The SIM-BIM2 model (Grote et al., 2006) calculates changes in the concentrations of a number of isoprene and monoterpene precursors within the chloroplast using a sequence of first-order Michaelis–Menten equations. Assuming the absence of specific storage structures, the production rate of isoprene and monoterpene is equal to the emission of these substances. The enzyme activities of isoprenoids that determine the production rates develop dynamically in relation to temperature and radiation at the leaf surface (Fig. 1).
Figure 1. Model overview: biochemical processes considered in biochemical isoprenoid emission model 2 (BIM2) together with links to photosynthesis and seasonal dynamics (phenology and seasonal isoprenoid synthase model (SIM) of enzyme activity). Dashed arrows, impacts; solid arrows, matter transport.
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The enzyme-activity model is combined with a phenological model that calculates the date of bud-burst from the cumulative sum of daily air temperature starting from the beginning of the year. From the day of bud-burst, foliage development is described by an empirical function. The same function is used to simulate litter fall starting from an empirically defined date. The primary substrates for the emission model are pyruvate and NADPH. These are provided by the photosynthesis model (Farquhar et al., 1980, with implementation from Martin et al., 2000; see Table 1 for parameter values). Pyruvate is then divided empirically into phosphoglycerate and triose-phosphate. This implementation results in a positive but nonlinear correlation between emitted carbon and photosynthesis. The proportion of carbon used for emission increases particularly rapidly if temperature increases beyond the optimum for carbon assimilation up to the optimum temperatures of the kinetic reactions involved in isoprenoid production (Zimmer et al., 2000; Grote et al., 2006). Stomatal conductance has been estimated using a vapour pressure sensitive Jarvis-type model approach (Jarvis, 1976) that has been parametrized with values from the ECOCRAFT database (Medlyn & Jarvis, 1999; Table 1).
The model system uses three different time steps. The enzyme activities and leaf development states are updated daily. The photosynthesis model is run in a subdaily time step that was set to 1 h in the present investigations. The carbon supply rate is linearly interpolated between time steps. Finally, the emission model uses a fixed time step of 7 s, throughout which the rate of precursor supply is assumed to be constant. The model has been evaluated on sunlit leaves of different oak species grown in the field or in glasshouses. More detailed descriptions of all parts of the model can be found in previous publications (Zimmer et al., 2000, 2003; Lehning et al., 2001; Grote et al., 2006).
For comparison, the basic algorithms of the Guenther model G93 (Guenther et al., 1993) for monoterpene emissions of plants without specific storage structures have also been implemented (Eqn 1). It should be noted that the G93 algorithm produces emission estimates in µg g−1 dry weight (DW) h−1 but the results are transformed into µmol m−2 d−1 to allow direct comparison with the SIM-BIM2 model outputs. For this transformation a molecular weight for monoterpenes of 136.24 has been used (Fuentes et al., 2000).
- ( Eqn 1b)
- ( Eqn 1c)
(I, layer-specific photosynthetically active radiation (µmol m−2 s−1); T, layer-specific foliage temperature (K); Tr, reference temperature (303 K); Tm, optimum temperature (314 K); α = 0.0027; Cl, constant that modifies the light response (1.066); Ct1 and Ct2, constants that modify the temperature response (95 000 and 230 000, respectively); R, general gas constant (8.3143 J K−1 mol−1); E, emission rate (µg g−1 DW h−1), Fl and Ft, light and temperature response functions (0–1). All parameter values are taken from Guenther et al. (1993). Es, species-specific standard emission factor (8.4 µmol µg g−1 DW h−1, after Staudt et al., 2002) at 1000 µmol m−2 s−1 and Tr.)
Both leaf-scale emission models were coupled to the same upscaling scheme. This program reads basic vegetation and soil properties from files. More detailed vegetation conditions such as biomass distribution within layers are calculated using species-specific routines, as described in the next paragraph. The program also reads daily climatic data (temperature, radiation and precipitation) which are assumed to reflect conditions above the canopy. The daily data are used to drive foliage development (SIM), whereas the physical conditions (CANOAK model) and the emission models (G93 and BIM2) are called in subdaily (hourly) time steps.
Upscaling of the isoprenoid emission rates requires the distribution of stand-level foliage biomass and leaf area index into a number of canopy layers. Foliage biomass distribution is described with a simple one-parametric distribution function formerly used for crown shape description (Grote, 2003):
- ( Eqn 2a)
- ( Eqn 2b)
- ( Eqn 2c)
(rIH, inverse relative height within the canopy (from 1 at the crown base to 0 at stand height); h, actual height within the canopy (m); hc, canopy depth (m); mfl, foliage biomass in canopy layer fl (kg DW m−2 ground); mt, total foliage biomass (kg DW m−2 ground); P, distribution parameter.)
Figure 2(a) and (b) show the impact of P varying between 1.5 and 3 on relative foliage distribution. The leaf area in each canopy layer is derived from foliage biomass and specific leaf area (SLA) in m2 kg−1. SLA determined in the middle of each canopy layer and is assumed to change linearly from maximum values occurring at crown base to minimum values at the top of the stand. It should be noted that, as a result of this weighting procedure, the same amount of foliage biomass will produce different total leaf area indices (LAIs) with different foliage distributions. For example, a total foliage biomass of 0.5 kg m−2 together with a SLA range between 4 and 10 results in LAI values between 4.1 and 2.9 if a change of P from 1.0 to 2.0 is assumed.
Figure 2. Dependence of the foliage distribution of Quercus ilex (holm oak) on the distribution parameter P (a) and comparison with measurements, redrawn after Sala et al. (1994) (b). ‘Valley’ and ‘ridge’ indicate two different sites investigated. Each symbol represents the amount of foliage relative to the total leaf mass per unit ground area (LMA) for one-tenth of the relative crown height.
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Furthermore, the parts of the model that deal with seasonality have been adjusted to fit the requirements of evergreen plants. This required dividing total foliage biomass into a number of leaf age classes calculated from the species-specific maximum longevity. The fraction of foliage that is lost from the original leaf biomass of each age class and thus the remaining foliage biomass are determined according to Eqn 3:
- ( Eqn 3)
(sn, fraction of foliage in a specific age class that has been lost (0–1); d, age of the foliage class (days); DL0, foliage age when litter fall starts (days); DL05, foliage age when half of the age class is gone (days) (see Table 1 for parameter values).)
The bud-burst model was taken from Lehning et al. (2001). All holm-oak-specific parameters except the growing degree day temperature necessary for flushing (Tc) were found in the literature (Table 1). Tc was fitted to enzyme activities measured on Quercus ilex trees in Montpellier during the years 1998 and 1999 (Fischbach et al., 2002; see also Grote et al., 2006).
Figure 3 shows the resulting development of foliage age classes together with the development of total foliage biomass in two years. For simplification, it is assumed that all foliage age classes are equally distributed across canopy layers. At the end of each year, all leaves in one age class are transferred into the next one. Calculated enzyme activities are applied to each age class using an age-specific reduction factor. This factor is equal to 1 for the first age class and is decreased for each precedent age class. For holm oak the enzyme activity is calculated by multiplying the previous year factor by 0.35 (Fischbach et al., 2002).
Figure 3. Relative development of foliage age classes (dvs) and total foliage biomass in two simulation years (age 0 is the age class that develops within the year in which the graph starts; other age classes are numbered accordingly). The initial foliage biomass was 0.55 kg dry weight (DW) m−2 ground (reflecting an annual average leaf area index (LAI) of approx. 4.0).
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Climatic parameters within the canopy and layer-specific foliage temperature were calculated on the basis of physical principles employing the model CANOAK (Baldocchi et al., 1999, 2002). This model has formerly been evaluated on oak, Eucalyptus saligna and mixed forest canopies (e.g. Funk et al., 2006) and has been adjusted to meet the requirements of the evergreen oak stands investigated here. Stand dimensions, leaf area and leaf area distributions are thus provided by this canopy/phenology model and updated in daily time steps. Additionally, holm-oak-specific physical properties of the foliage were parametrized using values from the literature (Inclan et al., 1999). As the CANOAK model also calculates soil temperatures and soil water content to close the energy balance of the stand, soil properties had to be defined (see ‘site description and simulations’). It should be noted that the CANOAK model calculates photosynthesis and stomatal conductance to consider the effect of water vapor fluxes on energy balance. Because these functions are necessary for the integrative calculations applied by CANOAK they were not abandoned in the coupled system but were parametrized using literature values as far as species-specific parameters were required (Inclan et al., 1999; Ghouil et al., 2003). However, the carbon supply for emission simulations is calculated by the SIM-BIM2 inherent photosynthesis model that was previously evaluated for holm oak (Grote et al., 2006). The inconsistency, however, is judged to be negligible as both assimilation algorithms are based on the same principle (Farquhar et al., 1980) and the impact of carbon supply is assumed to be small under nonstressed conditions (Grote et al., 2006).
The available climatic data (see ‘site description and simulations’) represent daily averages or sums of climate variables. However, both emission models as well as the canopy climate model need weather input at a higher temporal resolution. Therefore, instantaneous values for air temperature and radiation at the top of the canopy are calculated for each hour of the day from daily average temperature and radiation sum. For air temperature with algorithms from De Wit et al. (1978) have been used, while instantaneous radiation is described by a sine wave calculation, similar to that described in Berninger (1994):
- ( Eqn 4a)
- t sr = 12 − 0.5hd( Eqn 4b)
(ri, instantaneous radiation during daytime hours (W m−2); r0, daily radiation sum (J m−2); hd, day length (h); t, time during the day; tsr, time of sunrise; π, 3.1416.)
Site description and simulations
The sensitivity analysis of the coupled model was carried out on a virtual stand of holm oak (Quercus ilex L.), a species for which the parameters of the monoterpene emission models are available (Grote et al., 2006). All model runs were carried out with a CO2 air concentration of 370 ppm. As further driving forces, daily average air temperature and the daily sums of global radiation and precipitation were used from the Montpellier, Centre d’Ecologie Fonctionnelle et Evolutive/Centre National de la Recherche Scientifique experimental station for the years 1998 and 1999 (Staudt et al., 2002). The average annual temperature at this site is 13.5°C and the average annual precipitation is 883 mm. Other boundary conditions were selected from the description of a typical Mediterranean holm oak stand in the same region (Hoff & Rambal, 2003). Thus, all simulations were carried out using a stand height of 11 m, a crown base height of 1 m and a soil and root depth of 2.5 m. The soil is assumed to have a relatively small total water-holding capacity of 190 mm, resulting from a high volumetric fraction of stones (> 75%).
Foliage distribution and initial foliage biomass were varied to show the impact on microclimate, photosynthesis and monoterpene emission. If no other values are given, the foliage biomass was initialized as 0.55 kg dry matter m−2 ground, which was estimated after Lopez et al. (2001). Similar values have been reported by Cutini (2002) and Hoff & Rambal (2003). The foliage distribution parameter P was adjusted to literature data presented in Sala et al. (1994), as shown in Fig. 2(c,d). However, it should be noted that this parameter is likely to change with stand density and site, as indicated by studies on other species (e.g. Cermak, 1998; Parker & Russ, 2004). Therefore, this parameter was subjected to a sensitivity test and varied between 1.5 and 3.0.