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Key message By calibrating and validating a forest growth model for seven species in Germany and coupling it with a wind damage simulator, we specifically estimated the impact of wind damage on the net present value of Norway spruce and European beech in mixture and monoculture. Under risk, the net present value of spruce managements saw the sharpest declines, although the highest end net present value was still obtained through a heavily thinned spruce monoculture. Context Wind damage is one of the most important risks to Central European forests, and adaptation measures are essential. Aim Adaptive management strategies should simultaneously account for forest production and wind risk. We simu- lated the effect of adaptive measures on wind-risk in German forests. Methods A process-based forest growth model, “3-PG Mix”, was recalibrated and coupled with the storm damage risk model “Lothar”. We investigated the effect of thinning regimes on wind risk in monoculture and mixed species stands. The net present value of the simulated regimes was calculated and compared (risk vs. no risk). Results Spruce regimes achieved the highest net present values when risk was not considered. Considering risk in −1 spruce and beech mixtures and monoculture, all regimes reached values below 3000 € ha by year 120. The excep- −1 tion was a heavily thinned spruce monoculture at 4507 € ha , being the most profitable regime under risk. Conclusion We conclude, on the basis of this modelling study, that heavy thinning reduced storm risk and main- tained a higher net present value in spruce. Species mixture of beech and spruce saw net present values levels remain more constant under risk, while beech monoculture increased. Keywords 3-PG, Forest growth modelling, Forest wind damage, Climate change, Mixed forest Handling editor: Alexia Stokes. This article is part of the topical collection on "Risks of (not) adapting - Socio- ecological conflicts in forest management: risks of (not) adapting?" *Correspondence: Robin Bourke robin.bourke@ife.uni-freiburg.de Full list of author information is available at the end of the article © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. Bourke et al. Annals of Forest Science (2023) 80:19 Page 2 of 36 applied to estimate carbon sequestration in Sitka spruce 1 Introduction (Picea sitchensis) plantations in Scotland (Minunno et al. 1.1 P rocess‑based modelling and model description 2010). The model has also been calibrated for broadleaf Empirical yield and growth models have been devel- species such as birch (Betula spp.) (Potithep and Yasuoka oped and used to predict forest growth and productivity 2011) and European beech (Fagus sylvatica L.) in Baden- while assuming stable climatic conditions. In contrast Württemberg (Augustynczik et al. 2017), as well as for to empirical models, process-based forest growth mod- European beech and Norway spruce (Picea abies (L.) H. els estimate the physiological processes in the develop- Karst) by Trotsiuk et al. (2020) in Switzerland to reflect ment of forest stands, sensitive to changes in climatic the local growth conditions. Nölte et al. (2020) made a conditions, rather than generating results based on calibration for sessile oak (Quercus petraea (Matt.) Liebl.) measured growth from forest inventory data. The pro - in Germany, and a more comprehensive calibration of the cesses contributing to the growth of biomass are mod- main European tree species was carried out by Forrester elled through fitted functions, such as gross primary et al. (2021), utilising data from Switzerland. production, canopy conductance and transpiration. By 3-PG mix is an expansion to the model 3-PG which modelling these processes, it is possible to make plausi- accounts for deciduous and mixed species stands (For- ble estimations of future forest growth under changing rester and Tang 2016). 3-PG mix includes an expanded climate (Landsberg and Sands 2011) and make adaptive canopy and light absorption model and accounts for the decisions to safeguard main forest processes and func- dormant season of deciduous species and diameter dis- tions (Yousefpour et al., 2012). The process functions tributions of the given species. The ability to mix tree are defined by parameters which are dependent upon species makes 3-PG mix appropriate to German forests, local factors such as soil water content, soil fertility where a number of species and age classes need to be and climatic variations, which influence the projected represented in a single stand to provide a realistic repre- growth of the biomass. sentation of the forest composition and development. The process-based forest growth model “3-PG” (Lands - berg and Waring 1997, see Appendix, Table 2 for list of 1.2 Mixed forest stands and forest disturbances all abbreviations) has been chosen as the model to repre- Establishment of mixed forest stands has been widely sent the forest stand development in Germany because of recognized among adaptive measures as safeguarding its ability to predict biomass growth under changing cli- forest processes and functions under climate change matic conditions (in terms of precipitation, temperature (Pretzsch et al., 2017). Moreover, mixed stands have been and atmospheric CO and management). In addition, the shown to be important in the mitigation of economic 3-PG model is freely available, simple enough to require consequences of climate change. For example, mixed few inputs but also complex enough to react to variations stands of spruce and beech were shown to be more in climatic, soil and species, inter alia. It is also relatively robust to disturbances than pure stands, as well as the simple to parameterise for various forest types and has effects of stand mixtures on stand resistance, which can been validated for the functioning of its sub-models (For- have high economic importance (Friedrich et al. 2019). rester et al. 2020). However, there are potential limitations and strengths to 3-PG was initially used in Oceania and the USA to forest diversification, in the sense that diversification can quantify the effects of climate variation on forest biomass reduce economic risk and improve multi-functionality, growth (Landsberg & Waring 1997; Coops et al. 1998; but multi-functionality can also come at the price of eco- 2001) and was utilised for numerous species, includ- nomic losses (Knoke et al. 2017). Therefore, an evaluation ing conifers (Pinus; Pseudotsuga spp.) and broadleaves of various scenarios of forest growth under future climate (Eucalyptus; poplar) (also see Gupta & Sharma 2019 for change conditions is needed to assess the most promising complete overview). The model has been used extensively management strategies in the future. for modelling of Eucalyptus plantations without the need Forest disturbances also play a major role in defin - to conduct extensive ground measurements in temper- ing forest conditions and their growth. Therefore, it is ate and later tropical conditions (Landsberg and Waring crucial to integrate forest disturbances in the modelling 1997; Almeida et al. 2009). 3-PG has also been used to of forest processes. Wind is the most important distur- estimate the effects of climate on site productivity over bance agent in Germany, causing large-scale damages, time (Waring et al. 2014) and the effect of tree age on e.g. the Wiebke, Lothar and Kyril storms which occurred carbon storage (Zhao et al. 2009). For coniferous species, in the years 1990, 1999 and 2007 respectively (Jung et al., it has been used to estimate possible variation in tree 2016). Wind risk can be mitigated by manipulation of growth, due to climate variation, from such species as individual tree diameter and is our chosen method of Douglas fir (Pseudotsuga menziesii (Mirbel)) (Coops et al. assessing storm damage risk, as suggested by Mason and 2010) and Pinus taeda (Bryars et al. 2012) and has been B ourke et al. Annals of Forest Science (2023) 80:19 Page 3 of 36 Valinger (2013). Following on from previous studies (Zell of diameter, height and BA were derived from empiri- and Hanewinkel 2015; Gardiner et al. 2016; Müller et al. cally modelled growth functions (Schmidt et al., 2020). 2019), we implement a wind disturbance module in 3-PG The growth periods were divided into three different to account for wind in modelling and management of for- age classes of 34 to 64, 64 to 94 and 94 to 119. These age est stands. classes correspond to the time over which the German Having developed the coupled model, we will utilise it National Forest Inventories took place (1987 to 2012) and to test potential management strategies in German for- the progressions of growth in the transect data mirror ests, with a focus on the effect of thinning on storm dam - the growth over this period. age mitigation. We also assess the degree to which 3-PG’s Given that the stem density plays a fundamental role thinning functions allow for estimation of future biomass in the biomass calculations in 3-PG mix, and the stem growth, with and without storm impacts. Consider- number per stand in the calibration data was not avail- ing this, we calculate economic outcomes of the result- able, stem density was derived from the diameter and BA ing management scenarios with the coupled model. The stand values. The progression in stand density with age study is essential to provide process-based decision sup- was then interpreted as stand thinning, where the model port systems for finding economically efficient adaptive reaction to the removal of stems due management in turn solutions for wind prone forests. affects the development of stand biomass. The calibration The main goals of this study are as follows: (1) to cali - and validation process is described in detail in Appendi- brate a process-based model 3-PG to simulate monocul- ces 2 and 3. tures and mixed species stands in Germany, (2) integrate a disturbance module in 3-PG to account for wind dis- 2.2 Storm damage risk model “Lothar” turbances, and (3) evaluate alternative forest composition For the purpose of our analysis, 3-PG mix model was (monoculture vs. mixture) and management strategies integrated with the storm damage risk model “Lothar” (no thinning, BAU thinning, intensive thinning and light (Schmidt et al. 2010). Lothar is a statistical storm damage thinning) to mitigate wind disturbance risk. We analyse model and is based on an empirical dataset of large-scale the forest growth and wind risk of different strategies forest inventories. These inventories were a combination from an economic perspective, observing the best-per- of the German National Forest Inventory Data (1987 and forming strategies. 2002), as well as an inventory carried out in the aftermath of the Lothar storm on 26 December 1999. Through a comparison of standing trees before and after the Lothar 2 Methods storm, the critical wind speed during this storm event 2.1 Modelling approach could be identified (Schmidt et al. 2010). This model For our simulations, the process-based forest growth operates at the individual tree or stand level and uti- model 3-PG mix (Forrester and Tang 2016) was utilised, lises the height and diameter of the trees, as well as four applying Bayesian inference to calculate the param- Topex-to-distance variables (Scott and Mitchell 2005) eter values governing the model’s processes (as per, e.g. available at each stand location. These Topex variables Augustynczik et al. 2017; Trotsiuk et al. 2020; Forrester are sums of the terrain slopes measured in the eight car- et al. 2021). We calibrated a range of species within Ger- dinal directions from the given location. Negative Topex many, so that future analyses can be undertaken with values are the summits of hills or ridges, near-zero val- various mixture compositions. The chosen study areas ues correspond to plains and positive values represent contain a number of climatic and site conditions within valleys or depressions (Schmidt et al. 2010). The output Germany, which require each tree species to be cali- diameter and height distribution vectors from 3-PG mix brated for the range of conditions contained within the are then used as input variables for Lothar. The inputs for country’s national boundaries. The chosen tree species the Topex variables are derived from four separate ras- in this study are European beech, Norway spruce, Scots ter layers from which the stand coordinates indicate the pine (Pinus sylvestris L.), Douglas fir (Pseudotsuga men - relative Topex value. In addition, the model also consid- ziesii), European larch (Larix decidua Mill.), sessile oak ers the coordinates of the stand location, in terms of the and silver fir (Abies alba Mill.). Gauss-Kruger coordinate system, as another factor which The calibration of the model’s tree species mentioned influences the probability of storm damage. The individ - above was carried out using a dataset based on three ual tree species are also divided into categories regarding transects running through regional gradients (e.g. soil their windfirmness. These categories are beech/oak, fir/ type, soil water saturation and climatic condition) in Ger- Douglas fir, pine/larch and spruce. The formula (1) of the many (see Fig. 1). These location-dependent site values Lothar model is given by the following: Bourke et al. Annals of Forest Science (2023) 80:19 Page 4 of 36 Fig. 1 The German growth regions used for the calibration g = Species + log(DBH) + log(h) + TopexToDistance1 + TopexToDistance2 i 1i 2i 3i 4i 5i (1) + TopexToDistance3 + TopexToDistance4 + f (N , E) 6i 7i 2.3 Stand species composition effect where is the damage probability of a given species, In addition, an analysis was undertaken to show the dif- is the species parameter and the four Topex-to-distance ference in growth between a specific species grown in variables are the slope angle sums in the four wind direc- monoculture and mixture. Each species was simulated tions, and the f(N,E) is a smoothing function based on −1 starting with 500 stems ha and ran from 30 to 120 years the stand coordinates (Schmidt et al. 2010). old, except when a species and management-dependent The damage probability generated is also integrated minimum stem density was reached. To test the behav- to 3-PG mix so that it removes the proportion or stems iour of the tree species in mixture, we made simulations relative the given probability. However, this can also considering each species first in monoculture and then in function so that only the probability is provided but mixture with each other species. The additional mixture without the stem removal, in which case the stand does species had the same stem number as the target species, not react to storm damage probability. As with the thin- −1 −1 i.e. 250 stems ha , to a total of 500 stems ha , as for ning function in the 3-PG model, when a storm event monoculture. occurs, foliage, stem and root biomass are removed, We simulated monocultures and mixed stands to which is based on the difference in stem number before wind disturbance and evaluated the storm damage and after the event and the biomass thinning values risk related to the mixture or monoculture growth applied for that species. B ourke et al. Annals of Forest Science (2023) 80:19 Page 5 of 36 attributes. We stocked monocultures with 500 stems 3-PG and, depending on the level of risk, biomass will be −1 ha , and for mixed stands, each species was allocated removed from the foliage, stem and root variables. −1 250 stems ha . Additionally, we evaluated the effect on wind risk based on 4 management strategies, no thin- ning, BAU thinning, heavy thinning and light thinning. 2.5 Net present value calculation In the no thinning strategy, the only removal of stems An economic analysis of the simulated monocultures occurs through mortality or storm damage. All thin- and mixtures and management strategies was carried out ning regimes are carried out in 10-year intervals. The for two common species (Norway spruce and European BAU, heavy and light thinning values were based on beech) in Germany forestry, which can broadly repre- those used by Augustynczik et al. (2020) (which were sent conifer and broadleaf forestry, in order to quantify in turn derived from thinning levels used in the Ger- the relative effectiveness of each scenario considering man National Forest Inventory, in the case of BAU). net-discounted revenue and damage risk. The net present The remaining heavy and light thinning strategies were value was therefore calculated (2) as follows: species-specific stem removal intensities, greater and N t lesser than the BAU strategy respectively. However, NPV (i, N) = (2) t=0 (1 + i) these thinning rates sometimes resulted in the stand being thinned to a level where all stems were removed where t is the stand age, i is the discount rate and R is from the stand. Therefore, we capped the number of the net revenue, considering revenues and costs. We used allowable remaining stems for each species. For mixed timber prices and harvesting costs for Baden-Württem- species, we halved this number for each species. Once berg between 2000 and 2016, as also utilised in Zamora- the capping took place, we then left the stand unman- Pereira et al. (2021) for their economic analysis. We also aged for an additional 40 years, at which point we con- account for wood quality partitions of the analysed spe- sidered to be an end harvest, if the rotation end had cies, according to the yield tables for Baden-Württemberg not already been reached, in order to examine the vol- (Landesforstverwaltung Baden-Württemberg, 1993). We ume and net present value development after thinning. applied a discount rate of 2%. Extracted volume and end Here, we evaluated the influence of these management rotation volume were separated into 10-diameter classes strategies on the growth parameters affecting the wind with a corresponding net revenue per m . The sum of the damage risk, i.e. the height and diameter, as well as the discounted revenues was then calculated to give a net influence of the particular tree species properties on present value for each month of the simulation. In the said risk. We use the Mann–Whitney U-test and T-test case of storm-damaged timber, we consider stems to be to compare the difference in storm damage risk in these removed based on the damage risk probability. Any stems aforementioned cases. removed due to storm damage are consequently deval- ued to half of their value for a given diameter class, as per Müller et al. (2019). A guideline line as to the codes used 2.4 R isk‑moderated biomass growth to for calibration, Lothar model linkage with 3-PG and We compared these risk-modified biomass outputs with net present value calculation are provided in Appendix 5. the biomass outputs not considering risk, in order to The calculations were carried out. determine which management strategies enabled the best performance, with and without wind risk. No climate 3 Results change scenario was considered in this study, in order 3.1 Tree species parameter calibration, validation to evaluate stand growth under “normal” climatic condi- and volume estimation tions. In order to relate the wind damage risk to poten- The final derived parameter set is shown in Appendix tial biomass growth, we simulated the same management Table 4. In Fig. 2, in some cases, the prior parameters strategies and mixtures, but the biomass outputs were performed better; however, for the majority, there was moderated by the risk probability, updated on an annual improvement, when comparing the prior parameter set time scale. The P-value was considered to be a frac - with the posterior in estimating the calibration data. The tion of stems removed by a storm event. A comparable greatest improvement was the BA estimation of Scots method was also utilised by Müller et al. 2019, where the pine, which saw increases in the range of > 40%. The BA Lothar model was also utilised to calculate percentages of of Douglas fir in contrast saw a greater part of the spread removed timber from forest stands after a storm event. in the negative area of the x-axis, the widest outlier In this way, the removed biomass from a storm event being < − 25%. However, the overall spread of this variable functions in the same manner as the thinning function in Bourke et al. Annals of Forest Science (2023) 80:19 Page 6 of 36 Fig. 2 The differences in PBias between the prior parameter set and the posterior. The tree species are shown along with BA, DBH and height values. In this case, the X-axis shows the difference between the initial parameter set (from Forrester et al. 2021) and the parameters derived from the calibration. The negative range of the X-axis indicates where the derived parameters made inferior estimations of the variables and the positive range where the estimations were superior. On the zero line, there was neither improvement nor worsening of the performance is ~ 45%, with a median value at the origin of the x-axis, so the height estimation of Douglas fir is the most uncertain of the height estimations. The height of Norway spruce and Scots pine, while also uncertain (ranges of > 35% & Table 1 Mean percentage bias (Pbias) and standard 45%, respectively), their distribution is negatively skewed. deviation (SD) values for the plots used for validation of DBH, Apart from the BA and height of Douglas fir, all median height, basal area, and volume, as well as the mean of all four values showed an overall reduction in the bias. biases Error bias is an important tool to indicate the reliabil- DBH % Height BA % Volume % Mean % ity in the prediction of a given output variable, where the percentage bias shows the accuracy of the estimation of Spruce Pbias + 1.0 + 13.0 + 4.2 − 2.5 + 3.9 an output variable and the standard deviation given the Spruce SD 14.1 24.9 33.0 30.9 25.7 precision of the bias calculation. In Table 1, silver fir Beech Pbias + 3.3 + 6.7 − 28.3 − 26.5 + 11.2 shows the highest DBH bias, while the lowest DBH bias Beech SD 39.6 18.1 23.9 33.1 28.7 was in Norway spruce. For height, the highest was sessile Douglas fir + 3.5 + 10.6 − 24.6 − 5.7 − 4.0 oak, and the lowest was Silver Fir. For BA, the largest bias Pbias was in beech, and the lowest was sessile oak, and Euro- Douglas fir SD 10.9 26.1 39.9 14.3 22.8 pean larch had the highest volume bias and spruce the Larch Pbias + 5.6 + 8.8 + 21.1 + 31.7 + 16.8 lowest. Taking a mean of all four of the output variables, Larch SD 11.8 8.1 26.4 36.7 20.7 European larch had the highest mean bias and Douglas Silver fir Pbias + 9.2 + 2.1 + 84 + 13.0 + 8.2 fir the lowest. To speak of the deviations in the bias for Silver fir SD 18.1 9.1 23.7 9.2 15.0 each species, the species with the highest mean deviation Pine Pbias − 3.3 − 7.4 + 4.5 − 23.6 − 7.4 was Scots pine, and the lowest was silver fir. The largest Pine SD 30.1 14.7 65.7 59.6 42.5 deviations in the data came from BA and volume of pine, Oak Pbias + 7.4 − 18.5 + 2.4 − 20.8 − 7.4 while the lowest were the heights of larch and oak. Oak SD 25.6 4.5 31.7 31.3 23.3 B ourke et al. Annals of Forest Science (2023) 80:19 Page 7 of 36 Fig. 3 The four thinning regimes, with their related volume growth, are shown for beech monoculture (black), spruce monoculture (blue) and beech/spruce mixture (grey). The y-axis shows the extracted volume, and the x-axis shows the stand age from 30 to 120 years old. In the thinning regimes, extraction occurs in 10-year intervals until a minimum stem number is reached Additional results of the calibration and validation are The extracted volume is shown in Fig. 4, and of the three shown in Appendix Figs. 17 and 18. regimes, light thinning spruce monoculture also resulted 3 −1 In Fig. 3, both for monoculture and mixture, the no- in the highest level of extracted volume at 539 m ha 3 −1 thin regime had the highest volume at the end of the followed by BAU mixture at 490 m ha . 3 −1 rotation, 1011 m ha (beech), 869 m3 ha-1 (spruce) and Additional growth projections of the remaining spe- 3 −1 1535 m ha (mixture). For the other three regimes, total cies in mixture with beech can be found in Appendix monoculture and mixed volume achieved similar levels. Figs. 19–26. Bourke et al. Annals of Forest Science (2023) 80:19 Page 8 of 36 Fig. 4 The extracted volume of the three thinning regimes is shown for beech monoculture (black), spruce monoculture (blue) and beech/spruce mixture (grey). The y-axis shows the extracted volume, and the x-axis shows the stand age from 30 to 120 years old. Thinning occurs in 10-year intervals until a minimum stem number is reached 3.2 “L othar” model coupling tends to be in upper range, ~ 0.2–0.75, and further south, Figure 5 makes evident how beech, oak and pine display the range is rather ~ 0–0.2. Our analysis falls into the lat- the overall lowest storm damage risks, while Douglas ter category since the site coordinates for the plot used fir and Spruce have overall the highest. As can be seen are easting 3,460,000 and northing 5,380,000. in the figure, the higher risk species do not exceed a 0.25 Appendix Figs. 27 and 28 show the storm risk plot- P-value. This is consistent with Schmidt et al. (2010), ted against the height for the four thinning types in mix where the sensitivity analysis of the site coordinates of and monoculture simulations of beech and spruce, as the “Lothar” model shows a strong north/south gradi- well as the other species. The maximum height reached ent in the P-value. The P-value range further to the north depends on the management type in this case, but the B ourke et al. Annals of Forest Science (2023) 80:19 Page 9 of 36 Fig. 5 The progression of storm risk (p-value, y-axis) with age (30–120 years, x-axis) in no thin monoculture stands of the given species. Species are delineated by colour: beech, black; Douglas fir, blue; Silver fir, green; larch, red; oak, grey; pine, yellow; spruce, purple Fig. 6 The four regimes (BAU, heavy, light & no thin) compared when modified by storm damage for beech monoculture (black), spruce monoculture (blue) and beech/spruce mixture (grey). The y-axis shows the extracted volume, and the x-axis shows the stand age from 30 to 120 years old highest risk at a given height is more associated with monoculture stands with intense thinning. The no-thin the no-thinning monoculture and mixed simulations, strategy in both monoculture and mix holds the higher while the least risk at a given height tends towards the level of risk. This is especially true for spruce, whereas Bourke et al. Annals of Forest Science (2023) 80:19 Page 10 of 36 Fig. 7 The four regimes with their related extracted and salvaged volumes compared when modified by storm damage for beech monoculture (black), spruce monoculture (blue) and beech/spruce mixture (grey). The y-axis shows the extracted volume, and the x-axis shows the stand age from 30 to 120 years old Fig. 8 Net present value (NPV, y-axis) in €/ha progression over time (stand age, x-axis) for spruce monoculture (green), beech monoculture (orange) and beech/spruce mixture (blue), considering BAU, intensive and light thinning and a no-thin regime. Large vertical jumps in the NPV represent where a higher value diameter class has been reached B ourke et al. Annals of Forest Science (2023) 80:19 Page 11 of 36 Fig. 9 NPV (y-axis) progression over time (x-axis) for spruce monoculture (green), beech monoculture (orange) and beech/spruce mixture (blue), considering BAU, intensive and light thinning and a no-thin regime, where stems are removed based on storm damage risk. Large vertical jumps in the NPV represent where a higher value diameter class has been reached. Sharp drops in the NPV indicate where storm risk has removed stand volume in both cases, the heavy thinning strategy has an overall under heavy thinning. When considering extracted vol- lower risk level. It is also clear that at a relative height, ume however, mixed regimes perform better in terms of the wind damage susceptibility of spruce is far higher volume, while monoculture has less extracted volume. than of beech. In addition, the degree of increase in In Fig. 7, mixture also had the highest level of salvaged risk with height increase is much more pronounced and extracted volume in all cases. Due to effect of volume in spruce than it is in beech. In Appendix Fig. 27, it removed by the effect of storm damage, a large amount of can also be seen that, while that there is a difference volume is removed in the no-thin regime also. Here, the between the risk level of beech in mixture and mono- mixed strategies emerge with the highest volume extrac- culture at a given height, the management strategy used tion in all strategies. Heavily thinned spruce has the sec- plays a more decisive role in differentiating the risk ond highest volume at the end of 120 years. level. Intensive thinning yields the lowest risk in this case, while light thinning yields the highest risk of the thinning regimes. However, when observing the same 3.3 Economic evaluation figure, we see that beech mixed compared with beech In Fig. 8, beech and spruce monoculture are com- monoculture has uniformly the lowest risk when an pared with a 50/50 mixture of spruce and beech with intensive thinning is applied. the same total stem number, as was the case for the no- In Fig. 6, the total volume of high thin is virtually iden- risk volume projections above. Spruce is a very favour- tical to the monoculture until 120 years old. For the no- able option in this case, as even though its value declines thin regime and BAU, the spruce monoculture had the after ~ 80 years, it stays the most profitable species until 3 −1 highest end volume at 611 m ha . The extracted and the end. The mixture is the middle-ground strategy. We storm volume of the same stand are shown in Fig. 7, and see that beech is the least desirable species and remains considering storm damage risk, from the examples ana- the least profitable throughout. The least profitable sce - lysed, spruce monoculture manages to perform better nario overall was the no-thin beech monoculture, which than beech or mixture in all thinning strategies, except has the lowest NPV at every point in the rotation part. Bourke et al. Annals of Forest Science (2023) 80:19 Page 12 of 36 Figure 9 shows net present value per hectare versus the heterogeneity of the WETs, the bias ranges remain stand age, where volume is modified by risk and the within a level which is satisfactory to the intended pur- NPV values relate to the risk-modified volume projec - pose of the parameterisation. Compared with other cali- tions shown above. Spruce is the most profitable man - brations of European tree species in Germany and other −1 agement strategy, reaching 8600 € ha by 57 years. Central European countries (e.g. Forrester et al. 2021, However, this strategy then rapidly declines until the Augstynczik et al., 2017, Nölte et al. 2020), our results end of the rotation. The mixed strategies maintain a consider the wide geographical range for which we had more middle-ground status, whereby in the former to calibrate. In the case of validation, the range of values part of the rotation it is more profitable than beech however are wider, especially for the BA of Douglas fir but less profitable that spruce. Then, the profitability and pine. However, as seen in Table 1, while DBH and becomes less species specific and is more defined by the height remained low (under 15% PBias), for BA and vol- management. ume, the figures were generally higher, the volume of Comparing Figs. 8 with 9, spruce has a similar progres- larch being the most extreme value. Therefore, we must sion in NPV in both cases, until ~ 60 years, but contin- take these bias uncertainties into consideration when ues to increase when not considering risk and begins interpreting growth projections. This would apply to, to decrease after this point when considering risk. The for example Fig. 4, where the standard deviation shown maximum NPV reached when risk is not considered in Table 1 would indicate that especially beech has a −1 is ~ 11,100 € ha at 70 years old for the light thinning higher uncertainty in the volume parameter estimation; spruce monoculture. When risk is considered, the high- therefore, beech monocultures in mixture or monocul- −1 est NPV value achieved was ~ 8600 € ha for no-thin ture could have greater volume, since the parameter was spruce at ~ 58 years old. At the end of the 120 years when generally underestimated in the validation (see Table 1 & not considering risk, light thinning spruce was the most Appendix Fig. 18). profitable at 9517 € ha 1, while no-thin beech monocul- Yield is defined as the entire stand biomass from −1 ture was the least profitable at 2445 € ha . Considering stand establishment. A direct positive mixing effect is wind damage risk, the least profitable thinning strategy assumed when the mixed-stand productivity is greater at 120 years was the no-thin beech monoculture at 1328 than the productivity of the two pure stands of similar −1 € ha , and the most profitable was the heavily thinned size (ordinary overyielding) or when the mixed-stand −1 spruce monoculture at ~ 4508 € ha . In the risk-modi- productivity even exceeds the sum productivity of pure fied NPV estimation, by the end of the rotation, almost stands of species 1 and 2 (transgressive overyielding). all strategies converge to a similar range of values, i.e. In contrast, underyielding means that the productivity −1 between 1500 and 2500 € ha . The notable excep - of the mixed stand is less than that of the pure stands tions to these are the light and no-thin beech strategies, (Pretzsch 2009). When mixing Norway spruce and sil- which are lower, and the heavily thinned spruce, which ver fir, Huber et al. (2014) found that, on sites studied is distinctly above the other strategies. In the no-risk in Switzerland, the mixture of these species resulted in simulations, spruce was favoured for the entirety of the underyielding, although this was somewhat depend- rotation. Overall, although spruce in the former part and ent on-site factors. Vallet and Perot (2011) obtained beech in the latter part are most profitable, the mixture results indicating that silver fir growth was enhanced is both relatively profitable in the former and latter part in mixture, while Norway spruce’s growth remained of the rotation. unchanged. In our case, the comparison of monocul- When comparing these species using the statistical tests tural and mixed stands in Fig. 3 showed that the vol- in Appendix Table 5, there is no significant difference ume growth of the mixed stand underyielded in the between these species’ storm damage risk. Additionally, in thinned scenarios, since the total volume just slightly Appendix Table 6 when comparing the storm damage risk increased compared to beech monoculture but ~ 300 m (P-value) in terms of soil fertility, soil–water capacity and less than that of spruce monoculture. In contrast, the soil type, there were no significant differences. mixed-stand overyields by the end of rotation period, since it is closer to the volume of the spruce monocul- 4 Discussion ture than to the beech monoculture. Toigo et al. (2015) 4.1 C alibration and stand growth estimation made a comparison of several European species in vari- The DBH calculations for spruce, pine, oak and Beech ous mixture combinations, specifically beech/spruce, showed a general improvement in comparison with the eech/Fir, Fir/Spruce, Oak/Pine and Beech/Oak, which prior parameter set, following the calibration. Given showed growth gains especially for beech, fir and oak in B ourke et al. Annals of Forest Science (2023) 80:19 Page 13 of 36 mixture over monoculture. Additionally, Pretzsch et al. results in a reduced rotation length. This is not the (2013) obtained differing mixture effects for beech and case where no thinning takes place, but there is then oak, depending on site quality. They found that on high- no intermediate timber harvesting. However, the no- quality sites, the overall growth of beech and oak was thinning strategy sees the stand least affected by dam - reduced to a small degree. In our case, the growth of age risk, and therefore, factors, such as the extracted oak/beech mixed stands (e.g. Appendix, Fig. 26) showed volume and implied rotation length, will need to be a very small difference in volume comparing with beech considered in choosing the most appropriate strategy monoculture. Sterba et al. (2018) found that spruce involving risk. mixed with larch caused a large decrease in the growth of larch, while the spruce can underyield in the earlier 4.3 Economic evaluation of management strategies part of the rotation, it then over-yields in the latter part. and mixtures In our case, overall, the spruce/larch mixture yielded With regard to spruce monocultures, for Samariks et al. slightly under the spruce monoculture in Appendix (2020), changes in spruce management, involving timely Figs. 20, 22, 24 and 26. precommercial thinning and lower planting density, can ensure positive net present value and is most beneficial 4.2 Damage risk estima tion and growth projections, in areas of high wind risk. In addition, spruce need not modified by damage probability be changed as the dominant commercial species. The Spruce displays a lower risk than Douglas fir for the first case for lower density and active thinning is supported 80 years (approx.), but after this point, the damage risk in our simulation study, where later in the rotation the of spruce is greater than Douglas fir (Fig. 5). Douglas fir difference of more and less intensively managed spruce and spruce have far higher overall storm damage risk becomes more apparent when considering wind damage than the other species, in agreement with Albrecht et al. risk and by year 120, with a difference in value of ~ 2500 −1 (2013), where it was found that Douglas fir and Norway € ha . spruce have a similar level of damage probability. This In Griess and Knoke (2013), it was found that the difference would be due to the sensitivity of the model highest net present value for stands affected by risk to changes in the height, as well as the relative influence contained a high proportion of spruce and low pro- of the height and diameter ratio (Schmidt et al. 2010). portion of beech. This was due to a reduced risk Schelhass (2008) found that low height-diameter ratios level. They found that a near 50/50 mixture of spruce were most effective in avoiding damage, and in the and beech resulted in a lower net present value than case of Douglas fir, this ratio could be improved when spruce monoculture. However, the standard devia- mixed with beech, and Albrecht et al. (2012) found that, tion of the net present value was reduced in this although Norway spruce and Douglas fir have high eco - case. In our analysis, while we only consider 50/50 nomic value, this value is also counterbalanced by their mixtures, we see that the management strategies in relatively high risk of storm damage. Albrecht et al. mixture do not experience a large deviation from one (2015) found that intensified management reduced the another. Our results are consistent with the find- damage risk of silver fir (and Norway spruce). Suvanto ing that mixed stands have a lower net present value (2018) modelled storm risk for Norway spruce and under risk, as seen in Fig. 9. However, at its most −1 Scots pine and found that these species had higher dam- profitable, spruce monoculture is ~ 4500 € ha more age risks than broadleaf species. Scots pine in Fig. 5 profitable than the 50/50 mixture at 55–60 years begins with a higher storm damage risk than beech until old. This serves as an argument for the profitability about year 80 but then remains relatively constant, and of shorter rotation spruce monocultures under wind so pine has a lower damage risk in the latter part of the damage risk. Also, Knoke et al. (2005) advised that rotation. risk-averse forest owners should establish spruce As seen by the risk-modified beech and spruce mix - stands where 10–15% is beech admixture. Also, when ture, the beech monoculture performs the best, with the salvage logging is not undertaken in the aftermath of mixture either performing as well, but with a shorter a storm, there are no large negative economic impact rotation, or has an inferior performance. Clearly, when and provide an additional benefit to biodiversity volume growth in beech monoculture and in mixture (Knoke et al. 2021). with pine (Appendix, Fig. 22) is modified by risk, the We recognise that earlier studies, such as Pellikka volume growth progression of the stand mirrors that and Järvaenpää (2003), found that thinning could con- of beech monoculture quite closely. However, this also tribute to storm damage. However, given the greater Bourke et al. Annals of Forest Science (2023) 80:19 Page 14 of 36 diameter growth allowed by heavy thinning, our study levels of bias and deviation in the outputs. Nevertheless, indicates that this itself can be a mitigation factor which validation of monoculture and mixed stand data allowed can counteract the effect of canopy openings. A study for the successful simulation of height, DBH, BA and could be made of different thinning timings to find an volume. optimal timing to mitigate damage effects. In addition, We may also conclude, according to these modelling the calculated damage risk depends on the growth char- results, that the species, mixture and management affect - acteristics of specific species in the region in which it ing the stand density have an impact on storm damage is calibrated for, so the risk characteristics may change susceptibility of a forest stand. Intensive thinning gener- in different regions. Another aspect of our results is ally reduced the risk at a given height, and mixture also that, even if the net present value still remains high, reduced risk. damage risk can still be quite high while the high value We conclude that heavily thinned spruce stands are the and usable volume of spruce compensates for the dam- most profitable under storm risk, but spruce monocul - age risk. It also depends on the degree of projected cli- tures also experienced the sharpest decline in value dur- mate change effects of tree species growth, as projected ing the considered period. When other risks like drought, in Dyderski et al. (2017), but with future climate data, which has become a major source of stress for European the model can reproduce these effects in a subsequent forests in recent years and likely in the coming decades study. (Gazol and Camarero 2022), or insects are included, Neuner and Knoke (2017) found that spruce mono- these factors could lead to different conclusions as to the cultures’ annuities decline under climate change, most profitable strategy. although beech admixture mitigates this loss, and This modelling experiment provides the basis for a with low proportions of beech, the revenue is similar wider study on the susceptibility of various stand types to spruce monoculture but with reduced risk caused to wind risk and, in turn, enables a visible differentiation by warmer, drier climate. Although we do not consider between the best strategies when only considering timber climate change in this study, we see that spruce/beech production and those also considering wind damage risk. mixtures earn less than spruce, although the mixed However, given that forests are often required to achieve species strategies’ profitability remains more constant, multiple objectives, notably nature protection value and although less profitable. carbon sequestration, the methodology could also be While 3-PG mix can be calibrated for local climatic extended to include these factors under climate change conditions and for the growth parameters of particular scenarios. species in a given region, the Lothar model is a statis- tical model, based specifically on storm damage data within Germany. Therefore, while the specific model Appendix 1 may not be transferrable outside of its intended region Glossary of use, another localised wind damage risk model could be utilised in its placed, assuming that its inputs and outputs are compatible with 3-PG. In addition, since the Table 2 Glossary of abbreviations 3-PG model is primarily intended for use in relation to Abbreviation Full name managed forests, it of itself does not have the capabil- ity to reproduce the complexity of a natural forest. For BAU Business as usual this task, an individual tree model could better repre- 3-PG Physiological principles in predicting growth sent these complexities in such areas as high age, diam- FVA-NW “Nordwestdeutsche Forstliche Versuchsanstalt” — North- West German Forestry Research Institute eter and species heterogeneity, as well as gap dynamics, FVA-BW “Forstliche Versuchs- und Forschungsanstalt Baden- which are not represented in a stand-level model such as Württemberg” — Forestry Research Institute Baden- 3-PG. In the case of the Lothar model, the model could Württemberg still have relevance in unmanaged German forests, since Forst-BW “Forst Baden-Württemberg” — Forest Baden-Württem- it can be implemented at the individual tree level. berg WET “Wald Entwicklungstyp” — forest development type 5 Conclusion DBH Diameter at breast height The species parameters provide a basis for a projection of BA Basal area seven tree species in future forest conditions and, in turn, DWD “Deutsche Wetter Dienst” — German Weather Service the projection of future wind storm damage in German PBias Percentage bias forests. In the calibration, each species showed differing B ourke et al. Annals of Forest Science (2023) 80:19 Page 15 of 36 Table 3 The utilised biomass equations from Forrester et al. Appendix 2 (2017) for each calibrated tree species Methods Calibration inputs Foliage Root Stem Growth Regions: In our modelling approach, the tran- Beech Beech Beech Beech sects were separated into segments, corresponding Douglas fir Larch General Larch to the German “Wuchsgebiete” (Growth Regions), Conifer each of which displays unique environmental attrib- Silver fir General General Silver fir utes, contributing to the growth properties within the Conifer Conifer region. The growth regions used in the calibration cor - Larch Larch General Larch Conifer responded to the endpoints and intersections of the transects, as well as two additional regions in central Oak Oak Oak Oak Germany. This was to ensure that the variation in con - Pine Larch General Larch Conifer ditions within Germany could be accounted for. Spruce Spruce Spruce Spruce Climate: In order to run the model, monthly location- based climate data of temperature, precipitation and frost days were utilised, which were provided by the Environmental Meteorological Institute in University of Freiburg. The monthly solar radiation input was pro - parameters, e.g. the constant and power controlling vided by the DWD historical database (see References). the DBH scaling based on the stem mass, these param- Stand: Every age class was initialised with starting eters were varied at range of ± 0.010. In Bayesian cali- values for DBH, Height and Basal Area correspond- bration the initial parameter set is varied by comparing ing to a plot in the growth region in question. In the with a measured or empirical dataset using a likeli- model initialisation starting values for stem, foliage hood function. The likelihood function determines the and root biomass are required. In order to calculate probability of the parameters generating the same data these values generalised allometric equations (For- as the empirical dataset. Using Markov Monte Carlo rester et al. 2017) were applied to calculate the related Chains the model runs over a given number of itera- stand biomass of the stems, foliage and roots. These tions, to evaluate the most probable parameter values calculations were primarily based on stand mean DBH to generate the same output values as the calibration but additionally the stand basal area and/or stand age, data. For this calibration we specified 1250 iterations depending on the species. In some cases where the in two chains to give a total of 2500 iterations. Subse- specific species equations did not yield results corre- quently an output parameter set, a posterior, provides sponding to the initial values of the specific age class, updated parameter values with narrower parameter general equations for conifer or broadleaf trees were uncertainty ranges, which provide a better fit of the chosen, or indeed, from another species, if it yielded desired outputs to a given region. a better fit to the initial biomass values. These are The calibration was carried out using the R package shown in Table 3. “Bayesian Tools”. In the cases where linear models needed To aid in the understanding of the diameter, stem den- to be calibrated, e.g. for height function calibration, the sity and age class ranges used to parameterise the tree linear model calibrations were carried out using the nls species Figs. 10, 11, 12, 13, 14, 15 and 16 provide a guide- function in base R. line to these relationships. Appendix 3 Calibration process Posterior validation The first step of the calibration was to vary the param- The final step was to validate the derived parameter in eters manually until an approximate fit within the mixed stands. In both cases PBias were used as compara- initial parameter ranges (from Forrester et al. 2021) tive metrics for the validation. Plots in Baden Württem- was reached. These were then utilised as the starting berg were utilised to evaluate the efficacy of the derived parameters for the Bayesian calibration. The param- parameters, partially from the FVA-BW and partially eters were then permitted a ± 15% range of variation, from Forst-BW. The FVA-BW plots utilized climate data given that the chosen parameters have a large effect from the nearest weather stations, while in the case of on the model outputs. In the case of highly sensitive the Forst-BW plots the weather data was the same as Bourke et al. Annals of Forest Science (2023) 80:19 Page 16 of 36 Fig. 10 Stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate beech. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class Fig. 11 Stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate Douglas fir. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class B ourke et al. Annals of Forest Science (2023) 80:19 Page 17 of 36 Fig. 12 Stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate Silver fir. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class Fig. 13 The above shows stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate larch. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class Bourke et al. Annals of Forest Science (2023) 80:19 Page 18 of 36 Fig. 14 The above shows stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate oak. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class Fig. 15 The above shows stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate pine. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class B ourke et al. Annals of Forest Science (2023) 80:19 Page 19 of 36 Fig. 16 The above shows stems per hectare (y-axis) versus mean diameter (x-axis) for the data utilised to calibrate spruce. The colours of the points correspond to density/diameter relationships of particular age classes. The legend shows the number in years for the given age class was used in the monoculture calibrations i.e. maximum order to determine the degree of difference in the growth and minimum temperature per month, mean monthly rate with and without mixture. To determine the degree precipitation and mean total frost days per month. The of congruence between the 3-PG Mix modelled outputs mean monthly solar radiation was extracted from the and the calibration and validation age classes and stands, mean monthly solar radiation in relation to the sample Percentage Bias (Pbias) was utilised. point’s location. Mean DBH, Height, Basal Area and Vol- In Fig. 17, the box plots show where the PBias values ume metrics were the units of comparison for the FVA- are most concentrated in the distribution, the central BW and Forst-BW plots. Stem number per hectare was line in the box being the median value and the horizon- provided in the stand data from the FVA-BW and in tal lines and points are the outliers to the distribution. the case of the Forst-BW plots stems per hectare were The negative values on the x axis show where the model derived from the number of stems per plot which were underestimates the calibration data and positive values over 15 cm and were then extrapolated to the per hectare are where the model overestimates. The narrower and level. The number of inventory samples varied between closer the spread to the vertical zero line, the closer the the FVA plots but for the Forst-BW plots, while the sam- modelled values are to the calibration data. pling years varied, there were for each sample point three The derived parameters are shown in Table 4. Fig- measurements of DBH, Height, Volume and Basal Area. ures 17 and 18 show the distribution of the PBias For the Forst-BW plots, each tree had a calculated vol- of the species parameter calibration and validation ume (m3) and the mean value of the measured trees was respectively. To validate the simulations using the multiplied by the stems per hectare. For the Basal Area calibrated parameters, we compared mixed simula- the derived mean DBH was also converted to Basal Area tions with inventory stand data. Figure 17 shows the per hectare using the calculation (DBH / 2 / 100) * pi * PBias of the “obser ved” versus simulated projections stems/ha. of BA, DBH and Height. In general, the median of The tree biomass growth in the mixed stands from the values remains less than 10%, and some less than Baden Württemberg was then compared with mono- 5%, with some exceptions. This is especially evident culture stands with the same inputs for each species, in for the BA calculations for Spruce, Pine and Beech. Bourke et al. Annals of Forest Science (2023) 80:19 Page 20 of 36 Fig. 17 The Pbias (x-axis (%)) values in the calibration of the named tree species (y-axis) for basal area (green), diameter (orange) and height (blue) For validation (Fig. 18) of the derived parameters, improvement in the performance of the posterior volume was also added to the output variables which over the prior parameters. were subject to a PBias comparison. In addition, a In Fig. 19, for beech, DBH is highest when mixed comparison of the prior parameters to the poste- with oak (84 cm) and with spruce (79 cm) at the end rior parameters was carried out using the same sta- of the rotation. It is the most reduced when mixed tistical tests as were used for the validation of the with Douglas fir and Silver fir (29 cm and 26 cm parameters against stand data. For the most part, respectively). For comparison, beech in monoculture the derived posterior parameters show an improve- reaches a DBH of 65 cm by the end of its rotation. In ment over the prior parameter distributions. The Fig. 20, the shortest turn-around time for the stand main exception to this was the case of height projec- was 70 years old for the beech/scots pine mixture. The tions for Douglas fir. Douglas fir also did not show highest volume at the end of rotation was the beech/ a clear improvement in terms of the BA calculation Douglas fir mixture (1005 m3) and the lowest was and the median value was 0%. This is in contrast beech/pine (387 m3). For beech monoculture the end to the BA statistics for beech and pine, as this was volume was 488 m3. also the case for the diameter values of the same In Fig. 21, DBH is highest when beech is mixed species, where all comparisons showed improve- with oak (80 cm) and with spruce (78 cm). It is the ment in performance of the posterior over the prior. most reduced when mixed with Douglas fir and Sil- Larch and Fir showed a small improvement, e.g. ver fir (29 cm and 26 cm respectively). Beech in mon- median BA < 5%. The remaining species showed oculture reaches a DBH of 72 cm by the end of the B ourke et al. Annals of Forest Science (2023) 80:19 Page 21 of 36 Table 4 The table below shows the derived parameters for all seven calibrated species Name Fagus sylvatica Pseudotsuga Abies alba Larix decidua Quercus Pinus sylvestris Picea abies menziesii petraea pFS2 0.073 (0.067– 0.242 (0.227– 0.5951 1.05 (0.888– 1.581 (1.391– 0.629 (0.551– 0.475 (0.352– 0.078 0.253) 1.174) 1.750) 0.709) 0.562) pFS20 0.013 (0.013– 0.225 (0.212– 0.262 (0.229– 0.017 (0.016– 0.029 (0.028– 0.067 (0.061– 0.063 (0.056– 0.014 0.236) 0.286) 0.018) 0.031) 0.071) 0.067) aWS 0.084 (0.084– 0.098 (0.089– 0.083 (0.082– 0.125 (0.117– 0.072 (0.063– 0.124 (0.114– 0.042 (0.033– 0.092) 0.108) 0.084) 0.134) 0.081) 0.132) 0.052) nWS 2.493 (2.483– 2.356 (2.346– 2.343 (2.334– 2.314 (2.303– 2.46 (2.460– 2.316 (2.308– 2.428 (2.423– 2.501) 2.363) 2.352) 2.322) 2.469) 2.328) 2.433) pRx 0.602 (0.0.526– 0.519 (0.489– 0.769 (0.693– 0.727 (0.652– 0.352 (0.297– 0.656 (0.603– 1.096 (1.024– 0.678) 0.543) 0.844) 0.807) 0.429) 0.718) 1.153) pRn 0.054 (0.043– 0.132 (0.121– 0.206 (0.186– 0.053 (0.042– 0.062 (0.042– 0.282 (0.254– 0.261 (0.246– 0.061) 0.140) 0.228) 0.063) 0.085) 0.311) 0.274) gammaF1 0.004 (0.003– 0.016 (0.015– 0.002 (0.000– 0.03 (0.003– 0.021 (0.000– 0 0.002 (0.001– 0.005) 0.017) 0.003) 0.060) 0.085) 0.002) gammaF0 0.001 0.007 (0.002– 0.001 (0.000– 0.001 (0.000– 0.026 (0.000– 0.000 (0.000– 0.014 (0.013– 0.011) 0.002) 0.002) 0.040) 0.001) 0.014) tgammaF 60 60 60 0 0 60 60 gammaR 0 0.0001 0 0.0001 0.003 0.002 (0.001– 0.001 0.002) leafgrow 4 0 0 5 5 0 0 leaffall 11 0 0 11 11 0 0 Tmin 6.006 (5.717– 2.621 (1.761– 4.883 (3.561– 3.418 (3.029– − 1.527 (− 2.801 − 4.994 (− 6.121 4.504 (4.440– 6.261) 3.214) 6.133) 3.735) to − 0.628) to − 4.061) 4.548) Topt 21.541 (21.039– 24.87 (24.153– 24.783 (23.536– 24.914 (24.008– 15.594 (14.345– 26.843 (25.599– 24.98 (24.887– 21.951) 25.707) 26.075) 25.654) 16.805) 28.045) 25.092) Tmax 30.7907 30.731 (28.558– 36.325 (34.293– 30.937 (29.250– 44.601 (42.559– 46.081 (43.717– 29.003 (28.731– 32.310) 38.113) 32.874) 46.455) 47.456) 29.342) kF 1 1 1 1 1 1 1 fCalpha700 1.061 (1.010– 1.282 (1.225– 1.1966 1.078 (1.024– 1.1097 1.123 (1.108– 1.000 (0.991– 1.120) 1.335) 1.107) 1.141) 1.009) fCg700 0.8002 0.681 (0.613– 0.7069 0.731 (0.672– 0.8449 0.998 (0.941– 0.654 (0.614– 0.759) 0.805) 1.055) 0.708) m0 0 0 0 0 0 0 0 fN0 0.6 0.6 0.6 0.6 0.6 0.6 0.4 fNn 1 1 1 1 1 1 1 MaxAge 199.106 148.731 550 650 725 600 251.772 (241.794– (190.502– (140.265– 259.812) 209.110) 158.695) nAge 4 4 4 4 4 4 4 rAge 0.924 (0.921– 0.95 0.95 0.95 0.95 0.95 0.95 0.929) gammaN1 0 0 0 0 0 0 0 gammaN0 0 0 0 0 0 0 0 tgammaN 0 0 0 0 0 0 0 ngammaN 1 1 1 1 1 1 1 wSx1000 291.770 213.3776 313.462 225.38 (214.614– 151.836 202.3125 378.3186 (274.426– 235.938) (148.025– 312.342) 155.695) thinPower 1.447 (1.361– 1.5887 1.9777 1.983 (1.866– 1.836 (1.775– 1.6025 1.7732 1.538) 2.054) 1.890) mF 0.488 0.608 0.492 0.409 0.412 0.558 0.464 mR 0.436 0.563 0.446 0.312 0.373 0.48 0.391 mS 0.437 0.54 0.444 0.321 0.363 0.481 0.409 SLA0 24.72 6.56 12.32 13.83 18.49 4.29 8.71 Bourke et al. Annals of Forest Science (2023) 80:19 Page 22 of 36 Table 4 (continued) Name Fagus sylvatica Pseudotsuga Abies alba Larix decidua Quercus Pinus sylvestris Picea abies menziesii petraea SLA1 19.4 5 5.85 11.72 14.62 4.29 3.85 tSLA 35 44.7 18.1 14.5 7.35 1 25.1 k 0.458 (0.435– 0.645 (0.612– 0.64 (0.597– 0.341 (0.335– 0.644 (0.620– 0.479 (0.455– 0.269 (0.232– 0.483) 0.668) 0.686) 0.349) 0.673) 0.493) 0.315) fullCanAge 3 3 3 3 3 3 3 MaxIntcptn 0.32 (0.306– 0.411 (0.392– 0.3385 0.146 (0.135– 0.139 (0.129– 0.414 (0.398– 0.265 (0.259– 0.331) 0.422) 0.153) 0.146) 0.429) 0.271) LAImaxIntcptn 3 3 3 3 3 3 3 cVPD 5 5 5 5 5 5 5 alphaCx 0.036 (0.034– 0.05 (0.048– 0.026 (0.024– 0.061 (0.058– 0.032 (0.029– 0.03 (0.030– 0.031 (0.028– 0.038) 0.053) 0.028) 0.064) 0.035) 0.031) 0.032) Y 0.47 0.47 0.47 0.47 0.47 0.47 0.47 MinCond 0 0 0 0 0 0 0 MaxCond 0.017 0.029 (0.028– 0.021 (0.019– 0.014 (0.012– 0.0199 0.014 (0.013– 0.026 0.030) 0.024) 0.016) 0.014) LAIgcx 3.33 3.33 3.33 3.33 3.33 3.33 3.33 CoeffCond 0.044 (0.041– 0.062 (0.060– 0.0908 0.084 (0.081– 0.0477 0.062 (0.059– 0.077 (0.074– 0.046) 0.065) 0.087) 0.066) 0.080) BLcond 0.2 0.2 0.2 0.2 0.2 0.2 0.2 RGcGw 0.66 0.66 0.66 0.66 0.66 0.66 0.66 D13CTissueDif 2 2 2 2 2 2 2 aFracDiffu 4.4 4.4 4.4 4.4 4.4 4.4 4.4 bFracRubi 27 27 27 27 27 27 27 fracBB0 0 0 0 0 0 0 0 fracBB1 0 0 0 0 0 0 0 tBB 0 0 0 0 0 0 0 rhoMin 0.4 0.44 0.37 0.5 0.58 0.37 0.44 rhoMax 0.4 0.44 0.37 0.5 0.58 0.37 0.44 tRho 1 1 1 1 1 1 1 aH 37.73 46.09 30.91 40.17 1.31 45.69 46.09 nHB 17.85 24.57 16.78 19.84 0.691 23.01 24.57 nHC 0.00636 0.00576 0.00925 0.00398 0.1 0 0.00576 aV 0.000115 0.000139 0.000128 0.000047 0.000031 0.000118 0.000139 nVB 2.31 2.04 1.92 1.53 2 2.05 2.04 nVH 0.33 0.54 0.75 1.43 1.05 0.58 0.54 nVBH 0 0 0 0 0 0 0 Crown shape 3 3 3 3 3 3 3 aK 0.43 0.65 0.83 0.66 0.31 0.65 0.63 nKB 0.73 0.69 0.53 0.72 1.03 0.83 0.64 nKH 0 0 0 0 0 0 0 nKC 0.122 − 0.037 0 − 0.14 − 0.15 − 0.267 − 0.069 nKrh − 0.126 0.196 0 0.248 0 − 0.087 0.067 aHL 23.32 21.18 24.93 27.97 20.13 11.77 35.18 nHLB 14.95 24.73 25.09 28.73 19.05 17.01 27.18 nHLL 0 0 0 0 0 0 0 nHLC 0 0.002 − 0.002 − 0.002 0 0 − 0.005 nHLrh 0 0 0 0 0 0 0 Dscale0 − 2.439 − 1.568 − 2.052 − 1.624 − 0.861 − 1.049 − 2.023 DscaleB 1.008 1.982 1.077 1.235 0.958 0.801 1.136 Dscalerh 0.21 0.055 0.757 0 0 0 0.051 B ourke et al. Annals of Forest Science (2023) 80:19 Page 23 of 36 Table 4 (continued) Name Fagus sylvatica Pseudotsuga Abies alba Larix decidua Quercus Pinus sylvestris Picea abies menziesii petraea Dscalet 0.187 − 0.902 0 − 0.237 0 0.108 − 0.049 DscaleC 0.295 0.395 0.403 0.435 0 0.186 0.382 Dshape0 0.491 0.985 − 0.13 − 0.109 − 0.792 − 0.689 0.328 DshapeB 0.345 0 0.228 0.481 0 0.372 0.562 Dshaperh 0.701 0 0.777 0.639 0 0 0.037 Dshapet − 0.138 0 0 − 0.195 0 0 − 0.254 DshapeC − 0.128 − 0.073 0 0 0.583 0.111 − 0.117 Dlocation0 0.723 0.284 0.462 0.293 0.444 0.129 0.391 DlocationB 0.87 − 0.241 0.825 0.874 1.014 1.057 0.847 Dlocationrh 0 0.065 0 0 0 0 − 0.004 Dlocationt − 0.138 0.944 0 0 0 − 0.158 − 0.001 DlocationC − 0.111 − 0.152 − 0.2 − 0.224 0 − 0.103 − 0.187 wsscale0 − 3.508 − 3.454 − 3.118 − 2.768 − 2.438 − 2.905 − 3.366 wsscaleB 2.445 2.447 2.384 2.461 2.606 2.081 2.369 wsscalerh 0.401 0.118 1.255 0.114 0 0 0.222 wsscalet 0.174 0 0 − 0.192 0 − 0.026 − 0.033 wsscaleC 0.155 0.572 0.353 0.239 0 0.671 0.402 wsshape0 0.551 0.323 0.46 − 0.491 − 1.287 − 0.404 0.16 wsshapeB 0.288 1.369 0.107 0.489 0.553 0.405 0.461 wsshaperh 0.585 0 0.705 0.428 0 0 0.273 wsshapet − 0.158 − 1.263 0 − 0.19 0 − 0.098 − 0.241 wsshapeC − 0.188 0 − 0.196 0 0 0 − 0.085 wslocation0 − 0.081 − 0.854 − 0.168 − 1.092 − 0.966 − 2.999 − 0.937 wslocationB 1.915 − 0.126 1.555 1.88 1.651 2.564 2.005 wslocationrh − 0.795 0.112 0 0 0 − 1.081 − 0.735 wslocationt − 0.483 1.971 0 0 0 − 0.387 − 0.228 wslocationC − 0.1 − 0.609 − 0.282 − 0.469 0 0.291 − 0.194 rotation. In Fig. 22, the shortest turn-around time rotation was the beech/Douglas fir mixture (1143 m3) for the stand was 70 years old for the beech/Scots and the lowest was beech/Silver fir (448 m3). For beech pine mixture. The highest volume at the end was the monoculture the end volume was 697 m3. beech/Douglas fir mixture (839 m3) and the lowest In Fig. 25, DBH is highest when mixed with oak was / (332 m3). For beech monoculture the end vol- (59 cm) and with spruce (59 cm) at the end of the ume was 368 m3. rotation. It is the most reduced when mixed with In Fig. 23, DBH is highest when beech is mixed with Douglas fir and Silver fir (31 cm and 23 cm respec- oak (73 cm) and with spruce (71 cm). It is the most tively). Beech in monoculture reaches a DBH of 50 cm reduced when mixed with Douglas fir and Silver fir by the end of the rotation. In Fig. 26, the highest vol- (34 cm and 27 cm respectively). Beech in monoculture ume at the end of the rotation was the beech/Douglas reaches a DBH of 58 cm. In Fig. 24, the shortest turn- fir mixture (2012 m3) and the lowest was beech/Silver around time for the stand was 80 years old for the beech/ fir (1054 m3). For beech monoculture end volume was Scots pine mixture. The highest volume at the end of 1190 m3. Bourke et al. Annals of Forest Science (2023) 80:19 Page 24 of 36 Fig. 18 The Pbias (x-axis (%)) values in the validation of the named tree species (y-axis) for basal area (green), diameter (orange), height (blue) and volume (pink) B ourke et al. Annals of Forest Science (2023) 80:19 Page 25 of 36 Fig. 19 “Business as usual” management. DBH (diameter at breast height, y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) Bourke et al. Annals of Forest Science (2023) 80:19 Page 26 of 36 Fig. 20 “Business as usual” management. Volume (y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) Fig. 21 High-intensity thinning. The above graphs show mean DBH (diameter at breast height, y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) B ourke et al. Annals of Forest Science (2023) 80:19 Page 27 of 36 Fig. 22 High-intensity thinning. The above graphs show volume (y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) Fig. 23 Low-intensity thinning. The above graphs show mean DBH (diameter at breast height, y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) Bourke et al. Annals of Forest Science (2023) 80:19 Page 28 of 36 Fig. 24 Low-intensity thinning. The above graphs show volume (y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) B ourke et al. Annals of Forest Science (2023) 80:19 Page 29 of 36 Fig. 25 No thinning. The above graphs show mean DBH (diameter at breast height, y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) Bourke et al. Annals of Forest Science (2023) 80:19 Page 30 of 36 Fig. 26 No thinning. The above graphs show volume (y-axis) vs. stand age (x-axis) simulations for beech, comparing the growth in monoculture (black) with its growth in mixture (blue) with another species (red) B ourke et al. Annals of Forest Science (2023) 80:19 Page 31 of 36 Fig. 27 Height vs. (P storm risk) plots of beech in monoculture and mixture with Douglas fir, silver fir, larch, oak and pine considering BAU, heavy thin, light thin and no-thin regimes Bourke et al. Annals of Forest Science (2023) 80:19 Page 32 of 36 Fig. 28 Height vs. P (storm risk) plots of spruce in monoculture and mixture with Douglas fir, Silver fir, larch, oak and pine considering BAU, heavy thin, light thin and no-thin regimes B ourke et al. Annals of Forest Science (2023) 80:19 Page 33 of 36 Appendix 4 Mann–Whitney T‑test U‑test Statistics In Table 5 only pine mixed with larch was not different Spruce W p‑ Value t df p‑ Value in its risk level to monoculture, as well as Silver fir mix - Fertility low/high 996,048 0.6693 − 0.72723 2831.4 0.4671 tures with oak and pine. Spruce also did not see a signifi - Soil water low/ 1,010,692 0.8069 0.010785 2834 0.9914 cant difference when mixed with larch. All other mixture medium perutations showed significant difference. Soil water low/high 1,010,764 0.8043 0.021956 2834 0.9825 Soil clay/loam 1,010,476 0.8146 0.076402 2834 0.9391 Soil sandy/loam 1000,104 0.8094 − 0.02141 2834 0.9829 Table 5 The below table shows the Mann–Whitney U- (where W Soil sandy/clay 1000,104 0.8094 − 0.025089 2834 0.98 is the test statistic) and T-test (where t is the test statistic and df is the degrees of freedom) results comparing damage probability (P-values) in all species for significant difference with the Mann– Whitney U- and T-tests (P & p) Appendix 5 Utilised R packages, functions & code overview Mann–Whitney T‑test Model Parameterisation U‑test Package: Bayesian Tools library(BayesianTools) Species W P t df P Spruce/beech 1,383,578 2.2e-16 57.061 1546 2.2e-16 “Observed Data” <- “Reference Data” + Spruce/Douglas fir 1,119,676 1.505e-07 2.3695 2690.7 0.01788 rnorm(length(“Reference Data”), sd = “Parameter Stand- Spruce/silver fir 383,376 2.2e-16 − 40.404 1709.5 2.2e-16 ard Deviation”) Spruce/larch 283,920 2.2e-16 − 49.842 1537.4 2.2e-16 Spruce/oak 1,934,260 2.2e-16 67.653 1422.2 2.2e-16 “Selected Parameters” <- c(i:j) Spruce/pine 1,808,500 2.2e-16 57.759 1456 2.2e-16 Beech/Douglas fir 1,444,634 2.2e-16 67.56 1621.7 2.2e-16 “Likelihood” <- function(“Parameters”, sum = TRUE) { Beech/silver fir 1,298,474 2.2e-16 41.009 2343.8 2.2e-16 Beech/larch 1,167,974 2.2e-16 25.092 2422.7 2.2e-16 x <- “Initial Parameters” Beech/oak 187,296 2.2e-16 − 42.791 1166.7 2.2e-16 Beech/pine 775,032 0.6298 0.82968 1707.1 0.4068 “Predicted Data” <- “Model Output” Douglas fir/silver fir 294,120 2.2e-16 − 46.183 1877.3 2.2e-16 Douglas fir/larch 194,088 2.2e-16 − 58.593 1609.1 2.2e-16 “Difference” <- c(“Predicted Data” – “Observed Data”) Douglas fir/oak 26,568 2.2e-16 − 81.717 1425.3 2.2e-16 Douglas fir/pine 114,384 2.2e-16 − 68.988 1479.4 2.2e-16 “Likelihood Values” <- dnorm(“Difference”, sd = “Param - Silver fir/larch 1,419,580 2.2e-16 22.001 2408.2 2.2e-16 eter Standard Deviation”, log = TRUE) Silver fir/oak 1,984,012 2.2e-16 77.51 1466.9 2.2e-16 Silver fir/pine 1,717,732 2.2e-16 45.673 1784.6 2.2e-16 If (sum == FALSE) return(“Likelihood Values”) Larch/oak 1,949,380 2.2e-16 79.835 1539.2 2.2e-16 Larch/pine 1,576,876 2.2e-16 30.603 2246.9 2.2e-16 Else return (sum(“Likelihood Values”) Oak/pine 1,865,284 2.2e-16 76.516 1788.9 2.2e-16 “Prior Parameter Distributions” <- Table 6 The below table shows the Mann–Whitney U- (where createUniformPrior(lower = “Lowest Known Parameter W is the test statistic) and T-test (where t is the test statistic and Value”, upper = “Highest Known Parameter Value”, best df is the degrees of freedom) results comparing storm damage = “Initial Parameter Value”) probability (P-value) in soil fertility, soil water and soil type for a monoculture of Norway spruce “Bayesian Setup” <- createBayesianSetup(“Likelihood”, Mann–Whitney T‑test prior = “Prior Parameter Distributions”, names = row- U‑test names = “Selected Parameters”) Spruce W p‑ Value t df p‑ Value Fertility low/ 999,672 0.7941 − 0.37742 2833.3 0.7059 “Settings” <- list(iterations = 1250, nrChains = 2) medium Bourke et al. Annals of Forest Science (2023) 80:19 Page 34 of 36 “Posterior Parameter Distribution” <- “Average Stem Mass” <- “Stem Biomass” * 1000 / “Cur- runMCMC(bayesianSetup = “Bayesian Setup”, sampler = rent Stem Number” “DEzs”, settings = “Settings”) Net Present Value Calculation PriceStem <- “Stem- Lothar Model Coupling # Stand data wood Price” – “Harvesting Cost” “Dataframe”$BHD99 <- “Mean Stand Diameter” PriceInd <- “Industrialwood Price” – “Harvesting Cost” “Dataframe”$BAGRG <- “Species” PriceFuel <- “Fuelwood Price” – “Harvesting Cost “Dataframe”$H99 <- “Height” Stem <- “Proportion Sawlog” * PriceStem “Dataframe”$HD99 <- “Height/Diameter Ratio” Industry <- “Proportion Industrial Wood” * PriceInd “Dataframe”$sum_TOPEX1000_1_4 <- “Topex 1” Fuel <- “Proportion Fuelwood” * PriceFuel “Dataframe”$sum_TOPEX1000_14_27 <- “Topex 2” Net <- sum(Stem,Industry,Fuel) “Dataframe”$sum_TOPEX1000_9_32 <- “Topex 3” “Revenue” <- (“Extracted Volume” - (“Extracted Volume” * “Unusable Proportion”)) * Net “Dataframe”$sum_TOPEX1000_22_19 <- “Topex 4” “New Extracted Value” <- “Extracted Value” + (“Rev- enue” / ((1 + “Discount Rate”) ^ “Stand Age”)) “Dataframe”$RW <- “Longitude” “Dataframe”$HW <- “Latitude” Acknowledgements The study was aided by the provision of sample plot data by FVA-NW (transect for model calibration), as well as “Betriebsinventur der Stadt Freiburg i. Br.” and # Damage Prediction FVA-BW (model validation data). “Prediction” <- predict(“Lothar Model”,newdata= Authors’ contributions All authors contributed to the conceptualization and methodology of the ”Dataframe”) manuscript. RB performed all analyses and visualisation and wrote the main body of the text. RY provided general scientific supervision and review and “Prediction” <- 1 - (1/(1 + (exp(“Prediction”)))) editing of the manuscript. MH reviewed and edited the manuscript, as well as being responsible for project administration and project funding. The authors read and approved the final manuscript. #Fallen Stems and Lost Biomass Funding Open Access funding enabled and organized by Projekt DEAL. We acknowl- StemNoOld <- “Previous Stem Number” edge the main funding for this project Waldklimafonds, as part of the MiStriKli project (2019–2021), grant number 22WK416601. StemNo <- “Current Stem Number” - (“Current Stem Availability of data and materials Number” * “Prediction”) The datasets both analysed and generated for this manuscript are available from the corresponding author. “Removed Stems” <- (StemNoOld - StemNo) / StemNoOld Declarations Ethics approval and consent to participate “Foliage Biomass" <- “Foliage Biomass” * (1 - “Removed Not applicable. Stems” * “Biomass Lost Per Tree”) Consent for publication All authors of this manuscript give their informed consent for its publication. “Root Biomass" <- “Root Biomass” * (1 - “Removed Stems” * “Biomass Lost Per Tree”) Competing interests The authors declare that they have no competing interests. “Stem Biomass" <- “Stem Biomass” * (1 - “Removed Author details Stems” * “Biomass Lost Per Tree”) Chair of Forestry Economics and Forest Planning, University of Freiburg, Ten- nenbacherstr. 4 79106, Freiburg, Germany. B ourke et al. 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For Ecol Manage 257(6):1520–1531 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in pub- lished maps and institutional affiliations. Re Read ady y to to submit y submit your our re researc search h ? Choose BMC and benefit fr ? Choose BMC and benefit from om: : fast, convenient online submission thorough peer review by experienced researchers in your field rapid publication on acceptance support for research data, including large and complex data types • gold Open Access which fosters wider collaboration and increased citations maximum visibility for your research: over 100M website views per year At BMC, research is always in progress. Learn more biomedcentral.com/submissions
Annals of Forest Science – Springer Journals
Published: May 8, 2023
Keywords: 3-PG; Forest growth modelling; Forest wind damage; Climate change; Mixed forest
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