Post on 18-Jan-2023
Regional calibration of Hargreaves equation for
estimating reference ET in a semiarid
environment
P. Gavilan *, I.J. Lorite, S. Tornero, J. Berengena
IFAPA, Area de Produccion Ecologica y Recursos Naturales, Centro de Investigacion y Formacion
Agraria ‘‘Alameda del Obispo’’, Avd. Menendez Pidal s/n, 14004 Cordoba, Spain
Accepted 1 May 2005
Available online 25 May 2005
Abstract
The Hargreaves equation provides reference evapotranspiration (ETo) estimates when only air
temperature data are available, although it requires previous local calibration for acceptable
performance. This equation has been evaluated under semiarid conditions in Southern Spain using
data from 86 meteorological stations, comparing daily estimates against those from the FAO-56
Penman–Monteith equation, which was used as standard. Variability of results among location was
clearly apparent, with MBE ranging from 0.74 to �1.13 mm d�1 and RMSE from 0.46 to
1.65 mm d�1. Maxima under- and overestimation amounted to 24.5 and 22.5%, respectively. In
general, larger under- and overestimations occurred in stations located close to the coast and at inland
areas, respectively. Yearly means of windspeed (V) and daily temperature range (DT) fairly
influenced the accuracy of the equation. It was more accurate for windy locations with large DT,
and for locations with light wind conditions combined with low to moderate values of DT. According
to the values taken by V and DT, the stations were represented by points on the DT–V coordinate
plane, in which four regions were delimited. A regional calibration was carried out considering only
temperature and wind conditions. Correction was not necessary for stations located within two of
them; for the other two regions, new values for the empirical coefficient of the equation are suggested
(0.0027 and 0.0021). After correction, average RMSE and maximum and minimum MBE decreased
substantially (12, 24 and 41%, respectively), and 74 out of the 86 locations gave quite accurate
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Agricultural Water Management 81 (2006) 257–281
* Corresponding author. Tel.: +34 957 016 055; fax: +34 957 016 043.
E-mail addresses: pedrod.gavilan@juntadeandalucia.es (P. Gavilan), ignacioj.lorite.ext@juntadeandalucia.es
(I.J. Lorite), sonia.tornero.ext@juntadeandalucia.es (S. Tornero), joaquin.berengena@juntadeandalucia.es
(J. Berengena).
0378-3774/$ – see front matter # 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.agwat.2005.05.001
results, with relative values of MBE lower than 10% in most cases. Alternatively, another method
based on kriging interpolation was proposed to obtain, for each individual station, locally adjusted
values for the empirical coefficient as a function of the same variables. This second correction
procedure behaved even better than the first one. There was a 15% improvement in the average
RMSE, and maximum and minimum MBE values decreased 50 and 70%, respectively. At all
locations, relative values of MBE were less than 10% and in 70% of them were lower than 5%.
Validation was done by using data from 14 meteorological stations for other Spanish regions, and the
consequences from the application of the corrections proposed for an irrigation district are discussed.
# 2005 Elsevier B.V. All rights reserved.
Keywords: Calibration; Evapotranspiration models; Hargreaves; Reference evapotranspiration; Semiarid
environment
1. Introduction
The need for an accurate and easy method to estimate reference evapotranspiration
(ETo) has been stated by several authors (Allen, 1986; Heerman, 1986). Quantification of
ETo is necessary for crop production, management of water resources, irrigation
scheduling and environmental assessment (Sharma, 1985; Jensen et al., 1990). Several
empirical methods for ETo estimation have been proposed; they should be evaluated for
local conditions before being used (Pruitt and Doorenbos, 1977). Recently, the FAO-56
version of Penman–Monteith equation has been established as a standard for calculating
reference evapotranspiration (Allen et al., 1998). The calculation procedure requires
accurate measurements of air temperature and relative humidity, solar radiation and
windspeed. Unfortunately, there are a limited number of meteorological stations where
these climatic variables are accurately measured, even in developed countries. This lack of
meteorological data was resolved by Hargreaves et al. (1985) developing an easy approach
for calculating ETo. The Hargreaves equation (Hargreaves and Samani, 1985) requires only
daily mean, maximum and minimum air temperature, usually available at most weather
stations world-wide, and extraterrestrial radiation (Droogers and Allen, 2002). This
method behaves best for weekly or longer predictions although some accurate ETo daily
estimations have been reported in literature (Hargreaves and Allen, 2003).
The most recent and massive comparison using daily weather data between
Hargreaves equation and the ASCE Penman–Monteith (ASCE P–M) method, with the
latter used as reference, was made by Itenfisu et al. (2003). The analysis used data from 49
sites in 16 states in USA and showed that the ratio between ASCE Penman–Monteith and
Hargreaves ETo ranged from 1.43 to 0.79, with a mean of 1.06 and a standard deviation of
0.13. The Hargreaves equation tended to predict greater ETo than ASCE PM when mean
daily ETo was low, and vice versa. Besides, the Hargreaves equation is sensitive to
sensible heat advection, so that, when advection is severe, it underestimates ETo up to
25% for daily periods (Berengena and Gavilan, 2005). A similar study was carried out
with data from 37 meteorological stations of the CIMIS network, with like results
(Temesgen et al., 2005).
Several attempts to improve accuracy of Hargreaves equation have been made, mainly
by using windspeed, rainfall or atmospheric pressure as auxiliary variables in the equation
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281258
(Allen, 1993, 1995; Jensen et al., 1997; Droogers and Allen, 2002). However, the lack of
those data in most of the meteorological stations limits the development of functions for
adjusting the equation. In other cases, the authors themselves concluded that the
improvement was insufficient to recommend that kind of adjustment as a standard practice
(Allen, 1993). Therefore, the adjustment of the equation parameters to local conditions is
an alternative way to improve its estimations that should be explored (Jensen et al., 1997;
Xu and Singh, 2002; Martınez-Cob and Tejero-Juste, 2004; Samani, 2004).
Recently, Samani (2000) proposed a modification in the original equation to estimate
solar radiation and ETo (Hargreaves and Samani, 1982), based on the annual average of
daily temperature range DT (difference between daily maximum and minimum air
temperature), but this adjustment did not work well in Southern Spain (Vanderlinden
et al., 2004). More recently, two different attempts have been made to improve the
Hargreaves equation accuracy under semiarid conditions in two Mediterranean areas.
One was proposed by Martınez-Cob and Tejero-Juste (2004), who assumed that the
behavior of the equation would be similar at locations of semiarid regions with similar
wind conditions. They concluded that no local correction would be required for windy
locations, and they recommended using an empirical coefficient equal to 0.0020 for non-
windy locations, instead of the originally proposed (0.0023) by Hargreaves and Samani
(1985). The other attempt was made by Vanderlinden et al. (2004). In this case, the
authors carried out a regional calibration resulting in a correction based on the ratio T/DT,
where T is the long-term annual average of air temperature. Both studies were made in
two different semiarid areas in Spain, the first one in the Ebro River valley, in Aragon
(Northeastern Spain); and the second in Andalusia (Southern Spain). In both cases, a limited
number of meteorological stations were used (9 and 16 stations, respectively). Moreover, in
the second case, estimated, rather than measured solar radiation values, were used in the
calibration process, with no information being available to evaluate the quality of
meteorological data. On the other hand, no study has been reported so far which includes
temperature and windspeed to improve the estimations of the Hargreaves equation.
The objective of this work was to develop a regional calibration for Hargreaves equation
considering only temperature and wind conditions. For this task, a regional meteorological
network installed in 2000 in Andalusia was used. The procedure has been validated using
additional weather data from other locations in Spain.
2. Materials and methods
2.1. Area description
This study has been carried out in Andalusia (Spain), located between the meridians 18and 78W and the parallels 378 and 398N, occupying an extension around 9 Mha. The
climate is semiarid, typically Mediterranean, with very hot and dry summers. Therefore,
the water balance is extremely unfavourable to spring/summer crops. Additionally, a high
inter-annual variability in rainfall is present, so, although the water resources are highly
regulated, a clear insufficiency of the system has been detected in order to meet the increase
in water requirements.
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 259
In Andalusia 900,000 ha are irrigated (around 20% of the cultivated area) under a great
variety of conditions. Modern irrigation systems with supply on demand coexist with old
and obsolete surface irrigation systems, where low priced water is available due to
government subventions. These systems with reduced irrigation efficiency and low water
productivity represent around 55% of the total irrigated area. Additionally, the growth in
irrigated area in the last 15–20 years was not parallel to new water resources development,
giving origin to a structural water deficit estimated presently at 1300 hm3 (Corominas,
2002).
2.2. Weather data source
Weather data sets were obtained from 86 stations of the Agroclimatic Information
Network of Andalusia (RIA) (Fig. 1). This network is at present composed of 91 automatic
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281260
Fig. 1. Spatial distribution of the 86 RIA meteorological stations used in the analysis.
weather stations, although only 86 of these were used in the present study. The other five
stations have been recently installed and their data series were too short. This network was
deployed to provide coverage to most of the irrigated area (De Haro et al., 2003). It was
designed and installed during 1999–2000 by the Ministry of Agriculture, Fisheries and
Food of Spain (MAPYA) to improve irrigation water management. Funding came from the
European Union. Network exploitation and maintenance are carried out by the IFAPA
(Agricultural Research Institute of Regional Government of Andalusia). Each station is
controlled by a CR10X datalogger (Campbell Scientific) and is equipped with sensors to
measure air temperature and relative humidity (HMP45A probe, Vaisala), solar radiation
(pyranometer SP1110 Skye), wind speed and direction (wind monitor RM Young 05103)
and rainfall (tipping bucket rain gauge ARG 100). Air temperature and relative humidity
are measured at 1.5 m and wind speed at 2 m above soil surface. Mean semi hourly and
daily average values are registered for each meteorological variable. Transfer of data from
stations to the data-collecting seat (Main Center) is accomplished by using GSM modems.
The Main Center incorporates a server, which sequentially connects to each station to
download the information collected during the last 24 h. 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 the routine maintenance program
of the network, including sensor calibration and data validation. The collected values from
each station are checked for validity by different tests: range, step and persistence,
according to Meek and Hatfield (1994) and Shafer et al. (2000). Additionally, a specific test
has been performed for solar radiation measurements, according to Allen (1996).
Only daily averages were used for the study. At least two years of data per station were
used although for most of the stations (73 sites) three years were available and used.
Locations of the 86 stations are given in Table 1 and Fig. 1. Site elevations ranged from 4 to
1212 m above mean sea level; longitude, from 184600900W to 781404900W; and latitude,
from 3681701000N to 3881801400N. In Table 1, the annual average values of meteorological
stations are reported. Average annual precipitation ranged from 183 to 804 mm; average
annual air temperature, from 12.9 to 18.9 8C; relative humidity, from 54 to 74%; and
annual average windspeed, from 0.9 to 3.1 m s�1. Fifteen sites can be considered as coastal
and 71 as inland locations. Therefore, the geographic and climatic diversity of the sites is
evident and representative of the Andalusian irrigation districts.
2.3. ET reference methods
The use of a standard method to develop or calibrate an equation for computing ETo is
necessary when measurements of ETo are not available. Advantages and disadvantages of
this procedure are described by Irmak et al. (2003). The use of one equation to calibrate or
validate another equation is not recent and many authors have used and recommended this
procedure (Allen et al., 1998; Itenfisu et al., 2003; Irmak et al., 2003). In addition, the FAO
Expert Consultation on Revision of FAO Methodologies for Crop Water Requirements
recommended that empirical methods should be calibrated or validated using the Penman–
Monteith equation as reference (Smith et al., 1991). This equation has proved to behave
well under a variety of climatic conditions, and that is the reason why it was decided to use
the FAO-56 Penman–Monteith (FAO-56 P–M) equation as reference to evaluate and
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 261
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281262
Table 1
Summary of weather station site characteristics used in the study
Site Latitude
(8)Longitude
(8)Elevation
(m)
DT (8C) RH
(%)
V
(m s�1)
Rainfall
(mm year�1)
ETo
(mm d�1)
Region I
1 Cuevas Almanz. 37.258 1.799 20 10.2 64.5 1.1 201 3.3
2 Conil Frontera 36.337 6.131 26 11.0 73.3 1.3 411 3.3
3 Cadiar 36.924 3.182 950 10.6 57.7 1.3 507 3.3
4 Moguer Cebollar 37.241 6.801 63 11.8 69.1 1.4 443 3.4
5 Alcaudete 37.578 4.077 645 10.9 57.6 1.1 564 3.4
6 Malaga 36.757 4.536 68 11.1 63.3 1.2 492 3.5
7 Puebla Cazalla 37.219 5.349 229 12.0 61.3 1.4 582 3.7
Region II
8 La Mojonera 37.789 2.703 142 8.3 62.7 2.0 272 3.8
9 Almerıa 36.836 2.402 22 8.8 65.3 1.6 183 3.7
10 Nıjar 36.952 2.156 182 9.7 63.2 2.0 264 3.9
11 Finana 37.158 2.837 971 10.6 54.5 2.7 308 4.2
12 V. de Fatima 37.390 1.769 185 10.0 61.1 2.3 239 4.1
13 Tıjola 37.373 2.456 740 10.9 59.0 2.2 284 3.9
14 Adra 36.748 2.992 42 7.3 68.9 1.8 284 3.4
15 Sanlucar B. 36.835 6.294 22 11.8 73.1 2.4 544 3.8
16 Vejer Frontera 36.286 5.839 24 10.4 70.5 3.1 571 3.9
17 Jimena Frontera 36.414 5.384 53 11.7 69.9 2.2 795 3.7
18 Pto. Sta.Marıa 36.617 6.151 20 11.2 69.3 2.6 727 3.9
19 Hornachuelos 37.721 5.159 157 11.9 62.2 1.9 687 4.0
20 Iznalloz 37.417 3.550 935 11.6 58.1 2.1 651 3.8
21 Jerez Marq. 37.192 3.149 1212 11.9 56.4 1.8 381 3.5
22 Tojalillo-Gib. 37.319 7.018 52 11.6 66.9 2.1 692 4.0
23 Lepe 37.241 7.243 74 9.6 69.6 2.4 542 4.0
24 Gibraleon 37.414 7.059 169 10.8 66.6 1.8 724 3.8
25 Puebla Guzman 37.553 7.247 288 11.1 67.0 3.1 642 4.3
26 El Campillo 37.662 6.598 406 10.3 62.2 2.1 804 3.9
27 Palma Condado 37.386 6.540 192 11.1 65.0 1.9 664 3.8
28 S.Jose Propios 37.859 3.229 509 11.2 55.9 2.8 391 4.6
29 Sabiote 38.081 3.234 822 9.5 58.9 2.5 466 3.9
30 Mancha Real 37.917 3.595 436 11.7 56.9 2.0 434 4.0
31 Linares 38.06 3.648 443 11.3 57.9 2.0 484 4.0
32 Velez Malaga 36.797 4.130 49 11.9 63.7 1.7 457 3.9
33 Estepona 36.446 5.208 199 8.3 61.7 2.6 669 4.0
34 Sierra Yeguas 37.139 4.835 464 11.7 64.3 2.3 523 3.8
35 Churriana 36.675 4.502 32 10.2 64.5 2.1 432 3.9
36 Puebla Rıo II 37.081 6.045 41 11.7 71.9 1.8 563 3.7
Region III
37 Huercal-Overa 37.413 1.883 317 13.3 62.7 1.4 280 3.6
38 Adamuz 37.099 4.444 90 14.1 64.4 1.2 671 3.4
39 Pinos Puente 37.263 3.772 594 14.5 59.5 0.9 472 3.3
40 Zafarraya 36.841 4.152 905 12.5 66.1 1.3 684 3.1
41 Padul 37.020 3.599 781 12.8 59.1 1.2 444 3.4
42 Moguer 37.148 6.791 87 12.2 74.4 0.9 667 3.1
43 Niebla 37.348 6.734 52 13.2 69.3 1.5 702 3.6
44 Aroche 37.959 6.944 299 13.5 66.1 1.4 791 3.5
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 263
Table 1 (Continued )
Site Latitude
(8)Longitude
(8)Elevation
(m)
DT (8C) RH
(%)
V
(m s�1)
Rainfall
(mm year�1)
ETo
(mm d�1)
45 Torreblascop. 37.989 3.688 291 14.5 62.2 1.0 485 3.4
46 Ubeda 37.944 3.299 358 15.8 63.1 1.0 506 3.4
47 Marmolejo 38.057 4.118 208 15.0 67.1 1.4 669 3.5
48 Chiclana Segura 38.304 2.954 510 14.8 62.8 1.4 502 3.5
49 Higuera Arjona 37.950 4.006 267 14.9 63.2 1.0 527 3.3
50 Santo Tome 38.030 3.082 571 12.5 60.0 1.1 488 3.3
51 Jaen 37.892 3.770 299 14.9 60.9 1.5 431 3.7
52 Antequera 37.057 4.559 457 13.8 62.5 1.4 495 3.4
53 Archidona 37.078 4.429 516 14.7 64.8 1.1 519 3.2
54 Cartama 36.718 4.677 95 12.3 65.6 1.0 334 3.3
55 La Luisiana 37.526 5.227 188 12.9 64.1 1.5 620 3.6
56 Sanlucar Mayor 37.423 6.254 88 14.3 67.3 1.4 645 3.5
57 Villanueva Minas 37.614 5.682 38 14.6 68.2 1.2 681 3.3
58 Lora del Rıo 37.660 5.539 68 13.6 67.0 1.4 698 3.6
Region IV
59 Tabernas 37.092 2.301 435 12.8 57.9 2.0 265 4.0
60 Jerez Frontera 36.644 6.012 32 12.4 67.8 1.5 657 3.6
61 Basurta. Jerez 36.758 6.016 60 13.2 69.1 1.9 640 3.7
62 Villamartın 36.845 5.622 171 13.6 65.4 2.0 648 3.9
63 Belmez 38.255 5.208 523 13.0 63.2 2.4 578 4.0
64 Palma del Rıo 37.677 5.246 134 12.1 62.7 2.7 623 4.5
65 El Carpio 37.915 4.502 165 14.0 63.9 1.8 607 3.8
66 Cordoba 37.862 4.800 117 12.9 64.1 1.7 696 3.8
67 Santaella 37.524 4.884 207 12.9 62.9 1.8 570 3.9
68 Baena 37.693 4.305 334 13.4 60.0 1.6 463 3.9
69 Baza 37.566 2.766 814 14.8 59.7 2.0 382 3.9
70 Puebla D.Fad. 37.877 2.380 1110 14.1 62.1 2.7 317 4.0
71 Loja 37.170 4.137 487 13.7 61.8 2.0 450 4.0
72 Almonte 37.152 6.470 18 13.1 71.6 1.8 583 3.6
73 Pozoalcon 37.673 2.929 893 12.4 63.5 1.5 418 3.4
74 Pizarra 36.768 4.714 84 12.2 62.7 1.6 494 3.9
75 Palacios-Villaf. 37.180 5.937 21 12.8 70.4 1.9 600 3.7
76 Cabezas S. Juan 37.017 5.884 25 13.8 69.2 2.2 551 4.0
77 Lebrija 1 36.978 6.125 25 13.4 71.5 2.2 608 3.9
78 Lebrija 2 36.900 6.009 40 13.2 67.7 2.3 611 4.1
79 Aznalcazar 37.152 6.272 4 13.4 70.3 2.3 682 4.0
80 Puebla Rıo I 37.227 6.116 25 12.3 71.4 1.9 675 3.6
81 Ecija 37.594 5.075 125 13.5 62.4 2.0 537 4.1
82 Osuna 37.256 5.134 214 13.9 62.6 2.3 491 4.2
83 La Rinconada 37.458 5.924 37 13.0 67.8 1.9 681 3.7
84 Los Molares 37.177 5.672 90 13.7 67.2 2.4 565 4.2
85 Guillena 37.507 6.063 191 12.6 62.4 1.7 678 3.9
86 Carmona Tomejil 37.402 5.586 79 13.6 66.0 2.4 595 4.2
Note: DT: long-term annual mean of daily temperature range (difference between maximum and minimum
temperature of the day); RH: long-term average relative humidity of the day; V: long-term average wind
velocity; Rainfall: long-term annual average precipitation; ETo: long-term annual average reference evapo-
transpiration.
calibrate the Hargreaves equation in this work. That equation can be written as (Allen et al.,
1998):
EToPM ¼ 0:408DðRn � GÞ þ gð900=ðT þ 273ÞÞu2ðes � eaÞDþ gð1 þ 0:34u2Þ
(1)
where ETo is the computed reference evapotranspiration (mm d�1); D is the slope of
saturation vapor pressure versus air temperature curve (kPa 8C�1); Rn is the daily net
radiation (MJ m�2 d�1); G is the soil heat flux (MJ m�2 d�1); g is the psychrometric
constant (kPa 8C�1); T is the mean air temperature at 2 m height (8C); u2 is the daily mean
of wind speed at 2 m height (m s�1); es is the saturation vapor pressure (kPa); and ea is the
actual vapor pressure (kPa). All parameters were calculated using the equations provided
by Allen et al. (1998). The soil heat flux (G) was assumed to be zero over the calculation
time step period (24 h).
The Hargreaves equation (Hargreaves and Samani, 1985) can be written as:
EToH ¼ 0:0023RaðT þ 17:8ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTmax � Tmin
p(2)
where ETo is the computed reference evapotranspiration (mm d�1); Ra is the water
equivalent of the extraterrestrial radiation (mm d�1) computed according to Allen et al.
(1998); Tmax, Tmin and T are the daily maximum, minimum and mean air temperature (8C),
with T calculated as the average of Tmax and Tmin. 0.0023 is the original empirical
coefficient proposed by Hargreaves and Samani (1985).
2.4. Validation
Although the correction proposed in this work is based on regional calibration, with data
covering a diversity of climatic conditions (from subtropical coastal areas in the southeast
to semi-desert areas in the east), it is advisable to validate it. The proposed adjustment was
validated by using data from 14 meteorological stations located in different areas of Spain
and belonging to the Agroclimatic Information System (SIAR) from Ministry of
Agriculture, Fisheries and Food (MAPYA). Site elevations ranged from 6 to 717 m above
mean sea level; longitude, from 080802400W to 585600400W; and latitude, from 3783603600Nto 4181004800N. Average annual precipitation ranged from 144 to 892 mm; average annual
air temperature, from 11.3 to 18.6 8C; relative humidity, from 58 to 72%; and annual
average windspeed, from 1.2 to 2.6 m s�1. Two sites can be considered as coastal and 12 as
inland locations. Three years of measured daily weather data were used in the validation
process (from 2001 to 2003). The EToPM method was also used as reference for
comparison.
2.5. Statistical analysis
ETo estimates from both methods were compared by using simple error analysis and
linear regression. For each location, the following parameters were calculated (Willmott,
1982): mean bias error (MBE), root mean square error (RMSE), relative error (RE) and the
ratio between both average ETo estimations (R). Additionally, maximum, minimum, mean
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281264
and standard deviations of RMSE, MBE and R for each different group of locations
(Itenfisu et al., 2003) were also calculated.
MBE ¼Pn
i¼1ðyi � xiÞn
(3)
RMSE ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðyi � xiÞ2
n
s(4)
RE ¼ MBE
x� 100 (5)
R ¼ yave
xave
(6)
where n is the number of available days; yi is the estimated EToH; xi is the estimated EToPM;
xave and yave are the averages of EToPM and EToH for a given site, respectively.
3. Results
3.1. Penman–Monteith FAO-56 versus Hargreaves ETo
Variability from one location to another in the results of comparison between both
methods was clearly apparent. Thirty five locations significantly underestimated daily ETo
with respect to Penman–Monteith FAO-56 ETo and 21 clearly overestimated it. The
method provided satisfactorily good ETo estimations for 30 locations (under- or
overestimations were smaller than 5%). Considering all locations, the MBE values ranged
from 0.74 to �1.13 mm d�1, with a mean of �0.10 mm d�1 (Table 2). RMSE ranged from
0.46 to 1.65 mm d�1, with an average value of 0.80 mm d�1. Ratios between EToH and
EToPM mean values showed that maximum underestimation produced was as high as 24.5%
and the maximum overestimation found amounted to 22.5%. Considering only locations
where Hargreaves equation underestimated ETo, the MBE reached a minimum of
�1.13 mm d�1, with a mean value of �0.38 mm d�1. In this case, RMSE ranged from 0.51
to 1.65 mm d�1, with an average value of 0.85 mm d�1. The ETo ratio, as defined above,
was 0.903 indicating a mean underestimation of 10% derived from the use of Hargreaves
equation. In locations where Hargreaves equation overestimated ETo, the mean value of
MBE was equal to 0.29 mm d�1, ranging from 0.01 to 0.74 mm d�1, whereas RMSE
varied between 0.46 and 1.04 mm d�1, with an average value of 0.72 mm d�1. In the latter
case, R was 1.087, indicating a mean overestimation of 9%.
The greatest underestimations occurred mainly for stations located in coastal areas,
although there were some inland stations showing the same tendency. In all cases, high
windspeed and small DT values were found. By contrast, the greatest overestimations took
place at inland areas with high DT values and low windspeeds, although some
overestimations were also present near the coast. Therefore, the method was more accurate
for windy locations with high DT values, and for non windy sites with low or moderate DT
values. It can be concluded that the lack of agreement between both methods were not only
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 265
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Table 2
Summary of statistics from comparison between Hargreaves and Penman–Monteith FAO-56 ETo
RMSE (mm d�1) MBE (mm d�1) Ratio
Maximum Minimum Mean RMSE (%) Maximum Minimum Mean Maximum Minimum Mean
Underestimated 1.65 0.51 0.85 (0.254) 21.8 0.00 �1.13 �0.38 (0.285) 0.999 0.755 0.903 (0.070)
Overestimated 1.04 0.46 0.72 (0.149) 20.6 0.74 0.01 0.29 (0.226) 1.225 1.002 1.087 (0.069)
All locations 1.65 0.46 0.80 (0.224) 21.2 0.74 �1.13 �0.10 (0.424) 1.225 0.755 0.980(0.115)
Note: RMSE: root mean square error. MBE: mean bias error. Ratio: quotient between average Hargreaves ETo and Penman–Monteith ETo. The values within brackets are
standard deviation of mean.
affected by the geographical locations of the stations, but also, and mainly, by climatic
conditions.
Fifteen stations are located close to the coast. High underestimations occurred at 12 of
them, where MBE reached a minimum of �0.97 mm d�1, with a mean value of
�0.62 mm d�1. For two of them, the performance of the equation was good and only for
one there was a clear overestimation, with a MBE of 0.40 mm d�1. Annual mean value of
DT at coastal locations was 10 8C. Underestimations increased as the annual average DT
decreased. Therefore, as a first approximation, it may be inferred that when the annual DT
value is small, ETo tends to be underestimated as a consequence of the underestimation of
Rs by the Hargreaves equation.
At most of the inland stations, annual average of daily DT values was higher than 11 8C,
with an average of 12.8 8C. Locations with high DT values tended to overestimate ETo,
although variability observed under these conditions suggested that other factors could
affect the accuracy of the method, indicating that an adjustment based only on DT could be
insufficient. Furthermore, a certain correlation was found between annual average
windspeed and the accuracy of the method, with errors being greater for higher windspeed,
especially above 2 m s�1, when underestimations were more clear.
Inability of the Hargreaves equation to account for the effects of high windspeeds as
well as for high vapor pressure deficits (typical advective conditions in semiarid
environments) has been established (Martınez-Cob and Tejero-Juste, 2004; Berengena
and Gavilan, 2005; Temesgen et al., 2005). Thus, an adjustment including this new
variable would be more adequate, as these authors proposed. Although corrections based
on wind functions are not practical, because windspeed records are only available from
no more than a few weather stations, a calibration based on a qualitative knowledge of
windspeed conditions at the site could be enough (Martınez-Cob and Tejero-Juste,
2004).
A detailed analysis has been undertaken representing every station in a coordinate
system as a point defined by their respective annual DT and V mean values. For
convenience, four regions were delimited in the graph defined by DT = 12 8C and
V = 1.5 m s�1 (see Fig. 2). In the first region (DT < 12 8C and V < 1.5 m s�1) some coastal
stations and three inland locations were found, with annual mean windspeeds ranging from
1.1 to 1.4 m s�1 and MBE less than 0.11 mm d�1 (Table 3). Within the second region
(DT < 12 8C and V > 1.5 m s�1), the method usually underestimated as a result of the
increase in the aerodynamic component of the evapotranspiration, which is not accounted
for by the Hargreaves equation. In this case, the minimum MBE was �1.13 mm d�1 and
the maximum RMSE, 1.65 mm d�1. For the stations located in the third region
(DT > 12 8C and V < 1.5 m s�1) Hargreaves equation overestimated ETo, due to high DT
values, with an average overestimation of 0.43 mm d�1, which is the average value of the
MBE, and a maximum RMSE of 1.04 mm d�1. And finally, within the fourth region
(DT > 12 8C and V > 1.5 m s�1), the relatively high windspeeds tended to produce
underestimations, but this tendency was partially compensated by the opposite effect
produced by high values of DT, so that the MBE for this region was less than
�0.37 mm d�1, with only two exceptions in which average windspeed was very high
(higher than 2.7 m s�1). As it will be seen, in these cases – very high windspeed and high
DT – a specific correction should be applied. It can be thus concluded that, in our
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 267
conditions, stations located in regions I and IV do not require adjustment, whereas those
located in regions II and III should be adjusted to obtain more accurate estimates.
3.2. Adjusted coefficients
Forcing regressions lines – EToH on EToPM – through the origin, the ratio between
0.0023 and the regression slope would provide a locally adjusted coefficient of the
Hargreaves equation for each location (Fig. 3). For stations located in regions I and IV,
mean values of those new coefficients were close to 0.0023, they were 0.00235 and
0.00241, respectively, with deviations amounting to 2 and 5% over the original value. For
the latter case, the average of the adjusted coefficients rose so much due to the existence of
two stations in which the windspeed was especially high. For these, the adjusted
coefficients increased up to 0.0029. For region II the average value for the new coefficients
was 0.00273, which is about 19% higher than the original value, while for region III
became about 9% smaller (0.00209). So, it was proposed to use new coefficients equals to
0.0027 and 0.0021, instead of 0.0023, for stations located in regions II and III, respectively.
Stations located in regions I and IV should not require adjustment, although under high
wind conditions it may be advisable to increase up to 0.0026 the value of the coefficient for
stations located in region IV. This last coefficient is not taken into consideration in the
discussion that follows.
Corrected Hargreaves ETo values can then be easily obtained by knowing DT and
windspeed. The first variable is readily available for most locations, but this is not usually
the case for windspeed. However, a qualitative knowledge of windspeed conditions at the
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281268
Fig. 2. Distribution of each location in function of annual means of windspeed (V) and annual mean of daily
temperature range (DT).
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Table 3
Summary of statistics from comparison between Hargreaves and Penman–Monteith FAO-56 ETo using adjustment based on two coefficients before and after the adjustment
Region RMSE (mm d�1) MBE (mm d�1) Ratio
Maximum Minimum Mean RMSE (%) Maximum Minimum Mean Maximum Minimum Mean
Non-adjusted
I 0.96 0.46 0.61 (0.16) 17.8 0.11 �0.03 0.03 (0.054) 1.033 0.989 1.008 (0.016)
II 1.65 0.52 0.94 (0.26) 24.0 �0.09 �1.13 �0.52 (0.270) 0.976 0.755 0.866 (0.064)
III 1.04 0.56 0.75 (0.15) 22.1 0.74 0.10 0.43 (0.185) 1.225 1.027 1.128 (0.057)
IV 1.22 0.53 0.73 (0.16) 18.7 0.17 �0.66 �0.11 (0.202) 1.046 0.850 0.974 (0.050)
All 1.65 0.46 0.80 (0.22) 21.2 0.74 �1.13 �0.10 (0.424) 1.225 0.755 0.980(0.115)
Adjusted
I 0.96 0.46 0.61 (0.16) 17.8 0.11 �0.03 0.03 (0.054) 1.033 0.989 1.008 (0.016)
II 1.13 0.53 0.78 (0.17) 20.1 0.56 �0.52 0.05 (0.298) 1.145 0.887 1.017 (0.075)
III 0.79 0.44 0.59 (0.09) 17.2 0.38 �0.22 0.10 (0.175) 1.119 0.937 1.030 (0.052)
IV 1.22 0.53 0.73 (0.16) 18.7 0.17 �0.66 �0.11 (0.202) 1.046 0.850 0.974 (0.050)
All 1.22 0.44 0.70 (0.17) 18.7 0.56 �0.66 0.01 (0.239) 1.145 0.850 1.006 (0.062)
Note: RMSE: root mean square error. MBE: mean bias error. Ratio: quotient between average Hargreaves ETo and Penman–Monteith ETo. The values within brackets are
standard deviation of mean.
site will suffice, and the correction procedure will only require deciding whether the
location is windy or not, as Martınez-Cob and Tejero-Juste (2004) proposed. For this
purpose, these authors proposed using some indirect assessment of windspeed based on
such characteristics as topography of the area and presence of wind mills for wind power
energy production, besides any other data furnished by the national meteorological
institutions.
The use of two new coefficients improved prediction over the original Hargreaves
equation. After adjustment, the maximum MBE for locations in region II was reduced from
�1.13 to �0.52 mm d�1, which resulted in an improvement of 54% (Table 3 and Fig. 4).
The average increase in accuracy, quantified by the decrease of RMSE, was 17% (from
0.94 to 0.78 mm d�1). Maximum RMSE decreased from 1.65 to 1.13 mm d�1, which
resulted in an improvement of 31% (Fig. 5). Average RMSE in region III decreased by 21%
(from 0.75 to 0.59 mm d�1) and maximum MBE decreased from 0.74 to 0.38 mm d�1
(49% improvement). Considering all locations, the average RMSE was 0.70 mm d�1, an
average increase in accuracy of 12% with respect to the initial value. Finally, maximum and
minimum MBE were 0.56 and �0.66 mm d�1, which meant an improvement of 24 and
41%, respectively. After adjustment, standard deviation of RMSE and MBE decreased 25
and 44%, respectively, indicating the gain in uniformity. Adjustment was not applied to
eliminate high underestimations that occurred at the region IV stations, which were
affected by average windspeed above 2.5 m s�1. Here, it would be necessary to use a third
coefficient (0.0026) for strong-wind locations in that region, as previously stated. The
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281270
Fig. 3. Comparison of adjusted Hargreaves coefficients (C) obtained from individual fit, by kriging and according
to Vanderlinden et al. (2004) and Samani (2000).
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 271
Fig. 4. Comparison of unadjusted and adjusted MBE values using method based on two coefficients.
Fig. 5. Comparison of unadjusted and adjusted RMSE values using method based on two coefficients.
proposed correction improved accuracy for 43 out of the 51 locations included in the
regions affected by the adjustment (II and III). The other eight stations for which the new
coefficient did not improve the equation performance were located close to the region
borders (Fig. 2). For regions I and IV, not affected by the adjustment, 31 locations showed
quite accurate estimates, and the results were not satisfactory in only four cases. It can be
concluded that after the adjustment, 74 out of the 86 locations studied gave quite accurate
results, with relative values of MBE lower than 10% in most cases.
The use of only two adjustment coefficients, as described above, limits to a certain
degree the correction procedure. To get a more accurate adjustment, the kriging method
was applied to obtain adjusted coefficients based on DT and windspeed. Windspeed and DT
were used as independent variables, while the locally adjusted empirical coefficient was
taken as the dependent variable. Afterwards, new adjusted coefficients, functions of DT for
three windspeed conditions (low, moderate and high), were obtained by using linear
regression (Eqs. (7)–(9)):
Cadj ¼ �0:000117DT þ 0:003689 ðlowÞ (7)
Cadj ¼ �0:000098DT þ 0:003723 ðmoderateÞ (8)
Cadj ¼ �0:000087DT þ 0:003810 ðhighÞ (9)
Adopted limits from low to moderate and from moderate to high windspeed were 1.5
and 2.5 m s�1, respectively.
After the kriging adjustment, the average RMSE was reduced to 0.68 mm d�1, which
meant an improvement of 15% of the initial value (Table 4). Maximum and minimum
RMSE values were 1.22 and 0.39 mm d�1 (Fig. 6), which represented a reduction of 26 and
16%, respectively (Table 5). Standard deviation for RMSE was reduced 30%, indicating
the uniformity of the improvement. Maximum and minimum MBE were 0.37 and
�0.31 mm d�1, which was equivalent to a reduction of 50 and 70%, respectively (Fig. 7).
Comparing these values with the results of the adjustment based on two fixed coefficients,
an increase in accuracy of 5% for the average RMSE and of 26 and 25% for maximum and
minimum values of MBE, respectively, was obtained, which certainly justified preference
for this latter adjustment. Besides, after the adjustment, standard deviations for RMSE and
MBE were reduced by 30 and 66%, respectively, indicating that the correction was more
generalized. However, it should be noted that, after correction, some bias still remained in
the estimates. In fact, as can be seen in Fig. 7, a slight tendency to overestimate ETo at most
locations remained after adjustment, although in all cases MBE was smaller than
0.37 mm d�1 (representing 10% error on the average ETo) and at 70% of them, the error
was less than 5% of the average ETo. Adjustment improved accuracy at 65 locations.
Nevertheless, behavior was poor for region IV, as in most locations of this region
adjustment worsened results. Therefore, except at very windy locations, where the
adjustment was very good, it would be preferable not to apply the correction, considering
original results quite accurate.
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281272
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Table 4
Summary of statistics from comparison between Hargreaves and Penman–Monteith FAO-56 ETo using adjustment based on kriging before and after the adjustment
RMSE (mm d�1) MBE (mm d�1) Ratio
Maximum Minimum Mean RMSE (%) Maximum Minimum Mean Maximum Minimum Mean
Unadjusted 1.65 0.46 0.80 (0.224) 21.2 0.74 �1.13 �0.10 (0.424) 1.225 0.755 0.980 (0.115)
Two coefficients 1.22 0.44 0.70 (0.168) 18.7 0.56 �0.66 0.01 (0.239) 1.145 0.850 1.006 (0.062)
Kriging 1.22 0.39 0.68 (0.157) 18.2 0.37 �0.31 0.09 (0.145) 1.116 0.933 1.025 (0.040)
Note: RMSE: root mean square error. MBE: mean bias error. Ratio: quotient between average Hargreaves ETo and Penman–Monteith ETo. The values within brackets are
standard deviation of mean.
3.3. Comparison of alternative corrections
Most recent correction procedures for Hargreaves equation were proposed by Samani
(2000) and Vanderlinden et al. (2004). Both improvements are based only on the use of an
adjusted temperature dependent coefficient and were developed in USA and Southern
Spain, respectively. Fig. 3 compares the adjusted coefficients obtained from individual fit
using Eqs. (7)–(9), against those calculated according to approaches of Samani (2000) and
Vanderlinden et al. (2004). The horizontal line represents the original coefficient of
Hargreaves (0.0023). Values adjusted by Samani were generally smaller than 0.0023 and
produced underestimations in most instances. In this case, adjustment was not sufficient
because the Samani approach was developed using data from a greater variety of climates
throughout the USA. The approach of Vanderlinden et al. (2004) performed better,
although their correction was not sufficient to compensate underestimations at locations
included within region II and overestimations for region III. For developing their approach,
these authors used estimated, from bright sunshine hour, rather than measured solar
radiation values. These could have led to an underestimation of that variable (Gavilan,
nonpublished data), affecting the soundness of the approach.
3.4. Validation
Only kriging adjustment was subject to validation, as this method was considered more
global and accurate than that based on four regions in the DT and V domains (two fixed
coefficients). After the adjustment, average RMSE was reduced to 0.73 mm d�1, which
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281274
Fig. 6. Comparison of unadjusted and adjusted RMSE values using method based on kriging.
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Table 5
Improvement (%) obtained of applying adjustment based on two coefficients and kriging methods
RMSE MBE Ratio
Maximum Minimum Mean RMSE (%) Maximum Minimum Mean Maximum Minimum Mean
Two coefficients 26 6 12 (25) 12 24 41 90 (44) 7 12 3 (46)
Kriging 26 16 15 (30) 14 50 73 10 (66) 11 18 �4.6 (65.4)
Note: RMSE: root mean square error. MBE: mean bias error. Ratio: quotient between average Hargreaves ETo and Penman–Monteith ETo. The values within brackets are
standard deviation of mean.
represented a decrease of 7% (Table 6). Maximum and minimum RMSE values were 1.04
and 0.47 mm d�1, which represented a reduction of 5 and 11%, respectively. Standard
deviation of RMSE was reduced 10%. Maximum and minimum MBE were 0.33 and
�0.36 mm d�1, equivalent to a reduction of 51 and 55%, respectively. Finally, standard
deviations for RMSE and MBE were reduced 10 and 50%, respectively, indicating that
adjustment was generalized. The correction was adequate at 10 locations, especially at 7
sites. However, the adjustment worsened the original estimates at 4 locations (Fig. 8).
These poor results occurred again for stations located at region IV with windspeed lower
than 2 m s�1 (locations 9, 10 and 11). Again, it is advisable not to apply adjustment to these
stations, unless they were very windy locations (locations 7, 8, 12 and 13). Considering all
locations, adjustment limited the errors to 10% of average ETo and the errors were lower
than 5% at 6 of them.
3.5. Agronomic consequences
The Hargreaves equation has been frequently used to calculate crop water requirements
and for irrigation scheduling under semiarid conditions in the Guadalquivir valley in
Southern Spain (Pastor et al., 1999) and other regions in the world (Di Stefano and Ferro,
1997; Beyazgul et al., 2000). The equation allows more accurate calculations of crop water
requirements using locally adjusted coefficients. To illustrate this, real data from
Villafranca Irrigation District (VID) in the mid Guadalquivir Valley near Cordoba were
used. Using Penman–Monteith equation throughout the years 2001–2003 at the closest
station (weather station #38, Adamuz; Table 1), average yearly accumulated ETo was
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281276
Fig. 7. Comparison of unadjusted and adjusted MBE values using method based on kriging.
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Table 6
Summary of statistics from comparison between Hargreaves and Penman–Monteith FAO-56 ETo using adjustment based on kriging before and after the adjustment at
stations located in other regions of Spain
RMSE (mm d�1) MBE (mm d�1) Ratio
Maximum Minimum Mean RMSE (%) Maximum Minimum Mean Maximum Minimum Mean
Unadjusted 1.10 0.53 0.78 (0.18) 23.0 0.67 �0.82 �0.10 (0.38) 1.24 0.78 0.977 (0.11)
Adjusted 1.04 0.47 0.73 (0.16) 21.3 0.33 �0.36 0.13 (0.19) 1.12 0.90 1.039 (0.06)
Note: RMSE: root mean square error, MBE: mean bias error. Ratio: quotient between average Hargreaves ETo and Penman–Monteith ETo. The values within brackets are
the standard deviation of mean).
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281278
Fig. 8. Comparison of unadjusted and adjusted MBE values using method based on kriging at stations located in
other regions of Spain.
Fig. 9. Daily ETo estimates (monthly averaged) by Penman–Monteith FAO-56, Hargreaves and adjusted
Hargreaves equations at a representative location in the Guadalquivir Valley.
1232 mm (Fig. 9). Using Hargreaves equation, this figure was equal to 1451 mm, 17.8%
higher. This difference is more significant considering that 75% of the errors occurred
during irrigation season. For this period, from April to September, the accumulated ETo
was 929 and 1095 mm for Penman–Monteith and Hargreaves equations, respectively.
Corrected Hargreaves equation yielded 1287 and 971 mm, for the whole year and irrigation
season, respectively. Therefore, the adjusted Hargreaves equation overestimated the
accumulated ETo by only 4.5%, which is quite reasonable if we consider the uncertain
levels associated to other variables affecting the irrigation water use (principally crop
coefficient and system efficiency). In VID, the main crops are maize, cotton, sugar beet and
garlic. For these crops, using local crops coefficients (Lorite et al., 2004, adapted from
Allen et al., 1998), crop water requirements (ETr) were calculated for the whole growing
season. Water saving resulting from the use of corrected Hargreaves equation, ranged from
109 mm per year for cotton to 60 mm per year for garlic. Considering the whole irrigation
district, the water consumption will be affected depending on ETo estimation method.
Thus, consumption for VID was reduced by 11% using locally calibrated Hargreaves
equation instead of the original equation. These results show the importance of adjusting
empirical equations, such as the Hargreaves in the present case which affects yield and
waterlogging.
4. Conclusions
Results obtained from the comparisons of ETo daily estimates by Hargreaves equation
against Penman–Monteith FAO-56 – taken as standard – throughout the Andalusian region
(Southern Spain), showed a high spatial variability. At coastal areas, the Hargreaves
equation generally underpredicted ETo, although at some specific locations it was more
accurate, even overestimating in some cases. Behavior of the equation was less predictable
at inland areas, ranging from moderate underestimation to high overestimations.
Yearly means of windspeed (V) and daily temperature range (DT) appeared to affect the
accuracy of the equation. According to the values taken by those climatic variables, an
adjustment was proposed for some cases, consisting in the adoption of a different value for
the empirical coefficient; thus, the original coefficient (0.0023) should be replaced by
0.0021 when DT > 12 8C and V < 1.5 m s�1, and by 0.0027 when DT < 12 8C and
V > 1.5 m s�1. For all other cases, correction was not necessary. These locally adjusted
coefficients produced an important improvement in the equation performance.
An alternative method for adjustment based on kriging interpolation has been also
proposed and tested, yielding even better results. In this case, coefficients were not constant
for a group of stations as before, but they were individually obtained for each location as a
function of DT and V. This method was validated with data from other Spanish regions.
The adjustment based on kriging has proved more efficient, except at locations with
high DT and moderate windspeed. Under these conditions, a fixed value of 0.0026 is
suggested, but, as a general rule, it is recommended to calculate the coefficient by this
procedure for the rest of the cases.
The practical consequences of the proposed adjustment were made evident with data
from an irrigation district in the Guadalquivir valley. Using local crop coefficients for the
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 279
most important crops in the area, water consumption was reduced by 11% if the corrected
equation were used instead of the original one.
It should be taken into account that this study was based on the analysis of a limited data
set, with series never longer than 3 years. Given the year to year variability of climatic
variables, a more comprehensive study, including longer series of data (10 years or more),
is advisable to improve the reliability of the proposed adjustments.
Acknowledgments
The authors are grateful to two anonymous reviewers for their valuable comments and
suggestions. Furthermore, they thank Mr. Juan de Haro for his valuable work in the
Agroclimatic Information System of Andalusia.
References
Allen, R.G., 1986. A Penman for all Seasons. J. Irrig. Drain. Eng. ASCE 111 (4), 348–368.
Allen R.G. 1993. Evaluation of a temperature difference method for computing grass reference evapotranspira-
tion. Report submitted to the Water Resources Development and Man Service, Land and Water Development
Division, FAO, Rome. 49 pp.
Allen, R.G., 1995. Evaluation of procedure for estimating mean monthly solar radiation from air temperature.
Report, United Nations Food and Agricultural Organization (FAO), Rome.
Allen, R.G., 1996. Assessing integrity of weather data for reference evapotranspiration estimation. J. Irrig. Drain.
Eng. ASCE 122 (2), 97–106.
Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration: Guidelines for computing crop
water requirements. FAO Irrigation and Drainage Paper no. 56, Rome.
Berengena, J., Gavilan, P., 2005. Reference evapotranspiration estimation in a highly advective semiarid
environment. J. Irrig. Drain. Eng. ASCE 131 (2), 147–163.
Beyazgul, M., Kayam, Y., Engelsman, F., 2000. Estimation methods for crop water requirements in the Gediz
Basin of western Turkey. J. Hydrol. 229, 19–26.
Corominas, J., 2002. Hacia una nueva polıtica de aguas en Andalucıa. III Congreso Iberico sobre Gestion y
Planificacion de Aguas. Sevilla, 13–17 de noviembre de 2002 (in Spanish).
De Haro, J.M., Gavilan, P., Fernandez, R., 2003. The Agroclimatic Information Network of Andalucıa. In:
Proceeding of the Third International Conference on Experiences with Automatic Weather Stations,
Torremolinos, Spain. 19–21, February..
Di Stefano, C., Ferro, V., 1997. Estimation of evapotranspiration by Hargreaves formula and remotely sensed data
in semiarid Mediterranean areas. J. Agric. Eng. Res. 68, 189–199.
Droogers, P., Allen, R.G., 2002. Estimating reference evapotranspiration under inaccurate data conditions. Irrig.
Drain. Syst. 16, 33–45.
Hargreaves, G.H., Samani, Z.A., 1982. Estimating potential evapotranspiration. J. Irrig. Drain. Eng. ASCE 108
(3), 223–230.
Hargreaves, G.H., Samani, Z.A., 1985. Reference crop evapotranspiration from temperature. Appl. Eng. Agric. 1
(2), 96–99.
Hargreaves, G.L., Hargreaves, G.H., Riley, J.P., 1985. Agricultural benefits for Senegal River basin. J. Irrig. Drain.
Eng. ASCE 111 (2), 113–124.
Hargreaves, G.H., Allen, R.G., 2003. History and evaluation of Hargreaves evapotranspiration equation. J. Irrig.
Drain. Eng. ASCE 129 (1), 53–63.
Heerman, D.F. 1986. Evapotranspiration Research Priorities for the Netx Decade-Irrigation. ASAE Paper no. 86–
2626. St. Joseph Mich. ASAE.
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281280
Irmak, S., Irmak, A., Allen, R.G., Jones, J.W., 2003. Solar and net radiation-based equations to estimate reference
evapotranspiration in humid climates. J. Irrig. Drain. Eng. ASCE 129 (5), 336–347.
Itenfisu, D., Elliott, R.L., Allen, R.G., Walter, I.A., 2003. Comparison of reference evapotranspiration calculation
as part of the ASCE standardization effort. J. Irrig. Drain. Eng. ASCE 129 (6), 440–448.
Jensen, M.E., Burman, R.D., Allen, R.G. (Eds.), 1990. Evapotranspiration and Irrigation Water Requirements.
Committee on Irrigation Water Requirements of the Irrigation and Drainage Division of ASCE, New York.
Jensen, D.T., Hargreaves, G.H., Temesgen, B., Allen, R.G., 1997. Computation of ETo under non ideal conditions.
J. Irrig. Drain. Eng. ASCE 123 (5), 394–400.
Lorite, I.J., Mateos, L., Fereres, E., 2004. Evaluating irrigation performance in a Mediterranean environment. I
Model and general assessment of an irrigation scheme. Irrig. Sci. 23, 77–84.
Martınez-Cob, A., Tejero-Juste, M., 2004. A wind-based qualitative calibration of the Hargreaves ETo estimation
equation in semiarid regions. Agric. Water Manage. 64, 251–264.
Meek, D.W., Hatfield, J.L., 1994. Data quality checking for single station meteorological databases. Agric. For.
Meteorol. 69, 85–109.
Pastor, M., Castro, J., Mariscal, M.J., Vega, V., Orgaz, F., Fereres, E., Hidalgo, J., 1999. Respuestas del olivar
tradicional a diferentes estrategias and dosis de agua de riego. Investigacion Agraria: Produccion Vegetal 14
(3), 393–404 (in Spanish).
Pruitt, W.O., Doorenbos, J., 1977. Empirical Calibration, a Requisite for Evapotranspiration Formulae Based on
Daily or Longer Mean Climatic Data. Presented at International Round table Conference on Evapotranspira-
tion. International Commission on Irrigation and Drainage, Budapest, Hungary, 20 pp.
Samani, Z., 2000. Estimating solar radiation and evapotranspiration using minimum climatological data. J. Irrig.
Drain. Eng. ASCE 126 (4), 265–267.
Samani, Z., 2004. Discussion of ‘‘History and evaluation of Hargreaves evapotranspiration equation’’. J. Irrig.
Drain. Eng. ASCE 130 (5), 447–448.
Shafer, M.A., Fiebrich, C.A., Arndt, D.S., 2000. Quality assurance procedures in the Oklahoma Mesonetwork. J.
Atmos. Oceanic Technol. AMS 17, 474–494.
Sharma, M.L., 1985. Estimating evapotranspiration. In: Hillel, D. (Ed.), Advances in Irrigation, vol. 3. Academic
Press, London.
Smith, M., Allen, R.G., Monteith, J.L., Pereira, L.S., Perrier, A., Pruitt, W.O., 1991. Report on the expert
consultation on procedures for revision of FAO guidelines for prediction of crop water requirements. Land and
Water Development Division, United Nations Food and Agriculture Service, Rome.
Temesgen, B., Eching, S., Davidoff, B., Frame, K., 2005. Comparison of some reference evapotranspiration
equations for California. J. Irrig. Drain. Eng. ASCE 131 (1), 73–84.
Vanderlinden, K., Giraldez, J.V., Van Mervenne, M., 2004. Assessing reference evapotranspiration by the
Hargreaves method in Southern Spain. J. Irrig. Drain. Eng. ASCE 129 (1), 53–63.
Willmott, C.J., 1982. Some Comments on the Evaluation of Model Performance. Bull. Am. Meteorol. Soc. AMS
63 (11), 1309–1313.
Xu, C.Y., Singh, V.P., 2002. Cross comparison of empirical equations for calculating potential evapotranspiration
with data from Switzerland. Water Resour. Manage. 16, 197–219.
P. Gavilan et al. / Agricultural Water Management 81 (2006) 257–281 281