Remote Sensing of Environment 93 (2004) 68 – 76
www.elsevier.com/locate/rse
A simplified equation to estimate spatial reference evaporation from
remote sensing-based surface temperature and local meteorological data
Raul Rivasa,b,*, Vicente Casellesb
b
a
Instituto de Hidrologia de Llanuras, CC 44, B7300, Azul, Buenos Aires, Argentina
Departamento de Termodinámica, Universidad da Valencia, Dr Moliner 50, Burjassot, Valentia 46100, Spain
Received 9 January 2004; received in revised form 28 May 2004; accepted 26 June 2004
Abstract
A simplified equation to estimate spatial reference evapotranspiration (ETo_Ts) from remote sensing-based surface temperature (Ts) and
local standard meteorological data is suggested. It is based on a parameterization of the meteorological conditions of the first few meters of
the atmosphere through two parameters (a and b) which come from a simpler form of the Penman–Monteith equation:
ET o
Ts
¼ aTs þ b
This approach is of local nature since the parameters a and b must be estimated for a given area from meteorological data. The spatial
pattern and temporal evolution in ETo_Ts have been analyzed using 58 NOAA-AVHRR images from 1992 to 1996 in a flat, subhumid
region in the center of the Buenos Aires province, Argentina. The modelled ETo_Ts has been compared with local measurements, and
results indicate that the error of estimate is F0.6 mm day1.
D 2004 Elsevier Inc. All rights reserved.
Keywords: Spatial reference evaporation; Remote sensing; Surface temperature
1. Introduction
Evapotranspiration (ET) is an important variable in water
and energy balances on the earth’s surface. Understanding
the distribution of ET is a key factor in hydrology,
climatology, agronomy and ecology studies, among others.
On a global scale, about 64% of the precipitation on the
continents is evapotranspired. Of this, about 97% is
evapotranspired from land surface and 3% is open-water
evaporation.
In specific zones of the world, approximately 90% of the
precipitation can be evapotranspired (Varni et al., 1999).
This is to say that the greatest amount of water from the
* Corresponding author. Departamento de Termodinamica, Universtidad de Valencia, Dr Moliner 50, Burjassot, Valencia 46100, Spain. Tel.: +54
22 81 43 2666; fax: +34 96 354 3385.
E-mail address: [email protected] (R. Rivas).
0034-4257/$ - see front matter D 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.rse.2004.06.021
hydrologic system is transpirated and evaporated, which
shows that the appropriate estimation of the ET is basic.
The concept of potential evaporation (E0), popularized by
Thornthwaite (1948) in the context of the classification of
climate, has provided a useful avenue for setting a reference
level for actual evaporation in practical applications (Doorenbos & Pruitt, 1977) and in research (Villalobos & Fereres,
1990), as well as in regional and global analyses of
evaporation (Choudhury et al., 1994). Considerable progress has been made in our understanding of the physical
and the biological processes that determine evaporation rate
at local scale (meteorological stations). Empirical (e.g.
Doorenbos & Pruitt, 1977; Jensen et al., 1990) as well as
more physically based approaches are currently adopted for
the estimate of ET. A physically based equation for E0 was
derived by Penman (1948) by combining energy balance
equation with the aerodynamic equation for vapor transfer.
It was subsequently modified by Monteith (1965) to include
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
a canopy resistance for vapor diffusion out of stomata. The
Penman–Monteith (PM) equation can be used to estimate
evaporation from well-watered and stressed canopies,
depending upon the surface resistance. The beauty of the
PM is that it is able to substitute surface temperature with air
temperature and energy balance (Monteith & Unsworth,
1990). Apart from the above-mentioned equations, there are
many other equations which have been proposed for
estimating E0 (Jensen et al., 1990). By comparing 20
different methods of estimating E0, Jensen et al. (1990)
showed that the PM equation provides the best accurate
estimate of evaporation from well-watered grass or alfalfa
(called the reference crop evaporation) under varied climatic
conditions, humid and arid climatic regions, respectively.
An equation based on the PM model is now largely used as
the reference methodology, with adopted parameterization
for surface and aerodynamic resistances for obtaining
reference ET from agro-meteorological data (Allen et al.,
1998). This approach is still based on the equation
ET=K cETo (where K c is the crop coefficient) proposed by
Doorenbos and Pruitt (1977), which calculates a reference
ET for a standard surface referred to as ETo.
However, in regional studies, it is very important to find
out the regional variations of the ET. Therefore, at present,
the efforts are centered on extending these local measurements to regional scale.
Satellite remote sensing (RS) is an attractive tool for
obtaining information about the energy and water balance
and for detecting change and anomalies across landscapes or
even within individual fields (Boegh et al., 2002). Remote
sensing information allows us to extend the models to
regional scale where there are no meteorological data.
Many researchers have worked on developing models
that accept RS data as input to estimate potential
evaporation and actual evaporation. The direct but
complex relationships among surface temperature, soil
moisture, vegetation density and energy balance have long
been recognized by hydrologists, ecologists and meteorologists (Friedl, 2002). All studies in this domain use onedimensional models to describe the radiation, conduction
and turbulent transport mechanisms that influence surface
temperature and energy balance. Therefore, many different
strategies have been used; virtually all models of this
nature are based on principles of energy conservation. The
governing equation is thus the land surface energy balance
equation, which dictates that net radiation (R N) is balanced
by the soil heat flux ( G), sensible heat flux (H) and latent
flux (EE) at the surface as:
RN þ G þ H þ EE ¼ 0
ð1Þ
For most remote sensing-based energy balance studies,
it is assumed that R N and G are known or may be easily
computed. The two remaining terms, H and EE, are
turbulent flux quantities and very difficult to estimate.
69
Generally, these terms are modelled using one-dimensional
flux-gradient expressions based on a convection analogue
to Ohm’s law:
H¼
kE ¼
qCp
ðTo Ta Þ
ra
qCp ðeo ea Þ
g ðrv þ ra Þ
ð2Þ
ð3Þ
where q is the density of air, C p is the specific heat of air,
To and e o are the aerodynamic temperature and vapor
pressure, respectively, of the surface at the effective level
of heat and moisture exchange, Ta and e a are the temperature and vapor pressure, respectively, of the overlying
atmosphere, r a and r v are the aerodynamic and physiological resistances, respectively, to heat and moisture
transport at the surface, and c is the psychrometric
constant.
Eqs. (1) and (3) form the basis of so-called one-layer
(OL) energy balance models. No distinction between the
energy balance, temperature and vapor pressure regimes of
the vegetation canopy and the soil surface is made in those
models. OL model estimates EE as a residual from Eq. (1).
RS has been widely used with this type of framework to
estimate the turbulent flux component of the surface energy
balance. To do this, radiometric surface temperature
obtained from RS is used as a substitute for To in Eq.
(2) (see for example Inoue & Moran, 1997; Jackson et al.,
1977; Seguin & Itier, 1983). Over the last years, several
regional experiments have tested OL models in detail and
provided significant progress (see for example HAPEX,
Gourturbe et al., 1997; and MONSOON 90, Kustas &
Goodrich, 1994). At the same moment, results from these
experiments have allowed to find feebleness in OL models
and have pointed keys for future research. As an
alternative, two models have been developed that include
representations for distinct temperature and energy balance
regimes for the vegetation canopy and soil surface
(Choudhury & Monteith, 1988; Kustas, 1990). These
models are considerably more complex, but recent work
has shown them to be successful in overcoming some of
limitations for OL models.
These models require in situ measurements, and, in many
situations, this information is not available. For the application of models, it is necessary to measure net radiation, air
temperature, air relative humidity, wind speed, crop height
and leaf area index. In some cases, additional information is
required. This information is canopy temperature and soil
temperature, height and architecture of the plants, among
others. However, in many standard meteorological stations,
there is not the instrumentation to measure all these variables
required by the models. The lack of specific instrumentation
considerably limits the use of sophisticated models and
operational applications. Also, these models are often limited
due to the inherent complexity of those procedures.
70
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
However, in most cases, regional values are estimated by
models using standard meteorological data and RS as input
(e.g. Brasa et al., 1998; Caselles & Delegido, 1987;
Reginato et al., 1985). In this paper, following the Caselles
and Delegido (1987) philosophy, we have adapted the PM
equation for its use with Ts obtained by RS. This adaptation
is still based on the equation ET=K cETo, where ETo is
obtained from a linear relation, which simply requires the
calculation of two local parameters. The originality of this
paper is to use only standard meteorological data which are
available everywhere.
With this issue in mind, the objectives of this paper are
twofold. The first objective is to describe the adaptation of
the PM physical model and the necessary conditions for
applying it. The second objective is to test this adaptation
using field data. In this case, we have used a flat zone of
Argentina (Azul River Basin).
where R NSA is the net incoming short-wave radiation (MJ
m2 day1) and R NLz is the net outgoing long-wave
radiation (MJ m2 day1). The short-wave radiation can
be represented by:
RNSA ¼ ð1 aÞRS
and long-wave radiation can be represented by:
RNLz ¼ es r Ts4 ea Ta4
ð7Þ
ð8Þ
where a is the albedo of the surface (adimensional), R S is the
incoming solar radiation (MJ m2 day1), e s is the emissivity
of the surface (adimensional), r is the Stefan–Boltzman
constant (4.9109 MJ m2 K4 day1), e a is the emissivity
of the atmosphere (adimensional), Ts is the surface temperature (K) and Ta is the air temperature (K). Inasmuch, as we
want to come up with a simpler, linear relationship between
ETo and Ts, and we assigned a value to Ta, the thermal
radiation emitted by the earth takes on the following form:
Ts4 ccTs þ d
2. Model
The original form equation of PM model can be rewritten
as follows (Monteith & Unsworth, 1990):
ð ea ed Þ
DðRN GÞ þ qCp
ra
EETo ¼
rc
Dþc 1þ
ra
ð4Þ
C ðRN GÞ
D
rc
Dþc 1þ
ra
0
B
þB
@
1
C
A
k
1
C qCp
ea ed
k
ra
C
A
3
10
with c=(1.140F0.011) 10 K , d=(2.600F0.032) 10 K4,
a determination coefficient of 0.99 for a surface temperature
from 280 to 338 K and error estimation of F1.1 108 K4.
Therefore, by combining Eqs. (7)–(9), R N is:
RN ¼ ð1 aÞRs ces rTs des r þ es ea rTa4
where EETo is the latent heat flux (MJ m2 day1), D is the
slope of the vapor pressure curve (kPa 8C1), R N is the net
radiation (MJ m2 day1), G is the soil heat flux density (MJ
m2 day1), q is the density of air (kg m3), C p is the
specific heat of air (MJ kg1 8C1), e a is the saturation vapor
pressure of air (kPa 8C1), e d is the actual vapor pressure
(kPa 8C1), r a is the aerodynamic resistance (s m1), c is the
psychrometric constant (kPa 8C1) and r c is the crop canopy
resistance (s m1).
Following Smith et al. (1992), Eq. (4) can be divided into
two terms, a radiation term (ETrad) and an aerodynamic term
(ETaero) as:
0
1
B
ETo ¼ B
@
ð9Þ
8
rc
Dþc 1þ
ra
¼ ETrad þ ETaero
ð5Þ
The radiation term depends on incoming and outgoing
radiation of the surface, as well as the effects produced by
meteorological conditions. The radiation terms may be
written as:
RN ¼ RNSA RNLz
ð6Þ
ð10Þ
So, if we take into account Eq. (10), the term ETrad [Eq. (5)]
could be expressed as follows:
0
1
B
ETrad ¼ B
@
C
D
Dþc 1þ
rc
ra
C
A
ð1 aÞRs ces rTs des r þ es ea rTa4 G
k
!
ð11Þ
From Eq. (11), we can, on one hand, separate the part of the
equation which contains the surface temperature (ETrad_Ts)
from the rest (ETrad_Rs).
Thus, ETrad_Ts can be expressed as:
0
1
B
C ces rTs
D
B
C
ET rad Ts ¼ @
ð12Þ
rc A
k
Dþc 1þ
ra
and ETrad_Rs0as:
ET rad
Rs
B
¼B
@
1
C
C
rc A
Dþc 1þ
ra
ð1 aÞRs þ es rðea Ta4 dÞ G
k
D
ð13Þ
As our interest is in knowing the water demand for the
reference crop for average atmospheric conditions as a
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
71
Table 1
Values assumed in Eqs. (12) and (14)
Variable
Value range
Albedo reference crop
(Allen et al., 1989)
Height measurement
Crop height
Crop canopy resistance
(Allen et al., 1989)
Emissivity reference crop
(Valor & Caselles, 1996)
Emissivity of air near surface for a
standard atmosphere
(Brutsaert, 1984)
Surface temperature
Specific heat of air (kJ kg1 8C1)
Density of air (kg m3)
Aerodynamic resistance for a standardized
crop height and wind speed (U 2 in m s1
measured at 2 m) (Allen et al., 1989)
0.23
2m
0.12 m
70 m s1
0.985 (10.5–12.5 Am)
0.76 (15 8C)
Fig. 1. Behavior of ETrad_Ts [Eq. (12)] and ETrad_Rs+ETaero [Eq. (14)] for
the Azul Station. Monthly average meteorological data were used (Table 2).
26 8C
1.013
1.2
ra ¼ 208
U2
function of Ts, we have grouped and organized ETrad_Rs+
ETaero in the following form:
0
1
B
þ ET aero ¼ B
@
C
C
rc A
Dþc 1þ
ra
1
Dðð1 aÞRs þ es rðea Ta4 dÞ GÞ
k
ea ed
þ qCp
ð14Þ
ra
In this way, we can analyze independently the radiation term
which is dependent on Ts [Eq. (12)] and, on the other hand,
we can analyze the remaining effects [Eq. (14)] (the shortwave radiation and aerodynamics effects).
In order to analyze the annual behaviour of ETrad_Ts and
ETrad_Rs+ETaero, we have used the values established for the
reference crop (Table 1) in Eqs. (12) and (14) and the
monthly average data measured in a reference weather
station (Table 2). This weather station is located in the
Argentine plains and belongs to the National Network of
Climatic Stations. The results of the behavior of ETrad_Ts
and ETrad_Rs+ETaero are depicted in Fig. 1.
ETrad
Rs
1
Fig. 1 clearly indicates that ETrad_Ts has a greater
variation than ETrad_Rs+ETaero. For the value adopt for Ts
(26 8C), the observed variation of ETrad_Ts depends on the
mean monthly meteorological conditions of the first few
meters of the atmosphere (mostly, the mean air temperature and, to a lesser degree, the wind velocity). During
the summer, values are higher than those during the
winter. This is a logical behaviour and follows the
atmospheric variations registered at the weather station.
It can also be observed that the variation, with respect to
the mean ETrad_Rs for the different seasons, is not
significant.
If we take into account that Ts varies with time and that
Ts embodies the variations in the first few meters of the
atmosphere (Jackson et al., 1977; Price 1982, 1989; Kustas
ces r D
will
et al., 1989), we may assume that Dþc 1þ rc
k
ra
have minimum variations, and that the use of a single value
for the whole year would be appropriate (annual variations
are within 0.5 mm day1).
As for ETrad_Rs+ETaero, we see that its behaviour along the
year is much more stable and that its variations are of lesser
significance. That is related to the fact that ETrad_Rs+ETaero
represents the effects of the mean flow exchange in the first
meters of the atmosphere on a given crop which receives a
certain amount of energy. Given what has been explained in
the paragraphs above, we propose to estimate the evapotranspiration of the reference crop (ETo_Ts) from the surface
Table 2
Mean climatology at the Azul Station (Buenos Aires, Argentina) used in the analyses
Location name: Azul Station (Argentina), range 1950–2000
Coordinates: 36.78S – 59.18W, Altitude: 132 m
Variable
Month
1
2
3
4
5
6
7
8
9
10
11
12
Ta (8C)
HR %
R s (MJ m2 day1)
U 2 (m s1)
22.1
66.0
25.4
2.6
20.7
75.0
22.7
2.6
18.6
78.0
17.3
2.5
13.4
88.0
12.9
2.0
10.5
91.0
8.4
1.8
7.6
95.0
6.5
2.0
7.8
88.0
7.6
2.2
8.4
88.0
10.5
2.4
10.5
86.0
14.5
2.6
13.5
87.0
20.1
2.6
17.0
78.0
23.3
2.6
19.3
74.0
24.5
3.0
72
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
on a hypothetical surface which receives a given solar
radiation. Those parameters are site-specific and can be
calculated using meteorological data from conventional
weather stations.
In order to extend the proposed model to larger regions,
it is necessary to know the behaviour of parameters a and
b for different weather stations. The regional validity will
depend on the spatial homogeneity of the first meters of
the atmosphere, which will determine the limits of its
applicability.
3. Results
3.1. Study area
Fig. 2. Study area and locations of weather stations used in this paper.
temperature—obtained from satellite images—by means of
the following equation:
ETo
Ts
¼ aTs þ b
ð15Þ
where a and b can be approximately constant; variations are
within 0.5 mm day1. Then a is:
0
1
B
C ces r
D
C
a¼B
ð16Þ
@
rc A
k
Dþc 1þ
ra
and b is:
0
B
b¼B
@
1
1
C1
C
ðDÞðð1 aÞRs þ es rðea Ta4 dÞ
rc A k
Dþc 1þ
ra
ea ed
GÞ þ qCp
ra
ð17Þ
Parameter a represents the mean emission effect of the
reference surface for the given set of atmospheric conditions,
whereas parameter b quantifies the mean air-dynamic effect
The adaptation of the PM equation for its use with RS
has been applied in the Azul River Basin (center of Buenos
Aires Province, Argentina) (Fig. 2). The Azul River Basin
has a total catchment area of 6262 km2. This is a flatland
region with an average slope of less than 1%. Typical
slopes are 5% in the south and less than 0.2% in the more
conspicuously flat landscape (Usunoff et al., 1999; Varni et
al., 1999).
The average annual rainfall is 1005 mm (data from the
1988–2000 period at the Azul meteorological station); the
maximum monthly value is in March and the minimum is in
August. Average values for annual temperature, wind speed,
relative air humidity and solar radiation are 14.3 8C, 2.5 m
s1, 72% and 16.7 MJ m2 day1, respectively.
The climate is humid to subhumid, mesothermal, with
slight to zero water deficits (Thornthwaite climatic classification). The average annual evapotranspiration is 1090
mm, calculated with the PM FAO version (Allen et al.,
1998).
3.2. Estimation of parameters
Meteorological data from the only four stations (Azul,
Tandil, Olavarria and Benito Juarez) present in the area
were used to estimate a and b (Fig. 2). Data from January
1992 until December 1996 have been used. Firstly, a
consistent analysis of meteorological data in each station
has been realized. The variables used were maximum and
Table 3
Average climatology measured at the Olavarria Station used for the estimation of the parameters a and b
Location name: Olavarria Station (Argentina)
Coordinates: 36.98S – 60.38W, Altitude: 166 m
Variable
Month
1
2
3
4
5
6
7
8
9
10
11
12
Ta (8C)
HR %
R s (MJ m2 day1)
U 2 (m s1)
19.2
62
23.7
1.2
18.0
68
22.2
1.3
16.7
76
17.0
1.1
13.1
77
12.3
1.1
11.1
82
8.5
1.0
8.1
81
6.9
1.4
7.8
79
7.6
1.0
9.5
75
10.7
1.3
10.5
72
13.4
1.6
13.5
74
19.4
1.4
15.4
65
22.9
1.1
17.5
59
22.5
1.2
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
73
Table 4
Average climatology measured at the Azul Station used for the estimation of the parameters a and b
Location name: Azul Station (Argentina) IHLLA
Coordinates: 36.78S – 59.18W, Altitude: 132 m
Variable
Month
1
2
3
4
5
6
7
8
9
10
11
12
Ta (8C)
HR %
R s (MJ m2 day1)
U 2 (m s1)
21.4
60
30.3
1.0
19.9
66
27.2
1.1
18.3
74
22.3
0.9
13.9
74
16.7
1.0
11.5
80
12.2
0.9
7.8
79
10.3
1.2
7.5
77
11.1
0.8
9.5
73
14.8
1.2
10.7
69
20.0
1.4
14.4
72
25.5
1.2
16.7
62
29.5
1.0
19.3
56
31.1
1.0
minimum daily air temperature (8C), maximum and
minimum daily relative humidity (%), average daily wind
speed (m s1) and incoming solar radiation (MJ m2
day1), and from these, we obtained the averages for each
month (Tables 3–6). All measurements have been made at
2-m height and at the same time period.
From Eqs. (16) and (17), monthly average value of the
parameters a and b were calculated with meteorological
data (Table 7). It can be seen that the parameters are quite
homogeneous at the spatial scale, which encourages the use
of a mean single value of a and b parameters for the whole
domain.
3.3. Surface temperature determination
Of the original 100 NOAA-AVHRR temperature images
from 1990 to 1996, 58 were applied in the analyses that
follows. We rejected 42 images because they were not
representative of the complete week. A cloud mask, based
on a simple thresholding in the visible and thermal channels,
was applied to all images (Saunders & Kriebel, 1988). All
starting images are cloud-free pixels, though cloud margin
and haze effects may still exist. The images were geometrically rectified using coastline, rivers and lakes and with an
accuracy of F1 pixel. The atmospheric correction for the
visible and infrared channels was performed using the
Second Simulation of the Satellite Signal in the Solar
Spectrum (Vermote et al., 1997).
The model used for retrieving the land surface temperature Ts, from satellite data, was the model suggested by
Coll and Caselles (1997), which is based on the following
split-window equation:
Ts ¼ T4 þ ½1:34 þ 0:39 ðT4 T5 ÞðT4 T5 Þ
þ 0:56 þ að1 eÞ bDe
ð18Þ
where T 4 and T 5 are the brightness temperatures in AVHRR
channels 4 and 5, e is the average emissivity in AVHRR
channels 4 and 5, De is the spectral emissivity difference
between 4 and 5 channels and a and b depend on the
atmospheric water vapor content. Coefficients a and b have
been calculated from the precipitable total water vapor
content for a total of 100 atmospheric profiles measured in
the study area in winter and summer (SAZR Station, 36.56
latitude and 64.26 longitude). The results show that a is
approximately constant with a value ac50 K, whereas b
decreases with the water vapor content of the atmosphere,
taking values of bc115 K for winter and bc98 K for
summer.
The emissivity in each channel has been calculated
using the vegetation cover method of Valor and Caselles
(1996):
e ¼ ev Pv þ es ð1 Pv Þ
ð19Þ
where e v is the vegetation emissivity (0.985 in both
channels), e s is the soil emissivity (0.949 for channel 4
and 0.967 for channel 5) and P v is the vegetation cover,
which was estimated from NDVI.
Table 5
Average climatology measured at the Juarez station used for the estimation of the parameters a and b
Location name: B. Juarez Station (Argentina)
Coordinates: 36.78S – 59.88W, Altitude: 207 m
Variable
Ta (8C)
HR %
R s (MJ m2 day1)
U 2 (m s1)
Month
1
2
3
4
5
6
7
8
9
10
11
12
21.7
58
24.4
2.8
20.4
64
22.7
3.0
18.4
74
17.9
2.4
13.6
82
12.5
2.6
10.5
88
8.6
2.6
7.5
91
6.6
2.4
7.3
88
7.3
3.0
8.4
80
10.6
3.2
10.0
82
14.3
2.8
12.8
84
19.5
2.8
16.2
79
22.7
2.8
18.8
67
25.1
2.8
74
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
Table 6
Average climatology measured at the Tandil station used for the estimation of the parameters a and b
Location name: Tandil Station (Argentina)
Coordinates: 37.28S – 59.38W, Altitude: 175 m
Variable
Month
1
2
3
4
5
6
7
8
9
10
11
12
Ta (8C)
HR %
R s (MJ m2 day1)
U 2 (m s1)
21.6
72
25.4
2.8
20.6
74
22.6
2.8
18.7
81
17.1
2.2
13.8
87
12.6
2.4
10.8
90
8.1
2.0
8.1
93
6.2
2.0
7.8
93
7.3
2.2
8.8
84
10.2
2.6
10.6
84
14.3
2.8
13.6
83
20.0
3.0
17.1
78
23.3
3.2
19.0
74
24.5
3.4
3.4. Model error analysis
3.5. Model application
From Eq. (15), a sensitivity analysis of the model was
made. Then, the error in ETo_Ts can be derived from this
equation by applying error theory as:
Once the model was validated, it was applied for
obtaining maps of reference crop evapotranspiration from
Ts for two different hydrological periods at the Azul River
Basin. The model developed has been applied to obtain the
weekly average of ETo_Ts. Therefore, the Ts images were
appropriately selected to be representative of a week. A
previous analysis of daily images of Ts for a complete week
was made.
Each of the selected periods corresponds to months of
maximum evaporative water demand (spring and summer).
The first period corresponds to December 1992–March
1993, whereas the second period is December 1995–January
1996. Previous accumulated precipitation up to December
1992 was 1133 mm, whereas the total accumulated rainfall
up to December 1995 was 661 mm. Hence, the first period
is humid while the second is quite dry.
Maps for the humid period indicate a small demand of
water from the atmosphere due to the high air relative
humidity and the low air temperature (Fig. 4). It is also
possible to observe that there is no high spatial variability
for different dates within the period. The greatest relative
change in water demand took place in the first week of
March, as a consequence of a decrease in air relative
humidity and an increase in air temperature.
dETo
Ts
¼ ½ðTs yaÞ2 þ ðayTs Þ2 þ ðybÞ2 1=2
ð20Þ
where yETo_Ts is the error estimation of the proposed model,
ya is the error for parameter a, yb is the error for parameter
b and yTs is the error estimation of Ts. If we consider that
ya=0.01 mm day1 8C1 (see Table 7), yb=0.1 mm day1
(maximum error value of b in the Table 7), yTs=1.5 8C
(standard error for split window equation, Coll & Caselles,
1997) and Ts=26 8C (mean value for Ts at the Azul Station),
we obtain the error of the proposed model yETo_Ts=F0.5
mm day1.
In order to validate the model, a comparison was made
between the estimates from the PM FAO equation (Allen
et al., 1998)—using data for the Azul weather station—
which have an error of F0.3 mm day1 (Jensen et al.,
1990), and those emerging from the proposed model for a
set of 58 images. Taking into account that the geometric
correction error of images is F1 pixel, the average value
for Ts [Eq. (15)], corresponding to an area of 33 pixels,
was used.
Fig. 3 depicts the comparative results of the 58 values
of the ETo FAO version observed at the Azul weather
station and those estimated by the proposed model (ETo_Ts)
at the same station. Taking into account the 58 data sets, it
may be noticed that the proposed model shows a rather
low bias (0.04 mm day1) and a RMSE of F0.6 mm
day1.
Table 7
Values for the parameters a and b with the corresponding standard
deviation in brackets for the four meteorological stations used
Station
a (mm day1 8C1)
b (mm 8C1)
Azul
Tandil
Olavarria
B. Juarez
Mean value
0.12 (F0.01)
0.11 (F0.01)
0.12 (F0.01)
0.11 (F0.01)
0.12 (F0.01)
0.32
0.28
0.34
0.33
0.32
A mean value was also included.
(F0.15)
(F0.04)
(F0.12)
(F0.03)
(F0.10)
Fig. 3. Comparative results of the 58 values of the ETo FAO version
observed and those estimated by the proposed model [Eq. (15)] ETo_Ts, at
the Azul Weather Station.
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
75
Fig. 4. ETo_Ts (mm day1) maps for the Azul River Basin obtained by applying the proposed model [Eq. (15)] for 5 weeks from December 1992 to March 1993
(wet period).
As compared to the humid period, maps for the dry
period indicate a high atmospheric water demand both in
time and space (Fig. 5). Given the characteristics of such a
period (high water demand), the resulting maps also show
the influence of precipitations. Let us compare the map of
the second week of December with that of the first week of
January: in that time span, the mean regional rainfall was 35
mm, which led to an increase in the air relative humidity and
a decrease in the air temperature and, consequently, a
decrease in the water demand (ETo_Ts) as shown in the map
for the first week of January.
4. Conclusions
ETo estimates are very useful for practical applications
and research aiming at actual evapotranspiration estimations
at local and regional levels. Models that allow the estimation
of actual ET at the regional scale require a great deal of
information which is hardly available in many weather
stations.
This paper shows that the evapotranspiration of a
reference crop can be estimated by combining the surface
temperature—from satellite images—with conventional
weather information. To do so, the estimation of two
parameters related to the first few meters of the atmosphere
which come from a simpler form of the PM physical model
is imperative.
Parameters of the model have been calculated for a
region in the Argentine plains. The calculated values (which
used data from a local weather station) have been compared
to those from the PM FAO method. Results indicate that the
model shows no special trends and that the estimation error
is F0.6 mm day1.
The model has been applied for obtaining ETo_Ts maps at
the Azul River Basin (Argentine plains). Such regional
evapotranspiration crop reference maps, with validated
parameters, show the sensitivity of the model with respect
to changes in the mean climatic conditions in the
atmosphere. Thus, in the wet period, the ETo_Ts varies
between 2 and 5 mm day1, and in the dry period, it
changes from 2 to 6.5 mm day1.
The methodology presented in this paper and used for
obtaining of maps of regional reference evapotranspiration
has its basis in the ET=K cETo model standardized by FAO,
which allows its ready use worldwide by different specialists and technicians. However, this approach is of local
nature since the parameters a and b must be estimated for a
given area from meteorological data.
Acknowledgments
This work was supported by The Commission of the
European Communities (FEDER Founds) and Ministry of
Science and Technology (Contract REN 2001-3116/CLI)
and supported by the programme AlBan, European
Union Programme of High Level Scholarships for Latin
America (identification no. E03D06361AR). Foremost are
the Scientific Commission Research of Buenos Aires
(Argentina) and University National Center of Buenos
Aires.
Fig. 5. ETo_Ts (mm day1) maps for the Azul River Basin obtained by applying the proposed model [Eq. (15)] for 5 weeks from December 1995 to January
1996 (dry period).
76
R. Rivas, V. Caselles / Remote Sensing of Environment 93 (2004) 68–76
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