Model Scaling

Summary table of leaf to ecosystem scaling mechanisms with an indication of modelling and measurement techniques used at each level in the hierarchy. Also indicated are the primary, secondary, tertiary and long term effects of increased C_a and temperature at the ecosystem, whole plant, canopy and leaf levels. (Red gradient arrow indicates gradual transition of measurement techniques).

Scaling from leaf to canopy Responses of isolated leaves to short term changes in climate have been relatively well studied {Amthor, 1993 #1962}. Less is known, however, about the responses of plant canopies and communities to short term increases of Ca or responses at any level of organization to long term elevated CO2. Concern about the effects of climate change has stimulated interest in extrapolating knowledge of leaf level processes to the canopy, ecosystem and biosphere levels. Both spatial and temporal scales are important to such an extrapolation {Reynolds, 1992 #1838}. Figure 2 shows a typical leaf to ecosystem model hierarchy in which scaling errors may be introduced if information obtained at a lower level of the hierarchy is used directly to make predictions at a higher level of hierarchy without incorporating the interactions between components of an increasingly complex system {Reynolds, 1992 #1838}. For example a model of leaf photosynthesis scaled directly to the ecosystem level without recourse to canopy structure, rooting, nutrient available and other constraints is likely to contain significant errors in scaling and consequently will not respond correctly at the ecosystem level.

Ecological models that explicitly express many process and structures at several hierarchical levels and which are therefore composed of numerous coupled processes having many interactions tend to be complex and frequently hyper sensitive to slight changes in parameters {Allen, 1982 #1964}. There is a significant risk in such models that they will be unstable, difficult to modify and will lose their mechanisms in noise {Reynolds, 1991 #1967}. However in an effort to build models to predict ecosystem responses to climate change it is clear that only mechanistically rich models will permit us to extrapolate beyond existing data with any degree of confidence {Reynolds, 1986 #1968}.

Hierarchy theory {Allen, 1982 #1964; O'Neill, 1986 #1965} suggests that it is seldom necessary to look more than one level down in search for a mechanistic explanation of a systems behavior (e.g. biochemistry level for leaf and leaf fluxes for canopy level) and it is possible to use this concept to construct mechanistically rich ecosystem models in a hierarchical manner which remain stable and easy to manage (Figure 2). With this approach the mechanistic modelling of each hierarchical layer is emphasized via the mechanism that occurs at the level directly below coupled by constraints from the level above {O'Neill, 1988 #1966}. A given layer N in the model is parameterised by data (results) of the model at layer N-1 and constrained by the status of layer N+1 (Error! Reference source not found.). In this context model scaling is then a parallel development of the theory of how CO2 and temperature effects the system either directly via the physiology of plants or at higher levels in the hierarchy via indirect effects which migrate up through the hierarchy to the ecosystem level (Figure 2).

Hierarchical scaling of this sort encapsulates the technical aspects of information flow and linkage needed in mechanistically rich models and importantly allows testability of the scaling process at any level in the hierarchy. It therefore prevents the development of models which are impossible to interrogate and validate at less than the ecosystem level.

Scaling from canopy to ecosystem

The strong correlation between ecosystem characteristics and climate has been used for some time to predict directly from climatic data large scale distributions of ecosystem types {Emanuel, 1985 #209; Prentice, 1990 #1970}, net primary productivity within ecotypes {Lieth, 1978 #1947; Lieth, 1984 #956} and projected decomposition rates {Meentemeyer, 1978 #1973}. These empirical approaches have been incorporated into global carbon cycle models {Esser, 1991 #1755} and tested with global circulation climate models (GCM’s). However these empirical relationships cannot be used to identify the mechanisms that are responsible for observed or simulated responses at the ecosystem level.

Improved understanding of soil and vegetation processes and their interactions within ecosystems is leading to mechanistically rich general models that can be applied on a large scale {Running, 1988 #1735; Woodward, 1995 #1974}. Whilst such models still contain an empirical element at some level they represent a reasonable compromise between ease of parameterisation and incorporation of mechanism at the global and ecosystem level. These models typically use a variation of the simplified general plant type structure shown in Figure 4 to ascribe generalised properties to a given ecosystem.

The importance of natural grasslands in the global carbon cycle has been recognised {Hall, 1991 #1946; Long, 1992 #1180} and wimovac has been established to examine the grass type branch of the general plant type in considerable detail. However the canopy to ecosystem scaling methodology used in wimovac has been designed to be flexible enough to allow the introduction of tree specific processes at a later date.

Temporal Scaling

The temporal scales at which the plant carbon pool reaches equilibrium with other carbon pools of the bio-geosphere are vastly greater than the scale at which carbon dioxide directly effects growth via its effects on photosynthesis and stomatal aperture. If a model is to successfully predict the long term effects of climate change on vegetation it must therefore scale well across a very wide time span. Current empirical vegetation models generally run at a daily time interval in which state variables in the models are updated once per simulated day and represent a total of the days activity. The increasing use of mechanistically rich process based models has however necessitated that an instantaneous (per second) interval be used to allow incorporation of ‘real time’ physically based processes. This necessitates an additional numerical integration step to be performed in mechanistic models in order to scale from instantaneous to daily rates before a second integration step is used to scale from days to years.

Directly scaling from rates either in seconds or days, to years and hundreds of years without allowance for long term changes in the climate or vegetation and soil systems is likely to give poor results. Vegetation model temporal scale issues centre on predicted changes to climate and acclimation/adaptation of metabolism and growth of vegetation in response to environmental change. Empirical models generally do not include any mechanisms by which climate change and acclimation effects maybe mediated. However mechanistic vegetation models, such as wimovac, allow expression of short term climate change effects directly on the physiology of vegetation and long term effects of acclimation and adaptation via changing parameterisation of the physiological models. Although few field studies have examined the long term effects of continual elevation of CO₂ and temperature on natural vegetation initial indications do suggest that vegetation may show a number of adaptive changes in tissue C:N ratio’s, nitrogen use efficiency, nutrient uptake and water use {Stirling, 1996 #1977; Davey, 1997 #1978; Davey, 1996 #1976}. Acclimation has been reported in studies of coniferous trees and grassland species. In a review covering 39 tree species, {Gunderson, 1994 #1247} compared light saturated photosynthetic assimilation (A_sat) for plants grown at current ambient C_a and elevated C_a. Acclimation of photosynthesis measured at the current ambient C_a was apparent as an average 21% decrease in A_sat for plants grown at an elevated C_a compared with plants grown at an ambient C_a. When A_sat was measured at the growth C_a, an average enhancement of 44% was observed in plants grown at an elevated C_a by comparison to plants grown and measured at current ambient C_a. This observation is consistent with the theoretical prediction that relatively large declines in Rubisco activity can occur without affecting the enhancement effect of an elevated C_a on CO₂ uptake. C₃ grasses also show evidence of photosynthetic acclimation, and enhancement of photosynthesis at elevated C_a similarly appears to persist. Photosynthesis was enhanced by 35-46% in Lolium perenne grown at an elevated C_a despite photosynthetic acclimation {Nijs, 1988 #541; Ryle, 1992 #1251}. Leaves of Poa pratensis exposed to elevated C_a in a natural prairie ecosystem showed a 48% photosynthetic enhancement at growth C_a {Nie, 1992 #1410}. These observations are consistent with the view that Rubisco levels may be modulated to optimise N-use within the plant and that the decline in Rubisco activity remains one of the most consistent features of photosynthetic apparatus acclimation to elevated CO₂ concentration so far identified {Idso, 1989 #339; Allen, 1990 #20}. Although it is not currently possible to make broad scale predictions of the effects of acclimation on a range of ecosystems it is possible to modify the parameters of the mechanistic Farquhar and von Cammerer (1980, 1982) and Collatz (1992) models for C₃ and C₄ photosynthesis respectively in a systematic manner to simulate these effects. Further experimental work will be necessary before a true systematic understanding of the effects of acclimation on a broad range of vegetation types can be incorporated as a isolated mechanism in current vegetation models.

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