**E. Hurtado and M.M. Artigao,** Department of Applied Physics,
Polytechnical College of Albacete, University of Castilla-La Mancha, Albacete, and **V.
Caselles, **Department of Thermodynamics, Faculty of Physics, University of Valencia,
Burjassot, Spain

* *

L´évapotranspiration réelle peut être calculée à partir du rayonnement net journalier et de la différence entre la température de l´air et de surface des cultures en milieu de journée. Nous proposons d´estimer l´évapotranspiration à l'aide des modèles à une ou deux couches et d'une combinaison d´images Landsat et NOAA, les premières pour connaître la distribution des cultures et les deuxièmes pour déterminer la variation spatiale de la température. Cette méthode permet d´estimer l´évapotranspiration réelle avec une marge d'erreur de 0,9 mm par jour et, en conséquence, de contrôler les besoins d´irrigation.

The actual evapotranspiration can be calculated from daily net radiation and the
temperature difference between air and crop surface at midday. We propose estimating
actual evapotranspiration by using one or two layer models and combining Landsat and NOAA
images, the former for defining crop distribution and the latter for determining spatial
variation in temperature. This methodology allows for the estimation of actual daily
evapotranspiration with an error margin of 0.9 mm day^{-1}, and in consequence to
monitor water requirements.

Knowledge of evapotranspiration is useful for different aims like water budget calculations, climatological and meteorological studies. In arid regions evapotranspiration is a significant and often the dominant water flux leaving the Earth´s land surface, nearly all the inputs in the form of rain is lost trough evapotranspiration therefore the importance of this parameter for controlling watering schedule and determining crops productivity. We have applied this methodology to the Barrax and Tomelloso (Spain) areas, pilot experiment zones of the EFEDA project. (Bolle and Langer,1991)

Attempting to determine the energy transport in sparsely vegetated rangelands requires methods such as those proposed by Shuttleworth and Wallace (1985), Shuttleworth and Gurney (1990) or Kustas (1990) that consider the soil and canopy as separate sources or sinks for latent and sensible heat fluxes.

**FIGURE 1**

In these models the soil and canopy are each treated as a separate source (or sink) of
energy which involves the assignation of temperatures and humidities for each one of the
sources (or sinks) and for the atmosphere. A two layer model can be schemed by figure 1,
where T_{v} and T_{g} are the surface temperature of foliage and ground
surface respectively. T_{a} is the air temperature at screen level and T_{o}
is the canopy-air system temperature at level z=z_{o}+d, i.e. the level of the
sources/sinks of sensible heat, or of the hypothetical canopy air flow. H is the sensible
heat flux. If the canopy covers completely the soil a single layer model can be used
(Hurtado, 1994a).

The total radiation absorbed by the vegetation/soil system is R_{n}=R_{nv}+R_{ng}.
The division of R_{n} between latent and sensible components gives:

R_{nv }= LE_{v }+ H_{v (1)}

R_{ng }= LE_{g }+ H_{g }+ G (2)

Looking at figure 1 we can write:

H = H_{v }+ H_{g} (3)

*p*Cp (To - Ta) / ra= *p*Cp (Tv - To) / rv + *p*Cp (Tg - To) / rg
(4)where r_{a}, r_{v} and r_{g} are the appropriate aerodynamic
resistances.

Equation (4) can be written as:

T_{g }-T_{o}= (rg / ra) (To - Ta) - (rg / rv) (Tv - To) (5)

From equation (5) the expression for the T_{o }calculation can be obtained:

_{ (6)}

_{If ag }is the fractional ground area, observed from the nadir, the measured
infrared surface temperature T_{s} may be expressed as:

T_{s }= T_{g }a_{g}+(1- a_{g}) T_{v} (7)

and we can write:

T_{s}-T_{a }= (T_{o}-T_{a}) + a_{g }(T_{g}-T_{o})
+ (T_{v}-T_{o}) (1-a_{g}) (8)

Substituting (5) into (8) we have:

T_{s}-T_{a }= T_{o}-T_{a }+ a_{g} [ (rg/ra) (T_{o}-T_{a})
- (rg/rv) (T_{v}-T_{o}) ] + (1-a_{g}) (T_{v}-T_{o})
(9)

For bare soil a_{g }= 1 and r_{v} .Thus:

T_{s }- T_{a}= (1+ rg/ra) (T_{o }- T_{a}) (10)

If the canopy is fully closed a_{g }= 0. This yields :

T_{s }- T_{a}=(T_{o }- T_{a}) + (T_{v }- T_{o})
(11)

that is, the measured surface temperature T_{s }is equal to the foliage
temperature T_{v}, but T_{v }is not necessarily equal to T_{o}.

Arranging equation (9)we have :

T_{s }- T_{a }= (T_{o }- T_{a}) [1+ag (rg/ra)]+ [1 - a_{g
}-ag (rg/rv) (Tv - To)] (12)

Using the concept of equivalent resistance, r_{a}*, equation(4) can be written
as:

*p*Cp (To - Ta) / ra= *p*Cp (Ts - Ta) / ra* (13)

Substituting (12) into (13) we have:

_{ (14)}

_{FIGURE 2}

_{The equivalent resistance ra}*can be expressed as a function of individual
resistances as:

r_{a}*=r_{a }
(15)

Using the equivalent resistance concept, daily evapotranspiration can be obtained from the expression (Jackson, 1977) (Hurtado, 1994a):

ET_{d }= R_{nd}* - B (T_{s}-T_{a})_{i} (16)

where ET is the actual evapotranspiration (mm), Rn* = Rn / L is the net radiation
expressed in mm of water (mm), (T_{s}-T_{a}) is the temperature difference
between crop surface and air (K). The subscripts d and i indicate daily and instantaneous
at midday values respectively. B is a semiempirical coefficient, which mean value is given
by:

B = (R_{nd }/ R_{ni}) < *p*C_{p }/ r_{a}*
> (17)

where Y is air density (kgm^{-3}), Cp the specific heat of air at constant
pressure (Jkg^{-1}K^{-1}), ra* is the equivalent
ground-vegetation-atmosphere system (sm^{-1}), and L the latent heat of
vaporisation of water (JK^{-1}). The symbol<> means the average value over
the growing season of the crop. The ratio R_{nd}/R_{ni} is reasonably
constant for clear days, we have used 3 years for calculating this mean value.

So, evapotranspiration is estimated from net radiation measured at a meteorological
station and (T_{s}-T_{a})_{i }where T_{s} is obtained from
the satellite overpass coinciding with the approximate time of daily maximum temperature,
i.e., at about 13.00-14.00 solar time, and T_{a} from the daily maximum value of
the meteorological shelter.

For applying equation (16) in an operative way we need previously to calculate the B
values using climatic parameters (u, Rnd/Rni), crops parameters(h, LAI, w), and handheld
radiometric surfaces temperatures (T_{v}, T_{a}, T_{g}). From
these values and using a crop map elaborated from Landsat TM images by means a
classification technique, we can obtain a B map. Afterwards we need a procedure for
evaluating surface crop temperature from thermal NOAA-AVHRR images. Finally we need some
meteorological parameters like T_{a} and Rn. Figure 2 shows the different steps
that must be followed to apply this methodology.

The temperature from the satellite sensor is transformed into ground surface temperature by applying atmospheric and emissivity corrections by means of a split-window method (Coll, 1994). To combine NOAA and Landsat images The NOAA pixel must be transformed at Landsat size when the geometric correction is performed (Hurtado 1994b).

We have applied this methodology to the Barrax area (Albacete, Spain) where irrigated
crops cover completely the soil and to the Tomelloso area (Ciudad Real, Spain)where the
main crops are wine, sparse crops. In both zones evapotranspiration can be obtained with
reasonable precision (0.8 and 0.9mmday^{-1}). In the first place a single layer
model can be used while in the second one for obtain a similar precision a more complex
two layer model must be applied.

**Bolle, H.J. and Langer, I.** 1991*. Echival Field Experiment in a
Desertification-Threatened Area (EFEDA).* Field Experiment Plan. Meteorological
Institute, Free University of Berlin, Germany.

**Coll, C., Caselles, V., Sobrino, J.A. and Valor, E**. 1994. On the atmospheric
dependence on the split-window equation for land surface temperature. *Int.J. Remote
Sensing* (15)150-122.

**Hurtado, E., Caselles, V. and Artigao, M.M**. 1994. Estimating maize
evapotranspiration from NOAA-AVHRR thermal data in the Albacete area, Spain. *Int.J.
Remote Sensing* (15)2023-2037.

**Hurtado, E., Caselles, V. and Artigao, M.M**. 1994. Mapping actual
evapotranspiration by combining landsat TM and NOAA AVHRR images in the Barrax (Albacete)
region, Spain. *Societé française de photogrammétrie et télédétection*(137)
47-49.

**Jackson, R.D., Reginato, R.J. and Idso, S.B**. 1977. Wheat canopy temperature:a
practical tool for evaluating water requirements .*Water Resour. Res.* (13). 651-656.

**Kustas, W.P**. 1990. Estimates of evapotranspiration with a one and two
dimensional model of heat transfer over partial canopy cover.* J. Appl. Meteorol*.
(49). 135-153.

**Shuttleworth, J.and Wallace, J.S**. 1985.Evaporation from sparse crops-an energy
combination theory.*Q.J.R. Meteorol. Soc*.(111) 839-855.

**Shuttleworth, J.and Gurney, R.** 1990. The theoretical relationship between
foliage temperature and canopy resistance in sparse crops.*Q.J.R. Meteorol. Soc*.(116)
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