Incorporating forest growth response to thinning within biome-BGC

Incorporating forest growth response to thinning within biome-BGC

Forest Ecology and Management 242 (2007) 324–336 www.elsevier.com/locate/foreco Incorporating forest growth response to thinning within biome-BGC Ric...

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Forest Ecology and Management 242 (2007) 324–336 www.elsevier.com/locate/foreco

Incorporating forest growth response to thinning within biome-BGC Richard Petritsch, Hubert Hasenauer *, Stephan A. Pietsch Institute of Forest Growth Research, University of Natural Resources and Applied Life Sciences, Peter Jordan Str. 82, A-1190 Vienna, Austria Received 28 June 2006; received in revised form 29 November 2006; accepted 21 January 2007

Abstract Large-scale ecosystem models are designed to reproduce and quantify ecosystem processes. Based on plant functions or species-specific parameter sets, the energy, carbon, nitrogen and water cycles of different ecosystems are assessed. These models have been proven to be important tools to investigate ecosystem fluxes as they are derived by plant, site and environmental factors. The general model approach assumes uniform and fully stocked forests but since most European forests are managed (e.g., thinned) it is essential to understand the limits and precision of such models when applied to managed forest ecosystems. The purpose of this study is to investigate and incorporate common forest management practices within the large-scale ecosystem model Biome-BGC. Using ‘‘Monte-Carlo’’ simulations we analyze the theoretical response to current model settings assuming steadily decreasing changes in stand density. Results of the MC simulations as well as the comparison with measured data suggest that the resulting predictions will be biased. Using long-term experimental plots of Norway spruce (Picea abies L. Karst.) and common beech (Fagus sylvatica L.) forests with a well-documented thinning history, we propose a thinning subroutine, which addresses the changes in allocation patterns after stand density changes. Validation tests of improved model structure across different long-term experimental sites in Central Europe revealed unbiased and consistent simulation results. # 2007 Elsevier B.V. All rights reserved. Keywords: Thinning response; BGC-model; Prediction error; Fagus sylvatica; Picea abies

1. Introduction Central European forests have a long management history. During the pre-industrial period forest management consisted mainly of litter raking, fuel wood extraction, and timber production for local demand (Mayer, 1974). With the industrialization the demand for forest products substantially increased. Rigorous forest laws were enforced to avoid over cutting and as a result forest management practices such as tending, thinning and shelter woodcutting were developed and applied to ensure sustainable timber production (Assmann, 1970). While thinning generally does not increase production (Wiedemann, 1942; Assmann, 1970) it can shift the distribution of growth to larger, more valued trees. Thinning intensity is commonly assessed by the proportion of basal area removed. The remaining basal area of the stand is used as a measure that can help to predict the growth response after thinning. A large number of studies have investigated the relationship between

* Corresponding author. Tel.: +43 1 47654 4205; fax: +43 1 47654 4242. E-mail address: [email protected] (H. Hasenauer). 0378-1127/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2007.01.050

the residual basal area and the growth response following thinning. The results show that the volume increment per unit area does not decrease proportionally with decreasing basal area. The volume increment immediately after thinning is lower versus the situation before but it converges to the level of the unthinned stand when basal area increases. This relationship strongly depends on tree species, site quality, time of thinning and the intensity of thinning (Assmann, 1970; Hasenauer et al., 1997; Pretzsch, 2005). Based on these findings forest growth and yield models have been developed which are specifically designed to address the diameter and height growth response of individual trees, according to changes in competition (see Hasenauer, 1994; Monserud and Sterba, 1996; Pretzsch et al., 2002). Such tree growth models focus on timber production, the use of routine forest inventory data, and address site conditions based on site descriptors or site index functions. They have been successfully implemented in practical forest management planning (Hasenauer, 2006). Although tree growth models have been proven to be important silvicultural management tools they do not consider key ecosystem processes like water, carbon, nitrogen, and energy cycles. If we are only interested in timber production, a

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detailed assessment of these processes may be superfluous since it would make the model structure much more complex then needed. However, if we are interested in assessing potential changes in the water holding capacity, environmental changes on forest ecosystems, or degradation effects, tree growth models are too simplistic. Several studies (White, 1974; Aber et al., 1978; Hix and Barnes, 1984) have shown that thinning, expressed as the biomass extracted from the forest, influences the fluxes within forest ecosystems. One option to understand key ecosystem processes for forest growth is the application of biogeochemical-mechanistic models (BGC-Models). Conceptually these models consist of a formal description of ecosystem processes such as photosynthesis, transpiration, allocation, and decomposition. BGC-models are explicitly designed to study the complex interactions between ecosystems and the atmosphere, and thus, they may be seen as diagnostic tools to investigate potential impacts on forest ecosystems. These potential impacts can be attributed to changing environmental conditions or forest management practices. An important limitation of BGC models is that they operate on fully stocked even-aged stands. Compared to tree growth models (Hasenauer, 2006) they are not explicitly designed to be sensitive to varying stand density. For certain applications this may be a reasonable approach, however, if we are interested in the carbon balance of forests and how this may change under potential climate chance, the conceptual integration of thinning is essential. This is particularly important as forest management has been and still is the main driving impact for changes in forest growth within Europe (Kauppi et al., 1992). While considering management it is important to distinguish between historic management impacts and their likely impacts on the carbon balance of ecosystems (Berger et al., 2002; Schulze and Freibauer, 2005) and current management practices which mainly address changes in stand density (e.g., thinning). In a previous study, we have demonstrated how potential historic management impacts may be integrated within large-scale ecosystem models (see Pietsch and Hasenauer, 2002). The purpose of this study is to investigate and integrate density related forest management practices into large-scale ecosystem modeling. A species-specific adaptation (see Pietsch et al., 2005) of BIOME BGC (Thornton et al., 2002) was made. For unmanaged fully stocked stands we have demonstrated that for all major tree species in Central Europe the model produces unbiased and consistent results (Pietsch et al., 2005). This is an important precondition since each tree species exhibits its distinct behavior between changes in forest growth versus stand density (Assmann, 1970). This has been well documented in a large number of growth and yield studies but it has never been integrated in large-scale mechanistic ecosystem modeling, which is the purpose of this paper. The specific working steps of our study can be summarized as follows: (1) We start our analysis using ‘‘Monte-Carlo’’ simulations to investigate the current constraints of the model structure by assuming a steady increase in thinning intensity.

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(2) We compare model predictions with observations from managed long-term experimental sites of Norway spruce (Picea abies L. Karst.) and common beech (F. sylvatica L.) forests across Central Europe. (3) Based on these comparisons we improve and/or develop a thinning sub-module addressing the species-specific responses of key ecosystem processes (e.g., carbon cycle) to stand management. (4) We assess the accuracy and precision of the improved model predictions by species using field observations with a well-documented management history. 2. Methods 2.1. The model For this study, we used Biome-BGC Version 4.1.1 (Thornton et al., 2002) which included our recent extensions regarding hydrology (Pietsch et al., 2003), species representation (Pietsch et al., 2005) and self initialization (Pietsch and Hasenauer, 2006). The model operates on a daily time step and simulates the cycle of energy, water, carbon and nitrogen within a given ecosystem. The model requires meteorological input data, such as daily minimum and maximum temperature, incident solar radiation, vapor pressure deficit and precipitation. Aspect, elevation, nitrogen deposition and fixation, and physical soil properties were needed to calculate daily canopy interception, evaporation and transpiration; soil evaporation, outflow, water potential and water content, LAI, stomatal conductance and assimilation of sunlight and shaded canopy fractions; growth and maintenance respiration, GPP and NPP, allocation, litterfall and decomposition; mineralization, denitrification, leaching and volatile nitrogen losses. In the model, the carbon allocated to the leaves is multiplied by the specific leaf area (m2 leaf area per kg leaf carbon) to calculate leaf area index (LAI, m2 leaf area per m2 ground area). LAI controls canopy radiation absorption, water interception, photosynthesis, and litter inputs to detrital pools. Net primary production (NPP) was based on gross primary production (GPP), calculated with the Farquhar photosynthesis routine, (Farquhar et al., 1980) minus the autotrophic respiration. The autotrophic respiration included the maintenance respiration and is calculated as a function of tissue nitrogen concentration (Ryan, 1991). Growth respiration is a function of the amount of carbon allocated to the different plant compartments (leaf, root and stem). The remaining NPP is partitioned to the leaves, fine and coarse roots and stems as a function of fixed allocation patterns. These patterns are defined by the three model parameters f 1, f 2 and f 3 which give the allocation ratios among fine root C to leaf C ( f 1), stem C to leaf C ( f 2) and coarse root C to stem C ( f 3). In the calibration of the initial runs, we used the fixed speciesspecific allocation ratios (see Pietsch et al., 2005) resulting in distribution percentages for stem/leaf/fine root/coarse root carbon of 65.7% (stem), 17.3% (leaves), 7.6% (fine roots) and 9.4% (coarse roots) for common beech as well as ratios of 65.1% (stem), 21.5% (leaves), 7.8% (fine roots), 5.6% (coarse roots) and 48.2% (stem), 23.1% (leaves), 11.1% (fine roots),

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17.6% (coarse roots) for lowland and highland Norway spruce, respectively. 2.2. Consideration of management The main impact of forest management on ecosystem processes is the removal of biomass. In the model this is currently addressed by a reduction of the biomass pools. For example, a thinning event is applied as a relative reduction of the living biomass. Stem carbon is removed and considered to be harvested and according to the harvesting intensity all other pools, i.e. leaves, stems and fine and coarse roots, are reduced proportionally (Krapfenbauer and Buchleitner, 1981; Krapfenbauer, 1983). From the assumed harvested biomass, total leaf and fine root biomass is transferred to the litter pools and total coarse root mass to the coarse woody debris pools (Pietsch et al., 2005). This procedure corresponds to typical commercial thinning and differs from precommercial thinning based on the removal of biomass (Merganicˇova´ et al., 2005). 2.3. Simulation procedure Large-scale ecosystem models start any simulation with a self-initialization procedure or so called spinup run to enable model applications for locations where no observations of initial conditions are available. For this study we applied the latest version of the self-initialization process as suggested by Pietsch and Hasenauer (2006). This new spin up procedure includes a dynamic biomass mortality routine, and thus, avoids biased estimates of the initial pool sizes as they may occur if a fixed percentage of dead biomass is assumed. Next we considered potential degradation effects by mimicking historic forest management impacts (Pietsch and Hasenauer, 2002). For the self initialization run and the preindustrial land use history assessment, we used pre-industrial carbon dioxide concentration (280 ppm; IPCC WGI, 1996) and nitrogen deposition (0.0001 kg m2; Holland et al., 1999) rates, respectively. Since 1765 an increase in CO2 concentration (IPCC WGI, 1996) and nitrogen deposition to current levels, as given in Schneider (1998), is assumed (Table 2). This resulted in the model initialization prior to the actual simulation run for each location. For each stand of our study, species composition, current stand age, thinning intensity and time of thinning is available. Thus, the actual simulations start with an assumed planting or regeneration according to stand age. During the simulation, thinning is assumed if the biomass removal exceeds 5%. Species-specific differences in growth response due to thinning are considered using the available parameter sets for common beech, low- and high-land Norway spruce. Stem carbon predictions were converted into bole volume and used for comparison with observed data according to speciesspecific conversion factors. The conversion factors incorporated the bole fraction of aboveground timber, timber water and carbon content and timber density (see also Pietsch et al., 2005). The scheme of the simulation procedure is given in Fig. 1.

Fig. 1. Flow diagram of a simulation run.

3. Data 3.1. Field data For testing model performance we used data from 66 permanent research plots located at 12 different regions across Central Europe (Austria and Germany). These plots were: (1) Frauenwald/Hirschlacke, (2) Lehrforst (the experimental forest of the University of Natural Resources and Applied Life Sciences, Vienna), (3) the forests near Ottenschlag, (4) Litschau, (5) Arnoldstein, (6) Gmunden, (7) Mittersill, (8) Neuberg, (9) Elmstein, (10) St. Leonhard, (11) Fabrikschleichach, and (12) Hain/Rothenbuch. The regional distribution is given in Fig. 2. Forty-seven plots from 8 regions are covered with Norway spruce (P. abies L. Karst) and 19 plots from 5 different regions are stocked with common beech (F. sylvatica L.). The plots were established to study growth response to different thinning regimes and have a well documented management history. Every tree on the plot is tagged and the diameter at breast height, the tree height and the height to the live crown base was recorded periodically. The remeasurement intervals vary by plot and region and range from 2 to 15 years. All together, 89 growth periods following thinning are available for our analyses. Each tree on a given plot is remeasured, thus changes in stand density due to thinning versus natural mortality are distinguishable. Stand level values of removed volume during each thinning event were derived using volume equations

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Fig. 2. Sample plots in Central Europe used in this study.

according to Kennel (1973). The plots represented typical growth and yield plots as they were established for certain regions, forest types and site conditions to develop thinning guidelines for forest management practices in Central Europe. Table 1 gives an overview of the sample plots by region. Detailed site and stand characteristics are given in Table 2. Soil depth and texture necessary for running the model for each plot were classified according to the Austrian National Forest Soil Survey (Englisch et al., 1992).

for running the model were interpolated for the locations of our 66 plots using the point version of DAYMET (Petritsch, 2002). This procedure was recently validated for Austria (Hasenauer et al., 2003). Climate data for running DAYMET were provided by the Austrian and German National Weather Centers and includes daily weather data for up to 300 stations covering the years 1960–2003.

3.2. Climate data

4.1. Current model response to changes in stand density

Daily minimum and maximum temperature, precipitation, short wave radiation and vapor pressure deficit data necessary

We started our analysis by obtaining our species-specific version of BIOME BGC, which includes all our recent

4. Analyses and results

Table 1 General information about the sample plots Region Frauenwald/Hirschlacke Lehrforst Ottenschlag Litschau Arnoldstein Gmunden Mittersill Neuberg Elmstein St. Leonhard Fabrikschleichach Hain/Rothenbuch

Lon

Lat 0

13855 E 168180 E 158140 E 158000 E 138430 E 138470 E 128260 E 158350 E 78550 E 148530 E 108430 E 98220 E

0

48842 N 478410 N 488260 N 488590 N 468340 N 478490 N 478160 N 478400 N 498230 N 478590 N 498550 N 498590 N

FT

ST

Est

Re

Comment

S S/F/B/P S S/P

C C C C C/R L/R/C/F C/P C/R C

1977/1979 1980/1992 1980 1977 1993 1977 1977 1977 1872 1983 1870 1871

5 5 5 5 5 5 5 5 2–17 3–5 3–15 2–14

Bohemian Massif Rosalia mountain Bohemian Massif Near Czech Republic Carinthia Salzburg Tirol Styria Rhineland-Palatinate Lower Austria Bavaria Bavaria

S S S

C C

Lon/Lat is the geographical location (longitude/latitude) of the region, FT is the main forest type (S = Norway spruce, F = Fir, B = Common beech, and P = Scots pine), ST is the soil type (C = cambisols, R = rendzina, L = lithosols, F = fluvisols, and P = podzol), Est is the year when the sample plots were established, Re is the remeasurement period in years.

1 3 6 3 6 Fagus sylvatica Lehrforst Elmstein St. Leonhard Fabrick-schleichach Hain/Rothenbuch

599 400 570 430 427 (405–450)

8.4 9.3 7.9 7.9 7.9 (7.8–8.0)

802 814 1172 818 1088 (1063–1113)

0.39 0.50 0.75 0.5 0.5

(0.51–1.04) (0.39–0.66) (0.31–0.7) (6.4–8.8) (3.4–7.0) (4.7–6.6)

(474–568) (581–595) (460–1000) (900–1660) (900–1440)

The numbers in parenthesis give the data range (minimum–maximum) where applicable. N is the number of permanent research plots by location, Elev is the elevation above sea level, Temp the mean temperature, Prcp the annual precipitation, So.depth the soil depth, Ndep the current nitrogen deposition, Age the stand age at the reference year (RY), V the stand volume, dg the quadratic mean breast height diameter at the reference year (RY), and RY the reference year, which indicates the year of the last remeasurement of the plots within a given region.

2002 2002 1999 1990 1995/1974 50 10.0 (8–12) 45 (36–57) 10 (6–23) 9 (6–17) (48.4–58.8) (14.3–16.5) (41.1–52.9) (38.6–56.9) 12.4 54.1 15.0 46.9 46.2 (275–422) (213–282) (882–980) (543–758) 248 341 249 946 668 52 180 75 168 163 (158–168)

(28–103) (32–57) (28–103) (39–116) (37–112) (0.02–0.04)

(646–688) (1117–1129) (1271–1517) (1172–1408) (1089–1395) (7.1–7.6)

7.7 10.0 15.0 10.0 10.0

(5–32) (14–32) (22–30) (10–43) (5–17) (9–43) (9–47) (1–44) 14 25 26 27 10 16 20 28 (25.7–34.6) (35.0–40.4) (16.5–16.8) (3.1–28.2) (7.9–28.7) (23.8–41.1) (20.7–42.3) (21.2–44.8) 30.3 38.0 16.6 10.1 18.8 31.8 31.4 30.9 (750–1258) (835–1109) (296–741) (246–604) (462–913) (519–1344) (409–1396) (516–1152) 972 1013 484 455 724 922 857 741 (57–123) (126–131)

90 127 52 51 43 65 77 75 12.3 (11.3–13.3) 7.7 6.2 7.5 11.7 16.9 10.5 8.2 (0.48–0.55)

0.65 0.52 1.04 0.03 0.43 0.69 0.49 0.48 (967–1000)

984 794 848 661 1123 1417 1254 1177 (6.7–7.5)

7.1 8.5 6.2 7.4 8.3 7.2 5.6 5.8 (612–771)

5 4 4 8 4 8 5 9 Picea abies Frauenwald/Hirschlacke Lehrforst Ottenschlag Litschau Arnoldstein Gmunden Mittersill Neuberg

692 585 826 510 588 820 1260 1145

Thinning (% of V) dg (cm) V (m3 ha1) Age (years) Ndep (kg ha1) So.depth (m) Prcp (mm) Temp (8C) Elev (m) N Region

Table 2 Mean statistics of the 66 research plots grouped by tree species and region

2002/2000 2000 2000 2002 2003 2002 2002 2002

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RY

328

improvements (see Section 2.2) to test the current sensitivity of the model to changes in stand density using ‘‘MonteCarlo’’ simulation techniques. We took this approach to understand the intrinsic response of the current model structure to varying stand densities before any improvements and/or model changes were considered. In the next phase we were interested in the accuracy and precision of the resulting model predictions using the 66 plots covered with common beech and Norway spruce (see Table 2). All these plots have a well-documented management history and consisted of repeated individual tree measurements which allow a comparison between predicted and observed volume increment rates after thinning. For the Monte-Carlo simulations we selected two sites, one for Norway spruce and one for common beech. Both came from the Lehrforst, and since they were selected to be similar in climate and site conditions, they also allowed for a species comparison in growth response versus stand density. The response to thinning depends on the thinning intensity and the stand age at the time of thinning (Assmann, 1970). Thus, we applied ‘‘Monte-Carlo’’ simulations for 50 randomly chosen thinning intensities and stand ages at the time of thinning by species. Thinning intensities ranged from no thinning to 50% stem carbon removal. Stand ages at the time of thinning varied from 15 to 95 years. Fig. 3 gives the results of the 5-year volume increment by species and thinning intensity in percent of the unthinned stand. The results suggest that thinning may lead to an acceleration of growth compared to the same biomass fraction of unthinned stands as given by the 1:1 line. When thinning intensity was low, the modeled response of both species was similar. With increasing thinning intensity, the simulated growth acceleration for common beech was higher than for Norway spruce (Fig. 3). This is consistent with results from growth and yield studies (see Kramer, 1988; Spiecker, 1991; Kenk, 1998), who reported a higher growth response after crown release for the more shade tolerant beech versus a

Fig. 3. Five-year total stem volume increment rates in percent of the unthinned conditions using Monte-Carlo simulations. The results show 50 randomly chosen thinning intensities distributed across different stand ages at the time of thinning for spruce and beech. The fitted lines by species result form nonlinear regressions.

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Fig. 4. Comparison in growth efficiency (GE: NPP/LAI), water use efficiency (WUE: NPP/transpiration), nitrogen use efficiency (NPP/vegetation N) and radiation use efficiency (RUE: NPP/absorbed radiation) of thinned vs. unthinned conditions based on Monte-Carlo (MC) simulations. The MC runs cover random thinnings between 5 and 50% at stand age between 10 and 100 years. In the box and whisker plot, the line within a box is the median, the boundaries of the box indicate the 25th and 75th percentiles, and the whiskers give the 10th and 90th percentiles.

lower growth response of the more light demanding spruce. Obviously, a forest management response is implicitly included in the BGC-model although the model is considered to cover only fully stocked stands. This suggests that the growth efficiency (GE = NPP/LAI), the water use efficiency (WUE = NPP/transpiration), the nitrogen use efficiency (NUE = NPP/vegetation N) or the radiation use efficiency (RUE = NPP/absorbed radiation) may have changed with respect to the same biomass fraction of the unthinned stand. The analyses of the different parameters according to thinning intensities are given in Fig. 4. The results for WUE exhibited no significant differences, however, the RUE was significantly lower in the thinned stands (beech: t = 8.32, tcrit = 2.68, a = 0.01, d.f. = 49; spruce: t = 6.28, tcrit = 2.68, a = 0.01, d.f. = 49) versus the unthinned ones. Obviously immediately after thinning not all of the available radiation load can be used for NPP. In our Monte-Carlo simulations both species exhibited a significant increase in GE (beech: t = 14.0, tcrit = 2.68, a = 0.01, n = 50; spruce: t = 2.36; tcrit = 2.01; a = 0.05; n = 50) and NUE (beech: t = 8.28, tcrit = 2.68, a = 0.01, n = 50; spruce: t = 6.33; tcrit = 2.68; a = 0.01; n = 50) for the thinned stands versus the unthinned stand. Thinning leads to changes in modeled GE and NUE (Fig. 4) and this has resulted in a nonlinear modeled growth response (Fig. 3). This theoretical model behavior is consistent with findings from thinning experiments although these experiments only address volume growth–density relationships. With the current model settings (see Section 2.1.) we ran the model for each site using the species initializations given in Pietsch et al. (2005), Tables A1, A6, A7 for common beech, lowland Norway spruce and highland Norway spruce, respectively. For spruce, we grouped the plots located at an elevation >1000 m (Gmunden, Mittersill and Neuberg)

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and those <1000 (all other regions see Fig. 1), because different spruce variants (highland and lowland initialization) are available. Management intensity on each plot was derived from the single tree data as given in Section 3.1 and used for biomass reduction in the model as described in Section 2.2. For low volume increments the model predictions are consistent with the corresponding observations (Fig. 5A). With increasing volume increment, the model underestimates growth (Fig. 5A), resulting in biased and inconsistent estimates (Table 3). This is also evident in the trends of the standardized increment residuals (predicted–observed divided by the standard deviation of the observations) versus the predicted volume, thinning intensity, stand age, basal area as a measure for stand density, diameter at breast height and site index (see Fig. 5B). 4.2. Developing a dynamic carbon allocation model Although a reaction to thinning is implicitly included in the BGC model (see Figs. 3 and 4), this reaction is insufficient to achieve unbiased results (see Fig. 5, Table 3), because individual trees react to a reduction in competition with changes in their physiology. This affects the distribution patterns of assimilates between above and below ground biomass and between wood and leaf biomass as they may change in response to specific environmental conditions (Mooney and Winner, 1991). In individual tree growth models this effect is considered by parameters for the competition situation (Monserud, 1975; Hasenauer, 1994; Monserud and Sterba, 1996; Pretzsch et al., 2002) which change according to management. Within large-scale BGC models physiological reactions, like changes in the allocation patterns of assimilate are currently not addressed, because fixed ratios of carbon allocation to the different compartments (roots, stem, leafs) are assumed. This suggests that, similar to the thinning response factor of individual tree growth models, a dynamic simulation routine is needed to mimic the physiological reaction of trees to forest management, like, e.g. the temporal changes in allocation patterns following thinning. Since Biome-BGC is a process based ecosystem model a mechanistic description of thinning induced allocation changes would be desirable. Such a description is currently not available because physiological data from long-term thinning trials are missing. We decided to use a phenomenological approach following the growth response to thinning as implemented within tree growth models (Hasenauer, 2006). This allows us to develop a management sub-module to address the thinning response within BIOME-BGC according to the following principles: (i) The duration of growth changes following thinning depends on the thinning intensity. (ii) Thinning changes the allocation ratios of above to below ground biomass and stem to leaf biomass compared to unthinned conditions.

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Fig. 5. (A) Predicted vs. observed volume increments following thinning using the current model setup. The predicted values are derived by converting the stem carbon output of the BGC model to volume growth per hectare using the conversion factors given in Pietsch et al. (2005). The data come from all 66 sample plots and consist of 89 growth periods. (B) Trend analysis of standardized increment residuals (std. incr. res., i.e. predicted minus observed divided by the standard deviation of the observations) vs. predictor, thinning intensity, stand age, basal area, dbh, and site index.

(iii) Forest growth response to thinning starts with a time lag following thinning, approaches a peak and declines towards zero with increasing time since thinning. The actual duration of growth changes following thinning (Dact) is expressed as: Dact ¼ Dmax ð1  eTI=C Þ

(1)

where Dmax is the maximum duration of the expected thinning response, TI is the thinning intensity expressed as the percentage of the removed biomass and C is an empirical coefficient defining the slope of the exponential relationship between thinning intensity and the actual duration. In the implementa-

tion, Dact is rounded to the next integer. The conceptual framework for a Dmax of 20 years and C = 15 is given in Fig. 6A. Thinning changes the allocation ratios of above to below ground biomass and stem to leaf biomass compared to unthinned conditions. In the current model setting the allocation ratios f 1  f 3 ( f 1: leaves/fine roots, f 2: stem/leaves, f 3: stem/coarse roots; see Section 2.1) are fixed since thinning impact in fully stocked stand need not be addressed. According to the above outlined principles, we propose a concept which allows changes in the allocation ratios due to thinning. The parameter F sl derives the maximum change of the stem/leaf allocation ratio f 2. Since f 1 and f 3 are both related to above/

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Table 3 Summary statistics of the comparison between predicted and observed volume increments using the current model setting for all available growth periods Dti (m3/(ha year))

CI (m3/(ha year))

PI (m3/(ha year))

TI (m3/(ha year))

0.95 0.99 0.98 0.94*

1.9

11.6 . . . 6.5 11.9 . . . 6.9 10.9 . . . 7.5 2.5 . . . 1.4

22.2 . . . +4.1 21.3 . . . +2.6 21.2 . . . +2.8 5.4 . . . +1.1

25.4 . . . +7.3 24.5 . . . +5.8 23.3 . . . +5.0 6.1 . . . +1.8

0.91*

5.2

6.1 . . . 4.3

13.6 . . . +1.8

14.8 . . . +2.9

Nobs

Obs (m3/(ha year))

Di (m3/(ha/year))

SD (m3/(ha/year))

t

W

Spruce—lowland Spruce—highland All spruce plots Common beech

26 22 48 41

22.9 17.6 20.4 8.0

9.0 9.4 9.2 2.2

6.3 5.6 5.9 2.3

7.4* 7.8* 10.5* 6.1*

Summary

89

14.7

5.9

5.8

9.7*

The predicted values are derived by converting the stem carbon output of the BGC model to volume growth per hectare using the conversion factors given in Pietsch et al. (2005). Nobs is the number of observations given by the available growth periods following thinning interventions, Obs is the mean of the observations, Di the mean of the differences between predicted vs. observed volume growth, SD the standard deviation of the differences, t is the calculated t-value derived from a paired t-test (* indicates significant difference for a = 0.05 of the means), W is the calculated W-value of the differences derived from Wilk’s test for normality (Shapiro and Wilk, 1965, * indicates significant difference from normality), Dti is the trimmed mean of the differences and CI, PI, andp TIffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi are the confidence, prediction, and ffi 1/2 0 t 1=2 tolerance intervals. CI = D  S t n (Reynolds, 1984) or D  S t n (Rauscher, 1986), PI ¼ D  1 þ ð1=nÞ S t (Reynolds, i D i D 1(a/2),(n1) 1ða=2Þ;ðn1Þ 1ða=2Þ;ðn1Þ D i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1984) or Dti  1 þ ð1=nÞS0D t1ða=2Þ;ðn1Þ (Rauscher, 1986), TI = Di  SDg1y,n,1a) (Reynolds, 1984) or Dti  S0D g1g;n;1a (Rauscher, 1986) depending on the normality of the errors. n is the number of observations, t1(a/2),n1 the 1  a/2 quantile from the t-distribution with n  1 degrees of freedom and g1g,1a the tolerance factor for the normal distribution accounting for the probability that (1  g) 100% of the distribution D is within a probability of 1  a (for statistical tables, see e.g. Sachs, 1999). The trimmed mean errors Dti and the jackknifed variance estimates S0D as well as confidence CI, prediction PI, and tolerance intervals TI for errors that do not follow the normal distribution as indicated with a significant W-value are calculated after removing the lower and upper 10% of the observations.

belowground allocation, one single parameter F rs is added to describe the maximum change of the root to shoot allocation ratio. For F rs we assume no response delay following thinning because less carbon is needed for building fine and coarse roots. The growth of the stem and leaf pools are stimulated to

capture the opened crown space. The effect of F rs – the maximum change in the root to shoot allocation ratio – declines towards zero within the given time span Dact—the actual duration of the thinning effect (see Fig. 6B). This may be expressed as: 8  F rs ðDact  tÞ < 1 ; 0  t  Dact f rs ðtÞ ¼ (2) 100  Dact : 1; t > Dact where f rs gives the functional behavior of F rs over time, and t is the time in years after thinning. For the maximum change in the stem to leaf allocation ratio F sl we assume a lag phase (Ddelay) prior to the full effect, a constant phase (Dconst) for the full growth response, and a linear decline towards zero with increasing time since thinning—Dact (see Fig. 6C). The formal description of

Fig. 6. (A) Exponential function (dashed line) relating thinning intensity to the actual duration of the thinning response (Dact) for a maximum thinning duration of Dmax = 20 years. The stepwise increments (solid line) reflect the model implementation where Dact is rounded to the next integer. (B) Linear decline of the change vs. unthinned conditions in above to below ground allocation ratio implemented for Frs. (C) Scheme of the change in the stem to leaf carbon allocation ratio vs. unthinned conditions with delay phase (Ddelay) the constant phase (Dconst) of maximum allocation change, and the decline towards zero. Note that Ddelay is 1 year for spruce and 3 years for beech, respectively.

Fig. 7. Example of modeled changes in carbon allocation patterns after thinning 9.5% of the aboveground woody biomass resulting in 10 years of actual duration of thinning effects. (A) Norway spruce and (B) common beech.

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this behavior over t (the time in years after thinning) is given as: 8  F sl > > 1 þ ; > > < 100  f sl ðtÞ ¼ F sl ðDact  tÞ > 1 þ ; > > ð100  Dconst ÞðDact  Ddelay Þ > : 1;

Ddelay  t < Ddelay þ

Dconst ðDact  Ddelay Þ 100

Dconst ðDact  Ddelay Þ < t  Dact 100 0  t < Ddelay _ t > Dact Ddelay þ

This approach considers a temporary allocation change following thinning and addresses our third principle—forest growth response to thinning starts with a time lag, reaches a peak and declines towards zero. This temporary behavior is addressed by five parameters: the first is Dmax which together with the thinning intensity affects the actual duration of the thinning impact. The two parameters, F rs and F sl, give the maximum change of carbon allocation ratios for above/below ground and stem/leaf biomass. The two remaining parameters govern the temporal development of thinning impacts, i.e. Ddelay in years and Dconst in percent. Dconst is transformed in years according to the following expression Dconst ðDact  Ddelay Þ 100

evident: (i) at the beginning (F rs = F sl = 0%) volume increment is underestimated by 33.8%; (ii) as the parameters

(3)

F rs and F sl increase the underestimation of volume increment decreases and a set of F rs and F sl combinations (see Fig. 8A, bold line) exists where predictions are equal to the observations.

(4)

A conceptual example of these changes and how they may affect the modeled carbon allocation for Norway spruce and common beech is given in Fig. 7. It follows principles derived from growth and yield studies which are implemented in tree growth models to explicitly address forest growth response to varying thinning intensities (Monserud, 1975; Pretzsch et al., 2002; Hasenauer, 2006). 4.3. Model calibration For each tree species we chose data from the most eastern and the most western region to calibrate the new dynamic allocation model. The chosen plots were from the Lehrforst and Elmstein for common beech, and the Lehrforst as well as Frauenwald/Hirschlacke for lowland Norway spruce (see Fig. 2). For highland Norway spruce, no plots for model calibration were selected because (i) only three regions were available and (ii) it seems plausible to assume that the conceptual thinning response may be similar regardless of the spruce variant. For this study, we chose an exponential coefficient of C = 15 for the increase in actual duration Dact versus thinning intensity (see Eq. (1)). This assumes that maximum duration Dmax is reached at a thinning intensity of 45% (see Fig. 6A). Dmax of 20 years and the delay period Ddelay of 1 year for spruce and 3 years for beech are obtained from the literature (Wiedemann, 1942; Assmann, 1970; Spiecker, 1991; Pretzsch et al., 2002; Hasenauer, 2006). For spruce no constant phase of changed stem/leaf ratio is used and a linear decline similar to the root/shoot changes (see Fig. 6B, and C) is assumed. By varying the remaining two parameters (F rs and F sl, outlined in Fig. 8A) the following situations are

Fig. 8. Mean error of predictions with different values for the parameters of allocation change from root to shoot (Frs) and stem to leaves (Fsl). The interception lines with the 0% error plane indicate possible combinations of Frs and Fsl. The dotted lines give the standard errors for the allocation parameter combinations. (A) Norway spruce and (B) common beech.

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333

Fig. 9. (A) Predicted vs. observed volume increments after thinning for the improved (with allocation change) model. The predictions are derived by converting the stem carbon output of the BGC model to volume growth per hectare using the conversion factors given in Pietsch et al. (2005). Data from the 60 plots including 72 growth periods following thinning are presented. (B) Trend analysis of standardized increment residuals (Std. incr. res., i.e. predicted minus observed divided by the standard deviation of the observations) vs. predictor, thinning intensity, stand age, basal area, dbh, and site index.

Within these range of values we chose F rs = 90% and F sl = 86% since these combinations exhibited the smallest variation (SE = 6.3%, see Fig. 8A dotted line). Note that values for F rs > 90% were excluded because they would result in unrealistically low allocation rates for the root compartments. For beech the general model settings assumed no allocation changes due to thinning (F rs = F sl = 0%) resulting in an underestimation of volume increment rates by 31.8%. Varying the parameters F rs (maximum change of the allocation ratios for root/shoot) and F sl. (maximum change of the allocation ratios for stem to leaf) resulted in biased predictions. Since no period with 0% error was evident (Fig. 8B, medium grey surface) we

successively increased the constant phase of the stem/leaf allocation ratio until an intersection occurred at a Dconst of 80% of the total duration (Fig. 8B, light grey surface). Along the intersection (see Fig. 8B, bold line) the values F rs = 90% and F sl = 120% exhibited the smallest variation (SE = 6.7%, see Fig. 8B dotted line). Values for F rs > 90% were excluded to avoid unrealistically low allocation rates to the root compartments. 4.4. Model validation We applied the developed dynamic allocation model to assess the accuracy and precision of the resulting model

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Table 4 Summary statistics of the validation test using the new forest management sub-module only for those growth periods following thinning which were not used for model calibration Nobs

Obs (m3/(ha year))

Di (m3/(ha year))

SD (m3/(ha year))

t

W

Spruce—lowland Spruce—highland All spruce plots Common beech

17 22 39 33

21.0 17.6 19.1 8.0

1.9 0.1 0.8 0.4

7.4 5.8 6.5 2.7

1.0 0.1 0.7 0.9

0.95 0.97 0.98 0.99

Summary

72

14.0

0.2

5.1

0.4

0.95*

Dti (m3/(ha year))

0.0

CI (m3/(ha year))

PI (m3/(ha year))

TI (m3/(ha year))

5.6 . . . +1.9 2.5 . . . +2.6 2.9 . . . +1.3 0.5 . . . +1.4

17.9 . . . +14.2 12.3 . . . +12.4 14.1 . . . +12.6 5.2 . . . +6.0

22.9 . . . +19.2 15.6 . . . +15.7 16.8 . . . +15.2 6.4 . . . +7.3

0.7 . . . +0.7

5.4 . . . +5.3

6.2 . . . +6.2

The predicted values are derived by converting the stem carbon output of the BGC model to volume growth per hectare using the conversion factors given in Pietsch et al. (2005). Nobs is the number of observations given by the available growth periods following thinning interventions, obs is the mean of the observations, Di the mean of the differences between predicted vs. observed volume growth, SD the standard deviation of the differences, t is the calculated t-value derived from a paired ttest, W is the calculated W-value of the differences derived from Wilk’s test for normality (Shapiro and Wilk, 1965, * indicates significant difference from normality), Dti is the trimmed mean of the differences and CI, PI, and TI the confidence, prediction, and tolerance intervals. CIp=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Di  SDtffi1(a/2),(n1)n1/2 (Reynolds, 1984) or pare ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Dti  S0D t1ða=2Þ;ðn1Þ n1=2 (Rauscher, 1986), PI ¼ Di  1 þ ð1=nÞSD t1ða=2Þ;ðn1Þ (Reynolds, 1984) or Dti  1 þ ð1=nÞS0D t1ða=2Þ;ðn1Þ (Rauscher, 1986), TI = Di  SDg1y,n,1a (Reynolds, 1984) or Dti  S0D g1g;n;1a (Rauscher, 1986) depending on the normality of the errors. n is the number of observations, t1(a/2), n1 the 1  a/2 quantile from the t-distribution with n  1 degrees of freedom and g1g,1a the tolerance factor for the normal distribution accounting for the probability that (1  g) 100% of the distribution D is within a probability of 1  a (for statistical tables see e.g. Sachs, 1999). The trimmed mean errors Dti and the jackknifed variance estimates S0D as well as confidence CI, prediction PI, and tolerance intervals TI for errors that do not follow the normal distribution as indicated with a significant W-value are calculated after removing the lower and upper 10% of the observations.

predictions using plot data not used for model calibration: i.e. Hain/Rothenbuch, Fabrikschleinbach and St. Leonhard for common beech; Litschau, Ottenschlag and Arnoldstein for lowland Norway spruce and Gmunden, Mittersill and Neuberg for highland Norway spruce. For spruce we calibrated the new sub-module only with data from lowland experimental plots. Next, we were interested if the dynamic allocation model for spruce fits to both variants (lowland and highland). The resulting prediction produced unbiased and consistent results for the spruce growing in low and high elevations (cf. Fig. 2 and Table 2). Fig. 9A gives the differences between predicted versus observed volume increments from all validation plots. For the improved model no trends in residuals were evident (see Fig. 9B). We statistically validated our model enhancements by evaluating the range of errors and limits from the confidence, prediction and tolerance intervals calculated according to Reynolds (1984) and Rauscher (1986). The results exhibit that the enhanced model produces unbiased and consistent results for all species (see Table 4). 5. Discussion Large-scale ecosystem models such as BIOME BGC assume fully stocked even aged forests and are not designed to be sensitive to forest management impacts. Applying a management intervention keeps the external driving forces (i.e., climate) unchanged but the pool sizes of the vegetation biomass are affected (e.g., reduced). Consequently, thinning enhances the influx into vegetation biomass (see Fig. 3) and increases growth efficiency as a result of higher nitrogen use efficiency (see Fig. 4). According to our Monte-Carlo simulations these physicochemical reactions are an intrinsic property of the model (see Fig. 3). Standard model settings are developed for fully stocked even-aged forests and do not sufficiently address the observed growth response due to thinning (see Fig. 5). The observed surplus in growth reflects the biological component of

ecosystem changes. Individuals react to environmental change with physiological adaptation. For example, trees change their pattern of the assimilate distribution among the different compartments as it is evident from changes in the height to diameter relationship due to thinning (Pretzsch et al., 2002). In statistical tree growth models these changes are derived from measurements based on a large number of sample trees (Pretzsch et al., 2002; Hasenauer, 2006), and hence include the biological reaction in the changed allocation pattern. In large-scale mechanistic models, stand structural components are not included. The expected change in growth response to changing stand density is species specific. This confirms that the species-specific parameters as given in Pietsch et al. (2005) were an important pre-condition for testing the sensitivity of BGC-model applications to management interventions. The response to changing stand density may be divided into two factors: (i) physico-chemical reactions which suggest that more resources (nutrients and water) are available for each remaining tree because the total amount per unit area does not change (this may lead to higher growth rates of the remaining individuals versus the growth of unthinned stand conditions) and (ii) that trees adjust their physiological program according to the improved growing conditions. For instance, reduced competition enables trees to favor the growth of above versus below ground biomass growth (Mooney and Winner, 1991). After adopting the allocation routine by developing a submodule for forest management, the simulation output resulted in consistent and unbiased predictions (Table 4 and Fig. 9) versus the original model settings (Table 3 and Fig. 5). The management subroutine exhibits no trends between predicted minus observed volume increments versus thinning intensity, the basal area and the site index (Fig. 9B). While our model improvements produced unbiased and consistent estimates, the original model settings produced biased predictions (Fig. 5 and Table 3) since forest growth response to changes in stand density is not explicitly defined.

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The validation results for highland spruce suggest that although two different parameterizations are needed to describe the physiological program of lowland and highland varieties (Pietsch et al., 2005), their reaction to thinning is equally well covered by the calibration of the sub-module. This indicates that the physiology of spruce varieties differ according to site conditions, but the genetic program governing the reactions to changes in competition situation seems to be the same. Although a demand driven model of carbon allocation (Bartelink, 1998) would be desirable, our approach is a promising step to address stand density related changes in growth. For a demand driven approach more data on changes in resource availability would be needed. The consideration of forest management within large-scale biogeochemical-mechanistic modeling (BGC-models) is important because it extends the applicability of the model from unmanaged and fully stocked to managed forests. Considering the situation in Central Europe, forest management is still the main driving factor for growth variations (Kauppi et al., 1992). The enhancements presented in this study addresses these needs and allow us to analyze impacts of management strategies as they may affect pools and fluxes for a given forest ecosystem. The result of our work is an important step to improve the reliability of model predictions. It is evident that forest management influences timber production but it also affects carbon sequestration, transpiration rates and stand nutrient balance. Although we were unable to investigate and validate these important physiological effects due to the lack of data, our research provides a consistent and reliable framework based on empirical data from forest growth and yield experiments. Acknowledgements This research is part of the project Biogeochemical Forest Ecosystem Modeling in Austria funded by the Austrian Ministry of Agriculture, Forestry, Environment and Water as well as the Austrian Ministry of Science and Technology. We thank Hans Pretzsch, Chair of Forest and Yield Sciences, TU Munich, BRD for providing the experimental sites from Germany, Hubert Sterba for the data from the famous Hirschlacke site, and Markus Neumann from the Federal Research and Training Centre for Forests, Natural Hazards and Landscape (BFW) for providing the beech plots from St. Leonhart. Thanks to the Austrian and German National Weather Centers, for providing the regional climate records. Helpful review comments were provided by Bruce Michie and the two anonymous reviewers. References Aber, J.D., Botkin, D.B., Melillo, J.M., 1978. Predicting the effects of different harvesting regimes on forest floor dynamics. Can. J. For. Res. 8, 306–315. Assmann, E., 1970. The Principles of Forest Yield Study. Pergamon Press, New York, p. 506. Bartelink, H.H., 1998. A model of dry matter partitioning in trees. Tree Physiol. 18, 91–101.

335

Berger, T.W., Neubauer, C., Glatzel, G., 2002. Factors controlling soil carbon and nitrogen stores in pure stands of Norway spruce (Picea abies) and mixed species stands in Austria. For. Ecol. Manage. 159, 3–14. ¨ sterreichische Waldboden-ZusEnglisch, M., Karrer, G., Mutsch, F. 1992. O tandsinventur. Teil 1: Methodische Grundlagen. Mitt. Forstl. Bundesversuchsanst. Wien, 168, 5–22. Farquhar, G., von Caemmener, S., Berry, J., 1980. A biochemical model of photosynthesis CO2 fixation in leaves of C4 species. Planta 149, 78–90. Hasenauer, H. 1994. Ein Einzelbaumwachstums-Simulator fu¨r ungleichaltrige Fichten-Kiefern- und Buchen-Fichtenmischbesta¨nde. Forstliche Schriftenreihe Universita¨t fu¨r Bodenkultur Wien, p. 152. Hasenauer, H., Burkhart, H.E., Amateis, R.L., 1997. Basal area development in thinned and unthinned loblolly pine plantations. Can. J. For. Res. 27, 265– 271. Hasenauer, H., Merganicˇova´, K., Petritsch, R., Pietsch, S.A., Thornton, P.E., 2003. Validating daily climate interpolations over complex terrain in Austria. Agric. For. Meteorol. 119, 87–107. Hasenauer, H., 2006. Sustainable Forest Management: Growth Models for Europe. Springer, Berlin, p. 398. Hix, D.M., Barnes, B.V., 1984. Effects of clear-cutting on the vegetation and soil of an eastern hemlock dominated ecosystem, western Upper Michigan. Can. J. For. Res. 14, 914–923. Holland, E.A., Dentener, F.J., Braswell, B.H., Sulzman, J.M., 1999. Contemporary and pre-industrial global reactive nitrogen budgets. Biogeochemistry 46, 7–43. IPCC WGI, 1996. Technical summary. In: Houghton, J.T., Meira Filho, L.G., Callander, B.A., Harris, N., Kattenberg, A., Maskell, K. (Eds.), Climate Change 1995—The Science of Climate Change: Contribution of the Working Group I, to the Second Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, U.K., pp. 9–50. Kauppi, P.E., Mielika¨inen, K., Kuusela, K., 1992. Biomass and carbon budget of European forests, 1971–1990. Science 256, 70–74. Kenk, G., 1998. Behandlung von fichten und Durchfortungsergebnisse. AFZ. Der Wald 8, 420–421. Kennel, E. 1973. Bayerische Waldinventur 1970/71, Inventurabschnitt I: Großrauminventur, Aufnahme- und Auswertungsverfahren. Mu¨nchen, Forstliche Forschungsanstalt Mu¨nchen. p. 143. Kramer, H., 1988. Waldwachstumslehre. Paul Parey, Hamburg, Berlin, p. 374. Krapfenbauer, A., 1983. Von der Streunutzung zur Ganzbaumernte. Centralblatt fu¨r das gesamte Forstwesen 100, 143–174. Krapfenbauer, A., Buchleitner, E., 1981. Holzernte, Biomassen- und Na¨hrstoffaustrag Na¨hrstoffbilanz eines Fichtenbestandes. Centralblatt des gesamten Forstwesen 98, 193–223. Mayer, H., 1974. Wa¨lder des Ostalpenraumes. Gustav Fischer Verlag, Stuttgart, p. 344. Merganicˇova´, K., Pietsch, S.A., Hasenauer, H., 2005. Testing mechanistic modelling to assess impacts of biomass removal. For. Ecol. Manage. 207, 37–57. Monserud, R.A. 1975. Methodology for simulating Wisconsin northern hardwood stand dynamics. Ph.D. Thesis. University of Wisconsin, Madison, p. 156. Monserud, R.A., Sterba, H., 1996. A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria. For. Ecol. Manage. 80, 57–80. Mooney, H.A., Winner, W.E., 1991. Partitioning response of plants to stress. In: Mooney, H.A., Winner, W.E., Pell, E.J. (Eds.), Response of Plants to Multiple Stresses. Academic Press, San Diego, pp. 129–141. Petritsch, R. 2002. Anwendung und Validierung des Klimainterpolationsmo¨ sterreich. Master thesis, University of Natural dells DAYMET in O Resources and Applied Life Sciences, Vienna, p. 95. Pietsch, S.A., Hasenauer, H., 2002. Using mechanistic modelling within forest ecosystem restoration. For. Ecol. Manage. 159, 111–131. Pietsch, S.A., Hasenauer, H., 2006. Evaluating the self-initialization procedure of large scale ecosystem models. Global Change Biol. 12, 1658–1669. Pietsch, S.A., Hasenauer, H., Kucˇera, J., Cˇerma´k, J., 2003. Modeling effects of hydrological changes on the carbon and nitrogen balance of oak in floodplains. Tree Physiol. 23, 735–746.

336

R. Petritsch et al. / Forest Ecology and Management 242 (2007) 324–336

Pietsch, S.A., Hasenauer, H., Thornton, P.E., 2005. BGC-model parameters for tree species growing in central European forests. For. Ecol. Manage. 211, 264–295. Pretzsch, H., 2005. Diversity and productivity in forests: evidence from longterm experimental plots. In: Scherer-Lorenzen, M., Ko¨rner, Ch., Schulze, E.-D. (Eds.), Forest Diversity and Function: Temperate and Boreal Systems. Springer, Berlin/Heidelberg, pp. 41–64. Pretzsch, H., Biber, P., Dursky, J., 2002. The single tree-based stand simulator SILVA: construction, application and evaluation. For. Ecol. Manage. 162, 3– 21. Rauscher, H.M., 1986. The microcomputer scientific software series 4: testing prediction accuracy. U.S. For. Serv. Gen. Tech. Rep. NC-107, 23. Reynolds, M.R., 1984. Estimating the error in model predictions. For. Sci. 30, 454–469. Ryan, M.G., 1991. Effects of climate change on plant respiration. Ecol. Appl. 1, 157–167. Sachs, L. 1999. Angewandte Statistik, 9th ed., p. 881.

¨ sterreich. UmweltSchneider, J. 1998. Kartierung der nassen Deposition in O bundesamt Wien, p. 24. Schulze, E.D., Freibauer, A., 2005. Carbon unlocked from soils. Nature 437/ 438, 205. Shapiro, S.S., Wilk, M.B., 1965. An analysis of variance test for normality (complete samples). Biometrika 52, 591–611. Spiecker, H., 1991. Zur Dynamik des Wachtums von Tannen und Fichten Plenterwaldversuchsfla¨chen im Schwarzwald. AFZ 21, 1076–1080. Thornton, P.E., Law, B.E., Gholz, H.L., Clark, K.L., Falge, E., Ellsworth, D.S., Goldstein, A.H., Monson, R.K., Hollinger, D., Falk, M., Chen, J., Sparks, J.P., 2002. Modeling and measuring the effects of disturbance history and climate on carbon and water budgets in evergreen needleleaf forests. Agric. For. Meteorol. 113, 185–222. White, E.H., 1974. Whole-tree harvesting depletes soil nutrients. Can. J. For. Res. 4, 530–535. Wiedemann, E., 1942. Der gleichaltrige Fichten-Buchen-Mischbestand. Mitt. Forstwirtsch. Forstwiss. 13, 1–88.