3.1 Blocking Climatology
 Figure 1a presents NH blocking climatology from 40-year long NNR data [see also the study by (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012). Blocking frequency is shown as the number of days per year a blocked area occupies each grid point. As widely documented in the literature, two active regions of blocking occurrence emerge: North Pacific (hereafter PA blocking) and Europe-northeastern Atlantic (EA blocking). The latter generally exhibits higher frequency than the former, although the opposite is true during the summer (Figure 2a). EA blocking also shows a more zonally elongated geographical distribution than PA blocking, with a long tail to western Russia. In certain seasons, blocking frequencies over western Russia are separated from those over the North Atlantic and western Europe (e.g., November in Figure 2a) and are referred to as Ural blocking.
Figure 1. Climatology of NH annual-mean blocking frequency: (a) NNR, (b) historical multimodel mean, (c) historical multimodel mean minus NNR, (d) RCP 8.5 multimodel mean, and (e) RCP 8.5 minus historical multimodel mean. Units are number of blocked days per year. Contour intervals in Figures 1a, 1b, and 1d and Figures 1c and 1e are 4 and 2 days per year, respectively. Shaded areas in Figure 1c denote the number of models with significant positive bias minus the number of models with significant negative bias at the 95% level using a two-tailed Student's t test. Shaded areas in Figure 1e are the same as in Figure 1c except for significant model changes.
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Figure 2. Seasonal cycle of the NH blocking frequency as a function of longitude: (a) NNR, (b) historical multimodel mean, (c) historical multimodel mean minus NNR, (d) RCP 8.5 multimodel mean, and (e) RCP 8.5 minus historical multimodel mean. Units are days per month. Contour intervals in Figures 2a, 2b, and 2d and Figures 2c and 2e are 1 and 0.5 days per month, respectively. Shaded areas in Figure 2c denote the number of models with significant positive bias minus the number of models with significant negative bias at the 95% level using a two-tailed Student's t test. Shaded areas in Figure 2e are the same as in Figure 2c except for significant model changes.
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 The blocking climatology, derived from 17 CMIP5 historical runs, is illustrated in Figures 1b–1c. It is evident that the CMIP5 models can reproduce the overall geographical distribution of the NH blocking activities reasonably well. Noticeable biases are however present in frequency (Figure 1c). Most of all, EA blocking frequency is underestimated by about 30%. This is common to all the models analyzed in this study (Figure S1) and consistent with previous modeling studies [e.g., D'Andrea et al., 1998, Scaife et al., 2010]. In contrast, PA blocking frequency is overestimated by the models over broad regions. While this bias is less robust than EA blocking bias (see shading in Figure 1c in midlatitudes; see also Figure S1), it is still significant particularly on the poleward side of the climatological blocking frequency maxima. A similar overestimation was also reported in a recent study by (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012) as well as in a few climate models participating in the CMIP3 [Scaife et al., 2010].
 The above model biases in blocking frequency might be partly caused by the model resolution. It is well known that high-frequency eddy forcing, which is one of the most important maintenance mechanisms of blocking highs [e.g., Shutts, 1983; Nakamura et al., 1997], is very sensitive to the model resolution. Matsueda et al., , for instance, presented more accurate EA blocking climatology in a higher resolution model integration. However, a direct comparison between IPSL-CM5A-MR and IPSL-CM5A-LR, whose difference is only model resolution (Table 1), shows a negligible difference in EA blocking frequency (Figures S1c–S1d). A moderate increase in horizontal resolution instead leads to a slight decrease in EA blocking frequency. This result supports the finding of Scaife et al.  that EA blocking frequency is more sensitive to surface boundary conditions than atmospheric model resolution. Matsueda et al.  also indicated that the PA blocking frequency could be overestimated in a high-resolution model integration. However, no systematic relationship between PA blocking bias and model resolution is observed throughout the models (Figure S1). This is largely consistent with (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012) who showed that PA blocking frequency could be overestimated even in a coarse resolution model integration where high-frequency eddy activities are underrepresented. They suggested that the biases in time-mean flow could result in model biases in blocking frequency [see also Doblas-Reyes et al., 2002].
 The seasonal cycles of blocking frequency are illustrated in Figures 2a–2b. It presents the evolution of monthly mean NH blocking frequency as a function of longitude. The number of blocked days are simply counted along a given longitude band from 30c to 90∘ N for a given month. The longitudinal distribution of blocking frequency and its seasonality is reasonably well reproduced in the multimodel mean. Underestimation of EA blocking frequency is largely confined to the cold season, whereas overestimation of PA blocking frequency is found throughout most of the year (Figure 2c). It is also found that, although the models successfully reproduce the summertime peak in PA blocking, it is delayed by a month from August to September.
 Figures 3a–3b show the annual mean number of blocking events as a function of duration. The EA and PA blocking events, defined over 0–90∘ N and 25∘W − 42∘E and 0–90∘N and 151∘E − 220∘W, respectively, are separately illustrated along with a total number of blocking events over whole NH. In general, the number of blocking events exhibits an exponential decrease with duration. Comparison of CMIP5 to NNR data, however, reveals that, although not robust, short-lived blocking events, duration shorter than 9 days, are generally underrepresented by the models while long-lived ones are somewhat overrepresented (see black bars in Figure 3c). The bias in short-lived blocking events is mostly due to EA blocking events (see blue bars in Figure 3c). In most durations, PA blocking events show overestimation.
Figure 3. Annual mean frequency of blocking events as a function of duration: (a) NNR, (b) historical multimodel mean, (c) historical multimodel mean minus NNR, (d) RCP 8.5 multimodel, and (e) RCP 8.5 minus historical multimodel mean. Black, blue, and red bars denote blocking events over the NH, the EA, and PA sectors, respectively. Units are (Figures 3a–3d) number of events per year and (Figure 3e) percent of events per year, respectively. See the text for further details. Shaded bars in (Figure 3c) denote durations where the number of models with significant positive bias minus the number of models with significant negative bias at the 95% level using a two-tailed Student's t test is greater than 3. Shaded bars in (Figure 3e) are the same as in (Figure 3c) except for significant model changes.
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 What causes the model biases in blocking climatology? Although identification of exact cause(s) is beyond the scope of the present study, it is worthwhile to examine the possible relationship between high-frequency eddies and blocking events in the models. As addressed earlier, it is well documented that high-frequency eddies are one of the most important mechanisms of blocking formation and maintenance [Nakamura et al., 1997; Cash and Lee, 2000]. Any biases in high-frequency eddies, regardless of their origins (e.g., coarse model resolution, unrealistic physical parameterizations, misrepresentation of external forcings, etc), could hence result in biases in blocking frequency and duration.
 Figures 4a–4b present high-frequency eddy activities in the NNR and CMIP5 models, quantified by the standard deviation of 500 hPa geopotential height anomalies with periods shorter than 7 days. It can be seen that the CMIP5 models successfully reproduce the spatial distribution of high-frequency eddy activities. However, it is also evident that eddy activities are significantly underestimated in high latitudes and slightly overestimated in midlatitudes, indicating equatorward biases in the extratropical storminess particularly at the exit regions of the westerly jets over the two basins. The underestimated eddy activities in the North Atlantic are consistent with the EA blocking frequency biases on the poleward side of the climatological blocking frequency maximum (compare Figures 1a–1c and 4a–4c), indicating that misrepresentation of high-frequency eddies is likely one of the culprits of the EA blocking biases. However, a similar consistency is not found with PA blocking biases. This is even clearer if one examines individual models (see Figure S4). This result suggests that misrepresentation of high-frequency eddies alone would not be able to explain model biases in blocking frequency and duration. Other factors, such as time-mean flow and low-frequency variability, likely also play a role.
Figure 4. Climatology of annual mean standard deviation of 500 hPa eddy geopotential height with periods shorter than 7 days: (a) NNR, (b) historical multimodel mean, (c) historical multimodel mean minus NNR, (d) RCP 8.5 multimodel mean, and (e) RCP 8.5 minus historical multimodel mean. Contour intervals in Figure s 4a, 4b, and 4d and Figures 4c and 4e are 5 and 2 m, respectively. Shaded areas in Figures 4c and 4e denote the number of models with significant positive bias minus the number of models with significant negative bias at the 95% level using a two-tailed Student's t test.
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 To examine the possible impact of time-mean flow biases on PA blocking frequency biases, the analyses are extended to low-frequency energetics. This is motivated by the fact that blocking biases in the models are in qualitative agreement with those in low-frequency eddy activities, quantified by the standard deviation of 500 hPa geopotential height anomalies with periods longer than 10 days (not shown). A number of studies have shown that barotropic energy conversion from the time-mean flow to low-frequency eddies (BTC) is one of the major sources of low-frequency eddy kinetic energy in the exit regions of the westerly jets, where blocking forms most frequently [e.g., Simmons et al., 1983; Sheng and Derome, 1991ab]. In the midlatitudes, it is shown by Simmons et al.  that BTC is approximated by
where u and v are the zonal and meridional wind components, respectively; overbars represent a time average, primes denote deviations from the time mean; λ is the longitude; φ is the latitude; and a is the radius of the earth. The E-vector is defined as in the study by Hoskins et al. .
 Figures 5a–5c present the climatological E-vectors superimposed on the climatological geostrophic zonal wind in the NNR and CMIP5 models and their difference. Model biases in zonal wind exhibit a dipole pattern about the axis of the jets. This pattern resembles that of high-frequency eddies (compare Figures 4c and 5c), indicating equatorward biases both in high-frequency eddies and the time-mean flow. Stretching deformation, , also exhibits significant biases. In midlatitudes, negative biases in zonal wind centered over the eastern North Pacific causes a reduced over the central North Pacific where climatological E-vectors are negative. This enhances local BTC, likely leading to an overestimation of PA blocking frequency on the equatorward side of the PA blocking maximum (Figure 1c). However, high-latitude biases in zonal wind and E-vectors are rather weak and not consistent with a significant overestimation of blocking frequency over northeastern Siberia and Alaska. This result suggests that the energy transfer from the time-mean flow is not likely a cause of the PA blocking frequency biases in the models.
Figure 5. Climatological geostrophic zonal wind (contours) and low-frequency E-vectors:(a) NNR, (b) historical multimodel mean, (c) historical multimodel mean minus NNR, (d) RCP 8.5 multimodel mean, and (e) RCP 8.5 minus historical multimodel mean. Contour intervals in Figures 5a, 5b, and 5d and Figures 5c and 5e are 3 and 0.5 ms− 1, respectively. Shaded areas in Figures 5c and 5e denote the number of models with significant positive bias minus the number of models with significant negative bias at the 95% level using a two-tailed Student's t test.
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 It is noteworthy that EA blocking frequency biases are consistent with BTC. The zonal wind is underestimated on the poleward side of the Atlantic jet axis. This enhances over broad regions of the North Atlantic where E-vectors are directed westward, resulting in a reduced BTC.
 Alternatively, PA blocking biases could be caused by unrealistic low-frequency variability in the model. An example is the variability associated with El Niño-Southern Oscillation (ENSO). It is documented that North Pacific blocking highs tend to develop more frequently during La Niña winters than during El Niño winters [Renwick and Wallace, 1996; Chen and van den Dool, 1997]. This suggests that PA blocking frequency could be overestimated in coupled models if La Niña events are overrepresented. Figures 6a–6b show the composite blocking frequency difference between DJF winters during La Niña and El Niño conditions for the NNR and CMIP5 historical integrations. Here, La Niña and El Niño conditions are identified when the DJF-mean detrended Nino3.4 index is smaller than -0.5 K and larger than 0.5 K, respectively. The Nino3.4 index is obtained from the ERSST.V3B (observation used for the NNR) and individual models’ sea surface temperature (SST). Both composites show increased PA blocking frequencies during La Niña years, consistent with previous findings. However, PA blocking frequency increase in the CMIP5 models is biased equatorward and more importantly weaker than that in the NNR. The probability distribution function of Nino3.4 index in fact shows less frequent La Niña events in the models (Figure 6c). This result suggests that model biases in PA blocking frequency are not directly caused by ENSO-related low-frequency variability in the models.
Figure 6. DJF composite blocking frequency for El Niño minus La Niña winters: (a) NNR and (b) historical multi-model mean. Contour intervals are 1 day per year. Shaded areas in Figure 6a denote significant differences, and shaded areas in Figure 6b denote the number of models with significant positive differences minus the number of models with significant negative differences at the 95% level using a two-tailed Student's t test. (Figures 6c and 6d) PDF of DJF-mean de-trended Nino3.4 index for observations (thick black), historical multimodel mean (thick green), and RCP8.5 multimodel mean (thick orange). Thin green and orange lines in Figures 6c and 6d denote individual models for historical and RCP8.5 integrations.
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 In summary, EA blocking biases in the models are likely caused by the biases in high-frequency eddies and time-mean flow. However, the cause(s) that drive PA blocking biases is not clear. This result is not surprising as the formation and maintenance of blocking highs are highly nonlinear, involving various interactions among mean flow, low-frequency eddies, and high-frequency eddies. Further investigation is needed.
3.2 Future Changes
 With model biases described above in hand, this section examines potential changes in blocking frequency and duration in a warmer climate. The multimodel mean climatology, derived from 40 years (2060–2099) of RCP 8.5 runs, is presented in Figure 1d and compared with its counterpart derived from 40 years of historical runs (1966–2005) in Figure 1e. Only 13 models that have both historical and RCP 8.5 runs are used to make a direct comparison (see right-most column in Table 1).
 The geographical distribution of blocking frequency in the future climate is quite similar to the one in the present climate (Figure 1d). However, blocking frequency in a warmer climate is slightly decreased over the northeastern Pacific and northwestern Atlantic (Figure 1e). While the decrease is rather weak, it is found in about half of the models (see also Figure S5). This result is in agreement with previous findings [Matsueda et al., 2009; Sillmann and Croci-Maspoli, 2009; Barnes et al., 2012].
 In contrast to blocking frequency changes over the North Pacific and North Atlantic, blocking frequency over eastern Europe-Russia is predicted to increase in the future (Figure 1e). This increase of the so-called Ural blocking frequency is not robust across the models; however, a general tendency is observed in a number of models (Figure S5). In some models (e.g., HadGEM2-CC), the Ural blocking frequency change is statistically significant and even larger than PA blocking frequency change. A hint of the increased high-frequency eddy activities upstream of the Ural region (Figure 4e) further supports the potential increase in Ural blocking frequency.
 The seasonal cycle of the NH blocking activities in the RCP 8.5 integrations is compared with their historical counterparts in Figures 2d–2e. It is found that the reduced blocking frequencies over the North Pacific and North Atlantic, and the increased frequencies over eastern Europe-Russia, occur primarily during the fall and winter seasons, although they extend into spring over the North Pacific (see also Figure S6). Figures 3d–3e further present blocking frequency in a warm climate as a function of duration and its relative difference from a past climate. In Figure 3e, the relative change is computed by differencing both normalized frequency distributions and plotted with a percentage difference. This is to illustrate changes in duration, independent from changes in the number of events. Figure 3e shows no significant changes in the relative number of blocking events for all durations (see also Figure S7). This suggests that blocking frequency changes (Figures 1e and 2e) are largely the result of changes in the number of blocking events rather than changes in the duration of individual events.
 It is not clear why PA and EA blocking frequencies are decreased in RCP 8.5 integrations. Although high-frequency eddy activities are predicted to decrease over the east and west coasts of the North America (Figures 4d–4e), an overall resemblance to blocking frequency changes (Figures 1d–1e) is rather weak. The mean flow change likely contributes to the EA blocking frequency change. As shown in Figures 5d–5e, the Atlantic jet is predicted to weaken in a warm climate especially at the entrance regions of the jet. This causes increased stretching deformation over the North Atlantic. Since E-vectors are directed westward there, it implies weaker BTC (equation ((1))), supporting weaker low-frequency variability over the North Atlantic. This contrasts to the mean flow change over eastern North Pacific, which is not consistent with PA blocking change. Reduced PA blocking frequency may instead result from more frequent El Niño events (or less frequent La Niña events) in RCP8.5 integrations. In fact, Nino3.4 index shows a weak hint of enhanced El Niño events in RCP8.5 integrations (Figure 6d). However, investigation of individual models does not show a robust relationship between ENSO frequency change and PA blocking frequency change in a warm climate. Further studies are needed.
3.3 Sensitivity Tests
 The robustness of the above findings is extensively tested by changing the data resolution, the threshold value of the blocking index, the anomaly definition, and the blocking index itself. As described in section 2, all analyses are performed using interpolated data. The interpolation from high to moderate resolutions (e.g., T42), however, could result in an underestimation of blocking events as it smoothens the anomaly field. To examine the sensitivity to the data resolution, overall analyses are repeated using raw data for the selected models. The results are found to be insensitive to the data resolution (not shown).
 The sensitivity to the amplitude threshold, (A) in section 2, is also tested. The (A) is a relative quantity and varies from model to model. This introduces uncertainty in multimodel analyses as each run would have different minimum threshold of blocking anomalies. A sensitivity test is performed by applying the multimodel mean (A) to each model integration. Although not shown, no significant sensitivity is observed. This is because (A) does not vary much among the models. Since the 1.5 standard deviation level is a somewhat arbitrary choice, a sensitivity test is also performed by varying the standard deviation level of (A). Again, the results are qualitatively insensitive to the choice of standard deviation level.
 Although the anomaly z′, defined in section 2, filters out the long-term trend in the data, uncertainty in the anomaly definition in transient climate simulations still remains. To minimize the possible biases introduced by the expansion of the troposphere in a warming climate, overall analyses are repeated with the global daily mean 500 hPa geopotential height removed from each daily anomaly z′. The results are found to be insensitive to this choice of anomaly definition.
 A sensitivity test is extended to the blocking index itself. As introduced in section 2, the TM index is applied to the CMIP5 data and the results are summarized in Figure 7. Since the TM index takes different approach as compared to the hybrid index and detects blocking events only as a function of longitude, direct comparison is not straightforward. However, as illustrated in Figure 7b, the model biases and future changes in blocking frequency are qualitatively similar to those presented in Figures 1c and 1e. More specifically, the overestimation of the PA blocking frequency and the underestimation of the EA blocking frequency in the CMIP5 historical runs are evident. Additionally, an overall decrease in blocking frequency over the two basins is consistent with the result derived from a hybrid index, although the change in Ural blocking frequency is much weaker. Overall, this suggests that the results presented in this study are reasonably robust to the type of blocking index.
Figure 7. Longitudinal distribution of annual mean blocking frequency derived from the TM index: (a) thick black, green, and orange lines denote NNR, historical multimodel mean, and RCP8.5 multimodel mean, respectively. (b) Thick green and orange lines denote historical multimodel mean minus NNR and RCP8.5 minus historical multimodel mean. In both panels, thin green and orange lines denote individual models for historical and RCP8.5 integrations.
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