Pronounced differences between observed and CMIP5 simulated multidecadal

Transcription

1 Pronounced differences between observed and CMIP simulated multidecadal climate variability in the twentieth century Sergey Kravtsov 1 Keywords: global warming, forced vs. internal climate variability, stadium wave Index Terms: 00,,, 1, 0 Key points: Estimated internal (unforced) variability in observations has a much larger magnitude vs. that in CMIP models The model data mismatch is dominated by a low-order hemispheric multidecadal mode None of the CMIP models is able to reproduce the spatiotemporal structure of the observed multidecadal variability Department of Mathematical Sciences, Atmospheric Science group, University of Wisconsin-Milwaukee, P. O. Box 1, Milwaukee, WI 01, kravtsov@uwm.edu 1

2 Abstract: Identification and dynamical attribution of multidecadal climate undulations to either variations in external forcings or to internal sources is one of the most important topics of modern climate science, especially in conjunction with the issue of human induced global warming. Here we utilize ensembles of 0 th century climate simulations to isolate the forced signal and residual internal variability in a network of observed and modeled climate indices. The observed internal variability so estimated exhibits a pronounced multidecadal mode with a distinctive spatiotemporal signature, which is altogether absent in model simulations. This single mode explains a major fraction of model data differences over the entire climate-index network considered; it may reflect either biases in the models forced response or models lack of requisite internal dynamics, or a combination of both Introduction Dynamical inferences about the causes of observed climate change must necessarily rely on analyses of global coupled climate models of the type used in the Coupled Model Intercomparison Project Phase [CMIP; Taylor et al., 01]. However, these models are not entirely based on first principles, and can potentially misrepresent true climate dynamics, which may further complicate the interpretation of model simulations. For example, Zhang et al. [00] showed that multidecadal variations on top of a linear warming trend of the mean Northern Hemisphere surface atmospheric temperature in the twentieth century can equally well be rationalized as a radiatively forced signal in the fully coupled version of the GFDL.1 model, or as a response to

3 multidecadal variability of the North Atlantic sea-surface temperature (SST) in the model simulation with constant radiative forcing but variable Q-fluxes designed to mimic the observed SST evolution in the North Atlantic mixed layer. The caveat of the latter result is that the fully coupled GFDL model is by itself unable to produce multidecadal variations in the basin-wide North Atlantic SSTs known as the Atlantic Multidecadal Oscillation (AMO) comparable in magnitude with that of the observed AMO variability. Hence, either this model lacks dynamics required to generate realistic levels of internal multidecadal SST variability in the North Atlantic or, alternatively, it underestimates multidecadal variations in the forced SST response there. This is to some extent true for many other CMIP models [see Zhang and Wang, 01]. The perceived fundamental role of AMO dynamics in the climate change problem fueled a vivid (and ongoing) scientific debate around this issue (see Murphy et al. [01] and references therein). The differences between climate models and observations are, however, not confined to the North Atlantic. Wyatt et al. [01], Wyatt and Peters [01] and Kravtsov et al. [01] detected considerable mismatches in both the magnitude and spatiotemporal structure of the twentieth century s multidecadal variability defined via deviations from the long-term linear trend in a network of observed and CMIP simulated indices characterizing the Northern Hemisphere climate. Assuming that multidecadal discrepancies between the models and observations reflect differences in the observed and simulated internal climate variability, Mann et al. [01] and Steinman et al. [01a,b] challenged these findings and interpreted them to be an artifact of the linear detrending. Kravtsov and Callicutt (01) [hereafter KC01] utilized CMIP ensembles

4 1 of historical 0 th century simulations to isolate (nonlinear) forced signals and internally generated (residual) climate variability in CMIP models and observations. Here we apply the KC01 methodology for (nonlinear) forced-signal identification to an extended set of oceanic and atmospheric climate indices and expand the analyses of Kravtsov et al. [01] to compare the resulting estimated internal components of the observed and CMIP simulated climate variability. We find pronounced differences in the magnitude, time scale and spatial patterns of the observed and simulated variability, thus generalizing earlier conclusions of Kravtsov et al. [01] to the nonlinear forced signals and the entirety of the CMIP ensemble considered. We also show that the model data differences are dominated by a low-order multidecadal mode of variability, which appears to be altogether absent from the dynamical landscape of CMIP models Data and methods.1 Data sources and pre-processing We analyzed observed and simulated variability in a set of climate indices ( 00) subjectively chosen to sample the Northern Hemisphere s large-scale climate dynamics. We computed these indices in historical CMIP simulations encompassing the all-forcing (historicalall), greenhouse-gas (historicalghg) forcing and natural forcing (historicalnat) runs, as well as in the preindustrial control runs (Table 1). To process control runs, we further created 00 snippets 1-yr-long each, to match in length the duration of historical runs, randomly pulled from the multi-model ensemble of long preindustrial simulations available.

5 1 Three of the indices considered were identical to the ones used in Steinman et al. (01a) and KC01. They represent the Atlantic Multidecadal Oscillation [AMO: Kerr, 000; Enfield et al., 001], Pacific Multidecadal Oscillation [PMO: Steinman et al., 01a], and Northern Hemisphere Multidecadal Oscillation [NMO: Steinman et al., 01a]. The AMO and PMO indices were computed as the sea-surface temperature (SST) area averages over the 0ºN 0ºN, 0ºW 0º and 0ºN 0ºN, ºE 0ºW regions, respectively. The NMO index was formed by computing the 0ºN 0ºN mean surface atmospheric temperature (SAT) over ocean and over land separately, and then adding them together with the weights of 0.1 and 0. reflecting the ocean/land fractional composition of the entire Northern Hemisphere. Prior to further analysis, we computed the annual-mean values for all indices and formed anomalies by subtracting their 00 climatology Following Steinman et al. (01a) and KC01, we computed the observed SST indices by averaging over three SST products, namely the Hadley Centre Global Sea Ice and Sea Surface Temperature [HadISST: Rayner et al., 00], National Oceanic and Atmospheric Administration (NOAA) Extended Reconstructed Sea Surface Temperature (ERSST) [Xue et al., 00; Smith et al., 00], and Kaplan SSTs [Kaplan et al., 1; Parker et al., 1; Reynolds and Smith, 1]. Steinman et al. (01a) and KC01 used Goddard Institute for Space Studies (GISS) Surface Temperature [GISTEMP: Hansen et al., 0] Northern Hemisphere mean as their estimate for the observed NMO. This estimate may, however, be slightly different from the one computed using the original NMO definition, which only involves the data from 0ºN to 0ºN. To alleviate this possible discrepancy, we here used instead the gridded surface-temperature product

6 from NOAA s twentieth-century reanalysis [0CR: Compo et al., 0] and estimated the observed NMO using the exact recipe above. We must note that our main results are largely insensitive to the version of the observed NMO index used We also analyzed two additional well-known atmospheric indices based on the observed and simulated sea-level pressure (SLP) data using, once again, 0CR to define the observed SLP indices. These indices were the North Atlantic Oscillation index (NAO: Hurrell, 1; Hurrell and Deser, 00), as well as an analog of the Aleutian Low Pressure index ALPI [Beamish et al., 1]. We computed the NAO and ALPI as the leading principal components of monthly wintertime (DJFM) SLP over the Atlantic (1ºN ºN, 0ºW ºW) and Pacific (1ºN ºN, ºE ºW) regions, respectively [see Kravtsov et al., 01 for the resulting loading patterns]. In addition, we used the station based NAO index ( as an alternative NAO estimate. We normalized the observed and simulated monthly NAO and ALPI indices to have the unit standard deviation, and then formed and analyzed their DJFM-mean 00 time series. 1. Methodology Following KC01, we first estimated forced signals for each of the 1 individual models considered as the -yr low-pass filtered ensemble mean over the set of a given model s 0 th -century simulations (for each index), using the data adaptive filter of Mann [00]. Subtracting the forced signals of a given model from this model s individual simulations provides multiple realizations of this model s simulated internal variability. The resulting estimates of internal variability are, however, necessarily characterized by

7 smaller variance relative to that of the true internal variability, since the forced signal used to define them in fact contains some of the true internal variability due to insufficient averaging over a small number of individual model runs [Steinman et al., 01b; Frankcombe et al., 01]. To alleviate this problem, we derived model-dependent and frequency-dependent inflation factors (Fig. S1 of Supporting Information), which allowed us to obtain variance-bias-corrected estimates of the simulated internal variability for all of the 1 model simulations considered (see section S1 of Supporting Information). These inflation factors were computed from synthetic stochastic versions of the individual model simulations that mimic their statistical characteristics (section S of Supporting Information; Kravtsov et al. [00, 0]; Mann et al. [01]) As a byproduct of the latter procedure, we also obtained 0 estimates of the synthetic forced signals for each of the 1 models available, totaling 0 forced-signal estimates. Following Steinman et al. [01a,b], Frankcombe et al. [01], Kravtsov et al. [01] and KC01, we then rescaled each of these forced-signal estimates via least squares to best match the full observed time series of the climate index considered; this rescaling is meant to correct for climate sensitivity biases of individual models. Figure S of Supporting Information displays the multi-model ensemble-mean forced signals so estimated and their uncertainty defined as the spread among the 0 available estimates of the forced signal, along with the original (raw) observed indices. Subtracting these forced signals from the raw indices provides 0 estimates of the internal variability in each of the five observed indices considered. Following Frankcombe et al. (01), we also computed three additional estimates of the forced signal and the residual internal variability in observations based on rescaled multi-model

8 ensembles means (MMEMs) from CMIP s historicalall, historicalghg and historicalnat simulations using one-, two-, and three-factor scaling methods (see section S of Supporting Information for details) We then analyzed the resulting 1 (variance-bias-corrected) time series of the simulated internal variability, as well as 0 (KC01 synthetic ensemble) + (MMEM scaling approaches) estimates of the internal component of the observed internal variability for our network of five climate indices using the multi-channel version of the Singular Spectrum Analysis [SSA: Broomhead and King, 1; Elsner and Tsonis, 1] called M-SSA [Moron et al., 1; Ghil et al., 00]. M-SSA is an extended variant of a widely used Empirical Orthogonal Function (EOF) analysis technique [Monahan et al., 00], which looks for the space time patterns that maximize lagged covariance for a given multivariate time series within a range of M lags; M is referred to as the embedding dimension of M-SSA. The original raw time series can be fully recovered as the sum, over all modes, of the so-called reconstructed components (RCs) associated with each M- SSA mode. Prior to M-SSA analysis, we smoothed the internal components of the NAO and ALPI indices using the -yr running-mean boxcar filter to focus on multidecadal time scales. In addition, each index of the five-index network whether observed or simulated was normalized to have the unit standard deviation. We performed M-SSA analysis using embedding dimensions from M=0 to 0; all of the results reported below are robust with respect to the choice of M. 1 We verified the above KC01 methodology for isolating the forced and internal components of variability using the simulations from the Community Earth System Model (CESM) Large Ensemble Project (LENS: Kay et al., 01):

9 In particular, we showed that our methodology provides estimates of the two components consistent with those based on averaging realizations over the entire LENS ensemble (section S of Supporting Information, Figs. S and S).. Results.1 Variance of observed and simulated climate variability Figure 1 shows standard deviations of the observed and simulated internal variability for raw and low-pass filtered data, as a function of the filter time scale. Naturally, the more smoothing is applied to a time series, the less is the resulting standard deviation. Left panels display the standard deviations of the full internal variability for the five indices considered, with the mean values and the spread computed over the 1 samples of simulated internal variability and 0 samples of the internal component of the observed variability (see section.); also included are the estimates based on the 00-member control-run ensemble (see section.1). Strikingly, the observed internal variability has a large variance at decadal and longer time scales unmatched by that in the model historical simulation and control runs, for both the oceanic indices [consistent with KC01] and the atmospheric indices. Quantitatively, the standard deviations of all indices have a wide range of decadal-to-interdecadal time scales at which the null hypothesis of the observed and simulated internal variability being the same can be rejected in favor of the alternative hypothesis that the observed variability is larger, at the % significance level.

10 The standard deviations of the observed internal variability inferred using one-, two-, and three-factor scaling methods tend to be smaller than the ensemble-mean of standard deviations based on the KC01 method, but are generally consistent with the latter. The exceptions arise for the two-factor and three-factor estimates of the observed PMO and NMO internal variability, whose estimated magnitude falls below the standard uncertainty associated with the KC01 estimates. This property may, however, be simply an artifact of the two-factor and three-factor scaling procedure, which, for these indices, results in the estimated forced signal whose shape is inconsistent with the multimodel ensemble-mean signal (section S of Supporting Information, Fig. S) Right panels of Fig. 1 show the standard deviations of the observed and simulated data from which we subtracted the RCs associated with their respective leading M-SSA pairs (see section. below). This time, while the simulated internal variability still lacks some amplitude compared to the observed variability, the difference between the two is much reduced, thereby indicating that the dominant M-SSA pairs account for a major fraction of this difference. The present results were obtained with the M-SSA embedding dimension of M=0; the results with M=0 (and the values of M in between) are analogous (Fig. S of Supporting Information) Dominant multidecadal variability 0 1 Consistent with the results of section.1, M-SSA spectra of the observed and simulated climate networks display pronounced differences dominated by the leading M- SSA pair (Fig., upper panels). The spectra shown here are the space time variances

11 associated with the EOFs of the data trajectory matrix obtained by augmenting the original five-index time series by its M lagged copies; these space time (ST-) EOFs represent the M-SSA modes. In the observed spectra, the leading two M-SSA modes stand out with respect to the background spectrum of the remaining (trailing) M-SSA modes; by contrast, the simulated spectra are much more flat, and their dominant M-SSA modes account for a relatively smaller fraction of the total variance. Unlike the variances of the leading two modes, the variances of the trailing M-SSA modes based on the observed and simulated data are consistent, as reflected by their overlapping error bars Not only does the leading M-SSA pair of the observed internal variability have a much larger variance relative to that of the simulated variability, but it is also characterized by a completely different spatiotemporal structure absent from model simulations. Indeed, the variances associated with the projection of the trajectory matrices of simulated data onto the observed leading ST-EOFs (green error bars in the upper panels of Fig. ) are small relative to the corresponding variances of both observed and simulated M-SSA modes (blue and red error bars, respectively) Note that the M-SSA spectra based on the one-, two- and three-factor estimates of the observed internal variability are all consistent with the spectra based on the present KC01 estimation procedure. Furthermore, the M-SSA spectra for our estimates of the simulated internal variability in historical and preindustrial control runs are also consistent. Both of these properties strengthen the validity of our analysis and conclusions.

12 The dominant spatiotemporal pattern of the observed internal variability is best visualized by plotting the sum of two leading observed RCs (Fig., bottom panels). This pattern represents a coherent multidecadal signal propagating across the entire climate index network; Wyatt et al. (01) termed this signal the stadium wave. We found that the shape and phasing of the stadium-wave components (individual indices within the stadium-wave network) are sensitive to subtraction of nonlinear forced-signal estimates vs. subtraction of the linear trend, as in Wyatt et al. (01) and Kravtsov et al. (01). For example, the AMO component of the linearly detrended stadium wave computed by these authors has a negative phase in years 0 1, a positive phase during 1 1 period, and a negative phase again from 1 through 1, with the corresponding extrema reached in years (minimum), (maximum) and (minimum). By contrast, the AMO signal here defined via CMIP based forced-signal subtraction is negative during 1 and 1 00 periods, and positive in between, reaching minima in years and, and a maximum in year 1. Thus, the nonlinearity of the background forced trend estimated from CMIP simulations is clearly strong enough to significantly affect the propagation characteristics of the associated stadium wave. However, none of the CMIP models is able to mimic neither the observed spatial coherence in the internal variability within the climate network considered, nor the dominant multidecadal time scale of this variability (see Figs. S S of Supporting Information). 1 1

13 . Discussion Our study documents pronounced differences between the observed and CMIP simulated climate variability in the twentieth century. These differences are dominated by a coherent multidecadal hemispheric-scale signal present in the observed SST and SLP fields, but completely missing in any of the CMIP simulations. Our results are consistent with an earlier preliminary study by Kravtsov et al. [01], but generalize it to the entirety of the CMIP ensemble. Furthermore, we here focused on the (estimated) internal component of the observed and simulated climate variability, defined in terms of deviations from the CMIP based forced-signal estimates, rather than on the deviations from linear trend as in Kravtsov et al. [01] Our results are also broadly consistent with recent analyses of Cheung et al. [01], who documented substantial mismatches between their estimated internal components of the observed and CMIP simulated AMO, PMO and NMO variability. However, these authors used subtraction of the scaled CMIP MMEM signal to deduce the internal variability in historical simulations of individual CMIP models. Kravtsov et al. [01] and Kravtsov and Callicutt [01] showed that the residual variability so defined misrepresents the true internal variability in CMIP simulations and is, in fact, dominated by model error, that is, the differences between the true forced response of individual models and the MMEM response. The magnitude of the CMIP internal variability estimated by this method is, hence, much larger than that of the true simulated internal variability, and the spectral characteristics of the true and estimated internal variability are entirely different. Our present methodology alleviates these problems and provides consistent estimates of the CMIP simulated internal variability in the historical 1

14 and pre-industrial control runs. In particular, we find that Cheung et al. [01] underestimate the true differences between the observed (semi-empirical) internal variability and the internal variability in historical CMIP simulations Despite our explicit decomposition of the climate variability into the forced and internally generated components, dynamical attribution of the multidecadal model data differences still remains uncertain. On one hand, if our derived CMIP based forced signals are realistic, these differences must arise from internal climate-system dynamics presumably misrepresented in CMIP models, such as sea-ice dynamics [Wyatt and Curry, 01], oceanic mesoscale eddies [Siqueira and Kirtman, 01], positive cloud and dust feedbacks [Evan et al., 01; Martin et al., 01; Brown et al., 01; Yuan et al., 01], or SST forced NAO response [Kushnir et al., 00; Eade et al., 01; Stockdale et al., 01; Siegert et al., 01]. On the other hand, however, it is possible that CMIP models underestimate multidecadal variations in the true response of the climate system to external forcing or misrepresent the forcing itself [Booth et al., 01; Murphy et al., 01]; if this is true, the model data differences reflect the mismatch between the actual and CMIP simulated forced signals, whereas the real-world s internal climate variability may be consistent with that simulated by the models. In either case, we strongly believe that model development activities should strive to alleviate the present large discrepancies between the observed and simulated multidecadal climate variability, as these discrepancies hinder our fundamental understanding of the observed climate change. 1 Acknowledgements. The author acknowledges the World Climate Research Programme s Working Group on Coupled Modeling, which is responsible for CMIP, and thanks the climate modeling groups for making their model output available. The author 1

15 also thanks two anonymous reviewers for their comments. Section S of the Supporting Information contains the link to all data and MATLAB scripts for this paper. This research was supported by the NSF grants OCE- and AGS-. 1

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22 Table captions Table 1: CMIP twentieth century simulations used in this study. We selected the models with four or more historical realizations (fourth run for the MRI model was not available), and analyzed the runs for which sea-surface temperature (SST), surface-air temperature (SAT) and sea-level pressure (SLP) outputs were all available. Listed are: the number of realizations in historical runs with all forcings included and in the runs with greenhouse-gas (GHG) and natural (Nat) forcings only, as well as the length of the preindustrial control runs (in years). The (lowvariance) PI control runs of GISS models marked by the asterisks were not included in the final control-run ensemble to compensate for the absence of the (high-variance) GFDL-CM.1 and HadCM control runs (see KC01). 1

23 Figure captions Figure 1: Standard deviations (STDs) of the estimated observed (blue) and CMIP simulated historical (red) and control-run (black) internal variability for the five indices considered; top-to-bottom rows correspond to the results for the AMO, PMO, NMO, NAO and ALPI indices, respectively. Also included are the estimates of the observed internal variability based on the one-, two- and threefactor scaling methods of Frankcombe et al. (01); see legend. The STDs were computed for raw and boxcar running-mean low-pass filtered time series using different window sizes of K+1 yr, K = 0, 1,, 0 (shown on the horizontal axis); K = 0 corresponds to raw annual data, K = 1 to -yr low-pass filtered data and so on. Error bars show the 0% spread of the STDs, between 1 th and th percentiles of the available estimates of internal variability (see text for details). Shading indicates the range in which the observed internal variability is statistically larger than its historical (light shading only) or control-run counterparts (dark shading and light shading regions combined), at the % level; here, KC01 methodology was used to estimate the observed and simulated internal variability over the historical period. The NAO plot also includes the results (heavy black curve) based on an alternative, station based observed NAO index ( /climate-data/ hurrell-north- atlanticoscillation-nao-index-station-based). Left column: the results based on the full annual data; right column: the results based on the anomalies with respect to the leading M-SSA pair of the corresponding observed or simulated realization of internal variability (see text for details); the M-SSA embedding dimension M=0.

24 Comments: (i) The simulated multidecadal variability is much weaker than observed (left column). (ii) Much of this model data difference is rationalized by the leading M-SSA pair (right column) Figure : The M-SSA analysis of the observed and simulated internal variability in the AMO PMO NMO NAO ALPI climate-index network. Left column: the results of M-SSA analysis using the embedding dimension of M=0; right column: the same for M=0. Upper row: M-SSA spectra. The spectra based on the observed data ensemble-mean variances and their ±1 STD spread are in blue, the spectra based on CMIP model historical and control simulations are in red and black, respectively. The green error-bar plot (and lower black error-bar plot) represent the variances of the time series obtained by projecting the trajectory matrices from historical (or control) model simulations onto the ST-EOFs of the observed trajectory matrix. The spectra of the observed internal variability inferred using one-, two-, and three-factor scaling methods of Frankcombe et al. (01) are shown by x-symbols, circles and diamonds, respectively. Bottom row: Reconstructed components (RCs) corresponding to the leading M-SSA pair of the observed data. The NAO and ALPI RCs were multiplied by 1. For the purposes of better visualization, the RCs corresponding to different indices (channels) were vertically stacked by adding the constant offsets of +1, +, +, and + to the RCs for AMO, NAO, PMO and NMO indices, respectively. Comments: (i) Model data differences are dominated by the leading M-SSA pair, whose observed spatiotemporal structure is absent from models (upper row). (ii) This mode, in

25 observations, is characterized by a pronounced coherent multidecadal signal across the entire climate network considered (bottom row).

26 Table 1: CMIP twentieth century simulations used in this study. We selected the models with four or more historical realizations (fourth run for the MRI model was not available), and analyzed the runs for which sea-surface temperature (SST), surface-air temperature (SAT) and sea-level pressure (SLP) outputs were all available. Listed are: the number of realizations in historical runs with all forcings included and in the runs with greenhouse-gas (GHG) and natural (Nat) forcings only, as well as the length of the preindustrial control runs (in years). The (lowvariance) PI control runs of GISS models marked by the asterisks were not included in the final control-run ensemble to compensate for the absence of the (high-variance) GFDL-CM.1 and HadCM control runs (see KC01). Model Model Historical Historical Historical PI control # acronym GHG Nat 1 CanESM CCSM 01 CNRM-CM 0 CSIRO-MK GFDL-CM.1 GFDL-CM 00 GISS-E-Hp1 0 GISS-E-Hp 1* GISS-E-Hp 1* GISS-E-Rp1 0 GISS-E-Rp _ 1* 1 GISS-E-Rp 1* 1 HadCM 1 HadGEM-ES 1 IPSL-CMA-LR 00 1 MIROC _ 0 1 MRI-CGCM Total: 1 models 1 simulations simulations 1 simulations 0 () years

27 Figure 1: (see the remaining panels and figure caption on the next page)

28 Figure 1 (cont d): Standard deviations (STDs) of the estimated observed (blue) and CMIP simulated historical (red) and control-run (black) internal variability for the five indices considered; top-to-bottom rows correspond to the results for the AMO, PMO, NMO, NAO and ALPI indices, respectively. Also included are the estimates of the observed internal variability based on the one-, two- and three-factor scaling methods of Frankcombe et al. (01); see legend. The STDs were computed for raw and boxcar running-mean low-pass filtered time series using different window sizes of K+1 yr, K = 0, 1,, 0 (shown on the horizontal axis); K = 0 corresponds to raw annual data, K = 1 to -yr low-pass filtered data and so on. Error bars show the 0% spread of the STDs, between 1 th and th percentiles of the available estimates of internal variability (see text for details). Shading indicates the range in which the observed internal variability is statistically larger than its historical (light shading only) or control-run counterparts (dark shading and light shading regions combined), at the % level; here, KC01 methodology was used to estimate the observed and simulated internal variability over the historical period. The NAO plot also includes the results (heavy black curve) based on an alternative, station based observed NAO index ( /climate-data/ hurrell-north- atlantic-oscillation-naoindex-station-based). Left column: the results based on the full annual data; right column: the results based on the anomalies with respect to the leading M-SSA pair of the corresponding observed or simulated realization of internal variability (see text for details); the M-SSA embedding dimension M=0. Comments: (i) The simulated multidecadal variability is much weaker than observed (left column). (ii) Much of this model data difference is rationalized by the leading M-SSA pair (right column).

29 Figure : The M-SSA analysis of the observed and simulated internal variability in the AMO PMO NMO NAO ALPI climate-index network. Left column: the results of M-SSA analysis using the embedding dimension of M=0; right column: the same for M=0. Upper row: M-SSA spectra. The spectra based on the observed data ensemble-mean variances and their ±1 STD spread are in blue, the spectra based on CMIP model historical and control simulations are in red and black, respectively. The green error-bar plot (and lower black error-bar plot) represent the variances of the time series obtained by projecting the trajectory matrices from historical (or control) model simulations onto the ST-EOFs of the observed trajectory matrix. The spectra of the observed internal variability inferred using one-, two-, and three-factor scaling methods of Frankcombe et al. (01) are shown by x-symbols, circles and diamonds, respectively. Bottom row: Reconstructed components (RCs) corresponding to the leading M-SSA pair of the observed data. The NAO and ALPI RCs were multiplied by 1. For the purposes of better visualization, the RCs corresponding to different indices (channels) were vertically stacked by adding the constant offsets of +1, +, +, and + to the RCs for AMO, NAO, PMO and NMO indices, respectively. Comments: (i) Model data differences are dominated by the leading M-SSA pair, whose observed spatiotemporal structure is absent from models (upper row). (ii) This mode, in observations, is characterized by a pronounced coherent multidecadal signal across the entire climate network considered (bottom row).