A new approach for the construction of high-resolution gridded fields of reference evapotranspiration for the Austrian domain on a daily time step is presented. Gridded data of minimum and maximum temperatures are used to estimate reference evapotranspiration based on the formulation of Hargreaves. The calibration constant in the Hargreaves equation is recalibrated to the Penman–Monteith equation in a monthly and station-wise assessment. This ensures, on one hand, eliminated biases of the Hargreaves approach compared to the formulation of Penman–Monteith and, on the other hand, also reduced root mean square errors and relative errors on a daily timescale. The resulting new calibration parameters are interpolated over time to a daily temporal resolution for a standard year of 365 days. The overall novelty of the approach is the use of surface elevation as the only predictor to estimate the recalibrated Hargreaves parameter in space. A third-order polynomial is fitted to the recalibrated parameters against elevation at every station which yields a statistical model for assessing these new parameters in space by using the underlying digital elevation model of the temperature fields. With these newly calibrated parameters for every day of year and every grid point, the Hargreaves method is applied to the temperature fields, yielding reference evapotranspiration for the entire grid and time period from 1961–2013. This approach is opening opportunities to create high-resolution reference evapotranspiration fields based only temperature observations, but being as close as possible to the estimates of the Penman–Monteith approach.

The water balance in its most general form is determined by fluxes of precipitation, change in storage and evapotranspiration (Shelton, 2009). Particularly for evapotranspiration, measurement is rather costly, since it requires sophisticated techniques like eddy correlation methods or lysimeters. In hydrology, as well as agricultural sciences, the actual evapotranspiration as part of the water balance equation is mostly assessed from the potential evapotranspiration (PET). PET refers to the maximum moisture loss from the surface, determined by meteorological conditions and the surface type, assuming unlimited moisture supply (Lhomme, 1997). Since surface conditions determine the amount of PET, the concept of reference evapotranspiration (ET0) was introduced (Doorenbos and Pruitt, 1977). ET0 refers to the evapotranspiration from a standardised vegetated surface (grass) under unrestricted water supply, making ET0 independent of soil properties. Numerous methods exist for estimating ET0; differences arise in the complexity and the amount of necessary input data for calculation.

A standard method, recommended by the Food and Agricultural Organisation (FAO; Allen et al., 1998), is the Penman–Monteith (PM) formulation of ET0. There are of course countless other methods as thoroughly described in McMahon et al. (2013), but the PM equation is considered the most reliable estimate and serves as a standard for comparisons with other methods (Allen et al., 1998). PM is fully physically based and requires four meteorological parameters (air temperature, wind speed, relative humidity and net radiation). It utilises energy balance calculations at the surface to derive ET0 and is therefore considered a radiation-based method (Xu and Singh, 2000).

On the contrary, much simpler methods which use air temperature as a proxy for radiation (Xu and Singh, 2001) are applied as alternatives for regions where the input data are not sufficient to use PM. One of these simpler methods; the method of Hargreaves (HM; Hargreaves et al., 1985), is used in this paper. It requires minimum and maximum air temperature and extra-terrestrial radiation, which can be derived from the geographical location and the day of year. Hence, HM is more broadly applicable for many regions, because temperature observations are dense and easily accessible. Nevertheless, like most temperature-based methods, HM has been developed for distinct studies and regions also representing distinct climate conditions (Xu and Singh, 2001). To avoid large errors, these temperature-based methods need to undergo a recalibration procedure to make them applicable in different climatic regions than in those they were originally designed for (Chattopadhyay and Hulme, 1997; Xu and Chen, 2005).

In this paper, the method for constructing a data set of ET0 is presented on a daily time resolution and a 1 km spatial resolution based on the method of Hargreaves. The HM is calibrated to the PM in a station-wise assessment. Many studies describe recalibration procedures for ET0 estimations in general (Tegos et al., 2015; Oudin et al., 2005) and for the HM in particular (Pandey et al., 2014; Tabari and Talaee, 2011; Bautista et al., 2009; Gavilán et al., 2006) in order to achieve results comparable to PM. There are also some studies describing methods for creating interpolated ET0 estimates (e. g. Aguila and Polo, 2011; Todorovic et al., 2011). However, two main methodological frameworks emerged for the interpolation of ET0 (McVicar et al., 2007): (i) interpolation of the forcing data and then calculation of ET0, or (ii) calculation of ET0 at every weather station followed by an interpolation of ET0 onto the grid. Here, we follow the first approach and combine it with methods proposed by Tegos et al. (2015) and Mancosu et al. (2014) which use spatially interpolated ET0 model parameters. Gridded data of minimum and maximum temperatures are used as forcing fields for the application of the Hargreaves formulation of ET0. The novelty of this study is the application of elevation as a predictor for the interpolation of the recalibrated HM calibration parameter. Furthermore, these new calibration parameters are also variable in time, changing day by day for all days of the year. This approach goes a step further than the method of Aguilar and Polo (2011) which derived one new calibration parameter for the dry and one for the wet season of the year. An evaluation of the final gridded product is carried out by assessing different error metrics at grid points next to weather stations where PM ET0 is available, and also by comparing the ET0 fields with those of the operational ET0 estimates based on INCA (Integrated Nowcasting through Comprehensive Analysis, Haiden et al., 2011), the nowcasting system of the Austrian weather service.

The presented data set aims at bridging the best of two worlds by (i) using a method for estimating ET0 that is calibrated to the standard algorithm as defined by the FAO and (ii) being applicable to a comprehensive, long-term forcing data set, on a high temporal and spatial resolution.

Location, altitude and setting of the 42 meteorological stations used for calibration.

Location of the meteorological stations used for calibration; coloured circles around points indicate stations that are exemplary; displayed in other plots: Grossenzersdorf (blue), Weissensee Gatschach (green) and Rudolfshuette-Alpinzentrum (red).

The ET0 calculations are based on a high-resolution gridded data set of daily minimum and maximum temperatures calculated for the Austrian domain (SPARTACUS, see Hiebl and Frei, 2016), whereas the actual data stretch beyond Austria to entirely cover catchments close to the border. SPARTACUS is an operational, daily-updated data set starting in 1961. For the ET0 fields, the SPARTACUS temperature forcing is used for the period 1961–2013. The interpolation algorithm is tailored to complex, mountainous terrain with spatially complex temperature distributions. SPARTACUS also aims at ensuring temporal consistency through a fixed station network over the full time period, providing robust trend estimations in space. SPARTACUS uses the SRTM (Shuttle Radar Topography Mission, Farr and Kobrick, 2000) version 2 Digital Elevation Model (DEM). The SRTM DEM is also applied in the present study.

SPARTACUS provides the input data for calculating ET0 following the HM (Hargreaves and Samani, 1982; Hargreaves and Allen, 2003). However, a recalibration of HM is necessary to avoid considerable estimation errors. This is carried out in a station-wise assessment. Data of 42 meteorological stations (provided by the Austrian weather service ZAMG) are used to calibrate the HM to PM on a monthly basis. Figure 1 shows the location of these stations, which are spread homogeneously over Austria and cover different elevations and environmental settings (Table 1). Data of daily global radiation, wind speed, humidity, maximum and minimum temperatures for the period 2004–2013 are used to calculate ET0 simultaneously with HM and PM.

Numerous methods exist for the estimation of ET0, which is defined as the
maximum moisture loss from a standardised, vegetated surface, determined by
the meteorological forcing (Shelton, 2009). These methods can roughly be
classified as temperature-based and radiation-based estimates (Xu and Singh,
2000, 2001; Bormann, 2011). Following the recommendations of
the FAO (Allen et al., 1998) the radiation-based PM provides most realistic results and generally outperforms temperature-based
methods. The overall shortcoming of the PM is the data-intense calculation
algorithm which requires daily values of net radiation, wind speed,
humidity, maximum and minimum temperatures. Data coverage for these
variables is usually rather sparse, particularly if gridded data are
required. ET0 following the PM is calculated as displayed in Eq. (1):

In contrast to the radiation-based PM, the HM is based on daily minimum and
maximum temperatures (

Following these formulations the ET0 for all stations is calculated for the period 2004–2013.

In order to achieve a meaningful representation of ET0 by HM, an adjustment
of the calibration parameter (

Daily time series of ET0 in 2004 for ET0 based on PM
(ET0_p) and HM (ET0_h) at the station
Grossenzersdorf

As a first step, the monthly

Subsequently the daily, station-wise values of

Having these gridded

Monthly values of

The ARET fields are finally evaluated against station data and another ET0 product. Unfortunately, there is no long-term gridded data set of ET0 for the Austrian domain, so we used the ET0 of the nowcasting system INCA (Integrated Nowcasting through Comprehensive Analysis, Haiden et al., 2011) which yields daily fields of ET0 based on PM on 1 kmg 104 grid resolution. INCA uses weather stations, remote sensing data, rainfall radar data as well as DEM information to derive nowcasting fields of several meteorological variables. INCA is operational for several years, but due to constant changes in data input quality and other improvements we chose to use only the 5-year period from 2009 to 2013.

For the skill assessment of the ARET data set we calculate mean monthly values of mean bias, root mean square error (RMSE) and relative error (RE) of those grid points in ARET as well as INCA closest to a station with PM ET0.

Monthly root mean square error

Figure 2a shows, as an example, the daily time series of ET0 as derived by PM (ET0_p) and HM (ET0_h) in the year 2004 at the station Grossenzersdorf. The differences between those two are obvious as ET0_p shows clearly higher variability, with ET0_h underestimating the upward peaks in the cold season and downward peaks in the warm season. This feature is more noticeable in Fig. 2b, which shows the monthly averages over all stations, indicating the spread among all 42 stations. Here, an underestimation of the ET0_h compared to ET0_p from October to April is counteracted by an overestimation between May and September. On the other hand, ET0_p shows higher spread among stations compared to ET0_h except for November to January.

Figure 4 shows the adjusted

Monthly ET0 sums derived from ET0_p, ET0_h and ET0_h.c for three stations located at different altitudes.

For simplicity, for a first assessment the monthly values of

The complete monthly mean time series from 2004 to 2013 of
ET0_p, ET0_h and ET0_h.c for
three stations are shown in Fig. 5. At station Grossenzersdorf, the
underestimation of ET0_h in winter is reduced as well as the
overall underestimation at station Rudolfshuette-Alpinzentrum. On the other
hand, the overestimation in summer at station Weissensee-Gatschach is
considerably reduced with ET0_h.c. These features in
combination with the information on the altitude of the given stations
provide some information on more general characteristics of

Monthly variations of

The results of the spatial interpolation of

The climatological mean (1961–2013) of the final ARET fields is displayed in
Fig. 9a. Lowest daily mean values of below 1.5 mm day

Station-wise monthly third-order polynomial fit of the Hargreaves
calibration parameter

Figure 9b shows the ET0 field of 8 August 2013. For the first time on
that particular day, temperatures reached above 40

July, the month with the highest absolute values of ET0, shows considerable
variations in the last 53 years. As an example, the mean anomaly of ET0 in
July of 1983 with respect to the July mean of 1961–2013 is displayed in
Fig. 10a. This month was characterized by a considerable heat wave and
mean temperature anomalies of

Spatially interpolated

Climatological daily mean ET0 from 1961–2013

In Fig. 11 the overall benefits of the recalibration of the HM are
revealed. It shows the mean ET0 in July 2012, a month accompanied by a
considerable heat wave at the beginning and an overall temperature anomaly
of around

Error characteristics of ARET and INCA against station data.

Upper panel: absolute anomalies of ET0 sum in July 1983

July 2012 monthly mean ET0 based on

The overall performance of ARET compared to the station-wise PM estimates is displayed in Fig. 12. Figure 12a shows the monthly bias of the original HM ET0 and the calibrated ET0 of the nearest grid point. The bias is clearly reduced in nearly all months. However, in April, as the only exception, the bias of the calibrated grid point values is larger than the bias of the original estimation. The biases concerning different levels of altitude are reduced as well, as can be seen in Fig. 12b, which shows the biases in July, and Fig. 12c displaying the biases in January.

A comparison between ARET and INCA ET0 and station-based PM ET0 is given in
Fig. 13, showing ET0 on two different days in summer 2013. The first
example (Fig. 13a and b) is 4 June 2013, a day with mostly
overcast conditions, lower than average temperatures of between 7 to 12

However, comparing error characteristics in ARET and INCA against station
data (Table 2) for the period 2009–2013 reveals only minor differences. The
mean bias all year round is lower in INCA (0.03 mm day

By comparing the characteristics of ET0 based on HM and PM on a daily time
step, it became clear that a recalibration of

Boxplots of monthly mean bias of the station-wise original
Hargreaves ET0 (grey) and the ARET, recalibrated ET0 (red) against
PM ET0

ET0 fields of ARET

To reveal the sources of this altitude dependence of

Station-wise linear regression coefficient of the TOA radiation to
global radiation ratio against the square root of the diurnal temperature
range (

Figure 14 shows the linear regression coefficients of the square root of DTR and global top-of-atmosphere (TOA) radiation ratio on a daily timescale at the 42 stations used in this study. The idea is to get a better understanding of the parameterization embedded in HM, which tries to assess the amount of global radiation via the DTR and the TOA radiation. The coefficients show a distinct altitudinal dependency, particularly in winter. In January, the coefficients are generally high at altitudes between 300 and 1100 m a.s.l. At higher elevations they are dropping considerably, getting slightly negative above 3000 m a.s.l. at station Sonnblick. This altitude dependency is also apparent in the transitional season (cf. Fig. 14; April and October) although not as pronounced as in winter. In July, the coefficients are generally higher, roughly ranging between 0.15 and 0.30, with no change along altitude.

The reasons for the patterns in Fig. 14 seem to be rooted in the lower
atmospheric mixing ratios at the lowest stations, some of them located in
or near cities, which might dampen the DTR, although clear sky conditions
are apparent. At moderate altitudes between 400 and 1500 m a.s.l. the daily
temperature amplitude is more dominantly driven by surface energy balance
processes which reflect higher regression coefficients. Going further up,
the proportion of the DTR which is determined by large-scale air mass
changes rises, as the station locations reach up above the planetary
boundary layer into the free atmosphere. Thus, for any given value of
cloudiness, DTR is much smaller in winter and at high elevations than in low-elevation
environments where boundary layer processes are dominant. This
means that for yielding realistic values of global radiation relative to TOA
radiation, a much higher

Although these circumstances seem to be a drawback of the methodology, the
overall effect is only minor. Figure 15 shows the HM ET0 in dependence of
the DTR and the daily mean temperature. At low daily mean temperatures,
between

ET0 response to varying daily mean temperature and diurnal
temperature range; ET0 values are calculated with 1 April top-of-the-atmosphere radiation and the original

However, the procedure of altering the coefficient

Evaluating both the ARET and INCA gridded ET0 estimates against station-based ET0 revealed only minor differences in bias, RMSE and RE, which underpins the strength of the proposed calibration method. However, there are situations where the deviations compared to station-based ET0 are particularly large in both the ARET and the INCA data set. As an example for overcast conditions after a considerable amount of rainfall, for a couple of days we compared ARET to INCA ET0 (cf. Fig. 13) and found that ARET clearly overestimates ET0. Under the given circumstances, ARET cannot compete with INCA, which considers, through the use of PM, information on relative humidity, which might have a strong forcing on ET0 on that particular day (information that is not available in the ARET estimate). On the other hand, on a typical sunny summer day, INCA overestimates ET0, where ARET is rather close to the station estimates. There might be some biases in the radiation analysis in INCA causing this deviation from the station data. Global Radiation is calculated based on sunshine duration estimates (blended remote sensing and station data) driving a simple radiation model (Haiden et al., 2011).

As shown in the evaluation of the ARET fields against INCA, the error characteristics are rather similar, although in INCA ET0 is calculated using PM. The calibration of HM, though very simple, yields very satisfying results of the final product. Particularly when considering Austrian topography it comes clear that using a method like HM without calibration has major impacts on the result. Using noncalibrated HM ET0 data for rainfall–runoff modelling, for example, would introduce large errors and uncertainties. Given the fact that gridded data of ET0 based on PM are only available for a rather short time period from the INCA system, the ARET data set provides a sound alternative for ET0 estimates on a high spatial resolution covering the last 53 years.

In this paper, a gridded data set of ET0 for the Austrian domain from
1961–2013 on daily time step is presented. The forcing fields for estimating
ET0 are daily minimum and maximum temperatures from the SPARTACUS data set
(Hiebl and Frei, 2016). These fields are used to calculate ET0 by the
formulation of Hargreaves et al. (1985). The HM is calibrated to the
PM equation, which is the recommended method by the FAO (Allen
et al., 1998). This is done using a set of 42 meteorological stations from
2004–2013, which have full data availability for calculating ET0 by PM. The
adjusted monthly calibration parameters

This data set is highly valuable for users in the field of hydrology, agriculture, ecology (among others) as it provides ET0 in a high spatial resolution and a long time period. Data for calculating ET0 by recommended PM are usually not available for such long time spans and/or with this spatial and temporal resolution. However, the method presented in this study combined both strengths of long time series, high spatial and temporal resolution provided by the temperature-based HM and the physical, more realistic radiation-based PM by adjusting HM.

The authors want to thank the Federal Ministry of Science, Research and Economy (Grant 1410K214014B) for financial support. We also like to thank Johann Hiebl for providing the SPARTACUS data and for fruitful discussions on the manuscript. The Austrian Weather Service (ZAMG) is acknowledged for providing the data of 42 meteorological stations. We would also like to thank two anonymous reviewers for the valuable comments which improved the manuscript substantially. Edited by: J. Seibert