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Models for determining evapotranspiration

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.


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 Tv and Tg are the surface temperature of foliage and ground surface respectively. Ta is the air temperature at screen level and To is the canopy-air system temperature at level z=zo+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).

To Determination

The total radiation absorbed by the vegetation/soil system is Rn=Rnv+Rng. The division of Rn between latent and sensible components gives:

Rnv = LEv + Hv (1)

Rng = LEg + Hg + G (2)

Looking at figure 1 we can write:

H = Hv + Hg (3)

pCp (To - Ta) / ra= pCp (Tv - To) / rv + pCp (Tg - To) / rg (4)where ra, rv and rg are the appropriate aerodynamic resistances.

Equation (4) can be written as:

Tg -To= (rg / ra) (To - Ta) - (rg / rv) (Tv - To) (5)

From equation (5) the expression for the To calculation can be obtained:


B Determination

If ag is the fractional ground area, observed from the nadir, the measured infrared surface temperature Ts may be expressed as:

Ts = Tg ag+(1- ag) Tv (7)

and we can write:

Ts-Ta = (To-Ta) + ag (Tg-To) + (Tv-To) (1-ag) (8)

Substituting (5) into (8) we have:

Ts-Ta = To-Ta + ag [ (rg/ra) (To-Ta) - (rg/rv) (Tv-To) ] + (1-ag) (Tv-To) (9)

For bare soil ag = 1 and rv symb11.gif (855 bytes).Thus:

Ts - Ta= (1+ rg/ra) (To - Ta) (10)

If the canopy is fully closed ag = 0. This yields :

Ts - Ta=(To - Ta) + (Tv - To) (11)

that is, the measured surface temperature Ts is equal to the foliage temperature Tv, but Tv is not necessarily equal to To.

Arranging equation (9)we have :

Ts - Ta = (To - Ta) [1+ag (rg/ra)]+ [1 - ag -ag (rg/rv) (Tv - To)] (12)

Using the concept of equivalent resistance, ra*, equation(4) can be written as:

pCp (To - Ta) / ra=  pCp (Ts - Ta) / ra* (13)

Substituting (12) into (13) we have:



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

ra*=ra (15)

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

ETd = Rnd* - B (Ts-Ta)i (16)

where ET is the actual evapotranspiration (mm), Rn* = Rn / L is the net radiation expressed in mm of water (mm), (Ts-Ta) 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 = (Rnd / Rni) <  pCp / ra* > (17)

where Y is air density (kgm-3), Cp the specific heat of air at constant pressure (Jkg-1K-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 Rnd/Rni 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 (Ts-Ta)i where Ts 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 Ta 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 (Tv, Ta, Tg). 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 Ta 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) 497-519.

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