Emergent Behavior and Uncertainty in Multimodel Climate Projections of Precipitation Trends at Small Spatial Scales

5554 J O U R N A L O F C L I M A T E VOLUME 19 Emergent Behavior and Uncertainty in Multimodel Climate Projections of Precipitation Trends at Small Spatial Scales P. GOOD AND J. LOWE Hadley Centre for Climate Prediction and Research, Met Office, Exeter, United Kingdom (Manuscript received 27 June 2005, in final form 2 February 2006) ABSTRACT Aspects of model emergent behavior and uncertainty in regional- and small-scale effects of increasing CO 2 on seasonal (June August) precipitation are explored. Nineteen different climate models are studied. New methods of comparing multiple climate models reveal a clearer and more impact-relevant view of precipitation projections for the current century. First, the importance of small spatial scales in multimodel projections is demonstrated. Local trends can be much larger than or even have an opposing sign to the large-scale regional averages used in previous studies. Small-scale effects of increasing CO 2 and natural internal variability both play important roles here. These small-scale features make multimodel comparisons difficult for precipitation. New methods that allow information from small spatial scales to be usefully compared across an ensemble of multiple models are presented. The analysis philosophy of this study works with statistical distributions of small-scale variations within climatological regions. A major result of this work is a set of emergent relationships coupling the small- and regional-scale effects of CO 2 on precipitation trends. Within each region, a single relationship fits the ensemble of 19 different climate models. Using these relationships, a surprisingly large part of the intermodel variance in small-scale effects of CO 2 is explainable simply by the intermodel variance in the regional mean (a form of pattern scaling). Different regions show distinctly different relationships. These relationships imply that regional mean results are still useful, as long as the interregional variation in their relationship with impact-relevant extreme trends is recognized. These relationships are used to present a clear but rich picture of an aspect of model uncertainty, characterized by the intermodel spread in seasonal precipitation trends, including information from small spatial scales. 1. Introduction An issue of current interest (Houghton et al. 2001) is the uncertainty range of future climate change projections. Sets of slightly modified versions of essentially the same model (Murphy et al. 2004), and ensembles of structurally different models (e.g., Tebaldi et al. 2004) have both been used to explore different aspects of uncertainty. In understanding the possible socioeconomic impacts of climate change, land surface precipitation is one of the most important quantities to investigate (Houghton et al. 2001). However, in projections of future seasonal mean precipitation change at a given location, results from different models typically show a very large spread (Allen and Ingram 2002). Hence, a simple multimodel average of precipitation change at a Corresponding author address: P. Good, Hadley Centre for Climate Prediction and Research, Met Office, FitzRoy Road, Exeter, EX1 3PB, United Kingdom. E-mail: peter.good@metoffice.gov.uk chosen location is not particularly useful for estimating socioeconomic impacts. The spread in projections for any given location arises both from differences in model construction and from natural variability. The problem is exacerbated for precipitation due to the large magnitude of natural temporal variability, and to the presence of small-scale features in both climatological changes and natural variability. Small differences in the positioning of small-scale features can cause large intermodel discrepancies at any given location (Allen and Ingram 2002). Therefore, when comparing results from multiple models, it may be necessary to abandon information about the positioning of small-scale features. Giorgi et al. (2001) extracted a much more consistent picture by removing small-scale features via regional means (for regions such as the Amazon, Mediterranean, and north Australia), and Tebaldi et al. (2004) progressed further by producing Bayesian probability density functions (PDFs) of regional mean precipitation change. However, small spatial scales in precipitation fields

1 NOVEMBER 2006 G O O D A N D L O W E 5555 are likely to be important for socioeconomic impact assessments. Parts of a region may see multidecadal trends much larger than the regional mean referred to henceforth as regional trend extremes. Even without human influence on climate (i.e., for constant CO 2 ), precipitation at a given location will change over multidecadal time scales, simply due to natural variability. Even closely located points will see slightly different multidecadal trends. Such differences might be expected to be larger for precipitation than for surface temperature, because precipitation natural variability has small spatial scales. So even with constant CO 2,if 80-yr trends are calculated for each point within an extended region, these trends will all be different, forming a natural statistical distribution. The width of this regional trend distribution will depend in part on the magnitude of the variability. If atmospheric CO 2 is now allowed to increase, this natural distribution will be modified to a greater or lesser extent. A regional distribution, and its modification by increasing CO 2, may be classified into one of three cases: 1) the distribution width is narrow compared to the effect of increasing CO 2 (human influence dominates); 2) its width is broad (natural variability and human influence are both important), but the effect of CO 2 forcing is spatially uniform across the region (changing the distribution mean but not its shape); or 3) its width is broad, and the effect of CO 2 forcing varies across the region (the mean and shape of the regional trend distribution both change). Under case 1, the regional mean trend may be sufficient to describe the impact of increased CO 2. Under case 2, the regional mean trend is useful but must be interpreted with care. At locations where human influence happens to reinforce natural changes, the resulting trends may be much larger than the regional mean. An analogy exists for temporal climate extremes, where climate change has its greatest impact through enhancing stresses from existing natural cycles and variability, such as Mediterranean summer drought (McCarthy et al. 2001). Under cases 2 and especially 3, the relevance of regional mean used in previous studies may have limited direct relevance to the subregional socioeconomic impacts. This paper studies 80-yr CO 2 -forced precipitation (PPN) trends on a global basis from multiple models. New methods of comparing multiple climate models allow impact-relevant emergent behavior and uncertainty to be presented. In particular, relationships between large and small spatial scales are discovered. We use the same geographical regions as Giorgi et al. (2001) but retain information from small subregional spatial scales. We first show that whether taking either simple multimodel averages at any given location or regional means for a single model both remove an excessive amount of impact-relevant information. Then, techniques are developed to examine the statistical distribution of small-scale trends within a spatial region, allowing subregional information to be compared between models. Subregional effects of both natural variability and CO 2 forcing are demonstrated, giving a rich picture of impact-relevant information. A major tool developed here is a set of relationships that characterize changes due to increasing CO 2. These relationships link regional and small spatial scales. They demonstrate emergent behavior consistent across multiple different models and may have diverse future applications. Here they are used to generate a clear global picture of the spread in precipitation forecasts within the ensemble of different models. 2. Data and methods We study June August (JJA) means of precipitation (PPN) data from 19 different coupled ocean atmosphere climate models (Table 1), made available as part of the Intergovernmental Panel on Climate Change (IPCC) process. A single season is chosen for brevity. Horizontal model grid resolutions vary from 5 to 1. For each model, results from 80-yr control and transient experiments (both following a spinup) were used. The control run uses preindustrial greenhouse gas concentrations for all but three models; the National Center for Atmospheric Research (NCAR) and Meteorological Research Institute (MRI) models used present-day forcing. These differences in control state are unimportant compared to the model uncertainty presented below. The transient run in each case is forced by CO 2 increasing from the control by 1% per year. Each model is treated as providing equally probable realizations of both control and transient experiments. All calculations take place on the native model grid, without spatial interpolation or averaging of PPN fields. The following analysis was applied to each region in turn. To quantify how an observer might perceive the climate to be changing at each grid cell, we use the rate of PPN change measured by a least squares linear fit to the 80-yr time series (discussion on this choice of measure in appendix A). A trend is calculated separately for the transient and control integrations, each converted to a percentage of the control climate mean. All trends are expressed in units of % per 80 yr. Variability and trends over other time scales will be studied in the future. Now for the whole region, the distribution of trends

5556 J O U R N A L O F C L I M A T E VOLUME 19 TABLE 1. Climate models studied. Modeling group IPCC I.D. Citation Canadian Centre for Climate Modelling and CGCM3.1(T47) CCCma (2005) Analysis Canadian Centre for Climate Modelling and CGCM3.1(T63) Analysis Météo-France/Centre National de Recherches Meteorologiques (CNRM), CNRM Coupled Global Climate Model version 3 (CNRM-CM3) Salas-Mélia et al. (2005, manuscript submitted to Climate Dyn.) France Commonwealth Scientific and Industrial CSIRO Mark version 3.0 (CSIRO-Mk3.0) Cai et al. (2003) Research Organisation (CSIRO), Australia National Oceanic and Atmospheric GFDL Climate Model version 2.0 Delworth et al. (2006) Administration (NOAA)/Geophysical Fluid Dynamics Laboratory (GFDL), United States (GFDL-CM2.0) GFDL-CM2.1 Goddard Institute for Space Studies (GISS), GISS Model EH (GISS-EH) Schmidt et al. (2006) National Aeronautics and Space Administration (NASA), United States GISS-E-R State Key Laboratory of Numerical Modeling FGOALS-g1.0 Yongqiang et al. (2004) for Atmospheric Sciences and Geophysical Fluid Dynjamics (LASG)/Institute of Atmospheric Physics, China Institute for Numerical Mathematics (INM), INM Coupled Model version 3.0 Diansky and Volodin (2002) Russia (INM-CM3.0) Institut Pierre-Simon Laplace (IPSL), France IPSL Coupled Model version 4 IPSL (2005) (IPSL-CM4) Center for Climate System Research MIROC3.2(hires) Hasumi and Emori (2004) (CCSR)/National Institute for Environmental Studies (NIES)/Frontier Research Center for Global Change (FRCGC), Japan MIROC3.2, medium resolution version [MIROC3.2(medres)] Max Planck Institute for Meteorology (MPI), ECHAM5/MPI Ocean Model (MPI-OM) Jungclaus et al. (2006) Germany MRI, Japan MRI-CGCM2.3.2 Yukimoto and Noda (2002) NCAR, United States Community Climate System Model Collins et al. (2006) version 3 (CCSM3) Parallel Climate Model version 1 (PCM1) Washington et al. (2000) Hadley Centre for Climate Prediction and Research, Met Office (UKMO), United Kingdom UKMO Third Hadley Centre Coupled Gordon et al. (2000); Pope et al. (2000) Ocean Atmosphere GCM (UKMO-HadCM3) UKMO-HadGEM1 Johns et al. (2006) within the region is summarized as follows. This is done separately for both the transient and control runs, for each model. First the regional mean trend, is calculated. Then, PC 90, the 90th percentile of linear trends within the region, is estimated, by interpolating the discrete cumulative distribution function. PC 90 is the trend exceeded in 10% of that region (a regional trend extreme), that is, 10% of the region has a trend greater than PC 90. In the control run, PC 90 will be different to the regional mean, because natural variability causes different multidecadal trends at different points within the region. In the transient run, the difference between PC 90 and the regional mean is due both to natural variability and to the fact that the effect of CO 2 forcing will be inhomogeneous across the region. Similarly, PC 10, the 10th percentile of linear trends within the region, is estimated. The number of grid points within each region depends on the region size and model resolution. The smallest (largest) region is CAM (ANT), with 10 174 (340 5070) grid points. Two related regional trend extreme measures are also defined: PC and PC are each given by either the 10th or the 90th percentile of PPN trends, depending on the sign of the transientcontrol difference in the regional mean trend. If the latter is positive, PC PC 90 and PC PC 10 ; otherwise, PC PC 10 and PC PC 90. If the effect of increasing CO 2 forcing is sufficiently strong, PC in the transient run would correspond to points where random trends due to natural variability and the effect of increasing CO 2 both happen to have the same sign,

1 NOVEMBER 2006 G O O D A N D L O W E 5557 leading to a trend larger than the regional mean. By definition, 10% of the region has PPN trends of the same sign as and larger magnitude than PC. Some transient-control differences are also defined as follows: t PC PC t PC PC t c, c PC c PC 1 2 3 where the superscripts (t) and (c) indicate quantities calculated from the transient and control runs, respectively. Some important results below are based on transientcontrol differences in PC and in PC (labeled PC and PC, respectively). Such transient-control differences could arise from CO 2 forcing in the transient run, or just from natural variability. For those results involving multiple independent transient-control comparisons (i.e., those involving multiple climate models), the definitions of PC and PC suggest a focus for tests of significance. If natural variability is dominant (i.e., there is no significant effect of CO 2 forcing on a given result), then we could have obtained an equivalent result by comparing pairs of control runs rather than transient runs with control runs. In this case there could be no systematic, statistically significant difference between the results for PC and PC (the only differences would be due to random internal variability). This is because the labels PC and PC are assigned according to the sign of the regional mean difference transient-control. If we were actually comparing pairs of control runs, then there would be no basis for choosing which runs to label transient and which control. That is, the assignment of labels PC and PC would be arbitrary and could only affect the noise through internal variability. Therefore, it makes sense to focus any significance tests on finding asymmetry between the results for PC and PC. The usefulness of PC is compared with two other quantities: the trend in PPN, interpolated onto a common 2.5 grid ( gridpoint trends ); and, the trend in regional mean PPN. The comparison is done in terms of how representative their ensemble means are of the ensemble that is, how useful ensemble observables they are. For a quantity F, the usefulness of an ensemble observable is measured by the ensemble mean of F divided by the ensemble standard deviation. This is related to the Student s t statistic for the ensemble mean being greater or less than zero (the t statistic is just F divided by number of models). We quote the ensemble mean divided by the ensemble standard deviation because it is independent of the number of models, for sufficiently large ensembles. For a normally distributed quantity, if the ratio of the mean to the standard deviation equals 1, then the probability of a random sample having the same sign as the regional mean is about 84%. Therefore, if the ensemble mean of F divided by the ensemble standard deviation equals 1, the sign of F will be the same as that of the ensemble mean in about 84% of models (assuming a normal distribution). A value of 0.5 suggests that in around 30% of models F has the opposite sign to the ensemble mean, indicating a relatively poor ensemble observable. The ensemble mean divided by the ensemble standard deviation is calculated for each grid cell for the gridpoint trends and each region for and PC. For each of the three quantities, a global area-weighted cumulative distribution function is calculated, allowing the usefulness (as ensemble observables) of the three quantities to be compared. Then, PC and the regional mean trend are compared in terms of their magnitudes and how they are modified by increasing CO 2. A first look at the global pattern of regional trend extremes and their modification by increasing CO 2 is taken in terms of the ensemble means of PC 10 and PC 90. Then, relationships between PC,PC, and the regional mean trend are demonstrated for each region separately. These relationships suggest various applications. A first application is presented here, to explore model uncertainty in PPN trends at small spatial scales. The relevant methods are dependent on and so discussed in the context of the results presented below. Most of the results relate to the spread in results from different model runs. Natural variability is part of the uncertainty in PPN projections, so we do not wish to remove it. The analysis allows this uncertainty to propagate through, since each model has an independent contribution from variability. The significance of any signals of CO 2 forcing are discussed in the context of specific results. 3. Characterizing small-scale structure Figure 1 shows global area-weighted cumulative distribution functions of (ensemble mean)/(ensemble standard deviation) for three quantities: 1) the trend in PPN, interpolated onto a common 2.5 grid (gridpoint trends); 2) ; and 3) PC. This clearly shows that simply interpolating PPN to a common grid and taking the ensemble mean does not provide a particularly useful observable, and we discuss it no further. The other quantities are somewhat better, with the regional trend extreme measure PC being just as good an ensemble observable as the regional mean trend. However, the

5558 J O U R N A L O F C L I M A T E VOLUME 19 FIG. 1. Problems and partial solutions in multimodel PPN intercomparisons. Each line: area-weighted cumulative distribution function of (ensemble mean of T)/(ensemble standard deviation of T), where T is one of the following: linear trend calculated at each grid cell (double dashed line); regional mean trend (double solid line); or PC (thick solid line). intermodel differences are still great over large parts of the globe. Figure 2 tests whether regional trend extremes need be considered, or whether quoting the regional mean is sufficient (case 1 above). In the figure, (PC ) is plotted against the regional mean trend for each region and each model (transient experiment). The difference (PC ) is often as large as or greater than, and the points are highly scattered. Clearly, regional trend extremes can be considerably larger than the regional mean, and the regional mean is not a particularly good predictor of the regional trend extremes. Therefore case 1 cannot be assumed to be valid for these regions. Figure 3 tests whether the effect of increasing CO 2 in the transient run can be considered to be uniform across a region (case 2 above). Figure 3 is similar to Fig. 2, except the anomaly transient-control is plotted on each axis. The points cluster around a line of gradient 1.4. The significance of the gradient being greater than 1 is better than 1% [see Mann Kendall (MK) tests in section 4]. This may be clearly attributed to CO 2 forcing rather than natural variability (section 2), because a similar plot for PC has a gradient less than 1 (not shown). This shows that increased CO 2 tends to have a considerably larger effect on the regional extreme measure PC than on the regional mean (typically by around 40%). PC represents the 10% of a region containing the most extreme PPN trends those of most importance for impact assessment. Hence, direct use of regional mean climate change results could cause substantial underestimates of local socioeconomic impacts. That is, the effect of increased FIG. 2. Regional mean trend can substantially underestimate, and is not a good predictor of, regional trend extremes. Points: (PC ) vs (one point per region per model). CO 2 cannot in general be assumed to be uniform across these regions (case 2). From now on we focus on subregional diagnostics. Figure 4 provides a first look at the global pattern of regional trend distribution functions. Bias due to control climate drift is approximately removed (appendix B). Figure 4 illustrates, for each region, how natural variability and increasing CO 2 affect the ensemble mean distribution of 80-yr summer PPN trends (ensemble uncertainty presented later). In each region the bottom bar represents the control run, and its width is determined by natural variability. The ensemble mean picture is not a major result due to the large intermodel uncertainty (Fig. 1). The ensemble mean of the regional mean (transient-control) difference is significantly different from zero in only about half the regions (see appendix C for details). However, for all regions, in the FIG. 3. Subregional effects of increasing CO 2. Points: transientcontrol difference in regional extreme trend (PC ) vs transientcontrol difference in regional mean trend.

1 NOVEMBER 2006 G O O D A N D L O W E 5559 FIG. 4. Ensemble mean picture of the distribution of trends within each region, and the effect of increasing CO 2. Horizontal axis: 80-yr summer PPN trend, as a percentage of the local control climatological mean. Axis extends from 50% to 50%. Each region: three bars, each extending from PC 10 to PC 90. Thus, the right-hand end marks the trend exceeded in 10% of the region. Bottom bar: control run; top bar: transient run; middle bar: same width as bottom bar, but shifted by the regional mean in the transient run. Comparing the bottom two bars reveals the regional mean effect of increasing CO 2 in the transient run. Comparing the top two bars shows how the subregional effects of increased CO 2 broaden the distribution of trends. transient run, the ensemble mean of PC differs from the ensemble mean of by around a factor of 2 or more (see also Fig. 2). In every region, the differences between the ensemble means of PC 10 and, and PC 90 and, both have significance better than 0.001% (from a t test). It is also worth noting that in all 23 regions, the trend distribution width is broader in the transient than in the control runs (cf. top and middle bars). The statistical significance of this result is explored later (see subsequent discussion of Figs. 5 and 6). The picture varies substantially from region to region. For example, in the Amazon, the regional mean change is rather small (bottom two bars are similar), but some parts would be expected to see 80-yr PPN reductions of more than 40%. For South Asia (SAS), 80-yr trends of more than 30% are predicted for part of the region, much larger than the regional mean change. In other regions case 2 is not unreasonable such as Alaska and north Siberia, where CO 2 forcing causes a reasonably uniform PPN increase (the middle bar is similar to the top bar). For Central America, the Mediterranean, central Asia, and South Africa the most extreme decreasing trends are accounted for by natural variability reinforcing the regional mean CO 2 -forced trend (the left edges of the top two bars are level), but some small positive trends indicate some local differences in transient response. The very large bars in the Sahara and central Asia partly reflect nonnormal summer PPN statistics, making least squares linear trends somewhat unrepresentative. 4. Emergent behavior and uncertainty In Figs. 5 and 6 relationships between regional and small-scale effects of increased CO 2 are explored for each region separately. These plots have three important properties (demonstrated more formally below). 1) In most panels of Fig. 5, a rather tight, roughly linear relationship between PC and is found. This is also true for several regions for PC (Fig. 6). 2) The gradients of these relationships are often clearly different from unity. 3) The gradient for PC is larger than that for PC in all regions but AMZ. Since in any panel each point represents a different model, and PC and PC represent small spatial scales, these properties are of particular interest. Point 1 means that for any reasonable value of, values of PC and PC and hence PC 10 and PC 90 may be predicted. This may be done without any model-specific information, or without a model with that value of even existing.

5560 J O U R N A L O F C L I M A T E VOLUME 19 FIG. 5. Relatively tight multimodel relationships between the effects of increased CO 2 on regional extreme (PC ) and regional mean ( ) trends. Vertical axis: transient-control difference in regional extreme trend ( PC ). Horizontal: transient-control difference in regional mean trend ( ). Each point represents a different model. Solid line: unit gradient. Double dashed line: least squares fit constrained to pass through origin. M: MK test statistic indicating significance of a gradient 1. G: gradient of linear least squares fit. r: correlation coefficient between PC and. Effectively, this is a relative of the widely used patternscaling methodology (Santer et al. 1990; Mitchell 2003), but working with statistical distributions rather than spatial patterns. Point 2 means that the regional mean quantity contains model-independent information about the small-scale deviations from the regional mean (i.e., about PC and PC ). This suggests that different models have similar coupling be-

1 NOVEMBER 2006 G O O D A N D L O W E 5561 FIG. 6. Same as Fig. 5, but for PC. tween the large-scale effects of increased CO 2 and the local differences from the large scale. Possible mechanisms are CO 2 -forced shifts in large-scale rainbands (large local effects at the rainband boundaries); or changes in large-scale moisture supply or stability (local feedbacks determining the local PPN responses). Since the gradients appear to be systematically different for PC and PC (point 3), these results are probably due to CO 2 forcing rather than natural variability (section 2), but the statistical significance of this observation is quantified below. Point 3 also means that the larger the regional mean effect of increased CO 2, the broader the range of trends found in that region. Point 1 is now quantified. In every region, above 75%

5562 J O U R N A L O F C L I M A T E VOLUME 19 of the intermodel variance in PC is explained by (P in figure legend). For PC, this is true for 12 regions (exceptions mostly have one or two outlier models, or a shallow gradient with PC mostly close to zero, so generally of less importance for impacts). PC represents locations where natural variability opposes the regional mean trend, giving a smaller climate change signal and generally lower impact relevance than PC. The scatter in the relationships is generally larger toward the Tropics, presumably due to natural variability. Quantifying point 2, for each region a least squares linear fit was estimated, with a constraint to pass through the origin. Logically, the underlying relationship may be assumed to pass through the origin (although the assumption of a linear fit may be incorrect). This is because if 0, the sign of is undefined, so here either PC 10 or PC 90 are equally valid choices for the label PC. Since at 0, PC 10 will be negative and PC 90 positive, the results for both PC and PC will scatter symmetrically above and below the origin (in the large-sample limit). The least squares gradients span 1.1 2.0 for PC, and 0.4 1.3 for PC, indicating substantial interregional variation (only AMZ has a gradient larger than 1 for PC perhaps influenced by outliers, although caution is advised for AMZ). A gradient of 1.4 for a certain region means that the effect of CO 2 on the more extreme subregional trends (representing 10% of the region) is 40% larger than in the regional mean. Since these gradients are each approximately consistent with most of the ensemble of 19 different models, this is emergent behavior of clear impact relevance. For each region, the significance of an association between ( PC ) and is assessed using the nonparametric (and hence robust) MK rankcorrelation test (Mann 1945; Kendall 1975). This indicates the significance of a gradient different from 1 in Fig. 5. The same test is done for PC. The MK test is applicable without modification because the different models are independent in terms of natural variability. However, the assumption of a normal distribution for the MK test statistic under random variability can break down at small sample sizes, so the direct inference of significance may suffer from error. Of the 23 regions, MK score magnitudes larger than 1.6 (significance better than 10% for normally distributed MK score) was found for 17 (10) regions for PC (PC ). Furthermore, in 14 regions more than 50% of the intermodel variance in the difference PC is explained by alone. For PC, this is true for six regions. For a few regions (CAM, EAS, and SAF), a large least squares gradient is controlled by the constraint to pass through the origin. Judging from the other regions, a linear fit through the origin seems reasonable, but lower confidence is implied for CAM, EAS, and SAF. Tests of global (field) significance are described in appendix C. These take into account any cross correlation between the natural variability in different regions, which could influence significance. They are based on various measures of the relationships in Figs. 5 and 6 (using the linear fits and the MK test scores), and the asymmetry between those for PC and PC. The conclusion is that a set of relationships as strong as those in Figs. 5 and 6 is very unlikely to have occurred purely from natural variability, and hence can be attributed to CO 2 forcing in the transient run. Of course, the influence of CO 2 forcing relative to natural variability is larger in some regions than others. Now we present a first application of these results, exploring intermodel uncertainty in PPN trends for JJA. Uncertainty is measured by the intermodel spread, treating each model equally. The uncertainty limits would be narrowed if an assessment of each model s quality was included (e.g., Tebaldi et al. 2004). However, uncertainty limits would be broader if we took into account the fact that these models may not be independent. This is because they have the same basic physical equations, and in some cases similar parameterization schemes. Presenting uncertainty ranges for each of PC 10,PC 90, and separately would give a rather confusing picture. However, Figs. 5 and 6 demonstrate that PC 10 and PC 90 are rather closely coupled to the regional mean, in a linear and largely model-independent fashion. Therefore it makes sense to say that for a given region, the PPN response to increased CO 2 is more positive in one model (model A) than in another (model B). This is based simply on a comparison of the regional mean quantity from the two models. However, the coupling between PC 10,PC 90, and is such that the statement means much more than that model A has a larger regional mean trend. It also means that the CO 2 -forced broadening of the regional trend distribution (point 3 above) is larger in model A than model B, and by a reasonably well-defined amount (by the gradients in Figs. 5 and 6). Thus, we can rank the models uniquely according to their regional PPN response. The above result allows us to present a simple picture of model uncertainty for a scenario of increasing CO 2. First, we estimate the regional mean trend under increasing CO 2 in each model, given by in the transient run with a drift correction (appendix D). Then, the 25th and 75th percentiles of regional mean trend are calculated. The ensemble 75th percentile of is the regional mean PPN trend exceeded in 25% of models. It

1 NOVEMBER 2006 G O O D A N D L O W E 5563 FIG. 7. Intermodel uncertainty in regional statistical distributions of summer PPN trends. Horizontal axis: 80-yr summer PPN trend, as a percentage of the local control climatological mean. Axis extends from 50% to 50%. Each region: three bars, each extending from PC 10 to PC 90. Thus, the right-hand end of each bar marks the trend exceeded in 10% of the region. Bottom bar: control run (bar limits are the ensemble means of PC 10 and PC 90 for the control, as in Fig. 4). The top two bars represent two possible models ofthe transient run. Top bar: the ensemble 75th percentile. Middle bar: ensemble 25th percentile. Thin horizontal black lines crossing each end of every bar: estimated errors in PC 10 and PC 90. is estimated by linear interpolation of the discrete cumulative distribution function. It describes one possible, and not particularly extreme, model of regional climate change. Similarly, 25% of models will have more negative (less positive) than the ensemble 25th percentile. Neither percentile exactly matches an actual model, but each represents likely levels of regional precipitation response. Together they span the PPN response of 50% of models. Next, the ensemble 75th percentile of is used to predict values of PC and PC (from the gradients in Figs. 5 and 6). A best estimate of the ensemble 75th percentile of PC 90 in the transient scenario is then obtained by adding either PC (if is positive) or PC (if is negative) to the ensemble mean of PC 90 in the control run. The latter is the best estimate of PC 90 in the control run (uncertainty in this quantity is discussed briefly below). Similarly, the ensemble 75th percentile of PC 10 in the transient scenario, may be estimated. The same can be done for the other, equally possible model, as described by the ensemble 25th percentile of. Figure 7 presents the results. The lower bar in each region is identical to that in Fig. 4. The top bar represents the ensemble 75th percentile, and the middle bar the 25th percentile. Hence, the top bar always has a regional mean change more positive than the middle bar. These two bars together represent model uncertainty in future regional PPN trend distributions for JJA. The thin black lines crossing each end of every bar show the estimated errors in the end point of that bar. They are given as interquartile ranges for consistency, and account for intermodel spread in PC 10 and PC 90 in the control run (i.e., uncertainty in natural variability), and uncertainty in the gradients in Figs. 5 and 6 (top two bars only). In most regions, the former dominates. The large-scale picture of intermodel uncertainty in PPN trends is rather simple. In polar regions, the 25th and 75th percentile models differ only in magnitude of change. For example, over northern Siberia an increase is predicted, but of larger magnitude for the ensemble 75th percentile than for the 25th. Over Greenland, the situation is slightly more complicated: the distribution of trends is much broader for the ensemble 75th percentile than for the 25th; that is, uncertainty in local response is relatively large for this region. This can be seen in the very different gradients for GRL in Figs. 5 and 6. In the subtropics (e.g., WNA, CNA, MED, CAS, SSA, and SAF) the ensemble 75th percentile is often similar to the control run, but the 25th percentile shows large PPN decreases. In the Tropics, the picture is more

5564 J O U R N A L O F C L I M A T E VOLUME 19 uncertain, with the ensemble 75th and 25th percentiles disagreeing on the sign of change. Asian monsoon regions (SAS and SEA) show either little change (25th percentile model) or large increases (75th percentile) compared to the control run. Uncertainty in natural variability (PC 90 and PC 10 in the control run) is very small compared to uncertainty in the transient response everywhere except for the Amazon (about 50% of the transient response) and Sahara. Results for the Sahara (SAH) are hard to interpret due to nonnormal PPN statistics (so least squares linear fits are not particularly representative). The effect of the drift correction on PC 10 and PC 90 is mostly small: less than the estimated error in PC 10 and PC 90 or 5% (whichever is larger), except for the middle bars for CAM and SAF. The latter extend to 35% and 100% without drift correction. Extra caution is therefore advised for CAM and SAF. The aim of Fig. 7 is to illustrate model spread in projections of regional PPN under a scenario of increasing CO 2. Natural variability is part of the uncertainty in PPN trends, so part of the uncertainty in socioeconomic impacts. The effect of subregional natural variability is quantified by the width of the bottom bar in each region. The uncertainty, due to natural variability, in regional mean PPN trends is implicitly included in Fig. 7, as it broadens the intermodel spread in (hence increasing the spread between the top two bars in each region). In this figure the aim is simply to characterize intermodel spread. However, the uncertainty in the effects of increased CO 2 certainly plays an important role in the intermodel spread in. In every region, the difference between the ensemble 25th and 75th percentiles of has significance better than 1%, and the ensemble mean of is significantly different from zero in about half the regions (appendix C). We also found very similar results to Fig. 7 if much shorter, 80-yr control run segments are used for the drift correction (the same length as the transient run; not shown). This would not be the case if natural variability in was dominating the results in Fig. 7. Also, in Fig. 7, away from the Tropics the locations of the top two bars in each region are asymmetric about the origin. There is apparently a systematic large-scale pattern to this. The close relationship between the intermodel spread in and that in PC and PC was addressed earlier. 5. Conclusions Some new methods have revealed a rich picture of intermodel emergent behavior and model uncertainty in projected JJA seasonal precipitation trends over 80 yr of increasing CO 2. These methods introduce the assessment of small spatial scales and natural variability into regional-scale multimodel comparisons. Crucially, information from small spatial scale has been retained in the analysis, while allowing for the fact that different models may differ in where they locate physically similar small-scale features. In general, regional mean precipitation trends (used in several previous studies, e.g., Giorgi et al. 2001) do not well represent the sometimes much larger changes found at subregional scales. A measure of regional extreme trends was introduced, which performs at least as well as the regional mean in presenting a consistent ensemble mean picture, while focusing on small spatial scales. An important contributor to small-scale largemagnitude PPN trends is natural variability. This can locally reinforce CO 2 -forced precipitation trends, in the same way that natural cyclic stresses such as summer droughts are where climate change has its greatest socioeconomic impacts (McCarthy et al. 2001). The natural multidecadal variability considered here is an important property of each climate model simulation and may be modified by increased CO 2 (e.g., Schar et al. 2004). Therefore, we consider it important that it is included in climate change results before any subsequent impact analysis is performed. However, natural variability is only predictable in a probabilistic sense. Hence, there may be minimum spatial scales (related to the spatial scales of the variability), below which precipitation trends from multiple models can usefully only be combined in a statistical sense as done here. Furthermore, the effects of CO 2 forcing cannot be assumed to be uniform across these commonly used regions. Our results showed that the effect of increased CO 2 on the more extreme local trends within each region (representing 10% of the region area) can be considerably larger than that on the regional mean trend (typically by around 40%). We then demonstrated that for most regions, a surprisingly large part of the intermodel variance in smallscale departures from the regional mean trend is explainable simply by the intermodel variance in the regional mean. The relationship between large and small spatial scales varies substantially from region to region, but for most regions a single linear relationship fits quite well to all 19 different models. This suggests some emergent behavior that could direct future study. For example, applications similar to pattern scaling (Santer et al. 1990; Mitchell 2003) may be suggested, working with statistical distributions rather than spatial patterns. These relationships also imply that regional mean results are still useful, as long as the interregional varia-

1 NOVEMBER 2006 G O O D A N D L O W E 5565 tion in their relationship with the more impact-relevant extreme local trends is recognized. These results directed a study of intermodel uncertainty in the statistical distributions of CO 2 -driven JJA seasonal precipitation trends within different land regions. Large intermodel uncertainty is found, with substantial interregional variations, although following a fairly simple large-scale pattern. In polar regions, PPN increases are consistently found. In the subtropics, the interquartile range of PPN responses varies from little change to clear decreases with local decreases commonly exceeding 30% in the latter case. In the Tropics, local trends range from large and positive to large and negative. Our future work will apply this approach to other climate variables and investigate underlying physical mechanisms. Acknowledgments. The authors are supported by the U.K. Department for the Environment, Food and Rural Affairs under Contract PECD7/12/37. We acknowledge the international modeling groups for providing their data for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modelling (WGCM) and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity, and the IPCC WG1 TSU for technical support. The IPCC Data Archive at Lawrence Livermore National Laboratory is supported by the Office of Science, U.S. Department of Energy. We thank Chris Ferro for helpful discussions, and the reviewers and editor for useful comments, which strengthened the manuscript considerably. APPENDIX A Quantification of Trends To quantify trends at each grid cell, we use the rate of PPN change, measured by a least squares linear fit to the full time series. This is just used as a measure of how an observer at a given location (grid cell) might perceive the climate to be changing over a given time period (intentionally including the effect of natural variability). Obviously there are no data errors: the model seasonal precipitation for each year is known very precisely. We could have used other measures of how the observer perceives change, but without specifying a particular socioeconomic impact there is no objective reason to choose a different measure. Different segments of the same control run, or control runs from different models, will show different least squares linear trends, simply due to natural variability. Most of our results relate to intermodel spread, and the analysis allows the uncertainty due to the different manifestations of natural variability to propagate through. A common alternative measure of climate change is a multiyear mean (typically, 20 yr mean) difference between the transient and the control run, centered on some future year Y1. This measures how much the transient run has diverged from the control. However, as discussed above (appendix A), natural present-day PPN anomalies can affect the local impact of increasing CO 2. Fitting a linear trend to the whole time series takes account of these present-day anomalies, giving a rate of PPN change. Transient-control differences for some future year Y1 do not and hence can underestimate the most extreme local rates of change. A small further advantage of linear fits is that it involves choosing just a single artificial parameter (the length of the time series), whereas transient-control differences in, for example, 20-yr means have two (the year Y1, and the 20 in 20-yr means). APPENDIX B Control Climate Drift Corrections for PC 10 and PC 90 a. The climate drift problem Even following a spinup period and with atmospheric CO 2 concentrations fixed at preindustrial or presentday levels (the control run), climate models all show some degree of very long time-scale climate drift. Often this is due to heat storage in the deep ocean. It is apparent in multidecadal time series of surface atmospheric quantities averaged over large spatial scales. It is not possible to obtain precise multidecadal largescale average time series from historical observational data. Therefore, the only possible best estimate is that in the control climate, such large-scale multidecadal changes should be approximately zero (assumption 1). b. Typical solutions, and relevance to our work Often, climate drift is removed from climate change projections by examining multiyear transientcontrol differences at some future year Y1. Since the transient run is initialized to (and hence identical to) the control run at year 0, the transient-control difference centered on year Y1 measures how the transient run has diverged from the control an indication of net CO 2 -forced climate change. This process assumes that over the spatial and temporal scales of interest, the control run should (in an ideal model) show zero

5566 J O U R N A L O F C L I M A T E VOLUME 19 change from year 0 to year Y1 (as assumption 1). Such an assumption is reasonable for multidecadal trends of large area averages. However, in our work we are interested in multidecadal trends but at small spatial scales. Natural variability (fluctuations, as opposed to monotonic climate drift) can cause large multidecadal trends in PPN over small spatial scales. Hence, transient-control differences are not appropriate for our purposes. Alternatively, a linear fit may be made to the control run, estimating the climate drift over much longer time scales. This gradient can be subtracted from the multidecadal trend in the transient run. However, for small spatial scales, it is not obvious exactly how long the time scale of the fit should be so that it measures climate drift and not natural variability. It is certain to be rather larger than a century probably many centuries. Of the climate models studied in our work, control run results over many centuries are available for just a small subset of models. Hence, this approach is also likely to be inappropriate. c. Solution chosen for our work Since we are focusing on the quantities PC 10 and PC 90 (as well as the regional mean), it is only necessary to correct these quantities for climate drift. PC 10,PC 90, and the regional mean trend together characterize the statistical distribution of trends within a large-scale region (the regional trend distribution ). We consider how climate drift may affect this regional trend distribution. First, climate drift will affect the regional mean (the mean of the regional trend distribution). Since the regional mean is an average over large spatial scales, it is much more reasonable to accept assumption 1 for the regional mean. The regional mean drift trend is estimated as the regional mean trend in the control run. In the main paper corresponding to this supplementary material, we show that for increasing CO 2 there are relatively tight relationships between the regional mean trend and the quantities PC 10 and PC 90. In other words, for any given value of regional mean trend, values of PC 10 and PC 90 may be predicted. Therefore, if we assume that the same relationships hold for the trends caused by climate drift (assumption 2), we can use these relationships to transform the regional mean drift trend into estimates of drift trend corrections for PC 10 and PC 90. Assumption 2 is not expected to be precisely correct, but it is unlikely to be very wrong. We find that the correction in the distribution width (given by PC 90 PC 10 ) is in all cases very small compared to the intermodel uncertainty characterized in the main paper. This means that the details of assumption 2 are not particularly important for our results. Assumption 1 will also not be precisely correct. However, for the ensemble mean results (Fig. 4), we are mostly interested in the widths of the regional trend distributions. The correction described here mostly clarifies Fig. 4 by centering the control run bar on the origin. The regional mean change is not treated as a major result because of the large intraensemble spread. A regional mean drift trend needs to be more precisely estimated for Fig. 7 (appendix C). APPENDIX C Resampling Significance Tests This appendix describes field significance tests appropriate for the relationships in Figs. 5 and 6 and regional significance tests for the ensemble mean results in Fig. 4 and the ensemble uncertainty results in Fig. 7. Our major results measure differences between properties of 80-yr transient and control run segments. We wish to estimate statistical significance the probability of obtaining such results by chance from natural variability alone (indicating whether our results can be safely attributed to CO 2 forcing). Significance could be estimated by performing the same calculations but comparing pairs of different 80-yr control run segments, instead of transient with control. Repeating this many times with different control run segments would indicate the probability of obtaining our results purely from natural variability. However, the short length of some model control runs means that the number of independent 80-yr segments per model is limited. Another potentially important issue is the degree of cross correlation between the natural variability in different regions, which must be taken into account in estimates of field (global) significance. While significant global teleconnections are well known, it would be an interesting result if cross correlation between regions was strong in the context of our specific analysis, since this could imply a major simplification in the behavior of small and regional-scale precipitation variability over long time scales. However, this must still be assessed. Temporal (serial) autocorrelation can also bias statistics but is generally less of a problem for annual measures of precipitation than for other climatological fields such as surface temperature. We address these issues with a form of moving-blocks bootstrap resampling test. Bootstrap resampling and field significance are explored in detail by, for example, Wilks (1995). The application of such methods in the presence of serial autocorrelation, using the moving-blocks boot-