Session Synthesis Essay: Upscaling in Global Change Research
Danny Harvey, Session Chair
University of Toronto
Toronto, Canada
Session Synthesis Essay: Upscaling in Global Change Research
Danny Harvey, Session Chair
University of Toronto
Toronto, Canada
This session of the Aspen Global Change Institute (AGCI) examined the problem of upscaling in global change research. The term "global environmental change" was meant to mean changes that are global by virtue of the fact that they involve systemic changes in the properties of the atmosphere or ocean, or changes that, although local or regional in scale, are so widespread in their occurrence that they can be regarded as global-scale problems. The term "upscaling" was taken to mean the process of extrapolating from the site-specific scale at which observations are usually made or at which theoretical relationships apply, to the grid cell size found in global models used to study global environmental change. Upscaling is concerned with the development of relationships that are applicable at the grid-cell scale of models, so that they can be implemented in such models as part of the process of developing projections for the future. It is distinct from the problem of downscaling, which also arises in global change research. The latter is concerned with taking the output of global change models and deducing the changes that would occur at finer scales than resolved by the model. The two problems are not entirely independent, however, in that common processes underlie both scaling problems. Upscaling is a process-oriented problem, but there are other issues involving scale that do not constitute upscaling (or downscaling). For example, predictability generally depends on scale, but the determination and description of how predictability varies with scale is not a scaling problem.
This essay summarizes the introductory presentation made at the workshop by the author and chair, in which the major upscaling issues and problems in a wide variety of disciplines were identified, followed by a classification of upscaling problems in terms of the underlying causes and a comparison of the techniques that have been used to address the upscaling issue in different disciplines. This essay is a condensed version of a more extensive treatment of upscaling found in Harvey (1998), which is part of a special issue of Climatic Change based on the AGCI workshop.
Key Questions
A number of important questions of relevance to upscaling were identified at the beginning of the meeting, and answers or partial answers to some of the questions emerged and are presented in this overview. The key questions raised were:
(1) When is upscaling possible?
(2) For cases where upscaling is possible, how should it be done?
(3) For cases in which a given phenomenon has been (largely) independently examined at two or more scales by workers within the same discipline, how can results be properly intercompared?
"Upscaling" was taken to mean the process of extrapolating from the site-specific scale to the grid cell size found in global models used to study global environmental change.
(4) What are the implications of scaling issues for such things as predictability, parameterization, and the response and vulnerability of ecosystems and human societies to global and local environmental change?
(5) What are the relationships between upscaling and downscaling problems?
(6) How does the relationship between changes in variability and changes in the mean change as the scale changes?
(7) How does variability change with scale?
(8) How does predictability change with scale?
(9) How do errors propagate with scale?
Surface hydrology
Scaling issues arise in surface hydrology for three fundamentally different reasons: due to the existence of strong spatial heterogeneity in surface processes and rainfall intensity combined with strongly nonlinear processes; because different processes require a different minimum scale in order to occur in the first place; and because different processes can dominate the overall system at different scales.
Spatial heterogeneity combined with nonlinearity is particularly important for interception of rainfall by vegetation, and for infiltration and runoff. Subgrid-scale variations can occur in rainfall intensity, antecedent soil moisture, soil hydraulic properties, or in vegetative properties. The usual practice in atmospheric General Circulation Models (GCMs) is to employ a lumped model , in which a point process model is applied to the entire grid cell domain, with no change in structure, using the grid-cell average precipitation and surface properties. An alternative is to use a distributed model, in which the process model is applied at (distributed over) a large number of sites or patches within the grid cell, and the results are summed. This requires assuming some distribution function for the rainfall, and requires knowledge of the distribution of soil and vegetation properties within the grid cell. Distributed models can be applied in a deterministic manner using the specific spatial distribution of input parameters or in a stochastic manner, in which only the functions describing the probability distribution for each input parameter need to be known. An alternative to distributed models is to use a lumped model with effective parameters whose values are not simple arithmetic averages of the sub-grid parameter values. A problem with this approach is that there are parameters (such as soil hydraulic conductivity), where no single effective value works for all soil moisture conditions (Blöschl and Sivapalan, 1995).
When is upscaling possible? How should it be done? What are its implications for predictability?
The second scaling problem in surface hydrology is that different processes require a different minimum scale in order to occur. Surface runoff generation in nature involves two distinct processes: the occurrence of overland flow ("Hortonian" runoff) when precipitation rate exceeds infiltration rate, and precipitation on saturated regions. Hortonian overland flow is a point process, whereas saturated overland flow requires a minimum upslope catchment area before it can begin. Entekhabi and Eagleson (1989) developed a parameterization of runoff generation that incorporates these two separate mechanisms and their changing relative importance, during the coarse of a rainfall event, at the model grid scale.
The third scaling problem is that the dominant process can change as the scale under consideration changes. Thus, matrix flow - the flow of water through the pores within the bulk of a soil sample - gives way to preferential flow in certain concentrated regions when viewed at a larger scale (Blöschl and Sivapalan, 1995).
Surface-air fluxes of heat, trace gases, and momentum
In global-scale climate models, the vertical fluxes of heat, water vapor, and momentum between the land surface and atmosphere are usually computed using relationships that were developed at the scale of a few square meters to tens of square meters. These relationships are applied to the entire grid cell, without modification, using the grid-average parameter values as inputs. Since the heat fluxes depend non-linearly on surface moisture and resistance, there is the potential for large errors in the grid-average fluxes. A number of researchers have compared the grid-scale fluxes computed by this lumped approach with fluxes computed using a statistically distributed model. In some cases, the use of grid-average parameter values is a valid approach (e. g., Wood and Lakshmi, 1993; Sellers et al., 1995), while in other cases a distributed model is required ( e. g., Bonan et al., 1993; Li and Avissar, 1994; Arola and Lettenmaier, 1996).
Bonan et al. (1993) note that the true statistical distribution of key input parameters (leaf area index, stomatal resistance, soil wetness) is unknown, so the importance of subgrid-scale variability for global climate simulations cannot yet be assessed. As in the treatment of surface hydrology, an alternative to the use of a statistically distributed model is to apply the point process model to the entire grid cell, but using effective parameter values (the lumped approach), as in Chenbouni et al. (1995). A second alternative is to develop a new model structure that is applicable at the larger scale, an approach adopted by Wetzel and Chang (1987).
In some cases, the use of grid-average parameter values is a valid approach, while in other cases a distributed model is required.
Another key input, that is important for the vertical fluxes of heat, moisture, and momentum, is the roughness of the surface. The effective roughness height needed in order to compute the vertical flux of momentum between the surface and atmosphere at a scale of 10 km can be an order of magnitude larger than the local value. This is due to the existence of drag on dispersed obstacles covering a small fraction of the grid cell. However, the effective roughness height for heat (and water vapor) tends to decrease with increasing scale since heat transfer is not concentrated on obstacles. This essence of the scaling problem in this case is that the surface looks different at different scales.
Free-air vertical heat fluxes and interactions with clouds
The vertical fluxes of heat and water immediately adjacent to the land surface depend on turbulence, and thus involve random motions that have no preferred horizontal spatial structure. As one moves a few tens to hundreds of meters above the surface, however, organized air motions on a scale of one to several tens of kilometers can arise. These are referred to as mesoscale motions, and are intermediate in scale between turbulence and those motions that can be resolved by GCMs. These motions are dependent on surface heterogeneity, as variations in surface temperature (related to differences in soil moisture and albedo) can produce regions of concentrated uplift (convection), separated by regions of subsidence (sinking motion ). Given that mesoscale motions depend on the typical spatial extent of surface heterogeneities, as well as on the larger scale atmospheric conditions (such as stability and wind velocity), it might be possible to parameterize the effects of mesoscale motions. Lynn et al. (1995) and Zeng and Pielke (1995) present initial attempts at developing parameterizations of the effects of mesoscale motions on the vertical sensible and latent heat fluxes.
Interactions with clouds, which were not considered by Lynn et al. (1995) or Zeng and Pielke (1995), complicate the picture further. Wetzel and Boone (1995) proposed a parameterization for the effect of surface heterogeneity on non-precipitating cumulus clouds, using either deterministically or stochastically distributed surface patches coupled to a single atmospheric layer that covers all the patches. However, their scheme does not include the effects of mesoscale motions. Thus, although one may be able to successfully aggregate surface heterogeneity in computing grid-cell mean sensible and latent heat fluxes, a much more difficult and as yet unresolved scaling problem remains when it comes to interaction between the surface and clouds. It might be that the effect of mesoscale motions is simply to change the distribution of precipitation but not the total precipitation within a GCM grid cell, but the conditions under which this is the case remain to be defined.
A second scaling problem for clouds arises due to the existence of spatial variability within atmospheric grid boxes, involving humidity. At a given point, condensation requires a relative humidity of 100 percent. Upscaling to the grid-cell is accommodated in atmospheric models by setting the threshold for cloud formation at something less than 100 percent relative humidity, to account for the fact that parts of the cell can be saturated even when the mean relative humidity is less then 100 percent.
A third scaling problem related to clouds involves accounting for the effect of ensembles or collections of cumulus clouds within a single grid cell. A cumulus cloud modifies the air around it through detrainment of water vapor and liquid water at the top of the cloud, and through the induced subsidence of air adjacent to the cloud.
Given that mesoscale motions depend on the typical spatial extent of surface heterogeneities, as well as on the larger scale atmospheric conditions, it might be possible to parameterize the effects of mesoscale motions.
The mass flux and vertical extent of each cloud, however, depend on the large-scale atmospheric conditions. At any given time there will be a collection of cumulus clouds of varying thickness and hence varying heights of detrainment. The presence of each cumulus cloud in an ensemble influences the occurrence and characteristics of all the other clouds through its effect on the large-scale atmospheric conditions. The net effect is therefore not given by the direct effect of some "average" cumulus cloud in the ensemble. The essence of this scaling problem is (a) the existence of a spectrum of clouds of differing characteristics, and (b) the existence of feedback between the clouds and the large-scale environment. In spite of the complexity of this scaling problem, Arakawa and Shubert (1974) developed a parameterization that accounts for the mutual interactions of an ensemble of cumulus clouds.
A fourth scaling problem with respect to clouds arises from the fact that cloud albedo and emissivity depend nonlinearly on the vertically integrated cloud liquid or ice water content (LWC), and LWC can vary substantially within a GCM grid cell. Cloud feedbacks on climatic change depend on how LWC changes with climate and on the rate of change of cloud albedo and emissivity with LWC. Because of the nonlinearities involved, computation of the net cloud feedback using the mean cloud LWC and using a probability distribution of LWCs will yield different results, even for the same grid-mean change in LWC, if the within-grid cell variation in LWC is sufficiently large. Considine et al. (1997) present the first step in the development of a parameterization for the spatial variability of LWC in marine boundary layer clouds. The development of such a parameterization requires some hypothesis about the mechanisms causing spatial variation.
Simulating the impact of widespread deforestation
In assessments of the climatic impact of deforestation using climate models, the deforestation has been applied to entire model grid cells. Deforestation in reality proceeds as a growing patchwork of deforested areas, with secondary regrowth on abandoned patches (O'Brien, 1996). As noted in the review by Pielke and Avissar (1990), the juxtaposition of transpiring vegetation next to dry, bare land can generate circulations as strong as sea breezes. Given the importance of spatial variability in surface characteristics at a scale of a few kilometers to mesoscale motions, and the likely importance of mesoscale motions to the larger scale flow, the large-scale effects of deforestation could very well depend on the small-scale structure of deforestation.
Net photosynthesis and the response of ecosystems to higher atmospheric CO2
The net flux of carbon between plants and the atmosphere is closely associated with the vertical fluxes of heat and moisture, and a number of land surface models have been developed which simulate these coupled fluxes in an internally consistent manner (Bonan, 1995; Hunt et al. 1996; Sellers et al. 1996). Some of these models have been used to evaluate the present-day global distribution of net photosynthesis using a lumped approach, namely, applying leaf or canopy-scale relationships to grid squares 1° x 1° in size or larger (Hunt et al. 1996; Zhang et al. 1996). Pierce and Running (1995) assessed the errors incurred in using the lumped approach to estimate average net primary productivity (NPP) over an area of 110 km x 110 km in western Montana (about 1° x 1°). The effects of averaging the smaller scale variation in climate, topography, leaf area index, and soil water holding capacity were determined by comparing the lumped results with results obtained with a distributed model. The lumped approach gave areal-mean NPP that differed by 15 to 30 percent from the distributed approach, depending on the season.
The large-scale effects of deforestation could very well depend on the small-scale structure of deforestation.
In the case of the photosynthetic response to higher CO2, a scaling problem arises in four distinct ways. The first is the usual problem of spatial heterogeneity combined with nonlinearity, but here, there is important variation in the vertical, involving leaf temperature, nitrogen content, and the availability of light. Reynolds et al. (1992) investigated the importance of these effects using a multi-layer canopy model of scrub oak in effect, a deterministically distributed model. They found that substantial errors in the absolute carbon and water vapor fluxes can occur using a single-layer model for either present or doubled CO2, but that the relative response of an entire plant to a CO2 doubling differed little between distributed and lumped models.
The second way in which scaling of the photosynthetic response can be problematic is through feedback between the plant and the surrounding environment. If a higher CO2 concentration leads to a greater leaf area in the upper canopy layers, this will reduce the availability of light in lower canopy layers, and the response of the entire canopy will not be equal to the scaled response of an individual leaf. Feedback between the leaf and canopy scales has been shown to be important in modulating the response of evapotranspiration, at the scale of the canopy, to increasing CO2. At the scale of the leaf, higher CO2 tends to reduce evapotranspiration because it leads to partial closure of the stomata. However, in ecosystems such as closed forests, where the vegetation strongly influences the air humidity next to the plant, the effect of stomatal closure in all the leaves of the canopy is to reduce the canopy humidity, thereby tending to drive evapotranspiration rates back up (Jarvis and McNaughton, 1986).
The third way in which scaling can be problematic is as a result of feedback or interactions between different plant components. The initial stimulation of photosynthesis at the scale of the leaf leads to changes in the allocation of carbon and nitrogen to roots and shoots, which then feed back to the leaves and alter the photosynthetic response at the scale of the plant. However, in a case studied by Reynolds et al. (1993), these feedbacks reduced the plant-level photosynthetic response by only 10 percent compared to the long term leaf-level response.
If a higher CO2 concentration leads to a greater leaf area in the upper canopy layers, this will reduce the availability of light in lower canopy layers, and the response of the entire canopy will not be equal to the scaled response of an individual leaf.
A fourth consideration that gives rise to a scaling problem is that an atmospheric CO2 increase will not have the same relative effect on photosynthesis or water use in all species. Consequently, the interactions among species will be altered, thereby precluding a simple upscaling.
The response of forests to climatic change
The response of land plants to climatic change has been assessed using a variety of different approaches, and prominent among these different approaches has been the use of "gap" models which simulate the competition between different plant species within a small (about 10 m2) patch. All except the very most recent gap models assume the immediate availability of seed stock for all the species that could potentially grow in a given region. If these models were applied simply to evaluate the response to isolated disturbances in a restricted region, this would be an adequate assumption. However, when modeling continental-scale ecological responses to continental-scale climatic changes, this assumption is inappropriate because of the lag that would occur in reality between the time when the climate becomes appropriate for the growth of a species not currently found nearby, and the arrival of seeds from the closest initial occurrence of the species in question. Thus, a scaling problem arises due to the increasing importance of temporal lags as the spatial scale over which a response must occur increases.
Terrestrial and marine ecology
A number of upscaling issues arise in terrestrial ecology pertaining to the distribution of plants and animals. Among these issues are (a) the changing importance of different controlling variables at different scales; (b) the dynamics of heterogeneous landscapes, in particular, the role of interactions between adjacent landscape units and of landscape connectivity; and (c) the relationship between disturbances and the large-scale ecosystem structure.
The relative importance of different variables in explaining species distributions changes with scale, so observations at a small scale might not correctly identify the dominant processes that generate the large-scale pattern (Root and Schneider, 1995). Ecosystem models that operate at only one scale are not likely to incorporate mechanisms properly. This implies that prediction at the local scale must take into account local processes and their modulation by larger scale variables. Unless the correct processes are identified and properly represented, large-scale ecological impact assessments will be in error. A general problem in linking across scales is to determine the extent to which fine-scale detail can be neglected. Some detail is just noise, but in other cases, emergent phenomena can arise from the collective behavior of small-scale processes (Levin, 1992).
An atmospheric CO2 increase will not have the same relative effect on all species. Consequently, the interactions among species will be altered, thereby precluding a simple upscaling.
Spatial heterogeneity combined with dispersal alters the dynamics of species interactions in a number of ways (Levin, 1976). Hence, the response of animal species to climatic change will involve interactions between adjacent landscape units, as well as direct biotic-abiotic relationships at a fine-scale. This in turn implies that the heterogeneity of the landscape is important to the response, as also argued by Pickett and Cadenasso (1995). The input-response relationship is therefore likely to be different than that expected based on small-scale considerations alone.
Landscape connectivity a particular attribute of spatial heterogeneity is also crucial to species and their response to climatic change. Even in the absence of climatic change, connectivity is critical inasmuch as the survival of populations depends on the rate of local extinctions (within patches) and the ease of movement between patches (Turner, 1989). The importance of connectivity will be amplified when rapid shifts in climatic zones occur (Schwartz, 1992). Thus, knowing only the proportion of different landscape types within a GCM-size grid cell is not sufficient for predicting impacts.
The large-scale impact of climatic change will likely depend on the spatial (and temporal) scales of disturbances and on the interaction between disturbances and the small-scale structure of landscape variability. Turner et al. (1993) show how the spatial and temporal scales of disturbance influence the large-scale statistical properties of a landscape (for example, the proportions of the landscape in different successional stages). Conversely, the effect of a change in the disturbance regime, and how individual disturbances propagate, depends on the spatial arrangement of patches that are susceptible or resistant to disturbances (Turner et al., 1989). Landscape heterogeneity can enhance or retard the spread of disturbances. Thus, the impact of changes in large-scale climatic parameters, which alter the disturbance regime, will depend on subgrid-scale landscape variability.
Physical oceanography and sea ice
The global-scale ocean circulation depends on mixing processes occurring at a scale of 1 meter. This was first shown by Bryan (1987), who demonstrated, using a 3 -dimensional ocean GCM, that the intensity of the thermohaline overturning circulation depends on the value of the subgrid-scale diffusion coefficient. This coefficient , which is a prescribed parameter in ocean GCMs, is meant to represent the effect of vertical mixing processes that have a typical scale of 1 m. Diffusion is also used to represent the effects of horizontal mixing, but in this case the mixing involves eddies with a spatial scale of about 50 km. In both cases, the diffusion parameterization is an implicit upscaling that assumes the existence of an emergent property.
To what extent can fine-scale detail be neglected? Some detail is just noise, but in other cases, emergent phenomena can arise from the collective behavior of small-scale processes.
Two distinct scaling issues arise in the treatment of sea ice: (a) how the dynamic behavior of sea ice changes with scale, and (b) determination of the scale at which atmospheric forcing of sea ice motion is most directly applicable (Overland et al., 1995). An aggregate of ice floes behaves in ways that are quite different from the behavior of individual ice floes; in particular, ice behaves like a granular medium at the 0.1-1 km scale, while at a regional scale it behaves like a viscous fluid. Furthermore, the local velocity of sea ice cannot be directly related to the local atmospheric shear stress. Rather, the valid linkage is between regional atmospheric forcing and regional sea ice deformation. However, atmospheric forcing varies much more rapidly in time than the sea ice response, so the history of atmospheric forcing must also be taken into account.
Atmospheric chemistry
Scaling problems arise in the atmospheric chemistry of compounds that have a very short lifespan in the atmosphere, which results in strong spatial variations in their concentration, and where the reaction chemistry depends highly nonlinearly on concentration. The main difficulty involves NOx gases (NO and NO2), which have highly concentrated emission sources and have a lifespan of only a few days. Even fairly high resolution models (60 km x 60 km) cannot adequately represent the range of concentrations encountered in nature, so that significant errors in the projected impact of emission changes can still occur. An alternative to the computationally expensive approach of going to very high resolution in a global model is to compute the impact of changes in the emissions of a variety of pollutants for representative chemical conditions (e. g., clean continental, polluted continental, clean maritime, and polluted maritime), without trying to integrate globally, as in Thompson et al. (1990). This amounts to a refusal to perform upscaling, but still yields policy-relevant information.
Economics
The main concerns of economics with regard to global environmental change pertain to (1) estimating the costs of actions taken to prevent or minimize environmental changes, and (2) estimating the costs of environmental changes.
An aggregate of ice floes behaves in ways that are quite different from the behavior of individual ice floes; ice behaves like a granular medium at the 0.1-1 km scale, while at a regional scale it behaves like a viscous fluid.
The costs of greenhouse gas emission abatement can be assessed at the project, sectoral, or macro-economic scale. If costs are first estimated at the project level, then there is a need to scale up these costs by aggregating over the whole range of projects that could be undertaken in a sector or economy. This is the classical "bottom-up" approach, and entails comparing the lifecycle costs of currently used technologies and new, more efficient technologies that could be used in their place. These cost assessments depend on the prevailing (or projected) prices of energy, technology, and labor. The costs estimated for individual firms or projects cannot, however, be simply aggregated. This is because the implementation of efficiency measures by a single firm cannot noticeably affect the price of energy or of other factors, but if a large number of individual firms (and consumers) implement energy efficiency (or fuel switching) measures, this can be expected to noticeably influence prices and hence the ultimate reductions in emissions of greenhouse gases that are achieved. Thus, a scaling problem arises because of feedback between the small and large scales. This scaling problem is analogous to that of extrapolating the response of evapotranspiration (to a change in atmospheric CO2) from an individual leaf to a forest canopy.
At the other end of the scale spectrum is the "top-down" approach, in which economic correlations derived at the national scale are used in models of a national or the global economy. Top-down models do not involve upscaling in the sense of having to link processes or relationships derived at a small scale and applied at a larger scale. Rather, they are based on direct observations at the larger scale. However, when top-down models are used in a predictive mode under entirely different circumstances than in the past (as indeed they are), there is an implicit upscaling. This is because the large-scale response to a change in price involves the integrated effect of a large number of small-scale actions, and this integration is assumed when large-scale price-response relationships are used. Potential error arises in that a different set of detailed response options could come into play in the future. For example, there could be a greater role of non-price induced improvements in efficiency or fuel switching due to partial removal of barriers to energy-efficient investments by government action. The preferred solution to what can now be recognized as an upscaling problem is to provide enough detail that processes (response option) at the next lower level in the economic model hierarchy can be explicitly represented.
On the other hand, some of the potential costs of greenhouse gas abatement can be assessed only at scales beyond some minimum scale of analysis. These include costs related to shifts in investment patterns and changes in the rate of growth of productivity of labor and capital. Other scaling issues concern the question of whether there are economies or diseconomies with increasing scale, and the aggregation of risk.
With regard to the costs of environmental changes, the key upscaling issue is how to correctly integrate impacts across sectors and how to aggregate individual valuations of costs that are not reflected in market prices.
With regard to the costs of environmental changes, the key upscaling issue is how to correctly integrate impacts across sectors and how to aggregate individual valuations of costs that are not reflected in market prices.
Political Science
Political scientists have analyzed human-environment interactions at two scales. One is at the scale of small, stateless societies, while the other is at the international scale of nation states. Political scientists have found that the "tragedy of the commons" often does not occur in societies that lack a strong or any central control, and considerable attention has been devoted to explaining how self-interested actors are able to use resources sustainably in the absence of an overarching authority. This may present a useful analog to the problem of devising schemes for the international regulation of global resources by nation states, for which an overarching authority is also absent, if the insights gained from small-scale analysis can be applied to the global scale.
At the international scale, political scientists have found that relations often do not conform to the non-cooperative logic of the prisoner's dilemma.
At the international scale, political scientists have found that relations often do not conform to the non-cooperative logic of the prisoner's dilemma. Political scientists working at this scale try to understand the basis for sustained cooperation for a range of analytically distinct situations. Young (1994) indicates that there is a need to closely compare the local and international streams of analysis, and he presents some initial conclusions concerning the applicability and/or roles of pre-negotia, monitoring, and transparency at the local and international scales.
The preceding discussion is summarized in Table 1.1, which classifies upscaling problems in global change research according to the underlying fundamental cause, and in Table 1.2, which summarizes the solutions adopted.
Danny Harvey sums up with Bill Gough, Karen O'Brien and Marv
Waterstone (photo by Susan Hassol).
A common reason for an upscaling problem is the existence of spatial heterogeneity combined with nonlinearities in the relevant processes.
Causes of Upscaling Problems
A common reason for an upscaling problem is the existence of spatial heterogeneity combined with nonlinearities in the relevant processes. This problem arises in surface hydrology, the computation of surface-air fluxes of heat and water vapor, in plant physiological processes, in cloud dynamics, and in atmospheric chemistry. However, there are a number of other, conceptually distinct, reasons why upscaling problems arise.
First, it has been widely observed in marine and terrestrial ecology that different processes are primarily responsible for producing the spatial distribution of plants and animals at different scales. The same is also true with regard to human land use patterns, and for the driving factors for population growth and migration. This implies that correlations derived at one scale might not be applicable at a larger scale or to changes through time. It also implies that the simplification to a model (such as exclusion of certain processes or interactions) that is acceptable at one scale may not be acceptable at a different scale (this of course is well known in fluid dynamics).
Second, feedbacks can occur between the small-scale components of a system and the larger scale. This has the net effect of altering the relationship between large-scale driving factors and the aggregate response of the system. Thus, the response of transpiration from a leaf and ultimately from an entire forest canopy to changes in atmospheric CO2 concentration is strongly modulated by the effect of transpiration on the relative humidity within a forest canopy. Similarly, the effect of a change in energy prices (through a carbon tax, for example) on energy use at the scale of an individual firm and ultimately for an entire national economy is modulated by the feedbacks of energy demand on the price of energy.
Another conceptually distinct cause of an upscaling problem is the development of emergent properties. Emergent properties arise from the mutual interaction of small-scale components among themselves, whereas the feedback causation (discussed above) involves interaction between small-scale components and larger scale variables. The most striking example of the development of emergent properties is in sea ice, where the mutual interaction of individual ice floes imparts properties (such as viscous behavior) at the large scale which are not found in any of the constituent components.
Emergent properties arise from the mutual interaction of small-scale components, whereas the feedback causation involves interaction between small-scale components and larger scale variables.
The emergent properties that arise with increasing scale in sea ice depend largely on interactions at the edges between ice floes. Edge effects are also important to the dynamics of terrestrial ecosystems at larger scales. The edge effects in this case occur between landscape patches with different characteristics. The larger scale ecological characteristics (such as overall species diversity) also depend on dispersal from one patch to surrounding patches, so that both spatial heterogeneity and the characteristics (such as speed) of the dispersal process are critical to the system statistical properties and dynamics at the larger scale. To the extent that the ecosystem properties at the larger scale are different from those at the patch scale and depend on the mutual interaction between different patches, this provides another example of the occurrence of emergent properties as we scale up.
An upscaling problem can also arise when there is a temporal lag in the response of a system to a perturbation, if this lag increases the larger the spatial scale over which the adjustment to the perturbation must occur. A clear example is in the response of forest species composition to large-scale climatic change, when the climatic change is so large that the climate becomes suitable for species whose seedlings are not currently available at a given site. Correct modeling of the time-dependent response at a given site requires scaling up to a large spatial scale so that the gradual dispersal of species into new regions can be modelled.
Finally, aggregating environmental values and the costs of climatic change across individuals to the scale of a society presents upscaling problems for yet different reasons. A key issue here is to determine how to weight different values and costs when aggregating to the larger scale; the choice of weighting scheme contains implicit assumptions concerning the distribution of income, and depends on ethical judgments something that is not always explicitly acknowledged. The only thing that one can say with confidence is that the least defensible weighting is a uniform weighting, yet this is exactly what has been done in many cases. One can draw an analogy to the computation of effective parameter values for use in lumped models of physical systems; the correct effective value is usually anything but a uniform weighting of the individual values, and the correct weighting often changes with the conditions.
Solutions to Upscaling Problems
The solution adopted when upscaling is required depends in part on the underlying reason for the particular scaling problem in question. The first solution, which is not always a solution, is to ignore the problem. This is done, for example, when point process models are applied to an entire GCM grid cell without modification, or when estimated costs of climatic change are simply summed over all members of a society. In some cases this can be an acceptable approach, if the underlying nonlinearities are weak or if they fortuitously cancel. The task in this case is to determine the conditions under which the upscaling problem can be ignored.
In weighting different values and costs when aggregating to the larger scale, the least defensible method is a uniform weighting, yet this is exactly what has been done in many cases.
The second solution is to use a distributed point process model, whereby processes are computed for a number of distinct patches within a region, and the results summed. This is an acceptable approach for dealing with scaling problems that arise due to spatial heterogeneity combined with process nonlinearity, but is not valid when there are interactions between adjacent patches. An alternative approach is to apply the process model to the entire heterogenous domain but to use effective parameter values that account for the heterogeneity. A problem with this approach is that the relationship between the distribution of real parameter values and the effective parameter value can depend on the state of the system, and thus can change over time.
Where interactions between patches are important, it is necessary to either directly parameterize these effects, or to create a whole new model which incorporates these interactions and their effects. The parameterization approach can be used when the details of small-scale interactions do not matter. The simplest example is the diffusion parameterization to represent the effects of turbulent mixing or the random dispersal of plants and animals. The diffusion approximation works at scales where the unpredictability of specific events cancels out, and the overall statistical properties can be relied upon. A more complicated example is the parameterization of the effect of organized mesoscale motions on vertical heat fluxes. This is a case involving interactions between adjacent land surface patches, inasmuch as rising motion over one patch affects the tendency for rising or sinking motion over adjacent patches. In the case of cumulus cloud ensembles, in which feedbacks between the large-scale environment and the ensemble occur, but which also involve strong interactions between the members of the ensemble, rather complicated parameterizations have been developed which bear little resemblance to earlier parameterizations that considered only a single cloud interacting with its environment. Models of species diversity and the spread of disturbances also explicitly consider interactions between adjacent patches.
When spatial upscaling involves the integration of different components from one level within a system hierarchy to a higher level, the preferred approach is to link mechanistic models of the individual components, as discussed by Reynolds et al. (1993). For example, a model of plant growth would link modules involving shoot biomass, root biomass, and carbon and nitrogen substrate pools. The submodules themselves should be based on phenomenological relationships ( i. e., relationships based on a fundamental understanding of the processes involved, rather than being purely empirical) and parameterized with data collected at that level. The model would then be validated against data collected at the scale of interest and constrained by data at larger scales. Models that include mechanisms across a wide range of levels should be avoided because, as discussed by Reynolds et al. (1993), they tend to be very complex, unstable, and difficult to verify and alter.
When spatial upscaling involves the integration of different components from one level within a system hierarchy to a higher level, the preferred approach is to link mechanistic models of the individual components.
These principles can also be applied to the question of estimating the cost of greenhouse gas emission reduction measures at the scale of a national economy. As in models of sea ice dynamics or in the response of plants to higher atmospheric CO2 concentration, a model hierarchy can be identified, where different levels in the hierarchy roughly correspond to different spatial scales. Here, the lowest level in the hierarchy consists of models (and measurements) of the energy use by specific technologies (e. g., motors and commercial chillers). The next level up consists of models of individual buildings or industrial processes, where the integrated effect of individual technologies on the energy use at the scale of the building or industrial plant can be assessed. These provide estimates of cost-effective energy saving potential at the scale of the individual firm, the scale at which bottom-up assessments typically begin. The next level up consists of models of an entire sector or of a national economy. Based on the principle in hierarchy theory that assessments at level n should be based on the integration of models from level n-1 (O'Neill, 1988), national level assessments should be based on the integration of models at the next lower level, which involves individual energy end uses and energy supply choices. That is, considerable bottom-up detail needs to be built into top-down models if they are to be credible, and this is now being done to an increasing extent.
The next-to-last solution to the upscaling problem that has been considered here is to simply run a model at a fine enough resolution that the important processes can be explicitly represented. This approach has been used with some success in ocean GCMs to account for the effects of mesoscale (50 km) eddies on the large-scale flow. This has also been tried in models of tropospheric chemistry, but does not entirely work because strong variations in the concentrations of important chemical species can occur inside grid cells as small as 50 km x 50 km. An alternative in this case is to compute changes for different representative chemical regions but without attempting a global integration what is termed "Refuse" in Table 1.2.
Research Questions and Needs
Upscaling is widely required in models used to predict or understand global environmental change. An upscaling problem can arise for a variety of conceptually distinct reasons, and a number of distinct solutions have been applied to this problem. Greater recognition of the existence of upscaling problems by researchers across the spectrum of disciplines involved in global change research should, hopefully, lead to the formulation of better models for purposes of analysis and prediction. At the same time, it should lead to greater appreciation of the weaknesses of current approaches.
For this to happen, a number of specific research needs will have to be addressed. In the physical and biological sciences, these research needs are as follows:
(1) There is a need for information on the spatial variability that exists within 1° x 1° grid cells on a global basis. This is needed for parameters such as soil moisture holding capacity, soil infiltration rate, vegetation type, and leaf area index. In order to adequately characterize the probability distribution functions, information on means, variabilities, and skewness is required. Information is also needed on the spatial co-variation among variables.
Greater recognition of the existence of upscaling problems should, hopefully, lead to the formulation of better models for purposes of analysis and prediction.
(2) The conditions under which a lumped approach can be used instead of a distributed model approach need to be thoroughly investigated.
(3) For conditions in which a distributed approach is required, work is needed to determine which variables needed to be represented in a distributed manner and which can be safely averaged.
(4) When a statistically distributed model approach is used and the probability distribution functions could themselves change as large-scale conditions change, the ways in which they might change and the extent of such potential changes need to be determined. This is a possible problem in cloud modelling in particular, but it is unlikely to be a problem in the modelling of surface hydrology.
In both the biological and social sciences, an important area for further research is to determine ways to properly compare studies that were carried out at different scales. Levin (1992, p. 1953) raises the possibility that scaling laws can be developed (in ecology, at least) that allow such comparisons. There is scope for considerably more work on upscaling in all disciplines involved in global change research, but the greatest challenges may very well lie in the modeling of land-atmosphere-cloud interactions.
The need for upscaling has mixed implications for our ability to correctly predict changes at the model grid scale and larger. First, in cases such as soil moisture and precipitation, our ability to correctly predict changes in these variables at the grid scale improves as the simulation of the present conditions improves (see, for example, Meehl and Washington, 1988). Inasmuch as correct upscaling alters the grid -mean simulated values for the present climate, and generally improves the simulation, it will improve our predictability. On the other hand, if the probability distribution functions or parameterized interactions between units used in the upscaling algorithm are themselves subject to change as the climate changes, then predictability will worsen if these changes cannot be correctly anticipated.
In closing, it seems reasonable to believe that much of the information needed to improve our upscaling techniques could also help in dealing with the complementary scaling problem, which is not addressed here that of downscaling from grid-average output data to specific points within the grid. Downscaling techniques are reviewed in Bass and Brook (1997). In particular, much of the data that will need to be collected in order to construct probability distribution functions for surface and vegetation properties can, if also retained in a spatially distributed form, be used for downscaling.
In both the biological and social sciences, an important area for further research is to determine ways to properly compare studies that were carried out at different scales.
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