The forest factory creates forest patches based on different stem size distributions and species mixtures. We used 15 stem size distributions covering a gradient from young to old and disturbed to undisturbed forests. Species mixtures included all 256 possible combinations of Pinus sylvestris, Picea abies, Fagus sylvatica, Quercus robur, Fraxinus excelsior, Populus x canadensis, Betula pendula and Robinia pseudotsuga. We used the species parameter set and algorithms of the FORMIND model version for temperate forests within the forest factory . A total of 100 forest patches of each combination were built.

To generate forest patches, the forest factory randomly chose trees from the stem size distribution, assigned a species identity and planted them within a patch of 400 m2 size. To place a tree within a patch, the following rules must be met: (i) there must be enough space available for crowns of every tree, and (ii) every tree in the forest must have a positive productivity under its environmental conditions (light, temperature, water).

We used climate time series from the year 2007, measured at Hainich National Park, central Germany. We assumed this time series to be a typical example for a temperate year (in principle, it is possible to use climate data from any other location). In contrast to an artificially generated climate, this climate is perfectly physically consistent (with regard to light, air temperature and precipitation).

In a few cases, not all species of the mixture could be placed within a patch by the algorithm, so we rejected such forests. We ended up with 370 100 forest stands. For more details regarding the forest factory, see .

The calculation of AWP of trees was based on algorithms of the model FORMIND . In this model, the wood production of a single tree is calculated as the difference between climate variables driven respiration rates and photosynthesis. The photosynthesis rate (Ptree) results from the crown size, self-shading within the crown and available light at the top of the tree. The available light depends on the radiation above the canopy, reduced by the shading of larger trees within the forest stand. Furthermore, productivity can be limited due to air temperature and available soil water, which is expressed by the photosynthesis-limiting factor ϕ for each tree . Available soil water within the stand results from precipitation, interception and evapotranspiration of trees and runoff.

One part of the photosynthesis production of a tree (Ptree) is allocated to its maintenance respiration (and to non-wood tissues; Rm). Maintenance respiration depends on tree biomass and temperature ψ . The remaining organic carbon is transformed into newly grown aboveground wood (AWPtree) and a proportional growth respiration (rg). AWPtree=(ϕPtree-ψRm)(1-rg)

AWPtree was summed over all trees to obtain the productivity of the modelled forest stand – AWP (for a more detailed description of growth processes, see ).

To generate a set of 320 annual climate time series, we selected daily climate measurements of the Hainich station in central Germany between the years 2000 and 2004. This time series includes mean daily radiation, precipitation and air temperature (see Appendix , Fig. ). We separated these time series into five distinct time series of 1-year length. First, we increased or decreased the mean annual temperature of each year by adding or subtracting 0.5 ∘C steps between -1.5 and +2 ∘C. Second, we changed the amplitude of the annual temperature cycle for these time series variation of each year. To do so, we modified the standard deviation of each year by 4 % steps between -12 and +16 %. We ended up with five sets of climate time series (of 1-year length) that differ in temperature, precipitation and radiation. Each of these five sets includes 64 time series, which differ only in temperature (see Appendix , Fig. ). Temperature change was quantified using two indices: (i) mean annual temperature and (ii) annual temperature amplitude, which described the 95 % interquartile range of all daily temperature values of a given year. We did not model the effects of nitrogen and CO2 fertilization (as both do not vary strongly within 1 year) or extreme anomalies (e.g. pathogen attacks) on wood production. Figure a–c show the AWP for different annual temperatures for three different forest stands.

We analysed the sensitivity of every forest stand to temperature change following the approach of . For every forest stand, a general linear model was fitted relating wood production mean annual temperature (MAT) and intra-annual temperature amplitude (Q95), as well as the nuisance parameter year. AWP=αxMAT+βxQ95+γxyear+ϵ

For every forest, we calculated the relative change of productivity resulting from an increase of 1 ∘C: SIMAT=αAWP‾SIQ95=βAWP‾.

In our analysis, we excluded all forests stands for which AWP turns negative if the temperature rises by 1 ∘C (this occurs in 2 % of all stands).

We also determined the sensitivity of forests to temperature change using the German forest inventory to validate our results. However, the inventory does not include leaf area index (LAI) measurements. We therefore assumed the basal area as a proxy for LAI, and we selected subsamples of forests stands with similar structure (basal area, tree height heterogeneity, forest height and same species mixtures). In addition, we used elevation as a proxy for mean annual temperature, assuming temperature changes of 0.65 ∘C per 100 m on average . Only in the case of spruce and beech monocultures did we find enough data to calculate SIMAT values for several forest structures (for more details, see Appendix , Fig. ).

The comparison between the SIMAT estimation based on the German forest inventory with SIMAT values of corresponding forests from the forest factory showed quite good agreement (R2=0.65). However, the simulated SIMAT values of the forest factory slightly overestimated the sensitivity compared to the inventory-based values (Fig. ). This might be explained by the difference in the methods used because, in the case of the inventory, we used basal area instead of LAI and altitude instead of temperature. Another explanation could be that in our approach the climate time series showed relatively high and regular precipitation. In the German forest inventory, warmer sites might be more frequently exposed to water stress, which then reduced the SIMAT values.

We used three indices to describe the forest structure: LAI, maximum forest height (Hforest), which corresponds to the height of the largest tree in a forest stand, and tree height heterogeneity (θ), which was quantified by the standard deviation of the tree heights. To describe species composition, we used Rao's Q and species distribution index (ΩAWP). Rao's Q quantified functional diversity based on species abundances and differences in species traits (Botta, 2005, for details, see Appendix ). ΩAWP analysed the optimal location of species within the forest structure. ΩAWP is defined as the ratio of the forest's productivity to the maximum possible productivity of the forest without changing tree sizes or number . Hence, the maximum productivity can be obtained by varying only the species identities of trees in the forest stand. We changed the assigned species of each tree until we found the optimal species for each individual tree and its specific environmental condition. All five indices were nearly uncorrelated for the investigated forest stands (Appendix , Table ).

We applied boosted regression trees to quantify the influence of the five forest properties on SIMAT and SIQ95. Boosted regression trees are a machine learning algorithm using multiple decision (or regression) trees. It is able to address unidentified distributions . Each model was fitted in a forward stage-wise procedure to predict the response of the dependent variable on (SIMAT or SIQ95) to multiple predictors (tree height heterogeneity, forest height, LAI, Rao's Q and ΩAWP). To omit an overfitting with regard to maximal forest height, we classified forest stands into 18 classes. Each class had a width of 2 m, starting with 4 to 6 m and finishing with 36 to 38 m. The boosted regression trees tried an iterative process to minimize the squared error between predicted SI values and those of the data set. Hereby, part of the data were used for a fitting procedure and the rest was used for computing out-of-sample estimates of the loss function . This boosted regression tree analysis was performed in the R package gbm 2.1.1 .

We used a quarter of the data (randomly sampled) for the machine learning procedure. To get the best model, we varied the following four parameters of the boosted regression tree algorithm: learning rates (0.1, 0.05 and 0.01), the bag fractions (0.33, 0.5 and 0.66), the interaction depths (1, 3 and 5) and the cross validation (3-, 6- and 9-fold) assuming a Gaussian error structure (the default setting). The best-fitted boosted regression tree for both SIMAT and SIQ95 showed a learning rate of 0.1, a bag fraction of 0.66, an interaction depth of 5 and a 3-fold cross validation. These two models were used for all further analyses. The remaining 75 % of the data were used to validate the fitted boosted regression tree algorithm.

Here, we assumed forest height as a proxy for the successional stage of a forest. In every height class, we selected those 5 % of forests that showed the highest sensitivity values (SIMAT and SIQ95). We removed the forest height classes between 10 and 14 m, as they only contained only 15 forests. For all other classes, we analysed the relationship between height class and the forest properties (ΩAWP, Rao's Q, LAI and tree height heterogeneity).

In this theoretical study, we present a new climate sensitivity analysis (with regard to temperature) of AWP. This approach extends field observations and long-term model simulations, as it allows the analysis of existing forests but also of those that might exist in the future due to management changes and/or disturbances. Our approach includes only forest stands in which every tree has positive productivity and enough space for its crown. Hence, it is impossible, for instance, that light-demanding species grow below a closed canopy or forests are overcrowded. However, the data set also includes a few very unusual stand structures or species combinations, which cannot emerge in a natural system, but may result from disturbances or management. In the case of field observations, it is difficult to explore the influence of a single climate variable (e.g. temperature) on one target variable (e.g. AWP), as in most cases, several variables are altered at the same time (see also Appendix ). Process-based models are one option to analyse such relationships and separate these effects. The simulation of AWP with the FORMIND model in temperate forests has been successfully compared to eddy flux sites , the national German forest inventory and European yield tables .

An advantage of the forest factory approach is the huge set of various forests stands that can be analysed. The data set includes forest stands that often occur in temperate forests (even-aged spruce, pine and beech stands). However, it also includes hypothetical ones that could occur through alternative forest management or disturbances (fire, bark beetles, etc.). Hence, our data set of forest stands covers a much larger variety of forest property combinations compared to long-term forest simulations with the focus on natural forests in their equilibrium state e.g. or on monocultures e.g.. Long-term simulations with ecosystem models, which process modelled climate projections, face a trade-off between cascade uncertainty and path dependency . The accumulations of model uncertainties over such a process chain result in increasing uncertainty. Our study design tries to minimize this uncertainty and omit path dependencies by including only those processes that might be relevant for the research question. In this study, for instance, we omit the effect of climate change on regeneration and mortality. Furthermore, using several climate variables as model inputs but only analysing the effect of one variable might lead to incorrect interpretations of its effect. For example, temperature and radiation often correlate, and both might increase productivity. Therefore, in this study, we only vary one variable in all five sets of time series. This guarantees that there are no relationships between the target climate variable and the remaining climate variables.

As an increase in global mean temperature of 1.5 to 2 ∘C can hardly be avoided, even under the Representative Concentration Pathway (RCP) 2.6 climate scenario , this study focuses on temperature change. This RCP scenario predicts only small changes in annual precipitation levels for temperate regions. Hence, our approach focuses only on the effect of temperature change on wood production. However, this might be critical for the analysis of strong temperature changes (e.g. RCP8.5) which will result in an increased incidence of drought and changes in the annual temperature cycles and a strong change in CO2. Such more complex scenarios should be analysed in future studies. Further, we neglect the effect of time lags (e.g. bud building in the previous year). However, it is possible to extend the used time series to analyse the behaviour of the forest over longer time periods and study not only productivity but also effects on regeneration or mortality.

To characterize the annual temperature cycles, we used two variables: mean annual temperature and intra-annual temperature amplitude. Both variables can be varied independently. In the case of higher mean annual temperature, we observe an elongation of the vegetation period. This leads to higher forest productivity (if other resources are not limiting and explains why SIMAT is often positive. However, warmer summer temperatures can also lead to a decline in wood production due to an increase in respiration. In the case of increasing intra-annual temperature amplitude, more days with extreme temperatures will occur in a year. Thus, an increase of 1 ∘C-1 of intra-annual temperature amplitude will increase respiration more strongly compared to an increase of 1 ∘C-1 of mean annual temperature. Hence, the increase of intra-annual temperature amplitude normally has negative effects on the productivity (negative SI values).

The temperature sensitivity values obtained here are in the same range as those found for temperate ecosystems in heating experiments 4.4 ± 2.2 % ∘C-1. Within the 16 analysed studies reviewed by , the experimental plots show almost identical environmental conditions (soil, radiation and precipitation) and species composition. To heat the plots, greenhouses or infrared heaters were used. Another study, based on natural forest stands in New Zealand, found an AWP increase of between 5 and 20 ∘C-1 for forests, assuming no change in forest structure and species composition . The analysed plots were spread throughout New Zealand, and warmer temperatures coincided with higher radiation . Hence, the analysed temperature effect also includes the influence of radiation. In our setting, however, the influence of temperature is independent of radiation as in. We also found a good correlation between SI values derived from growth measurements of the German forest inventory and simulated SI values based on the forest factory (Fig. , Appendix , Fig. ).

Our findings might be relevant for future management strategies for temperate forests. Specifically, our new understanding of which species benefit most from rising temperatures (Fig. 6) suggests possible strategies, e.g. replacing spruce monocultures with mixtures of deciduous trees. Further, based on the analysis of which forest structure benefits most from rising temperatures (Figs. 4, 5, 6), early-stage even-aged forests should include mainly pioneer species. In the mature stage, we predict a positive effect of temperatures on wood production for a mixture of climax species including different tree sizes. These climax species could be planted below the canopy of the pioneer species in young forests. In our approach, we do not simulate the establishment of very young trees. However, during the conversion between these two forest types, one big challenge might be the removal of the pioneer trees without damaging the young trees that will build the mature forest.

Most global vegetation models represent vegetation as fractional cover of different plant functional types within a grid cell e.g. Lund–Potsdam–Jena (LPJ);. Only a few global vegetation models include a more detailed representation of vegetation structure and functional diversity . It would be interesting to perform the analysis presented here with global vegetation models which include structure to better understand the mechanisms driving forest systems' sensitivity to climate change.

Besides the global vegetation models, forest gap models, which have been restricted to local stands, are now able to simulate forest dynamics in regions or even entire continents . Studies using global vegetation models or large-scale forest gap models simulate natural succession. Our analysis indicates that natural and managed (or disturbed) forest systems, which differ in forest structure, might react differently to climate change. Hence, we suggest considering forest structure in future analyses of global vegetation. Such information on forest structure might be derived from remote sensing.