>). Meteo station tracks and records air temperature, precipitation, wind speed, relative humidity, dew point and sun duration. The measurements are collected at 2.0 meter above the top of the vegetation.
Figure 1. Study area map.
Figure 2. Monthly temperature ranges and monthly precipitation at Karshi site, comparing the long-term data and measurements from the study period.
2.2. Evapotranspiration Estimation Methods
The FAO Penman-Monteith (PM) equation for calculating ETo can be expressed as  :
where EToPM is reference evapotranspiration (mm day−1), Rn is net radiation at the crop surface (MJ・m−2・day−1), G is soil heat flux density (MJ・m−2・day−1), Ta is mean daily air temperature at 2 meter height (˚C), U2 is wind speed at 2 meter height (m・s−1), es is saturation vapour pressure (kPa), ea is actual vapour pressure (kPa), ∆ is slope vapour pressure curve (kPa ˚C−1), γ is psychrometric constant (kPa・˚C−1).
The Hargreaves-Samani (HS) equation  requires less observations, with only Tmax (˚C) and Tmin (˚C) needed for calculation of reference evapotranspiration:
where 0.0135 is a factor for conversion from American to the International system of units, kRs is the radiation adjustment coefficient (the common value kRs = 0.17 is used), and Ta is average temperature of day.
2.3. Modification and Validation
To modify the HS equation, we calculated the bias correction factor using the formula suggested by Teutschbeina and Seiberta (2012)  . The formula calculates the bias correction factor divides mean monthly evapotranspiration obtained from the PM equation by mean monthly evapotranspiration obtained from the HS equation:
where MMCV is mean monthly climate variable. Weather data from 2011 to 2015 were used for calibration and weather data from 2016 and 2017 were used for validation of the model. Afterwards, the identified bias correction factors for each month were considered in estimation of ETo in HS method for 2016 and 2017. Consequently, statistical performance between the non-calibrated EToHS and EToHSm was checked.
2.4. Evaluation Criteria
For evaluating the results of HS and corrected HS methods, the root mean square error (RMSE), the relative error percentage (REP), coefficients of determination (R2) and index of agreement (d)  were used. The formulas of RMSE and index d are as follows:
where Pi is predicted values, Oi is observed values, O is average of Oi and n is the total number of data.
3. Results and Discussion
Figure 3 illustrates comparisons of estimated mean monthly ETo values using EToPM and EToHS methods during the years from 2011 to 2017. According to the results, the tendency and majority monthly mean values match up pretty well, with only the non-calibrated HS method underestimating ETo mainly in June, July and August, which contradicts outcomes by Lima et al. (2013)  , who found overestimates of ETo in HS method comparing to PM method in sub-humid regions of Brazil. In particular, research PM method indicates similar values of ETo in other months of compared years, when compared to PM method. The mean relative error percentage between EToPM and EToHS during the estimated years were 10%, 17% and 11% in June, July and August, respectively. In Karshi the estimated annual ETo for 2016 was 1573 mm with maximum (8.87 mm/day) and minimum (1.25 mm/day). A similar trend in ETo for the same period for northern part of Uzbekistan, Khorezm province was observed by Awan et al. (2011)  , where PM method provided slightly lower (1375 mm) long-term (1987-2005) annual ETo with maximum (7.36 mm/day) observed in July and minimum (0.64 mm/day) observed in January.
The relationship between daily EToPM and EToHS values from 2011 to 2017 (2016 and 2017 none calibrated) is demonstrated in Figure 4. According to estimations, the correlation between daily EToPM and EToHS is high with the
Figure 3. Comparison of the mean monthly EToPM and EToHS methods in Karshi steppe, Kashkadarya province, Uzbekistan during the years from 2011-2016.
Figure 4. Correlation between daily EToPM and EToHS methods in Karshi steppe, Kashkadarya province, Uzbekistan during the years for 2011 (a), 2012 (b), 2013 (c), 2014 (d), 2015 (e), 2016 (f), 2017 (g).
coefficients of determination (R2) of 0.88 in 2011, 0.91 in 2012, 0.89 in 2013, 0.86 in 2014 and 2015, 0.91 in 2016 and 0.88 in 2017, and p-values are less than 0.0001 which means the results are statistically significant. However, the method of HS underestimates the ETo value during the period from June to August in every year of observation, which can be seen in Figure 3. A similar trend for the same period were observed by Moeletsi et al. (2013)  , where PM and HS were compared in different environmental conditions in South Africa.
Table 1 demonstrates the results of statistical analyses of EToHS and EToHSm versus EToPM for estimating daily ETo during the years between 2011 and 2017. According to the results, the coefficient of determination and index of agreement between the variable is high in each year. However, the percentage of relative root mean square error is high and not acceptable.
Table 2 demonstrates the results of statistical analyses of EToHS and EToHSm versus EToPM for estimating monthly ETo during the years between 2011 and 2017. According to the results, the coefficient of determination and index of agreement between the variable is high (close to 1.0) in each year, which represents a high correlation between the variables. According to Stöckle et al. (2004)  , most obtained indexes of agreement and coefficients of determination exhibit good performance, which are in the range of 6 to 20 percent. Moreover, relative error percentage of yearly sum ETo during the observation period varies from 0.65 to 8.88 percent. Furthermore, from Table 1 and Table 2, it should be noted that the values of relative root mean square error in monthly
Table 1. Statistical performance of the EToHS and EToHSm versus EToPM for estimating daily ETo during 2011 and 2017 in Karshi steppe, Kashkadarya province, Uzbekistan.
Table 2. Statistical performance of the EToHS and EToHSm versus EToPM for estimating monthly ETo during 2011 and 2017 in Karshi steppe, Kashkadarya province, Uzbekistan.
ETo is much lower than those of daily base.
Because of the high values of RMSE and RRSME, EToHS method cannot be used in our study area to estimate ETo. However, according to Teutschbeina and Seiberta (2012)  , it is possible to improve the accuracy of climatic parameters by modifying the parameters to local conditions through identifying and application of a bias correction factor. The bias correction factor was calculated for every month using data from 2011 to 2015 (calibration period), and afterwards the identified bias correction factors were used for the data of 2016 and 2017 to validate the HS method (EToHSm) in daily base. The received bias correction factors for each month are shown in Table 3.
In the months from June to August, the bias correction factor is higher as expected and ranged from 1.10 to 1.17. The HS method has a lower sensitivity to air temperature during the summer months in comparison to the PM method. That is why the values of bias correction factors are higher during June, July and August. Moreover, it also notable that statistical parameters of the monthly modified EToHSm is more desirable than daily modified EToHSm. After modification of the EToHS, all statistical indicators improved in positive direction. Modification of the EToHS allowed improving the accuracy of the ETo calculation. Also, the application of the bias correction factor reduced the relative root mean square and relative error percentage in monthly base ETo by twofold. The relative root mean square errors of EToHS were 15% and 17% in 2016 and 2017, respectively. The calibration process reduced these values to 6% in 2016 and 8% in 2017. As a result of the calibration process, the statistical performance of the relative root mean square errors and index of agreement changed from “good” to “very good” in the terms of the statistics according to adopted similar standards in validation of ETo estimation Stöckle et al. (2004)  .
Table 3. The bias correction factor Hargreaves-Samani equation for each month using data from 2011 to 2015 for Karshi steppe, Kashkadarya province, Uzbekistan.
Based on the results, the modified EToHS equation is suitable for predicting ETo in arid continental climate of Karshi region in southern Uzbekistan. When data on solar radiation, humidity and wind speed is missing because of technical capacity and financial limitations of weather stations, it is possible to modify the HS methods and more accurately calculate ETo. Measuring evapotranspiration is highly important for understanding and ultimately intervening into the water cycle of natural systems, especially in the water balance of different critical users of water, like large scale irrigated areas. This is particularly true in the field of water management, where water resources have to be managed very clearly from the water basin to the irrigated fields, eventually reaching to smaller areas and users. If reliable and consistent information regarding evapotranspiration can be accessed with less time, temporal estimation and at low cost, it can be used to analyze the performance of irrigation systems and devise better management alternatives. The macro-level analysis of information can not only help understand the patterns and implications of the existing management strategies on the overall water use, it can also indicate the necessary changes required to manage water more beneficially and minimize the negative impacts. If ET based irrigation is widely adopted by the WUAs, it can result in larger water savings, which then can be diverted to expand agriculture for other purposes and improve ecological situation in the region. Additionally, the findings suggest that the methods used in this paper can be applied in data limited regions to calculate ETo, as well as to estimate future ETo values using global climate models, to inform decision making and develop more effective agricultural practices on water management, irrigation scheduling and crop production.
This research is a first attempt to implement the bias correction factor to calibrate the HS method for conditions along the Amudarya basin in Central Asia. The application of the bias correction factor to adjust the HS to PM method in order to estimate ETo was proved by statistical analyses. According to the analyses (see Figure 5), the majority of the variations between EToPM and EToHS methods are happening during the summer period (June to August), while ETo values of both methods in other months are statistically acceptable, which implies that the HS method can be implemented without correction during the other months. This paper did not investigate the reasons for the higher bias correction factors during the summer period in the particular climatic and territorial region; therefore it could be a subject of research in future studies. It should also be noted that the identified and verified bias correction method can be applied to the ETo values estimated from the downscaled global circulation models for the particular climate region and properly forecast future ETo values by the HS method, as some of those models are not adequate for ETo calculation using the PM method due to data limitations.
Figure 5. Comparison of the monthly EToHS (a) (c) and EToHSm (b) (d) in Karshi steppe, Kashkadarya province, Uzbekistan during 2016 and 2017.
This paper was developed within the framework of IWMI’s USAID Partnerships for Enhanced Engagement in Research (PEER) Cycle 5 project “Implications of climate change, land use and adaptation interventions on water resources and agricultural production in Transboundary Amu Darya river basin,” and the analyses are based on data collected under the project. This work was supported by the funding provided under USAID PEER Cycle 5 project [grant number 5-523]. Authors acknowledge USAID PEER program and express deepest appreciation to all those who actively contributed and helped to complete this paper.