216 P. van der Keur et al. Agricultural and Forest Meteorology 106 2001 215–231
sensing data see, e.g. Ottlé et al. 1996 for a review. The first method is based on conversion of observed
thermal radiance into surface temperature, which is then used to calculate sensible heat flux. The latent
heat flux is then calculated from the surface energy balance as a residual of the net radiation, estimated
ground heat flux and the RS estimated sensible heat flux Hatfield, 1983; Moran et al., 1989; Kustas, 1990.
The second method relies on estimation of surface energy fluxes from either remotely sensed vegetation
index data and surface radiant temperature Tucker et al., 1981; Gillies et al., 1994 or from surface bright-
ness temperatures as measured with a microwave ra- diometer Njoku and Patel, 1986. Surface brightness
temperature can be used to infer the soil moisture content of the upper few centimeters of the soil profile
e.g. Wang et al., 1989 and used as a boundary condi- tion for the calculation of the surface evaporation rate
where soil evaporation is the dominant component of the latent heat flux Sellers, 1991. Alternatively, ac-
tive microwave RS radar can be used to infer top soil moisture content or in combination with passive mi-
crowave RS Chauhan, 1997. The third method, and the one pursued in this study, relies on the ability to
infer information on the photosynthetic capacity and the minimum canopy resistance r
min c
from spectral vegetation indices e.g. Asrar et al., 1984; Monteith,
1977; Sellers, 1985, 1987; Sellers et al., 1992a,b. Specifying the correct change in minimum canopy re-
sistance with time is crucial and incorporates changes in both leaf area index and stomatal resistances Dol-
man, 1993. This link is here taken as the point of departure for the use of remotely sensed data in mod-
eling evapotranspiration processes in soil–vegetation– atmosphere–transport schemes SVATS models, at
various spatial scales. No direct means is yet available to monitor minimum stomatal resistance from space,
but subtle shifts in the reflectance spectrum in visible wavelengths that relate to diurnal changes in photo-
synthetic efficiency also mirror changes in stomatal resistance Gamon et al., 1992. In this study, however,
focus is on the unstressed stomatal resistance r
min c
, i.e. minimum canopy resistance, that is upscaled through
LAI. It can be inferred by RS data, and therefore in- herently contains information on plant physiological
status through r
min c
and LAI. Sellers 1991 summa- rizes the limitations of all three approaches to convert
satellite sensed data to the desirable surface param- eters including problems with sensor calibration,
atmosphericgeometric correction, conversion of radi- ance to surface parameters and finally conversion of
surface parameters to biophysical quantities.
The soil–plant–atmosphere system model DAISY Hansen et al., 1991 was prepared to accommodate
use of remotely sensed, initially ground based, data for simulation of evapotranspiration. In the present
approach, simulated actual evapotranspiration was ei- ther at potential rate and estimated empirically from
standard meteorological data e.g. Makkink, 1957 or less than potential rate being controlled by the extrac-
tion of soil water by plant roots Hansen et al., 1991. This method precluded the incorporation of remotely
sensed data in the model in the sense proposed in this paper. Instead, an energy balance approach based
on a two-source resistance network, allowing sparse canopy cover, is added to the model. Stomatal resis-
tance is part of this resistance network and regulates the amount of water available through stomata path-
ways for plant transpiration and intake of carbon diox- ide for photosynthesis. Thus, in summary, unstressed
stomata resistance scaled to the canopy level by LAI can be related to both RS data, i.e. spectral vegetation
indices, and actual canopy resistance and has the po- tential to provide a link between SVAT modeling and
RS data.
The purpose of this paper is to describe the method followed to prepare the DAISY model for RS data in-
put as envisaged within the framework of the Danish funded RS-MODELearth observation project. The
two-source model, allowing for sparse canopy cover Shuttleworth and Wallace, 1985; Shuttleworth and
Gurney, 1990, is added to the DAISY model struc- ture and modeled surface energy fluxes, soil moisture
content and crop development are validated against experimental data from a winter wheat plot under
Danish conditions.
2. Model concepts
2.1. DAISY model description The soil–plant–atmosphere system model DAISY
Hansen et al., 1991 is a deterministic, one-dimensio- nal, mechanistic model for the simulation of crop
production and water and nitrogen balance in the root
P. van der Keur et al. Agricultural and Forest Meteorology 106 2001 215–231 217
zone. The model includes sub-models for evapotran- spiration, soil water dynamics based on the Richard’s
equation, water and nitrogen uptake by plants, soil heat flow due to conduction and convection. Soil min-
eral nitrogen dynamics are based on the convection– dispersion equation and nitrogen transformation in
the soil is simulated as mineralization–immobilization turnover MIT, nitrification and denitrification. The
crop model simulates plant phenological develop- ment, gross and net photosynthesis, growth and
maintenance respiration and root penetration and root distribution. The model considers root, stem, leaf and
storage organs. Of special interest in this study is the simulation of leaf area index, which only depends on
simulated leaf dry matter and the development state of the plant. The crop model takes water and nitrogen
stress into account. In addition, the model includes a module for agricultural management practice. The
model is described in detail elsewhere Hansen et al., 1991; Petersen et al., 1995. The model has been
validated in a number of studies de Willigen, 1991; Jensen et al., 1994; Diekkrüger et al., 1995; Svendsen
et al., 1995; Smith et al., 1997.
2.2. SVAT resistance network approach adapted to DAISY
The model was extended to include a canopy re- sistance approach for simulation of surface energy
fluxes, latent and sensible heat flux, and thereby im- plementing a regulatory mechanism for vapor flow
from the canopy to the atmosphere which can be linked to remotely sensed data.
During periods in the early growing season and after harvest, the contribution of bare soil evaporation can-
not be ignored, thus a ‘sparse crop canopy’ approach was adopted, i.e. a modified Shuttleworth–Wallace
model Shuttleworth and Wallace, 1985; Shuttleworth and Gurney, 1990. DAISY simulated water and heat
flow in an underlying soil profile was utilized to predict bare soil evaporation, i.e. no soil resistance
expressions were applied.
2.3. Two-source model approach Early in the growing season and after harvest of
the agricultural crop, energy fluxes calculated by the one-source ‘big leaf’ model Monteith, 1965, assum-
ing fully developed canopy cover, are contaminated by contributions from the bare soil. The two-source
model applied in this study allows for partitioning of incoming solar energy into a soil and a vegetative frac-
tion divided by leaf area index, thus compensating for the shortcomings of the simplified one-source model
under sparse crop cover conditions. Shuttleworth and Wallace 1985 derived a resistance network type
model which allowed for energy partitioning and approached a closed canopy as well as bare soil con-
ditions in the two limiting cases when LAI comes near to full canopy value and zero, respectively. Later
Choudhury and Monteith 1988 developed a similar model and included the interaction of evaporation
from the soil and foliage expressed by changes in the saturation vapor pressure deficit of air in the
canopy. Shuttleworth and Gurney 1990 extended the model by Shuttleworth and Wallace 1985 with a
relationship between surface temperature and canopy behavior in sparse canopies as part of an effort to
couple multi-source models to remote sensing data. The studies mentioned here all use soil resistances for
describing vapor flow from the soil to the atmosphere. Numerous expressions have been derived for soil re-
sistances as function of water content or soil vapor density and diffusivity see Bastiaanssen 1996 for a
review. In this study, use of empirical soil resistance formulations was circumvented by the coupling of
the two-source model to the DAISY model. In this more physically based method soil evaporation was
calculated by the Richard equation as upward driven water flow towards the soil surface, i.e. exfiltration,
based on the evaporative demand determined by the potential evaporation as a function of the energy
available through the LAI function and restricted by the hydraulic properties of the upper soil layer.
The sparse crop energy balance is described as follows, refer to Fig. 1.
Sensible heat flow between mean source height and reference height
H
a
= ρc
p
T
c
− T
a
r
aa
1 Sensible heat flow between leaf surface and mean
source height H
l
= ρc
p
T
l
− T
c
r
ac
2
218 P. van der Keur et al. Agricultural and Forest Meteorology 106 2001 215–231
Fig. 1. Schematic representation of resistance network and energy fluxes for the two-source SVAT component of the DAISY model.
Aerodynamic resistances r
as
, r
ac
and r
aa
as well as energy fluxes λE and H with indices s, l and a are defined between mean source
height and soil, leaf, and reference height, respectively. T
s
, T
c
and T
a
are defined as temperatures at soil surface, mean canopy height and reference height, respectively.
Sensible heat flow between soil surface and mean source height
H
s
= ρc
p
T
s
− T
c
r
as
3 Latent heat flow between mean source height and
reference height λE
a
= λ e
c
− e
a
r
aa
4 Latent heat flow between leaf surface and mean
source height λE
l
= λ e
∗ l
− e
c
r
sc
+ r
ac
5 Latent heat flow between soil surface and mean
source height λE
s
is calculated in DAISY as the sum of upward flowing water from the soil matrix below
and evaporation from eventual ponded water. It is as- sumed that the lateral flux between the soil and the
mean canopy source height is negligible, i.e. water re- leased at the soil surface is transported without lateral
loss to the mean canopy height node. In Eqs. 1–5, T
a
, T
c
, T
l
and T
s
K are temperatures of air, in-canopy at mean source height, leaf and soil surface, respec-
tively, and e
a
, e
c
, e
s
kg m
−3
are water vapor con- tents at reference height, canopy mean source height
and soil surface. It is assumed that stomatal air space in the leaves is at 100 humidity, therefore e
∗ l
is sat- urated vapor pressure at the leaf surface. All fluxes
are in W m
−2
. Resistances r
aa
, r
as
, r
ac
and r
sc
s m
−1
are defined in Eqs. 17, 18, 22 and 24, respec- tively, and λ is latent heat of vaporization of water
J kg
−1
. Conservation of fluxes through the canopy yield Eqs. 6 and 7
Conservation of sensible heat H
a
− H
l
− H
s
= 0 6
Conservation of latent heat λE
a
− λE
l
− λE
s
= 0 7
Conservation of energy for the plant canopy leads to
λE
l
+ H
l
= A
l
8 and for the soil surface
λE
s
+ H
s
= A
s
9 Furthermore, as mentioned above, it is assumed that
the stomatal air space in the leaves is at 100 and that this humidity kg m
−3
is a function of the leaf surface temperature
e
∗ l
= e
∗ a
+ ∆T
l
− T
a
10 where ∆ is the slope of the saturation function for
water vapor at T
a
. A
l
and A
s
in Eqs. 8 and 9 is energy that must be transmitted as sensible and latent heat into the air from
the plant canopy and the soil surface, respectively, expressed in Eqs. 11 and 12
A
l
= R
n
1 − e
−kL
11 and
A
s
= R
−kL n
− G 12
where R
n
is net radiation W m
−2
, G is ground heat flux W m
−2
, L is leaf area index and k is an extinction parameter k = 0.5. R
n
is net radiation described as R
n
= 1 − αS
i
+ L
d
− L
u
13 where S
i
is global radiation W m
−2
, α albedo and L
d
and L
u
downwards and upwards longwave radia- tion W m
−2
, respectively, in which net long radia- tion L
d
− L
u
is a function of T
a
and e
a
. Net radiation
P. van der Keur et al. Agricultural and Forest Meteorology 106 2001 215–231 219
is thus estimated from standard meteorological data: global radiation S
i
, air temperature T
a
, vapor pressure e
a
and from relative duration of sunshine n
sun
. The longwave component is calculated by means of the
Brunt 1932 equation Rosenberg et al., 1983 L
d
− L
u
= σ T
4 a
b
1
− b
2
p e
a
b
3
+ b
4
n
sun
14 where air temperature T
a
is in K, e
a
in kPa, b
i
are constants b
1
= 0.53, b
2
= 0.0065, b
3
= 0.1 and b
4
= 0.9 and σ is the Stefan–Boltzmann constant. The relative duration of sunshine n
sun
is derived by rewriting the Prescott 1940 formula
S
i
= a
p
+ b
p
n
sun
S
ex
15 where S
i
is measured global radiation and S
ex
is the extraterrestrial radiation, a function of latitude and
time of year, and a
p
and b
p
are site specific coeffi- cients. For the Danish Foulum location at 56
◦
30
′
N an average of the daily values found at DeBilt
52
◦
N, Kohsiek, 1971, unpublished and Matanuscka- Anchorage, Alaska 61
◦
N, Baker and Haines, 1969 were used references from Brutsaert 1982, p. 135,
i.e. a
p
= 0.21 and b
p
= 0.50. The phase difference in calculated extraterrestrial radiation and measured
global radiation at solar and local time, respectively, is accounted for. G is calculated from T
s
and a DAISY calculated upper soil temperature, T
G = k
h
T
s
− T 1z
16 where 1z is depth of the upper soil layer and k
h
is ther- mal conductivity of that layer returned by the DAISY
model. Eqs. 1–3 are substituted in Eq. 6, Eqs. 4 and
5 in Eq. 7 and Eqs. 11 and 12 in Eqs. 8 and 9, respectively. Then a linear system of five equations
Eqs. 6–10, and five unknowns, T
s
, T
c
, T
l
, e
c
and e
∗ l
is obtained and solved using a Gauss–Jordan elim- ination. For each time step the involved resistances
in the linear equation system are computed using Eqs. 17–29. Then, sensible and latent heat fluxes
can be calculated by back substitution in Eqs. 1–5.
2.4. Network resistances In unstable temperature lapse conditions, vertical
motions are enhanced by buoyancy, effectively reduc- ing the aerodynamic resistance r
aa
Thom, 1975. This can be accounted for by applying a stability correction
factor based on the Businger–Dyer profiles Dyer and Hicks, 1970; Dyer, 1974; Businger, 1988. Eq. 17
including the stability ψ functions ψ
m
and ψ
h
, de- fined for unstable conditions in Paulson 1970 and for
stable conditions in Webb 1970, is applied by, e.g. Dolman 1993
r
aa
= 1
ku
f
ln z
ref
− d h − d
+ ψ
∗ m
− ψ
∗ h
h nKh
× exp
−n 1 −
z + d
h − 1
17 where h is vegetation height m, d is displacement
height m, z is roughness length m, u
f
is friction velocity m s
−1
, z
ref
is reference height usually 2 m and n is an eddy decay coefficient with a typical
value of about 2.5. Kh is an eddy diffusion coeffi- cient and defined in Eq. 19. The stability functions
ψ
∗ m
and ψ
∗ h
are defined as ψ
∗ m
= ψ
m
z
ref
L
o
− ψ
m
hL
o
and ψ
∗ h
= ψ
h
z
ref
L
o
− ψ
h
hL
o
in which L
o
is the Obukhov stability length. Stability conditions between canopy mean height and reference
height are here evaluated by the Richardson number R
i
Thom, 1975, unstable when R
i
0 and stable when R
i
0. It is commonly assumed similarity hypoth- esis, that under fully forced convection conditions a
single canopy aerodynamic resistance term, r
aa
, rather than separate aerodynamic resistances for vapor and
heat flow, r
av
and r
ah
, can be used to calculate both latent and sensible heat fluxes, i.e. r
aa
= r
av
= r
ah
Thom, 1975. Nichols 1992 derived r
av
and r
ah
sep- arately from measured latent and sensible heat fluxes,
respectively, by the Bowen ratio method above 0.75 m high sparsely vegetated shrubs in west central Nevada,
USA. It was found that r
av
generally was one order of a magnitude higher than r
ah
. Under the conditions at Foulum for 1997 it is assumed that the similarity hy-
pothesis is valid until derived values from eddy covari- ance measurements become available for verification.
Resistance between soil surface and canopy air, r
as
, is derived by Choudhury and Monteith 1988
r
as
= h e
α
k
α
k
Kh e
−α
k
z
s
h
− e
−α
k
d+z h
18 and the eddy diffusion coefficient Kh
Kh = κ
2
uh − d lnz
ref
− dz 19
220 P. van der Keur et al. Agricultural and Forest Meteorology 106 2001 215–231
where α
k
is attenuation coefficient of eddy diffusiv- ity through sparse canopy set to 2.0, z
s
=10
−2
m is roughness length for the soil surface, κ is the von Kár-
máns constant =0.41, u is wind speed at reference height and the rest previously defined. In common with
Choudhury and Monteith 1988 and Shuttleworth and Gurney 1990 d and z
are calculated as functions of leaf area index derived from second-order closure
theory Shaw and Pereira, 1982, yielding Eqs. 20 and 21 in which c
d
is the mean drag coefficient for a leaf, set to 0.05 Shuttleworth and Gurney, 1990
d = 1.1 h ln1 + c
d
L
0.25
20 and
z =
z
s
+ 0.3hc
d
L
0.25
for 0 ≤ c
d
L ≤ 0.2 0.3h
1 − d h
for 0.2 c
d
L ≤ 1.5 21
The aerodynamic resistance between leaves and mean source height is defined by Jones 1983 and Choud-
hury and Monteith 1988
r
ac
= α
u
2aL w
uh
0.5
1 1 − e
−0.5α
u
22 where uh is wind speed at h
uh = u lnh − dz
lnz
ref
− dz 23
and w =0.01 m is average leaf width, a =0.01 m s
−12
is a constant and α
u
=3.0 is attenuation coefficient for wind speed.
Finally, canopy resistance r
sc
is parameterized fol- lowing Dickinson 1984, Jarvis 1976 and Noilhan
and Planton 1989 by using four constraint functions F
1
to F
4
and taking into account the physiology of the vegetation as applied by, e.g. Bougeault 1991 and
Tourula and Heikinheimo 1998 r
sc
= r
min s
L F
1
F
2
F
3
F
4 −1
24 where F
1
is a function related to solar radiation and here parameterized following Dolman et al. 1991
F
1
= S
i
T + S
i −1
1000100 + T
−1
25 where T is taken to be 250 W m
−2
as optimized for oats in Dolman 1993.
The response of stomata to changing ambient hu- midity has been the subject of some controversy
Monteith, 1995a; Lhomme et al., 1998 and it has been proposed that stomata respond to the rate of
transpiration rather than air humidity per se Mott and Parkhurst, 1991. However, as there are uncertainties
as how to upscale alternative constraint formulations as proposed by Monteith 1995b from leaf to canopy,
the Lohammar et al. 1980 environmental function is applied based on the findings that in many species, the
stomatal resistance increases as the relative humidity decreases, i.e. as the leaf-to-air water vapor concen-
tration difference increases Turner, 1991, thus
F
2
= 1 + ζ e
∗ a
− e
a −1
26 using the value of 0.57 kg
−1
m
3
for ζ , applied by Verma et al. 1993 for tall grass.
Although many parameterizations of stomatal resis- tance neglect the influence of ambient air temperature
see Lhomme et al. 1998 for a review it has earlier been stated, e.g. Dickinson 1984, that stomatal re-
sistance usually shows a decrease with increasing air temperature to a maximum value and then an increase
at still higher ambient temperatures. This temperature optimum varies with species and can be increased by
growth at high temperatures and vice versa. F
3
related to air temperature Dickinson, 1984
F
3
= 1 − ξT
ref
− T
a 2
27 where ξ = 0.0002 K
−2
Jarvis, 1976. T
ref
is a ‘refer- ence temperature’ Noilhan et al., 1991 or optimum
temperature as explained above Turner, 1991 set to 298 K by Dickinson 1984.
Stomatal resistance increases as the soil dries, where soil water status influences stomatal conductance ei-
ther through its influence on leaf water potential or by changes in the level of phytohormones produced by
roots in response to soil dehydration. These processes are represented by the F
4
function taking account of water stress Bougeault, 1991
F
4
= θ − θ
wilt
θ
c
− θ
wilt
28 where θ
c
and θ
wilt
are soil water content at ‘field capacity’ at 2.0 pF and ‘wilting point’ at 4.2 pF,
respectively, and estimated from soil hydraulic prop- erties as described later in Section 4. The root zone
P. van der Keur et al. Agricultural and Forest Meteorology 106 2001 215–231 221
soil moisture content θ is calculated as an average of DAISY simulated water content at nodes within
0–100 cm. The minimum resistance r
min c
, i.e. r
min s
L in Eq. 24 is the parameter of interest for linking energy
balance modeling, e.g. latent heat flux evapotranspi- ration, to remote sensing data. However, as such data
is not yet available for this study, minimum canopy resistance is estimated from r
c
in Eq. 29 Allen et al., 1989; FAO, 1990
r
c
= r
day
0.5L =
200 L
29 where r
day
is the average daily 24 h stomatal resis- tance of a single leaf. Sellers et al. 1992a,b estimated
r
min c
to be between 40 and 120 s m
−1
for crops, cor- responding to LAI values from 5 to 1.7, respectively,
in Eq. 29.
3. Study area and 1997 field campaigns
