Biases of the wintertime Arctic Oscillation in CMIP5 models

Figure 1(a) shows the spatial pattern of the wintertime AO in ERA dataset, which explains 31.7% of the total variance. In the positive phase of AO, strong negative SLP anomalies are observed over the Arctic, and strong positive SLP anomalies are located over the midlatitude Atlantic (figure 1(a)). Although positive SLP anomalies are present over the North Pacific, their magnitude is much weaker than that over the Atlantic. These features, which are also present in NCEP dataset (not shown), are consistent with previous studies (e.g. Thompson and Wallace 1998, 2001). The spatial correlation of AO's SLP patterns between ERA and NCEP dataset is 0.99 over the Northern Hemisphere, suggesting the robustness of the AO pattern in ERA and NCEP datasets. Therefore, the results obtained in ERA dataset are referred to as 'observations' in the following sections.

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In MME, the variance explained by AO is 32.4%, similar to that (31.7%) in observations, but the pattern of AO exhibits large differences. The Pacific (Atlantic) center of AO in the SLP filed is much stronger (weaker) in MME than in observations (figures 1(a)–(c)), and this feature can be seen in most of the individual models (not shown). Similar biases are also found in the 500 hPa geopotential height (Z500) (figures 1(d)–(f)), implying the quasi-barotropic characteristics of the AO's structure and its biases. The biases of AO pattern are expected to influence the related surface air temperature (SAT) anomalies. In observations, positive AO corresponds to significant warming over the southeastern North America and northern Eurasia continent and cooling over the northeastern North America and northern Africa (figure 1(g)). In MME, by contrast, the magnitudes of SAT anomalies are much weaker throughout the Northern Hemisphere except over small regions to the south and southeast of Lake Baikal (figures 1(h) and (i)). Moreover, the warm anomalies over northwestern North America were incorrectly represented as cold anomalies in MME due to the exaggerated Pacific center of AO (figures 1(g) and (h)). Again, these biases exist in almost all the individual models (not shown). These results suggest that the CMIP5 models tend to simulate an excessively strong (weak) Pacific (Atlantic) center of AO and thereby biased teleconnections of AO. With these biases, the skill and reliability of future climate projections made by the CMIP5 models may be limited.

With a weak Pacific center and a strong Atlantic center, the observed AO pattern (figure 1(a)) resembles the North Atlantic Oscillation (NAO). Defining the NAO as the first EOF mode of SLP over the North Atlantic (20°N–90°N, 9°W–40°E) and the NAO index as the corresponding PC (Hurrell et al 2003), the temporal correlation coefficient between indices of AO and NAO is 0.94 for the period 1961–2005 (figure 2(a)), and the spatial correlation coefficient between the regressed SLP patterns of AO and NAO over the Northern Hemisphere is 0.98 (figure 2(b)). It suggests that the wintertime AO and NAO are somewhat difficult to distinguish in observations, consistent with previous studies (e.g. Rogers and McHugh 2002, Feldstein and Franzke 2006). In CMIP5 models, the temporal (spatial) correlation coefficient between AO and NAO is 0.83 (0.95) in MME, and it exceeds 0.55 (0.6) in all the 39 CMIP5 models (all exceeding 99.9% confidence level). It suggests that the observed similarities between AO and NAO can be generally captured by the CMIP5 models. Nevertheless, the AO seems to bear more resemblance to the North Pacific dominant mode (NPM, see the definition in section 3) rather than the NAO in some of CMIP5 models (e.g., those below the diagonals in figures 2(a) and (b)). The temporal (spatial) correlation coefficient between the AO and NAO is slightly weaker than those between the AO and NPM in these models (figures 2(a) and (b)). However, these models are not essentially different from the others, but rather may be seen as extreme cases, in which the Pacific variability is so large that it dominates. Moreover, the NAO-like pattern, with the seesaw between the Arctic and North Atlantic actually also exists in these models, although the strength is weaker than that in North Pacific section. Therefore, these models are also employed in this study. In fact, the results reported in this study remain almost the same if the models below the diagonals of figures 2(a) and (b) are removed from the analyses (not shown).

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The bias pattern of AO-related SLP in CMIP5 models (figure 1(c)) quite resembles the observed second EOF of SLP over the Northern Hemisphere (figure 3, also see lower left panel of figure 4 in Wallace and Thompson 2002), which mainly represents the leading SLP variability over the North Pacific (Wallace and Thompson 2002, Rodionov et al 2005, Zhou et al 2012). Defining the wintertime North Pacific dominant mode (NPM) as the first EOF of SLP over the North Pacific (20°N–65°N, 120°E–120°W) and the NPM index (NPMI) as the corresponding PC, the observed correlation coefficient between AO and NPM indices (r_AO–NPM) is only 0.16 (figure 2(a)). However, 34 out of 39 CMIP5 models simulate stronger r_AO–NPM that is higher than 0.3, exceeding the 95% confidence level. This result indicates that the linkage between AO and NPM is overestimated by the CMIP5 models, which may be the cause of the biased AO pattern.

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To validate the possible influence of the AO–NPM linkage on the intensity of the Pacific center of AO pattern, the North Pacific center index (NPCI) is defined as the area-averaged AO-related SLP anomalies (i.e., the regressed SLP anomalies onto the AOI) over the North Pacific (25°N–60°N, 150°E–120°W) to represent the intensity of the Pacific center of AO pattern. Figure 2(c) shows the scatter diagram of intermodel variability between the NPCI (y-axis) and r_AO–NPM (x-axis) based on the 39 CMIP5 models, MME, and observations. The highly linear clustered dots suggest that a high and positive r_AO–NPM tends to correspond to a strong Pacific center of the AO pattern both in models and observations. This inference is further supported by the high intermodel correlation coefficient between the x and y variables in 39 models, which reaches 0.91 and exceeds the 99.9% confidence level. In addition, the intermodel regression pattern, that is, the intermodel AO patterns are regressed onto the normalized intermodel r_AO–NPM, was calculated. It is clearly that a Pacific high-pressure center resembling the biased AO pattern (figure 1(c)) emerges in the regression pattern (figure 2(d)). This result further confirms that a high and positive r_AO–NPM is corresponding to a stronger Pacific center of the AO pattern among CMIP5 models. All these results suggest that the excessively strong Pacific center of AO in CMIP5 models is a mutual result of the excessively strong positive r_AO–NPM.

To further support the above argument, the 39 CMIP5 models were divided into high correlation groups (HCG) in which r_AO–NPM is higher than 0.45 and the low correlation groups (LCG) otherwise³ . Based on this criterion, 27 (12) models were classified to the HCG (LCG). In the HCG, the Pacific center of AO is stronger than the Atlantic center (figure 4(a)), and the patterns and teleconnections of AO (figures 4(a), (c) and (e)) are very similar to the MME of all 39 models (figures 1(b), (e) and (h)). In the LCG, by contrast, the Pacific center of AO is weaker than the Atlantic center (figure 4(b)), and the patterns and teleconnections of AO (figures 4(b), (d) and (f)) are quite similar to observations (figures 1(a), (d) and (g)) although the intensity of Atlantic center is still weaker than that in observations (figures 1(a) and 4(b)). This result confirms our argument that the patterns and teleconnections of AO are more reasonable if the AO–NPM linkage is weak in CMIP5 models.

In addition, the variances explained by AO (EOF1 of Northern Hemispheric SLP) were calculated in LCG and HCG, respectively. It reveals that AO explains 27.7% (34. 5%) of the total variance in LCG (HCG), which is lower (higher) than that in observations (i.e., 31.7%). Meanwhile, the EOF2 of Northern Hemispheric SLP explains 17.1% (15.7%) of the total variance in LCG (HCG). There results indicate a relatively high variance explained by EOF1 and low variance explained by EOF2 in HCG, and an opposite case in LCG. Therefore, it is inferred that the higher variance explained by AO in HCG than in LCG is because some of the NPM variability is extracted as AO variability in HCG.

The AO-related pattern and teleconnections in CMIP5 models and the consequent conclusions may be less reliable given the biases reported in section 3.1, so it is important to correct these biases to better represent the AO-related features in models. In observations, the Pacific center of AO is weak (figure 1(a)) and the linkage between AO and NPM is marginal (r = 0.16). In order to obtain a realistic AO variability in CMIP5 models, the NPM-related variability is suggested to be removed from the AO variability through a linear regression method (Wang et al 2007, Chen et al 2013a) as follows:

$$\begin{eqnarray*}&&{\rm{A}}{\rm{O}}{{\rm{I}}}_{{\rm{R}}{\rm{M}}\_{\rm{N}}{\rm{P}}{\rm{M}}}={\rm{A}}{\rm{O}}{\rm{I}}-{r}_{{\rm{A}}{\rm{O}}-{\rm{N}}{\rm{P}}{\rm{M}}}\times {\rm{N}}{\rm{P}}{\rm{M}}{\rm{I}},\end{eqnarray*}$$

where ${r}_{{\rm{A}}{\rm{O}}-{\rm{N}}{\rm{P}}{\rm{M}}}$ is the correlation coefficient of the NPMI with respect to the AOI and the ${\rm{A}}{\rm{O}}{{\rm{I}}}_{{\rm{R}}{\rm{M}}\_{\rm{N}}{\rm{P}}{\rm{M}}}$ is the NPM-independent AOI. The${\rm{A}}{\rm{O}}{{\rm{I}}}_{{\rm{R}}{\rm{M}}\_{\rm{N}}{\rm{P}}{\rm{M}}}$ is then used as the bias-corrected AOI in models to calculate the AO-related pattern and teleconnections via linear regression. In observation, the AO-related SLP pattern changes little after removing the NPM variability (figures 1(a) and 5(a)), so do the Z500 (figures 1(d) and 5(c)) and SAT patterns (figures 1(g) and 5(e)) of AO. The spatial correlation coefficients between the original AO patterns and teleconnections (figures 1(a), (d) and (g)) and their ${\rm{A}}{\rm{O}}{{\rm{I}}}_{{\rm{R}}{\rm{M}}\_{\rm{N}}{\rm{P}}{\rm{M}}}$-related counterparts (figures 5(a), (c) and (d)) all exceed 0.99. In MME, by contrast, the SLP pattern of AO has changed markedly when the NPM-related variability is removed. The excessively strong Pacific center is significantly weakened and the amplitude of the Atlantic center is recovered to be comparable to the observations (figures 1(a), (b) and 5(b)). Similar improvements can also be found in Z500 and SAT fields. For example, the anticyclonic center of Z500 over the North Pacific is significantly weakened and those over the North Atlantic and Northeast Asia are strengthened to be more close to observations (figures 1(d), (e) and 5(d)). Meanwhile, the spurious cold anomalies over the northwestern North America are corrected (figures 1(h) and 5(f)), and the SAT pattern in MME is more close to observations after the NPM signal is removed (figures 1(g) and 5(f)). These significant improvements can be also found in almost every model (not shown). These results suggest that the linear removal of the NPM variability from AO can significantly improve the pattern and teleconnections of AO in CMIP5 models. Of course, one should keep in mind that this bias-correction is a statistical method that does not improve the model dynamics.

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