iLand uses a radiation use efficiency (RUE) approach (cf. Medlyn et al. 2003) to derive gross primary productivity at the canopy level, mainly following Landsberg and Waring (1997). The target entity for this computation is the resource unit, taking into account individual tree competition for light.

radiation interception

The fraction of intercepted photosynthetically active radiation above canopy (pPAR, dimensionless {0,1}) is calculated at the level of resource units (i.e., ≈stands, or sites in the context of LANDIS-II) by means of Beers law (Lieffers et al. 1999), Eq. (1):

\[\begin{aligned} pPAR=1-e^{-k\cdot \frac{\sum_{j=1}^{n}LA_{j}}{SA}} \end{aligned} \]

Eq. 1

with LA_j the leaf area (m^-2) of the j^th individual on the resource units (RU) stocked area (SA, m²) and k the extinction coefficient. Total intercepted radiation at resource unit level is thus calculated by Eq. (2):

\[\begin{aligned} APAR=PAR\cdot SA\cdot pPAR \end{aligned} \]

Eq. 2

with PAR the photosynthetically active radiation per unit area (MJ∙m^-2).

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gross primary production

Gross primary production (GPP, gC) is the product of utilizable photosynthetic active radiation (uAPAR, MJ) and the effective radiation use efficiency (ε_eff, g MJ^-1), Eq. 3-5

\[\begin{aligned} GPP=uAPAR\cdot \varepsilon _{eff} \end{aligned} \]

Eq. 3

\[\begin{aligned} uAPAR=APAR\cdot min(f_{temp}\: ;\: f_{sw}\: ;\: f_{VPD}) \cdot f_{age} \end{aligned} \]

Eq. 4

\[\begin{aligned} \varepsilon _{eff}=\varepsilon _{0}\cdot f_{N}\cdot f_{CO_{2}} \end{aligned} \]

Eq. 5

with f denoting environmental modifiers and ε₀ the maximum radiation use efficiency. GPP is calculated monthly, to capture the intra-annual variability of the climate modifiers on APAR (Eq. 4). The effect of the environment differs with species, i.e. the modifiers f are species-specifc. Furthermore, absorbed radiation of every individual depends on its leaf area as well as on the position in the canopy and radiation use strategy. Combining Eq. 3-5 with competition-based radiation partitioning at the level of individuals and species-specific environmental modifiers we compute individual tree GPP, while preserving consistency with the stand level approach of Landsberg and Waring (1997).

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environmental modifiers

• temperature response
• soil water response
• vapor pressure deficit response
• nitrogen response
• CO2 response

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respiration and aging

We follow Waring et al. (1998) in assuming a constant respiration fraction of GPP to derive net primary production (NPP, Eq.6),

\[\begin{aligned} NPP=GPP\cdot r \end{aligned} \]

Eq. 6

with an respiration fraction r of 0.47 (cf. Waring et al. 1998). Although this simplified derivation of NPP is not undisputed (cf. , Medlyn and Dewar 1999, Mäkelä and Valentine 2001) it has proven to yield robust results in numerous applications. Moreover, implementing a more detailed approach to simulate autotrophic respiration would be beyond the scope of iLand.

Declining productivity potential with age is accounted for by Landsberg and Waring (1997) by an aging modifier (f_age). While the original approach used age relative to a maximum attainable age as explanatory variable Seidl et al. (2005) in a similar approach substituted relative height for relative age. Empirical studies point towards a size (i.e. height)-related pattern of growth decline (e.g., Bond et al. 2007), inter alia as a result of hydraulic limitations (e.g., Ryan et al. 2006). However, although hydraulic limitations with increasing size are common, no universal relationship has been found (Ryan et al. 2006) and other factors, associated with physical age (e.g., Munne-Bosch and Alegre 2002) might be relevant. Niinemets (2002), for instance, showed that both tree height and physical age were related to growth decline. A review over aging and remaining uncertainty in our understanding of growth decline processes is given by Bond (2000).

Due to the limited process understanding and the intermediate process resolution in iLand we generally follow the simplified approach of Landsberg and Waring (1997), applying an aging modifier (f_age) to account for aging-related limitations on NPP (see Eq. 4). Based on previous experiences within the PICUS framework we used both relative age (age_rel) and relative height (h_rel) to derive an indicator for a trees' age status, AI (Eq. 8, with age_rel and h_rel calculated as current age and height relative to the species-specific maximum). We applied a harmonic mean to combine the age- and height- related aging components and used their complementary values so that AI reaches 1 if any of the two components reaches its maximum (Eq. 8). AI was subsequently applied in the two-parameter function suggested by Landsberg and Waring (1997) to derive the aging effect on productivity (Eq. 9).

\[\begin{aligned} AI=1-\frac{2\cdot (1-age_{rel})\cdot (1-h_{rel})}{2-age_{rel}-h_{rel}} \end{aligned} \]

Eq. 8

\[\begin{aligned} f_{age}=\frac{1}{1+(\frac{AI}{m_{age}})^{n_{age}}} \end{aligned} \]

Eq. 9

where m_age and n_age the empirical constants. Unlike Landsberg and Waring (1997), f_age is calculated and applied at the level of individual trees in iLand. We used the values of Landsberg and Waring (1997) as starting points for the latter, a re-parametrization to observed values might, however, be necessary at a later point. Using a composite of relative age and size allows for an aging effect in both fast growing stands (where mostly relative height drives f_age) and on poor sites (i.e. where the maximial attainable height is far below the species maximum), where a gradual age decline is induced by the linearly increasing physical age.