Estimation of evapotranspiration by FAO Penman- Monteith Temperature and Hargreaves-Samani models under temporal and spatial criteria. A case study in Duero Basin (Spain)

Use of the Evapotranspiration based scheduling method is the most common one for irrigation programming in agriculture. There is no doubt that the estimation of the reference evapotranspiration (ETo) is a key factor in irrigated agriculture. However, the high cost and maintenance of agrometeorological stations and high number of sensors required to estimate it creates a non-plausible situation especially in rural areas. For this reason the estimation of ETo using air temperature, in places 20 where wind speed, solar radiation and air humidity data are not readily available, is particularly attractive. Daily data record of 49 stations distributed over Duero basin (Spain), for the period 2000-2018, were used for estimation of ETo based on seven models against Penman-Monteith FAO 56 with temporal (annual or seasonal) and spatial perspective. Two Hargreaves-Samani models (HS), with and without calibration, and five Penman-Monteith temperature models (PMT) were used in this study. The results show that the 25 models ́ performance changes considerably depending on whether the scale is annual or seasonal. The performance of the seven models was acceptable from an annual perspective (R> 0.91, NSE> 0.88, MAE <0.52 mm · d and RMSE <0.69 mm · d). For winter, no model showed a good performance. In the rest of the seasons, the models with the best performance were three: PMTCUH, HSC and PMTOUH. HSC model presents a calibration of Hargreaves empirical coefficient (kRS). In PMTCUH model, kRS was calibrated and 30 average monthly values were used for wind speed, maximum and minimum relative humidity. Finally, PMTOUH model is as PMTCUH model except that kRS was not calibrated. These results are very useful to adopt appropriate measures for an efficient water management, especially in the intensive agriculture in semi-arid zones, under the limitation of agrometeorological data. 35 https://doi.org/10.5194/nhess-2019-250 Preprint. Discussion started: 9 August 2019 c © Author(s) 2019. CC BY 4.0 License.

are very useful to adopt appropriate measures for an efficient water management, especially in the intensive agriculture in semi-arid zones, under the limitation of agrometeorological data.

Introduction
A growing population and its demand for food increasingly demand natural resources such as water. This, linked with the uncertainty of climate change, makes water management a key point for future food 45 security. The main challenge is to produce enough food for a growing population that is directly affected by the challenges set in the management of agricultural water, mainly with irrigation management (Pereira, 2017).
Evapotranspiration (ET) is the water lost from the soil surface and surface leaves by evaporation and, by transpiration, from vegetation. ET is one of the major components of the hydrologic cycle and represented 50 a loss of water from the drainage basin. Evapotranspiration (ET) information is key to understanding and managing water resources systems (Allen et al., 2011). ET is normally modeled using weather data and algorithms that describe aerodynamic characteristics of the vegetation and surface energy.
In agriculture, irrigation water is usually applied based on the water balance method in the soil water balance equation that allows the calculation of the decrease in soil water content as the difference 55 between outputs and inputs of water to the field. In arid areas where rainfall is negligible during the irrigation season an average irrigation calendar may be defined a priori using mean ET values (Villalobos et al., 2016). The Food and Agricultural Organization of United Nations (FAO) improved and upgraded the methodologies for reference evapotranspiration (ETo) estimation by introducing the reference crop (grass) concept, described by FAO Penman-Monteith (PM-ETo) equation (Allen et al., 1998). This 60 approach was tested well under different climates and time step calculations and is currently adopted worldwide (Allen et al., 1998, Todorovic et al., 2013Almorox et al., 2015). To estimate crop evapotranspiration (ETc) is obtained by function of two factor (ETc = Kc· ETo): reference crop evapotranspiration (ETo) and crop coefficient (Kc) (Allen et al. 1998). ETo was introduced to study the evaporative demand of the atmosphere independently of crop type, crop stage development and Wind speed (u), solar radiation (Rs), relative humidity (RH) and temperature (T) of the air are required to estimate ETo. Additionally, vapor pressure deficit (VPD), soil heat flux (G) and net radiation (Rn) measurements or estimates are necessary. The PM-ETo methodology presents the disadvantage that required climate or weather data that are normally unavailable or low quality (Martinez and Thepadia, 80 2010) in rural areas. In this case, where data are missing, Allen et al. (1998) in the guidelines for PM-ETo recommend two approaches: a) using equation of Hargreaves-Samani (Hargreaves and Samani, 1985) and b) using PM temperature (PMT) method that requires data of temperature to estimate Rn (net radiation) and VPD for obtaining ETo. In these situations, temperature-based evapotranspiration (TET) methods are very useful (Mendicino and Senatore, 2012). Air temperature is the most available meteorological data, 85 which are readily from most of climatic weather station. Therefore, TET methods and temperature databases are solid base for ET estimation all over the world including areas with limited data resources (Droogers and Allen, 2002).The first reference of the use of PMT for limited meteorological data was Allen (1995), subsequently, studies like those of Allen et al. (1996), Annandale et al. (2002, were carried out with similar behavior to HS and FAO-PM, although there was the disadvantage of a greater 90 preparation and computation of the data than the HS method. On this point, it should be noticed that the researchers do not favor to using PMT formulation and adopting the HS equation, simpler and easier to use (Paredes et al., 2018). Authors like Pandey et al. (2014) performed calibrations based on solar radiations coefficients in Hargreaves-Samani equations. Today, PMT calculation process is easily implemented with the new computers (Pandey and Pandey, 2016;Quej et al., 2019). 95 Todorovic et al., (2013) reported that, in Mediterranean hyper-arid and arid climates PMT and HS show a similar behavior and performance while for moist sub-humid areas the best performance was obtained by PMT method. This behavior was reported for moist sub-humid areas in Serbia (Trajovic, 2005). Several studies confirm this performance in a range of climates (Martinez and Thepadia, 2010;Raziei and Pereira, 2013;Almorox, et al., 2015;Ren et al., 2016). Both models (HS and PMT) improved when local 100 calibrations are performed (Gavilán et al., 2006;Paredes et al., 2018). These reduce the problem when wind speed and solar radiation are the major driving variables.
Studies in Spain comparing HS and PMT methodologies were studied in moist sub-humid climate zones (Northern Spain) showing a better fit in PMT than in HS. (Lopez Moreno et al., 2009). Tomas-Burguera (2017) reported for the Iberian Peninsula a better adjustment of PMT than HS, provided that the lost 105 values were filled by interpolation and not by estimation in the model of PMT.
Normally the calibration of models for ETo estimation is done from a spatial approach, calibrating models in the locations studied. Very few studies have been carried out to test models from the seasonal point of view, being the annual calibration being the most studied. Meanwhile spatial and annual approaches are of great interest for climatology and meteorology, for agriculture, seasonal or even monthly calibrations and spatial perspective in the Duero basin (Spain). The models evaluated were two Hargreaves-Samani (HS), with calibration and without calibration and five Penman-Monteith temperature model (PMT) analyzing the contribution of wind speed, humidity and solar radiation in a situation of limited agrometeorological data.

Description of the Study Area
The study focuses on the Spanish part of the Duero hydrographic basin. The international hydrographic Duero basin is the most extensive of the Iberian Peninsula with 98073 km 2 , it includes the territory of the Duero river basin as well as the transitional waters of the Oporto Estuary and the associated Atlantic 125 coastal ones (CHD, 2019). It is a shared territory between Portugal with 19214 km 2 (19.6 % of the total area) and Spain with 78859 km 2 (80.4%). The Duero river basin is located in Spain between the parallels 43º 5' N and 40º 10' N and the meridians 7º 4' W and 1º 50' W ( Fig. 1). This basin is almost exactly with the so-called Submeseta Norte, an area with an average altitude of 700 m, delimited by mountain ranges with a much drier central zone that contains large aquifers, being the most important area of agricultural 130 production. The Duero Basin belongs in its 98.4% to the Autonomous Community of Castilla y Léon.
The 70% of the average annual precipitation is used directly by the vegetation or evaporated from surface, this represents 35.000 hm 3 . The remaining (30%) is the total natural runoff. Mediterranean is the predominant climate. The 90% of surface is affected by summer drought conditions. The average annual values are: 12 ºC of temperature and 612 mm of precipitation. However, precipitation ranges from minimum values of 400 mm (South-Central area of the basin) to a maximum of 1800 mm in the northeast of the basin (CHD, 2019). According to Lautensach (1967), 30 mm is the threshold definition of a dry month. Therefore, between 2 and 5 dry periods can be found in the basin (Ceballos et al., 2004).
Moreover, the climate variability, especially precipitation, exhibited in the last decade has decreased the water availability for irrigation in this basin (Segovia-Cardozo et al., 2019).

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The Duero basin has 4 million hectares of rainfed crops and some 500,000 hectares irrigated that consumes 75% of the basin's water resources consumption. Barley (Hordeum vulgare L.) is the most important rainfed crop in the basin occupying 36% of the National Crop Surface followed by wheat    (Table 1). Each station incorporates measurements of air temperature (T) and relative humidity (RH; Vaisala HMP155), precipitation (ARG100 rain gauge), solar global radiation (pyranometer SKYE SP1110) and wind direction and wind speed (u) (wind vane and RM YOUNG 05103 anemometer). ). Sensors were periodically maintained and calibrated, and all data were recorded and averaged hourly on a data logger (Campbell CR10X and CR1000). Characteristics of the 180 agrometeorological stations were described by (Moratiel et al., 2011(Moratiel et al., , 2013a. For quality control, all parameters were checked, the sensors were periodically maintained and calibrated, all data being recorded and hourly averaged on a data logger. The database calibration and maintenance are carried out by the Ministry of Agriculture. Transfer of data from stations to the Main Center is accomplished by modems; the Main Center incorporates a server, which sequentially connects to each station to download the 185 information collected during the day. Once the data from the stations are downloaded, they are processed and transferred to a database. The Main Center is responsible for quality control procedures that comprise SPAIN PORTUGAL FRANCE Duero Basin the routine maintenance program of the network, including sensor calibration, checked for validity values and data validation. Moreover, the database was analyzed to find incorrect or missing values. To ensure that good quality data were used, we used quality control procedures to identify erroneous and suspect 190 data. The quality control procedures applied are the range/limit test, step test consistency an internal test (Estevez et al., 2016).
The period studied was from 2000 to 2018, although the start date may fluctuate depending on the availability of data. Table 1 shows the coordinates of the agrometeorological stations used in the Duero

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Basin and the aridity index based on UNEP (1997). Table 1 the predominance of the semi-arid climate zone with 42 stations of the 49, being 2 arid, 4 dry-sub humid and 1 moist sub-humid.

FAO Penman-Monteith (FAO-PM)
The FAO recommend the PM method as the one for computing ETo and evaluating other ETo models 205 like the Penman-Monteith model using only temperature data (PMT) and other temperature-based model (Allen et al., 1998). The method estimates the potential evapotranspiration from a hypothetical crop with an assumed height of 0.12 m having aerodynamic resistance of (ra) 208/u2, (u2 is the mean daily wind speed measured at a 2 m height over the grass) and a surface resistance (rs) of 70 s·m -1 and an albedo of 0.23, closely resembling the evaporation of an extension surface of green grass of uniform height, 210 actively growing and adequately watered. The ETo (mm·d −1 ) was estimated following FAO-56 (Allen et al. 1998): In Eq. 1, Rn is net radiation at the surface (MJ m -2 d -1 ), G is ground heat flux density (MJ m -2 d -1 ),  is the The scarce availability of agrometeorological data (global solar radiation, air humidity and wind speed mainly) limit the use of the FAO-PM method in many locations. Allen et al., (1998) (Hargreaves andSamani, 1982, 1985). The Hargreaves andSamani, 225 1982, 1985) method is given by the following equation (2): where ETo is the reference evapotranspiration (mm day -1 ); Ho is extraterrestrial radiation (MJ·m -2 ·d -1 ); kRS is the Hargreaves empirical coefficient, Tm, Tx and Tn are the daily mean, maximum and minimum air temperature (°C), respectively. The value kRS was initially set to 0.17 for arid and semiarid regions 230 (Hargreaves and Samani, 1985). Hargreaves (1994) later recommended to use the value of 0.16 for interior regions and 0.19 for coastal regions. Daily temperature variations can occur due to other factors such as topography, vegetation, humidity, among others, thus using a fixed coefficient may lead to errors.
In this study, we use the 0.17 as original coefficient (HSo) and the calibrated coefficient kRS (HSc).The kRS reduces the inaccuracy and consequently thus improving the estimation of ETo. This calibration was done 235 for each station.

Penman-Monteith Temperature (PMT)
The FAO-PM, when applied using only measured temperature data is denominated to as Penman-Monteith Temperature (PMT) retains many of the dynamics of the full data FAO-PM (Pereira et al., 2015;Hargreaves and Allen, 2003). Humidity and solar radiation are estimated in the PMT model using

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where Rs is solar radiation (MJ·m -2 ·d -1 ) ; Rns is net solar shortwave radiation (MJ·m -2 ·d -1 ); Ho is extraterrestrial radiation (MJ·m -2 ·d -1 ); Ho was computed as a function of site latitude, and solar angle and the day of the year (Allen et al., 1998). Tx is daily maximum air temperature (ºC), Tn is daily minimum air temperature (ºC). For kRS Hargreaves (1994) recommended to use kRS = 0.16 for interior regions and kRS = 0.19 for coastal regions. For better accuracy the coefficient kRS can be adjusted locally (Hargreaves and Allen 2003). In this study two assumptions of kRS were made, one where a value of 0.17 was fixed and another where it was calibrated for each station.

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Where PMT is the reference evapotranspiration estimate by Penman-Monteith temperature method (mm·d -1 ); PMTrad is the radiative component of PMT (mm·d 1 ); PMTaero is the aerodynamic component of PMT (mm·d -1 ); Δ is the slope of the saturation vapor pressure curve (kPa °C -1 ), γ is the psychrometric constant (kPa °C -1 ), Rns is net solar shortwave radiation (MJ m -2 d -1 ), Rnl is net longwave radiation (MJ m -2 d -1 ), G is ground heat flux density (MJ m -2 d -1 ) considered zero according to Allen et al.1998 , Tm is 275 mean daily air temperature (°C), Tx is maximum daily air temperature, Tn is mean daily air temperature, Td is dew point temperature (ºC) calculated with the Tn according to Todorovic et al. (2013), u2 is wind speed at 2 m height (m s -1 ) and es is the saturation vapor pressure (kPa). In this model two assumptions of kRS were done, one where a value of 0.17 was fixed and another where it was calibrated for each station.
(2) Average monthly value of wind speed

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(3) Average monthly value of maximum and minimum relative humidity.

Performance assessment.
Model´s suitability, accuracy and performance were evaluated using coefficient of determination (R 2 ; Eq.
[9]) of the n pairs of observed (Oi) and predicted (Pi) values. Also, the mean absolute error (MAE, mm·d - The results were represented in a map applying of the Kriging method with the Surfer® 8 program. In the study period the data indicated that the Duero basin is characterized by being a semiarid climate zone (94% of the stations) where the P / ETo ratio is between 0.2-0.5 (Todorovic et al., 2013). The mean annual rainfall is 428 mm while the average annual ETo for Duero basin is of 1079 mm, reaching the maximum values in the zone center-south with values that surpass slightly 1200 mm (Fig. 2).   PMTOUT and HSo showed a slightly higher performance than PMTO2T and PMTC2T, being these last two models the worst behaviors showed (Fig.3). The performance of the models (PMTO2T, PMTOUT and PMTOUH] improve as the averages of wind speed (u) and dew temperature (Td) values are incorporated.

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The same pattern is shown between the PMTCUH models, where the mean u values and Td are     (Table 3). The model that shows the best performance independently of the seasonal is the PMTCUH. The models 390 that can be considered in a second level are the HSC and the PMTOUH. During the months of more solar radiation (summer and spring) the performance of the HSC model is slightly better than the PMTOUH model. The following models: HSo, PMTO2T, PMTC2T and PMTOUT, have a much lower performance than the previous models (PMTOUH and HSC). The model that has the worst performance is the PMTO2T..
The northern area of the basin is the area in which lower MAE shows in most models and for all seasons.

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This is due in part to the fact that the lower values of ETo (mm·d -1 ) are located in the northern zone. On the other hand, the eastern zone of the basin shows the highest values of MAE error due to the strong winds that are located in that area.
During the winter the seven models tested show no great differences between them, although the PMTCUH is the model with the best performance. It is important to indicate that during this season the RMSE (%) is 400 placed in all the models above 30%, so they can be considered as very weak models. According to Jamieson et al. (1991) and Bannayan and Hoogenboom (2009) the model is considered excellent with a normalized RMSE (%) less than 10%, good if the normalized RMSE (%) is greater than 10 and less than 20%, fair if the normalized RMSE (%) is greater than 20% and less than 30%, and poor if the normalized RMSE (%) is greater than 30%. All models that are made during the spring season (MAM) can be 405 considered as good / fair since their RMSE (%) fluctuates between 17-20%. The seven models that are made during summer season (JJA) can be considered as good since their RMSE varies from 12 to 16%.
Finally, the models that are made during autumn (SON) are considered fair / poor fluctuating between the values of 22-32%. The models that reached values greater than 30% during autumn were the model PMTC2T (31%) and PMTO2T (32%) also with a clear tendency to overestimation (Table 3) In the use of 410 temperature models for estimating ETo, it is necessary to know the objective that is set. For the management of irrigation in crops is better to test the models in the period in which the species require the contribution of additional water. In many cases applying the models with an annual perspective with a good performance can lead to more accentuated errors in the period of greater water needs. The studies of different temporal and spatial scales of the temperature models for ETo estimation, can give valuable 415 information that allow to manage the water planning in zones where the economic development does not allow the implementation of agrometeorological stations due to its high cost.
These data are in accordance with the values cited by other authors in the same climatic zone. Jabloun and Sahli (2008) (Todorovic et al., 2013, Raziei and Pereira, 2013, Paredes et al., 2018 445 PMT models have improved considering the average wind speed. In addition, trends and fluctuations of u have been reported as the factor that most influences ETo trends (Nouri et al., 2017, McVicar et al., 2012Moratiel et al., 2011). Numerous authors have recommended to include, as much as possible, average data of local wind speeds for the improvement of the models as Nouri and Homaee (2018) and Raziei and 450 Pereira (2013) in Iran, Paredes et al. (2018) in Azores islands (Portugal), Djaman et al. (2017) in Uganda, Rojas and Sheffield (2013) in Louisiana (USA), Jabloun and Shali (2008) in Tunisia and Martinez-Cob and Tejero-Juste (2004) in Spain, among others. In addition, even ETo prediction models based in PMT focus their behavior based on the wind speed variable (Yang et al., 2019). It is important to note that the PMTOUT generally has a better performance than the PMTC2T except for spring. The difference between 455 both models is that in the PMTC2T kRS is calibrated with wind speed set at 2 m/s and in the PMTOUT kRS is not calibrated and with an average wind. In this case the wind speed variable affects less than the calibration of kRS since the average values of wind during spring (2.3 m/s) is very close to 2 m/s and there is no great variation between both settings. In this way, kRS calibration shows a greater contribution than the average of the wind speed to improve the model (Fig.5 E, F). In addition, although u is not directly 460 considered for HS, this model is more robust in regions with speed averages around 2 m/s (Allen et al. 1998 andHomaee, 2018) On the other hand errors in the estimation of relative humidity cause substantial changes in the estimation of ETo as reported by Nouri and Homaee (2018) and Landeras et al. (2008).

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The results  daily average values of ETo around 1 mm due to low temperatures, radiation and VPD. The model that showed the best performance was PMTCUH followed by PMTOUH and HSC for annual and seasonal criteria. PMTOUH is slightly less robust than PMTCUH during the maximum radiations periods of spring and summer since the PMTCHU performs the kRS calibration. The performance of the HSC model is better in the spring period, which is similar to PMTCHU. The spatial distribution of MAE errors in the basin

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shows that it is highly dependent on wind speeds, obtaining greater errors in areas with winds greater than 2.8 m/s (east of the basin) and lower than 1.3 m/s (south-southwest of the basin). This information of the tested models in different temporal and spatial scales can be very useful to adopt appropriate measures for an efficient water management under limitation of agrometeorological data and under the recent increments of dry periods in this basin. It is necessary to consider that these studies are carried out on a 500 local scale and in many cases the extrapolation of the results on a global scale is complicated. Future studies should be carried out in this line from a monthly point of view since there may be high variability within the seasons. Allen, R. G.: Evaluation of procedures for estimating grass reference evapotranspiration using air