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Simulating structural forest patterns with a forest gap model: a model evaluation
Ecological Modelling 181 (2005) 161–172
Simulating structural forest patterns with a forest gap model: a model evaluation Anita C. Rischa,∗,1 , Caroline Heirib , Harald Bugmannb b
a Swiss Federal Institute for Forest, Snow and Landscape Research, Z¨ urcherstrasse 111, 8903 Birmensdorf, Switzerland Mountain Forest Ecology, Department of Environmental Sciences, Swiss Federal Institute of Technology Z¨urich, 8092 Z¨urich, Switzerland
Received 2 September 2003; received in revised form 4 May 2004; accepted 4 June 2004
Abstract Ecological models can be characterized by their degree of generality, reality and precision. Any model, being a deliberate simplification of reality, cannot excel in all three aspects. Forest gap models have been widely used for studying tree population dynamics, but their predictions have not often been tested for their local precision, but rather for their broad agreement with descriptions of near-natural vegetation. The objectives of our study were (1) to evaluate the performance of the forest gap model ForClim, which had been developed striving for generality and realism, in simulating the long-term development of structural features in Swiss mountain forests; and (2) to examine whether and how the model needs to be changed to improve its precision for a specific site. We used long-term forest data (45 years) from three different forest types in the Swiss National Park. Initial simulation runs for the most dominant forest type in the study area failed to reproduce the observed structural patterns. A detailed analysis of the growth performance of individual trees led to the conclusion that a modified height–diameter function was required, which presumably increases the generality of the model. The new model structure led to simulated stand features that were broadly consistent with observations. After, in addition, taking local variations of model parameters (on mortality, browsing, and seedling establishment rates) into account, we were able to considerably improve the performance of ForClim in simulating the structural features of the different mountain forest stands. We suggest that from the point of view of its revised structure, the ForClim model is principally suitable for site-specific applications, but local precision can only be achieved by site-specific parameter estimation procedures. We conclude that model evaluation and validation as conducted in this study could be quite useful for increasing the reliability of simulations performed with this class of models. © 2004 Elsevier B.V. All rights reserved. Keywords: ForClim; Long-term forest data; Growth function; Forest succession; Validation
∗
Corresponding author. Tel.: +1 315 443 4746; fax: +1 315 443 2012. E-mail address: [email protected] (A.C. Risch). 1 Present address: Department of Biology, Syracuse University, 207 Biological Research Laboratory, 130 College Place, Syracuse NY 13244, USA. 0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2004.06.029
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1. Introduction Forest gap models are individual-tree based, semimechanistic simulators designed to study tree population dynamics on small patches of land that have been used in many studies, typically to evaluate the dynamics of tree species composition at specific places over time (cf. Botkin et al., 1972; Shugart, 1984; Bugmann, 2001). The underlying ecological concept of all these models is the view of stochastic, cyclical succession, also known as “shifting-mosaic” dynamics (cf. Watt, 1947; Bormann and Likens, 1979). To date, several dozens of forest gap models have been developed, described, and applied to a wide variety of forest types, mainly located in temperate and boreal climate zones (e.g., Solomon et al., 1981; Shugart, 1984; Urban and Shugart, 1989; Prentice et al., 1993; Bugmann, 1997; Fischlin and Gyalistras, 1997). However, it has only rarely been explored how widely applicable one particular model of this family could be. Levins (1966) suggested that ecological models can be characterized by the degree to which they are realistic, precise, and general. According to Levins (1966), any given model can excel in two of the three aspects, but not in all three at the same time. In the sense of this paradigm, most forest gap model studies sacrificed generality in favor of realism and (local) precision. Over the past 10 years, we have been striving to develop a forest gap model (ForClim) that is as simple as possible and that incorporates robust and widely applicable representations of the ecological effects of climatic variables (Bugmann, 1996). The aim of these developments was to be able to study forest dynamics under a wide range of climatic conditions in different biogeographical areas of the boreal and temperate regions. We showed that the model is broadly applicable to forests in Europe, in eastern North America, in the Pacific Northwest of the US (all treated in Bugmann and Solomon, 2000) and in northeastern China (Shao et al., 2001). In other words, sensu Levins (1966) we were striving for generality and realism of the model, potentially at the expense of local precision. Up to now, our own as well as many other modeling studies have mostly focused on simulating temporal changes in tree species composition (e.g., Shugart, 1984; Hasenauer et al., 2000), and they have generally been validated by comparing simulation results with coarse descriptions of potential natural vegetation
(e.g., overview in Shugart, 1984; Lexer, 2000) or national forest inventory data (e.g., L¨offler and Lischke, 2001). Yet, even though gap models could also be useful for predicting local structural forest patterns (e.g., size distributions), which would increase their power in predicting ecosystem development, only few studies have been conducted in this context up to date (e.g., Lindner et al., 1997). The main reason for the lack of such research is that most long-term forest data are from managed stands (forest trial experiments), where natural successional processes are disguised by human interventions (cf. Lindner et al., 1997). Long-term data on structural features from unmanaged forests that span several decades are rare (cf. Bugmann, 1996). Thus, little is known on the accuracy of forest gap models in simulating structural features of unmanaged stands. Therefore, the objectives of this study were to (1) evaluate the performance of the “general and realistic” (Levins, 1966) forest gap model ForClim in simulating structural features based on a unique data set on longterm forest dynamics from the Swiss National Park; and (2) to examine what kind of changes to the model (structure and parameter estimates) would be required to improve the local precision of this model in the context of this site-specific study.
2. Material and methods 2.1. Study site The Swiss National Park (SNP) is located in the southeastern part of Switzerland and covers an area of approximately 170 km2 , 50 km2 of which are forested. The area was not influenced directly by humans during most of the 20th century. The elevation ranges from 1350 to 3170 m above sea level (m a.s.l.). The mean annual precipitation and mean annual temperature are 925 ± 162 mm and 0.2 ± 0.7 ◦ C (mean ± standard deviation; measured at the weather station in Buffalora located just outside the Park, 1980 m a.s.l.). The SNPs forests are composed of five conifer species. Mountain pine (Pinus montana Miller), Swiss stone pine (Pinus cembra L.), and European larch (Larix decidua Miller) are the dominating tree species, while Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst) are less abundant (Zoller, 1995). Both Scots pine and Norway spruce
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are not competitive in the cold and dry climate at high elevations in the SNP (Ellenberg, 1996; Keller et al., 1998). Today, stands dominated by Mountain pine occupy large parts of the SNP, while other areas are covered with forests dominated by Swiss stone pine (or a mixture of Swiss Stone pine/larch), and mixed species stands (all five species; Risch et al., 2003, 2004). 2.2. Long-term forest data A database for the SNPs forests exists for the year 1957 (Kurth et al., 1960). The database contains information on the number of trees/ha in certain DBH (diameter at breast height) classes sampled on 2050 systematically distributed plots, which was then consolidated to 131 stands (Kurth et al., 1960). Today, only the stand level data are available. We re-sampled 19 of the 131 stands in 2001/2002. They were located within an area of approximately 80 km2 in the center of the Park at elevations between 1700 and 2200 m a.s.l., and were selected randomly in proportion to their abundance in 1957 (Kurth et al., 1960). The 19 stands were then divided into stand types based on their species composition, tree density and stand density in 1957: (1) stands dominated by Mountain pine (hereafter referred to as “mountain pine”); (2) stands dominated by Mountain pine but with considerable amounts of all other species (“mixed”); and (3) stands dominated by Swiss stone pine or Swiss stone pine/larch (“stone pine”). These three groups contained six, six, and seven stands (Risch et al., 2003). We sampled 16 points in each stand on a systematic grid of 70 m × 70 m or 40 m × 40 m, depending on stand size, using the point-centered quarter method (Greig-Smith, 1983). Trees taller than breast height were sampled, and tree density (number of stems/ha) for different DBH classes was calculated per species and stand (for a detailed description see Risch et al., 2003, 2004). The numbers of trees/ha per DBH class and species were then averaged for the three different stand types “mountain pine”, “mixed”, and “stone pine” and both sampling years. 2.3. The gap model ForClim The horizontally non-explicit forest model used in this study is ForClim. In this model as well as in
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many other forest gap models, establishment, growth and mortality of individual trees are simulated on small patches of land (often 1/12 ha) as a function of species natural histories and the extrinsic and intrinsic conditions of the stand. To obtain forest development at larger spatial scales, the successional patterns of patches from many simulation runs are averaged. This concept is supported by plant succession studies, which show that a forest ecosystem may be described by the average growth dynamics of a multitude of patches with different successional ages. Shugart (1984) provided a comprehensive overview of the background and general formulation of forest gap models. ForClim consists of three modular submodels, each of which can be run independently or in combination: ForClim-E is a submodel for the abiotic environment, including a soil water balance model developed by Bugmann and Cramer (1998). ForClim-S is a submodel for soil carbon and nitrogen turnover, modified from Pastor and Post (1985). ForClim-P is a submodel for tree population dynamics based on the well-established concept of gap dynamics (Watt, 1947; Shugart, 1984). The specific assumptions, equations and parameter estimation procedures for the ForClim model were described in detail by Bugmann and Solomon (2000) and the references contained therein. The version used in this study differs from the latest published version (Bugmann and Solomon, 2000) in two respects, both of which have been accomplished in unpublished research prior to the present study. • It uses a log-normal distribution for sampling time series of monthly precipitation data from long-term statistical parameters, as opposed to the normal distribution used in earlier versions of ForClim. This change was introduced because particularly in dry areas, precipitation is not distributed normally around the long-term mean, and assuming a normal distribution leads to a strong overestimation of the frequency of months with very little or even zero precipitation. • The tree regeneration routine was changed to account for differences in regeneration strategies of shade-tolerant and shade-intolerant tree species, following the rationale by He and Mladenoff (1999) for a spatially explicit landscape model. There is an ecological trade-off in the sense that shade-
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intolerant tree species often produce more offspring under favorable conditions than shade-tolerant ones (Kimmins, 1997). To take this into account, the multiplier kLa was included in the calculation of the number of newly established trees in ForClim. kLa is a species-specific parameter that describes the light tolerance, ranging from 1 (most shade-tolerant) to 9 (least shade-tolerant). Thus, with this change we effectively assume that shade-intolerant trees produce up to nine times as much offspring as shade-tolerant trees. 2.4. Initialisation of ForClim with measured 1957 data An initialization of the 1957 forest stand data on a 833 m2 patch-size scale was necessary because of the patch size used in ForClim (see above). To accomplish this, we used the structure generator (Strugen) of the forest growth model SILVA (Pretzsch, 2001). Strugen is powerful in generating detailed forest data based on inventory data (stems/ha in different DBH classes), while simultaneously considering the spatial interactions between trees. We generated a 1-ha forest patch for each specific forest stand type using Strugen in a first step. Since Strugen assigns an x–y coordinate for each tree when generating the patch, we were able to divide the one-hectare patch into twelve 833 m2 sub-patches in a second step. Each of these sub-patches contained a certain number of trees defined by their x–y coordinates. This procedure was repeated 10 times, resulting in a total of 120 sub-patches. These sub-patches were imported into ForClim for simulation, and the model was run for each of these 120 patches. A summary of the initialized and the empirical data per stand type can be found in Fig. 1. ForClim only considers trees with a DBH larger than 1.27 cm, whereas the empirical data contain all trees with a DBH larger than 0.1 cm. As the 1957 data only contained an average number of trees for this particular DBH class, we were not able to reduce the historic data set to only contain trees with a DBH larger than 1.27 cm. Thus, all trees with DBH larger than 0.1 cm had to be kept in the empirical data set, whereas the model results do not include the trees between 0.1 and 1.26 cm in DBH. Thus, DBH class 0–4 cm is not shown in Fig. 1.
2.5. Simulation of structural features between 1957 and 2001/2002 Using the initialized 1957 data, we (1) simulated the development of the most widespread forest stands (“mountain pine”) with the standard model formulation as described above for the time period of 1957 to 2001/2002; (2) analyzed the simulation results from (1) in terms of local precision. We identified a modeling problem and subsequently improved the model (structural modifications), and again simulated the development of the “mountain pine” stand type between 1957 and 2001/2002 in order to analyze whether our changes lead to higher precision in forest stand simulation; (3) used the structurally improved model and calibrated some of the species-specific model parameters based on ecological rationale and “local” field data to improve the fit between simulated and observed data for the mountain pine stands; (4) applied the model to the other two stand types (“stone pine” and “mixed”). Climate data for all simulations were taken from the weather station Buffalora (1980 m a.s.l.) located just outside the Park. For the “mountain pine” stands, which were located on south slopes, ForClim was set up to simulate dry conditions (i.e., the parameter for slope/aspect (kSlAsp) was set to +2). For the other two stand types, which were located on north or west slopes, kSlAsp was set to −2. 3. Results 3.1. Simulation results with the original ForClim model for the “mountain pine” stand type. Simulating the structural development of the “mountain pine” stands between 1957 and 2001/2002 with the model yielded poor results. Total number of stems/ha and biomass decreased to almost zero. Analyzing the simulation output revealed that (i) most of the trees died shortly after 1957; and (ii) no regeneration took place under the canopy of the initial stand. To determine the cause of this behavior, we analyzed the structural reasons for poor tree growth and excessive mortality in the model. We found that the height to
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Fig. 1. Comparison of initialized and empirical 1957 data for all three stand types. Stems/ha of all species within a certain DBH class are added.
diameter relationship of individual trees was responsible for this artifact. Specifically, most of the larger trees died soon after 1957, as they were approaching their maximum height. The growth function implemented in ForClim V2.9 is based on a parabolic relationship between tree height and DBH (Botkin et al., 1972). As a result, a tree grows only minimally in diameter as it approaches its maximum height, and growth comes to a complete stop when maximum height is reached. As trees that grow very slowly are subject to enhanced mortality in ForClim (cf. Botkin et al., 1972; Bugmann, 1994), they die within a short time. Although it has been argued that a parabolic height–diameter relationship has several advantages (Ker and Smith, 1955), we consider this behavior to be questionable from a bio-
logical point of view. Therefore, we decided to replace the parabolic height–diameter function in ForClim with an asymptotic one, which is biologically more plausible (cf. Lindner et al., 1997), because maximum height is only reached when tree diameter approaches infinity, thus avoiding large trees to become subject to an excessive growth-related mortality rate. 3.2. Structural model modifications 3.2.1. Implementation of a new height–diameter relationship The new asymptotic function implies that trees still grow in DBH after reaching their maximum height. The function includes Eq. (1), following Leemans and
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Table 1 Linear regressions H = sD + 137 [cf. Eq. (2)] for the five dominating tree species of the SNP
Pinus montana Pinus cembra Pinus sylvestris Picea abies Larix decidua
s
n
r2
P-value
41 55 58 59 62
557 100 100 90 100
0.55 0.79 0.53 0.82 0.78
<0.001 <0.001 <0.001 <0.001 <0.001
H, tree height; D, tree diameter; n, number of trees.
Prentice (1989): H = a + b(1 − ecD )
(1)
where H is the height of a tree, a = 137 cm (breast height), b = Hmax − a, Hmax is the maximum height of a certain tree species, c = −s/b, where s is a parameter denoting initial height growth relative to diameter growth, i.e., the “skinniness” of a tree, and D is the diameter at breast height (DBH). If we assume tree volume V to be proportional toD2 H (cf. Moore, 1989), V can be expressed as V = D2 (a + b[1 − ecD ]) = (a + b)D2 − bD2 ecD
(2)
For the derivative of V with respect to D, we find dV = 2(a + b)D − DbecD (cD + 2) dD = D(2Hmax − becD (cD + 2))
(3)
Following Moore (1989), we derived a new diameter growth equation, which is given by dD = gD dt
1 − H/Hmax 2Hmax − becD (cD + 2)
(4)
where g is the growth rate (cm/year). We calculated values of the parameter s (skinniness of a tree) for the dominant tree species present in the SNP using empirical data from 1957 (Kurth et al., 1960) to 2001/2002 (Table 1). The implementation of the new growth function Eq. (4) resulted in version 2.9.3 of ForClim.
3.2.2. Simulation with new height–diameter relationship (ForClim V2.9.3) for the “mountain pine” stand type Using ForClim V2.9.3 for simulating the structural development of the “mountain pine” stand type from 1957 to 2001/2002 yielded increasing biomass and decreasing total number of stems/ha, as observed in the empirical data (Fig. 2). The simulated stand contained 2113 stems/ha in 1957 and 1191 in 2001/2002. These numbers are 10–15% lower than the empirical values (1957: 2438, 2001/2002: 1350). However, the empirical data contain all trees with DBH larger than 0.1 cm, and not only the ones with DBH larger than 1.27 cm as the model does. Based on the number of trees with DBH between 0.1 and 1.27 cm calculated from the 2001/2002 data, we would expect a density that is up to 8% lower in the simulated data set. Thus, by implementing a new height–diameter equation, we were able to simulate stand density development in close agreement with empirical observations, without any parameter “tuning”. Simulated biomass was overestimated for the year 2001/2002 compared with the empirical value. However, the simulated values represent stem plus foliage biomass, whereas the measured data refer to stem biomass alone; thus, an overestimation of 10–20% has to be expected. A comparison between the simulated and empirical structural features for the year 2001/2002 [density (stems/ha) and basal area (BA; m2 /ha)] according to the different DBH classes can be found in Fig. 3, model run 1. While the number of stems/ha was slightly higher than the one of the empirical data, BA was found to be much too high. In the next step of the analysis, we evaluated possible inaccuracies in the model parameter values as a possible source for these divergences. 3.3. Tree species-specific parameter changes (model calibration) A closer analysis of the simulation results (Fig. 3, model run 1) showed that too many large trees survived. As growing conditions in the SNP are fairly rough (hot dry summers, cold winters with high snow pack), only few trees reach their maximum age. Of the 384 Mountain pine trees sampled in 2001/2002, only three were found to be older than 200 years, which would correspond to less than 1% of all trees reaching half the maxi-
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Fig. 2. Modeled development of the “mountain pine” stand type between 1957 and 2001/2002, using ForClim V2.9.3. Left: simulated cumulative biomass (trees/ha). The open circle indicates empirical values estimated for this stand type in 2001/2002 (106 trees/ha bole biomass, unpublished data). No value for empirical 1957 biomass is available. Right: simulated total number of stems per hectare (closed circles). The two open circles indicate the empirical number of stems/ha.
mum age of 400 years. However, the default age-related mortality parameter kDeathP (Bugmann, 1994) implemented in ForClim is based on the assumption that 1% of all established saplings (DBH = 1.27 cm) survive to the species-specific maximum age. This clearly is not the case in the SNP. Thus, we increased the value of this parameter from its default value of 4.605 (cf. Bugmann, 2001) to 9.21 (Fig. 3, model run 2). This change reflects the assumption that only 1‰ of the saplings reach their maximum age. The corresponding simulation results (“model run 2”, Fig. 3) yielded slightly too few stems/ha, but total BA was much closer to the empirical observations. We undertook a second approach to better approximate local conditions in the SNP by changing the values of the two parameters “browsing susceptibility” (kBrow) and “rate of seedling establishment” (kEstP) based on site-specific observations from the SNP (note that the default value of the parameter kDeathP, 4.605, was used for these simulations). These changes of kBrow and kEstP had the following effects: (i) they increased stress-induced seedling mortality; and (ii) decreased the number of saplings, especially of nonwind-dispersed species. Risch et al. (2003) reported high browsing percentages for the five tree species found in the SNP: Mountain pine 17%, Swiss stone pine 37%, Larch 81%, Norwary spruce 83%, Scots pine (only few saplings found) 0%. The estimation for browsing pressure was thus obtained from the empirical data (2001/2002), whereas for seedling establish-
ment we had no field data, and thus assumed 10 times lower establishment rates for the bird-dispersed Swiss stone pine compared to the four other species, which are wind-dispersed. As can be seen in Fig. 3 (model run 3), these two changes were only effective in reducing the number of Swiss stone pine and Norway spruce trees in DBH class 5–9 cm, but they did not considerably change total number of stems/ha or BA compared to model run 1. However, the reduction of Swiss stone pine and Norway spruce trees in DBH class 5–9 cm still yielded results closer to the empirical data. Finally, we combined the changes made in model run 3 (browsing and establishment) with the ones made in model run 2 (mortality) (Fig. 3, model run 4). Using this modified model setup, the simulated number of stems/ha was lower than observed, but BA was comparable to the empirical data. Yet, trees seem to grow faster in the model than in reality, resulting in highest BA for DBH classes 20–49 cm, compared to DBH classes 10–29 cm in the empirical data. However, in this simulation run some larch trees were able to establish, as observed in the empirical data. Overall, when comparing the four model runs (1–4) conducted for the “mountain pine” stand type, we found that ForClim was relatively robust in simulating species composition. Only the species composition in DBH class 5–9 cm was affected by the different model setups. The structural features, however, showed some differences. The number of stems/ha in DBH class 5–9 cm were generally underestimated in all model runs, while
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Fig. 3. Empirical and simulated number of stems/ha and BA per DBH class in the “mountain pine” stand type in 2001/2002. Simulations were conducted with four different model setups of ForClim V2.9.3. Model run 1: no changes, model run 2: kDeathP 9.21 instead of the default value 4.605, model run 3: kEstP, kBrow adjusted, model run 4: kEstP, kBrow and kDeathP changed.
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Fig. 4. Empirical and simulated number of stems/ha and BA per DBH class in the “stone pine” stand type in 2001/2002.
they were slightly too high for trees with DBH larger than 30 cm. Yet, overall, we conclude that the model can be considered fairly robust to changes in model parameters when simulating stand structural features. Since model run 4 yielded the results closest to the observed data, we used this modified setup of ForClim V2.9.3 for simulating the structural development of the “stone pine” and “mixed” stand types.
3.4. Model application to the “stone pine” and “mixed” stand types The comparison between simulated and empirical structural features for the year 2001/2002 of the “stone pine” stand type can be found in Fig. 4. Comparing the simulated and empirical results, it can be seen that the number of Norway spruce trees with DBH between 5
Fig. 5. Empirical and simulated number of stems/ha and BA per DBH class in the “mixed” stand type in 2001/2002.
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and 19 cm was overestimated. However, these trees did not contribute much to the BA in either of these two DBH classes. In general, the model underestimated the number of large trees (DBH larger than 30 cm), leading to an underestimation in BA. The simulated structural development of the “mixed” stand type is shown in Fig. 5. While stand density and BA were similar for the empirical and simulated results, species composition yielded major differences. Our observations in the Park revealed high numbers of large Scots pine and larch trees. In the model, Scots pine was not able to establish at all, and only a few larch trees were detected after 45 years of simulation. Again, too many Norway spruce trees were simulated for small DBH classes. Further, Mountain pine trees seemed to survive much better in the model than actually observed. Overall, the simulations of the mixed stand type yielded the poorest results when comparing empirical and simulated data.
4. Discussion The aim of this study was to test and improve the performance of a general forest gap model, ForClim, with respect to its ability to precisely simulate forest structural features at a specific location (cf. Levins, 1966). After replacing the parabolic height–diameter relationship used in model version V2.9 by an asymptotic function (resulting in ForClim version V2.9.3), we were able to simulate long-term stand structural development in the SNP that approximated empirical observations fairly well. The remaining differences between simulated and observed data may result from errors in both the empirical data source and the model itself, as discussed below. The empirical data might contain some error due to the relatively low number of samples per stand type in 2001/2002 (6, 6 and 7, respectively; see Section 2), the different sampling schemes, or different sampling size areas in 1957 versus 2001/2002. The most conspicuous example for these problems is evident from the large numbers of larch and spruce trees with DBH larger than 30 cm of the mixed stands in the data set sampled in 2001/2002, compared to the much lower number of these species found in 1957 (Fig. 5). With regard to the accuracy of the model in its simulation of the three different stand types, we found that in the
“mountain pine” type the number of small trees (DBH between 5 and 19 cm) was underestimated. A potential reason for this could be that in the model too large tree crowns are assigned to Mountain pine trees (cf. Bugmann, 1994). In the SNP, most Mountain pines have very small crowns. This leads to fairly open stands (canopy closure is around 45%) in which regeneration is abundant (Risch et al., 2003). Thus, competition for light is most likely much lower than in stands with higher canopy closure (Oliver and Larson, 1996), and regeneration therefore should be more numerous. ForClim, in its current setup, does not account for such local differences that may affect regeneration, and therefore the model tends to underestimate the number of small trees in the SNP. In order to further improve model behavior, the parameterization of Mountain pine should be adjusted for the study area, i.e., the model should account for the small crown sizes. The slight overestimation of number of trees/ha with DBH larger 29 cm most likely results from small discrepancies in the number of trees (simulated versus observed in 1957) in the initialization data set, which are due to the method used. In the “stone pine” stand type, the most evident differences between simulated and empirical data after 45 years were the high number of simulated Norway spruce trees with DBH between 5 and 19 cm. Naturally, Norway spruce would not be competitive in the inner-alpine climate with low precipitation and temperatures (Ellenberg, 1996; Keller et al., 1998), and therefore this species would regenerate poorly even on moist north-slopes (A. Risch, personal observations). Even though the model was run using temperature data too low to allow this species to be competitive in higher size classes (Ellenberg, 1996; Keller et al., 1998), the north-slope moisture conditions assumed by the model likely were favorable for Norway spruce to successfully compete. Thus, our results suggest that the way Norway spruce is parameterized in ForClim may make this species overly sensitive to soil water availability, while temperature seems to be less limiting. In further studies, the parameterization of Norway spruce should be evaluated in more detail, especially when the model is used to simulate forest development at specific locations in inner-alpine dry regions. The “mixed” stand type yielded the poorest results. While again the number of stems/ha and BA were somewhat too low, the modeled species composition
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did not match the observed data. Especially the lack of Scots pine in the simulated data is evident. A possible reason for these differences could be that of these stands were found on sites where the local micro-climate most likely was different from the one measured at the weather station used for the simulations. These stands were either found in narrow canyons, where it is moister, or on west-slopes at somewhat lower elevation (Kurth et al., 1960). Both these microclimates may lead to conditions that allow Scots pine to establish. To improve the simulation output in ForClim, climatic data that are characteristic of this stand type would need to be collected. Overall, we found that ForClim yielded fairly good results in predicting long-term structural changes in different forest stands. The model behavior could potentially be further improved by implementing a light-dependent value of the parameter s of the height–diameter relationship, as Lindner et al. (1997) did for long-term simulations with the forest gap model FORSKA. Also, changes in the parameterization of the tree species present in the SNP, or increasing the number of samples in the field surveys may lead to a better match between simulated and measured data. Little information is available on whether gap models could yield results of comparable accuracy to simulations conducted with forest stand models such as, e.g., SILVA (Pretzsch, 1992, 2001; Kahn and Pretzsch, 1997). Lindner et al. (1997) suggested that they probably would not. However, gap models have to date mostly been tested for reproduction of species composition and little is known on how well they reproduce structural patterns. We are convinced that the replacement of the parabolic height–diameter relationship by an asymptotic equation in ForClim has increased the generality and realism of the model while simultaneously bringing a local benefit for its application in the SNP. The calibration of three species-specific parameters (browsing, establishment, and mortality rates), however, certainly is valid for the precise study area only. Thus, it appears that the structure of ForClim, particularly after the modification made in the present study, is general, which is what the model has been developed for (Bugmann and Solomon, 2000), yet it can be calibrated for higher local precision using species-specific parameters based on local data, or qualitative knowledge of site-specific ecological processes.
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Thus, we conclude that the generality of ForClim (sensu Levins, 1966) does not come at the cost of a strong lack of local precision. Rather, a certain degree of local precision can be achieved by site-specific parameter estimation. We would like to emphasize that the validation of gap models with long-term data and their subsequent application in a “prognostic” mode could not only be used for simulating forest structural patterns, but such a procedure can also lead to insights into model problems that need to be and can be corrected. Once these models are validated, it will be possible to provide more reliable answers to applied research questions, such as those dealing with the long-term development of forest stands under specific management regimes, the impacts of climate change on these stands, or assessments of carbon storage in forest ecosystems.
Acknowledgements We thank Peter Biber, Forest Yield Science at the Technological University in Munich, for letting us use Strugen, St´ephanie Schmid for helping with the stand initialization in Strugen and Manuel Bleichenbacher for providing several programs for data conversion. We are grateful to several volunteers for their help during data collection. This study was funded by the Swiss Federal Institute of Technology, Zurich (grant No. TH1’/01-1). We also would like to express our gratitude to the Swiss National Park Service for the administrative and logistic support of our research in the SNP, and to two reviewers for useful comments on an earlier version of this manuscript.
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Bugmann, H., 2001. A comparative analysis of forest dynamics in the Swiss Alps and the Colorado Front Range. For. Ecol. Manage. 145, 43–55. Bugmann, H., Cramer, W., 1998. Improving the behaviour of forest gap models along drought gradients. For. Ecol. Manage. 103, 247–263. Bugmann, H.K.M., Solomon, A.M., 2000. Explaining forest composition and biomass across multiple biogeographical regions. Ecol. Appl. 10, 95–114. Ellenberg, H., 1996. Vegetation Mitteleuropas und der Alpen in o¨ kologischer, dynamischer und historischer Sicht, fifth ed. UTB, Stuttgart. Fischlin, A., Gyalistras, D., 1997. Assessing impacts of climatic change on forests in the Alps. Global Ecol. Biogeogr. 6, 19–37. Greig-Smith, P., 1983. Quantitative Plant Ecology, third ed. Blackwell, Oxford. Hasenauer, H., Burgmann, M., Lexer, M.J., 2000. Konzepte der Wald¨okosystemmodellierung. Cbl. Ges. Forstw. 117, 137–164. He, H.S., Mladenoff, D.J., 1999. The effects of seed dispersal on the simulation of long-term forest landscape change. Ecosystems 2, 308–319. Kahn, M., Pretzsch, H., 1997. Das Wuchsmodell SILVA— Parametrisierung der Version 2.1 f¨ur Rein- und Mischbest¨ande aus Fichte und Buche. Allg. Forest Jagdztg. 168, 115–123. Keller, W., Wohlgemuth, T., Kuhn, N., Sch¨utz, M., Wildi, O., 1998. Waldgesellschaften der Schweiz auf floristischer Grundlage. Mitt. Eidg. Forsch. Anst. Wald Schnee Landsch. 73, 93–357. Ker, J.W., Smith, J.H.G., 1955. Advantages of the parabolic expression of height–diameter relationships. For. Chron. 31, 235–246. Kimmins, J.P., 1997. Forest Ecology: A Foundation for Sustainable Management, second ed. Prentice-Hall, Upper Saddle River, NJ. Kurth, A., Weidmann, A., Thommen, F., 1960. Beitrag zur Kenntnis der Waldverh¨altnisse im Schweizerischen Nationalpark. Mitt. Schweiz. Anst. Forst. Versuchsw. 36, 221–379. Leemans, R., Prentice, I.C., 1989. FORSKA, a general forest succession model. Department of Plant Ecology, Uppsala University, Uppsala, Sweden. Levins, R., 1966. The strategy of model building in population biology. Am. Sci. 54, 421–431. Lexer, M.J., 2000. Simulation der potentiellen nat¨urlichen Vegeta¨ tion in Osterreichs W¨aldern. In: Vergleich von statischen und dynamischen Modellkonzepten. Habilitationsschrift. Universit¨at f¨ur Bodenkultur, Wien. Lindner, M., Siev¨anen, R., Pretzsch, H., 1997. Improving the simulation of stand structure in a forest gap model. For. Ecol. Manage. 95, 183–195.
L¨offler, T.J., Lischke, H., 2001. Incorporation and influence of variability in an aggregated forest model. Nat. Res. Model. 14, 103–137. Moore, A.D., 1989. On the maximum growth equation used in forest gap simulation models. Ecol. Model. 45, 63–67. Oliver, C.D., Larson, B.C., 1996. Forest Stand Dynamics. Wiley, New York, NY. Pastor, J., Post, W.M., 1985. Development of a linked forest productivity–soil process model. US Department of Energy, ORNL/TM-9519. Prentice, I.C., Sykes, M.T., Cramer, W., 1993. A simulation model for transient effects of climate change of forest landscapes. Ecol. Model. 65, 51–70. Pretzsch, H., 1992. Konzeption und Konstruktion von Wuchsmodellen f¨ur Rein- und Mischbest¨ande. Forstl. Forschungsber. M¨unchen 115, 332. Pretzsch, H., 2001. Modellierung des Waldwachstums. Blackwell, Berlin. Risch, A.C., Nagel, L.M., Sch¨utz, M., Kr¨usi, B.O., Kienast, F., Bugmann, H., 2003. Structure and long-term development of subalpine Pinus montana Miller and Pinus cembra L. forests in the central European Alps. Forstw. Cbl. 122, 219–230. Risch, A.C., Sch¨utz, M., Kr¨usi, B.O., Kienast, F., Wildi, O., Bugmann, H., 2004. Detecting successional changes in long-term empirical data from subalpine conifer forests. Plant Ecol. 172, 95–105. Shao, G., Bugmann, H., Yan, X., 2001. A comparative analysis of the structure and behavior of three gap models at sites in northeastern China. Clim. Change 51, 389–413. Shugart, H.H., 1984. A Theory of Forest Dynamics: The Ecological Implications of Forest Succession Models. Springer, New York, NY. Solomon, A.M., West, D.C., Solomon, J.A., 1981. Simulating the role of climate change and species immigration in forest succession. In: West, D.C., Shugart, H.H., Botkin, D.B. (Eds.), Forest Succession: Concepts and Application. Springer-Verlag, New York, NY, pp. 154–177. Urban, D.L., Shugart, H.H., 1989. Forest response to climate change: a simulation study for southeastern forests. In: Smith, J.B., Tirpak, D. (Eds.), Potential Effects of Global Climate Change on the United States. EPA, Washington, DC. Watt, A.S., 1947. Patterns and processes in the plant community. J. Ecol. 35, 1–22. Zoller, H., 1995. Vegetationskarte des Schweizerischen Nationalparks. Erl¨auterungen. Nationalpark–Forschung Schweiz 85, 1–108.
Simulating structural forest patterns with a forest gap model: a model evaluation Anita C. Rischa,∗,1 , Caroline Heirib , Harald Bugmannb b
a Swiss Federal Institute for Forest, Snow and Landscape Research, Z¨ urcherstrasse 111, 8903 Birmensdorf, Switzerland Mountain Forest Ecology, Department of Environmental Sciences, Swiss Federal Institute of Technology Z¨urich, 8092 Z¨urich, Switzerland
Received 2 September 2003; received in revised form 4 May 2004; accepted 4 June 2004
Abstract Ecological models can be characterized by their degree of generality, reality and precision. Any model, being a deliberate simplification of reality, cannot excel in all three aspects. Forest gap models have been widely used for studying tree population dynamics, but their predictions have not often been tested for their local precision, but rather for their broad agreement with descriptions of near-natural vegetation. The objectives of our study were (1) to evaluate the performance of the forest gap model ForClim, which had been developed striving for generality and realism, in simulating the long-term development of structural features in Swiss mountain forests; and (2) to examine whether and how the model needs to be changed to improve its precision for a specific site. We used long-term forest data (45 years) from three different forest types in the Swiss National Park. Initial simulation runs for the most dominant forest type in the study area failed to reproduce the observed structural patterns. A detailed analysis of the growth performance of individual trees led to the conclusion that a modified height–diameter function was required, which presumably increases the generality of the model. The new model structure led to simulated stand features that were broadly consistent with observations. After, in addition, taking local variations of model parameters (on mortality, browsing, and seedling establishment rates) into account, we were able to considerably improve the performance of ForClim in simulating the structural features of the different mountain forest stands. We suggest that from the point of view of its revised structure, the ForClim model is principally suitable for site-specific applications, but local precision can only be achieved by site-specific parameter estimation procedures. We conclude that model evaluation and validation as conducted in this study could be quite useful for increasing the reliability of simulations performed with this class of models. © 2004 Elsevier B.V. All rights reserved. Keywords: ForClim; Long-term forest data; Growth function; Forest succession; Validation
∗
Corresponding author. Tel.: +1 315 443 4746; fax: +1 315 443 2012. E-mail address: [email protected] (A.C. Risch). 1 Present address: Department of Biology, Syracuse University, 207 Biological Research Laboratory, 130 College Place, Syracuse NY 13244, USA. 0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2004.06.029
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1. Introduction Forest gap models are individual-tree based, semimechanistic simulators designed to study tree population dynamics on small patches of land that have been used in many studies, typically to evaluate the dynamics of tree species composition at specific places over time (cf. Botkin et al., 1972; Shugart, 1984; Bugmann, 2001). The underlying ecological concept of all these models is the view of stochastic, cyclical succession, also known as “shifting-mosaic” dynamics (cf. Watt, 1947; Bormann and Likens, 1979). To date, several dozens of forest gap models have been developed, described, and applied to a wide variety of forest types, mainly located in temperate and boreal climate zones (e.g., Solomon et al., 1981; Shugart, 1984; Urban and Shugart, 1989; Prentice et al., 1993; Bugmann, 1997; Fischlin and Gyalistras, 1997). However, it has only rarely been explored how widely applicable one particular model of this family could be. Levins (1966) suggested that ecological models can be characterized by the degree to which they are realistic, precise, and general. According to Levins (1966), any given model can excel in two of the three aspects, but not in all three at the same time. In the sense of this paradigm, most forest gap model studies sacrificed generality in favor of realism and (local) precision. Over the past 10 years, we have been striving to develop a forest gap model (ForClim) that is as simple as possible and that incorporates robust and widely applicable representations of the ecological effects of climatic variables (Bugmann, 1996). The aim of these developments was to be able to study forest dynamics under a wide range of climatic conditions in different biogeographical areas of the boreal and temperate regions. We showed that the model is broadly applicable to forests in Europe, in eastern North America, in the Pacific Northwest of the US (all treated in Bugmann and Solomon, 2000) and in northeastern China (Shao et al., 2001). In other words, sensu Levins (1966) we were striving for generality and realism of the model, potentially at the expense of local precision. Up to now, our own as well as many other modeling studies have mostly focused on simulating temporal changes in tree species composition (e.g., Shugart, 1984; Hasenauer et al., 2000), and they have generally been validated by comparing simulation results with coarse descriptions of potential natural vegetation
(e.g., overview in Shugart, 1984; Lexer, 2000) or national forest inventory data (e.g., L¨offler and Lischke, 2001). Yet, even though gap models could also be useful for predicting local structural forest patterns (e.g., size distributions), which would increase their power in predicting ecosystem development, only few studies have been conducted in this context up to date (e.g., Lindner et al., 1997). The main reason for the lack of such research is that most long-term forest data are from managed stands (forest trial experiments), where natural successional processes are disguised by human interventions (cf. Lindner et al., 1997). Long-term data on structural features from unmanaged forests that span several decades are rare (cf. Bugmann, 1996). Thus, little is known on the accuracy of forest gap models in simulating structural features of unmanaged stands. Therefore, the objectives of this study were to (1) evaluate the performance of the “general and realistic” (Levins, 1966) forest gap model ForClim in simulating structural features based on a unique data set on longterm forest dynamics from the Swiss National Park; and (2) to examine what kind of changes to the model (structure and parameter estimates) would be required to improve the local precision of this model in the context of this site-specific study.
2. Material and methods 2.1. Study site The Swiss National Park (SNP) is located in the southeastern part of Switzerland and covers an area of approximately 170 km2 , 50 km2 of which are forested. The area was not influenced directly by humans during most of the 20th century. The elevation ranges from 1350 to 3170 m above sea level (m a.s.l.). The mean annual precipitation and mean annual temperature are 925 ± 162 mm and 0.2 ± 0.7 ◦ C (mean ± standard deviation; measured at the weather station in Buffalora located just outside the Park, 1980 m a.s.l.). The SNPs forests are composed of five conifer species. Mountain pine (Pinus montana Miller), Swiss stone pine (Pinus cembra L.), and European larch (Larix decidua Miller) are the dominating tree species, while Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst) are less abundant (Zoller, 1995). Both Scots pine and Norway spruce
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are not competitive in the cold and dry climate at high elevations in the SNP (Ellenberg, 1996; Keller et al., 1998). Today, stands dominated by Mountain pine occupy large parts of the SNP, while other areas are covered with forests dominated by Swiss stone pine (or a mixture of Swiss Stone pine/larch), and mixed species stands (all five species; Risch et al., 2003, 2004). 2.2. Long-term forest data A database for the SNPs forests exists for the year 1957 (Kurth et al., 1960). The database contains information on the number of trees/ha in certain DBH (diameter at breast height) classes sampled on 2050 systematically distributed plots, which was then consolidated to 131 stands (Kurth et al., 1960). Today, only the stand level data are available. We re-sampled 19 of the 131 stands in 2001/2002. They were located within an area of approximately 80 km2 in the center of the Park at elevations between 1700 and 2200 m a.s.l., and were selected randomly in proportion to their abundance in 1957 (Kurth et al., 1960). The 19 stands were then divided into stand types based on their species composition, tree density and stand density in 1957: (1) stands dominated by Mountain pine (hereafter referred to as “mountain pine”); (2) stands dominated by Mountain pine but with considerable amounts of all other species (“mixed”); and (3) stands dominated by Swiss stone pine or Swiss stone pine/larch (“stone pine”). These three groups contained six, six, and seven stands (Risch et al., 2003). We sampled 16 points in each stand on a systematic grid of 70 m × 70 m or 40 m × 40 m, depending on stand size, using the point-centered quarter method (Greig-Smith, 1983). Trees taller than breast height were sampled, and tree density (number of stems/ha) for different DBH classes was calculated per species and stand (for a detailed description see Risch et al., 2003, 2004). The numbers of trees/ha per DBH class and species were then averaged for the three different stand types “mountain pine”, “mixed”, and “stone pine” and both sampling years. 2.3. The gap model ForClim The horizontally non-explicit forest model used in this study is ForClim. In this model as well as in
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many other forest gap models, establishment, growth and mortality of individual trees are simulated on small patches of land (often 1/12 ha) as a function of species natural histories and the extrinsic and intrinsic conditions of the stand. To obtain forest development at larger spatial scales, the successional patterns of patches from many simulation runs are averaged. This concept is supported by plant succession studies, which show that a forest ecosystem may be described by the average growth dynamics of a multitude of patches with different successional ages. Shugart (1984) provided a comprehensive overview of the background and general formulation of forest gap models. ForClim consists of three modular submodels, each of which can be run independently or in combination: ForClim-E is a submodel for the abiotic environment, including a soil water balance model developed by Bugmann and Cramer (1998). ForClim-S is a submodel for soil carbon and nitrogen turnover, modified from Pastor and Post (1985). ForClim-P is a submodel for tree population dynamics based on the well-established concept of gap dynamics (Watt, 1947; Shugart, 1984). The specific assumptions, equations and parameter estimation procedures for the ForClim model were described in detail by Bugmann and Solomon (2000) and the references contained therein. The version used in this study differs from the latest published version (Bugmann and Solomon, 2000) in two respects, both of which have been accomplished in unpublished research prior to the present study. • It uses a log-normal distribution for sampling time series of monthly precipitation data from long-term statistical parameters, as opposed to the normal distribution used in earlier versions of ForClim. This change was introduced because particularly in dry areas, precipitation is not distributed normally around the long-term mean, and assuming a normal distribution leads to a strong overestimation of the frequency of months with very little or even zero precipitation. • The tree regeneration routine was changed to account for differences in regeneration strategies of shade-tolerant and shade-intolerant tree species, following the rationale by He and Mladenoff (1999) for a spatially explicit landscape model. There is an ecological trade-off in the sense that shade-
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intolerant tree species often produce more offspring under favorable conditions than shade-tolerant ones (Kimmins, 1997). To take this into account, the multiplier kLa was included in the calculation of the number of newly established trees in ForClim. kLa is a species-specific parameter that describes the light tolerance, ranging from 1 (most shade-tolerant) to 9 (least shade-tolerant). Thus, with this change we effectively assume that shade-intolerant trees produce up to nine times as much offspring as shade-tolerant trees. 2.4. Initialisation of ForClim with measured 1957 data An initialization of the 1957 forest stand data on a 833 m2 patch-size scale was necessary because of the patch size used in ForClim (see above). To accomplish this, we used the structure generator (Strugen) of the forest growth model SILVA (Pretzsch, 2001). Strugen is powerful in generating detailed forest data based on inventory data (stems/ha in different DBH classes), while simultaneously considering the spatial interactions between trees. We generated a 1-ha forest patch for each specific forest stand type using Strugen in a first step. Since Strugen assigns an x–y coordinate for each tree when generating the patch, we were able to divide the one-hectare patch into twelve 833 m2 sub-patches in a second step. Each of these sub-patches contained a certain number of trees defined by their x–y coordinates. This procedure was repeated 10 times, resulting in a total of 120 sub-patches. These sub-patches were imported into ForClim for simulation, and the model was run for each of these 120 patches. A summary of the initialized and the empirical data per stand type can be found in Fig. 1. ForClim only considers trees with a DBH larger than 1.27 cm, whereas the empirical data contain all trees with a DBH larger than 0.1 cm. As the 1957 data only contained an average number of trees for this particular DBH class, we were not able to reduce the historic data set to only contain trees with a DBH larger than 1.27 cm. Thus, all trees with DBH larger than 0.1 cm had to be kept in the empirical data set, whereas the model results do not include the trees between 0.1 and 1.26 cm in DBH. Thus, DBH class 0–4 cm is not shown in Fig. 1.
2.5. Simulation of structural features between 1957 and 2001/2002 Using the initialized 1957 data, we (1) simulated the development of the most widespread forest stands (“mountain pine”) with the standard model formulation as described above for the time period of 1957 to 2001/2002; (2) analyzed the simulation results from (1) in terms of local precision. We identified a modeling problem and subsequently improved the model (structural modifications), and again simulated the development of the “mountain pine” stand type between 1957 and 2001/2002 in order to analyze whether our changes lead to higher precision in forest stand simulation; (3) used the structurally improved model and calibrated some of the species-specific model parameters based on ecological rationale and “local” field data to improve the fit between simulated and observed data for the mountain pine stands; (4) applied the model to the other two stand types (“stone pine” and “mixed”). Climate data for all simulations were taken from the weather station Buffalora (1980 m a.s.l.) located just outside the Park. For the “mountain pine” stands, which were located on south slopes, ForClim was set up to simulate dry conditions (i.e., the parameter for slope/aspect (kSlAsp) was set to +2). For the other two stand types, which were located on north or west slopes, kSlAsp was set to −2. 3. Results 3.1. Simulation results with the original ForClim model for the “mountain pine” stand type. Simulating the structural development of the “mountain pine” stands between 1957 and 2001/2002 with the model yielded poor results. Total number of stems/ha and biomass decreased to almost zero. Analyzing the simulation output revealed that (i) most of the trees died shortly after 1957; and (ii) no regeneration took place under the canopy of the initial stand. To determine the cause of this behavior, we analyzed the structural reasons for poor tree growth and excessive mortality in the model. We found that the height to
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Fig. 1. Comparison of initialized and empirical 1957 data for all three stand types. Stems/ha of all species within a certain DBH class are added.
diameter relationship of individual trees was responsible for this artifact. Specifically, most of the larger trees died soon after 1957, as they were approaching their maximum height. The growth function implemented in ForClim V2.9 is based on a parabolic relationship between tree height and DBH (Botkin et al., 1972). As a result, a tree grows only minimally in diameter as it approaches its maximum height, and growth comes to a complete stop when maximum height is reached. As trees that grow very slowly are subject to enhanced mortality in ForClim (cf. Botkin et al., 1972; Bugmann, 1994), they die within a short time. Although it has been argued that a parabolic height–diameter relationship has several advantages (Ker and Smith, 1955), we consider this behavior to be questionable from a bio-
logical point of view. Therefore, we decided to replace the parabolic height–diameter function in ForClim with an asymptotic one, which is biologically more plausible (cf. Lindner et al., 1997), because maximum height is only reached when tree diameter approaches infinity, thus avoiding large trees to become subject to an excessive growth-related mortality rate. 3.2. Structural model modifications 3.2.1. Implementation of a new height–diameter relationship The new asymptotic function implies that trees still grow in DBH after reaching their maximum height. The function includes Eq. (1), following Leemans and
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Table 1 Linear regressions H = sD + 137 [cf. Eq. (2)] for the five dominating tree species of the SNP
Pinus montana Pinus cembra Pinus sylvestris Picea abies Larix decidua
s
n
r2
P-value
41 55 58 59 62
557 100 100 90 100
0.55 0.79 0.53 0.82 0.78
<0.001 <0.001 <0.001 <0.001 <0.001
H, tree height; D, tree diameter; n, number of trees.
Prentice (1989): H = a + b(1 − ecD )
(1)
where H is the height of a tree, a = 137 cm (breast height), b = Hmax − a, Hmax is the maximum height of a certain tree species, c = −s/b, where s is a parameter denoting initial height growth relative to diameter growth, i.e., the “skinniness” of a tree, and D is the diameter at breast height (DBH). If we assume tree volume V to be proportional toD2 H (cf. Moore, 1989), V can be expressed as V = D2 (a + b[1 − ecD ]) = (a + b)D2 − bD2 ecD
(2)
For the derivative of V with respect to D, we find dV = 2(a + b)D − DbecD (cD + 2) dD = D(2Hmax − becD (cD + 2))
(3)
Following Moore (1989), we derived a new diameter growth equation, which is given by dD = gD dt
1 − H/Hmax 2Hmax − becD (cD + 2)
(4)
where g is the growth rate (cm/year). We calculated values of the parameter s (skinniness of a tree) for the dominant tree species present in the SNP using empirical data from 1957 (Kurth et al., 1960) to 2001/2002 (Table 1). The implementation of the new growth function Eq. (4) resulted in version 2.9.3 of ForClim.
3.2.2. Simulation with new height–diameter relationship (ForClim V2.9.3) for the “mountain pine” stand type Using ForClim V2.9.3 for simulating the structural development of the “mountain pine” stand type from 1957 to 2001/2002 yielded increasing biomass and decreasing total number of stems/ha, as observed in the empirical data (Fig. 2). The simulated stand contained 2113 stems/ha in 1957 and 1191 in 2001/2002. These numbers are 10–15% lower than the empirical values (1957: 2438, 2001/2002: 1350). However, the empirical data contain all trees with DBH larger than 0.1 cm, and not only the ones with DBH larger than 1.27 cm as the model does. Based on the number of trees with DBH between 0.1 and 1.27 cm calculated from the 2001/2002 data, we would expect a density that is up to 8% lower in the simulated data set. Thus, by implementing a new height–diameter equation, we were able to simulate stand density development in close agreement with empirical observations, without any parameter “tuning”. Simulated biomass was overestimated for the year 2001/2002 compared with the empirical value. However, the simulated values represent stem plus foliage biomass, whereas the measured data refer to stem biomass alone; thus, an overestimation of 10–20% has to be expected. A comparison between the simulated and empirical structural features for the year 2001/2002 [density (stems/ha) and basal area (BA; m2 /ha)] according to the different DBH classes can be found in Fig. 3, model run 1. While the number of stems/ha was slightly higher than the one of the empirical data, BA was found to be much too high. In the next step of the analysis, we evaluated possible inaccuracies in the model parameter values as a possible source for these divergences. 3.3. Tree species-specific parameter changes (model calibration) A closer analysis of the simulation results (Fig. 3, model run 1) showed that too many large trees survived. As growing conditions in the SNP are fairly rough (hot dry summers, cold winters with high snow pack), only few trees reach their maximum age. Of the 384 Mountain pine trees sampled in 2001/2002, only three were found to be older than 200 years, which would correspond to less than 1% of all trees reaching half the maxi-
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Fig. 2. Modeled development of the “mountain pine” stand type between 1957 and 2001/2002, using ForClim V2.9.3. Left: simulated cumulative biomass (trees/ha). The open circle indicates empirical values estimated for this stand type in 2001/2002 (106 trees/ha bole biomass, unpublished data). No value for empirical 1957 biomass is available. Right: simulated total number of stems per hectare (closed circles). The two open circles indicate the empirical number of stems/ha.
mum age of 400 years. However, the default age-related mortality parameter kDeathP (Bugmann, 1994) implemented in ForClim is based on the assumption that 1% of all established saplings (DBH = 1.27 cm) survive to the species-specific maximum age. This clearly is not the case in the SNP. Thus, we increased the value of this parameter from its default value of 4.605 (cf. Bugmann, 2001) to 9.21 (Fig. 3, model run 2). This change reflects the assumption that only 1‰ of the saplings reach their maximum age. The corresponding simulation results (“model run 2”, Fig. 3) yielded slightly too few stems/ha, but total BA was much closer to the empirical observations. We undertook a second approach to better approximate local conditions in the SNP by changing the values of the two parameters “browsing susceptibility” (kBrow) and “rate of seedling establishment” (kEstP) based on site-specific observations from the SNP (note that the default value of the parameter kDeathP, 4.605, was used for these simulations). These changes of kBrow and kEstP had the following effects: (i) they increased stress-induced seedling mortality; and (ii) decreased the number of saplings, especially of nonwind-dispersed species. Risch et al. (2003) reported high browsing percentages for the five tree species found in the SNP: Mountain pine 17%, Swiss stone pine 37%, Larch 81%, Norwary spruce 83%, Scots pine (only few saplings found) 0%. The estimation for browsing pressure was thus obtained from the empirical data (2001/2002), whereas for seedling establish-
ment we had no field data, and thus assumed 10 times lower establishment rates for the bird-dispersed Swiss stone pine compared to the four other species, which are wind-dispersed. As can be seen in Fig. 3 (model run 3), these two changes were only effective in reducing the number of Swiss stone pine and Norway spruce trees in DBH class 5–9 cm, but they did not considerably change total number of stems/ha or BA compared to model run 1. However, the reduction of Swiss stone pine and Norway spruce trees in DBH class 5–9 cm still yielded results closer to the empirical data. Finally, we combined the changes made in model run 3 (browsing and establishment) with the ones made in model run 2 (mortality) (Fig. 3, model run 4). Using this modified model setup, the simulated number of stems/ha was lower than observed, but BA was comparable to the empirical data. Yet, trees seem to grow faster in the model than in reality, resulting in highest BA for DBH classes 20–49 cm, compared to DBH classes 10–29 cm in the empirical data. However, in this simulation run some larch trees were able to establish, as observed in the empirical data. Overall, when comparing the four model runs (1–4) conducted for the “mountain pine” stand type, we found that ForClim was relatively robust in simulating species composition. Only the species composition in DBH class 5–9 cm was affected by the different model setups. The structural features, however, showed some differences. The number of stems/ha in DBH class 5–9 cm were generally underestimated in all model runs, while
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Fig. 3. Empirical and simulated number of stems/ha and BA per DBH class in the “mountain pine” stand type in 2001/2002. Simulations were conducted with four different model setups of ForClim V2.9.3. Model run 1: no changes, model run 2: kDeathP 9.21 instead of the default value 4.605, model run 3: kEstP, kBrow adjusted, model run 4: kEstP, kBrow and kDeathP changed.
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Fig. 4. Empirical and simulated number of stems/ha and BA per DBH class in the “stone pine” stand type in 2001/2002.
they were slightly too high for trees with DBH larger than 30 cm. Yet, overall, we conclude that the model can be considered fairly robust to changes in model parameters when simulating stand structural features. Since model run 4 yielded the results closest to the observed data, we used this modified setup of ForClim V2.9.3 for simulating the structural development of the “stone pine” and “mixed” stand types.
3.4. Model application to the “stone pine” and “mixed” stand types The comparison between simulated and empirical structural features for the year 2001/2002 of the “stone pine” stand type can be found in Fig. 4. Comparing the simulated and empirical results, it can be seen that the number of Norway spruce trees with DBH between 5
Fig. 5. Empirical and simulated number of stems/ha and BA per DBH class in the “mixed” stand type in 2001/2002.
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and 19 cm was overestimated. However, these trees did not contribute much to the BA in either of these two DBH classes. In general, the model underestimated the number of large trees (DBH larger than 30 cm), leading to an underestimation in BA. The simulated structural development of the “mixed” stand type is shown in Fig. 5. While stand density and BA were similar for the empirical and simulated results, species composition yielded major differences. Our observations in the Park revealed high numbers of large Scots pine and larch trees. In the model, Scots pine was not able to establish at all, and only a few larch trees were detected after 45 years of simulation. Again, too many Norway spruce trees were simulated for small DBH classes. Further, Mountain pine trees seemed to survive much better in the model than actually observed. Overall, the simulations of the mixed stand type yielded the poorest results when comparing empirical and simulated data.
4. Discussion The aim of this study was to test and improve the performance of a general forest gap model, ForClim, with respect to its ability to precisely simulate forest structural features at a specific location (cf. Levins, 1966). After replacing the parabolic height–diameter relationship used in model version V2.9 by an asymptotic function (resulting in ForClim version V2.9.3), we were able to simulate long-term stand structural development in the SNP that approximated empirical observations fairly well. The remaining differences between simulated and observed data may result from errors in both the empirical data source and the model itself, as discussed below. The empirical data might contain some error due to the relatively low number of samples per stand type in 2001/2002 (6, 6 and 7, respectively; see Section 2), the different sampling schemes, or different sampling size areas in 1957 versus 2001/2002. The most conspicuous example for these problems is evident from the large numbers of larch and spruce trees with DBH larger than 30 cm of the mixed stands in the data set sampled in 2001/2002, compared to the much lower number of these species found in 1957 (Fig. 5). With regard to the accuracy of the model in its simulation of the three different stand types, we found that in the
“mountain pine” type the number of small trees (DBH between 5 and 19 cm) was underestimated. A potential reason for this could be that in the model too large tree crowns are assigned to Mountain pine trees (cf. Bugmann, 1994). In the SNP, most Mountain pines have very small crowns. This leads to fairly open stands (canopy closure is around 45%) in which regeneration is abundant (Risch et al., 2003). Thus, competition for light is most likely much lower than in stands with higher canopy closure (Oliver and Larson, 1996), and regeneration therefore should be more numerous. ForClim, in its current setup, does not account for such local differences that may affect regeneration, and therefore the model tends to underestimate the number of small trees in the SNP. In order to further improve model behavior, the parameterization of Mountain pine should be adjusted for the study area, i.e., the model should account for the small crown sizes. The slight overestimation of number of trees/ha with DBH larger 29 cm most likely results from small discrepancies in the number of trees (simulated versus observed in 1957) in the initialization data set, which are due to the method used. In the “stone pine” stand type, the most evident differences between simulated and empirical data after 45 years were the high number of simulated Norway spruce trees with DBH between 5 and 19 cm. Naturally, Norway spruce would not be competitive in the inner-alpine climate with low precipitation and temperatures (Ellenberg, 1996; Keller et al., 1998), and therefore this species would regenerate poorly even on moist north-slopes (A. Risch, personal observations). Even though the model was run using temperature data too low to allow this species to be competitive in higher size classes (Ellenberg, 1996; Keller et al., 1998), the north-slope moisture conditions assumed by the model likely were favorable for Norway spruce to successfully compete. Thus, our results suggest that the way Norway spruce is parameterized in ForClim may make this species overly sensitive to soil water availability, while temperature seems to be less limiting. In further studies, the parameterization of Norway spruce should be evaluated in more detail, especially when the model is used to simulate forest development at specific locations in inner-alpine dry regions. The “mixed” stand type yielded the poorest results. While again the number of stems/ha and BA were somewhat too low, the modeled species composition
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did not match the observed data. Especially the lack of Scots pine in the simulated data is evident. A possible reason for these differences could be that of these stands were found on sites where the local micro-climate most likely was different from the one measured at the weather station used for the simulations. These stands were either found in narrow canyons, where it is moister, or on west-slopes at somewhat lower elevation (Kurth et al., 1960). Both these microclimates may lead to conditions that allow Scots pine to establish. To improve the simulation output in ForClim, climatic data that are characteristic of this stand type would need to be collected. Overall, we found that ForClim yielded fairly good results in predicting long-term structural changes in different forest stands. The model behavior could potentially be further improved by implementing a light-dependent value of the parameter s of the height–diameter relationship, as Lindner et al. (1997) did for long-term simulations with the forest gap model FORSKA. Also, changes in the parameterization of the tree species present in the SNP, or increasing the number of samples in the field surveys may lead to a better match between simulated and measured data. Little information is available on whether gap models could yield results of comparable accuracy to simulations conducted with forest stand models such as, e.g., SILVA (Pretzsch, 1992, 2001; Kahn and Pretzsch, 1997). Lindner et al. (1997) suggested that they probably would not. However, gap models have to date mostly been tested for reproduction of species composition and little is known on how well they reproduce structural patterns. We are convinced that the replacement of the parabolic height–diameter relationship by an asymptotic equation in ForClim has increased the generality and realism of the model while simultaneously bringing a local benefit for its application in the SNP. The calibration of three species-specific parameters (browsing, establishment, and mortality rates), however, certainly is valid for the precise study area only. Thus, it appears that the structure of ForClim, particularly after the modification made in the present study, is general, which is what the model has been developed for (Bugmann and Solomon, 2000), yet it can be calibrated for higher local precision using species-specific parameters based on local data, or qualitative knowledge of site-specific ecological processes.
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Thus, we conclude that the generality of ForClim (sensu Levins, 1966) does not come at the cost of a strong lack of local precision. Rather, a certain degree of local precision can be achieved by site-specific parameter estimation. We would like to emphasize that the validation of gap models with long-term data and their subsequent application in a “prognostic” mode could not only be used for simulating forest structural patterns, but such a procedure can also lead to insights into model problems that need to be and can be corrected. Once these models are validated, it will be possible to provide more reliable answers to applied research questions, such as those dealing with the long-term development of forest stands under specific management regimes, the impacts of climate change on these stands, or assessments of carbon storage in forest ecosystems.
Acknowledgements We thank Peter Biber, Forest Yield Science at the Technological University in Munich, for letting us use Strugen, St´ephanie Schmid for helping with the stand initialization in Strugen and Manuel Bleichenbacher for providing several programs for data conversion. We are grateful to several volunteers for their help during data collection. This study was funded by the Swiss Federal Institute of Technology, Zurich (grant No. TH1’/01-1). We also would like to express our gratitude to the Swiss National Park Service for the administrative and logistic support of our research in the SNP, and to two reviewers for useful comments on an earlier version of this manuscript.
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