THE USE OF G E N E R A L C I R C U L A T I O N M O D E L S IN THE A N A L Y S I S OF THE E C O S Y S T E M IMPACTS OF CLIMATIC C H A N G E

W. L A W R E N C E GATES

Climatic Research Institute and Department o f Atmospheric Sciences, Oregon State University, Corvallis, OR 97331, U.S.A.

Abstract. The use of general circulation models in the estimation of the impact of climatic change on theglobalecosystem is seen to depend primarily on their ability to reliably depict the seasonal and geographical distribution of the changes in surface climate variables. While present GCMs generally simulate the observed distribution of surface air temperature reasonably well, they show significantly different changes in the equilibrium temperature as a result of doubled CO 2 , for example. These disagreements are attributed to differences in the model's resolution and parameterization of subgrid-scale processes. Such model-dependent errors notwithstanding, much more information of possible use in impact analysis can be extracted from general circulation model simulations than has generally been done so far. The completeness, consistency and experimental possibilities offered by simulated data sets permit the systematic extraction of a wide variety of statistics important to the surface ecosystem, such as the length of the growing season, the duration of rainless periods, and the surface moisture stress. Assuming further model improvements, the elements of a model-assisted methodology for climate impact analysis are seen to be: (1) the determination of the seasonal and geographical distribution of that portion of simulated climatic changes which are both statistically and physically significant; (2) the transformation of the (significant) large-scale climatic changes onto the local scale of impact (the climate 'inversion' problem); and (3) the design of specific statistical parameters or functions relevant to local ecosystem impacts.

1.

Introduction and Overview

A t m o s p h e r i c climate models seek to synthesize the large-scale distribution o f the climate b y application of the physical laws governing the atmosphere's structure and behavior. With realistic b o u n d a r y conditions and with numerical m e t h o d s which give a spatial resolution o f a few hundred kilometers, such models have been reasonably successful in reproducing the continental-scale features of the observed distribution o f temperature, pressure and circulation. Other climatic elements such as cloudiness and precipitation are less well simulated, however, and show large regional and local errors due to their strong d e p e n d e n c e on the m o d e l s ' parameterization o f sub-grid-scale processes. In spite of these limitations, models o f the atmospheric general circulation (or GCMs) have been used in a n u m b e r o f experiments designed to show the climatic changes likely to result from increased levels o f CO2. Even though such results must be viewed with considerable caution (and have yet to be analyzed in an insightful manner), more GCM experiments have been made for the C02 problem than for any o t h e r specific climate question. In general, these simulations have shown that an average global warming of

Climatic Change 7 (1985) 267-284. 0165-0009/85/15. 9 1985 by D. ReidelPublishing Company.

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several degrees C may accompany a doubling of atmospheric CO2, with the largest increases in surface temperature occurring in the higher latitudes in winter. Although some CO2 experiments show a drying over the mid-latitude continents, the regional changes of precipitation and soil moisture have not been reliably modeled. Further experimentation is needed in order to improve the model's overall accuracy, and simulations are needed over longer periods of time. When models including realistic interactions with the surface biomass and the oceans are available, they will be increasingly useful as tools with which to estimate the likely CO2-induced changes of biophysical effects and of the associated surface climatic variables. These considerations lead us to recognize several aspects or characteristics of climate information which are important in a comprehensive analysis of the impacts of climatic change on the terrestrial ecosystem: (1) description of the geographical and seasonal distribution of a simulated climatic change, rather than only global or annual averages; (2) description of the degree of uncertainty or likely error accompanying the distribution of the change of each climatic variable; (3) transformation of the climate change simulated on a model's large scale into information on the local scales on which climatic impacts occur; and (4) interpretation of the modeled climatic change in terms of variables or functions which are of direct relevance to the estimation of ecosystem impacts. The purpose of this paper is to address these questions as part of an exploration of the use of climate models in impact estimation. After briefly reviewing current models' capabilities and their projection of CO2-induced climatic changes, we will consider the elements of a model-assisted impact analysis methodology. 2.

Review of Climate Models and their Results

2.1. GCMs as Climate Models

Among climate models, only GCMs contain the physical detail and geographical resolution necessary for even regional impact assessment; steady-state climate models or models with only one or two dimensions will therefore not be considered, although such models are useful for other purposes. As noted earlier, GCMs are based on the fundamental dynamical equations describing large-scale atmospheric motion. Together with boundary conditions at the earth's surface (which usually consist of specifications of the sea-surface temperature and sea ice, and the land surface's elevation and albedo), and the radiative input at the top of the atmosphere, the behavior of the atmosphere's wind, temperature, pressure, density and humidity is determined by the equations of motion, the first law of thermodynamics, the continuity equations for mass and water vapor, and the equation of state. At the ground surface most GCMs also calculate the temperature and soil moisture on the basis of equations for the surface heat and water balances. Other quantities such as convective fluxes, cloudiness, and precipitation are determined from parameterizations which relate these sub-grid-scale processes to the large-scale variables resolved by the model. After a GCM's parameterizations and boundary conditions have been fixed, the rate of change of the primary or prognostic variables of the model is determined at a global net-

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work of discrete gridpoints (or in terms of a finite number of spherical harmonics, if a spectral rather than finite-difference formulation is used). The solution is then advanced in time, and the procedure is repeated until an integration of the necessary length has been achieved. After a time which may vary from a few months to several years, depending upon the particular model and initial conditions used, the behavior of the model approaches a statistical equilibrium in the sense that its time-averaged statistics are no longer sensibly changing (although the model continues to simulate synoptic-scale weather and seasonal variations). These statistics then define the model's climate, and the average distributions of such variables as the pressure, temperature and precipitation may then readily be determined. The climate of a standard or control integration determined in this way may then be compared with the observed present climate in order to determine the model's systematic errors, and compared with the climate of an experimental integration in which a boundary condition or parameterization has been changed in order to determine the resulting change of climate. The statistical significance of these comparisons depends on the model's simulated fluctuations as well as the mean state. We may summarize the use of GCMs as climate models by referring to Table I in which the characteristic model input and output are listed from the viewpoint of the surface climate. Here the initial conditions are the distributions of the primary or basic variables at each model level. In a climate simulation which typically extends over many months or years, the equilibrium climate statistics are essentially independent of the initial conditions (although the solution's approach to statistical equilibrium is generally delayed if unreasonable or inconsistent initial conditions are used). The boundary conditions required by atmospheric GCMs are the distribution of surface topography (including the surface elevation and surface type or land use), the surface albedo, and the distribution of sea-surface temperature and sea ice. (When an ocean model is coupled to the atmosphere, the sea-surface temperature and the distribution and mass of sea ice become output from the model rather than input.) The solar radiation at the top of the (model) atmosphere is usually either held fixed or assigned the normal daily and/or seasonal variation. Other physical parameters in an atmospheric GCM which are usually adjusted to more-or-less realistic values are the albedo of clouds, the diffusion coefficients for the horizontal and vertical turbulent mixing of heat, momentum and moisture by sub-grid-scale processes, and the soil water capacity which helps to determine the simulated surface moisture. Except in simulations with increased C02, the atmospheric composition is usually not changed. The output available from GCMs for the analysis of simulated climate includes the three-dimensional distribution of the same basic variables used as input initial conditions (pressure, temperature, humdity, wind, cloudiness, soil moisture and snow cover), along with other surface variables and processes parameterized in the model. These include the rates of precipitation and evaporation, the net surface flux of both short- and long-wave radiation, the turbulent flux of sensible heat at the surface, and the surface runoff. These quantities may in turn be used to reconstruct a variety of other processes related to specific climatic stresses or effects on the ecosystem, such as water use efficiency or wind chill, many of which are not routinely observed.

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TABLE I. Characteristic input and output of an atmospheric GCM INPUT Initial conditions (Basic variables, as in output) Boundary conditions (principally at earth's surface) Surface elevation Surface type (water, ice, land use) Surface albedo Sea-surface temperature and sea ice Solar radiation (at model top) Physical parameters Cloud albedo Diffusion coefficient(s) Soil water capacity Atmospheric composition OUTPUT Basic variables Pressure Temperature Humidity Wind Cloudiness Soil Moisture Snow Cover Auxiliary variables, processes Precipitation Evaporation Surface radiative flux (short- and long-wave) Surface sensible heat flux Surface runoff 2.2. Simulation o f Present Climate Although current GCMs differ in their computational resolution and in their parameterization o f physical processes, they show general agreement in their simulation of the largescale features of global climate. This characteristic performance of GCMs is illustrated by the comparison of the simulated and observed distributions of surface air temperature shown in Figure 1. Here the model has realistically simulated the major pools of cold air found over the northern hemisphere continents in February, and has reasonably portrayed the mid-latitude zones of strong north-south temperature contrast. The largest errors in surface air temperature in this model, as in other GCMs, occur over the North Atlantic ocean and Europe, where the observed penetration of relatively warm air into high latitudes is not well simulated. This error is at least partly due to the model's neglect of northward heat transport in the ocean. We may also note that errors as large as 10 K also occur in the vicinity of mountains. After temperature, the next most important climatic element for the surface ecosystem

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Fig. 1. The distribution of mean February surface air temperature (K) as simulated in a control integration of the GFDL GCM with a uniform-depth mixed-layer ocean (above), and as observed (below). The regions above 300 K and below 270 K are shaded. Redrawn from Manabe and Stouffer (1980). is probably the precipitation. GCMs simulate precipitation as a result of large-scale vertical motion, such as that associated with convergence near cyclones, and as a result of convective motion associated with vertical instability on a local scale. The latter type of precipitation occurs on scales below a GCM's resolution, and is therefore parameterized in terms of the large-scale distribution of temperature and humidity. The total precipitation (i.e., the sum of large-scale and convective-scale precipitation) simulated by current GCMs is in reasonable agreement with the observed long-term average, although there are discrepancies as large as a factor o f two in the local precipitation rate in some (mostly tropical)

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regions (see for example, Washington and Meehl, 1984, or Manabe and Stouffer, 1980). GCMs also simulate the average seasonal cycle of precipitation, including the seasonal migration of the tropical rain belt and the large-scale seasonal shifts of surface temperature and precipitation which accompany the monsoons. Several atmospheric GCMs have now been integrated for more than ten years' time, and have shown themselves capable of simulating not only the average seasonal cycle but a realistic degree of interannual variability as well (see, for example, Manabe and Hahn, 1981). Such year-to-year differences in the model's climate are primarily the result of its simulation of the unstable transient cyclones in middle latitudes, whose local behavior is not predictable over climatic time ranges. Noting that this internal or natural variability occurs without interannual changes in boundary conditions, it may be regarded as a sort of climatic noise inherent in a realistic GCM. The presence of such irregular (and essentially unpredictable) fluctuations in a climatic record complicates the detection of a climatic change caused by changes in physics or boundary conditions, such as increased CO2.

2.3. Simulation of CO2-Induced Climatic Change As noted earlier, a large number of experiments have been made in which the atmospheric CO2 concentration in a GCM has been doubled (or quadrupled) relative to its value in a control run. In such simulations, the model is integrated until its solution has achieved an approximate statistical equilibrium; the time required depends primarily on the degree of ocean-atmosphere interaction included in the model, and varies from a few months without an interactive ocean to several decades with a coupled oceanic GCM. The CO~ -induced climate changes are then examined for significance against the (natural) variability displayed in the control. The most recent and comprehensive of such experiments (which include an interacting mixed-layer ocean of uniform depth and realistic geography) show that on the annual and global average the near-surface atmosphere warms by 2 - 4 ~ when CO2 is doubled, in overall agreement with earlier results from simplified models with a swamp-like ocean and no seasonal cycle (Manabe and Wetherald, 1975; Washington and Meehl, 1983). Specifically, the GFDL model used by Manabe and Stouffer (1980) indicates a 2.0 ~ increase of average surface-air temperature with doubled CO2 (found by halving their results for quadrupled C Q ) , while Washington and Meehl (1984) have found an average 3.5 ~ warming with doubled CO2. Analysis of the warming by latitude and season shows that the largest increases of surface-air temperature occur in the higher latitudes during winter as illustrated in Figure 2. This poleward amplification, and hence much of the global average change itself, is caused mainly by simulated changes in the distribution of snow and ice, and shows substantial variations among GCMs, as noted, for example, by Schlesinger (1983). To estimate the ecosystem's response to CO2-induced warming requires a precise knowledge of the geographical distribution of the simulated temperature change. With disagreement by a factor of two present in even the globally-averaged warming, it is perhaps not surprising that the regional changes are quite uncertain. Such warming may in

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variability in both space and time due to its dominance by convective-scale processes. Nevertheless, there is some evidence of a slight increase of tropical precipitation (as might be expected in a warmer atmosphere) and a slight increase of the average precipitation in mid-latitudes with increased CO2, along with a reduction in soil moisture in some continental areas (Manabe et aL, 1981). The identification of the precipitation changes in specific geographical areas is a priority task for climate impact assessment, but as with temperature, the local changes may also be model-dependent.

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These comparisons serve to remind us that even if these (or other) models were to agree in their simulations of today's climate, there is no guarantee that their projections of a future CO2-induced climate would agree (or that such projections would agree with nature). 2.4. Modeling Problems and Improvements

In searching for reasons for the disagreements among GCMs in their portrayal of climatic changes, such as those due to increased CO2 noted above, we may recall that the models contain different parameterizations of many climate-sensitive processes. An important task for scientists concerned with climate simulation is therefore to systematically compare the models' treatment of sub-grid-scale processes, such as those occurring in the surface boundary layer and in convection, cloud formation and precipitation. These processes are dominated by turbulent transfers, and their treatment in GCMs is based upon relations which in many cases have not been adequately established. Without more adequate data bases it will also not be possible to decide which of several formulations is superior in general. Improvement of the parameterization of s'~b-grid-scale processes, however, may be expected to reduce the disagreement among GCMs' climates only if the disparity in the resolution of the models is reduced at the same time. This failure of parameterization changes to narrow the differences in model performance is not so much due to truncation error (which will itself cause models of different resolution to simulate slightly different climates), but rather to the likelihood that a particular parameterization will not work equally well in GCMs which have different resolutions. Recognition of this linkage between parameterization and resolution will help to accelerate the rate of progress in the improvement of atmospheric GCMs. Aside from the improvement of the atmosp'~eric GCM itself, the next most important problem for climate modeling is undoubtedly the treatment of the ocean. This is especially true in the longer-term simulations designed to show the effects of increased atmospheric CO2, since the oceans effectively regulate the atmosphere's long-term behavior through their absorption, storage, transport and selective release of large amounts of heat. In atmospheric GCMs with prescribed sea-surface temperature this interaction is not allowed to operate, and this has markedly lowered such models' sensitivity to increased CO2 (Gates et al., 1981 ;Mitchell, 1983 ; Gilchrist, 1983). When the global ocean is treated as a swamp as by Washington and Meehl (1983), or as a mixed layer of uniform depth as by Manabe and Stouffer (1980) and Washington and Meehl (1984), a larger response to increased CO2 is found, although the effects of ocean currents and interaction with the deeper ocean are still neglected. No results from the application of fully-coupled atmosphere-ocean GCMs to the CO2 problem have yet been published; such simulations will presumably be necessary to provide definitive information on the climate's response to increased CO2, including the all-important seasonal and geographical distributions. Another problem which has so far been given little attention is the ecosystem's interaction with a changed climate. In almost all GCMs the surface vegetation is considered

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only for the purpose of assigning a surface albedo (and possibly a surface roughness and soil moisture capacity); an interactive parameterization would permit the surface vegetation (and perhaps other portions of the ecosystem) to respond to a changing climate, and thereby to help determine the nature of the eventual equilibrium climate itself. Such parameterization would be especially important in the case of CO2-induced climate changes, since the direct biological response of the ecosystem to rising CO 2 could then also be considered. 3.

The Use of GCM Statistics in Climate Impact Estimation

Among the various kinds of information available from climate models, that from GCMs is of particular value for the estimation of the possible impacts on the ecosystem. This is due to four characteristics: (1) the output or solutions from a GCM form a complete set of data in both space and time, and address a comprehensive array of variables; (2) the GCM-simulated data are internally consistent with each other, and hence can be used for the diagnosis of a variety of physical processes; (3) the climatic effects of specific factors can be assessed from separate experimental integrations under controlled conditions; and (4) the performance of a GCM can, at least in principle, be systematically improved by the incorporation of better parameterizations and solution procedures. These diagnostic advantages, however, must be tempered by the realization that the effective development and use of climate models goes hand-in-hand with the availability of adequate observational data. 3.1. Local GCM Statistics In spite of the presence of model errors and the acknowledged inability of GCMs to resolve smaller-scale features, a great deal of information which may be useful in the estimation of local ecosystem impacts can be extracted from a GCM climate simulation. To illustrate this, we consider the statistics simulated at a single GCM grid point during the course of integrations with both normal and increased atmospheric CO2. This is done in Figure 4 for the soil or ground wetness (a scaled measure of surface soil moisture) simulated by the OSU GCM at the grid point 34 N, 100 W. Here the frequency of occurrence of daily mean ground wetness in each season is shown from three years' data in a control run (with normal CO2) and for a single year's data in an experimental run with quadrupled CO2. In spring (defined as the months March, April and May) and summer the ground wetness distribution is not much changed, but in fall and winter increased CO2 appears to have resulted in significantly drier and wetter soil, respectively, than under normal conditions. Although we do not expect a large response to increased CO2 in this particular model experiment (since the sea-surface temperatures were specified from climatology), these results at least illustrate the kind of local analysis which can be made. Were such changes of soil wetness indeed found to be characteristic of the local climatic response to increased CO2 in longer simulations with more comprehensive model(s), they would be useful in estimating the impacts associated with a variety of activities related to the local eco-

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Fig. 4. The seasonal frequency distribution of daily means of the ground or soil wetnees simulated by the OSU GCM (Gates et al., 1981) at a gridpoint in Oklahoma (34 N, 100 W). The values for each season of a three-year simulation with normal CO2 are shown as dashed lines (when distinguishable from zero), and those with quadrupled CO2 are shaded. Here each season is three months long, with winter being December, January and February. (Redrawn from Gates and Bach, 1981). system. In addition to a single variable's distribution (or histogram), we may examine the joint frequency distribution of variables in the form of a scatter diagram. For the same grid point considered earlier (at 30 N, 100 W), the joint distributions of soil or ground wetness and surface air temperature are shown in Figure 5 for each season. Here the daily average values from the three-year control integration with normal CO2 are shown as dots, while those from parallel one-year integrations with doubled and quadrupled CO2 are shown as crosses and squares, respectively. In no season has higher CO2 significantly changed the

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TABLE II : Modeled climatology of number of days without precipitation and of length of the growing season at 34 o N, 100 ~ W in a control simulation and in simulations with doubled and quadrupled CO~

Number of days without precipitation Simulation

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(RMS) interannual variability of the number of days without precipitation is in the transition seasons o f late spring and fall. With increased C Q (and especially with quadrupled CO2) the number of days without precipitation is reduced in most (but not all) months, with the most significant reductions occurring in late spring and early summer. Such changes could have a significant effect on the growth of local crops, although possible changes of other factors would also have to be considered. One of these shown in Table II is the length of the growing season (defined as the number o f days between the last occurrence of freezing in spring and the first occurrence in fall); here the lengthening b y 46 days with quadrupled CO2 is significantly greater than the RMS change, and is accompanied b y slightly higher summer t e m p e r a t u r e s .

3.2. The Estimation o f Climatic Changes on the Scale o f the Ecosystem The examples shown above are only a small part of the many statistics which can be extracted from GCM experiments. In the estimation of the effects of increased CO2 on specific portions o f the local ecosystem, other measures and formats readily come to mind, such as changes o f plants' water use efficiency and changes of crop yields. Attention should also be given to changes in the frequency o f occurrence of presently extreme events, many o f which have important effects on the local ecosystem, especially in marginal zones where one or another climatic variable is a limiting factor. No matter how imaginative the extraction of such statistics from a GCM simulation m a y be, they are limited b y the fact that they are not truly local statistics, but represent averages on the scale o f the grid elements or box in the model; most GCMs, we may recall, neither incorporate nor provide information on scales smaller than a few hundred kilometers. The effective size or scale o f the ecosystem on which climatic impacts actually occur, on the other hand, is usually much smaller than this. We are therefore faced with the problem o f estimating climate changes on a local scale from the essentially large-scale

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results of a GCM. This has been called the 'climate inversion' problem, since it represents the reverse or inversion of the familiar problem of parameterization (Kim et al., 1984). One approach to this problem is to exam: he the statistical relationship between the variations of, say, monthly mean local ol station data and the corresponding variations of monthly means averaged over an area comparable to that of a GCM grid element. The anomalies at each locality will in general be related to the regional or large-scale anomaly in different ways, depending upon the local geography, the prevailing circulation, and possibly other factors. By examining the variations at each station in a selected area, we may quantify this relationship for each climatic variable in terms of the empirical orthogonal functions (or EOF) which define the dominant spatial patterns of local variations which occur in conjunction with variations of the areal mean. This is illustrated for the surface air temperature and precipitation in Figure 6, in which the structure of the first EOF (which explains more of the variance than any other pattern) is shown for a set of 49 stations in the state of Oregon. Here the isolines are proportional to the fraction of the state-wide variation which is shared by the local variation; in this case the first EOF accounts for 78% and 81% of the total variance of the local temperature and precipitation, respectively (Kim et al., 1984). The structure of these patterns (whose most important time variation is seasonal) clearly shows the predominant influence of the north-south Cascade and coastal mountain ranges. In this way the grid-scale results from a GCM's simulation could be systematically assigned or distributed on a local scale, although local dynamical models meshed with the GCM itself might also be used. Such a climatic inversion or downscale transformation at least gives the statistically most probable local distribution of anomalies when only the area-average anomaly is given. These techniques may be viewed as providing an alternative to the linear interpolation of large-scale results, which themselves could be expressed in terms of EOFs, as in Steyaert et al. (1977). When developed for other areas and for other periods (recall that only monthly means were considered here), such information should be useful in crop yield models and help in the modeling of the climatic response of other portions of the local ecosystem (Bach et al., 1981). 3.3. Towards a Model-Assisted Impact Estimation Methodology In order to take fullest advantage of the unique features of climate models (and GCMs in particular) in the estimation of climate's impact on the ecosystem, it is helpful to recognize that various aspects of the problem are closely related to each other. As noted earlier, a climate impact is first determined on the local scale of the ecosystem, and thence aggregated to determine the large-scale or global impact (taking the appropriate economic, social and political factors into account). This process is shown as step 5 in Figure 7, but is not directly related to the use of climate models. Likewise, step 4 in this figure involves the development of impact models for the estimation of the local ecosystem's response to local climate changes, and belongs more to impact modeling than to climate modeling. The other three steps identified in Figure 7, however, are relevant to the use of climate models in impact estimation, and are shown in telTns of their increase of climate informa-

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involves a judgment of the seriousness of the model's errors in comparison with the observed climate; it does little good, for example, to simulate a climatic change with high statistical precision if the model's climate itself has unacceptably large errors. Increased consideration of this aspect is necessary in order to accelerate progress in the definitive identification of CO2 's climatic effects. Although determination of the significant portions of a large-scale climate change increases the climate information available from a GCM, there remains the problem of translating this (significant) information to the smaller scales on which ecosystem impacts usually take place; this is the 'climate inversion' problem considered earlier, and is identified as step 2 in Figure 7. Whether furnished by statistical and/or dynamical methods, this estimation of local climatic changes considerably increases the amount of climate information which may be useful in impact studies. Appropriate transfer functions for this large-

The Use of General Circulation Models

283

to small-scale transition should therefore be determined for at least those regions where an important climate impact is anticipated. Once such local climate change data are available, their usefulness for impact estimation may be further increased by using them to construct a variety of statistical measures or functions involved in the local ecosystem response to climate. This is identified as step 3 in Figure 7, and is illustrated by the statistics in Table II (although there grid-point rather than truly local data were used). Such impact-related statistics will usually be specific to each locality and to each component of the local ecosystem. The steps shown in Figure 7 leading from the output of GCM experiments (such as those with increased CO2) to the determination of the ecosystem's response, are the essential elements of a model-assisted impact estimation strategy. Much further work is needed on each of these steps, however, as well as on the improvement of the underlying GCMs themselves, before a systematic methodology can be said to exist. This problem provides an opportunity for sustained and fruitful collaboration between climate modelers and ecosystem impact specialists, as each group learns to use the information provided by the other. Such a methodology will be of particular value in the analysis of climate experiments which are focused on the most sensitive aspects of the ecosystem, and in which the feedbacks between the climate and the local ecosystem are taken into account. Acknowledgements This paper was prepared for presentation at the UNEP/WMO/ICSU Study Conference on the Sensitivity of Ecosystems and Society to Climate Change: Possible Impacts of Increased CO~ in the Atmosphere, held during 1 9 - 2 3 September, 1983 in Villach, Austria. The research reported here was supported in part by the National Science Foundation and the Department o f Energy under Grants ATM-8205992. I thank Kelly Redmond and several anonymous reviewers for their comments on an earlier version of this report, and Elizabeth Webb and Naomi Zielinski for their typing assistance.

References Bach, W., Pankrath, J., and Schneider, S. H. (eds): 1981, Food-Climate Interactions, Proceedings of an International Symposium, Berlin, 9-12 December, 1980, D. Reidel, Dordrecht, 504 pp. Gates, W. L. and Bach, W.:1981, 'Analysis of a Model-Simulated Climate Change as a Scenario for Impact Studies', Report for the German Federal Environmental Agency, R & D No. 104-02-513, 163 pp. Gates, W. L., Cook, K. H., and Schlesinger, M. E.: 1981, 'Preliminary Analysis of Experiments on the Climate Effects of Increased CO2 with an Atmospheric General Circulation Model and a Climatological Ocean', J. Geophys. Res. 86, 6385-6393. Gilchrist, A.: 1983, 'Increased Carbon Dioxide Concentrations and Climate: The Equilibrium Response', in W. Bach et al. (eds.), Carbon Dioxide: Current Views and Developments in Energy/Climate Research, D. Reidel, Doxdrecht, pp. 219-258. Kim, J.-W., Chang, J.-T., Baker, N. L., Gates, W. L., and Wilks, D. S.: 1984, 'The Statistical Problem of Climate Inversion: Determination of the Relationship between Local and Large-Scale Climate', Mon. Wea. Rev. 112, 2069-2077. (See also J.-W Kim et al., Report No. 22, Climatic Research Institute, Oregon State University, Corvallis, 1981, 25 pp.)

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Manabe, S. and Hahn, D. G.: 1981, 'Simulation of Atmospheric Variability', Mon. l~ea. Rev. 109, 2260-2286. Manabe, S. and Stouffer, R. J.: 1980, 'Sensitivity of a Global Climate Model to an Increase of CO 2 Concentration in the Atmosphere', J. Geophys. Res. 85, 5529-5554. Manabe, S., Wetherald, R. T., and Stouffer, R. J.: 1981, 'Summer Dryness due to an Increase of Atmospheric CO~ Concentration', Climatic Change 3 , 3 4 7 - 3 8 6 . Mitchell, J. F. B.: 1983, 'The Seasonal Response of a General Circulation Model to Changes in CO 2 and Sea Temperatures', Quart. J. Roy. Meteor. Soc. 109, 113-152. Schlesinger, M. E.: 1983, 'A Review of Climate Model Simulations of CO~ -induced Climatic Change', Report No. 41, Climatic Research Institute, Oregon State University, Corvallis, 135 pp. Steyaert, L. R., LeDuc, S, K., and McQuigg, J. D.: 1977, 'Principal Components of Large-Scale General Circulation Features: Interpretation and Use in Climate/Crop Yield Models', Preprints, 5th Conference on Probability and Statistics in the Atmospheric Sciences ( 1 5 - 1 8 Nov. 1977, Las Vegas), American Meteorological Society, Boston, 16-21. Washington, W. M. and Meehl, G. A.: 1983, 'General Circulation Model Experiments on the Climatic Effects Due to a Doubling and Quadrupling of Carbon Dioxide Concentration, J. Geophys. Res. 88, 6600-6610. Washington, W. M. and Meehl, G. A.: t984, 'Seasonal Cycle Experiment on the Climate Sensitivity Due to a Doubling of CO 2 with an Atmospheric General Circulation Model Coupled to a Simple Mixed-layer Ocean Model', J. Geophys. Res. 89, 9475-9503. (Received 15 August, 1984; in revised form 26 December, 1984)