2.7 USING ANOVA TO ESTIMATE THE RELATIVE MAGNITUDE OF UNCERTAINTY IN A SUITE OF CLIMATE CHANGE SCENARIOS Julie A. Winkler*, Jeffrey A. Andresen, Galina Guentchev, Eleanor A. Waller, and James T. Brown Michigan State University, East Lansing, Michigan 1. INTRODUCTION An emerging research focus in global change studies is the identification, quantification, and communication of uncertainty. Uncertainty is a particular concern for integrated assessments, including those involving the impact of climate, as the uncertainty associated with each component of an assessment can propagate through the assessment process. This uncertainty “cascade” (Mearns and Hulme, 2001) places severe constraints on policy recommendations derived from impact assessments. Katz (2002) argues that a fully probabilistic approach should be the ultimate goal of uncertainty analysis. Previous attempts to assign probabilistic values have usually involved identifying the major sources of uncertainty, representing these uncertainty sources as probability density functions, driving a model (e.g., climate model) using multiple values from the probability density functions, and combining the model outcomes into an output probability density function (Wigley and Raper, 2001). A major difficulty of this approach is defining appropriate probability density functions for the uncertainty sources. Typically, either a uniform distribution is assumed or the distribution is defined subjectively based on expert judgment. A second important limitation is that uncertainty in the model structure is not considered. Jones (2000) proposed a somewhat simpler approach whereby multiple scenarios are used to estimate the “quantifiable range of uncertainty” for a particular source. Ideally, the quantifiable range approaches the total range of uncertainty if a diverse group of scenarios is selected. If more than one uncertainty source exists, then conditional probabilities can be calculated by first defining the second uncertainty source in terms of the first, next assuming a uniform distribution for each source, then randomly sampling the component uncertainties across their respective quantifiable uncertainty ranges and finally multiplying the samples from each source. An advantage of this approach is that uncertainty in model structure is included, although only implicitly. A limitation, of course, is the simplistic and likely unrealistic assumption of uniform distributions for the uncertainty sources. Also, it is difficult using this approach to simultaneously consider more than two sources of uncertainty. * Corresponding author address: Julie A. Winkler, Michigan State University, Department of Geography, East Lansing, MI 48824-1115; email winkler@msu.edu. We propose an alternative method for evaluating and communicating uncertainty that involves 1) the use of a large suite of local climate change scenarios to estimate a quantifiable range of uncertainty and 2) the application of analysis of variance (ANOVA) and related non-parametric procedures to determine the relative magnitude of multiple sources of uncertainty, the “interaction” between the uncertainty sources, and the statistical significance of the source and interaction terms. The motivation for this study is summarized by Katz (2002) who states that “The field of climate change impact assessment will be better off in the long run the sooner it is recognized how severely underestimated uncertainty presently is” (p. 182). For this demonstration, the ANOVA technique is applied to 240 annual scenarios and 960 seasonal scenarios of the projected change in the mean and standard deviation of temperature. The scenarios were originally developed to assess the potential impact of a perturbed (approximately 2xCO 2 ) climate on agriculture in the lake-modified zones surrounding the Great Lakes and are unique in terms of the shear number of scenarios for a region. Uncertainty sources were defined as 1) the downscaling methodology used to develop the scenarios, 2) the choice of coarse-scale GCM output to which the downscaling methodology was applied, 3) the location for which the scenario was constructed, 4) the predictand (i.e., maximum or minimum temperature), and 5) season. Admittedly, between-location, between- predictand and between-season differences are frequently of interest to users of climate scenarios and typically would not be considered uncertainty sources. However, inclusion of these terms in the ANOVA analysis allows their magnitude relative to the two primary uncertainty sources (i.e., downscaling methodology and GCM simulation) to be assessed. 2. DATA AND METHODS Simulations from four GCMs (Canadian Climate Center (CCC) GCMII, the Hadley Center UKTR, Max Planck Institute (MPI) ECHAM3, and the Goddard Institute of Space Studies (GISS) Version IV) were used in the scenario development. As the scenarios were developed over an extended period of time, the characteristics of the GCMs vary widely. Two approaches were employed to downscale the GCM simulations to six locations surrounding the Great Lakes. First, the GCM-simulated series of daily maximum or minimum temperature from the land gridpoint nearest the station location were used directly (referred to as the GRDPT scenarios). Second, a regression-based statistical downscaling methodology,