of temperatures, several authors related linearly measured blackbody surface temperatures with Landsat DNs 
(Lathrop & Lillesand, 1987 ; Moran et al., 1989 ; Moran, 1990 ; Palmer, 1993). They then corrected the 
obtained blackbody temperatures for emissivity effect using this first order approximation : 
Tbb" = £-Ts" (2) 
where e is the surface emissivity, and n is comprised between 4 and 5, usually considered equal to 4, which is 
rigorously true only when the Stefan-Boltzmann law applies, i.e. not for a given bandwidth. This 
approximation can be done also because the downward atmospheric radiance reflected by the ground can be 
neglected (Palmer, 1993). 
Our methods refers to eq. (1), and tries to relate blackbody temperatures to Landsat DNs using 
the following equation : 
TBB = K 2 Inf—+ 1| (3) 
/ Udn+a J 
Emissivity effects are then removed as presented above in eq. (2). If blackbody temperatures 
of at least a cold and a warm target can be measured or estimated, eq. (3) shows that coefficients a and b can be 
derived, and eq. (3) can then be used to transform the Landsat DNs into blackbody temperatures. 
2.2. Surface energy balance 
The classical expression of surface energy balance equation is as follows : 
Rn = G + H + LE (4) 
where Rn is the net radiation flux, G the soil heat flux, H the sensible heat flux and LE the latent heat flux or 
évapotranspiration. 
The net radiation Rn can be obtained from the classical expression of the surface radiative 
budget : 
Rn = (l-a)Rg + eRa- eoTs 4 (5) 
where a is the surface albedo, Rg is the shortwave incoming solar radiation, Ra is the longwave incoming 
(atmospheric) radiation, e is the surface emissivity, and a is the Stefan-Boltzmann constant 
(5.67.10~ 8 W. m~ 2 . KT 4 ). Ra can be estimated for clear-sky conditions from ground-based measurements of air 
temperature and vapor pressure using the relation (Brutsaert, 1975): 
Ra = 1.24(ea/7a) I/7 oTa 4 ( 6 ) 
where ea is the vapor pressure (mb) and Ta is the air temperature (K). 
The soil heat flux G can usually be expressed as a linear function of net radiation depending 
on vegetation cover. Practically, G varies linearly from 0.3 Rn for bare soil to 0.1 Rn for full vegetation cover 
(Clothier et al., 1986 ; van Oevelen et al., 1993). 
The sensible heat flux H can be expressed as : 
H = £Q-(T,-Ta) (7) 
ra 
where pCp is the air volumetric heat capacity (» 1200 J.m'TK‘1), ra is the aerodynamic resistance (s/m) 
corrected for stability/unstability effects and for the additional resistance effect due to the difference between 
radiative and aerodynamic surface temperature, usually referring to the kB ' 1 resistance (Prévôt et al., 1993). 
As reminded in the introduction, LE is physically related to surface temperature Ts and that, 
for a given surface under given climatic conditions, Ts ranges from a minimum Ts mm corresponding to 
maximal évapotranspiration LE=LEp , to a maximum Ts max corresponding to no-evapotranspiration LE= 0. 
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