Northern Hemisphere (NH) blocking climatology is examined using a subset of climate models participating in the Coupled Model Intercomparison Project phase 5 (CMIP5). Both historical and Representative Concentration Pathway (RCP) 8.5 integrations are analyzed to evaluate the performance of the CMIP5 models and to identify possible changes in NH blocking frequency and duration in a warmer climate. Comparison with reanalysis data reveals that CMIP5 models can reproduce the NH blocking climatology reasonably well, although the frequency of Euro-Atlantic blockings, particularly those with relatively short duration, is significantly underestimated during the cold season. In most models, overestimation of the Pacific blocking frequency is also evident for all durations throughout the year. In comparison to historical integrations, RCP 8.5 integrations show significant decreases in blocking frequency over both the North Pacific and north Atlantic regions, with a hint of increasing blocking frequency over western Russia. However, there is no noticeable change in the duration of individual blocking events for all durations.
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 Atmospheric blocking is one of the most dramatic examples of extratropical low-frequency variability. Traditionally, it refers to a synoptic-scale high-pressure system, often accompanied by low-pressure system(s) at lower latitudes that remains quasi-stationary for days to weeks, interrupting the zonal flow [e.g., Rex, 1950]. Since blocking highs are persistent and quasi-stationary by definition, they affect surface weather and climate in a major way. For instance, a blocking high often causes a significant increase in surface temperature beneath it and enhanced storm activity around it [e.g., Trigo et al., 2004]. Striking examples are the 2003 European and 2010 Russian heat waves that resulted from exceptionally long-lasting summer-time blocking events. Both these events lead to record breaking surface air temperatures and significant increases in mortality rates [Black et al., 2004; Dole et al., 2011]. In winter, blocking highs have been identified as one of the most important causes of cold surges in the Europe and Eurasia, leading to an abrupt temperature drop with heavy precipitation [e.g., Park et al., 2011].
 The crucial role that blocking plays in surface weather (especially in extreme weather) has underlined the need for the reliable simulation of blocking events by climate models. It is however well documented that climate models often underestimate Northern Hemisphere (NH) blocking frequency, especially over the North Atlantic and Europe [e.g., D'Andrea et al., 1998, Doblas-Reyes et al., 2002, Scaife et al., 2010, Barriopedro et al., 2010a]. While detailed causality is still an active area of research, this underestimation has been attributed to the limited model resolution, misrepresentation of surface boundary conditions, and uncertainties in physical parameterizations that lead to the biases in the time-mean flow and high-frequency eddies [e.g., Matsueda et al., 2009, Scaife et al., 2010, Scaife et al., 2011].
 Recent studies have shown that the frequency of NH blocking events may decrease in the future, in response to global warming. By analyzing CMIP3 models, Barnes and Hartmann  and Barnes et al.  documented a statistically significant decrease in blocking frequency over both the North Pacific and North Atlantic in the 21st century. They however found no evidence in blocking duration change. While a similar frequency change is also found in model sensitivity tests [Matsueda et al. 2009; Sillmann and Croci-Maspoli, 2009], different studies show slightly different results in duration change. For example, Sillmann and Croci-Maspoli  showed a possible increase in maximum blocking duration over the Euro-Atlantic region, whereas Matsueda et al.  showed a possible reduction in long-lived blocking events.
 It should be noted that, despite the importance of blocking events, only a few studies (as listed above) have documented possible changes in blocking activities in a warmer climate. As a matter of fact, the future projection of NH blocking highs was not commented in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) [Solomon et al., 2007] which is largely based on the CMIP3 data. This lack of documentation partly results from availability of daily data. Although blocking is typically examined using 500 hPa geopotential height or upper-tropospheric dynamic fields such as potential temperature on the 2-PVU surface or upper-tropospheric PV anomalies, these data sets were not archived in the CMIP3 in daily or subdaily resolution. Of the few studies based on CMIP3 models, Scaife et al.  and Barnes et al.  used zonal wind, assuming geostrophic balance, to characterize the NH blocking climatology in the CMIP3 models.
 The primary goal of this study is to examine the NH blocking climatology in the present and future climate as simulated by the CMIP5 models. Extending and updating previous studies, we evaluate state-of-the-art climate models in the context of present-day blocking climatology and document the multimodel projection of blocking frequency and duration in the 21st century. This goal is achieved by applying a hybrid blocking index (E. Dunn-Sigouin, S.-W. Son, and H. Lin, Evaluation of Northern Hemisphere blocking climatology in the Global Environment Multiscale (GEM) model, Mon. Wea. Rev., in press, 2012), that is essentially a combination of the two widely used blocking indices (i.e., the Dole-Gordon type index and Tibaldi-Molteni type index), to daily 500 hPa geopotential height fields in both historical and RCP integrations as described below.
2 Data and Methodology
 The model data used in this study are historical and RCP 8.5 runs from a subset of climate models participating in the CMIP5 [Taylor et al., 2012]. Briefly, historical runs are 20th century climate integrations with all observed climate forcings. RCP 8.5 runs are scenario integrations with a rapid warming, specifically with an anthropogenic radiative forcing of 8.5 Wm− 2 at 2100. All available models that archived daily geopotential height fields are used: i.e., a total of 17 models for historical integrations and 13 models for RCP 8.5 integrations as of June 2012 (Table 1). If multiple realizations are available, only the first ensemble member is considered.
Table 1. Description of CMIP5 Models Used in This Analysis (Resolutions refer to atmospheric model resolution and horizontal resolution is approximate for spectral models)
Horizontal Res. (lat.× lon.)
T42 (2.8 ∘ × 2.8 ∘)
T63 (2.8 ∘ × 2.8 ∘)
(0.75 ∘ × 0.75 ∘)
N96 (1.875 ∘ × 1.25 ∘)
(1.875 ∘ × 3.75 ∘)
(1.25 ∘ × 2.5 ∘)
(1.875 ∘ × 3.75 ∘)
T85 (1.4 ∘ × 1.4 ∘)
T42 (2.8 ∘ × 2.8 ∘)
T63 (1.875 ∘ × 1.875 ∘)
T63 (1.875 ∘ × 1.875 ∘)
TL159 (1.125 ∘ × 1.125 ∘)
f19 (1.875 ∘ × 2.5 ∘)
T42 (2.8 ∘ × 2.8 ∘)
(0.9 ∘ × 1.25 ∘)
TL127 (1.4 ∘ × 1.4 ∘)
T42 (2.8 ∘ × 2.8 ∘)
 All model output is first interpolated onto the lowest model resolution, namely, 2.8∘ latitude by 2.8∘ longitude (Table 1). Blocking statistics are then derived using this interpolated data. To minimize the effect of internal variability in climatology, analyses are performed for a sufficiently long period. Specifically, 40 years, 1966–2005 for historical runs and 2060–2099 for RCP 8.5 runs, are considered. Although not shown, overall results are found to be insensitive to the choice of analysis period. For instance, use of last 20 years, i.e., 1986–2005, yields essentially the same results but with a larger intermodel difference.
 The performance of the CMIP5 models is evaluated by comparing the blocking climatology derived from historical integrations to that of the National Centers for Atmospheric Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) reanalysis [NNR, Kalnay et al., 1996]. Future changes in blocking activities are then quantified by comparing historical runs with RCP 8.5 runs. All results are shown in terms of the multimodel mean, and their significance is shown as the difference between the number of models showing statistically significant positive differences minus the number of models showing statistically significant negative differences. To further illustrate intermodel difference and statistical uncertainty, individual models are also presented in the auxiliary materials.
2.1 A Hybrid Index
 The blocking index employed in this study is a hybrid index that combines the two widely used indices, the Dole-Gordon type (DG) index [Dole and Gordon, 1983] and the Tibaldi-Molteni type (TM) index [Tibaldi and Molteni, 1990], in a simply way (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012). The DG index typically identifies blocking events as persistent geopotential height anomalies at 500 hPa. It provides 2-D (latitude-longitude) statistics of blocking highs but is known to suffer from arbitrary blocking anomaly thresholds and possible misdetection of quasi-stationary ridges as blocking highs. In contrast, the TM index defines blocking events with the reversal of the meridional gradient of absolute geopotential height at 500 hPa. Since the local gradient is evaluated about the reference latitude, it yields blocking statistics as a function of longitude only. Unlike the DG index, this index is applicable to short-term data in which climatology is not robustly defined. However, it is known that blocking frequency can be significantly underestimated if the mean state is biased [Scaife et al., 2010]. Prescribing the reference latitude is another caveat. See the studies by Barriopedro et al. [2010b] and (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012) for further details of the advantages and disadvantages of these two indices.
 In this study, the above two approaches are combined into a single hybrid index: i.e., a contiguous area of blocking anomalies is identified from the 500 hPa geopotential height field as in the DG index, and then, a reversal of the meridional gradient of geopotential height is ensured as in the TM index. Here the anomaly, z′, is not simply defined by the deviation from the long-term mean. It is instead defined by filtering out both the seasonal cycle and interannual variability from the 500 hPa geopotential height field [Sausen et al., 1995], then normalized by the sine of latitude, taking the latitudinal variation of the Coriolis parameter into account [Dole and Gordon, 1983]. As such, z′ can be directly related with 500 hPa eddy stream function in the context of quasi-geostrophic dynamics. More specifically,
where z is 500 hPa geopotential height (Z) divided by the sine of latitude, is a running annual mean of z centered on a given day, is a mean seasonal cycle derived from z∗ which is a running monthly mean of z - centered on a given day.
 More specifically, the blocking events are identified as follows. The potential blocking events are tested by searching the closed positive contours of z′, satisfying the minimum amplitude (A) and spatial scale (S). They are tracked in time, ensuring a sufficient overlap in blocking areas (O) within 2 days. The detected anomalies are then tested as to whether they block the flow by assuring the reversal of the meridional gradient of the absolute 500 hPa geopotential height on the equatorward side of the anomaly maximum. In this regard, the anomaly field determines not only the spatiotemporal scale of blocking highs but also their reference latitudes. If all of these conditions are satisfied for a consecutive period of days (D), the anomalies are finally labeled as blocking highs.
 In this study, the amplitude threshold (A) is set to 1.5 standard deviation of geopotential height anomalies over 30∘ − 90∘ N for a 3-month period centered at a given month. The remaining threshold values are set to (S) = 2.5×106km2, (O) = 50%, and (D) = 5 days, for both NNR and CMIP5 data. See the study by (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012) for further details.
 The above approach conveniently provides 2-D statistics of blocking highs, minimizing possible misdetection. A similar approach, but applying the gradient reversal first, was also proposed by Barriopedro et al., [2010b]. However, a hybrid index still needs to prescribe anomaly criteria that are subject to the analysis. Among others, the amplitude threshold (A), a relative quantity to a given climate state, may differ from model to model and from the present to future climate. This could increase uncertainty in the multimodel analyses. This issue is addressed in section 3.3.
2.2 A TM Index
 To examine the robustness of the findings to the choice of blocking index, the TM index, based on the study by Tibaldi and Molteni , is also applied. It defines blocking highs as the local instantaneous gradient reversal in 500 hPa geopotential height field, Z. The equatorward and poleward gradients of Z, GHGS, and GHGN are computed at each longitude, λ, for the selected reference latitudes, φ:
 If the following two conditions are satisfied for at least one of Δs at a given longitude, the longitude is identified as being blocked:
 Note that the Δs are slightly modified from the original ones to match the data resolution used in the present study and that GHGS is reduced in magnitude. The blocking frequencies obtained with this index are compared to those of the hybrid index in section 3.3
2.3 Variable of Interest
 In this study, blocking events are detected by using 500 hPa geopotential height field. This differs from the recent approaches that utilize dynamical variables such as the potential temperature on the dynamic tropopause [Pelly and Hoskins, 2003] and the potential vorticity anomalies in the upper troposphere [Schwierz et al., 2004]. Although these variables could be more advantageous, they are not readily available from the CMIP5 archive. More importantly, it has been shown that most blocking events with a significant amplitude and substantial spatial scale are reasonably well detected in all variables [Barnes et al., 2012].
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.
 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.
 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.
 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.
 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.
 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.
 This study examines the NH blocking climatology as simulated by the CMIP5 models. Both historical and RCP 8.5 runs are examined to evaluate the performance of the CMIP5 models in comparison to NNR and to identify possible changes in blocking frequency and duration in a warmer climate.
 Comparison to reanalysis data reveals that the CMIP5 models can reproduce the NH blocking climatology reasonably well. It is however found that the EA blocking frequency is generally underestimated in most models during the cold season. This is mostly due to the short-lived blocking events with duration shorter than 9 days. In contrast, the PA blocking frequency is largely overestimated throughout the year for almost all durations. Although this result contrasts to previous modeling studies which have typically documented underestimation of the blocking frequency over both the North Pacific and Atlantic in a moderate-resolution climate model integration [e.g., D'Andrea et al., 1998;, Doblas-Reyes et al., 2002; Matsueda et al., 2009; Barriopedro et al., 2010a], a similar result is documented for the latest operational model (E. Dunn-Sigouin, S.-W. Son, and H. Lin, in press, 2012) and for certain models participating in the CMIP3 [Scaife et al., 2010].
 In comparison to historical integrations, the RCP8.5 integrations show a weak hint of reduced blocking frequency over the North Pacific and North Atlantic especially during the fall and winter. This result largely confirms previous findings that are based on different data and different blocking indices [Matsueda et al., 2009; Sillmann and Croci-Maspoli, 2009; Barnes and Hartmann, 2010; Barnes et al., 2012]. In contrast to North Pacific and North Atlantic blocking events, blocking events over eastern Europe and Russia, the so-called Ural blocking, are predicted to marginally increase in a warmer climate. There is, however, no systematic change in the duration of individual blocking events for all durations.
 The causes of model biases and future changes of blocking frequency are not clear especially over the North Pacific. While further analyses are needed, preliminary analyses indicate that underestimation of blocking frequency over the Euro-Atlantic and a future decrease in blocking frequency over the North Atlantic are consistent with model biases and predicted changes in high-frequency eddy activities and time-mean flow. A similar consistency, however, is not observed over the North Pacific, indicating that model biases and predictions of PA blocking events in the CMIP5 models are likely associated with multiple factors. Further studies are needed to identify exact causal relationship.
 We thank Junhyung Bae and Joowan Kim for their assistances in processing model data. We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and thank the climate modeling groups (listed in Table 1 of this paper) for producing and making available their model output. For CMIP, the U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The work of S.W. Son was supported by research settlement fund for the new faculty member of SNU.