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:
, (1)
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):
, (4) , (5)
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):
, (6) , (7)
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).