J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21 3
Henderson-Sellers et al., 1995; Pollard and Thomp- son, 1995; Carlson and Bunce, 1996; Bunce et al.,
1997; Brown and Rosenberg, 1997; Grossman-Clarke et al., 1999. Friend and Cox 1995, using a single
column model, found a decrease in evapotranspiration of 22 for doubled CO
2
experiments over an Ama- zon tree canopy. Henderson-Sellers et al. 1995 and
Pollard and Thompson 1995 used off-line versions of land surface parameterizations in the GENESIS
LSX and CCM1-Oz BATS general circulation models, respectively, to diagnose doubled [CO
2
] ef- fects on transpiration. These two models in their
off-line form prescribe atmospheric conditions so that no dynamic interaction occurs between the sur-
face fluxes and the mixing layer. For both studies, the stomatal resistance was doubled to parameterize
doubled [CO
2
] for wet grassland canopies and re- ported a decrease in transpiration of 28 and 18 for
Pollard and Thompson 1995 and Henderson-Sellers et al. 1995, respectively. Carlson and Bunce 1996
performed a sensitivity test in a corn and soybean study by representing the effects of doubled [CO
2
] on stomatal resistance by increasing the stomatal re-
sistance from 0 to 150 and observed a subsequent decrease in transpiration ranging from 0 to 25.
Grossman-Clarke et al. 1999 simulated a 5 de- crease in total seasonal canopy transpiration under
elevated [CO
2
] 370–550 mmol mol
−1
using a wheat crop model and, Brown and Rosenberg 1997 found
decreases in evapotranspiration of 3–10 and 4 for corn and soybeans respectively for a 40 stomatal
resistance increase.
The results from these canopy studies are interesting and important because the results expressed either as
TR
decrease
or TR
decrease
SR
increase
are much less than those observed for research conducted at the scale of
the single leaf. The discrepancy between the results in the literature for studies conducted at the scale of a sin-
gle leaf compared with those from canopy models in- dicate that other factors besides the stomatal resistance
are interacting to alter the transpiration at the canopy scale. Feedbacks in ambient humidity, wind speed, ra-
diation, and vegetation structure significantly impact the flux of water vapor from the canopy Jarvis and
McNaughton, 1986; McNaughton and Jarvis, 1991; Aphalo and Jarvis, 1993; Baldocchi, 1994; Jacobs and
DeBruin, 1997; Raupach, 1998; Steduto and Hsiao, 1998a–c.
This paper presents the results of a modeling ap- proach used to investigate how plant inter-canopy and
boundary layer feedbacks alter the decrease in transpi- ration when perturbed in doubled [CO
2
] under differ- ing environmental conditions. The results are reported
both in terms of the percentage ratio
3
, the decoupling coefficient, Ω Jarvis and McNaughton, 1986 as well
as the stomatal resistance to total aerodynamic resis- tance ratio r
s
:r
a
.
2. Methodology
2.1. Model descriptions Two numerical models were used in this study:
The off-line version of the land surface exchange pa- rameterization of the GENESIS GCM LSX and the
Penn State University Biosphere-Atmosphere Model- ing Scheme PSUBAMS. The LSX model is a 1-D
soil-vegetation-atmosphere-transfer model SVAT in which atmospheric boundary conditions are prescribed
so that no dynamic interaction occurs between the surface and mixing layers Pollard and Thompson,
1995. PSUBAMS, on the other hand, is a 1-D atmo- spheric boundary layer SVAT Carlson and Boland,
1978; Carlson, 1986; Taconet et al., 1986; Lynn and Carlson, 1990 model ABL-SVAT that allows dy-
namic interaction between the surface fluxes and at- mosphere. With this capability, the impact of the mix-
ing layer on any transpiration change may be studied Carlson and Bunce, 1996; Bunce et al., 1997.
To conduct doubled [CO
2
] comparisons between LSX and PSUBAMS, similar initial conditions were
specified in each model to represent a comparable environment prior to the doubled [CO
2
] investiga- tion. The initial conditions necessary as input for each
model and the specific values chosen for the stan- dard scenario are provided in Table 1. Transpiration,
a prognostic field that involves a complex series of interactions among model variables, from both LSX
and PSUBAMS were within 40–50 W m
−2
during the simulation period 8:00 a.m.–4:00 p.m..
3
Comparatively, this is preferable to quoting the absolute de- crease in transpiration as in previous studies, where the stomatal
resistance increase and so, the decrease in transpiration varied considerably.
4 J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21
Table 1 The initial conditions used in the corn and soybean model comparisons for LSX and PSUBAMS
a
Input parameter Units
Corn LSX Corn PSU
Soybean LSX Soybean PSU
Leaf area index LAI
b
4.0 4.0
4.0 4.0
Fractional vegetation cover F
veg
c
100 100
100 100
Vegetation height
d
m 1.2
1.2 1.0
1.0
Minimum stomatal resistance c
e
s m
−1
50 50
50 50
Leaf width lw m
0.06 0.06
0.08 0.08
Foliage emissivity ε
f
0.97 0.97
0.97 0.97
Roughness Length z
o
m 0.12
0.12 0.10
0.10 Coolest 70 m air temperature in diurnal cycle
◦
C 16
– 16
– Warmest 70 m air temperature in diurnal cycle
◦
C 17
– 17
– Relative humidity at 70 m
62 –
62 –
Horizontal wind speed at 70 m m s
−1
7.0 –
7.0 –
Initial soil water content of all soil layers 0.65
– 0.70
– Single leaf reflectance visible
e
0.11 –
0.08 –
Single leaf reflectance NIR
e
0.58 –
0.51 –
Single leaf transmittance visible
e
0.07 –
0.07 –
Single leaf transmittance NIR
e
0.25 –
0.47 –
Vegetation orientation factor
f
0.18 –
0.0 –
Ratio of maximum root depth to canopy height
g
0.10 –
0.10 –
PAR function coefficients a, b J m
−3
, W m
−2
8750, 6 –
8750, 6 –
VPD constant K hPa
0.012 –
0.067 –
Effective heat capacity of a leaf surface J m
−2
K
−1
4218 –
4218 –
Surface layer water availability –
0.32 –
0.60 Root zone layer water availability
– 0.40
– 0.56
Beta β
h
– 0.0
– 0.06
Slope of the sub-critical portion of the water potential function b
1 h
– −2 × 10
−5
– −2 × 10
−6
Slope of the super-critical portion of the water potential function b
2 h
– 3.0
– 10.0
Critical leaf water potential ψ
c h
MPa –
−1.6 –
−1.4 Critical solar parameter S
c h
W m
−2
– 450
– 350
Plant resistance
h
MPa W m
−2 −1
– 0.005
– 0.006
Cuticular resistance
h
s m
−1
– 1000
– 5000
Sounding data
◦
C –
i
– –
i
–
a
The input parameters in bold are used in both models while those italicized and in normal print only correspond to LSX or PSUBAMS, respectively.
b
LAI = 4 is chosen to simulate a moderately dense canopy corresponding to conditions in early July corn, Sellers and Dorman 1987; soybean, Baldocchi 1992. Moreover, LSX is designed to execute using two-sided LAI despite a one-sided initialization. It was decided
for consistency that both LSX and PSUBAMS run with a one-sided LAI.
c
Values of F
veg
are 100 since modeling patches of bare soil with vegetation is not a focus in this study.
d
Determined from Sellers and Dorman 1987 corn and Baldocchi 1992 soybeans.
e
Obtained from Sellers 1985 corn and Baldocchi 1992 soybeans.
f
The vegetation orientation factor for both corn and soybeans was obtained from Ross 1981.
g
The ratio of the root depth to canopy height for both crops was left the same as that already in LSX.
h
The corn and soybean physiological parameters were obtained from Lynn and Carlson 1990 and refer to the stomatal resistance parameterization.
i
Sounding data is not included.
J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21 5
In order to observe the response of doubled [CO
2
] for different plants, simulations were performed for
both corn and soybeans. These two crops were cho- sen for three reasons. First, these two species are
cash crops and are important for agriculture. Second, they represent different plant classes and vary in their
metabolism corn — C
4
; soybean — C
3
. Lastly, data collected from doubled [CO
2
] experiments Wilson and Bunce, 1997; Wilson et al., 1999 were readily
available and easily incorporated into the model sim- ulations.
2.2. Stomatal resistance parameterizations Model runs were undertaken for four cases defined
by the stomatal resistance parameterization SRP as listed below:
1. LSX with its original SRP — indicated by LSX
current
. 2. PSUBAMS with its original SRP PSU
current
. 3. LSX with a ‘field-derived’ SRP replacing its orig-
inal SRP LSX
field
. 4. PSUBAMS with the same ‘field-derived’ SRP as
in 3 replacing its original SRP PSU
field
. All four cases parameterized the effect of doubled
[CO
2
] on stomatal resistance by incorporating a [CO
2
] function fCO
2
into the SRP to represent an increase in stomatal resistance from present day to doubled
[CO
2
]. The value for the increase in stomatal resis- tance for the first two cases LSX
current
and PSU
current
was assigned on the basis of the information contained in Cure and Acock 1986, which reported on average
an increase in stomatal resistance of approximately 30 for corn and soybeans for doubled [CO
2
] studies, therefore, fCO
2
was set to 1.3. The remaining two cases LSX
field
and PSU
field
made use of field measurements Wilson and Bunce, 1997; Wilson et al., 1999. The corn and soybean
plants were grown and measured in open-top cham- bers outdoors over three seasons 1993–1995 where
three [CO
2
] were used ambient, 1.5× ambient, and 2× ambient. Responses to vapor pressure deficit,
photosynthetic photon flux density, and air tempera- ture were made by placing the leaf in the leaf chamber
and incrementing humidity, photosynthetic photon flux density, and air temperature. These experiments
were where specific field data were collected a to determine the change in the minimum stomatal resis-
tance from present day to doubled [CO
2
] and, b to derive more representative environmental functions
for the SRP, i.e. for air temperature T, vapor pres- sure deficit VPD, solar irradiance S and soil water
content SWC. In these cases, fCO
2
was set to 2.4 and 1.32 for corn and soybeans, respectively; these
were based on measurements of minimum stomatal resistance under both CO
2
concentrations. Formula- tions and function definitions for these four cases are
outlined in Tables 2–4 — Table 2 illustrates the gen- eral form used to conduct each case while Tables 3
and 4 provide more detail for the functions included in the stomatal resistance formulation.
Another important aspect of the study was to ob- serve how different environmental conditions might
impact upon the transpiration change for doubled [CO
2
]. Therefore, this paper also presents, for both present day and doubled [CO
2
], tabulated results for a series of simulations termed scenarios for vary-
ing environmental conditions listed in Table 5 for each of the four cases. Table 5 indicates which initial
conditions were changed in each of the scenarios as compared to the standard scenario Table 1 which
are shown in Section 3.
2.3. Quantification of results As mentioned earlier, results from this study are
reported by a percentage ratio TR
decrease
SR
increase
× 100, for comparison with the literature, and by
a non-dimensional parameter, Ω, as developed by Jarvis and McNaughton 1986 and McNaughton and
Jarvis 1991. The percentage ratio is composed of both the decrease in transpiration TR
decrease
and the increase in stomatal resistance SR
increase
. The TR
decrease
and SR
increase
are defined in Eqs. 1 and 2 where SR
presentday
, SR
doubled
, TR
presentday
, and TR
doubled
are the stomatal resistance and transpira- tion for present day and doubled CO
2
, respectively. The sign convention was adopted so that transpira-
tion decrease and stomatal resistance increase are positive.
SR
increase
= SR
doubled
− SR
presentday
SR
presentday
× 100 1
TR
decrease
= TR
presentday
− TR
doubled
TR
presentday
× 100 2
6 J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21
Table 2 A description of the four cases used for doubled CO
2
investigation
a
Case name Stomatal resistance parameterization
Formulation R
min
f CO
2
for doubled [CO
2
] simulations
b
Functions dependent on [CO
2
] Corn
Soybeans Corn
Soybeans LSX
current
: uses current SRP from LSX
r
s
= r
min
f S fT fVPD fSWC fCO
2
50.0 50.0
1.30 1.30
No PSU
current
: uses current SRP from PSUBAMS
r
s
= r
min
f S fT fψ
e
fCO
2
50.0 50.0
1.30 1.30
No LSX
field
: uses field derived SRP
r
s
= r
min
f S fT fVPD fSWC fCO
2
79.0 24.7
2.40 1.32
Yes PSU
field
: uses field derived SRP
r
s
= r
min
f S fT fVPD fSWC fCO
2
79.0 24.7
2.40 1.32
Yes
a
The definitions for the individual functions in the stomatal resistance formulation are given in Tables 3 and 4.
b
f CO
2
is equal to 1.0 for all present day simulations.
Table 3 Definition of functions included in the stomatal resistance parameterization for LSX
current
and PSU
current a
Case name Definition of functions
LSX
current a
f S = PARPAR
c
+ 1 PARPAR
c
+ r
min
r
max
f VPD =
1 − e
s
T − e
air
K
−1
f T = 1.0 + 0.0016T
leaf
− 298
2
UP
max
= U
c
LAI + SAI 6
P
6 1
f
root
i w
−b
wilt
− wi
−b
w
−b
wilt
− 1 PSU
current b
f S = 1 − exp
−1 S
c
S
−1
f ψ
e
= r
min
+ b
1
ψ
e
+ b
2
ψ
e
− ψ
c
1ψ r
min
f T = 1.0
a
PAR: photosynthetic active radiation W m
−2
; PAR
c
: constant photosynthetic flux ac + b W m
−2
; a, b, c are species dependent variables refer Table 1; r
min
: minimum stomatal resistance s m
−1
, r
max
= ab + c s m
−1
; e
s
T: equilibrium vapor pressure at the temperature of the leaf hPa; e
air
: vapor pressure in the interleaf air spaces, K: VPD vapor pressure deficit constant Pa
−1
; T
leaf
: leaf temperature K; UP
max
: maximum water uptake rate kg m
−2
s
−1
fSWC refer Table 2 affects the stomatal resistance in the following manner. fSWC is equal to 1 at all times except when the transpiration rate exceeds UP
max
. In the event of this condition, the stomatal resistance is increased until the transpiration rate is equal to UP
max
and a balance exists. U
c
= 0.0002 kg m
−2
s
−1
; LAI: leaf area index; SAI: stem area index;
P
6 1
f
root
i = sum of the fraction of roots in all six soil layers; wi = soil water content in soil layer
i ; w
wilt
= constant wilting point; b: empirical soil exponent.
b
S : total solar irradiance W m
−2
, S
c
: critical solar parameter m
2
W
−1
; r
min
: minimum stomatal resistance s m
−1
; ψ
e
: epidermal water potential MPa; fψ
e
: epidermal water potential function discontinuous linear function; b
1
: slope of the sub-critical portion of ψ
e
, b
2
: slope of the super-critical portion of ψ
e
; ψ
c
: critical leaf water potential, 1ψ: value of 0 or 1 depending on value of ψ
e
.
J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21 7
Table 4 Definition of functions included in the stomatal resistance parameterization for LSX
field
and PSU
field
Case Vegetation type
Defnition of functions LSX
field
and PSU
field a
Corn f S =
[1 − e
−SK
]
−1
f VPD
p
= [1 − 0.0120 VPD]
−1
f VPD
d
= [1 − 0.0073 VPD]
−1
f T = 1.0
f SWC = [1 + 0.065 ψ
soil
]
−1 b
Soybeans f S =
[1 − e
−SK
]
−1
f SWC = [1 + 0.065 ψ
soil
]
−1 b
For T
l
303 K: f VPD
p
= 10
− 0.039383 VPD
−1
, f T
p
= 1.0 For T
l
303 K: f VPD
d
= 10
− 0.030334 VPD
−1
, f T
d
= 1.87 For 303 K T
l
308 K: f VPD
p
= 10
{−0.09383+[0.00317T
l
−303]} −1
, f T
p
= {1.0 − [0.0441T
l
− 303]}
−1
For 303 K T
l
308 K: f VPD
d
= 10
{−0.030334+[T
l
−3030.000664]} −1
, f T
d
= {0.536 + [0.0928T
l
− 303]}
−1
T
l
308 K: f VPD
p
= 10
− 0.023536 VPD
−1
, f T
p
= 1.28 T
l
308 K: f VPD
d
= 10
− 0.07014 VPD
−1
, f T
d
= 1.0
a
S : photosynthetic active radiation for LSX
field
W m
−2
; S: total solar irradiance for PSU
field
W m
−2
; K: constant dependent upon species and CO
2
concentration W m
−2
; p: denotes used for present day [CO
2
]; d: denotes used for doubled [CO
2
]; VPD: vapor pressure deficit hPa; ψ
soil
: soil water potential MPa; T
l
: leaf temperature K.
b
Used for PSU
field
only, LSX
field
used fSWC as described in Table 3.
At the scale of a single stoma on a leaf, the decrease in transpiration and the increase in stomatal resistance
are proportional, 3 ds
r
s
r
= dTR
TR 3
Since it is assumed that the leaf temperature and the bulk air are unaffected by fluxes from a single
stoma. The terms s
r
and TR are the stomatal resistance and transpiration at a specified time during the day
under present day [CO
2
] while ds
r
and dTR represent the change in the stomatal resistance and transpiration
between the present day and doubled [CO
2
] model runs at the same time in the day. This illustrates that
the change in transpiration is under 100 stomatal control. As the scale increases to include the leaf and
then the surface layer in the atmosphere, however, the feedback on the vapor pressure deficit VPD increases
and, stomatal control of transpiration decreases. This effect is shown by the analytical solution containing
the parameter 1−Ω
ds
r
s
r
1 − Ω = dTR
TR 4
It is important to note that the change in transpi- ration with change in [CO
2
] depends not only on the direct increase in stomatal resistance, but also on the
sensitivity of transpiration to changes in environmen- tal conditions e.g. those of the VPD, or those defined
by the aerodynamic resistance, etc. Aphalo and Jarvis, 1993; Steduto and Hsiao, 1998a–c. The term
1−Ω, therefore, not only quantifies the percent de- crease in transpiration for a percent increase in stom-
atal resistance due to a change in [CO
2
] but also the magnitude of any feedback initiated by external influ-
ences. Consequently, 1−Ω and so the stomatal con- trol of transpiration, is dependent upon the ratio of the
stomatal resistance to the total aerodynamic resistance this being defined as the sum of the leaf boundary
layer resistance and the aerodynamic resistance from the roughness length to the top of the surface layer.
The usefulness of this ratio in this study is discussed later.
The decoupling coefficient Ω, ranges from 0 to 1 and is a measure of how strongly decreases in transpi-
ration are coupled to increases in stomatal resistance. At the lower limit Ω = 0, the transpiration is under
100 stomatal control SR
increase
= TR
decrease
and the canopy is completely coupled to the atmosphere.
As the value of Ω increases towards unity, a percent change in stomatal resistance will produce a decreas-
ing percent change in transpiration so that at the other
8 J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21
Table 5 A summary of the LSX and PSUBAMS input parameters for specific scenarios
a
Scenario description LSX
PSUBAMS Parameter
Value Units
Parameter Value
Units Standard
SWC
6 b
0.95 M
o
M
r d
0.700.70 Medium soil water content
SWC
6
0.65 M
o
M
r
0.500.56 Low soil water content
SWC
6
0.45 M
o
M
r
0.300.40 High wind
U
70
11 m s
−1
U
S d
ˆ 18
m s
−1
SWC
6
0.80 M
o
M
r
0.620.72 Low wind
U
70
2.2 m s
−1
U
S
2.5 m s
−1
SWC
6
0.80 M
o
M
r
0.670.73 High surface layer humidity
RH
70
95 T−T
d d
ˆ 1
◦
C SWC
6
0.90 Ω
d
0.05 m
M
o
M
r
0.700.70 Low surface layer humidity
RH
70
45 T−T
d
20
◦
C SWC
6
0.90 Ω
0.025 m
M
o
M
r
0.700.70 Reduced solar irradiance
SOL
n
240 W
SOL
n d
236 W m
−2
SWC
6
0.95 m
−2
M
o
M
r
0.710.75 Coupled canopy
U
70
12 m s
−1
U
S
20 m s
−1
LAI 2
LAI 2
Leaf width 0.03 0.05
c
m Leaf width
0.03 0.05
c
m SWC
6
0.85 M
o
M
r
0.680.70 Decoupled canopy
U
70
3 m s
−1
U
S
2.5 m s
−1
LAI 7
LAI 7
Leaf width 0.08 0.10
c
m Leaf width
0.08 0.10
c
m SWC
6
0.85 SWC
6
0.710.75 Biomass increase
LAI in 2X 4.4 5.2
c
LAI in 2X CO
2
4.4 5.2
c
CO
2
SWC
6
0.95 M
o
M
r
0.700.71 High surface layer temperature
T
70
range 23–25 25–28
c ◦
C T
S d
ˆ 24
◦
C SWC
6
0.95 M
o
M
r
0.700.71
a
The table lists the input parameters that were changed from those listed in Table 1 to conduct each scenario. For each scenario, eight model runs were performed — both present day and doubled [CO
2
] settings for the four cases listed in Table 2.
b
The subscript 6 illustrates that all six soil layers were initialized with the same value and ˆ indicates that the change depicted was performed for all levels in the sounding.
c
The values in parentheses correspond to soybean initial conditions when different from that of corn.
d
1 M
o
and M
r
refer respectively to the surface and root zone layer water availabilities and are arranged in this order under the values column, 2 U
S
, T
S
, and T−T
d
refer to the wind speed, temperature, and dewpoint depression in the input sounding, 3 Ω refers to the integrated precipitable water, 4 SOL
n
refers to the noontime magnitude of the incoming solar irradiance after reduction to 25.
extreme Ω = 1, transpiration is under 0 stomatal control and, a percent change in stomatal resistance
produces no change in transpiration so that the canopy is completely decoupled from the atmosphere. Typi-
cal values of Ω for temperate forests are around 0.2 while those for crops and grassland generally range
from 0.5 to 0.9 Jarvis, 1985a,b; Meinzer and Grantz, 1989; Lee and Black, 1993. For a corn canopy un-
der light winds and wet soil conditions, Steduto and Hsiao 1998c reported values of Ω ranging from 0.5
J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21 9
Table 6 The decrease in transpiration and Ω for the 12 corn scenarios
a
Scenario description Vegetation type — corn
1 TR
Ω LSX
current
PSU
current
LSX
field
PSU
field
LSX
current
PSU
current
LSX
field
PSU
field
Standard 9–10
6–11 46–54
28–40 0.64–0.71
0.64–0.81 0.75–0.77
0.76–0.82 Medium soil water content
9–10 6–11
46–54 27–39
0.64–0.71 0.64–0.82
0.75–0.77 0.76–0.83
Low soil water content
b
8–10 5–10
44–52 26–39
0.66–0.75 0.66–0.83
0.76–0.79 0.77–0.84
High wind 10–12
6–14 50–57
32–45 0.57–0.66
0.50–0.80 0.73–0.75
0.74–0.80 Low wind
6–8 4–7
39–48 21–30
0.74–0.80 0.76–0.87
0.78–0.81 0.82–0.87
High surface layer humidity 9–10
6–9 46–55
29–37 0.55–0.67
0.69–0.80 0.75–0.77
0.78–0.82 Low surface layer humidity
9–10 6–14
46–54 29–41
0.61–0.65 0.60–0.82
0.76–0.77 0.75–0.83
Reduced solar irradiance 11–12
14–15 58–62
47–48 0.52–0.60
0.50–0.55 0.80–0.81
0.76–0.77 Coupled canopy
15–16 10–16
55–60 39–50
0.46–0.52 0.46–0.66
0.70–0.71 0.70–0.75
Decoupled canopy 6–7
4–6 31–46
19–27 0.76–0.81
0.77–0.86 0.79–0.85
0.84–0.88 Biomass increase
2–4 3–7
41–50 25–36
0.84–0.94 0.70–0.90
0.76–0.78 0.77–0.84
High surface layer temperature 7–8
1–10 43–50
18–37 0.74–0.76
0.67–0.95 0.77–0.78
0.77–0.88
a
The table presents ranges of the respective values — any important differences and diurnal trends are discussed in the text. The diurnal trend of the decrease in transpiration and Ω for LSX follow generally the same pattern during the day in all the scenarios. The
decrease in transpiration had its maximum value early in the morning and in the late afternoon with a minimum value during the middle of the day. The decoupling coefficient, Ω, obtained its maximum value during the middle of the day with minimums in the early morning
and later afternoon. In PSUBAMS, the decrease in transpiration and Ω also follow a similar diurnal trend in all scenarios. The decrease in transpiration had its maximum value early in the morning and decreased to its minimum value late in the afternoon. The decoupling
coefficient, Ω, had its lowest value early in the morning and increased to its maximum value late in the afternoon. Percent increases in stomatal resistance are not shown as the increase ∼30 did not vary between scenarios.
b
Indicates scenario was conducted under non-water stress conditions.
to 0.8 for the majority of a day with a rapid drop-off later in the afternoon towards zero.
A particularly useful yardstick in understanding changes in Ω under varying environmental conditions
is the magnitude of the ratio between the stomatal resistance to that of the total aerodynamic resistance
r
s
r
a
. This ratio is important for two reasons. First, the greater r
s
r
a
, the larger a given percent increase in stomatal resistance imposed to simulate doubled
[CO
2
] will impact upon the transpiration. This is so since an equivalent imposed percent increase in
stomatal resistance increases the absolute value of stomatal resistance r
s
if it is initially large, more than if it is initially small and therefore produces
more of a change in the total resistance from the leaf through the surface layer Jarvis and McNaughton,
1986; McNaughton and Jarvis, 1991; Steduto and Hsiao, 1998a–c. This idea is important when viewing
the differences between corn and soybeans using the field derived parameterizations where values for the
minimum stomatal resistance are very different. Sec- ond, r
s
r
a
varies substantially in the other scenarios where the environmental conditions alter r
a
so that the sensitivity of transpiration to an increase in stomatal
resistance varies. Therefore, the impact of this ratio is evident in Tables 6 and 7 when viewing the differences
in Ω between scenarios. For example, the sensitivity of transpiration is found to be different between high
and low wind conditions as a result of r
s
r
a
being greater in windy conditions lower r
a
than in calm conditions.
3. Results