Response and risk in rural ecosystems: from models and
plots to defined universes
Jock R. Anderson
∗Rural Development Department, World Bank, Washington, DC, USA
Abstract
This essay was prepared as an invited closure of a thematic session on “Scaling and Extrapolation” at the CGTE Conference on “Food and Forestry: Global Change and Global Challenges”. It is addressed to those who prognosticate at the global or other large levels about food and forestry systems, and who naturally confront several problems, and inevitably also some risk. The problems range from conceptual and practical to measuremental and statistical. For other than simplistic models, many constraints apply to procedures used to aggregate from small-scale to large-scale representations of agricultural systems, whether they be biophysical or socioeconomic, especially when uncertainty is explicitly recognized. Model-linking procedures work well in some cases but by no means all. The risks encountered in such work are similarly wide-ranging, depending on the intrinsic uncertainties, context, analyst and audience. These spectrums of problems and risks, along with some suggestions for what practically can be done about them (largely involving ad hoc simulation modeling), are examined from a response-analysis perspective across a range of biophysical and social phenomena pertinent to terrestrial ecosystems. Attention is given to policy applications of scaled-up models. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Aggregation; Agriculture; Modeling; Policy; Scaling; Uncertainty
1. Introduction
The author comes to this topic from a background in response analysis (e.g., Dillon and Anderson, 1990), risk analysis (e.g., Anderson et al., 1977; Hardaker et al., 1997), and global analysis/forecasting (e.g., Anderson et al., 1988; Crosson and Anderson, 1992, 1994). In spite of the dual dangers of discovery of personal inconsistency, and of possible delusions of self-citation, there is here an opportunity to review some experiences germane to the topic of scaling up. Of the literature perused that seemed central to this topic, Schneider (1994) was the most instructive, as well as the most entertaining.
∗Tel.:+1-202-473-0437; fax:+1-202-614-0084. E-mail address: janderson@worldbank.org (J.R. Anderson).
2. Context
The national and international policy agenda is in-creasingly encompassing global and regional issues, as evidenced, for instance, for agriculture and forestry, by forums such as the present (e.g., Committee on Long-Run Soil and Water Conservation, 1993; OECD, 1998a,b) and the diverse activities of the global envi-ronment facility (GEF) (e.g., GEF, 1998, 1999; Pagi-ola, 1999). This is to say that policy makers concerned with agriculture, broadly defined, have rather lifted their horizons in recent times to seek to address much broader issues than was their former, usually more na-tional, want. In the World Bank, analogous concerns have led to changing my department from agricultural to rural (World Bank, 1997a), and to a determination for the rural staff to work beyond merely agricultural
issues to ensure effective and relevant linkages across social and environmental as well as other more tradi-tional spatial and investment considerations, in what the Bank calls Environmentally and Socially Sustain-able Development.
Clearly it is not just the changing perception of the importance of supra-national issues that has facilitated such broader purviews. The technology now avail-able to analysts has greatly expanded the opportuni-ties, and these are being increasingly seized. GIS and GPS, electronic computers, contemporary software, and modeling capability generally, have all surely led to significant expansion in the capacity for well-tuned even inexperienced analysts to do so much more than their parents could ever have hoped to do at higher levels of both resolution and aggregation.
And yet life is still not necessarily all so easy. The misleading nature of assessment of sustainability ques-tions at crop-plot or field level, while ignoring other linked elements of the landscape, such as forests and less-agriculturally managed areas (Leach and Mearns, 1996), has given greater recognition of the need for broad spatial scales of analysis, such as at the ecosys-tem (Gregory and Ingram, 2000) or catchment (Tinker and Anderson, 1996) levels. This is overtly the case for global-level issues such as concerning the atmo-sphere, but analogously pertains too to the geosphere and biosphere.
The problematic of this paper can now be stated. Many research workers have their hands-on inves-tigative activities primarily at the level of field plots or process models, and yet are interested in saying something sensible (perhaps to policy makers) about the behavior of some defined “universe”, at a wider or more aggregate level of a system. To do this they must use a process such as addition, multiplication, aggregation, magnification, transformation or general-ization. Within this unsettled set of procedures, there are possibilities of combinations of method, and op-portunities for error, such as fallacy of composition; in short, the challenge of the scaling-up problem.
For agricultural resource analysts, scaling up seems to be mainly concerned with the representativeness of plot-level observations for making statements about the status of a resource such as soil in a patch-mozaic agriculture (Scoones and Toulmin, 1999, p. 29, 31, 41). Agricultural ecologists take this idea to a higher level of generality (Fresco and Kroonenberg, 1992).
Engineers call scaling work dimensional analysis, and there are well agreed procedures for particular classes of scale models. For yet others, the scaling-up problem is more one of the difficulty of getting widespread adoption of worthy technical solutions that seem to work well in local “islands of success” in developing agriculture (Pretty, 1995, 1997). More specifically, in the context of World Bank operations, it usually means handling the challenge of moving from a pilot operation to a “full-scale” project. In-deed, the World Bank President has recently opined that the most pressing problem facing Bank staff and their clients is that of scaling up from project-level activities that work well enough at that typically more bounded level, to wider endeavors that really make a difference in poverty alleviation at the national level and beyond; or else “the race” is being lost.
For the level of generality sought in this overview, it may be that there are no general fixes widely appli-cable to diverse phenomena. To consider briefly one of the more general treatments observed, White et al. (1998, Table 19.3) offer tantalizing advice — tanta-lizing because there is no further discussion of these “problem-solving” suggestions in the paper — about “scaling up” under three heads:
synthesis across sites — GIS and modeling (these
two data sources/methods for all the three), site similarity studies;
extrapolation of practices — extrapolation domain
definition; and
links among system levels — watershed studies,
decision support systems.
The sections pertaining to response and risk that follow set out considerations that point to some pos-sibly useful procedures. Needless to say, adequate scaling-of-model insight is a necessary but not a suf-ficient condition for good policy making at global ecosystem levels, but the latter large topic is beyond the scope of this paper, covered herein by Norse and Tschirley (2000).
3. Response and aggregation
3.1. Conceptual
function (f) linking a set of micro-level variables
y =f (x, z, u), (1)
where y is output, x a controlled input, z an uncon-trolled factor, and u is a random term, to a universe of macro-level process function (F) and corresponding variables linked in
Y =F (X, Z, U ), (2)
and where all variables can be thought of as vec-tors. The main scaling concern in this paper is spatial. Needless to say, it is not just the response relations themselves, but the findings that arise from their in-terpretation that hold interest for the analyst. One can, with difficulty, imagine a world of perfect information, where the random or disturbance terms could be omit-ted, as indeed they are largely in this section. In gen-eral, however, they will have to be considered, if for no other reason than the Uncertainty Principle of Mod-eling: “Refinement in modeling eventuates a require-ment for stochasticity” (Mihram, 1972, p. 15). This Principle and its application are pursued more vigor-ously in the second main section, which is addressed explicitly to risk. For the present purpose, it is taken as given that analysts are primarily interested in what happens on average in a response process of this type, so that analytic endeavor in this section is focused on reliable estimation of the means or expected values of the respective variables. To the extent that this may re-quire probability specification, methods such as those alluded to in the later section on risk will be needed.
It must be recognized, however, that many response processes do involve the intervention/participation of decision makers who may not be indifferent to risk (which happily generates employment for applied so-cial scientists, such as agricultural economists). Most people most of the time, in fact, are technically averse to risk, and thus as individuals or in groups act other than simply to maximize the mean value of an objec-tive function. So, even if the “scaling-up analyst” is prepared to ignore risk (as is assumed in this section), the fact that some or all of the agents whose behavior is being represented (implicitly or explicitly) in the pro-cess of aggregating micro-relations to macro means that risk and risk aversion are inherent in the process, and thus are only ignored at the peril of the analyst.
3.2. Practical
Many different approaches are available to attempt to aggregate from the means of Eq. (1) to those for (2). Schneider (1994, Chapter 14) discusses six scal-ing strategies used in ecology: (i) use a multiplication factor (simple adding being a special case); (ii) use limited-scope bounds; (iii) use a variable with large scope to calculate a variable of more limited scope; (iv) use statistical scaling-up; (v) use H.A. Simon’s hier-archy theory (based on human organizations); (vi) use the principle of similitude. After reviewing the meri-ts and problems with each, he sides with two other groups of authors led by E.B. Rastetter and J.A. Weins, respectively, in recommending for practical purposes a combination of strategies built around (v) and (i), with supplementary use of dimensional reasoning of (vi) and good judgment, resorting to statistics only for verification. The temptation is resisted here to fiddle with fractal geometry and illustrate the insights of al-lometric relationships, such asy = axb, to focus on metabolism (e.g., West et al., 1999), and to explore scaling issues as to why bats can and humans have trouble flying (Costanza, 1991, p. 54).
such models is that, while aggregation of technical relationships may be relatively straightforward, such simplicity does not hold for aggregating behavioral relationships.
For more general (than the linear/polynomial) micro-production response relationships, the mathema-tics of adding up can imply rather restrictive oppor-tunity for direct formal aggregation, even for some of the simplest cases and where the disturbances are dropped. The subject is treated in depth by Chambers (1988, pp. 182–202), who in discussing aggrega-tion over optimizing firms, details the few classes of function that can be aggregated, along with their confining mathematical properties (technically, ho-mothetic functions under conditions of separable pro-duction). The situation is considerably more complex when the uncertainty terms are included, particularly when these are not merely additive homoscedastic (constant-variance) error terms, but depend on the levels of the real variables x and z. Although seldom recognized in empirical work, such heteroscedastic processes are likely to be the norm in applied pro-duction processes (e.g., Just and Pope, 1978; Griffiths and Anderson, 1982; Anderson and Hazell, 1994) because typically both controlled and uncontrolled inputs/factors influence risk experience. Thus unless a high price of narrow mathematical and zero stochastic specification is paid, little can be done to aggregate algebraically even simple response functions under general conditions. It does seem, however, that ana-lytic aggregation at this level of generality has seldom, if ever, been done. Among the difficulties that may have discouraged such endeavor would be the neces-sity for accounting for the risk aversion of producers (Dillon and Anderson, 1990, p. 154), if indeed the aggregate models were to represent a direct summa-tion of the results of their optimizing behavior. The difficulty hinges on the greater challenge in aggregat-ing behavioral response relationships relative to that faced in aggregating technological relationships. This is doubtless why agricultural economists in dealing with aggregate risk-responsive behavior have usually elected to work directly with aggregate data in, say, supply response analysis (Dillon and Anderson, 1990, pp. 181–184).
There is one special case of plot-to-regional scal-ing that seems deservscal-ing of a revisit from the present vantage point, which was brought to mind in
contem-plating the free-air carbon-dioxide enrichment (FACE) investigations (e.g., Jamieson et al., 2000). The late Bruce Davidson was struggling to use the available but sparse experimental data to draw implications about commercial farm yields in a then-hypothetical Ord River irrigation scheme in northern Western Australia. He observed a systematic non-linear association be-tween matched experimental plot and nearby farm crop yields that was similar across a range of crops and ecologies (Davidson, 1962). With colleagues, these results were successfully generalized in a production economics setting, which more recently would have been categorized as a meta-production relationship, that emphasized and accounted for the differing in-tensities of inputs, such as labor and capital, beyond those formally under test in the experiments (David-son and Martin, 1956; David(David-son et al., 1967). This bit of history is mentioned because the same issue haunts any generalization of f(x) to F(X), in the styles of Eqs. (1) and (2), if the corresponding bundles of the (z, Z) and (u, U) vectors are not analogously mea-sured and accounted for in the scaling up. A seeming gap in the scaling-up literature, however, is a careful empirical quantification of the relationship between experimentally measured changes in (as opposed to merely levels of) partial productivity measures associ-ated with, say, varietal change (see also Alston et al., 1995, pp. 338–340).
One of the obvious general approaches to aggrega-tion is to resort to sampling theory, although it seems remarkably underused in this field of potential appli-cation. The essence of such an approach is the idea that the plots that form the basis of the sample from which inferences are drawn about the relevant
popu-lation should be “appropriately” (e.g., Scheaffer et al.,
Where spatial (probably GIS-based) knowledge of some of the Z variables permits, a scheme of stratified random sampling could usefully be used, in order to ensure deliberate representativeness as well as greater precision in the sample design. Indeed, working with such ideas about the structure of the defined universe rapidly takes one into a second statistical approach to seeking efficient extrapolation, namely the use of principles of experimental design (e.g., Mendenhall, 1968).
Several principles are relevant, without compromis-ing the key roles of randomness and representative-ness. One is blocking, wherein systematic allocation of treatments (i.e., specified combinations of X vari-ables) among blocks, perhaps defined in terms of some of the Z variables, enables the treatment effects to be observed more precisely for a given size of sample. Another is partial factorial combination, perhaps of both X and Z variables, to accomplish an efficient and parsimonious coverage of the space of interest, by us-ing designs such as the central composite. These lead naturally to evolutionary designs, wherein with the help of the digital computing revolution, automatic sequencing of a succession of experimental designs takes the analyst to maximal or other optimal settings of the X response variables.
Statistics thus has a clear place in the aggrega-tion of plot-level data and relaaggrega-tionships to a defined universe, and thus underlines the propriety of includ-ing a stochastic disturbance term in the formulation. But what else works? It has been noted that algebra per se is of limited utility. Programming models are easier and have a reasonable record of achievement, provided that the disturbance/uncertainty terms are not of interest. But on a priori grounds, the best gen-eral approach in terms of workability must reside in ad hoc digital simulation methods, resorting as necessary to Monte Carlo sampling methods, as are taken up in Section 4. While workable in general, such methods necessarily involve explicit and prob-ably adaptive modeling of the aggregation process; what some authors describe as “teaching” or “tuning” the aggregate model. Evidently there is consider-able scope for analyst ingenuity in using weighting data at different levels of resolution, as revealed by some of the discussions in this CGTE Theme (such as Jamieson et al., 2000), and a critical need for ground-truthing/calibration in some cases, such
as in soil carbon and soil organic matter modeling (Schlesinger, 1999).
One final subtlety might be noted. This is an aspect of the “adding-up” problem of aggregate relationships, whereby the underlying resource situation is carefully captured in the modeling procedure, well illustrated in recent work by Cynthia Rosenzweig and colleagues at NASA/Goddard Institute on the treatment of water dynamics in crop production. In thinking about such issues, one is reminded of the saga of the Limits to
Growth/World Dynamics modeling of the early 1970s,
and the mis-specification of many key technology and resource-supply dynamics (e.g., Rothkopf, 1976) and embodied inconsistencies and fallacies (e.g., Zeckhauser, 1973).
On resource considerations in adding up matters, at least in the context of examining agricultural produc-tivity changes at the aggregate level, it may be salutary to return (as did Alston and Pardey, 1996, p. 129) to some early work of Schultz (1956) and his concept of an ideal ratio of “all outputs” to “all inputs” being ap-proximately unity. It seems likely that many studies of agricultural productivity have overstated the growth of multi-factor productivity (and thus also the implied returns to investment in agricultural research) because of a tendency for technologies developed to involve a faster rate of exploitation of unmeasured components of the natural resource stock, and thus an understate-ment of the flow of inputs (Alston et al., 1995). As has usually been the case, Schultz is doubtless right, and many incautious practitioners have probably been at fault in their findings about the aggregate impact of apparently relevant plot-level response data. The caution here is thus for analysts to do a more compre-hensive job in accounting for all the real inputs into a response process, before claiming too much achieve-ment in productivity growth at the aggregate level.
3.3. Policy
state of the art has advanced to the point where any sort of standard can be imposed is moot, although the Schulze (2000) exposition may lead to a more common language.
While the progress that has been made is certainly something to be excited about, this observer remains pessimistic about the robustness of some of the interim findings, and the operative call does indeed seem to be one for further self-critical research. Some of the rese-arch needed concerns best use of the new tools them-selves, especially the information-intensive GIS meth-ods (e.g., Wood et al., 1999). For others the needed research is at the biophysical process level itself, as indicated by the Schlesinger (2000) discussion of car-bon sequestration and, for a rather different example, by the pesticide resistance dynamics relationships in different forms of IPM (e.g., Archibald, 1988; Schill-horn van Veen et al., 1997). Lest it seem that there is some prejudice here against the natural sciences, it should be noted that there are ample controversies to be resolved among the social sciences. One bridging issue relates to the aggregation concept of “gross natu-ral product”, especially as a relevant indicator when it comes to environmental policy (e.g., de Groot, 1992, p. 254). To take another rather different case relevant to a discussion of agricultural aggregation, consider Cochrane’s Treadmill Hypothesis. Cochrane (1958) viewed farmers as the victims of technological change, because only early adopters of new and more produc-tive innovations would benefit (and then only briefly), as the increased output induced by the improved productivity depressed prices (assuming inelastic aggregate demand), and while consumers benefited from lowered commodity prices, farmers had to keep running the treadmill to try to survive. Fortunately, the grain of truth in this hypothesis does not apply in many if not most instances, as persuasively argued by Alston and Pardey (1996, p. 180). But it is instructive to remind evaluators of applied agricultural research, as they seek to aggregate up from perhaps plot-level estimates of improved agricultural productivity occa-sioned by some research activity to estimates of the returns to research investment, that empirical issues of market structure are key to determining the nature and distribution of the benefits of research — a topic dealt with in instructive detail by Alston et al. (1995). It would be inappropriate to conclude this section on other than a positive note, however. The
encour-aging thing for the evolution of better policy analy-sis concerning world agriculture, such as alluded to by Alexandratos (1995) and Anderson (1995), is that there is now real dialogue among policy makers work-ing at the regional and global levels, and the existence of cogent scaled-up models, notwithstanding the vary-ing degrees of refinement, has surely informed and facilitated such dialogue. But there is room for im-provement in practice.
4. Risk and aggregation
4.1. Conceptual
A world devoid of risk would be one in which global analysis and pontification was relatively easy but it would probably for most be really boring. Fortunately, this problem of boredom seldom exists, as risk is alive, if not well, in models of global or other large aggre-gate dimension. In this section, attention is refocused on the disturbance terms u and U in Eqs. (1) and (2), and any other sources of uncertainty (such as unpre-dictable climatic variables, which may be elements of
z and Z) that may enter into the probability
distribu-tions of the performance measures y and Y. The trans-formation from the level of u to the defined universe level of U is seldom straightforward except in trivial cases of linear aggregation. The encouraging news of the contemporary Computer Era is the readiness with which stochastic processes can be modeled and thus in-principle combined in explicit aggregations.
variability (and the modest contribution to it by plant breeders) of British cereal yields. Crop growth mod-els, even at the plot/model level, clearly already in-volve some aggregation of component responses and risks. The question to be addressed here is how these model-level risks aggregate to risks at the level of some defined universe, which may be a field, a farm, a district, a region or beyond. Although he went on to examine models of economies and of the world, Anderson regrettably did not explicitly deal with the question of aggregating from one level to another.
At one level, such aggregation is conceptually simi-lar to the aggregation of response without explicit risk consideration, being analytically difficult but amenable to block-busting simulation procedures. But since in this case: (a) it is sets of (likely multivari-ate) distributions describing the uncertain behavior of micro-systems such as Eq. (1) and (b) the aggrega-tion of these to those distribuaggrega-tions describing Eq. (2) must also deal with the complexities and stochas-tic dependencies involved in the transformation, it seems appropriate to characterize this new aggrega-tion problem as being of an order of magnitude more demanding of information, technology, and analytical skill. Add on the further challenge of embodying the adaptive risk-management behavior of farmers con-fronted with such uncertainties as climate change, and it is readily apparent why analysts such as Southworth et al. (2000) deserve our admiration. Clearly, the task of attempting to validate such data-intensive exer-cises, let alone present findings in a comprehensible form, is a potentially daunting one.
This is not the place to become distracted with the technicalities of measuring risk. Procedures for elici-ting and processing distributions that in many cases are necessarily subjective are detailed in many sources (e.g., Hardaker et al., 1997). Many devices can be used to describe risk, most generally by reference to complete distribution functions. For simplicity here, use is made of a convenient simple (and therefore demonstrably imperfect) measure, the coefficient of variation (CV or C[.]), namely the ratio of a standard deviation to its corresponding expected value. The convenience stems from the fact that this is a dimen-sionless measure but is one with some intuitive appeal that can be compared across very different variables. To take some concrete examples of values of CVs at different levels, consider some of the data reported
by Anderson (1979) for the Australian rural sector. Net farm incomes of wool-growing farms had CVs of about 0.8 and farm wheat yields had CVs of about 0.4, so farm experience at this level is quite risky (see also Anderson et al., 1989). At the aggregate level, however, things are much less variable, although still the source of considerable risk at the regional level and a still significant contributor to macro-economic instability. At that time, Australian net farm income had a CV of about 0.09, and the gross value of ru-ral production about 0.29. Anderson was at the time trying to assess what proportion of such aggregate variability was attributable to climatic variation per se, and concluded that about 40% of the CVs was the result of climate. He has not had the opportunity to reassess the situation, but would hazard a guess that with the most recent decade of experience, climate has become an even greater source of risk to the rural sector (Anderson, 1991), while agriculture has continued to decline as a share of the total economy.
For those of global-modeling bent, it is perhaps more interesting to ask questions about the extent to which technology and climate change have contributed to changing risk experience in the diverse niches of world agriculture (Anderson and Scandizzo, 1984). Soon such modelers will also wish to ask in addition how globalization and new trade agreements have al-tered the risk environment. All such good questions are likely to involve taking some stance on how risk is aggregated in the models assembled for analysis.
4.2. Practical
Hitherto here, the importance of grappling with risk has been portrayed as only being to ensure reliable estimation of the all-important means of uncertain quantities. It is especially the case that special steps need to be taken in models, where component uncer-tain quantities are asymmetrically distributed and/or correlated, and when they are combined in non-linear mathematical operations (Anderson and Doran, 1978). These special steps are readily enough handled in modern spreadsheet-based programs such as @Risk and CrystalBall, with the proviso that the applicable multivariate distributions can be adequately elicited and specified.
farms is design of crop insurance schemes. Among many aspects to be considered is the nature of the distribution of yields of insured crops. Under the sampling independence assumptions of the Central Limit Theorem, it would be anticipated that yields that are averages would tend towards being normally distributed. Indeed, Just and Weninger (1999) found the normality of yield to be almost impossible to reject in a diversity of US crop yields measured at various levels of aggregation. To the extent that yields are approximately normal/Gaussian, probability spec-ification and risky choice are greatly simplified, as is any aggregation of probability distributions.
An increasing amount of analytical work in the agricultural sector is being done at a multi-market level, recognizing that a focus at the farm level tells a diminishing part of the sectoral story. Techniques for analyzing flows of agricultural product through the complete marketing chain to the ultimate consumers are becoming more readily available, and are even now to hand for the rather specific issue of evaluation of the effects of changes brought about through re-search and development activities at the various levels (e.g., Alston et al., 1995, p. 71). Dealing adequately with risk in such multi-market settings is, however, still a rather untilled field, involving as it does usually challenging aggregation problems.
For reasons of potential balance in these disciplinary judgments, let this partially informed observer make a tentative best-practice award nomination. It has long been a strong impression that, when it comes to the technology of modeling, scaling, validating and inter-preting for managerial purpose, the hydrologists are doing best. Perhaps this enthusiasm has to be qualified somewhat by noting that they usually work on more bounded systems, where verification possibilities are relatively available, and the level of aggregation is in most cases not beyond a river basin, but there is clearly considerable challenge in modeling both the response and stochastic relationships, which are usually handled impressively (e.g., as illustrated by the contributions in Sposito, 1998, and in this Theme by Schulze, 2000). In the world of crop modeling it seems that there has developed some concern for a reverse aspect of those discussed above, namely procedures (usually based on empirical regressions) for “downscaling” model re-sults (analogous to the Davidson case of small real plot results discussed earlier) so that predicted (mean)
yields match those observed at farm level more closely (e.g., Lansigan et al., 1997). In terms of the topic of this section, the surprising thing is that these authors did not express the same concern for reconciling pre-dictions of the riskiness of yields. Perhaps this issue often may be deserving of closer attention?
For the themes of the GCTE Conference, the han-dling of risk at the aggregate level seems still some-what undeveloped, perhaps reflecting some of the modeling challenges mentioned, perhaps for a lack of appreciation of the possible roles of risk and risk aversion in decision making at this level (Anderson and Dillon, 1988), perhaps because of a perception that risk is a second-order consideration in the grand scheme of things (Anderson et al., 1987), perhaps because of ignorance, or even prejudice.
4.3. Policy
Just how important formal accounting for risk might be is a good question. For conventional investments there can be a rough and ready test of whether risk per se is worth being troubled by at all. For instance, Hardaker et al. (1997) offer a general approximation procedure based on CVs of what is being considered
C[x], of what it is being added to C[y], the correlation
between x and y (g), the size of the mean of x relative to that of y (B), and a measure of relative risk aver-sion R (a number between, say, 1 and 2), viz.D = RC[x]{0.5C[x]B+gC[y]}, and then risk can be dis-regarded if the deduction D is “small”, say<0.02.
Problems at the global level do not fit well into this crude guideline, since the quantities at stake may be very large, and even though society as a whole may be close to risk-neutral in large public decisions, the future of the planet and humanity is a significant issue, and on a scale worthy of attention and potential invocation of the Precautionary Principle. But what is inescapable is that, to the extent that risk-averse peo-ple play active parts in the processes whose effects are being aggregated in global perspectives, risk is inherent to the reality being modeled, and can be ig-nored only if there is no real concern for relevance of findings.
profound uncertainty about effects, benefits and even costs (Anderson and Thampapillai, 1990; Stocking, 1996; Shaxson et al., 1997). Much progress has been made in this field (e.g., El-Swaify, 1999) but, espe-cially in the developing world, the significance of soil erosion and land degradation more generally is still too poorly understood (which is to say, poorly measured and modeled, especially at other than rather local levels of aggregation (Biot et al., 1995).
It is well and good to speak of solving problems of scaling up to answer questions of global change, but how the global estimates are to be variously validated and evaluated is a key question of method and poli-cy. In spite of increasing efforts and commitment to such work, the adequacy of these seems both uncer-tain and unlikely (e.g., Rawlins, 1994; World Bank, 1997b). Surely, progress will involve refinements of GIS, as well as national and international efforts to as-semble conformable and cogent data on indicators of status and change. Only through such more effective monitoring will it be possible to assess the adequacy of the scaling methods that will increasingly come to be relied upon. The cross-checking through use of a multiplicity of sources, such as is used by USDA FAS for crop assessment, seems an appropriately cautious approach.
5. Conclusion
Progress has clearly been made on many fronts of relevance to the scaling problems in global change analysis. When the Commission on Sustainable De-velopment gets to deal with Agriculture in 2000, how-ever, the chances are that the progress will be found to be wanting, and insufficient on several counts. More work by many people in a wide range of disciplines is evidently required.
No easy general answers are apparent to this obser-ver, particularly if analysts go the possibly important extra mile and seek to accommodate risk as well as mean response in their scaling-up endeavors. Some of the procedures sketched above may prove to be worthy but further development and much refinement seems necessary, especially in the rather under-attended field of dealing with risk. As is nearly always the case in transdisciplinary endeavor, active interactions and synergies among analysts of diverse background will
help to make the work less isolated and more able to exploit productive complementarities.
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