed at 10 m height above the ground surface and number of sunshine hours in monthly time scale were used. These data were converted to the standard form of the input parameters of FAO-56 PM ET0 model.

2.2 Calculation of the Reference Crop Evapotranspiration (ET0)

The FAO-56 PM model for estimating ET0 (Allen et al. 1998) is as follows:

$$ E{T}_o=\frac{0.408\varDelta \left({R}_n-G\right)+\gamma \frac{900}{T_{mean}+273}{u}_2\left({e}_s-{e}_a\right)}{\varDelta +\gamma \left(1+0.34{u}_2\right)} $$
(1)

where ET0 is reference crop evapotranspiration (mm.day−1), Δ is the slope of vapor pressure versus temperature curve at temperature Tmean (KPa.°C−1), γ is the psychrometric constant (KPa.°C−1), u2 is the wind speed at a 2 m height (m.s−1), Rn is the net radiation at crop surface (MJ.m−2.d−1), G is the soil heat flux density (MJ.m−2.d−1), T is the mean daily air temperature at 2 m height (°C), and (es-ea) is the saturation vapor pressure deficit (KPa).

2.3 Sensitivity Analysis

The sensitivity of ET0 in each month to the four key climatic variables including Tmean, actual vapor pressure (ea), u2 and Rn were investigated in all selected stations. For this purpose, the parameters were changed within a range of −20 to +20 % at an interval of ±5 % (eight scenarios) and then the percent change of ET0 was calculated (Goyal 2014). Finally, the percent changes of the mentioned climatic parameters against percent changes of the output ET0 were plotted as a sensitivity curve. Sensitivity curves were plotted for all stations in annual and monthly time scales.

3 Results and Discussion

Figure 2 shows temporal pattern of Tmax, Tmean, Tmin, u2, sunshine hours in a month (n), percent of mean relative humidity (RH) and ET0 (mm/month) at five stations namely Abadan, Bandar Anzali, Chabahar, Esfahan and Sabzevar, in monthly time scale. The same plots for three other stations are shown in Fig. 3. According to Figs. 2 and 3, the air temperature pattern is almost the same for all the sites. It usually reaches to the maximum (minimum) value in July (January). The difference between Tmax and Tmin remain approximately constant for most of the stations (except Bandar Anzali and Chabahar). Bandar Anzali station experiences the largest value of Tmax-Tmin in July, which is the hottest month of Iran. This parameter declines to a minimum values at January, which is the coldest month of Iran. This station is known as a humid station located in the shore of Caspian Sea having the largest amount of annual precipitation across the country (Dinpashoh et al. 2004).

Fig. 2
figure 2

Temporal pattern of meteorological parameters in the case of five stations. Note: the left column indicate ET0, Sunshine hours and RHmean. Middle column indicate Tmax, Tmean and Tmin. Right column shows WS (u2) Panels 1–5 are for Abadan Bandar Anzali, Chabahar, Isfahan and Sabzevar stations, respectively

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Fig. 3
figure 3

Temporal pattern of meteorological parameters. Note: explanation is same as in Fig. 2. The first, 2nd and 3rd panel are for Sanandaj, Tabriz, and Zahedan, respectively

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The temporal pattern of u2 is not the same for all the selected stations (Figs. 2 and 3). The maximum value of wind speed in all stations is about 3.6 (m/s) in Abadan in June and in contrast, the minimum value of u2 belonged to Esfahan (~0.78 m/s) in December. The largest difference between the highest and lowest value of u2 in a year belonged to the Tabriz (~2.1 m/s) following Abadan (~1.9 m/s) and Sabzevar (~1.8 m/s). Figures 2 and 3 show the pattern of n, RH and ET0 (mm/month). The pattern of n is nearly similar to the air temperature. All stations (except Chabahar) experienced the maximum (minimum) amount of n at summer (winter). On the other hand, most of the stations experienced the lowest (highest) value of mean RH in summer (winter).

The pattern of ET0 is nearly similar to the air temperature and sunshine hours. The lowest value of ET0 mainly occurs in the coldest month of winter (i.e. January), while the highest value occurs in the hottest month of summer (i.e. July). Generally, ET0 values gradually increases from January and reaches to the maximum amount in July. It declines and reaches to the lowest value in December. The pattern of ET0 is same for all stations except Chabahar. This coastal station which is located at the south east of Iran, is mainly affected by monsoon system comes from the Bay of Bengal and Pakistan to Iran from June to October. Such variation in the meteorological parameters of Chabahar in monsoon season causes ET0 to be starting to decrease about 2 months early.

3.1 Results of the Sensitivity Analysis

Figure 4 shows the curves of the sensitivity analysis of ET0 obtained by FAO-56 PM model for each of the weather parameters in the selected stations in annual time scale. Sensitivity curves of ET0 to climatic variables are generally linear. Also, the slope of lines for sensitivity of ET0 to ea is negative for all stations. According to Fig. 4, at six stations including Abadan, Chabahar, Sabzevar, Sanandaj, Tabriz and Zahedan the most sensitive variable on ET0 is Tmean. At Bandar Anzali and Isfahan, ea and Rn are the most sensitive variable, respectively. On the other hand, ea is the less sensitive variable on ET0 at Abadan, Isfahan, Sabzevar, Sanandaj, Tabriz and Zahedan. At Bandar Anazali and Chabahar, WS is the less sensitive variable.

Fig 4
figure 4

Percent changes in ET0 with respect to changes in climatic variables in annual time scale

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In response to the increase Tmean by +20 %, the larger and less value of percent change in ET0 are about 16.7 % and 10.3 % at Chabahar and Isfahan, respectively. Change in actual vapor pressure had a large effect on ET0 at Bandar Anzali as a representative of humid climatic station of Iran. But, ET0 was found to be less sensitive to change in ea in Isfahan as a representative of arid climate station. WS had a less effect on ET0 in all stations as, 20 % increase in WS cause to ET0 increase just about 8.8 % in Abadan. Unlike WS, Rn approximately had a more effect on ET0 at all stations.

Table 2 shows the value of percent change in ET0 in monthly time scale for all climatic stations. In this Table, the four months namely January, April, July and October are selected to represent winter, spring, summer and autumn, respectively. As can be seen in Table 2, each parameter in annual time scale had the greatest impact on ET0, has the greatest impact in monthly time scale.

Table 2 Estimated ET0 in response to increase in climatic variables by 20 %
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According to Table 2, Tmean has larger effect on ET0 during autumn months in all selected stations. On the other hand, ET0 in the summer months is more sensitive to Tmean compared to winter months at all of the eight selected stations. In winter, the air temperature is too low for growing crops and pasture. Therefore, winter’s ET0 is not important from the view of crop production in Iran. Sensitivity of ET0 to change in ea is more pronounced in summer comparing winter (except Chabahar). Although actual vapor pressure (ea) in FAO-PM model is an exponential function of air temperature, a large increase in ET0 is expected for an increase in Tmean at all station (except Chabahar) during summer months. Sensitivity of ET0 in winter months to WS is less than that in summer months at all stations except Bandar Anzali and Chabahar. At two stations, sensitivity of ET0 to WS in winter months is more than summer months. During spring months, sensitivity of ET0 to change in Rn is pronounced at most of stations.

In this study, we investigated the interaction parameters in different scenarios on ET0 at all stations in monthly and annual time scale. Because in fact all meteorological parameter are independent, have effect to each other and change at the same time. Table 3 and 4 presents the percentage change in ET0 for a scenario of 10 % and 20 % increase in Tmean and WS and 10 % and 20 % decrease in ea respectively.

Table 3 Estimated ET0 in response to increase in Tmean and WS by 10 % and decrease in ea by 10 %
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Table 4 Estimated ET0 in response to increase in Tmean and WS by 20 % and decrease in ea by 20 %
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According to Table 3, in annual time scale increasing Tmean and WS by 10 % and decreasing ea by 10 % yielded ET0 increasing 16.9 % at Chabahar. But, if the change is 20 % causes ET0 increasing about 36.4 %. Also, in monthly time scale 10 % increase in Tmean and WS as well as 10 % decrease in Rn yielded ET0 to be increase to about 30.5 % in December at Bandar Anzali.

The results of this study showed change in ET0 with respect to change in climatic variables varied by month and station. Irmak et al. (2006) found increase in ET0 with respect to increase in climatic variable changed by month. Also Eslamian et al. (2011) reported the effective climatic variables on evapotranspiration are changing, though in each region the variables have significant long-term trends and persistence.

According to Irmak et al. (2006) in summer months ET0 was most sensitive to Tmax at Bushland, Scottsbluff and Twitchell, located in USA whereas it was equally sensitive to both Tmax and solar radiation, Rs, at Clay Center of USA. Zhang et al. (2010) found that Tmean is the least sensitive variable to ET0 variation in Shiyang river basin of northwest China. The change of Tmean has slightly less effect on ET0 computed by FAO-56 PM in winter season in Rajasthan, India as compared to summer season (Goyal 2004). This is consistent with our findings to all selected stations. Dinpashoh et al. (2011) reported an increasing wind speed trends at eastern Iran. Therefore, it can be concluded that increasing trends of ET0 at the east part of Iran is mainly due to the increasing trends of u2. Zhang et al. (2010) found that wind speed plays an important role in ET0 changes at northern parts of the Shiyang river basin of China. Goyal (2004) in Rajasthan, India reported increasing trend for ET0 with increase in Rn.

4 Conclusions

Although there is a few studies about evapotranspiration conducted in different region of Iran, however, none of them were analyzed the sensitivity of ET0 to weather parameters in different scenarios. In this study, 40 years climatic data was used and the sensitivity of ET0 to four key weather parameters namely Tmean, ea, u2 and Rn was analyzed at eight selected stations of Iran. The results showed that most portion of annual ET0 belongs to the summer months (June, July and August). On the other hand, in most part of Iran, the most of agricultural activities are done in summer months. Therefore, sensitivity analysis of ET0 would be more important in summer months comparing the winter months. Using the fixed values for the mentioned weather parameters and changing a certain climatic parameter by ± 5 %, ± 10 %, ± 15 % and ± 20 %, the percent change in ET0 computed for all months and years for selected stations. Results showed that ET0 is more sensitive to Tmean for most of the stations of Iran. ET0 is more sensitive to Tmean in summer months comparing winter months at all stations. It was found that nearly all parts of Iran exhibited increasing trends for Tmean (Dinpashoh et al. 2011). It is very important for decision makers to search ways for optimum water use techniques to face this problem. In contrast, ET0 is less sensitive to WS especially in summer months comparing winter months at six stations. Most parts of Iran will be face to lack of sufficient water for water related activities especially agriculture comparing past years. That is due to drought, high demand and global warming. These factors will cause changes in climatic parameters. On the other hand, changes in climatic parameters cause to change in ET0. Increasing the value of ET0 causes to increase demand for agricultural water. However, other factors such as available water, crop type, irrigation type and etc. also have effect on the agricultural water management. Furthermore, the population of Iran and standards of people sanitation will increase in future. Therefore, management and efficient use of water should be a priority in Iran.