Scaling Issues in Forest Succession Modeling
Harald Bugmann
Potsdam Institute for Climate Impact Research (PIK)
Potsdam, Germany
Scaling Issues in Forest Succession Modeling
Harald Bugmann
Potsdam Institute for Climate Impact Research (PIK)
Potsdam, Germany
Observations, experiments and modeling in ecology are often performed at very small scales in time and space, typically covering several weeks to a few years and several square meters to a few hectares, respectively. Many ecologists have noted that ecological knowledge is difficult to scale up in time and space, and therefore one wonders how present-day research results can be applied to alleviating concerns about the future development of the ecosphere. For at least three reasons, scaling is difficult in ecology: firstly, because ecosystems are organized hierarchically, with many feedback processes across scales; secondly, because ecosystems are highly non-linear systems; finally, because ecosystems are spatially heterogeneous ("patchy") as a consequence of spatial variations in (micro-) climatic and edaphic (influenced by soil) properties as well as disturbance regimes. Yet, there are still many instances where research results obtained at small scales are extrapolated linearly to much larger scales. A particularly impressive example for this is a study where the findings from experiments with sour orange trees during one growing season were extrapolated linearly across temporal and spatial scales to address questions relating to the long-term behavior of the global carbon cycle.
Bugmann reviewed the state-of-the-art regarding scaling issues in forest gap models, the most widespread class of models used to describe and project the dynamics of forest composition across several centuries (Shugart, 1984). Most emphasis was put on spatial upscaling, but temporal upscaling and downscaling issues were briefly covered as well.
Upscaling
Two different modes of upscaling were distinguished (see Figure 1.7 below). Firstly, implicit upscaling was discussed, i. e. taking scale-dependent features into account while developing model equations so as to formulate the model according to the requirements of its particular scale. Using three examples from forest gap models, Bugmann showed that this way of scaling is quite important, but hasn't always been taken into consideration appropriately.
Figure 1.7
Temporal and spatial scales and how they are bridged in forest gap models. In most of these models, tree physiology is not treated explicitly. Instead, the scale transition A is handled by introducing scaled, aggregated response functions ("parameterizations"). The gap dynamics hypothesis (Shugart, 1984) is used to achieve the scale transition B from the tree to the patch. A statistical interpretation of the results from many simulated patches is applied to derive the behavior of an entire forest (Bugmann et al., 1996) (C). Finally, spatially distributed simulation is employed to bridge the gap between an individual forest and forested landscapes/regions (D). A and B are implicit scaling methods, whereas C and D are explicit scaling methods. The figure is adapted from Urban et al. (1987).
Scaling is difficult in ecology because ecosystems are organized hierarchically, they are highly nonlinear systems, and they are spatially heterogeneous.
Secondly, explicit scaling was addressed, i. e. using procedures that typically involve numerical simulations to scale up the response of a local model in space and/or time. Based on the categorization by King (1990), Bugmann provided examples from gap modeling studies using two different extrapolation methods. Specifically, he presented simulation results aimed at recovering the spatial pattern of natural forest vegetation for the federal state of Brandenburg, Germany, which covers almost 30,000 km2. To apply gap models at such large spatial scales is a real challenge - earlier studies typically dealt with applying these models at a couple of individual sites scattered across a landscape. The results from the study showed that spatial extrapolation to such large scales is possible, given that there are no large-scale disturbances such as fires or insect attacks that determine the behavior of the system at the landscape to regional scales. For the case of Brandenburg, this assumption is probably realistic, whereas it would be wrong in other regions, e. g., in the boreal forest. The optimistic corollary of this is that we appear to be narrowing the spatial gap between climate models and impact models.
Spatial extrapolation to such large scales is possible, given that there are no large-scale disturbances such as fires or insect attacks that determine the behavior of the system at the landscape to regional scales.
Unfortunately, the simple models used in these examples do not and can not provide all the variables that are required for land surface parameterizations, such as albedo and the vegetation-dependent fluxes of latent and sensible heat. On the other hand, the more detailed succession models that provide these variables are much more difficult to upscale to the regional level because they require many input variables at a high temporal resolution, which are quite difficult to provide at the landscape scale. Moreover, simulations with these models at the regional scale would hardly be feasible due to their high computational demand.
Given dynamic models that are based on differential or difference equations, it is tempting to speculate that scaling up in time simply corresponds to numerical integration. Indeed, in cases where the model is not very complex and can be integrated easily over longer periods of time, numerical integration is most often used for temporal upscaling. In the case of gap models, there appears to be no immediate need to employ other methods of temporal upscaling because the model behavior can rather easily be simulated for several centuries to a few millennia. However, with other kinds of models numerical integration is often impractical. For example, most detailed physiological models can barely be integrated for several hundred years due to computer hardware limitations. Even if this is feasible, integration errors may add up to such an extent that the signal of the model is buried in the noise of the integration.
More importantly, in some cases numerical integration may not be appropriate at all due to internal model constraints. For example, with respect to gap models it is typically assumed that seeds of all species are available at any site and at any time; it is only the environmental conditions that control the exclusion of species from the establishment process. This implies that migrational lags usually are not considered in these models. Hence under scenarios of climatic change, the models may be too optimistic with respect to the availability of new species that could grow if they were there, but in reality will not grow because they require many years to immigrate.
To study the sensitivity of a gap model to the assumption of unlimited versus limited seed availability, a series of simulations along an environmental gradient in central Europe was performed with the ForClim model (Bugmann, 1996). Climate was assumed to change in a step fashion by +3°C in simulation year 800. In one set of simulations, an arbitrary migrational lag of 300 years was introduced, i. e., the species not present under current climate were assumed to be available only after simulation year 1100. This can lead to quite different projections of the species composition and aboveground biomass during several centuries after the climate has changed. For example, at the site Davos (see Figure 1.8 below) the subalpine Larix decidua - Picea abies forest simulated under the current climate is gradually replaced by a montane Abies alba - Fagus sylvatica - P. abies forest by year 1300 if unlimited propagule availability is assumed (Figure 1.8a). Assuming a migrational lag of 300 years (Figure 1.8b) induces a persistence of the subalpine forest after simulation year 800, whose biomass is reduced due to increased reproduction failure of the dominant species, P. abies, and an increase in the abundance of A. alba. When the other species become available in year 1100, the total biomass recovers, and the abundance of A. alba decreases under the competition with deciduous species, most notably F. sylvatica. Under this scenario, the composition of the montane forest reaches an equilibrium only by year 1600 (Figure 1.8b). These simulations corroborate the suggestion of earlier studies (e. g., Solomon, 1997) that it is important to take plant migration into account if we are to reliably assess the transient behavior of the biosphere, e. g., with respect to carbon storage.
Figure 1.8
Example of a temporal upscaling problem in forest gap models when neglecting migrational lags induced by climatic change. The behavior of the ForClim model is simulated for 800 years under current climate, starting from bare ground, for the site Davos (Switzerland). In year 800, an arbitrary step change of the climate of +3°C is imposed on the model, assuming that the new climate remains constant until the end of the simulation in year 1600. The upper panel shows the model behavior when assuming no migrational lag, as done in most studies published to date. The lower panel is based on the assumption that all the species not present under the current climate require 300 years to migrate naturally to this high-elevation site, which is located in a complex topography with many migrational barriers.
Under scenarios of climatic change, the models may be too optimistic with respect to the availability of new species that could grow if they were there, but in reality will not grow because they require many years to immigrate.
Downscaling
Finally, the discussion of downscaling problems showed that the derivation of regionalized scenarios of climate change that are relevant at the spatial scale of forest gap models is an indispensable prerequisite for realistic impact assessments with these models in many geographical areas (Bugmann, 1997). Based on the application of the ForClim model, Bugmann concludes that at least some forests appear to be quite sensitive to the magnitude of projected climatic changes, and simply using grid-cell average anomalies from GCS simulations is most likely inappropriate to drive ecosystem models.
References
Bugmann, H., 1996, A simplified forest model to study species composition along climate gradients, Ecology 77:2055-2074.
Bugmann, H., 1997, Sensitivity of forests in the European Alps to future climatic change, Clim. Res. 8:35-44.
Bugmann, H., Fischlin, A. and Kienast, F., 1996, Model convergence and state variable update in forest gap models, Ecol. Modelling 89:197-208.
King, A. W.. 1990, Translating models across scales in the landscape in: Turner, M. G. and Gardner, R. H. (eds.), Quantitative methods in landscape ecology, Ecological Studies, Springer, New York, Vol. 82, pp. 479-517.
Shugart, H. H., 1984, A theory of forest dynamics. The ecological implications of forest succession models, Springer, New York, 278 pp.
Solomon, A. M., 1997, Natural migration rates of trees: Global terrestrial carbon cycle implications, in: Huntley, B., Cramer, W., Morgan, A. V., Prentice, H. C. and Allen, J. R. M. (eds.), Past and future rapid environmental changes: The spatial and evolutionary responses of terrestrial biota, Springer, Berlin, 455-468.
Urban, D. L., O'Neill, R. V. and Shugart, H. H., 1987, Landscape ecology, Bioscience 37:119-127.
At least some forests appear to be quite sensitive to the magnitude of projected climatic changes, and simply using grid-cell average anomalies from GCS simulations is most likely inappropriate to drive ecosystem models.
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