ESTIMATION OF REFERENCE EVAPOTRANSPIRATION IN A MOUNTAINOUS MEDITERRANEAN SITE USING THE PENMAN-MONTEITH EQUATION WITH LIMITED METEOROLOGICAL DATA

– In recent decades many authors have adopted the PenmanMonteith formula as the standard way to estimate reference evapotranspiration from climate data. The main drawback associated with the Penman-Monteith method is the relatively high data demand: temperature, solar radiation, relative humidity and wind speed are the minimum inputs required by the formula. In the Spanish Pyrenees historical databases usually consist of temperature and rainfall only, although an improvement in data acquisition is expected in terms of parameters monitored. Under situations of data scarcity, some authors recommend the use of less data intensive methods, such as the empirical Hargreaves equation. Other authors suggest that it is better to estimate the missing parameters and to apply the Penman-Monteith equation. This paper presents a study on the accuracy of the Penman-Monteith method for a situation where some parameters have to be estimated from available temperature, and wind speed data must be replaced by a constant value. The results have been compared with the information available for a location in the central Spanish Pyrenees (period 1999-2003) where parameters required by the Penman-Monteith method have been monitored. A comparison is then made with the Hargreaves model in order to assess the most appropriate method for calculation of the reference evapotranspiration. The results indicate that the use of the Penman-Monteith formula results in errors in reference evapotranspiration ETo estimation of different magnitude and sign throughout the year. However, in general, it offers a more accurate estimation of reference evapotranspiration than the Hargreaves formula.


ESTIMATION OF REFERENCE EVAPOTRANSPIRATION IN A MOUNTAINOUS MEDITERRANEAN SITE USING THE PENMAN-MONTEITH EQUATION WITH LIMITED METEOROLOGICAL DATA
J. I. LÓPEZ-MORENO 1 , T. M. HESS 2 AND S. M. WHITE 2 1 Instituto Pirenaico de Ecología, CSIC, Campus de Aula Dei, Apartado 13034, 50080-Zaragoza, Spain 2 Institute of Water and Environment, Cranfield University, Silsoe, Beds, MK45 4DT, IUK nlopez:@ipe.csic.es ABSTRACT.-Inrecent decades many authors have adopted the Penman-Monteith formula as the standard way to estimate reference evapotranspiration from climate data.The main drawback associated with the Penman-Monteith method is the relatively high data demand: temperature, solar radiation, relative humidity and wind speed are the minimum inputs required by the formula.In the Spanish Pyrenees historical databases usually consist of temperature and rainfall only, although an improvement in data acquisition is expected in terms of parameters monitored.Under situations of data scarcity, some authors recommend the use of less data intensive methods, such as the empirical Hargreaves equation.Other authors suggest that it is better to estimate the missing parameters and to apply the Penman-Monteith equation.This paper presents a study on the accuracy of the Penman-Monteith method for a situation where some parameters have to be estimated from available temperature, and wind speed data must be replaced by a constant value.The results have been compared with the information available for a location in the central Spanish Pyrenees (period 1999Pyrenees (period -2003) ) where parameters required by the Penman-Monteith method have been monitored.A comparison is then made with the Hargreaves model in order to assess the most appropriate method for calculation of the reference evapotranspiration.The results indicate that the use of the Penman-Monteith formula results in errors in reference evapotranspiration ET o estimation of different magnitude and sign throughout the year.However, in general, it offers a more accurate estimation of reference evapotranspiration than the Hargreaves formula.

Introduction
Evapotranspiration is the sum of the volume of water used by vegetation (transpiration) and that evaporated from the soil and intercepted precipitation.Water entering the evaporation phase of the hydrological cycle becomes unavailable for generation of runoff or replenishment of groundwater.As a global average, 57% of annual precipitation returns to the atmosphere due to evapotranspiration, and this value may reach 90-100% in arid or desert areas (SANCHEZ-TORIBIO, 1992).Seasonal evapotranspiration mainly depends on the characteristics of the weather and plant cover (structure, density, vegetative cycle).These factors vary with time due to both climate fluctuations and land use/land cover changes.Since evapotranspiration is a very important part of the water cycle, any change in climate or plant cover can affect the availability of water resources.
Mountain areas are the main runoff sources in Mediterranean environments.For this reason a number of studies have been focussed on the recent evolution of stream flow in relation to possible changes in climate and/or land cover, especially in the Pyrenees (GALLART & LLORENS, 2004;GARCÍA-RUIZ et al., 2001;BEGUERÍA et al., 2003).In the Spanish Pyrenees no generalized precipitation or temperature trend has been observed for the period since the middle of the 20 th century, although important fluctuations (Pirineos, 2009, Vol. 164, 7-31, ISSN 0373-2568) have been identified at a decadal scale.During the same period the enlargement of shrub areas and forests occurred after the generalised abandonment of cultivated fields on the hill slopes located under 1600 m a.s.l.Likewise, the sub-alpine grasslands have increased in density and are affected by a natural colonization of trees.BEGUERÍA et al. (2003) attribute the statistically significant decrease in stream flow of the Pyrenean rivers to these land use/ land cover changes.The study of evapotranspiration would help in this case to understand and parameterise the changes that occur at the scale of the hydrological cycle and the consequences for water resources.The concept of a reference evapotranspiration (ET o ) can be used to estimate the climatic effect on evapotranspiration and represents the evapotranspiration from a hypothetical, reference surface (ALLEN et al., 1994).
Many equations are used to estimate ET o .They can be divided into two main groups, i) those that are empirical and have lower data requirements, and ii) those that are physically-based and require proportionately more data.In a scenario of climate and land use change, a physically or process-based approach offers more flexibility and does not depend on relationships which may be changing over time.The International Commission for Irrigation (ICID), the Food and Agriculture Organization of the United Nations (FAO) and the American Society of Civil Engineers (ASCE) have adopted the Penman-Monteith (PM) method (ALLEN et al., 1998) as the standard way to compute ET o from climate data.PM is widely used because: a) it is a predominantly physically-based approach and so it can be used globally, b) it has been widely tested using lysimeter data from a wide range of climate conditions (ALLEN et al., 1994;ITENFISU et al., 2000).
The main drawback of using the PM method is the relatively high data demand, requiring solar radiation, temperature, wind speed and relative humidity data.In the Pyrenees, as in the majority of mountain areas, the scarcity of meteorological data is a frequent problem.As a result, there are few continuous time periods or sites with all the parameters required for the PM method.In the literature it is possible to find two different suggestions for ET o estimation with scarce data: i) to estimate indirectly the absent parameters from the available data in order to use PM equation (ALLEN et al., 1998); or ii) to calculate ET o using a less data intensive formula.For this, second route, the empirical Hargreaves (HG) equation is considered to be a good option (XU & SINGH, 2001;DROOGERS & ALLEN, 2002;MARTINEZ-COB, 2002).
This paper provides an evaluation of the possible errors resulting from the use of the PM approach for the Central Pyrenees, where many of the input data must be estimated from other available information.Specifically, the objectives of this work are: a) to estimate the relative humidity and solar radiation from maximum and minimum temperature data using different methods b) to assess the error in ET o due to the estimation of both solar radiation and relative humidity, c) to assess the error in ET o due to the absence of wind speed as an input to the PM equation, d) to assess the resultant combined error in ET o due to the use of estimated parameters instead of monitored data, and e) to compare the results from the PM equation using estimated parameters with the less data intensive HG equation.

Study site and used data
The Pyrenees is a mountainous area located in the north-east of the Iberian Peninsula.Precipitation increases towards the north along the altitudinal gradient, and to the west because of the Atlantic influence.The average annual precipitation in the northernmost sector of the range reaches values above 2000 mm, with around 600-800 mm in the lowest areas.Most of the precipitation falls in autumn and spring (GARCÍA-RUIZ et al., 2001).The summer is relatively dry (with occasional rainstorms), when long anticyclonic periods are frequent.
The mean annual temperature decreases from north to south and it is mainly controlled by the altitude.Above 1000 m a.s.l. the average annual temperature is lower than 10 ºC.At 2000 m the mean annual temperature is around 5 ºC.The thermic gradient varies, according to different authors, between 0.49 ºC and 0.6 ºC (GARCÍA-RUIZ et al., 1985;DEL BARRIO et al., 1990).
Throughout the Spanish Pyrenees the meteorological data collected at most monitoring sites consists of daily mean, maximum and minimum temperature, and daily precipitation.However, some sites have other data for short periods, and a new network of monitoring stations is currently being installed.Thus, although precipitation and temperature data are found at all sites, many locations have some coverage of other data types, particularly cloud cover at 08:00 hours.
The meteorological station of Yesa (515 m a.s.l.; Lat.42-37-92, Long.01-11-24W) is located on the south west edge of the Pyrenean range and has supplied a continuous data set of the required parameters for the PM equation (Pirineos, 2009, Vol. 164, 7-31, ISSN 0373-2568) (Pirineos, 2009, Vol. 164, 7-31, ISSN 0373-2568) from February 1999 to December 2003.The station is managed by the Govern of Navarra region (http://meteo.navarra.es/estaciones/estacion_detalle.cfm?IDestacion=10).Figure 1 shows the daily series of temperature, precipitation, wind speed, relative humidity and solar radiation recorded during the available period.Series have been previously checked to detect potential anomalous values, no gaps were found for any variable in the whole studied period.Mean annual temperature at Yesa station is 13.7 ºC, and oscillates between 22.38ºC in August and 5.03ºC in January.The annual evolution of solar radiation is very similar to temperature although the maximum and minimum annual values occur in June and December respectively.Mean annual precipitation is 810 mm with most rain falling in the autumn and winter seasons.Relative humidity tends to increase from summer to winter, but the daily series show a high variability.Finally wind speed tends to remain constant throughout the year around 2ms -1 , although a slight variability is found, as well as isolated events which exceed 5ms -1 , more details about the characteristics of wind speed in Yesa will be discussed in results.

Estimation of the reference evapotranspiration
Two approaches were used to estimate reference evapotranspiration, (i) the Penman-Monteith (PM) equation with missing parameters estimated from the available data, and (ii), the HARGREAVES (HG) (1985) equation based on temperature alone.

Estimation of parameters for Penman-Monteith
The PM equation can be expressed as the sum of a radiation component and an aerodynamic component, (1) where Δ slope of vapour pressure curve, kPa °C-1 (2) where γ psychrometric constant, kPa °C-1 ρ atmospheric density kg m -3 cp specific heat of moist air, 1.013 kJ kg -1 °C-1 ra aerodynamic resistance, s m -1 ea mean saturation vapour pressure, kPa ed actual vapour pressure, kPa Then, (3) where ET o reference evapotranspiration, mm d -1 The net radiation, R n , can be estimated from solar radiation, temperature, humidity, date and latitude.Soil heat flux, G, can be estimated from the change in mean air temperature between two days.The humidity terms, ea and ed, can be determined from maximum and minimum air temperature and relative humidity respectively, whilst ra and γ* are both functions of the mean daily wind speed.The parameters Δ, γ and λ are all dependant on mean air temperature.Hence, ET o can be derived from daily observations of maximum and minimum temperature, relative humidity, solar radiation and wind speed (see ALLEN et al., 1998 for a full description of the equations used).
In this study, ET o has been calculated using an evapotranspiration modelling package called WaSimET (HESS, 2000) that follows the methods of ALLEN et al. (1998).Although maximum and minimum air temperature data are commonly available, relative humidity, solar radiation and wind speed are often missing.This study focuses on the estimation of these parameters, and the resultant errors in ET o .

Solar Radiation
Where no radiation data are available, they are best estimated from sunshine duration.In this case, the only data related to sunshine are the observations of cloud cover.Two equations have been tested in order to obtain the shortwave radiation from the available data:

Relative Humidity
The mean daily vapour pressure deficit (ea -ed) in the P-M equation is usually determined from air temperature and relative humidity.
The mean saturation vapour pressure, ea, is estimated from ( 6) where e o (T) is the saturation vapour pressure at temperature, T, and is estimated from ( 7) The mean daily vapour pressure, ed, is estimated from where h r is the mean daily relative humidity.
The mean daily vapour pressure, ed, can also be taken to be the saturation vapour pressure at mean daily dew-point temperature, T d .T d is usually relatively constant during the day, and night-time minimum temperature, T min , tends to come into equilibrium with T d .Thus, ed can be approximated from (9) This assumption has been shown to work well in a range of climates except in arid and semiarid areas (KIMBALL et al., 1997).

Wind Speed
Wind speed is an important variable required by the PM equation, but it is irregularly measured in the Pyrenean stations.The extrapolation from nearby stations is not recommended because large differences in wind speed are recorded even over short distances due to the topographic heterogeneity of mountain areas.
In order to assess the effect of the lack of this variable in the estimation of ET o, it has been necessary to assume that wind speed presents similar values throughout the study area, although this is probably an under-estimate for high mountain areas.For this study a constant wind speed of 2 ms -1 has been assumed.This is justified as: a) In the absence of any information on wind speed, ALLEN et al. (1998) recommend use of 2 ms -1 as an average of global wind speed measurements, and b) mean wind speed at Yesa (1999Yesa ( -2003) ) was 2.07 ms -1 .et al. (1985) combined the relationship between temperature range and solar radiation used above, with an empirical relationship between solar radiation, temperature and reference evapotranspiration.Thus, the Hargreaves equation can be used to estimate ET o from maximum and minimum temperature alone (HARGREAVES & ALLEN, 2003):

HARGREAVES
where T is the mean air temperature, °C, and other symbols are as defined above.R a is the extraterrestrial radiation expressed as an equivalent evaporation depth.

Error estimation
To assess the accuracy of the estimated values of relative humidity and solar radiation, as well as the deviation of the constant value of wind speed in relation to the measured speed, these have been compared with observed data from the Yesa automatic weather station.Also, ET o obtained from PM using monitored values of R s , H r and wind speed have been compared with i) ET o obtained with estimated parameters, and ii) using the Hargreaves equation.Differences between observed and estimated data series have been measured by means of different error estimators: mean bias error, MBE (eq.11), standardized mean bias error, SMBE (eq.12), mean absolute error, MAE (eq.13) and standard mean absolute error, SMAE (eq.14), defined as follows:  Figure 2 shows the correlation between observed and estimated Rs values with (Fig. 2a) and without (Fig. 2b) cloud cover data.The error of the estimation is high for the extended HG approach including cloud cover: MBE = -0.18 and MAE = 6.2.The non-extended equation gives lower errors: MBE = -0.21and MAE = 3.3.The noticeable increase in accuracy of the estimation without cloud cover is probably due to the subjective manner in which cloud cover data is acquired, with the accuracy of the data depending on the ability of the observer.In addition, cloud cover data are usually only recorded in the morning and the variability through the day is not taken into account.At Jaca, 50 km eastward, cloud cover data have been collected at 07:00, 13:00 and 18:00 h from 1970-1988.These data show considerable variability during the day and the difference of the average of the three observations compared with values collected at 7 a.m. is 1.65 octas, a difference of 20.2%.These results suggest that the use of such data are not recommended when only one daily observation is available, and when the quality of the observations cannot be veri- (Pirineos, 2009, Vol. 164, 7-31, ISSN 0373-2568) Figure 2. Correlation between observed and predicted R s values for Yesa station, using (a) extended Hargreaves equation (eq.5) and (b) non extended Hargreaves equation (eq.6).Figura 2. Correlación entre los valores observados y predichos de R s para la estación de Yesa, utilizando (a) la ecuación extendida de Hargreaves (eq.5) y (b) la ecuación no extendida (eq.6).

Calculation and validation of the required parameters
fied.Errors in cloud cover can lead to large errors in the estimation of R s , so, in this study the non-extended HG equation (eq.6) has been used.This method of solar radiation estimation has been successfully tested in other locations of the Iberian Peninsula (CASTELLVI, 2001).
Table 1 shows the monthly average errors obtained in the estimation of R s from temperature data.MBE and SMBE present low values throughout the year, indicating that the daily sign of the error does not show any seasonal pattern.MAE oscillates between 1.55 and 4.28 MJ m -2 d -1 in December and April respectively.MAE is bigger in the months with higher solar radiation, but SMAE suggests that the maximum relative error is from the middle of autumn to the middle of spring, when the error exceeds 30% of the observed R s .The error estimators shown in Table 1 suggest a high ability of equation 6 to predict Rs from temperature data.

Relative humidity
Table 2 shows the results from comparing the measured relative humidity at Yesa and the estimated H r values from eq.8.MAE shows similar values throughout the year, oscillating between 9.12 and 12.72 %, but it tends to increase from winter to summer when it is considered as a relative value with regard to the monthly H r (SMAE).MBE and SMBE indicate the major importance of the error during the warm season, when the results stress a clear underestimation of H r .During the cold and wet period the sign of the error occurs randomly, so the MBE is close to 0. The climate characteristics of Yesa explain the seasonal distribution of the error.The moderate summer dryness conditions observed in summer lead to a difference between minimum temperature and dew point temperature that implies an underestimation of Hr.The disappearance of water stress conditions in winter leads to an increase of the accuracy of Hr estimation as a consequence of the equilibrium between T min and T d .3 shows the observed error when the wind speed (Ws) data are replaced by a constant value of 2 ms -1 .In Yesa mean Ws is very close to the proposed constant value during May, June, September and October.However, wind speed is underestimated in July, August and October; and overestimated from November to April.Thus, MBE shows a period around summer with positive signs, reaching values of 0.2 ms -1 (SMBE=0.11).In contrast, the sign of the MBE is negative in winter with a maximum amount of 18% of the observed wind speed in February.MAE has two periods of high values (over-estimation and under-estimation) separated by months of spring and autumn when the absolute error declines.The absolute expected error for a day can exceed 0.3 ms -1 in February, April and August, which gives values of SMAE of 0.16, 0.14 and 0.18 respectively.

Solar radiation
Figure 3 shows the estimated error in ET o calculation when it is necessary to replace the instrumental R s data by the estimated values from temperature (eq.4).MBE shows a low error throughout the year, with values close to 0. Thus, the error does not exceed 1% of the mean monthly ET o in any case.The annual evolution of MAE is very similar to the evolution of the absolute error in R s estimation (Table 1), suggesting that the effect of error in R s calculation has a direct effect on the PM equation.The expected absolute error in a given day is below 0.42 mm throughout the year.Standardized mean absolute error never exceeds 10% of the monthly ET o .These results suggest that solar radiation may be replaced by an estimate obtained from the daily range of temperature, without serious implications for calculation of ET o .Thus, on a monthly basis the expected error is almost zero, whilst the expected average daily error is below 10% of the monthly ET o .

Relative humidity
Figure 4 shows the effect of the replacement of H r monitored by H r estimated on the PM equation by means of eq. 8. MBE indicates that for the months when H r was underestimated (Table 2), ET o is overestimated.As relative values (SMBE), the error may exceed 5% of the monthly average ET o , reaching 11% in October.Mean absolute error indicates high errors in winter, whilst the lower daily error is observed in summer.It is interesting to note that the months with the lowest absolute error in H r estimation provide the highest values of absolute error in ET o estimation, and vice-versa.This fact is explained by the variability of the response of the PM equation to H r throughout the year.To support this conclusion, ET o was calculated using H r data with errors of different magnitude.The relationship between the monthly errors in H r and ET o estimations was expressed linearly (Fig. 5), and the slope of the regression lines is different according to the sensitivity of the PM equation to H r variation in each month.Thus, the sensitivity of PM is very high from November to September, when H r is successfully estimated.For the months when the Hr estimation shows less accuracy, the sensitivity of the ET o response is lower.Thus SMAE during summer is lower than 0.1, whilst during the months with high sensitivity it can exceed 0.3.

Wind speed
In section 4.1.3it has been shown that the use of a constant value of wind speed may lead to noticeable deviations in comparison to the real wind speed.The effect of the error in wind speed leads to an MBE that oscillates between -0.06 mm in February and 0.06 in August.This means that SMBE is between -0.08 when wind speed is underestimated, and 0.03 when the wind speed is overestimated.Figure 6 shows that the monthly estimation of ET o is only affected by the absence of wind speed information in some months of the cold season, never exceeding 8 % of the monthly ET o .The highest values of MAE are observed during summer when the daily estimation of ET o falls around 0.25 mm.The high evapotranspiration during this period explains the low values of SMAE.Thus the maximum values of SMAE are observed in February and November with 0.14 in both cases.(Pirineos, 2009, Vol. 164, 7-31, ISSN 0373-2568) Figure 6.Observed error in ET o estimation as consequence of the absence of relative wind speed.Figura 6. Errores observados en la estimación de ET o a consecuencia de la ausencia de datos de velocidad de viento.

Combining the errors
The resulting error in the calculation of ET o due to the use of R s and H r estimated from temperature information and use of a constant value of wind speed shows noticeable variations in magnitude and timing relating both to the parameter replaced and the season.The variability of the error due to the parameter replaced depends on the error in the estimation of the parameter (4.1) and the weight of each variable in the PM equation.The seasonal variability that each parameter causes in ET o estimation depends on (i) the pattern of error in parameter estimation throughout the year (as a consequence of the aridity, seasonal patterns of wind sped, etc.), and (ii) the different monthly sensitivity of the PM equation to possible errors in the estimation of the required parameters.Thus, Figure 7 represents the error caused by the absence of each parameter calculated in sections 4.2.1, 4.2.2 and 4.2.3 and the combined error when all three parameters are replaced.It is necessary to consider that on a given day the errors caused by each parameter can be in different directions.Thus, in the absence of more than one of the required parameters, the resulting error may be the sum of several deviations of the same sign, or errors of different sign may counteract one another.The largest SMBE observed is due to the absence of wind speed data with negative values in November, December and February.The two former months show low error due to the absence of Rs and H r , so the total error due to the absence of all three parameters is -0.13 and -0.14 % respectively.Otherwise, in February a large and negative SMBE is also observed due to the absence of H r, so this is the month when the largest total error occurs with an underestimation of ET o of -0.19 %.The important overestimation caused by the absence of H r in September and October is counteracted by the errors in the other two parameters, so the total error is very close to 0. In January, although the SMBE of the three parameters is low, the coincidence of negative values of H r and wind speed leads to a total error of -0.14 %, so this is the month with the second largest error of the year.The relationship between the observed partial SMBEs during the rest of the year leads to low values of the combined SMBE.
The absence of relative humidity data is the main source of error shown by SMAE from September to March.The use of a constant value of wind speed is the second highest cause of SMAE error from October to March.During spring and summer the highest values of absolute error in ET o are caused by the absence of solar radiation.The lowest standard mean absolute error is observed during summer (around 0.1) and it tends to increase continuously later.The largest combined SMAE occurs from November to February with values close to or exceeding 30% of the observed ET o .During some months the monthly combined error is the sum of the errors obtained in the three absent parameters, whilst in other months the combined error is less than that obtained by the absence of only one parameter, as a consequence of the counteracting of the deviations within the PM equation.(Pirineos, 2009, Vol. 164, 7-31, ISSN 0373-2568) Figure 7. Observed error in ET o estimation as consequence of the absence of solar radiation, relative humidity and wind speed.Figura 7. Errores observados en la estimación de ET o a consecuencia de la ausencia de radiación solar, humedad relativa y velocidad de viento.

Comparison between Penman-Monteith and Hargreaves equations
Figure 8 shows the SMBE and SMAE obtained in the calculation of ET o using the PM equation with the parameters indirectly estimated compared with ET o calculated by means of the HG equation.On a monthly basis, SMBE indicates a better performance of the PM method.Thus, PM gives insignificant errors from March to October, whilst HG tends to overestimate ET o noticeably from May to August.The rest of the year the differences are less marked, although the PM method out-performs the HG estimation during November, December, and January.The Hargreaves equation shows better estimations during the mild periods (March-April and September-October).In fact HG is slightly more accurate than PM in February, March, April, September and October.Figure 8 suggests that the comparison of methods using annual values, may lead to masking of significant deficiencies in the ET o calculation.Thus, in Yesa, the HG equation would provide a very low value of error on an annual basis, as a result of the counteracting effects of the sign of the error for different months.SMAE indicates that the higher errors in ET o estimation are expected using HG in most of the months for a given day.PM is clearly more accurate from May to August and from November to January.HG only shows better results in October and February.In March, April and September significant differences are rarely found.

Discussion and conclusions
Many authors consider that the PM formula is the most accurate method for estimation of reference evapotranspiration (JENSEN et al., 1990;ALLEN et al. 1994;1998;XU & SINGH, 1998;DROOGERS & ALLEN, 2002).This is the reason for adopting the PM method as the standard way to compute reference evapotranspiration by the International Commission of Irrigation (ICID), the Food and Agriculture Organization (FAO) and the American Society of Civil Engineers (ASCE).
The high data demand of PM, as for most of the physically-based approaches, is the major problem to its application in areas where complex weather stations are not available.When one or more of the required parameters are unavailable there are two possibilities: a) to use this equation with indirectly estimated parameters; b) to use less demanding formulae, such as the HG equation, based on empirical relationships between temperature, radiation and ET o .DROOGERS & ALLEN (2002) suggested that under scarce climatic data availability, the HG equation can be considered as a good alternative for ET o estimation, in its original formulation (HARGREAVES & SAMANI, 1985) or including precedent precipitation as a predictor variable.Recently, MAR-TINEZ-COB ( 2002) suggested an adequate fit between HG and PM in the Ebro Depression Valley, NE Spain.Later, MARTINEZ-COB & TEJERO (2004) proposed calibration of the HG equation in those stations where wind speed is lower than 2 ms -1 , in the same study area.XU & SINGH (2001) obtained satisfactory results when comparing HG with other temperature-based methods, using the PM formula as reference method to compute ET o .In spite of the good results obtained for HG, these authors indicate several disadvantages.Thus, HG tends to overestimate ET o in low ET o areas and to underestimate it in sectors with high ET o. (DROOGER & ALLEN, 2002;XU & SINGH, 2002).Also, the necessity to calibrate the equation according to the annual rainfall has been assessed, because HG overestimates in humid regions whilst it underestimates in arid areas (JENSEN et al., 1990;AMATYA et al., 1995;DROOGERS & ALLEN, 2002;HARGREAVES & ALLEN, 2003).STÖCKLE et al. (2004) concluded that HG without calibration provide poor agreement with PM ET o results for either daily or weekly periods.Another drawback related to HG is the associated error when it is applied for short time periods.Thus, HARGREAVES & ALLEN (2003) do not recommend the use of the HG equation for periods shorter than five days.Other authors consider inadequate the use of HG for intervals shorter than a week (JENSEN et al., 1990;CHOISINEL et al., 1992;DROOGERS & ALLEN, 2002).Such a restriction hinders the study of runoff generation and transport of sediment and nutrients, since ultimately, changes in water balance at a daily level are usually required.The difficulty to apply the HG equation worldwide without calibration and the limitation of the time scale applicability leads some authors to prefer the PM equation with a reduced data set, through the indirect estimation of the absent parameters.Thus, CHRISTIANSEN & WORLTON (1998) did not find significant errors using the FAO-PM with only temperature and solar radiation.ALLEN et al. (1998) concluded that, in areas of low data availability, PM provides more accurate ET o estimations than Hargreaves, in spite of the indirect estimation of R s , H r and wind speed.Recently, STÖCKLE et al. (2004) considered PM equation using estimated parameters as a suitable method for calculating weekly ET o .
In this paper, the information provided by the automatic weather station at Yesa has been used to i) assess the accuracy of the estimation of relative humidity and solar radiation from temperature data and the error obtained when wind speed is replaced by a constant value; and ii) to measure the error in ET o estimation as a consequence of the replacement of the monitored parameters by indirectly estimated H r , R s and wind speed.In addition, the estimated ET o values obtained by means of the PM formula with estimated parameters, and by means of the Hargreaves equation have been compared.The error obtained in parameter estimation varies in magnitude, sign and seasonal distribution along the year.The influence of the error observed in each estimated parameter on ET o estimation also shows high variability.This variability depends on (i) the accuracy of the parameter estimation and (ii) the sensitivity of the PM equation to changes in a given variable.Both factors vary throughout the year, so the distribution of the error amount and sign explains the seasonal variations seen.The combined error due to the absence of R s , H r and wind speed is the result of the sum, or the counteracting, of the individual errors.The SMBE suggests that using PM the error obtained in ET o estimation at monthly level is low, except from November to February when ET o is significantly underestimated.The absolute errors show higher values than mean errors.Thus, from November to February MAE exceeds 25% of the monthly reference evapotranspiration.From March to October the magnitude of the error decreases with values below 15%.
This paper suggests that it is preferable to estimate ET o by means of the PM equation even though some of the required parameters must be indirectly estimated.This conclusion is supported by the better results obtained with PM than with the HG equation.The improvement of ET o estimation is especially noticeable during summer, coinciding with the season when the highest water stress occurs (more ET o and less precipitation).During this season higher accuracy in the estimation of the water losses is required for the assessment of water resource availability and irrigation planning.In addition, PM is a much more flexible method than HG, which will permit incorporation of new monitored data as they become available.The accuracy of the method should improve noticeably with reliable information to correct the errors that show seasonal patterns, such as wind speed and relative humidity.
a) HARGREAVES et al. (1985) showed that the relative solar radiation (i.e.global radiation at the surface, R s , as a proportion of extraterrestrial radiation, R a ) could be estimated from the maximum and minimum temperature by, (4) Where R s is the global radiation at the surface, MJ m -2 R a is the extraterrestrial radiation, MJ m -2 and is determined from latitude and date using the methods detailed in ALLEN et al., 1998.T max and T min are the maximum and minimum air temperature, °C a,b are coefficients.This method for the solar radiation estimation has been successfully tested in other locations of the Iberian Peninsula (CASTELLVI, 2001).b) Supit and van KAPPEL (1998) extended the Hargreaves equation by introducing a term based on cloud cover: (5) ESTIMATION OF REFERENCE EVAPOTRANSPIRATION IN A MOUNTAINOUS MEDITERRANEAN... Where: C w is the mean daytime cloud cover in octaves and a, b, c are empirical coefficients that have been calibrated for a number of stations in Europe (SUPIT & VAN KAPPEL, 1998).
of observations O = Observed value  O mean of observed values P = predicted value i = counter for individual observed and predicted valuesThe purpose of the work is to know the expected error in parameters and ET o estimations, including the events that can be considered as outliers.Thus, error estimators or efficiency model indices which reduce the effect of the outliers, such as RSME, Efficiency model or Willmott´s D(WILLMOTT, 1982) have not been considered.The described error estimators supply different information.MBE indicates the expected average and the sign (over-estimation or sub-estimation) of the error for a given period.MAE indicates the observed average error for each observation in absolute terms.The standardized errors (SMBE and SMAE) consider the magnitude of the error in relation to observed values in a given period, so it is possible to compare the error of different periods of calculation.
4.1.1.Solar radiationThe empirical coefficients a and b have been estimated from the correlation between observed R s and (see equation 4) where a is the slope and b is the constant of the regression equation.Observed R s data comes from the automatic weather station at Yesa for the period 1999-2003.The coefficients were obtained using the Rs values observed during 1999, and the observations from 2000 to 2003 were used to validate.The obtained coefficients (a=0.17;b=0.76) agree with the values given by SUPIT &VAN DER GOOT (2003) for the surrounding locations in the Iberian Peninsula.The station is installed on a plot of irrigated grass so the condition for R s data acquisition is adequate (LLASAT & SNYDER, 1998).

Figure 3 .
Figure 3. Observed error in ET o estimation as consequence of the absence of solar radiation.Figura 3. Error observado en la estimación de ET o a consecuencia de la ausencia de datos de radiación.

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Figure 4. Observed error in ET o estimation as consequence of the absence of relative humidity.Figura 4. Error observado en la estimación de ET o a consecuencia de la falta de datos de humedad relativa.

Figure 5 .
Figure 5. Error in ETo estimation for different inaccuracy levels of H r estimation.Figura 5. Error en la estimación de ET o a consecuencia de diferentes niveles de inexactitud en la estimación de H r .

Figure 8 .
Figure 8.Comparison of error in ET o using Penman Monteith and Hargreaves equations.Figura 8. Comparación de los errores de ET o utilizando las ecuaciones de Penman Monteith y Hargreaves.

Table 1 .
Observed error in Rs estimation from temperature data.Tabla 1. Errores observados en la estimación de Rs a partir de datos de temperatura.

Table 2 .
Observed error in Hr estimation from temperature data.Tabla 2. Errores observados en Hr a partir de datos de temperatura.