## 2 Materials and Methods
### Process-Based Growth Model  
There are a wide variety of physiologically-based process models, but only a few have been designed to scale projections of photosynthesis, structural growth and mortality across landscapes (see the review by [PERSON] _et al._[17]). Among the most widely used is the 3-PG model [27]. The 3-PG model differs from others primarily in a number of simplifying assumptions: (1) that monthly mean climatic data are adequate to capture major trends; (2) that autotrophic respiration (R\({}_{\text{a}}\)) and net primary production (NPP) are approximately equal fractions of gross photosynthesis (GPP); and (3) that the proportion of NPP allocated to roots increases from 25% to 60% as nutrients (particularly nitrogen) become progressively less available. 3-PG also differs from most other models by including subroutines for thinning and defoliation, which are important attributes as outbreaks of insects and disease become more frequent. The model calculates gross photosynthesis, canopy evaporation and transpiration, growth allocation and litter production at monthly intervals (\(\Delta t\)). It reduces potential photosynthesis and transpiration by imposing restrictions on stomatal conductance through modifiers, taking values between 0 = complete restriction and 1.0 = no restriction, that account for the effects of frost, high vapor pressure deficits and deficits in soil water content. The soil water modifier is determined from the ratio of the amount of water available in the root zone of the trees (_ASW_) to the maximum value (_ASW\({}_{\text{max}}\)_). _ASW\({}_{\text{max}}\)_ is the water holding capacity of the soil, which is the difference between the water content in the root zone at field capacity and at the wilting point. For any given month, ASW is calculated from:  
\[ASW(t+\Delta t)=ASW(t)+(P-E-T) \tag{1}\]  
where _ASW\((t)\)_ is the value at the beginning of the month and \(P\), \(E\) and \(T\) denote the monthly values of precipitation, evaporation and transpiration, respectively. The model includes a term to account for rainfall interception by the forest canopy; this water is assumed to be lost by evaporation, giving \(E\). Transpiration is calculated from the Penman-Monteith equation, which incorporates a canopy conductance term derived from stomatal conductance and LAI. If the value of _ASW_ on the left-hand-side of Equation (1) exceeds _ASW\({}_{\text{max}}\)_, i.e._, the whole root zone is at field capacity, the excess is assumed to be lost as runoff or drainage. At monthly time steps, the model is unable to compute a snow water balance accurately, although one may assume that precipitation in months with average temperatures below freezing is largely in the form of snow. At annual time steps, the model sums monthly changes in tree number, mean diameter, stand basal area, above-ground volume and biomass and updates the changes in LAI. To account for seasonal adjustments in temperature optima [41] and to incorporate the large genetic variation among populations of Douglas-fir, we broadened the range for which photosynthesis could remain above 50% of maximum to lie between 0 \({}^{\circ}\)C and 35 \({}^{\circ}\)C by setting minimum, optimum and maximum temperatures at \(-\)7 \({}^{\circ}\)C, 18 \({}^{\circ}\)C and 40 \({}^{\circ}\)C, respectively. The photosynthetic response at temperatures below -2 \({}^{\circ}\)C was truncated to zero, because, below that threshold, stomata are closed [42]. The fertility-dependent growth modifier in the 3-PG model is a function of the soil fertility rating, FR, which ranges between zero, for the poorest soils, to unity for most fertile soils [27]. [PERSON] and [PERSON] [43] in their book \"Physiological Ecology of Forest Production\" define soil fertility as a site property and, therefore, the same for all species. Differences among species in their response are incorporated into the model by altering how photosynthetic efficiency is changed and the way that growth is allocated above and below ground.