1. Introduction
Atmospheric circulation can be described in a number of ways, one of which is as modes of low-frequency circulation variability (hereafter referred to simply as “circulation modes”). They typically consist of two or more remote centers between which circulation variables (usually sea level pressure or geopotential heights) are highly (whether negatively or positively) correlated. Circulation modes influence not only conditions in free atmosphere, such as wind speed and direction, humidity, and temperature, but also climate variables at the ground.
Wallace and Gutzler (1981) were the first to have detected circulation modes (referred to as “teleconnections” by them) in the Northern Hemisphere in winter. They used one-point correlation maps for the detection. Pioneering studies in the 1980s (Horel 1981; Rogers 1981; Barnston and Livezey 1987) proved that rotated principal component analysis (PCA) is a suitable tool for identifying circulation modes. Most studies using PCA to detect circulation modes are based on correlation or covariance matrix of gridded geopotential heights or sea level pressure (e.g., Thompson and Wallace 2000; Huth 2006; Compagnucci and Richman 2008), although other options are also possible. The principle of PCA is to obtain a set of new variables (principal components), which are uncorrelated both in space and time. Circulation modes appear as a few leading components, which explain high amounts of variance. Every component (mode) is characterized by its eigenvalue (which quantifies the variance that the component explains), loading, and score. In the setting of PCA used for detection of circulation modes, loadings are maps of correlations or covariances of the modes with the original data field, while scores are time series quantifying the intensity of the mode at a particular time instant (e.g., a month if monthly means are used as data input). Rotation of relevant principal components (i.e., a linear transformation of components into a new set of coordinates) is usually necessary to secure that the detected modes are realistic—that is, that they correspond to the underlying autocorrelations structures, represented by one-point autocorrelation maps (e.g., Richman 1986; Huth 2006; Compagnucci and Richman 2008; Lian and Chen 2012; Kohyama and Hartmann 2016). The realism of modes in this sense does not imply that they represent known dynamical processes. In fact, the association of individual modes with specific dynamical and physical processes is far from straightforward. The existence and maintenance of very few modes in the northern extratropics only has so far been explained in terms of physical processes, the North Atlantic Oscillation (NAO) being such an example (Spensberger et al. 2020).
The possible limitation of PCA is that it is a linear method, whereas many atmospheric processes contributing to variability of atmospheric circulation are nonlinear. Although some attempts have been made to extend the concept of PCA toward nonlinearity by using artificial neural networks and to implement nonlinear PCA to studies of atmospheric circulation (Monahan 2000; Hsieh 2004; Teng et al. 2007), this research direction appears to have been abandoned later. The possible reasons are that the interpretation of outputs of nonlinear PCA is much less straightforward, the calculations require substantially more computer time, and nonlinearity tends to be detected even where none in fact exists (Christiansen 2005).
The choice of specific parameters in PCA influences both spatial structure and temporal behavior of circulation modes. First, one has to make a decision on whether a correlation or covariance matrix is employed. Huth (2006) demonstrates that spatial structure of circulation modes is influenced only marginally by this choice. Second, there are several approaches to account for a decreasing area of grid boxes toward the pole, which may affect spatial representation of circulation modes. And finally, the number of principal components to be retained and rotated must be determined.
Any method to describe and analyze atmospheric circulation captures only a part of the continuum of its variability. Certain uncertainty is inherent to all approaches: for example, the choice of the detection and tracking method in analyses of blockings and cyclone tracks (Ulbrich et al. 2009; Woollings et al. 2018) and the choice of the classification method and number of types in classifications of circulation patterns (Stryhal and Huth 2017). In analyses of circulation modes, this uncertainty is manifested in the sensitivity to the number of modes (i.e., number of components rotated). We chose the particular methodology, which is described below, with the objective to minimize these uncertainties.
Reanalyses are the most suitable datasets for identification of circulation modes because they contain data on a regular grid. Reanalyses are produced by a numerical weather prediction model, into which the observed data are assimilated. However, both the model characteristics (resolution, model configuration, data assimilation design, etc.) and assimilated observations (their quantity, quality, and coverage) cause differences between individual reanalyses. Wang et al. (2013) note that uncertainty in reanalyses is brought about by temporal changes in the amount of assimilated data. The introduction of satellite observations after 1979 (e.g., Sturaro 2003; Dee and Uppala 2009; Dee et al. 2011) and operational vertical sounder after 1998 (Fujiwara et al. 2017; Long et al. 2017) have also been reported to cause inhomogeneities in reanalyses. All these potential biases and discontinuities, which project into reanalyses, may also affect the circulation modes.
Reanalyses differ in the data they assimilate: surface-input reanalyses make use of surface data only, such as pressure, surface winds, sea ice distribution, and sea surface temperature, whereas full-input (standard) reanalyses use also observations of free atmosphere, including radiosonde and satellite data (Fujiwara et al. 2017). In surface-input reanalyses, data in free atmosphere are completely calculated by the model and are constrained by surface observations only, which is also likely to introduce bias. Surface-input reanalyses cover more than a century-long period, starting at least in the beginning of the twentieth century. Full-input reanalyses span a shorter time period when radiosondes are routinely available (approximately since the middle of the twentieth century).
Intercomparisons of reanalyses generally conclude that differences between them are mostly small over areas with a high density of observational data, while considerably larger where data are sparse (Harnik and Chang 2004; Wang et al. 2006; Bromwich et al. 2007; Hodges et al. 2011; Wang et al. 2016). Furthermore, various processes and phenomena in the upper atmosphere are poorly reproduced or completely absent in surface-input reanalyses simply because data from the free atmosphere are not available to them. For example, a rather unreal response of the upper troposphere and stratosphere to volcanic eruptions (Fujiwara et al. 2015), missing sudden stratospheric warmings and quasi-biennial oscillation (Pišoft et al. 2013; Butler et al. 2017), an overestimation of 500-hPa geopotential heights over Greenland in summer (Belleflamme et al. 2013), fewer cyclones in the Northern Hemisphere (Wang et al. 2016), stronger easterlies and higher blocking activity over Europe (Rohrer et al. 2018), and lower occurrence of westerly and northwesterly circulation types (Stryhal and Huth 2017) have been detected in 20CRv2 relative to full-input reanalyses. The last study points to a considerably different representation of circulation types in reanalyses even over the data-rich region of central Europe. On the other hand, major storm tracks in the Northern Hemisphere in 20CRv2, ERA-20C, and JRA-55 agree well with radiosonde observations, in contrast to NCEP-1 and ERA-40 where large biases were detected (Chang and Yau 2016).
Representation of cyclones in full-input reanalyses shows rather good agreement (Zahn et al. 2018). The number of pressure formations over the Northern Hemisphere appears to depend on the horizontal resolution: the reanalyses with a higher resolution, such as MERRA and ERA-Interim, produce more cyclones with stronger intensity (Tilinina et al. 2013; Wang et al. 2016; Pingree-Shippee et al. 2018) and also more anticyclones (Pepler et al. 2018). Differences in the number of cyclones between NCEP-1 and ERA-40 were reported by Trigo (2006) and Wang et al. (2006).
We are not aware of any study that would compare reanalyses from the point of view of circulation modes. This paper is intended to fill this gap, its goal being to compare the spatial representation of circulation modes between five reanalyses that have been most commonly used in climatological studies recently. We intentionally investigate circulation modes in all seasons since only few studies analyze circulation modes in other seasons than winter and if so, they typically focus on the strongest modes, such as the NAO (e.g., Folland et al. 2009; Linderholm et al. 2011; Sun and Wang 2012; Lin 2014; Soulard and Lin 2017). No study that looks at all the modes in the northern extratropics in all seasons has been published for more than 25 years (i.e., since the reanalyses have become available and widely used). We evaluate the realism of the modes in the statistical sense, that is, whether and to what extent they correspond to the underlying correlation structures; it is not our intention to associate the modes with physical and dynamical processes that induce and maintain them. The analysis is performed by rotated PCA of 500-hPa heights in the Northern Hemisphere extratropics.
2. Data and methodology
We evaluate five widely used reanalyses (Table 1) that cover the period from September 1957 to August 2002 (i.e., 45 years altogether). The exception is JRA-55, which starts only in January 1958; its analysis period is therefore shifted one season forward, covering March 1958–February 2003, so that the number of months in each season is equal in all reanalyses (135). Our choice of reanalyses has been governed by two requirements: 1) we examine reanalyses that have been frequently utilized in climatological studies, and those of atmospheric circulation and variability modes in particular, and 2) we intend to cover the longest possible period in which all the reanalyses overlap. Moreover, the period covering a sufficiently long time both before and after 1979 enables us to evaluate the impact of the assimilation of satellite data in full-input reanalyses (see section 4d).
Reanalyses used in this study, their category, and references.
PCA in S-mode (i.e., with grid points arranged in columns and months in rows of the input data matrix) with a correlation matrix is employed for identification of circulation modes in the Northern Hemisphere extratropics delimited by 20°N. Circulation modes are calculated for each season separately—winter (DJF), spring (MAM), summer (JJA), and autumn (SON). Monthly anomalies of 500-hPa geopotential heights from the long-term monthwise average are used. Computation of circulation modes is performed on the grid with 5° × 5° resolution. All reanalyses except 20CRv2c are directly downloaded in 2.5° × 2.5° resolution; then only every other point in both directions is included in the analysis. 20CRv2c is downloaded in its original resolution (2° × 2°) and subsequently interpolated by spline interpolation to 2.5° × 2.5°.
Because meridians converge toward the pole, there is higher density of points in the vicinity of polar regions. There are some options how to deal with this issue (Huth 2006); here we opt for using a quasi-equal-area grid where points are randomly excluded from the regular latitude–longitude grid so that the mean area of a grid box is approximately the same for all parallels (Araneo and Compagnucci 2004). The number of excluded points increases toward the pole while all of them are kept on parallels in low latitudes. The exact position of excluded points does not affect the shape of circulation modes (Huth 2006). The total number of grid points included in the analysis is 699, the North Pole being excluded.
The components are rotated by varimax rotation (Richman 1986), which leads to a better representation of modes. There are several criteria to determine the optimum number of rotated components, which may give outputs differing even more than by an order of magnitude (e.g., Serrano et al. 1999). Here we follow O’Lenic and Livezey (1988), who recommend a criterion based on a scree plot (i.e., graph showing the dependence of variance explained by each component on its rank) where the components are ordered by explained variance. The general guidance is that the components should be cut at a noticeable drop (step) in the graph; typically, the rightmost drop (i.e., the largest possible number) is chosen. In an ideal case, the drop is clearly present and occurs for the same number of components for all reanalyses. In reality, however, one has to make compromise between the presence of a drop, the amount of explained variance, the stability of the modes (the stability meaning here the insensitivity of their spatial patterns to the number of rotated components), and their similarity across reanalyses, which makes the determination of the optimum number of components to rotate a subjective task to some extent. Figure 1 displays the scree plots for all the four seasons, with candidate drops and the rotated numbers of components highlighted. Note that in summer, the eigenvalue spectra are rather flat, without pronounced drops, with the exception of ERA-40, in which the candidate drop is localized to the 14th component; that position is therefore used to approximate the number of components to rotate in other reanalyses, too.
Scree plots with 20 leading principal components and the percentage of their explained variance (on the y axis) in five reanalyses for individual seasons. Red dots show the numbers of rotated components that we apply; green dots show candidate drops, i.e., the numbers of components complying with O’Lenic and Livezey’s (1988) criterion. The graphs are indented from each other by 0.01 in order to facilitate display.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Scree plots with 20 leading principal components and the percentage of their explained variance (on the y axis) in five reanalyses for individual seasons. Red dots show the numbers of rotated components that we apply; green dots show candidate drops, i.e., the numbers of components complying with O’Lenic and Livezey’s (1988) criterion. The graphs are indented from each other by 0.01 in order to facilitate display.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Scree plots with 20 leading principal components and the percentage of their explained variance (on the y axis) in five reanalyses for individual seasons. Red dots show the numbers of rotated components that we apply; green dots show candidate drops, i.e., the numbers of components complying with O’Lenic and Livezey’s (1988) criterion. The graphs are indented from each other by 0.01 in order to facilitate display.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
The number of components that we interpret, compare between reanalyses, and discuss may be different from (i.e., smaller than) the number of components rotated (Table 2). This is because we have to seek a compromise between the interpretability and realism (in terms of the correspondence with correlation structures) of all the rotated modes and their stability and similarity between reanalyses. That is, in some cases (combinations of reanalysis and season) it is necessary to rotate more components than how many modes seem to actually occur. There are two reasons for it. First, if the lower number of components, equal to the number of really occurring modes, is rotated, one of the really occurring modes is, somewhat paradoxically, not detected; it only appears in the analysis if an additional component is included into rotation. Second, the rotation of the lower number of components results in a substantially lowered similarity of the modes with other reanalyses; this happens because of a somewhat random redistribution of variance among the rotated modes. As we intend to maximize the similarity of modes between reanalyses, we sacrifice the use of the “correct” number of modes to this maximization in some cases. The additional modes typically do not correspond to autocorrelation structures and/or are different in individual reanalyses; therefore, we tend to look at them as representations of noise and do not keep them in the further analyses and discussions.
Number of rotated and used principal components and variance explained by the rotated modes.
Loadings represent correlations between the principal component and monthly mean 500-hPa heights. Therefore, statistical significance of differences between loadings is evaluated as statistical significance of a difference between correlations, that is, with the use of Fisher transformation: correlation coefficients r1, r2 are transformed to (Huth et al. 2006; Pokorná and Huth 2015)
and the test statistic is then
where ni is the sample size. We are entitled to employ Fisher transformation because the principal component loadings are approximately normally distributed. The number of grid points with a significant difference between reanalyses closely approximates the area of the northern extratropics where loadings are significantly different from each other. That area is then weighted by the area where the loading is significantly different from zero in at least one of the two compared reanalyses. Thus, a proportion (in %) of the area with nonzero loadings where the differences of loadings between reanalyses are significant is calculated.
The terminology of circulation modes (Table 3) is adopted from Barnston and Livezey (1987, hereinafter BL). The modes not recognized in BL are identified by their rank according to the variance explained in ERA-40 (e.g., “mode 3” if it explains the third largest amount of variance), unless explicitly stated otherwise. The polarity of loadings as provided by PCA is random to some extent; we set the polarity to be equal to modes in BL. The polarity of the modes not appearing in BL follows that in ERA-40.
Abbreviations and full names of circulation modes.
3. Results
a. General characteristics of circulation modes
In this section, general remarks on differences between reanalyses and a brief explanation of some methodological options are provided.
The variance explained by the retained and rotated principal components is roughly similar in all reanalyses; the spread is of the order of a few percent, with the largest (5.5%) occurring in summer (Table 2). In winter and autumn, 9–10 circulation modes are identified in all reanalyses. Circulation modes in winter explain more variance due to a stronger and more pronounced circulation, the spatial structures of which are larger than in other seasons and concentrate in fewer modes as a result. Autumn, on the contrary, is the season with the lowest explained variance (Table 2), which is caused by a relatively small number of detected modes (the drop in Fig. 1 occurs after the 10th mode). However, the rotation of more than 10 components, that is, a larger share of variance explained, in autumn does not bring additional interpretable modes; that is why we deem that a relatively low explained variance in autumn is a real feature. In spring and summer, circulation is generally more scattered and regionalized, with a shorter autocorrelation distance. More circulation modes (12–14) with somewhat lower explained variance are needed to reasonably describe it.
The normalized percentage of grid points with significant differences between loadings was calculated for all pairs of reanalyses, all circulation modes, and all seasons. It is presented in Fig. 2 where boxplots display the percentage of grid points with significant differences of all circulation modes between all pairs of reanalyses in all seasons. The higher the values of boxplot, the lower the similarity of the two compared reanalyses. Generally, reanalyses have the highest agreement in winter and autumn, while the lowest agreement is found in summer. In winter, spring, and also in summer, the different behavior of surface-input reanalyses, which exhibit larger differences from the other reanalyses, is evident. In autumn, the distinction of the two groups of reanalyses is not visible: the differences are rather similar among reanalyses and tending to concentrate in the circulation modes sensitive to the number of rotated components (see section 3e).
Tables with boxplots showing the normalized proportion (%) of grid points with significant differences (for a detailed explanation see text) for all pairs of reanalyses in all seasons. The central line of the boxplot is the median; the lower and upper edges denote the lower and upper quartile. The upper and lower whiskers extend to 1.5 times the interquartile range from the respective edges, with the outliers lying beyond the whiskers denoted by dots.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Tables with boxplots showing the normalized proportion (%) of grid points with significant differences (for a detailed explanation see text) for all pairs of reanalyses in all seasons. The central line of the boxplot is the median; the lower and upper edges denote the lower and upper quartile. The upper and lower whiskers extend to 1.5 times the interquartile range from the respective edges, with the outliers lying beyond the whiskers denoted by dots.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Tables with boxplots showing the normalized proportion (%) of grid points with significant differences (for a detailed explanation see text) for all pairs of reanalyses in all seasons. The central line of the boxplot is the median; the lower and upper edges denote the lower and upper quartile. The upper and lower whiskers extend to 1.5 times the interquartile range from the respective edges, with the outliers lying beyond the whiskers denoted by dots.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Figure 2 also helps determine the most representative reanalysis, which we use as a reference for the display of circulation modes thereinafter. We select from full-input reanalyses, which should be, considering the amount of assimilated data, more reliable and opt for ERA-40 because it exhibits the lowest differences from 20CRv2c and ERA-20C in all seasons but spring (Fig. 2). Circulation modes in ERA-40 are displayed and discussed later; modes in other reanalyses are displayed for all seasons in the online supplemental material in Figs. S1–S4 in the online supplemental material. The modes are displayed in the order of the explained variance in the particular reanalysis.
b. Winter
All circulation modes in ERA-40, the normalized percentage of the area where all pairs of reanalyses significantly differ from each other, and correlations of scores between all circulation modes in all pairs of reanalyses are displayed in Fig. 3. Most of the circulation modes identified in winter in ERA-40 are highly similar to those in BL. Three most prominent modes in ERA-40 are WPO, NAO, and PNA. The variance that all the modes together explain in individual reanalyses is in the range of 69%–72%.
(top right) Circulation modes in winter in ERA-40: PCA loadings (contour interval is 0.2; positive contours are solid, negative contours are dashed; zero contour is omitted for the sake of clarity), their abbreviated name, and percentage of explained variance are shown below the maps. (top center) Proportion (%) of area with statistically significant differences between loadings normalized by the area with nonzero loadings. (top left) Correlation of scores for all pairs of reanalyses. (bottom) Pairs of reanalyses are denoted by symbols defined in the bottom table.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(top right) Circulation modes in winter in ERA-40: PCA loadings (contour interval is 0.2; positive contours are solid, negative contours are dashed; zero contour is omitted for the sake of clarity), their abbreviated name, and percentage of explained variance are shown below the maps. (top center) Proportion (%) of area with statistically significant differences between loadings normalized by the area with nonzero loadings. (top left) Correlation of scores for all pairs of reanalyses. (bottom) Pairs of reanalyses are denoted by symbols defined in the bottom table.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(top right) Circulation modes in winter in ERA-40: PCA loadings (contour interval is 0.2; positive contours are solid, negative contours are dashed; zero contour is omitted for the sake of clarity), their abbreviated name, and percentage of explained variance are shown below the maps. (top center) Proportion (%) of area with statistically significant differences between loadings normalized by the area with nonzero loadings. (top left) Correlation of scores for all pairs of reanalyses. (bottom) Pairs of reanalyses are denoted by symbols defined in the bottom table.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
The spatial differences and correlations of scores are closely related, which is evident in Fig. 3 (top center and left): larger differences between loadings correspond to lower correlations of scores and vice versa. Perfectly spatially matching modes would have identical temporal course of scores; the scores of modes with entirely dissimilar spatial patterns would have uncorrelated scores. The information provided by comparisons of loadings and comparisons of scores thus largely overlaps; therefore, we limit the display and discussion of differences in the further text to the spatial representation of loadings.
The differences between reanalyses are largest for two Eurasian modes, EU1 and EU2 (Fig. 3, top left). EU1 consists of a positive center over northern Europe and two negative centers—one over northern Asia and another, less pronounced, over southwestern Europe. In 20CRv2c, all of its centers have a different shape or position (Fig. 4a): the negative center over southwestern Europe is shifted northeastward, the main positive center is shifted eastward to northeastern Europe and the negative Asian center is located more southeastward, approximately over northwestern China. Additionally, the latter is stronger and more extensive in 20CRv2c. The different position and shape of centers is the main cause of spatial dissimilarity between 20CRv2c and other reanalyses, which is confirmed by the position of points with significant differences in the top-right map in Fig. 4a. Autocorrelation maps for the two grid points with the highest and lowest loadings in ERA-40 and 20CRv2c (Fig. 4b) localize the differences to southern and southeastern parts of Asia where one can see different magnitudes of autocorrelations. It is particularly evident in the autocorrelation maps for the eastern center (Fig. 4b, right column). Since autocorrelation maps in the other reanalyses for the same grid points as in Fig. 4b are very similar to those in ERA-40 (not shown), one may conclude that the differences manifest different behavior of 20CRv2c over southern half of Asia, which is likely why EU1 is displayed in 20CRv2c differently from other reanalyses.
(a) EU1 in winter in 20CRv2c and ERA-40 and the position of grid points with significant differences in loadings between 20CRv2c and ERA-40. (b) Autocorrelation maps for the grid points with the most positive (crosses) and negative (dots) loadings in (top) ERA-40 and (bottom) 20CRv2c; 20CRv2c in red, ERA-40 in gray.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) EU1 in winter in 20CRv2c and ERA-40 and the position of grid points with significant differences in loadings between 20CRv2c and ERA-40. (b) Autocorrelation maps for the grid points with the most positive (crosses) and negative (dots) loadings in (top) ERA-40 and (bottom) 20CRv2c; 20CRv2c in red, ERA-40 in gray.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) EU1 in winter in 20CRv2c and ERA-40 and the position of grid points with significant differences in loadings between 20CRv2c and ERA-40. (b) Autocorrelation maps for the grid points with the most positive (crosses) and negative (dots) loadings in (top) ERA-40 and (bottom) 20CRv2c; 20CRv2c in red, ERA-40 in gray.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Differences in the appearance of EU2 are illustrated for ERA-20C and NCEP-1 in Fig. 5. They have their roots in the sensitivity to the number of rotated principal components: Fig. 5 shows that 9 and 10 rotated components result in different shapes of EU2 in both reanalyses. The difference concentrates particularly in the negative Eurasian center, which is smaller and has no extension toward eastern Eurasia in NCEP-1 for 10 rotated components. Also the main positive center over Europe/North Atlantic is shifted and has a slightly different shape. EU2 looks very similar in both reanalyses if 9 components are rotated, but the similarity is much lower for 10 rotated components. This is a manifestation of the compromise in the number of components to rotate; a better overall correspondence of modes between reanalyses is achieved at the expense of a reduced correspondence for one particular mode. If we decided to rotate 9 instead of 10 components, the better correspondence of reanalyses in the display of EU2 would be outweighed by a generally worse correspondence for most other modes.
EU2 in winter in NCEP-1 and ERA-20C for 9 and 10 rotated components.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
EU2 in winter in NCEP-1 and ERA-20C for 9 and 10 rotated components.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
EU2 in winter in NCEP-1 and ERA-20C for 9 and 10 rotated components.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
c. Spring
In spring, 12 circulation modes are identified (Fig. 6). Circulation modes explain roughly about 69% of variance in all reanalyses. The most prominent modes in ERA-40 are SZ, NP, and WPO (see Table 3 for expansions of mode names). SZ is, however, absent in 20CRv2c; it does not appear even if different (smaller or larger) numbers of components are rotated. It seems to be at least partly attached to WPO, being reflected in its stronger zonal center over subtropical Eurasia, and to the third mode (explaining 6.8% of variance, not appearing in any other reanalysis, and denoted as “xxx” in Fig. S1), which forms a strong center over Asia. The highest differences are, similarly to winter, revealed between surface-input and full-input reanalyses. The differences are particularly large for WPO and NAO (Fig. 6), which we discuss below.
As in the center and right top part of Fig. 3, but for spring. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center and right top part of Fig. 3, but for spring. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center and right top part of Fig. 3, but for spring. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
WPO consists of two main zonally elongated centers over the North Pacific along the 50° and 25°N parallels, both attaining maximum loadings near the date line. The representation of the southern center is fairly different in the three reanalyses shown in Fig. 7a. In 20CRv2c, it forms a long belt over the subtropics almost around the globe. This belt is particularly strong over Eurasia and northern Africa and also over large parts of Pacific Ocean as is documented by the position of points with significant differences from ERA-40 in Fig. 7a. On the other hand, the belt over the subtropics is weaker, shifted northward, and confined to the Pacific in ERA-20C. The northern center has also a different shape and position in the three reanalyses, but the difference is less pronounced. The autocorrelation maps for the grid point with the highest loading in the subtropical center provide no clue for a different appearance of WPO in different reanalyses (left column in Fig. 7b) since they look fairly similar in all three reanalyses. This suggests that reanalyses do not differ from each other in correlations within the subtropical belt. There are, however, some differences in correlations of the subtropical belt with the WPO northern center. Although the differences are rather weak, they are notable: the autocorrelations tend to be strongest and their values over 0.2 to be most spatially extensive for 20CRv2c, while weakest and least extensive for ERA-20C. The extent and strength of subtropical autocorrelations with the WPO northern center are thus in agreement with the strength and spatial extent of the southern center of WPO: they are largest and strongest in 20CRv2c, moderate in ERA-40, and smallest and weakest in ERA-20C.
(a) WPO in spring in three reanalyses in the top row and the position of grid points with significant differences in loadings between the reanalyses in the bottom row. (b) Autocorrelation maps for the points with the most positive (red dots) and negative (red crosses) loadings in 20CRv2c for 20CRv2c, ERA-20C, and ERA-40.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) WPO in spring in three reanalyses in the top row and the position of grid points with significant differences in loadings between the reanalyses in the bottom row. (b) Autocorrelation maps for the points with the most positive (red dots) and negative (red crosses) loadings in 20CRv2c for 20CRv2c, ERA-20C, and ERA-40.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) WPO in spring in three reanalyses in the top row and the position of grid points with significant differences in loadings between the reanalyses in the bottom row. (b) Autocorrelation maps for the points with the most positive (red dots) and negative (red crosses) loadings in 20CRv2c for 20CRv2c, ERA-20C, and ERA-40.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
The appearance of NAO is very different in 20CRv2c (Fig. 8a): in comparison with full-input reanalyses (note that NAO in NCEP-1 and JRA-55 is almost identical to ERA-40 as shown here), the negative North Atlantic center is weaker and less extensive, the positive southern center splits into two separated parts, and the southernmost negative center is completely missing. The entire pattern over the North Atlantic appears to be shifted southward in 20CRv2c. NAO in ERA-20C (Fig. S2) is more similar to full-input reanalyses than to 20CRv2c. Nevertheless, the surface-input reanalyses share the feature that additional centers over North America and North Pacific are attached to the NAO pattern. Autocorrelation maps for the two Atlantic centers of NAO in 20CRv2c (Fig. 8b, top) are fairly similar to ERA-40 (Fig. 8b, bottom). There is no hint in the autocorrelation maps for 20CRv2 of the link with the upstream center over the northeastern Pacific along 150°E. On the other hand, the southern Atlantic center tends to separate into two cores, one over the western Atlantic and the other over the western United States, in the autocorrelation maps for 20CRv2c, unlike those for ERA-40 where the southern Atlantic center is more compact. Autocorrelation maps for the western centers of NAO in 20CRv2c (middle row in Fig. 8b) exhibit only a very weak link with the Atlantic centers; they clearly resemble PNA, however, which itself is not detected in 20CRv2c as a separate mode. This suggests a (probably unrealistic) connection of NAO with PNA in 20CRv2c through exaggerated correlations between the two southern positive centers. The NAO in 20CRv2c is thus likely an amalgamation of two actually independent modes, PNA and NAO.
(a) NAO in spring in 20CRv2c and ERA-40. (b) Autocorrelation maps for the four points with the most positive (dots) and negative (crosses) loadings in 20CRv2c and ERA-40 (only for the pair of eastern points).
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) NAO in spring in 20CRv2c and ERA-40. (b) Autocorrelation maps for the four points with the most positive (dots) and negative (crosses) loadings in 20CRv2c and ERA-40 (only for the pair of eastern points).
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) NAO in spring in 20CRv2c and ERA-40. (b) Autocorrelation maps for the four points with the most positive (dots) and negative (crosses) loadings in 20CRv2c and ERA-40 (only for the pair of eastern points).
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
d. Summer
In summer, 14 circulation modes are identified (Fig. 9), although not all of them appear in all reanalyses (e.g., mode 11 occurs in the surface-input reanalyses only). Only six of the modes have been described earlier in BL. Total explained variance ranges from 64.3% to 69.8%. The four strongest modes in ERA-40 (SZ, NAO, mode 3, and NP) explain more than 4% of variance and are among the six most important circulation modes in all other reanalyses. Although most of summer circulation modes may seem to be rather weak (explaining only 3%–4% of variance), their realism is supported by autocorrelation maps (Figs. S5 and S6).
As in the center and right top part of Fig. 3, but for summer, with the exception of mode 11, which is taken from ERA-20C because it is not identified in ERA-40. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center and right top part of Fig. 3, but for summer, with the exception of mode 11, which is taken from ERA-20C because it is not identified in ERA-40. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center and right top part of Fig. 3, but for summer, with the exception of mode 11, which is taken from ERA-20C because it is not identified in ERA-40. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
The most prominent mode in summer, SZ, is characterized by a circumglobal belt in the subtropics and is noted for the highest spatial differences: for example, in 20CRv2c it is located farther south, especially in the Eastern Hemisphere, and lacks a ridge visible in all other reanalyses over central to eastern Asia (Fig. 10a and Figs. S1–S4). Yet, its representation is particularly different in NCEP-1; significant differences from other reanalyses are located over large regions of Eurasia and northern Africa, reflecting that SZ is stronger there than in other reanalyses, while being weaker over the western North Pacific and North America (Fig. 10a). This is confirmed in autocorrelation maps in Fig. 10b. Moreover, time series of SZ in NCEP-1 do not fit other reanalyses either, particularly before 1965 when SZ attains suspiciously negative values (Fig. 10c).
(a) SZ in summer in NCEP-1, JRA-55, and 20CRv2c and positions of the grid points with statistically significant differences between loadings. (b) Autocorrelation maps for the most positive loading from ERA-40 in NCEP-1 and ERA-40 (red dots). (c) Time series of scores of SZ in summer in NCEP-1, JRA-55, and 20CRv2c.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) SZ in summer in NCEP-1, JRA-55, and 20CRv2c and positions of the grid points with statistically significant differences between loadings. (b) Autocorrelation maps for the most positive loading from ERA-40 in NCEP-1 and ERA-40 (red dots). (c) Time series of scores of SZ in summer in NCEP-1, JRA-55, and 20CRv2c.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(a) SZ in summer in NCEP-1, JRA-55, and 20CRv2c and positions of the grid points with statistically significant differences between loadings. (b) Autocorrelation maps for the most positive loading from ERA-40 in NCEP-1 and ERA-40 (red dots). (c) Time series of scores of SZ in summer in NCEP-1, JRA-55, and 20CRv2c.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
e. Autumn
Ten circulation modes are identified in autumn, all of them being identified also in BL. The strongest modes are SZ, PNA, and EU1. The modes exhibit a relatively high resemblance between reanalyses (Fig. 11) except the two modes featuring a circumglobal belt in the subtropics, SZ and EA. Autumn is the only season when differences between surface-input and full-input reanalyses do not stand out.
As in the center and right top part of Fig. 3, but for autumn, with the exception of SZ, which is taken from ERA-20C because it is not identified in ERA-40. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center and right top part of Fig. 3, but for autumn, with the exception of SZ, which is taken from ERA-20C because it is not identified in ERA-40. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center and right top part of Fig. 3, but for autumn, with the exception of SZ, which is taken from ERA-20C because it is not identified in ERA-40. For the explanation of symbols in the left graph, see the bottom part of Fig. 3.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
SZ differs between reanalyses over vast parts of Eurasia and central and southern Atlantic (Fig. S7), which may imply different autocorrelation structures in reanalyses predominantly over the low latitudes. Weaker circulation variability there may also contribute to this difference. Moreover, SZ does not appear in ERA-40, even when fewer or more components are rotated. The circulation mode in ERA-40 closest to SZ is displayed in Fig. S7; however, its similarity with SZ is fairly low.
The representation of EA in JRA-55 and ERA-40 is different from the other reanalyses, which strongly contributes to the overall higher dissimilarity of the two reanalyses from the rest. It is, however, largely an artifact of PCA. EA in ERA-40 is sensitive to the number of rotated components as it exhibits a larger correspondence with other reanalyses if 11 instead of 10 principal components are rotated (Fig. 12), mainly because the circumglobal subtropical belt is detached from it. Nonetheless, a better agreement of most other circulation modes is achieved when 10 principal components are rotated, which is demonstrated by mode 6 and EU2 in Fig. 12: centers of both modes are shifted for 11 components, changing their appearance in comparison to the 10-component solution and worsening their correspondence with other reanalyses. This is the reason why rotation of 10 components is preferred, even though the spatial representation of EA has lower resemblance with other reanalyses then. In JRA-55, PCA cannot reveal the structure of EA similar to other reanalyses, even after various numbers of components are rotated. Nevertheless, the autocorrelation maps for centers of EA in JRA-55 resemble other reanalyses (Fig. S8), which suggests that a different appearance of EA in JRA-55 is again an artifact of the analysis method.
EA, mode 6, and EU2 in autumn in ERA-40 and NCEP-1 for 10 and 11 rotated components.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
EA, mode 6, and EU2 in autumn in ERA-40 and NCEP-1 for 10 and 11 rotated components.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
EA, mode 6, and EU2 in autumn in ERA-40 and NCEP-1 for 10 and 11 rotated components.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
4. Discussion
The previous section suggests that there are two major reasons for differences in how individual modes are identified in reanalyses: (i) real differences (biases) in correlation structures and (ii) reasons inherent to PCA, in particular the sensitivity of modes to the number of principal components rotated. Higher sensitivity to rotation appears in autumn when the spatial structure of a few circulation modes changes considerably with different numbers of rotated components. However, here we attempt to attribute the real differences in modes, which are not artifacts of the analysis method, to deficiencies known to exist in reanalyses.
a. 20CRv2c
Previous studies (van den Besselaar et al. 2011; Lindsay et al. 2014; Stryhal and Huth 2017; Rohrer et al. 2018) reported positive sea level pressure biases in 20CRv2(c) over Eurasia and Europe, mainly over its northeast, while larger agreement with NCEP-1 was found over oceans (Wang et al. 2013). However, we do not reveal any substantial differences in circulation modes over Europe. Our results localize possible biases in 500-hPa heights to southern half of Asia where both PCA and autocorrelation maps (Figs. 4 and 7) point to different shapes of, for example, EU1 in winter, WPO in spring, and SZ in autumn, summer, and spring in 20CRv2c. In spring, the peculiarities of 20CRv2c give rise to the mode centered over southern Asia that does not appear in any other reanalysis (third mode in the order of explained variance; denoted as “xxx” in Fig. S1).
Furthermore, the behavior of some circulation modes in spring (NAO and mode 6) and summer (e.g., NP, PT) in 20CRv2c suggests a different orientation of spatial autocorrelations over and near North America: 20CRv2c seems to have stronger autocorrelations across the continent, resulting, for example, in the merger of NAO with PNA in spring (Fig. 8b). This points to additional possible biases over the subtropical eastern Pacific and adjacent North America. To investigate whether these biases really occur and where exactly they are located, Pearson correlations of 500-hPa anomalies between 20CRv2c and full-input reanalyses are calculated; results are presented here for ERA-40 only (Fig. 13, left), which are very similar to all other reanalyses. Correlations tend to be lower in spring and summer and in low latitudes especially over southern half of Asia, northern Africa, and the eastern Pacific. This coincides with what the spatial structure of modes suggests: discrepancies over southern and central Asia between 20CRv2c and other reanalyses appear for EU1 in winter and partly also in summer and for SZ in spring, summer, and autumn; moreover, the third spring mode not appearing in any other reanalysis is located there. The low correlations over the subtropical eastern Pacific and southwestern North America correspond to a different behavior of NAO and mode 6 in spring and several Pacific circulation modes in summer.
(left) Pearson correlations of long-term (1957–2002) monthly 500-hPa anomalies between 20CRv2c and ERA-40 and (right) differences in the correlations between 20CRv2c and ERA-40 before and after 1980. Green dots indicate points for which time series are displayed in Fig. 14.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(left) Pearson correlations of long-term (1957–2002) monthly 500-hPa anomalies between 20CRv2c and ERA-40 and (right) differences in the correlations between 20CRv2c and ERA-40 before and after 1980. Green dots indicate points for which time series are displayed in Fig. 14.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
(left) Pearson correlations of long-term (1957–2002) monthly 500-hPa anomalies between 20CRv2c and ERA-40 and (right) differences in the correlations between 20CRv2c and ERA-40 before and after 1980. Green dots indicate points for which time series are displayed in Fig. 14.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
The number of assimilated surface pressure observations in 20CRv2c over “problematic” areas has increased since the 1970s (Cram et al. 2015). Hence, we calculated differences in correlations between ERA-40 and 20CRv2c separately for periods 1957–79 and 1980–2002 to examine whether the reported biases predominantly result from the shortage of assimilated data in the former period in 20CRv2c. The larger agreement of both reanalyses in the later period (Fig. 13, right) seems to reflect the increased amount of surface data in 20CRv2c, although one can find small areas with worse correspondence (e.g., over low latitudes of the Pacific Ocean in summer). Furthermore, we visualize time series of anomalies in 20CRv2c and ERA-40 at three grid points with low correlations (Fig. 14) located in southern Asia and Pacific. All of them share a similar feature: differences between the time series tend to be larger prior to 1980. After 1980, the convergence of both reanalyses is confirmed by an increase in correlations. Thus, we demonstrate that a peculiar behavior of several modes over southern half of Asia and in the eastern Pacific/southwestern North America domain in 20CRv2c is real, due to a different behavior of the 500-hPa height data, in particular before 1980.
Time series of 500-hPa anomalies in 20CRv2c and ERA-40 at three points denoted by green dots in the left panel of Fig. 13; r is the Pearson correlation coefficient.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Time series of 500-hPa anomalies in 20CRv2c and ERA-40 at three points denoted by green dots in the left panel of Fig. 13; r is the Pearson correlation coefficient.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
Time series of 500-hPa anomalies in 20CRv2c and ERA-40 at three points denoted by green dots in the left panel of Fig. 13; r is the Pearson correlation coefficient.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
The location of disagreement between 20CRv2c and other reanalyses in data-sparse regions suggests that insufficient assimilated data (only surface pressure, sea ice distribution, and sea surface temperature), and hence a little constraint of the reanalysis output by observations, are the likely cause of the discrepancies that we identified. This is supported by the fact that the correspondence of 20CRv2c with other reanalyses (as illustrated in Fig. 13 for ERA-40) has increased since the 1970s, which coincides with the period when the number of assimilated surface pressure (Cram et al. 2015) and also sea surface temperature observations (Woodruff et al. 2011) has increased.
b. ERA-20C
Interestingly, the other century-long reanalysis, ERA-20C, exhibits a better congruity with the other reanalyses than 20CRv2c, despite also assimilating surface observed data only. In fact, there is just one occasion when and where modes in ERA-20C differ from the rest of reanalyses: it is in spring over the northern North Pacific and eastern Asia where northern centers of WPO and NP are weaker in ERA-20C (Fig. 7 and Fig. S2). The different structure of WPO is also confirmed in autocorrelation maps (Fig. 7b); therefore, this discrepancy results from the reanalysis itself and is not a statistical artifact of PCA. An overall better correspondence of ERA-20C with full-input reanalyses (also Stryhal and Huth 2017) might be caused by assimilation of surface winds, which are lacking in 20CRv2c (Befort et al. 2016), or simply by another model used.
c. Full-input reanalyses
The mutual agreement of full-input reanalyses is fairly good, mainly between ERA-40 and JRA-55, although some spatial differences are detected. The most prominent is a different representation of SZ in summer in NCEP-1 (Fig. 10), which responds to errors detected in 500-hPa heights over Asia and partly northern Africa (Zhao and Fu 2009). These errors, which manifest also in the spatial structure of the EA mode (Fig. S9), result in an artificial increasing trend in 500-hPa heights prior to mid-1970s, accompanied by a sudden increase in sea level pressure in mid-1960s and early 1970s over eastern Asia (Inoue and Matsumoto 2004). The errors are manifestations of incorrect encoding of sea level pressure between 1948 and 1967 (Kistler et al. 2001); they are also reported by Wu et al. (2005), Yang et al. (2002), and Greatbatch and Rong (2006), the latter extending the area affected by the errors toward northern Africa.
d. Circulation modes before and after 1979
One would expect a better agreement of reanalyses after 1979 when satellite observations were introduced into full-input reanalyses, and the amount of pressure and sea surface temperature observations increased in surface-input reanalyses (section 4a). Hence, spatial differences between reanalyses are also computed separately for periods 1957–78 and 1979–2002. EU1 is not detected in the earlier period in any reanalysis and we do not find any support for its absence before 1979 in literature; therefore it is likely that its absence is a manifestation of sampling uncertainty due to a rather short analysis period.
Figure 15 clearly demonstrates a better correspondence of the majority of circulation modes in the later period, mainly between full-input reanalyses, in which the inclusion of satellite data results in their improved accuracy. Nevertheless, spatial structures of Eurasian modes NA and EU1 are different in surface-input reanalyses in the later period. The most likely explanation is again the uncertainty due to a short analysis period, although the biases in 20CRv2c over Eurasia may still affect circulation modes despite the higher congruence with ERA-40 after 1980 (section 4a).
As in the center top panel in Fig. 3, but for (left) 1957–78 and (right) 1979–2002. EU1 is not detected in the first period.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center top panel in Fig. 3, but for (left) 1957–78 and (right) 1979–2002. EU1 is not detected in the first period.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
As in the center top panel in Fig. 3, but for (left) 1957–78 and (right) 1979–2002. EU1 is not detected in the first period.
Citation: Journal of Climate 33, 24; 10.1175/JCLI-D-19-0904.1
In the period after 1979, several more recent reanalyses are available (CFSR; Saha et al. 2010; MERRA-2; Gelaro et al. 2017; ERA5; Hersbach et al. 2020). They assimilate larger amounts of data, and also additional data types (e.g., aerosol observations); therefore, a better agreement among them in representation of the modes may be expected. The comparison of circulation modes with those additional reanalyses may be a subject of a future research but only speculatively, we would expect large congruity with full-input reanalyses since all the reanalyses assimilate free atmosphere and satellite data.
5. Conclusions
Atmospheric reanalyses are often considered as almost perfect representations of a three-dimensional state of the atmosphere. However, they differ one from another in how they describe important atmospheric features, phenomena, and processes. This applies to atmospheric circulation as well. Here we analyze modes of atmospheric low-frequency variability, which have not been compared between reanalyses so far.
Circulation modes in the Northern Hemisphere extratropics are identified by rotated PCA of 500-hPa heights in individual seasons. A careful analysis is needed to distinguish real differences in the modes between reanalyses, reflecting differences in underlying autocorrelation structures, from differences caused by a particular application of PCA, most notably due to the sensitivity to the number of principal components rotated. The spatial structure of the modes appears, fortunately, to be fairly little sensitive to the particular choice of the number of components. In a few cases, however, the rotation of fewer or more principal components leads to a noticeable change in the spatial representation of the modes. A comparison of the spatial representation of the modes with correlation maps and a comparison of modes obtained for various numbers of components rotated are tools sufficient for distinguishing real differences in the modes between reanalyses from differences stemming from the PCA method.
We quantify the differences between reanalyses by the normalized percentage of grid points (which approximates the percentage of area) where component loadings significantly differ between reanalyses. The differences concentrate to a few modes in each season. The comparison shows that differences between surface-input reanalyses assimilating only surface observations (20CRv2c and ERA-20C) and full-input reanalyses (ERA-40, JRA-55, and NCEP-1) are mostly higher than differences within both groups. The only exception is autumn when the differences between reanalyses are more due to the PCA methodology (i.e., the sensitivity to the number of rotated components) than to their deficiencies. The reanalysis differing most from the remaining ones throughout the year is 20CRv2c.
Differences in spatial structure of circulation modes may point to biases in reanalyses. This is predominantly the case of 20CRv2c, in which biases are located mainly over southern half of Asia and subtropical eastern Pacific. These biases are larger prior to 1980, while getting substantially smaller afterward, which reflects mainly increases in the number of assimilated pressure observations there. On the contrary, the other surface-input reanalysis, ERA-20C, exhibits only minor differences from other reanalyses and has a higher resemblance with full-input reanalyses, all of which we consider, due to much more data assimilated, as more reliable.
Although differences between reanalyses are minor for most of the modes, the representation of some modes in some seasons is considerably sensitive to the choice of a reanalysis. Therefore, the use of a single reanalysis in climatological studies involving modes, such as studies of effects of atmospheric circulation on surface climate conditions and interpretation of climate model outputs (whether their validation or studies of future climate conditions), may be misleading. The use of multiple reanalyses is highly recommended. If there is a necessity for using a reanalysis covering the entire twentieth century, ERA-20C rather than 20CRv2c is recommended to be the first choice since it appears to be in a closer agreement with standard, full-input reanalyses. Nonetheless, full-input reanalyses should be preferred whenever it is possible.
Acknowledgments
This research was supported by the Czech Science Foundation, project 17-07043S. Martin Hynčica was also supported by the Grant Agency of the Charles University, student project 426216. We further acknowledge the following organizations for providing the reanalysis data: NOAA/OAR/ESRL PSD, Boulder, Colorado, United States for NCEP-1 and 20CRv2c; ECMWF, Reading, United Kingdom for ERA-40 and ERA-20C; and JMA, Tokyo, Japan for JRA-55.
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