Model simulations
To explore the questions II and III in Introduction, we conducted two
kinds of model calculation. First, we employed a simulation analysis to
examine the effects of leaf-trichome resistance on the gas-exchange
rates under diurnal environmental variations across the elevational
gradient during the summer season (Appendix S5). We calculated leaf
temperature, the photosynthetic rate, transpiration rate, and water-use
efficiency of leaves at various trichome thicknesses (0.0-1.0 mm which
covers the range of field observed values in each site; Table 3) for
each elevational site by using the field-obtained environmental
variables (e.g., air temperature, relative humidity, PPFD, wind speed,
atmosphere pressure) and leaf morphological (i.e., leaf characteristic
dimension, trichome thickness) and physiological traits (i.e.,Vcmax , Jmax , stomatal
coefficient of Leuning model, temperature dependence of photosynthesis).
We calculated the photosynthetic rate (A ), the transpiration rate
(E ), water-use efficiency (=A /E ; WUE), and leaf
temperature (Tl ) of leaves every ten minutes, and
calculated the daily photosynthetic rate and daily transpiration rate as
the sum of A per day and the sum of E per day,
respectively (the models described later). The daily water-use
efficiency was calculated as the daily photosynthetic rate divided by
the daily transpiration rate. For the environmental variables, we used
two-week field-measured air temperature and relative humidity measured
at each site and photosynthetic photon flux density (PPFD) measured at
the 2400 m site every ten minutes in September 2017. For the data of
wind speed and air pressure, we took fixed values at each elevational
site from Campbell & Norman (2010) and Giambelluca et al. (2014) (see
Table 1). For the leaf traits, we used characteristic leaf dimension,
trichome thickness, Vcmax , andJmax measured at each elevational site. Since the
measurements of temperature dependence of gas-exchange traits are very
time consuming and logistically difficult in remote fields, we used
values of the stomatal coefficient and temperature dependence of
photosynthesis only at the 2000 m site as representative values while
the temperature dependence of photosynthetic parameters may slightly
differ depending on growth temperature (Hikosaka, Ishikawa, Borjigidai,
Muller, & Onoda, 2006).
Second, we employed a sensitivity analysis to examine what extent each
of leaf and environmental factor influences the results of simulation
analysis mentioned above. We calculated A , E , WUE, andTl by using the various combinations of leaf
morphological and physiological variables (trichome thickness,
characteristic leaf dimension, stomatal coefficient,Vcmax ) and environmental variables (air
temperature, relative humidity, PPFD, wind speed, atmosphere pressure).
Because the results with other temperature dependence ofVcmax and Jmax from Kattge
& Knorr (2007) showed the trends similar to those with the temperature
dependence in M. polymorpha measured at 2000 m site (Amada
unpublished data), we used the temperature dependence in M.
polymorpha in the sensitivity analysis (Table 3).
For these simulation and sensitivity analyses, the other physical (e.g.,
diffusion coefficients of air, heat, water vapor, and
CO2) and physiological parameters (e.g., the Rubisco
kinetics and the activation energy) were taken from the previous studies
(see Table 2; Bernacchi et al., 2001; Campbell and Norman, 2010; Jones,
2014; Kattge & Knorr, 2007; Leuning, 1995). The values of these
measured characteristics and constant parameters used for the model
simulations are listed in Table 2 and 3, respectively. In this study,
trichome effects on the gas-exchange traits (i.e., daily photosynthetic
rate, the daily transpiration rate, and the daily water-use efficiency)
were expressed as follows:
where XP and XG are the
values of each daily characteristics with and without leaf-trichome
resistance, respectively. Trichome effects on leaf temperature, and the
gas-exchange traits were expressed as differences in the values of each
physiological characteristics between with and without leaf-trichome
resistance.
For both simulation and sensitivity analyses, to calculate A ,E , and Tl in leaves with and without
leaf-trichome resistance, we solved simultaneous equations (Eqs. 2-7
described below and Eqs. S1-39 in Appendix S1-3; see the programming
code available in Appendix S4).
We used the steady-state energy-balance model for a single leaf
consisting the net heat gain from radiation, the net sensible-heat flux,
and the net latent-heat flux (see Appendix S1; Figure 1; Campbell &
Norman, 2010; Jones, 2014). In this study, we assumed that leaf
trichomes decrease the conductance (i.e., increase resistance) to both
gas-exchange and sensible-heat fluxes but do not influence the
absorptance and emissivity of radiation because the leaf trichomes inM. polymorpha exist on the lower side of leaf surface (Amada et
al., 2017; Hoof et al., 2007; Tsujii et al., 2016). We expressed the
conductance to sensible-heat (gH ) and water-vapor
(gν ) fluxes including the effects of
leaf-trichome resistance with an assumption that the leaf trichomes and
stomata exist only on the lower side as follows (Campbell & Norman,
2010; Jones, 2014):
, (2)
, (3)
where rH and rν are
resistances to the sensible-heat flux and the transpiration
respectively, gHa and gHtare the boundary-layer and trichome-layer conductances to the
sensible-heat flux respectively, and gνa ,gνs , and gνt are the
boundary-layer, stomatal, and trichome-layer conductances to the
transpiration respectively. We assumed that leaf trichomes do not affect
the boundary-layer conductance (outside of trichome layer) while
leaf‐surface roughness due to leaf trichomes could decrease
boundary‐layer resistance if the roughness increases turbulence
(Schreuder, Brewer, & Heine, 2001). Assuming that the air in the
trichome layer is still, gHt andgνt in Eqs. 2-3 can be expressed as follows
(Amada et al., 2017; Benz & Martin, 2006; Ehleringer & Mooney, 1978;
Meinzer & Goldstein, 1985):
where rHa and rνa are
leaf-trichome resistances to the heat and water‐vapor fluxes
respectively, ρ is the molar density of air,DH and Dν are the heat and
water‐vapor diffusion coefficients in still air, φ is porosity,τ is tortuosity, and δt is the thickness
of trichome layer. Here we assumed that difference betweengHt and gνt depends just
on the differences of diffusion coefficients (i.e.,DH and Dν ). For leaves
without leaf trichomes (glabrous leaves), rHt andrvt in Eqs. 4-5 are set to zero. Assuming that
laminar flow prevails in the boundary layer, gHaand gνa in Eqs. 4-5 are expressed as follows
(Campbell & Norman, 2010):
where rHa and rνa are the
boundary‐layer resistance to heat and water‐vapor fluxes respectively,Re is Reynolds number, Pr is Prandtl number, Sc is
Schmidt number, d is characteristic leaf dimension in the
direction of airflow, and 1.4 is a coefficient for the effect of air
turbulence (Campbell & Norman, 2010). In these parameters, ρ ,DH , and Dν depend on the
values of temperature and pressure at each site (see Appendix S2;
Campbell & Norman, 2010). Calculations of the dimensionless numbers
(Re , Pr , Sc ) were described in Appendix S2.
When the stomatal conductance to H2O flux
(gvs ) in Eq. 3 is given, leaf temperature
(Tl ) can be calculated by the combination of Eqs.
2-7 and energy balance model (see Appendix S3; Campbell and Norman,
2010). The stomatal conductance to CO2 flux
(gcs ) was calculated by using the
stomatal-conductance model (see Appendix S3; Leuning, 1995). To
calculate the photosynthetic rate, we employed the C3biochemical model for photosynthesis according to Farquhar et al. (1980)
and Medlyn et al. (2002) (see Appendix S3).