14 J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21
4. Discussion
4.1. Corn The results illustrate that for all four cases, as in-
dicated by the magnitude of Ω Fig. 1, the percent decrease in transpiration is significantly less than the
percent increase in stomatal resistance, i.e. the per- centage ratios modeled are less than those reported
in the literature 36–76 for studies conducted at the scale of a single leaf. These resultant changes
are consistent to what was discussed by Field et al. 1995 and illustrated by Carlson and Bunce 1996
and Bunce et al. 1997 which reported transpiration decreases of 1–5 for similar canopy model studies
and stomatal resistance increases. The results from LSX
field
and PSU
field
are best compared with other quoted 1-D canopy model studies: Pollard and Thomp-
son 1995 and Henderson-Sellers et al. 1995, who reported decreases in transpiration of 28 and 18, re-
spectively, for a 100 increase in stomatal resistance. LSX
field
and PSU
field
parameterized doubled [CO
2
] through increases in stomatal resistance of 150–200
and demonstrated a decrease in transpiration in the range of 28–54. Although the range is greater than
Pollard and Thompson 1995 and Henderson-Sellers et al. 1995, the results here are consistent with their
findings since the increase in stomatal resistance illus- trated here is 50–100 larger.
The reduced percentage ratios are a result of neg- ative inter-canopy LSX and PSUBAMS and mix-
ing layer PSUBAMS feedbacks that act to reduce the transpiration decrease initiated by doubled [CO
2
]. These feedbacks are manifested through an increase
in the VPD from present day to doubled [CO
2
]. In Fig. 4a, a schematic demonstrates the mechanisms
whereby the VPD feedback acts to decrease the rate of transpiration decline with increasing stomatal resis-
tance. This negative feedback is represented in both models. PSUBAMS demonstrates an additional neg-
ative feedback that is manifested by the inclusion of a mixing layer. Interaction with the mixing layer acts
to produce less of a decrease in transpiration by fur- ther increasing the VPD change from present day to
doubled [CO
2
]. This produces a more pronounced restoring gradient for transpiration. Other studies have
shown that the change in transpiration was less sen- sitive to an increase in stomatal resistance when a
convective boundary layer was included Jacobs and DeBruin, 1997; Raupach, 1998.
The processes depicted in Fig. 4a are clearly evi- dent in model output data for some intermediate vari-
ables. Fig. 5a–d illustrates the leaf temperature and inter-canopy vapor pressure changes for two scenar-
ios in which the transpiration change was observed to be different — the standard scenario and the low wind
speed scenario. These data are for the LSX
current
and PSU
current
cases. It can be seen in Fig. 5a–d that in both scenarios, the leaf temperature increases and the
inter-canopy vapor pressure decreases, these in turn produce a restoring gradient for transpiration VPD
Fig. 5e. The standard scenario is more sensitive to an increase in stomatal resistance compared to the low
wind speed scenario because r
s
r
a
is greater — a re- sult of a larger aerodynamic resistance Fig. 5f.
The impact of such mixing layer feedbacks is great- est during the afternoon when the surface fluxes have
penetrated into the mixing layer. This effect is clearly evident in Fig. 1 for both SRP’s but more easily seen
by comparing the models with their original SRPs: Fig. 1 shows that the decrease in transpiration is less
higher values of Ω for PSU
current
than LSX
current
for the majority of the day starting at around 11:00 a.m.
and intensifying over the course of the day. As is evident in Table 6, the other scenarios show
some significant changes in the decrease in transpi- ration where the perturbing of selected initial condi-
tions refer Table 5 alter r
s
r
a
and the VPD to the extent that the magnitudes of the negative feedbacks
are also affected. Both models using both SRP’s indi- cate that the magnitude of the negative feedbacks are
less under strong winds, reduced solar irradiance, and strongly coupled canopies sparse canopies with small
leaves under windy conditions. On the other hand, light winds, high solar irradiance, warm temperatures,
and strongly decoupled canopies dense canopies with large leaves under calm conditions show that the feed-
backs are greater in magnitude. The variation of at- mospheric humidity produced no significant change in
the transpiration decrease. The scenarios that indicate an increase in the transpiration decline also showed
a larger value of r
s
r
a
under present day [CO
2
] and vice versa for the scenarios that show a decrease in
transpiration decrease. The combination of the two effects — the VPD increase and the magnitude of
r
s
r
a
— determine the magnitude of the transpira-
J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21 15
Fig. 4. Schematics of bioatmospheric feedback mechanisms.
tion decrease given a constant increase in stomatal resistance.
The transpiration changes illustrated here are im- portant to water use efficiency WUE. Doubled atmo-
spheric [CO
2
] is expected to increase WUE by both increasing the CO
2
assimilation rate and so growth rate as well as decreasing transpiration. The change in
CO
2
assimilation is not addressed in this study but the overwhelming majority of the data support the view
that doubled [CO
2
] will increase the CO
2
assimilation rate. The results from these canopy simulations in this
study suggest the idea that the increase in WUE will not be as great as that reported in the literature for stud-
ies conducted at the scale of a single leaf assuming CO
2
assimilation is unchanged between scales. This is so since the decrease in transpiration for a given
stomatal resistance increase the percentage ratio is less for these canopy model simulations than that re-
ported in the literature for studies conducted at the leaf scale. It is important to note, however, that these simu-
lations were conducted under non-water stress condi- tions which, of course, can significantly alter the water
balance in the vegetation and so the WUE.
4.2. Soybeans The soybean results illustrate a greater diurnal vari-
ation for the decrease in transpiration, but still indicate the existence of negative feedbacks as the percent
decrease in transpiration is substantially less than the percent increase in stomatal resistance high values
of Ω — Fig. 2, i.e. the percentage ratios modeled are less than those reported in the literature 36–76
for studies conducted at the scale of a single leaf. As illustrated by Fig. 3, the decrease in transpiration for
LSX
current
increases during the day as a result of an in- crease in the stomatal resistance increase. This behav-
ior results from a positive VPD feedback as illustrated conceptually in Fig. 4b. The increase in stomatal re-
sistance increase from present day to doubled [CO
2
]
16 J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21
Fig. 5. Corn diuranal variation of the a standard scenario leaf temperature; b standard scenario inter-canopy vapor pressure; c low wind speed scenario leaf temperature; d low wind scenario inter-canopy vapor pressure; e the increase in vapor pressure from present
day to doubled [CO
2
] for the standard and low wind speed scenarios, and f r
s
r
a
for the standard and low wind speed scenarios.
J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21 17
Fig. 6. Soyabean diurnal variation of the a standard scenario leaf temperature; b standard scenario inter-canopy vapor pressure; c low wind speed scenario leaf temperature; d low wind scenario inter-canopy vapor pressure; e the increase in vapor pressure from present
day to doubled [CO
2
] for the standard and low wind speed scenarios, and f r
s
r
a
for the standard and low wind speed scenarios.
18 J.C. Gottschalck et al. Agricultural and Forest Meteorology 106 2001 1–21
during the day is because the f VPD
2× 4
is greater than f VPD
P 5
as a result of the increase in VPD from the initial increase in leaf temperature and de-
crease in inter-canopy humidity previously described. Feedbacks that would initiate a further increase in the
stomatal resistance and, therefore, a decrease in tran- spiration have been described by Jacobs and DeBruin,
1997 and, Raupach, 1998. Consequently, when simulating a doubled [CO
2
] environment for soybeans — in addition to the increase in stomatal resistance
parameterized by f CO
2
— an additional increase in stomatal resistance occurs as a result of f VPD
2×
being greater than f VPD
P
over the course of the day. The positive VPD feedback Fig. 4 is observed
in model intermediate variables similar to the nega- tive VPD feedback. Fig. 6a–d illustrates the leaf tem-
perature and inter-canopy vapor pressure changes for both the standard and low wind scenarios. These data
are for the LSX
field
and PSU
field
cases. Fig. 6a–d show increases in leaf temperature and decreases in
inter-canopy vapor pressure for both scenarios and models. Because the dependence of soybeans to VPD
measured in the field is strong Wilson and Bunce, 1997, the increase in VPD produces a substantial
increase in r
s
from present day to doubled [CO
2
] Fig. 6f through f VPD Fig. 6e. The greater in-
crease in VPD and so f VPD from present day to doubled [CO
2
] for PSU
field
is likely the result of the inclusion of the mixing layer model. This enhanced
positive feedback was also cited in Jacobs and De- Bruin 1997. Unlike the low wind scenario for corn,
the greater restoring gradient for transpiration simu- lated here has an additional effect on the transpira-
tion. Although the restoring gradient for transpiration negative feedback occurs, similar to corn, it is com-
pensated for and cancelled by the stronger positive VPD feedback through f VPD Fig. 4b, since un-
der low wind conditions the leaf temperature increases more and so VPD, f VPD, and r
s
do as well. The reason the impact on the decrease in transpiration is
so pronounced is due to the soybean’s high sensitiv- ity to VPD — large value for K VPD constant in
f VPD; Table 1. Although f VPD
2×
is greater than f
VPD
P
for corn as well, corn is insensitive to VPD
4
f VPD in doubled [CO
2
] .
5
f VPD in present day [CO
2
].
a lower value of K in f VPD so that the stomatal resistance increase is mainly a result of f CO
2
only. LSX
field
and PSU
field
show less sensitivity in the transpiration to doubled [CO
2
] higher values of Ω compared to LSX
current
and PSU
current
. This is a result of a lower r
s
r
a
ratio: the minimum stomatal resistance for LSX
current
and PSU
current
is 50 s m
−1
while for LSX
field
and PSU
field
it is 24.7 s m
−1
. Consequently, the numerator in r
s
r
a
for LSX
field
and PSU
field
is lower than for LSX
current
and PSU
current
. Moreover, for the field derived cases, it is important to note that
since r
s
r
a
is less for soybeans than corn in all scenar- ios, the sensitivity of transpiration for soybeans was
less than corn except where otherwise noted. Unlike corn, the scenarios under different atmo-
spheric and surface conditions do not produce clear changes in transpiration decrease for doubled [CO
2
]. The magnitude of the decrease in transpiration and Ω
in both models varies depending on the initial environ- mental conditions; consequently, generalizations con-
cerning the magnitude of the transpiration are more difficult to make for soybeans. Table 7 illustrates the
varying nature of the response for the percent transpi- ration decrease and Ω for the remaining scenarios. The
differences are imposed by and, depend upon the mag- nitude of the positive feedback induced by the VPD.
5. Conclusion
