where:
(Rn - LE)day : daily integral of the difference (Rn - LE);
B = constant
To: instantaneous surface temperature at midday;
Ta: instantaneous air temperature at midday;
n=1
8 Evaporation
167
was a milestone in the development of remote sensing methods to determine actual
evaporation through the surface heat balance approach. This equation indicates
that the excess available energy (i.e. Rn-LE) is proportional to the difference between surface and air temperature. This empirical relationship implies that the ratio of sensible heat flux to (To-Ta), i.e. the aerodynamic resistance to sensible heat
transfer, is a constant. Net radiation, as well as LE, was observed at one location
over a homogenous crop of wheat. Both Rn and LE are daily values, while (T 0-T a)
is instantaneous. Interest for this approach developed rapidly and diverse experimental, theoretical and modelling studies were undertaken. Land heterogeneity
was given scarce attention initially. At heterogeneous land changes in net radiation
are significant (e.g. Menenti, 1984) and force changes in surface temperature comparable with the observations of Stone et ai. (1975) on temporal changes. This
explains why investigations dealing with regions where albedo was rather variable
used measurements of both surface temperature and albedo to estimate evaporation
(Gurney and Hall, 1983; Menenti, 1984). Studies have been published, however,
using this linear relationship in modified forms (e.g. Nieuwenhuis et aI., 1985) to
map actual evaporation. It should be noted that the spatial variability of other land
surface properties such as aerodynamic roughness determines spatial patterns of
surface temperature related to evaporation in a more complex manner.
Initially, improvements were sought along two avenues:
use of different values ofB in the linear relationship (see 8.3.3) to account for
differences in land surface properties (Seguin and Itier, 1983; Sandholt and
Andersen, 1993; Carlson and Buffum, 1989; Thunnissen and Nieuwenhuis,
1990);
detailed modelling of heat and momentum transfer at the land - atmosphere interface (e.g. Carlson et aI., 1981; see 8.3.4);
8.3.3 Improved linear relationships (2]
The linear relationship rests on many assumptions, one of which is the uniqueness
of the radiometric surface temperature T rad. The latter is not unique as a matter of
principle due to the dependence on view angle when a target is observed with a
radiometer. While changes with view and azimuth angles may be negligible for a
complete canopy, changes are large for partial canopies (e.g. Kimes et aI., 1983).
Caselles et ai. (1992) demonstrated that large deviations from linearity were due to
the view and azimuth angles and that different values of the parameters in the linear relationship had to be calculated for each observation geometry and target.
Building upon the results of Wetzel et ai. (1984), Carlson and Buffum (1989) pro-
(Rn - LE)day : daily integral of the difference (Rn - LE);
B = constant
To: instantaneous surface temperature at midday;
Ta: instantaneous air temperature at midday;
n=1
8 Evaporation
167
was a milestone in the development of remote sensing methods to determine actual
evaporation through the surface heat balance approach. This equation indicates
that the excess available energy (i.e. Rn-LE) is proportional to the difference between surface and air temperature. This empirical relationship implies that the ratio of sensible heat flux to (To-Ta), i.e. the aerodynamic resistance to sensible heat
transfer, is a constant. Net radiation, as well as LE, was observed at one location
over a homogenous crop of wheat. Both Rn and LE are daily values, while (T 0-T a)
is instantaneous. Interest for this approach developed rapidly and diverse experimental, theoretical and modelling studies were undertaken. Land heterogeneity
was given scarce attention initially. At heterogeneous land changes in net radiation
are significant (e.g. Menenti, 1984) and force changes in surface temperature comparable with the observations of Stone et ai. (1975) on temporal changes. This
explains why investigations dealing with regions where albedo was rather variable
used measurements of both surface temperature and albedo to estimate evaporation
(Gurney and Hall, 1983; Menenti, 1984). Studies have been published, however,
using this linear relationship in modified forms (e.g. Nieuwenhuis et aI., 1985) to
map actual evaporation. It should be noted that the spatial variability of other land
surface properties such as aerodynamic roughness determines spatial patterns of
surface temperature related to evaporation in a more complex manner.
Initially, improvements were sought along two avenues:
use of different values ofB in the linear relationship (see 8.3.3) to account for
differences in land surface properties (Seguin and Itier, 1983; Sandholt and
Andersen, 1993; Carlson and Buffum, 1989; Thunnissen and Nieuwenhuis,
1990);
detailed modelling of heat and momentum transfer at the land - atmosphere interface (e.g. Carlson et aI., 1981; see 8.3.4);
8.3.3 Improved linear relationships (2]
The linear relationship rests on many assumptions, one of which is the uniqueness
of the radiometric surface temperature T rad. The latter is not unique as a matter of
principle due to the dependence on view angle when a target is observed with a
radiometer. While changes with view and azimuth angles may be negligible for a
complete canopy, changes are large for partial canopies (e.g. Kimes et aI., 1983).
Caselles et ai. (1992) demonstrated that large deviations from linearity were due to
the view and azimuth angles and that different values of the parameters in the linear relationship had to be calculated for each observation geometry and target.
Building upon the results of Wetzel et ai. (1984), Carlson and Buffum (1989) pro-