114 D. Amarakoon et al. Agricultural and Forest Meteorology 102 2000 113–124
Bruin and Holtslag 1982 is a simple empirical mod- ification of Priestley and Taylor 1972 scheme, and
it appears useful in estimating surface latent heat flux from surfaces with short crops when the surface is
supplied with enough water to evaporate. The prac- tical advantage of this scheme is the fact that only a
few measurable input parameters are required to es- timate latent heat flux apart from the two empirical
parameters α
′
and β. The results of De Bruin and Holtslag 1982 have shown that the scheme has the
same skill as Penman–Monteith approach Monteith, 1965; Brutsaert, 1982. Penman–Monteih approach
Monteith, 1965; Brutsaert, 1982 is a more complete scheme, but requires a relatively large number of input
parameters.
The objective of our study was to examine the ap- plicability of De Bruin and Holtslag 1982 scheme
for estimating latent heat flux and evaporation in Ja- maica, which has a tropical climate. The scheme was
developed in the Netherlands, which has a temperate climate and appear to have the potential for practical
applications. If its applicability can be verified under tropical environmental conditions, it may be a useful
tool, especially in agricultural meteorology, for esti- mating latent heat flux and hence evaporation from
surfaces covered with short vegetation and irrigated regularly. For testing De Bruin and Holtslag 1982
scheme, we estimated the quantities stated below using that scheme and the data collected over fields
with grass during the periods January to February of 1994, January to February of 1990 and August to
September of 1989. The quantities estimated were daytime 07:00–18:00 hours values of i 20 min and
hourly latent heat flux, ii average evaporation for the three periods of data collection and iii evaporation
on individual days. The estimated values were then compared with corresponding measured values using
linear regression analysis and calculating percentage deviations where appropriate.
2. Consideration of schemes
The Penman scheme Penman, 1948 which was originally intended for evaporation from an
open-water surface, but shows general applicability to any wet surface Brutsaert, 1982, can be cast in
the form including the heat flux into the surface: E =
1 1 + γ
R
n
− GŴ
λ +
γ 1 + γ
× f ue
∗
− e
Ŵ 86400
1 where E is the evaporation in mm during the time in-
terval Ŵ in seconds, e and e are the saturation vapor pressure at air temperature θ and vapor pressure in
mb, respectively, 1 the slope of the e versus air tem- perature curve at θ , R
n
the net radiation in W m
− 2
, G the heat flux into the surface in W m
− 2
, λ the latent heat of vaporization and γ the psychrometric constant
which is equal to c
p
p 0.622. In the definition of γ ,
c
p
is the specific heat capacity of dry air at constant pressure, p is the atmospheric pressure and 0.622 is
the ratio of the molecular weight of water vapor to that of dry air. In Eq. 1 the function fu is a func-
tion of the wind speed u and the product fue−e is in mm day
− 1
. The form of fu originally proposed by Penman 1948 is the following.
f u = 0.261 + 0.54u
2 where u is the mean wind speed in m s
− 1
at 2 m above the surface. The expression corresponding to Eq. 1
that represents the latent heat flux, l in W m
− 2
, can be given in the form
l = 1
1 + γ R
n
− G +
γ 1 + γ
× f ue
∗
− e
λ 86400
3 Eq. 1 has been widely used to estimate poten-
tial evapotranspiration Brutsaert and Stricker, 1979; Katul and Parlange, 1992; Parlange and Katul, 1992;
Konzelmann et al., 1997. Potential evapotranspiration generally refers to Brutsaert, 1982 the maximum
rate of evapotranspiration from a large area covered completely and uniformly by an actively growing
vegetation with adequate moisture at all times. The wind function given by Eq. 2 has been used in
Eq. 1 Brutsaert and Stricker, 1979; Konzelmann et al., 1997 to study potential evaporation for time
intervals of the order of a day. For shorter periods, the inclusion of the atmospheric stability Brutsaert,
1982; Katul and Parlange, 1992; Parlange and Katul, 1992 in fue−e in Eq. 1 has been found more
appropriate.
D. Amarakoon et al. Agricultural and Forest Meteorology 102 2000 113–124 115
The scheme of Priestley and Taylor 1972 is the best-known simplification of Penman 1948 scheme
and is based on the concept of equilibrium evapora- tion Slatyer and McIlroy, 1961 from moist surfaces.
Slatyer and McIlroy 1961 had presented the idea that over a very large homogeneous and thoroughly
moist surface under well established steady conditions e
tends to e. A consequence of this is the vanishing of the second term containing e−e from Eq. 1
and hence the first term in Eq. 1 may be considered to represent a lower limit to evaporation from moist
surfaces which the authors referred to as the equilib- rium evaporation. In our work, equilibrium evapora-
tion is denoted by E
eq
and the corresponding equi- librium latent heat flux which is the first term on the
right hand side of Eq. 3 is denoted by l
eq
. Priestley and Taylor 1972 treated the equilibrium evaporation
as the basis for an empirical relationship for evapora- tion from a wet surface under conditions of minimal
advection. After analyzing data over ocean and satu- rated land surfaces they presented a scheme for wet
surface evaporation, which is of the form
E = αE
eq
4 where the parameter α in Eq. 4 is known as the
Priestley–Taylor parameter or coefficient. For large saturated land and advection-free water surfaces,
Priestley and Taylor 1972 concluded that the best estimate for α is 1.26. As mentioned in the literature
Brutsaert, 1982; Cargo and Brutsaert, 1992 there is enough experimental evidence to support the va-
lidity of a value around 1.26 for α. Eichinger et al. 1996 have derived an analytical expression for α
and their results have shown good agreement with the value 1.26. The equation for the latent heat flux l
corresponding to Eq. 4 is
l = αl
eq
5 The scheme of De Bruin and Holtslag 1982 can be
presented in the form l = α
′
1 1 + γ
R
n
− G + β
6 where α
′
and β are empirical constants and the first term on the right-hand side is the same as α
′
l
eq
. Ac- cording to the energy balance equation for the earth’s
surface, R
n
, G, l and the sensible heat flux H can be linked by the equation,
R
n
= l + H + G
7 Combining Eqs. 6 and 7, the sensible heat flux H
can be given by H =
[1 − α
′
1 + γ ]
1 + γ R
n
− G − β
8 De Bruin and Holtslag 1982 have performed mea-
surements over a 100 m×100 m field covered with short grass of about 8 cm in height. They have ana-
lyzed data for two periods. During one period, which they call the normal period, the ground had been wet-
ter than the other period to which they refer as the dry period. For the normal period, the analysis of hourly
latent heat flux data has shown that α
′
can be assigned the value 0.95 and the β value 20 W m
− 2
. For the dry period, the values are 0.65 and 20 W m
− 2
, respectively. The results have shown that the hourly values of l es-
timated using Eq. 6 and the above α
′
and β values compare well with experimentally determined l values
and the values calculated using the Penman–Monteith approach Monteith, 1965; Brutsaert, 1982 which is
a more complete scheme. The values of H estimated using Eq. 8 have also shown reasonably good agree-
ment correlation coefficient of 0.92 and a root mean square error of 38 of average H with experimen-
tally determined H values. Furthermore, their results have indicated that daily mean of α Priestley–Taylor
coefficient is about 10 greater than its hourly value during daytime, and that α=1.26 yields good results
for daily values of latent heat flux.
3. Site description and environmental conditions
