Major sudden stratospheric warmings (SSWs) represent one of the most abrupt phenomena of the boreal wintertime stratospheric variability, and constitute the clearest example of coupling between the stratosphere and the troposphere. A good representation of SSWs in climate models is required to reduce their biases and uncertainties in future projections of stratospheric variability. The ability of models to reproduce these phenomena is usually assessed with just one reanalysis. However, the number of reanalyses has increased in the last decade and their own biases may affect the model evaluation.
Here we compare the representation of the main aspects of SSWs across reanalyses. The examination of their main characteristics in the pre- and post-satellite periods reveals that reanalyses behave very similarly in both periods. However, discrepancies are larger in the pre-satellite period compared to afterwards, particularly for the NCEP-NCAR reanalysis. All datasets reproduce similarly the specific features of wavenumber-1 and wavenumber-2 SSWs. A good agreement among reanalyses is also found for triggering mechanisms, tropospheric precursors, and surface response. In particular, differences in blocking precursor activity of SSWs across reanalyses are much smaller than between blocking definitions.
Major sudden stratospheric warmings (SSWs) constitute the most important
phenomena of the Northern Hemisphere polar stratospheric variability in
wintertime. They are abrupt warmings of the polar stratosphere that lead to
a deceleration of the polar vortex and a reversal of the typical westerly
circulation (Andrews et al., 1987). SSWs can be classified into two
different types according to the structure of the polar vortex during the
event. Accordingly, the polar vortex is either displaced from the polar cap
(vortex displacement,
SSWs represent a clear example of stratosphere–troposphere coupling in both
directions. First, they are usually preceded by an enhancement of wave
activity (e.g., Matsuno, 1971). Although this enhancement can take place in
the lower troposphere, recent studies have shown that it often happens
within the stratosphere or tropopause region and depends on the
stratospheric mean flow conditions (Sjoberg and Birner, 2014; Birner and
Albers, 2017; de la Cámara et al., 2017; White et al., 2019). The
sources of upward-propagating wave activity are mainly located in the
mid-to-upper troposphere and correspond to anomalous circulation events such
as a deepened Aleutian low (e.g., Garfinkel et al., 2010) or blocking highs,
among others (e.g., Martius et al., 2009; Nishii et al., 2011;
Ayarzagüena et al., 2011; Barriopedro and Calvo, 2014). Based on the
wave activity preceding SSWs, they are commonly classified into wavenumber-1
(WN1) or wavenumber-2 (WN2) events (e.g., Bancalà et al., 2012;
Barriopedro and Calvo, 2014). This classification produces subsets of events
similar to the
In terms of downward coupling, the SSW signal propagates downward and
reaches the troposphere as revealed from composite analyses (Baldwin and
Dunkerton, 2001), although there is still uncertainty about this
tropospheric response when analyzing individual events (e.g., Gerber et al.,
2009). One of the suggested factors that may contribute to the spread of the
surface signature of SSWs is the type of event. However, while some studies
have shown that only
SSWs are a key element when analyzing stratospheric variability. The frequency and seasonality of SSWs are common metrics to assess the effects of tropospheric and oceanic phenomena on the polar night jet (PNJ). These metrics are also used to evaluate the stratospheric response to climate change (e.g., Taguchi and Hartmann, 2006; Charlton-Perez et al., 2008; Ayarzagüena et al., 2018). Indeed, in modeling studies most of them use simulations that are previously validated by comparing their results with reanalysis datasets (e.g., Charlton et al., 2007; McLandress and Shepherd, 2009; Kim et al., 2017). However, the number of reanalyses has increased in the last decade; although the observational data used in the assimilation process are the same, the reanalysis models are different and so the final products may also be different (Fujiwara et al., 2017). As happens with other atmospheric models, reanalyses also have biases and this can affect the model evaluation (Fujiwara et al., 2017).
Due to quality improvements associated with the assimilation of satellite data, modern reanalyses, such as ERA-Interim, NASA-MERRA, and NCEP-CFSR, only cover the post-satellite period since 1979. This means that the number of available reanalyses to assess the model performance in the pre-satellite era is smaller than in the post-satellite period. In addition, the amount of data to assimilate is also limited in the former period. All this might produce artificial differences in results before and after the inclusion of satellite data. Gómez-Escolar et al. (2012) documented a change in some SSW features from the pre-satellite to the post-satellite era in NCEP-NCAR and ERA-40 reanalyses. For instance, the intraseasonal distribution and the amplitude of the SSW-associated warming showed differences between both periods, potentially due to a change in the type of assimilated data. With the availability of the new JRA-55 reanalysis, which is the only one that applies an advanced data assimilation scheme to upper-air data during the pre-satellite era, revisiting this topic seems appropriate.
In this study, we aim to assess the performance of the most widely used
reanalyses in representing SSWs. To do so, first the main characteristics
of SSWs are examined for all datasets to quantify the degree of agreement
across reanalyses. Both pre- and post-satellite periods are compared to
investigate whether discrepancies among reanalyses in the representation of
the main SSW characteristics depend on the examined period. Secondly, we
address the dynamical forcing of SSWs in all datasets, including precursors
such as blockings. Finally, the surface impact of SSWs retrieved from the
different reanalyses is analyzed. Special emphasis is given to the
assessment and robustness of the potential differences in the forcing and
surface impact of WN1 and WN2 SSWs, as well as
Our work is a contribution to Chapter 6 of the Stratosphere-troposphere Processes And their Role in Climate (SPARC) Reanalysis Intercomparison Project (S-RIP) initiative, which aims to assess stratosphere–troposphere coupling in reanalyses. In the framework of this initiative, a few recent studies have addressed some aspects of the representation of polar stratospheric variability in reanalyses. In particular, Martineau et al. (2018) and Hitchcock (2019) also investigate SSW-related aspects. The former analyzes the momentum budget during SSWs restricted to the post-satellite period, while Hitchcock (2019) compares the representation of stratosphere–troposphere coupling in both pre and post-satellite periods, with an emphasis on the impact of including pre-1979 data. Different from these studies, our work provides a comprehensive inter-reanalyses comparison of the most important and typical aspects and processes associated with SSWs in both pre- and post-satellite eras. Additionally, we explore further the characteristics of WN1 and WN2 SSWs that have not yet been investigated.
The structure of the paper is as follows. The data used and methodology applied are described in Sect. 2. Section 3 compares the performance of the main characteristics of SSWs across reanalyses. Section 4 focuses on the dynamical forcing of the events and Sect. 5 addresses the performance of reanalyses in representing the surface impact of SSWs. The main conclusions are summarized in Sect. 6.
We have used daily data from the following reanalyses: ERA-40 (Uppala et
al., 2005), ERA-Interim (Dee et al., 2011), JRA-25 (Onogi et al., 2007),
JRA-55 (Kobayashi et al., 2015), NASA-MERRA (Rienecker et al., 2011),
NCEP-CFSR (Saha et al., 2010), NCEP-DOE (Kanamitsu et al., 2002), and
NCEP-NCAR reanalysis (Kalnay et al., 1996). More details about the different
reanalyses can be found in Fujiwara et al. (2017). For the comparison across
different reanalyses, all data were used at the common regular grid of
2.5
The methodology for the intercomparison follows the S-RIP specifications. As such, the analysis has been carried out for two different periods: historical (1958–1978) and comparison (1979–2012). Given the periods covered by each reanalysis, only ERA-40, NCEP-NCAR, and JRA-55 are employed in the historical period. In contrast, all the above listed reanalyses are used in the comparison period with the exception of ERA-40, because it ends in 2002. The performance of each reanalysis is evaluated against a multi-reanalysis mean (MRM), herein considered an “unbiased” reference. In the historical period the MRM refers to the average of the three reanalyses that cover that period, while in the comparison period, the MRM is defined as the average of the most recent reanalyses of each center (ERA-Interim, NCEP-CFSR, JRA-55, and NASA-MERRA). Hereafter, anomalies for each reanalysis are defined as the departure of the field from the daily climatology of each reanalysis. In the historical period, the climatology covers the whole period (i.e., 1958–1978), whereas the comparison period uses the 1981–2010 baseline. Unless otherwise stated, statistical significance of the results is computed with a Monte Carlo test of 1000 permutations, each one containing the same number of cases and dates as the SSWs of each composite but with random years of occurrence.
We have used the list of SSWs and common dates identified by Butler et al. (2017) and provided for the S-RIP initiative (Chapter 6), unless otherwise
indicated. First, for each reanalysis, SSWs are identified based on the
reversal of the zonal-mean zonal wind at 60
Classification of the common SSWs into WN1 and WN2 events in the
comparison period. (In brackets the
Nevertheless, in the very first part of our study, we have addressed the
opposite question and quantified the possible discrepancies in the frequency
of SSWs among reanalyses when the same criterion is applied to all datasets.
In that case, we have imposed the World Meteorological Organization definition for the identification of
SSWs in each reanalysis. The definition is based on the reversal, within
SSWs are classified following two definitions:
WN1 and WN2 SSWs were selected by applying a zonal Fourier decomposition of
the daily 50 hPa geopotential height data at 60
We have applied the following diagnostics proposed by Charlton and Polvani (2007) to evaluate the dynamical signatures associated with the occurrence
and development of SSWs:
Amplitude of the SSW in the middle stratosphere (hereafter Amplitude of the SSW in the lower stratosphere (hereafter Deceleration of the PNJ (hereafter Wave activity prior to SSW (hereafter
The anomalous meridional eddy HF averaged over 45–75
As a second step, the methodology by Nishii et al. (2009) was applied to
analyze the role of different forcing processes in the occurrence of SSWs.
This methodology is based on the decomposition of daily anomalous eddy HF
into two components, which correspond to the interaction between
climatological waves and anomalous waves (second and third right-hand terms
of Eq. 1) and the inherent contribution of anomalous waves (first right-hand
term of Eq. 1):
The precursor role of blocking in SSWs has been discussed across studies (e.g., see Castanheira and Barriopedro, 2010, for an overview), although there is not a clear consensus on this topic. The divergent results of previous studies may partially be attributed to different methodologies of blocking detection (e.g., Woollings et al., 2008). In this study, three different blocking definitions have been used to address this question. The three methodologies use daily geopotential height at 500 hPa (Z500) and span almost all approaches to blocking definition. The first method is based on the occurrence of regional and persistent meridional Z500 gradient reversals (the absolute method, ABS; e.g., Scherrer et al., 2006). The second metric involves the detection of persistent and quasi-stationary Z500 anomalies, computed with respect to the local climatological field (the anomaly method, ANO; e.g., Sausen et al., 1995). Finally, a combined method of absolute and anomaly Z500 fields (the mixed method, MIX) is used, providing a double perspective of blocking (Barriopedro et al., 2010). Several criteria are imposed to ensure that the detected episodes represent large-scale, quasi-stationary, and persistent high-pressure systems. See Woollings et al. (2018) for more details about blocking definitions.
In this section, the main signatures of SSWs (frequency, type of events, and process-based diagnostics) are analyzed for each period and compared among the different datasets.
Frequency of SSWs per decade and ratio of vortex displacement (
First, we have analyzed the results for the frequency and type of events
when the same criterion is applied to each dataset. Table 2 shows the mean
frequency of events and the ratio of
The 21 d running mean of the daily climatology (solid lines) and
standard deviation (dashed lines) in the historical period (1958–1978) of
Conversely, in the comparison period, there is a good agreement in both the
frequency and ratio of
Regarding SSW seasonality, Fig. 2 shows the smoothed seasonal
distribution of SSW per decade. This distribution has been computed by
counting the number of SSWs within the
SSW total frequency distribution within
The processes involved in the occurrence of SSWs have been compared across reanalyses by using the diagnostics defined in Sect. 2.4. In this case, and in the rest of the paper, we have used the common dates of SSWs to make sure the differences found across reanalyses are not due to the inclusion of different events.
Figure 3 shows the statistics (mean, median, and interquartile range) of the
dynamical benchmarks for all reanalyses in the two periods. A quick
comparison of the MRM of these benchmarks for both periods reveals that SSWs
are preceded by a similar anomalous strengthening of wave activity at
100 hPa, are associated with a comparable deceleration of the PNJ, and have a
similar amplitude in the middle and lower stratosphere in both periods. Only
slight differences are found in the median of
Box plots showing the distribution of the dynamical benchmarks of
SSWs (amp010, amp100, decelu, and actwav) in the historical (1958–1978) and
comparison (1979–2012) periods. The interquartile range is represented by
the size of the box and the red line (black cross) corresponds to the median
(mean). Whiskers indicate the maximum and minimum points in the distribution
that are not outliers. Outliers (red crosses) are defined as points with
values greater than
The comparison period shows good agreement among all reanalyses as all
datasets are characterized by similar median, mean, and spread values (Fig. 3e–h). Nevertheless, slight deviations can be found for NCEP-NCAR in the
distribution of
A similar analysis has been carried out separately for WN1 and WN2 SSWs in
the comparison period (Fig. S1 in the Supplement). All datasets reproduce a similar behavior
for both types of events and all diagnostics, with the exception of the
associated deceleration of the PNJ in the middle stratosphere: WN2 SSWs are
related to larger decelerations of the PNJ, probably because they are
usually preceded by a stronger polar vortex than WN1 SSWs (Albers and
Birner, 2014; Díaz-Durán et al., 2017). These results also confirm
the overall good agreement across reanalyses except for the deficiency of
NCEP-NCAR concerning
Figures 4 and 5 show the composited anomalous eddy HF, area-averaged between
45 and 75
By applying the methodology by Nishii et al. (2009) we have analyzed the
contributing role of the different HF terms to the occurrence of SSWs. The
MRM decomposition of the HF in the comparison period shows that the
strongest peak ([
Same as Fig. 4 but for the comparison period (1979–2012).
Given the documented differences in the dynamical forcing of different types
of SSWs (e.g., Smith and Kushner, 2012; Barriopedro and Calvo, 2014), we have
repeated the analysis separately for WN1 and WN2 SSWs (Fig. 6). It has only
been done for the comparison period, due to the low sample size of WN2
events for the historical one. Although there is not a univocal relationship
between
Same as Fig. 5 but for
The comparison among reanalyses reveals that all datasets can reproduce the above differences between WN1 and WN2 SSWs. The spread is higher for WN2 SSWs than for WN1 SSWs (Fig. 6b, d, f, h, j, and l), particularly for the anomalous HF term (Fig. 6l). However, considering the differences in HF values between WN1 and WN2 SSWs (i.e., by dividing the standard deviation by the MRM), the resulting spread becomes comparable for both types of SSWs (not shown).
To investigate the tropospheric patterns preceding SSWs, we have analyzed the averaged Z500 anomalies in the 10 d prior to the central date of each type of SSW (Fig. 7). As in the previous section, we have focused on the differences between WN1 and WN2 events in the comparison period only. The chosen time window corresponds to the peak of the strongest anomalies of HF in Fig. 5a. It is also the approximate time that planetary waves take to propagate from the troposphere to the stratosphere (Limpasuvan et al., 2004). The results reveal statistically significant differences between the precursors of WN1 and WN2 SSWs (Fig. 7c). The precursor signal for WN1 SSWs shows a predominant WN1-like structure, with negative anomalies of Z500 over the North Pacific and eastern Asia and positive anomalies over northern Canada, the North Atlantic, and western Siberia (Fig. 7a). This agrees with the pattern identified by previous studies such as Limpasuvan et al. (2004) and Garfinkel et al. (2012) for all SSWs. Most of these centers of action project onto the climatological WN1 of the MRM, especially the one over the North Pacific (e.g., Garfinkel and Hartmann, 2008), explaining the high positive values of the interaction term of HF (e.g., Martius et al., 2009; Nishii et al., 2011). Differently, the precursor signal of WN2 SSWs shows strong negative Z500 anomalies over Canada and Greenland and positive anomalies over the northeastern Pacific (Fig. 7d). The main anomalous centers coincide geographically and in sign with the antinodes of the climatological WN2 of the MRM (e.g., Garfinkel and Hartmann, 2008). Although this pattern agrees with the preferred blocking precursors of WN2 SSWs (Barriopedro and Calvo, 2014), it seems counterintuitive with the predominant role of the anomalous waves found in Fig. 6 for these events, although we are looking at very different levels in the two figures. The same apparent contradiction was already highlighted by Smith and Kushner (2012). Nevertheless, the tropospheric and stratospheric results might not be so contradictory as suggested at the first sight. As indicated in the Introduction section, recent studies have given evidence of the importance of the stratospheric contribution in the amplification of anomalous wave activity prior to an SSW (e.g., Sjoberg and Birner, 2014; Birner and Albers, 2017; de la Cámara et al., 2017). This contribution seems particularly relevant in the case of WN2 SSWs, when an initial vortex structure close to its resonant point can split the vortex with only a small increase in tropospheric wave forcing (Plumb, 1981; Albers and Birner, 2014). Based on our results, this tropospheric wave forcing might result from the constructive interference of anomalous and climatological waves.
The agreement among reanalyses is very good (Fig. 7b and e). Only very small differences appear in the tropospheric pattern over the North Pacific, which are larger for WN2 than for WN1 SSWs, in agreement with the comparison of wave activity (Fig. 6). We stress that the largest differences in wave activity among reanalyses are found in the middle stratosphere and hence the Z500 deviations from the MRM are smaller than those in the HF composites. The lower spread among reanalyses in tropospheric fields compared to that in the stratosphere is expected based on the larger number of assimilated data.
The positive Z500 anomalies identified in the previous section may imply an
increased blocking frequency over those locations prior to the occurrence of
each type of SSW. Similarly, a below-normal activity of blocking before SSWs
might translate into negative Z500 anomalies. Here, we identify blocking
precursors of WN1 and WN2 SSWs by performing 2-D composites of the blocking
frequency (in % of winter days) for the [
This blocking signal is reproduced by all methods and reanalyses (not shown), although the intensity, significance, and spatial extension of the anomalies vary with the blocking definition. For example, the precursory signal of SSWs in ABS is confined to smaller regions than in ANO and MIX, eventually becoming nonsignificant. These differences between methods do not only refer to the blocking signal prior to SSWs but also to the climatology (Fig. 8g–i), which can be explained by the different aspects captured by each blocking indicator (Barriopedro et al., 2010). Reanalyses show a reasonable agreement in the blocking frequency results and they even agree on the statistical significance of changes in the blocking frequency for the ANO and MIX methods, which show a noticeable deviation from the climatology prior to SSWs. Thus, the disagreement between previous studies regarding the precursor role of blocking in SSWs is better explained by the blocking definition than the chosen reanalysis.
Finally, the surface signal after the occurrence of SSWs was explored by compositing the mean sea-level pressure (MSLP) anomalies of the [5, 35] d period for all events. The time interval was selected following Palmeiro et al. (2015), who identified the strongest negative values of the Northern Annular Mode (NAM) index in this period. We found a general good agreement in the surface signal of all SSWs across reanalyses in both historical and comparison periods (not shown). Similar to the previous sections, we present here only the MSLP composites for WN1 and WN2 SSWs and the comparison period (Fig. 9a and d). WN1 and WN2 SSWs show a significant negative NAM-like pattern response with positive anomalies over the polar cap in both cases. However, some slight differences between WN1 and WN2 events are found. Over the northeastern Pacific, MSLP anomalies of different sign (positive for WN2 SSWs and negative for WN1 SSWs) were also detected prior to the occurrence of SSWs (see Fig. 7 and also in MSLP maps, not shown). Thus, they may be a remainder of the tropospheric precursors, as also suggested by Charlton and Polvani (2007). In the European Atlantic sector, negative anomalies after WN1 SSWs extend over the whole Atlantic Ocean and western and central Europe (Fig. 9a), while those related to WN2 SSWs are shifted towards Eurasia (Fig. 9d). Nevertheless, these differences are only statistically significant in western and central Europe and the Mediterranean region, where the response to SSWs is significantly stronger in WN2 than in WN1 SSWs (Fig. 9c). Interestingly, despite their small extension, the different surface responses for WN1 and WN2 SSWs reported here show very good agreement across reanalyses (Fig. 9b and e). Note that the deviations from the MRM are very low for both types of SSWs. Additionally, the regions with the highest disagreement across reanalyses do not correspond to the areas with the largest differences in the surface fingerprint of WN1 and WN2 SSWs. Thus, although small, the differences in surface responses detected between both types of events are robust across reanalyses.
Same as Fig. 7 but for MSLP and the [5, 35] d period after SSWs. Contour interval is 2 hPa for MRM composites and differences and 0.1 hPa for the standard deviation of the reanalyses.
In the last decades, many studies have focused on the surface signal of
In this study, we have compared the representation of the main features,
triggering processes, and surface fingerprint of SSWs in different
generations of reanalyses. Apart from a direct assessment of the SSW
characteristics in the pre- and post-satellite periods, questions concerning
the representation of SSWs by reanalyses have been addressed thanks to the
larger number of datasets available for the post-1979 period. Unlike most
studies that focus on An overall good agreement across reanalyses is found in the representation
of the main features of SSWs. However, there are differences across
reanalyses, particularly in the historical period, concerning the
characteristics of SSWs in the middle stratosphere such as amplitude or
deceleration of the PNJ. Some of the discrepancies also extend to
climatological fields and their variability and are more pronounced for the
NCEP-NCAR reanalysis, in agreement with Badin and Domeisen (2014). Arguably,
the characteristics of the reanalysis models, including the location of
their upper lid, play an important role in that period, when the performance
of the reanalysis is preferentially determined by the characteristics of the
underlying model. These limitations also affect the comparison period, but
to a much less extent, due to the availability of satellite data in the
upper levels. In general, SSWs (frequency, type, and dynamical benchmarks) do not
substantially differ between the historical and comparison periods. Only the
seasonal distribution of SSWs reveals robust differences between both
periods with a shift towards a later occurrence in the satellite period, in
agreement with Gómez-Escolar et al. (2012) and Hitchcock (2019). SSWs are mainly associated with anomalous wave packets immediately before
their onset. However, the interference with climatological stationary waves
plays a predominant role several days before the SSW onset. This behavior is
robust across reanalyses during the comparison period, but subject to
considerable uncertainties during the historical period concerning the wave
activity in the middle stratosphere. WN1 and WN2 SSWs and their tropospheric precursors display differences in
the comparison period that are robustly captured by all reanalyses. WN1
events are mainly triggered by the interaction between climatological and
anomalous waves during long-lasting and moderately intense peaks of HF
anomalies. Conversely, WN2 events are related to intense but short-lived
pulses of HF arising from anomalous wave packets. The results resemble those
by Smith and Kushner (2012) for The tropospheric precursor signal shows predominant
WN1-like and WN2-like structures for WN1 and WN2 SSWs, respectively. This is consistent with the
spatial distribution of blockings preceding both types of SSWs. For WN1
SSWs, there is an enhanced activity over the western Atlantic and below
normal frequencies over the eastern Pacific, with nearly opposite patterns
for WN2 SSWs. A robust pattern emerges for all reanalyses but there are
substantial differences among blocking definitions. Both WN1 and WN2 SSWs have significant impacts on surface weather
characterized by a negative NAM pattern but with some differences in
southern and central Europe. These differences are significantly different
between WN1 and WN2 events and robust across reanalyses during the
comparison period.
In summary, we conclude that the representation of SSWs is, in general, robust in both periods of study for the available reanalyses, and overall not different between the pre- and post-satellite eras. This would agree with Hitchcock (2019), who recommended the consideration of using data prior to 1979 in dynamical studies for stratosphere–troposphere coupling as it might be advantageous for reducing the sampling uncertainty for many purposes. However, in our study some discrepancies in the historical period were identified, particularly for the NCEP-NCAR reanalysis, which limit its use for this period in model evaluation initiatives. Furthermore, this work provides some guidelines, highlighting discrepancies among reanalyses concerning SSWs and identifying related aspects that may be sensitive to the chosen reanalysis. Although robust, some reanalyses results (such as the differences between types of SSWs) should be taken with caution in this period due to the limited sampling.
NCEP-NCAR and NCEP-DOE reanalyses data were provided by the NOAA/OAR/ESRL
PSD, Boulder, Colorado, USA, from their Web site at
The supplement related to this article is available online at:
BA, FMP, DB, NC, and UL designed the analysis and wrote the paper. BA, FMP,
and DB carried out the analysis of the reanalyses data and drafted the
figures. KS provided the algorithm for identification of
The authors declare that they have no conflict of interest.
This article is part of the special issue “The SPARC Reanalysis Intercomparison Project (S-RIP) (ACP/ESSD inter-journal SI)”. It is not associated with a conference.
This research has been supported by the FP7 Environment (STRATOCLIM 603557 project under program FP7-ENV.2013.6.1-2), the Spanish Ministry of Economy and Competitiveness (PALEOSTRAT project, grant no. CGL2015-69699-R), and Blanca Ayarzagüena was funded by the Universidad Complutense de Madrid (Ayudas para la contratación de personal postdoctoral de formación en docencia e investigación en los departamentos de la UCM project).
This paper was edited by Bernd Funke and reviewed by Daniela Domeisen and one anonymous referee.