1. Introduction
The North Atlantic Oscillation (NAO) and Pacific–North American (PNA) pattern are the two most prominent modes of the low-frequency variability over the Northern Hemisphere (NH). The modes of interannual or interdecadal variability are not stationary; however, their patterns are changing over time. Ulbrich and Christoph (1999) were the first to describe an eastward shift of centers of NAO; they found the shift in a simulated climate with higher CO2 concentrations. The shift was then confirmed in observed data by Hilmer and Jung (2000) and Jung et al. (2003) who reported a simultaneous eastward shift of the northern center and southern center. Using the moving period analysis, Wang et al. (2012) found that since the 1970s, the eastward shift of NAO was more prominent than the shift observed in the 1920s. They also reported a slight northward shift of the southern center during the 1940s. In the study by Moore et al. (2013), the NAO patterns were compared across four periods during the twentieth century. The authors observed minor differences in the position of the centers, indicating that the shifts in NAO are not gradual. Vietinghoff et al. (2021) reported a northward and north-eastward shift of the NAO centers in historical, control, and scenario model runs. The transition paths of the centers were found to be zigzagging, which seems to be consistent with the findings of Moore et al. (2013). The oscillation of centers around their geographical means and a slow, gradual eastward shift were described by Piskala and Huth (2023, hereinafter PH23).
Evidence suggests that also the PNA pattern has undergone shifts over time. Wallace et al. (1993) contrasted PNA-like modes during the periods of 1946–55 and 1981–89, which showed a lowering of 500-hPa geopotential heights over the North Pacific and their rise over Canada. Trenberth and Hurrell (1994) investigated the eastward shift of the Aleutian low pressure system during the 1970s, which was linked to changes in storm tracks in the Pacific. Lee et al. (2012) reported an eastward shift in the entire PNA pattern between 1958–77 and 1978–2002, which was attributed to a shift in storm tracks as well. Moreover, Wang et al. (2013) demonstrated an increase in both the frequency and intensity of strong cyclones over the midlatitude Pacific during the twentieth century. Chien et al. (2019) described and discussed a significant eastward shift of the PNA from a PNA-like pattern to what they call “North American winter dipole” pattern, with more pronounced centers over eastern Canada and the east Pacific.
The abovementioned studies are difficult to directly compare since they differ in their design. The spatial changes of modes are investigated using the sea level pressure fields (Jung et al. 2003; Zhang et al. 2008; Wang et al. 2012), 500-hPa geopotential heights (Wallace et al. 1993; Ulbrich and Christoph 1999; PH23), or upper-tropospheric levels above 300 hPa (Lee et al. 2012; Chien et al. 2019; Mezzina et al. 2020). The modes are identified at both the hemispheric scale and within regional domains, such as North Atlantic–Europe and Pacific–North America. However, as noted by Huth and Beranová (2021), the spatial structure of patterns is prone to be sensitive to the choice of the domain. The findings can also be affected by the variations in the methods used. Modes are typically identified through the principal component analysis (PCA), which is a widely employed technique since the 1960s (Kutzbach 1967; Craddock 1973; Wallace and Gutzler 1981). However, there are various settings of PCA that lead to different results, such as the rotation of principal components (PCs) (Richman 1986; Barnston and Livezey 1987; Rogers and McHugh 2002), similarity matrix (Huth 2007; Hannachi et al. 2007), and the grid type and horizontal resolution (Craddock 1973; Huth 2006). In our previous study (PH23), we noted that the choice of periods being compared, as well as their length, can impact results and interpretation of shifts in the spatial structure of modes.
The choice of the data source also plays a key role; models (Handorf and Dethloff 2012; Lee et al. 2019) including projections of future climate (Chen et al. 2018; Vietinghoff et al. 2021) or reanalyses (Wang et al. 2013; Hynčica and Huth 2020) are usually used to detect changes in NAO and PNA. It is worth noting that the modes of variability may differ depending on the reanalysis used, as emphasized by Hynčica and Huth (2020). The differences are caused mainly by the type and amount of assimilated data. In general, the lesser the observations assimilated in a region, the greater the differences between reanalyses (Harnik and Chang 2004; Hodges et al. 2011; Wang et al. 2016; Slivinski et al. 2021). Reanalyses that rely solely on surface observations, such as pressure, temperature, winds, sea ice distribution, and sea surface temperature, typically provide longer datasets that cover periods as far back as the nineteenth century (we refer them as surface-input reanalyses). However, due to the limited availability of observations during earlier periods, the assimilated data may be sparse and less reliable (Wang et al. 2012; Bell et al. 2021). On the other hand, there are reanalyses that assimilate all observations, including measurements from radiosondes and satellites, which, however, are only available from the 1950s and 1979, respectively (we refer them as full-input reanalyses). Therefore, the full-input reanalyses use data that typically cover a shorter time period than surface-input reanalyses. Nevertheless, as noted by Sturaro (2003), Fujiwara et al. (2017), or Long et al. (2017), the introduction of radiosondes and satellites may also introduce inhomogeneities and discontinuities in reanalyses, which could potentially impact even the circulation modes.
The spatial extent and positions of the NAO and PNA centers can undergo substantial changes when detected by PCA. Notably, sudden shifts and changes may occur even between two consecutive periods, as highlighted in PH23. These changes can arise from several factors: data inhomogeneities, the sensitivity of modes to the number of PCs retained during rotation, or the independent truncation and rotation processes applied to each period. Some of the sudden shifts are too pronounced to represent genuine changes in variability between periods and are more likely artifacts of the PCA method. However, as PH23 advocated, it is crucial to identify these shifts when using PCA for detecting spatial changes over time, to avoid interpreting long-term trends based on patterns influenced by PCA artifacts.
The occurrence of the sudden shifts appears to be largely random. To investigate this further, we analyze multiple reanalysis datasets to determine whether these sudden changes are consistently observed across different datasets during the same time. In this study, we use all available long-term reanalyses that contain the ensemble members as well as state-of-art ERA5 dataset. We show the level of uncertainty in individual datasets using both the ensemble mean and all ensemble members. Additionally, we demonstrate how even a minor change in the analyzed data can impact the order of PNA and NAO, the amount of variance explained by them, and their location and spatial structure.
2. Data and methods
In this study, we evaluate five reanalyses, presenting details on the number of ensemble members, grid resolution, the covered periods, and references in Table 1. Among them, three are surface-input reanalyses: 20CRv2, 20CRv3, and ERA-20C. It is important to note that the 20CRv3 reanalysis is an update of 20CRv2, as it addresses the issue of sparse data in the early periods by assimilating up to 25% more observations. However, the additional observations do not fully cover remote regions such as North Pacific and polar regions of North America where the centers of PNA are typically located. In contrast, ERA-20C, the reanalysis dataset provided by ECMWF, uses a completely different model and assimilation method.
Reanalyses employed in this study, their resolution, number of ensemble members, time period covered, and references.
We also utilize two full-input reanalyses, including the state-of-the-art ERA5, which is regularly updated up to almost the present. The data are initially provided at a grid resolution of 0.5°; however, for better spatial comparison between reanalyses, we consider every fourth grid point to achieve a final resolution of 2°. In addition, we include the oldest available reanalysis, NCEP/NCAR, which is not ensemble based but is commonly used in other studies and regularly updated.
Our focus is on the circulation patterns within the northern extratropics, i.e., north of 20°N. We use winter (DJF) monthly means of 500-hPa geopotential heights to calculate anomalies. To remove the annual cycle, we subtract the corresponding monthly averages. The seasons are identified by the year to which January falls. The gridpoint values are weighted by the square root of the cosine of latitude to adjust for a decreasing size of gridbox areas toward the pole (Thompson and Wallace 2000; Jackson 2003).
We detect atmospheric modes of variability using orthogonally rotated S-mode PCA, where grid points are represented in columns and months in rows (Compagnucci and Richman 2008). We use the covariance as a similarity metric (Huth 2006). We decided to rotate nine modes, which is the best choice for most reanalyses in winter season (Hynčica and Huth 2020). We recognize that there are various approaches available to ascertain the number of principal components (Peres-Neto et al. 2005), which, however, often widely differ in their recommendation. Nevertheless, we are only interested in the two strongest modes; therefore, the choice of the number of modes is not a critical issue since both NAO and PNA exhibit relatively low sensitivity to the number of rotated modes (Baxter and Nigam 2013). Therefore, we subject nine principal components to the varimax orthogonal rotation (Richman 1986) in all analyses in order to achieve simple structure of PCs and to facilitate their interpretation. The spatial structure of the modes is represented by correlations between the time series of each mode and the 500-hPa height anomalies; they are also referred to as loadings. The natural neighbor interpolation method (Sibson 1981) is employed to calculate the contour lines of correlations displayed in figures.
Number of 40-yr long periods analyzed for each reanalysis in the ensemble mean.
3. Full period
In all reanalyses employed, the NAO and PNA patterns (rightmost column in Figs. 1 and 2, respectively) are distinct and easy to recognize. The NAO patterns vary in specific details, such as the presence of two centers in the positive belt for 20CRv3, ERA5, and NCEP/NCAR and the geographic range of the southern negative belt, which spans from North Africa to central Asia. The primary distinction of the PNA pattern among reanalyses is the location of its center over North America and Canada. In the ERA-20C, ERA5, and NCEP/NCAR reanalyses, the center extends (although with weak correlations only) over Siberia into central Asia, while in both versions of 20CR, it is confined to North America. Overall, the NAO and PNA patterns differ primarily in their finer details, but their position and spatial extent of all centers are consistent. This is in accordance with findings of Hynčica and Huth (2020), which indicate that dissimilarities between reanalyses are noticeable in all seasons, but winter exhibits the least variability, with the highest level of agreement seen in the most prominent modes, including PNA and NAO.
(right) Loadings of NAO for the full periods and selected 40-yr periods for the ensemble mean. Positive values are represented by solid contours, negative values are represented by dashed contours, and the zero contour is omitted. The contour interval is 0.2.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
Reanalyses vary more in how much variance NAO and PNA explain. The variance explained for both ensemble mean (dots) and ensemble members (boxes) is presented in Fig. 3. As expected, surface-input reanalyses exhibit greater variability among ensemble members due to the increased uncertainty associated with a weaker constraint by assimilated observations. Notably, in 20CRv2, 20CRv3, and ERA-20C reanalyses, NAO explains a significantly higher amount of variability in the ensemble mean than in all ensemble members. On the other hand, the ensemble mean PNA tends to explain less variance compared to the majority of members. This is in line with findings by PH23 that in 20CRv2, the Pacific–North American modes tend to explain less variance in the ensemble mean compared to the ensemble members. This is due to the uneven distribution of assimilated data prior to the 1940s (Krueger et al. 2013) as well as the averaging process to gain the ensemble mean fields. The model generates variability in data-sparse regions, which is not constrained and controlled by assimilated observations. Thus, in the early periods, individual ensemble members vary more one from another, and more so in data-sparse areas, such as the North Pacific and North American Arctic. The averaging process then reduces this variability. The opposite behavior of the European–North Atlantic modes is simply a manifestation of a smaller share of their variance on the total variance in the ensemble mean and a larger share of their variance in the ensemble members. Figure 3 shows that the other two surface-input reanalyses, 20CRv3 and ERA-20C, behave in the same way as 20CRv2.
Variance explained by NAO and PNA. The ensemble mean is represented by dots, while the ensemble members are shown as boxes. The boxes indicate the first and third quartile, the central line represents the median, and the whiskers indicate the maximum and minimum values.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
In terms of explained variance, NAO is the strongest mode across all ensemble mean datasets. The greatest separation is observed in 20CRv3, where NAO and PNA differ by more than 4 percentage points. In contrast, in ERA-20C, NAO and PNA explain almost the same amount of variance. However, different results are obtained for ensemble members. In 53 out of 56 members of 20CRv2 and in 6 out of 10 members of ERA-20C, the order of the two strongest modes is reversed relative to the ensemble mean. Interestingly, this phenomenon is not observed in 20CRv3 and ERA5, in whose ensemble members NAO consistently explains more variance than PNA.
4. Ensemble mean in 40-yr moving periods
The explained variance, spatial structure and extent, and order of the two leading modes can change substantially over time (PH23). We perform PCA to obtain NAO and PNA for each 40-yr long period with 1 year step, so the two consecutive periods overlap almost completely, each step replacing just 2.5% of the analyzed data. Despite this, results may differ considerably from one period to the next.
a. Explained variance
Figure 4 (top) shows variance explained by NAO and PNA. Its trends are fairly similar across all reanalyses. In 20CRv3, there is a discernible decrease in the variance explained by NAO between the first period of 1836–75 and the period of 1902–41, after which the trend switches into an increase. The early decrease in explained variance is also evident in 20CRv2. However, in the subsequent periods, the two versions of the 20CR reanalysis start to diverge from each other. NAO in 20CRv3 explains approximately 15% of the variance since about 1921–60, while in 20CRv2, it is only about 12%. Nevertheless, decreases and increases in explained variance coincide in the two versions of 20CR. NAO in ERA5, ERA-20C, and NCEP/NCAR typically explains around 14% of variance. These three reanalyses generally exhibit a high level of agreement. Occasional sudden drops and rises tend to coincide in all or almost all reanalyses. An example is a substantial decline in explained variance in 1970–2009, which is followed by a sharp increase. This pattern is consistent across all reanalyses, which suggests that the rather sudden change in explained variance is a real phenomenon rather than a product or artifact of a specific reanalysis model or a statistical artifact of PCA.
(top) Variance explained in the ensemble mean and 40-yr moving periods, and (bottom) the congruence coefficient between 40-yr moving periods and the full period for (left) NAO and (right) PNA.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
The degree of similarity in explained variance between reanalyses is even higher for PNA. The explained variance shows a generally increasing trend with occasional fluctuations until the period 1947–86. Since then, the trend changes its sign and the amount of variance explained by the PNA pattern declines in all reanalyses. While the trend is consistent across the reanalyses for most of time, the early periods between 1872–1911 and 1898–1937, when PNA accounts for substantially less variability in 20CRv2 than in 20CRv3, deviate from this. Similarly to NAO, the majority of reanalyses agree in variations from one period to the next.
b. Order of modes
A change in the explained variance can result in a shift in the order of modes. All reanalyses exhibit changes in the order of NAO and PNA in the ensemble mean, as shown in Fig. 5. The most substantial changes in their order occur in reanalyses 20CRv3 and 20CRv2 during the early periods. While NAO is the strongest mode in both reanalyses during the early periods, PNA is relatively marginalized and ranks even as only the seventh mode. Typically, during the early periods, NAO explains about 5 percentage points more variance than PNA. It is caused by the averaging process, which also results in a decline in the explained variance of PNA for the ensemble mean fields. In the mid- and late periods, 20CRv3 experiences a higher frequency of switches in the order, and the gap between the explained variance of NAO and PNA is typically narrower than in 20CRv2. It is interesting to note that periods when PNA explains more variance than NAO prevail in ERA-20C. Despite this, NAO is ranking as the first leading mode for the full period. The ERA5 and NCEP/NCAR reanalyses also show changes in the order of two leading modes with NAO mostly being the strongest and with the widest gap in the explained variance during the most recent periods.
The order of NAO (dotted) and PNA (solid) in 40-yr periods (left axis), with the difference in variance explained between NAO and PNA (in percentage points) represented by a black line with shaded areas (right axis).
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
c. Spatial changes
Two types of spatial shifts of NAO and PNA patterns were identified in 20CRv2 by PH23, namely, slow gradual shifts of centers and their sudden changes from period to period. Congruence coefficient, which quantifies the degree of similarity of NAO and PNA between the full period and 40-yr moving periods, can capture the presence of such shifts (Fig. 4, bottom). A sudden drop or rise of the coefficient can be interpreted as a sudden change in spatial structure or position (shift) of the pattern. As Fig. 4 shows, the sudden ups and downs in congruence are present in all reanalyses.
NAO exhibits a high degree of similarity (congruence coefficients over 0.95) with the full period for the vast majority of moving periods (Fig. 4, bottom). The patterns of NAO are well defined and easily identifiable in all 40-yr periods. Figure 1 displays in its left-hand part NAO in 40-yr periods with a 20-yr step. It shows that certain features in the patterns exhibit similar developments in all reanalyses. One example of this is the southern belt of positive values over the Atlantic, which is characterized by one distinct center in 1902–41 in the three longest reanalyses, 20CRv3, 20CRv2, and ERA-20C, while in periods 1922–61 and 1942–81, this center is divided into two cores: a major one over the Atlantic and a smaller one over Europe. This feature is in accord with ERA5 in the latter period. The periods around 1962–2001 are notable for the significant decline in congruence coefficients that occurred in all reanalyses (Fig. 4). The spatial patterns illustrating significant decreases in the similarity between two consecutive periods are depicted in Fig. 6. To enhance readability of maps, we characterize the NAO only by the ±0.2 isolines. The sudden decrease in the degree of similarity in 20CRv3, 20CRv2, ERA5, and NCEP/NCAR originates from a southward shift of both major centers; this is better visible in the animation of NAO patterns with a 1-yr step in the online supplemental material 1. The congruence coefficients rise again in the subsequent periods, and the centers return back to the north. Only in 20CRv3, 20CRv2, and ERA-20C, it is possible to recognize the long-term and gradual changes in the NAO pattern when the northern center is slightly moving eastward during the twentieth century.
The NAO pattern in two consecutive 40-yr periods with the most pronounced decline in the congruence coefficient that occurs around the period 1962–2001. For clarity, only the ±0.2 isolines are shown.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
The fluctuations in congruence coefficients for PNA (Fig. 4, right) suggest more frequent shifts and changes in the pattern compared to NAO. During the early periods of 20CRv3 and 20CRv2, the degree of similarity is relatively low, congruence dropping below 0.9. The pattern of PNA is substantially modified in the early periods: The centers over the Gulf of Mexico and over northwestern North America are rather weak and, particularly the former one, of a limited spatial extent (Fig. 2, left), the entire pattern constituting a zonally oriented tripole rather than a meridionally oriented quadrupole. There is a trend of increasing similarity in 20CRv3, ERA5, and NCEP/NCAR, which reaches a peak around the period of 1966–2005. However, the remaining datasets, 20CRv2 and ERA-20C, display a different trend pattern, as the degree of similarity has been decreasing since 1922–61 and resuming an increase only after 1950–89. Similar to the NAO, certain features of the PNA pattern exhibit similar development across all reanalyses (Fig. 2). One notable feature is the development of a tongue of positive values extending from the Arctic through Siberia into central Asia. It can be observed in all reanalyses for periods 1942–81 and 1962–2001, although it appears to be shrinking and weakening between these two periods. Moreover, supplemental material 2 illustrates a gradual disappearance of the tongue even in the more recent periods in ERA5 and NCEP/NCAR.
Both PNA and NAO patterns exhibit sudden changes from period to period, which are related to drops and rises in the similarity degree. Supplemental materials demonstrate that some of the substantial drops are due to the presence of patterns that are quite different from the canonical PNA and NAO structures. Figure 7 provides a few examples of modes, which, although have been marked as NAO and PNA based on their highest degree of similarity, do not faithfully represent the NAO (PNA) circulation. The method we use requires us to label one of nine PCs as NAO and one as PNA, even though these patterns do not accurately capture the NAO (PNA) circulation. Although Baxter and Nigam (2013) found that NAO and PNA patterns are little sensitive to the number of rotated components, our findings suggest that under certain conditions, an inappropriate number of rotated PCs can affect even the most prominent modes.
Illustration of modes identified as NAO or PNA, which substantially deviate from canonical NAO or PNA patterns.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
5. Ensemble members
The ensemble members characterize uncertainty in data and can help reveal whether detected changes in spatial patterns are random or not. Figure 8 shows the explained variance and degree of similarity of NAO and PNA obtained for each ensemble member. The early periods exhibit higher variability among members. In both 20CRv3 and 20CRv2, the variability explained by NAO varies between 9% and 15%. The variance explained by the ensemble mean NAO is consistently higher than that of individual members, which is in line with the findings of PH23. In the mid- to late periods, the spread among individual members of the ensemble is diminishing. The sudden drops and rises in the explained variance or degree of similarity occur occasionally among ensemble members; they seem to become more frequent after about 1941–80. Moreover, around 1962–2001, the vast majority of ensemble members experienced a drop in the explained variance or degree of similarity. Similar to the results observed in the ensemble mean, this further indicates a genuine phenomenon and a change in variability that is consistently present across all employed reanalyses.
As in Fig. 4, but additionally with individual ensemble members (thin lines).
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
During the early periods, there is also a high variability in the explained variance of PNA across ensemble members (Fig. 8). The values are more widely dispersed, ranging from 8% to 18%. The ensemble means of 20CRv2 and 20CRv3 almost consistently explain less variability than individual ensemble members. As we have previously demonstrated (PH23), this effect arises from the process of averaging to obtain the ensemble mean. This is evident in the weaker centers over Canada and the southern United States during the early periods. Figure 9 displays ensemble members with the highest and lowest similarity and the ensemble mean in the initial period for both 20CRv3 and ERA-20C. While the dispersion of centers is more pronounced for PNA, we observe a higher level of agreement for NAO. This characteristic is consistent across all surface-input reanalyses, including 20CRv2 (PH23), 20CRv3, and ERA-20C. We conclude that the model’s ability to generate variability over remote areas is not restricted by a lack of assimilated data. However, this results in a loss of variability in ensemble mean fields due to the averaging process.
The NAO and PNA patterns for the ensemble members (identified by small numbers left of the map for the PNA pattern) with (top) the lowest congruence coefficient, (middle) highest congruence coefficient, and (bottom) the ensemble mean in the initial period of 20CRv3 and ERA-20C.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
The sudden drops and rises in the degree of similarity mainly occur during the early periods in 20CRv2, while in 20CRv3, they are mostly present in periods around 1900–39. There are also some drops and rises shortly before the period 1940–79. However, there is no temporal correspondence between the reanalyses: Drops in 20CRv2 and ERA-20C occur earlier, while drops in 20CRv3 occur later. Thus, there is no indication that the sudden changes in PNA are caused by factors that are present in all the reanalyses.
6. Discussion
The presented results show two types of shifts and changes. The gradual long-term shifts and sudden changes from period to period. We have recognized a slight eastward shift of the northern center of NAO, which is present in all employed reanalyses but NCEP/NCAR (supplemental material 1). These results follow findings of Jung et al. (2003), Wang et al. (2012), or Moore et al. (2013). However, we did not find evidence of a consistent and gradual shift in the position of the southern center of NAO. As demonstrated by Vietinghoff et al. (2021), locations of both centers are subject to fluctuations, resulting in a zigzag rather than a narrow gradual pathway. The NCEP/NCAR reanalysis has the shortest duration and lowest resolution, which both may be factors contributing to the absence of a pronounced eastward shift.
Various factors have been proposed to account for this eastward shift, including the impact of greenhouse gases (Ulbrich and Christoph 1999), storm track changes (Luo et al. 2010), the strength of the background flow (Luo and Gong 2006), stratospheric circulation patterns (Dong et al. 2011), variations in solar activity (Gimeno et al. 2003), or the Atlantic multidecadal oscillation (Börgel et al. 2020). However, the studies differ in design and time scale and thus do not necessarily result in detectable shifts in patterns derived by PCA from 40-yr periods. The majority contributions, however, can slightly modify the distribution of total variance over a certain area and, consequently, the final patterns of modes. As we have demonstrated, PCA-derived patterns of modes can be sensitive to the analyzed period and even to slight modifications of the total variance fields.
Nevertheless, all the long-term reanalyses can capture the eastward shift when using moving PCA. Interestingly, the degree of similarity for NAO exhibits a remarkably consistent temporal development across all reanalyses. Specifically, a decline followed by an increase is observed around the period 1962–2001, which manifests itself as a slight southward shift of the NAO pattern, followed by its subsequent northward shift. This is evident in all reanalyses regardless of the model and assimilated data used; therefore, this feature is likely real.
On the other hand, the drop between two consecutive moving periods occurs although total variance remains almost unchanged (see the geographical distribution of variance in Fig. 10). We offer the following interpretation of sudden changes in the spatial structure of modes: PCA picks individual autocovariance patterns as PCs, which collectively approximate total variance best. There may be two competing patterns with a very close relevance to PCA, which then may pick one of them in one period and the other in the next period. This demonstrates itself in a sudden shift of spatial pattern of a mode without any noticeable change in the variance structure. However, more investigation of this phenomenon is needed.
Standard deviation of 500-hPa geopotential heights in consecutive periods 1961–2000 and 1962–2001 for the ensemble mean of 20CRv3. The contour interval is 10 m.
Citation: Journal of Climate 38, 6; 10.1175/JCLI-D-24-0037.1
During the analyzed period (see supplemental material 2), the PNA structure undergoes significant changes. All reanalyses exhibit a slow, gradual northward shift and shrinkage of the center over Canada. However, we do not recognize any eastward shift described in literature (Lee et al. 2012; Chien et al. 2019). In the ensemble mean, PNA tends to explain less variance compared to individual ensemble members. The phenomenon of lower variability in ensemble mean fields compared to ensemble members was also documented by Wang et al. (2013) in their analysis of cyclone tracks in data-sparse regions during the nineteenth century. Similarly, Rohrer et al. (2019) reported significant inhomogeneities in the variability of storm tracks prior to 1950 when comparing surface-input reanalyses.
7. Conclusions
In this study, we compared spatial structures of NAO and PNA and their development in time across five reanalyses, viz., 20CRv2, 20CRv3, ERA-20C, ERA5, and NCEP/NCAR. We employed winter monthly mean anomalies of 500-hPa geopotential heights of ensemble mean fields as well as of all ensemble members. Both full-length periods of each reanalysis and moving 40-yr periods with a 1-yr step are analyzed. We presented spatial shifts of NAO and PNA since the mid-nineteenth century, as well as changes in the variance explained by the modes and the similarity degree between the modes defined for the full periods and for the 40-yr periods.
The leading mode in all ensemble mean datasets is NAO, followed by PNA as the second mode. However, the order is reversed in ensemble members, especially in 20CRv2 and ERA-20C. The ensemble mean NAO, calculated for the full period, explains substantially more variability than NAO in all individual ensemble members in all long-term reanalyses (20CRv2, 20CRv3, and ERA-20C). The opposite tendency is observed for PNA in both versions of 20CR but not in ERA-20C. The variability in the results among ensemble members is higher for PNA than for NAO in the long-term reanalyses. This discrepancy arises from the lack of assimilated observations in data-sparse regions, which limits the model’s ability to constrain variability during earlier periods. However, this is not observed in ERA5 (for which the variability among ensemble members is low because it is limited to later periods when reanalysis members are well constrained by observations; moreover, ERA5 assimilates much more observations than the long-term reanalyses do, which even more constrains individual ensemble members toward the mean). The results demonstrate that the use of ensemble mean from long-term reanalyses may overestimate the variability explained by NAO.
All the described results, that is, the explained variance, the order of modes, and spatial changes are closely related to each other. A sudden drop in similarity indicates considerable spatial shifts of modes and changes that are often associated with a decrease in the explained variance and, consequently, in a change in the order of modes. The biggest differences between NAO and PNA are seen during the early periods. Specifically, the dominance of NAO is observed in 20CRv2 and 20CRv3, PNA being considerably weaker. This effect is attributed to the process of averaging the ensemble members to obtain the ensemble mean. However, this effect is absent in other reanalyses. Therefore, we may conclude that assimilated data sufficient to reproduce PNA in the ensemble mean fields has been available since the early twentieth century, while the constraint of reanalyses by observations in the nineteenth century is weak. The lack of constraint particularly over the North Pacific results in different patterns of PNA developing in individual ensemble members, which leads to a smoothed field and weak PNA in the ensemble mean. Therefore, we strongly recommend using ensemble members instead of only the ensemble mean prior to 1900 when analyzing low-frequency variability in 20CRv2 or 20CRv3.
Individual reanalyses differ in the amount and type of data assimilated, the length of the period, or even the model itself. Nevertheless, our results demonstrate that the trends in explained variance and spatial changes of both PNA and NAO are similar among the reanalyses. The eastward shift of the northern center of NAO was observed in all datasets except for NCEP/NCAR, which is the shortest reanalysis with the lowest resolution among those employed. There is also a slow northward shift and shrinkage of the PNA center over Canada that is present in all reanalyses. We conclude that temporal changes detected in our study, including long-term trends, are likely to have a fundamental basis. However, the sudden changes from period to period are at least in their part artifacts arising from the reanalyses or the PCA algorithm itself.
We have identified a decrease in the similarity degree of the NAO pattern during the periods around 1962–2001 consistent across all employed datasets. This decline in the congruence coefficient is linked to a sudden southward shift in the mode, indicating a change in variability present in the reanalyses, irrespective of the assimilation data source or model used. Nevertheless, further investigation into this topic is needed.
Acknowledgments.
This research was supported by the Czech Science Foundation, project 17-07043S. V. P. was also supported by the Grant Agency of Charles University, student project 426216.
Data availability statement.
The data that support the findings of this study are openly available in the NOAA Physical Sciences Laboratory (PSL) at https://psl.noaa.gov/data/gridded/data.20thC_ReanV2.html (Compo et al. 2011), https://psl.noaa.gov/data/gridded/data.20thC_ReanV3.html (Slivinski et al. 2019), and https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html (Kalnay et al. 1996); the Climate Data Store (CDS) Catalogue at https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels-monthly-means (Hersbach et al. 2020); and the ECMWF Archive Catalogue at https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-20th-century-using-surface-observations-only (Poli et al. 2016).
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