seasonal differences in extratropical potential vorticity variability at tropopause levels

Seasonal differences in extratropical potential

vorticity variability at tropopause levels

M. A. LinigerClimate Services, Federal Office of Meteorology and Climatology, Zurich, Switzerland

H. C. DaviesInstitute for Atmospheric and Climate Science, Eidgenossische Technische Hochschule, Zurich, Switzerland

Received 13 February 2004; revised 4 June 2004; accepted 21 June 2004; published 10 September 2004.

[1] The distribution of extratropical potential vorticity (PV) on isentropic surfaces thattransect the tropopause is a key feature of planetary-scale teleconnection patterns,synoptic-scale weather systems, and mesoscale stratosphere-troposphere exchange. Here aNorthern Hemisphere January and July climatology is presented for the mean andvariability patterns of the PV using the so-called European Centre for Medium-RangeWeather Forecasts reanalysis-15 (ERA-15) data set. It is derived taking into account thestrong seasonal cycle of the tropopause height and the sharp quasi-latitudinal gradient ofPVon the isentropic surfaces together with the accompanying bimodality in the scale andamplitude of positive and negative anomalies. The bimodality is both emphasized andcircumvented by comparing conventional standard deviation measures of the variabilitywith those of separate depictions of the probability density function structures ofpositive and negative anomalies. It is shown that in winter the zonal heterogeneity ispronounced and the variability (e.g., storm track) patterns exhibit a rich spatial structurewith marked differences between the Pacific and Atlantic. In contrast, in summer theheterogeneity on the lower stratospheric portion of the isentropic surfaces is much weaker,but there remain regions of high variability over oceanic regions on the troposphericportion of the surfaces. The results relate directly to the structure and dynamics of stormtracks and their spatial and seasonal variation. INDEX TERMS: 3319 Meteorology and

Atmospheric Dynamics: General circulation; 3309 Meteorology and Atmospheric Dynamics: Climatology

(1620); 3362 Meteorology and Atmospheric Dynamics: Stratosphere/troposphere interactions; KEYWORDS:

reanalysis, isentropes, storm tracks, Rossby waves, PDF, climatology

Citation: Liniger, M. A., and H. C. Davies (2004), Seasonal differences in extratropical potential vorticity variability at tropopause

levels, J. Geophys. Res., 109, D17102, doi:10.1029/2004JD004639.

1. Introduction

[2] In the extratropics, synoptic-scale variability is highthroughout the troposphere. At lower and midtroposphericlevels the variability is both well known and widelydocumented and led to the identification of confined regionsof high cyclone frequency, referred to as ‘‘storm tracks’’across the northern Atlantic and Pacific [Koppen, 1881;Petterssen, 1956]. An associated structure is also found invariance fields of geopotential height [see, e.g., Blackmon,1976]. This variability has been interpreted in terms of finiteamplitude baroclinic waves whose structure and evolutionvary with geographical location [Wallace et al., 1988].[3] At tropopause levels the corresponding anomalies are

associated with undulations of the tropopause, Rossbywaves, and Rossby wave breaking. From a potential vor-ticity (PV)–potential temperature (TH) perspective, there isa strong link of the tropopause level variability with the

underlying synoptic surface structures [e.g., Hoskins et al.,1985; Davis and Emanuel, 1991; Morgan and Nielsen-Gammon, 1998].[4] Tropopause undulations can take the form of merid-

ionally elongated structures, also referred to as streamers[Appenzeller and Davies, 1992]. These stratospheric intru-sions are associated with strong positive PV anomalies andare often related to nascent surface cyclones and extremeweather events [Massacand et al., 1998]. Furthermore,tropopause folds and subsequent PV cutoffs contribute tocross-tropopause transport [Vaughan et al., 2001; Linigerand Davies, 2003; Sprenger et al., 2003]. The dynamicalcounterparts, anticyclonic structures of low PV values, alsoconstitute a significant part of the flow structure in theextratropics. In particular, quasi-stationary ‘‘blocking’’anomalies are associated with positive tropopause heightanomalies [Pelly and Hoskins, 2003; Schwierz et al., 2004].The strong correlation of tropopause-level PV to quantitiessuch as ozone [e.g., Danielsen, 1968; Danielsen et al., 1987;Vaughan and Price, 1991; Beekmann et al., 1994; Rao etal., 2003] and upper tropospheric humidity [Appenzeller et

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, D17102, doi:10.1029/2004JD004639, 2004

Copyright 2004 by the American Geophysical Union.0148-0227/04/2004JD004639

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al., 1996a; Liniger and Davies, 2003] underlines the cen-trality of the PV pattern at upper tropospheric and lowerstratospheric levels to atmospheric dynamics.[5] The strong linkage between the upper level PV

distribution and the underlying weather systems and itsstrong correlation with other quasi-conserved tracers makesPV a suitable quantity to study the statistical properties ofsynoptic variability and the associated transport processes.Most studies of PV variability in upper levels have focusedon winter months: The low- and high-frequency contribu-tions of the dynamical and residual transient forcing werelocated by Brunet et al. [1995], and the PV distributionwas linked to (conservative) Rossby waves and estimatesderived of the diabatic, divergent, and rotational PV budgets[Edouard et al., 1997]. This technique was then applied to39 winters of National Centers for Environmental Predictionreanalysis data with an additional focus on low-frequencyvariability [Derome et al., 2001]. Likewise, well-knownindices such as the North Atlantic Oscillation and Pacific-North American pattern are evident in the monthly meanisentropic PV distribution and are related closely to Atlanticand European precipitation patterns [Massacand, 1999;Massacand and Davies, 2001a, 2001b].[6] However, it remains to determine the space-time

climatology of the upper level PV variability. The compi-lation of statistics of local PV values is hampered bytechnical difficulties because of the bimodal structure foundin their temporal probability density functions (PDF)[Swanson, 2001]. This bimodality exhibits an interannualand geographical variation and affects the physical inter-pretation of PV statistics. A related complication is thestrong interseasonal variation of the tropopause and isen-tropic height [e.g., Appenzeller et al., 1996b].[7] In this study, a climatology of local high-frequency

isentropic PV variability is derived that treats positive andnegative anomalies separately. The focus is not on a specificspatial or isentropic height but rather on the geographiclocation and the vicinity to the tropopause. This is achievedby selecting appropriate isentropes and allowing thecorresponding PV anomaly thresholds to have a seasonaldependence. This technique delivers a unique data set toaddress various aspects of the local interseasonal variabilityof near-tropopause anomalies.[8] First, the data set used for this study is described

(section 2), and the results from a conventional approach ofmean and standard deviation are presented (section 3).Then, the technique for a climatology of positive andnegative upper level PV anomalies is set out (section 4),and the interseasonal variation of the geographical anomalydistribution and its variability are examined (section 5).Thereafter the statistical PV distribution (section 6) and thespecial case of strong positive anomalies are investigated inmore detail (section 7). Finally, an interpretation of theresults is given in section 8.

2. Data Set and Procedure for Selection ofIsentropes

[9] This study makes use of the European Centre forMedium-Range Weather Forecasts (ECMWF) reanalysis(ERA)-15 data that cover the period 1979–1993 with aspectral resolution of T106 and 31 levels [Gibson et al.,

1999]. Model level data with a 6-hour time resolution wereinterpolated to a 1� grid and then used to calculate the PVand its interpolation onto isentropes. Instead of consideringa 3-month season of distributions, 2 representative monthsare used for Northern Hemispheric winter and summer:January and July. This restriction results in richly structuredpatterns.[10] An inspection of TH and PV in the zonal monthly

mean reveals a strong interseasonal variability of both thevertical position of the isentropes and the tropopause(Figure 1). Hence an individual isentrope’s (e.g., TH =320 K) intersection with the dynamical tropopause (definedas 2 potential vorticity unit (PVU) surface, following Holtonet al. [1995]) undergoes a strong meridional shift from 40�Nin January to 70�N in July. Further, more interannualvariability and trends have been observed in tropopauseheight over the ERA-15 period [Kiladis et al., 2001; Santeret al., 2003]. To partially account for these seasonal andinterannual variabilities, a specific isentrope is selected foreach individual month that intersects the tropopause at 45�Nin the zonal monthly mean. In effect, this enables us tofocus on extratropical tropopause variability by removing aportion of the interseasonal, interannual, and decadal vari-ability. The resulting values selected for TH vary from308 K in winter to 339 K in summer (Figure 2). Note thatthe interannual variability of the selected THs is �5 K forall months. Inspection of Figure 1 indicates that the selectedisentropes cross the upper level region of highest barocli-nicity (i.e., steep isentropes) that is located between 35� and40�N at around 350 hPa in January and between 40� and45�N at above 300 hPa in July. The remainder of the studyis based on these selected isentropes.[11] To illustrate the reduction of interannual and decadal

variability, two time series of PV values on the selectedisentropes are examined (Figure 3). Two points are chosen invicinity to the climatological tropopause and respectivelystrong and weak high-frequency variability (see sections 3and 5). The first point is located in a region in the center ofthe Atlantic storm track (Figure 3a). The strong high-frequency variability is not reflected in an interseasonal orinterannual variability. Further, there is no indication forlong-term fluctuations or a trend. The second point is locatedover eastern Asia (Figure 3b). This region is characterizedby a trough with relatively weak high- frequency vari-ability. Here there is a clear seasonal variation with highPV values in January and low values in July. However, theinterannual variability is even smaller than over the NorthAtlantic.[12] The investigated period of 15 years is relatively short

from a climatological perspective. However, the high tem-poral resolution and the absence of long-term fluctuationsand trends give an estimate about the statistical robustnessof the following results.

3. Conventional Approach

[13] In a first step, mean and standard deviation of thelocal PV values are analyzed on the selected isentropes. Theclimatological PV mean (PV) for January resembles andrelates to the typical stationary wave pattern (Figure 4a).Strong troughs and PV gradients are found over easternNorth America and are somewhat less pronounced over

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eastern Asia. They are located immediately upstream of theAtlantic and Pacific storm tracks. The ridges are positioneddownstream of the troughs, �90� farther east over thePacific and �60� over the Atlantic. Meridional gradientsare weak on the tropospheric side of the ridges overCalifornia and Spain at the end of the storm tracks. TheEurasian continent is characterized generally by weakgradients, but some isentropes cut the boundary layer inthe Himalayan region. For the Pacific storm track a regionof very low meridional gradients is found between thetrough and the ridge over Alaska. In contrast, the gradientsalong the Atlantic storm track weaken downstream of theridge at the end of the storm track. The overall structure ofthe January mean is more pronounced but similar to thewinter PV values shown by other studies [e.g., Derome etal., 2001; Massacand and Davies, 2001b].[14] The highest values in the standard deviation are

located between the 2 and 4 PVU contours of PV; that is,the maxima are not located at the climatological 2 PVUtropopause but are meridionally shifted into the strato-sphere. Zonally, the maxima are collocated with the ridgesat the end of the corresponding storm tracks. The Pacific-American variability maximum is weaker and narrower, andthere are indications that it consists of two relative maxima,one collocated with the trough over the western NorthAmerican and a weaker one over the North Pacific up-stream of the trough. At the end of the storm tracks theEuropean maximum is much stronger and broader. Withinthe climatological troposphere the variability is rather small,and this is associated with the narrow range of PV valueswithin the troposphere (see section 4). Overall, the merid-ional distribution of the standard deviation correlates wellwith PV with the maximum between 2 and 4 PVU. Thisrelationship was noted and utilized for a statistical descrip-tion of the PV variability as a function of the PV valuegiven by Swanson [2001]. However, the zonal asymmetry

of the standard deviation illustrates the limited applicabilityof this approach.[15] In July the PV pattern exhibits a less pronounced

wave structure (Figure 4b). In particular, the east Asiantrough and the ridges over the Mid-Atlantic and easternPacific are no longer clearly identifiable. Nevertheless, thereare some notable deviations from the zonal mean: Over thePacific and North Atlantic, there is equatorward extensioninto the subtropics, and a small ridge can be identified overeastern Asia.[16] The July standard deviation is significantly higher

than in January (note the different scale intervals). Again,there is a good correlation with PV, exhibiting a weak zonalvariability. However, the maximum is shifted to values of

Figure 1. Latitude-height cross section of Northern Hemispheric zonal mean of PV (shaded area) (inPVU) and TH (dashed curves from 280 to 400 K with a spacing of 10 K) for (a) January and (b) Julyfrom 1979 to 1993. The solid curve denotes the isentropes cutting the tropopause at 45�N. Pressure levelsare indicated by solid horizontal lines (spacing of 100 hPa).

Figure 2. TH (in K) of isentrope that cuts the tropopausein monthly zonal mean at 45�N in dependency of month.Each line represents a year from 1979 to 1993, with earlieryears shaded lighter.


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PV between 4 and 6 PVU, clearly higher values than inJanuary.[17] The maxima of variability is located within the

climatological stratosphere, both in January and (even morepronounced) in July. The lack of variability within theclimatological troposphere stands in contrast to a highvariability of synoptic weather systems in the storm trackregions and illustrates the complications arising from the

application of conventional statistical measures to PVvalues.

4. Identification Technique for PV Anomalies

[18] Here an alternative approach is set out to describe thePV variability. The technique is designed to identify posi-tive anomaly (PA) and negative anomaly (NA) frequencies

Figure 3. Time series of PV values at the selected isentropes at (a) 40�W, 47�N and (b) 130�E, 40�N.Shown are 6-hour values (light shaded curve), a running average with a window size of 3 months (darkshaded curve), and a running average with a window size of 1 year (dashed curve).

Figure 4. Monthly averaged PV (contour lines of 0.2, 0.8, 2, 4, 6, and 8 PVU) from 1979 to 1993 for(a) January and (b) July and standard deviation (shaded area) (note the different contour spacing betweenFigures 4a and 4b).


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separately with a seasonal varying threshold to ease inter-seasonal comparisons.[19] A PV value is identified as an anomaly if it deviates

from the climatological mean PV by a certain thresholdPV value (dPV). The local PV anomaly frequency is thencalculated for the positive and negative PV anomaliesseparately. Positive (negative) anomaly frequencies areonly considered within the climatological troposphere(stratosphere).[20] The threshold dPV is determined on the basis of the

seasonal characteristics of the PV values. For example, thereis a stronger vertical stratification and larger vertical PVgradient within the polar stratosphere in the zonal mean inJuly than in January (Figure 1). This results in a muchbroader tail toward high PV values in the hemispheric PDFof PV values.[21] To account for such features, the cumulative distri-

bution functions (CDFs) of PV for the different months arefirst investigated in detail to establish objectively definedthreshold values. The PDFs of area weighted PV values arecompiled from the entire Northern Hemisphere over allyears and time steps and are then integrated to obtain theCDFs for each selected isentrope.[22] The resulting CDFs for January and July are shown

in Figure 5. This depiction relates PV values to thegeographical area covered by them. The weak gradients ofPV within the troposphere between 0 and 1 PVU corre-spond to the steep slopes of the CDFs for both January andJuly. For PV values higher than 1 PVU the CDF is lesssteep, representing the stronger PV gradients. For PV valuesabove �4 PVU the differing PV gradients in January andJuly (see Figure 1) can be identified by the weaker slope ofthe CDF for July. In July, PV values above 8 PVU contrib-ute more than 5% to the hemispheric area but only anegligible fraction in January. The distribution for Januaryis consistent with both the instantaneous global CDF[Ambaum, 1997] and the local PDF of PV values inmidlatitudes in a winter climatology [Swanson, 2001].[23] The values for dPV are now chosen to insure an

equal weighting of both NA and PA in regard to the areacovered by the anomalies. The dPVs are determined such

that the area enclosed by the ‘‘2 PVU + dPV’’ contourdeviates from the area enclosed by the 2-PVU contour byd = 10% of the hemispheric area. This procedure isillustrated in Figure 5 by the horizontal lines at a distanced below (above) the ratio of the hemispheric area enclosedby 2 PVU for the PA (NA) threshold.[24] The conditions and resulting threshold values for NA

and PA, both for January and July, are summarized in Table 1.Note that all PV values are considered that differ from theclimatological mean PV by more than the threshold dPV.Thus, in a region with a climatological PV value of 6 PVU aninstantaneous PV value of 3 PVU is counted as an NA.[25] The threshold values for the NA (PA) are now applied

to every grid point of the instantaneous 6-hour isentropic PVdistributions within the climatological stratosphere (tropo-sphere). The local frequency of occurrence is then con-structed by counting all grid points fulfilling the outlinedconditions for every January (July) from 1979 to 1993 at thesame location.

5. Positive and Negative Anomalies

[26] We consider the anomaly distributions for Januaryand July. In January the NA frequency pattern is character-ized by maxima between 2 and 4 PVU (Figure 6a). Highvalues are zonally confined to the climatological ridges witha broad maximum over the mid–North Atlantic and aweaker one over western North America. The Atlanticmaximum broadens toward Europe and separates from thetropopause slightly poleward over eastern Europe andSiberia. The American maximum consists of two relativemaxima, collocated with the ones observed for the standarddeviation (see Figure 4a). The minimum over the pole isextended equatorward toward eastern Asia and, much lesspronounced, toward eastern North America. The overallstructure is very similar to that of the stratospheric part ofthe standard deviation (see Figure 4a). The narrow bandwith very low frequency directly poleward of the climato-logical tropopause is due to the sparseness of PV values of<0 PVU. The stronger threshold value for the summer NAresults in a wider band.[27] The PA frequency on the tropospheric side also

exhibits some similarities to the pattern for the standarddeviation. However, the separate treatment of PAs results inmore pronounced features. The maxima of PA occurrenceare closely aligned with the tropopause and are zonallymore elongated than their NA counterpart. The highestfrequency is found along the storm tracks, broadening

Figure 5. CDFs of area weighted PV values from theentire Northern Hemisphere from 1979 to 1993 on theselected isentropes for all time steps for January (shadedcurve) and July (solid curve). See text for furtherexplanations.

Table 1. Conditions and Threshold Values for January and July

for Negative Stratospheric Anomalies and Positive Tropospheric

Anomaliesa

NA PA

ConditionsAnomaly PV < PV + dPVNA PV > PV + dPVPA

Hemisphere PV < 2 PVU PV > 2 PVU

Threshold ValuesJanuary dPVJan

NA = �2.1 PVU dPVJanPA = 1.4 PVU

July dPVJulNA = �2.8 PVU dPVJul

PA = 1.2 PVUaNA, negative stratospheric anomalies; PA, positive tropospheric

anomalies; PV, potential vorticity; PVU, potential vorticity unit.


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downstream, collocated with the weaker meridional gra-dients in PV.[28] In July the regions of high NA frequency shift

toward higher PV values to around 4 or 5 PVU, dependingon the longitude (Figure 6b). Further, the anomaly maximaare found more upstream than in January; both maxima arenow collocated with the oceans. Thus the Atlantic maxi-mum is shifted only slightly, whereas the American one islocated 60� eastward over the central Pacific. Again, theAtlantic maximum separates from the tropopause northwardover eastern Europe.[29] The PA frequency in July exhibits pronounced

southwestward tongues over the central North Atlanticand eastern North Pacific. These tongues extend from theend of the storm tracks into the subtropical domain around30�N. Aweaker signal of this feature can be discerned in thePV structure.

[30] In contrast to the standard deviation the anomalyfrequency has a much more detailed structure within theclimatological troposphere. Further, the values are within avery similar range for January and July, as desired by thechoice of threshold values depending on the PV distributionof the corresponding month.

6. PDF Structures

[31] The approach adopted also allows a detailed inspec-tion of local PDFs along selected meridians. Two regionsrepresenting two different dynamical regimes are chosen:(1) the meridian 40�W that bisects the Atlantic storm track(Figure 7) and (2) the meridian across the trough of weakvariability over China at 130�E (Figure 8). The meridianscontain the two points used to illustrate the homogeneity ofthe time series of PV values (see Figure 3).

Figure 6. Frequency of positive and negative anomalies (shaded area) and monthly averaged PV asisolines (0.2, 0.8, 2, 4, 6, and 8 PVU) for (a) January and (b) July from 1979 to 1993. Positive (negative)anomalies are shown only within the climatological troposphere (stratosphere).

Figure 7. Local PV value histograms (vertical axis) along 40�W for (a) January and (b) July (contourvalues of 0.16, 0.5, 1, 3, and 6% and bin size of 0.2 PVU) for all latitudes (horizontal axis). The shadedline denotes the climatological mean PV, and solid lines correspond to the threshold PV + dPV used forpositive (negative) anomalies within the climatological troposphere (stratosphere). The dashed linedenotes the same for strong positive anomalies discussed in section 7.


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[32] In general, the tropospheric part of the PDF is verynarrow (between 0 and 2 PVU) and has a broad tail towardpositive values. Within the stratosphere the distribution iswider (from 2 up to 10 PVU) and exhibits a confined tailtoward low PV values. For both regions the higher valuesare evident in July.[33] The local mean PV values indicate a strong differ-

ence between the meridional PV gradient over the Atlanticand over China. In January the PV gradient is weaker overthe Atlantic, whereas the Asian gradient is weaker in July.[34] The meridional gradients of the local mean values

are linked to both higher PV values in the stratosphere(values are similar over the Atlantic and China) and theoverlap of tropospheric and stratospheric values. Thisoverlap is much stronger over the Atlantic because of theAtlantic storm track. In the dynamically calmer region overChina in winter the overlap is very small (around 40�N). Insummer, however, the PDFs over Asia between 50� and70�N are extremely wide, exhibiting no clear bimodalstructure.[35] To indicate what kind of PV values contribute most

to the PV anomaly frequencies, the threshold for theidentification of NA and PA is denoted in Figures 7 and8. The PA frequency is dominated by stratospheric PVvalues, both over the Atlantic and Asia. Hence the PVfrequency is very sensitive to stratospheric anomalies thatcan be associated with high PV values.[36] For the NA, however, tropospheric PV values con-

tribute significantly only over the Atlantic in the regionfrom 50� to 75�N in winter and from 50� to 65�N insummer. Over Asia the NA frequency is less influencedby tropospheric PV values because of the weaker bimodal-ity of the PDF. This corresponds to the wide band of lowNA frequencies found in this region.[37] From the PDFs over the North Atlantic it can be

further inferred that the expansion of the PA toward thesubtropics is mainly caused by stratospheric PV values.Analogously, the local NA maximum over Asia observedaround 60� north of the small ridge (see Figure 6b) canbe attributed to values with a significant portion of tropo-spheric PV values (Figure 8b).[38] Evidently, the PDFs are subject to a strong variability

with regard to location and season. Note that the PV and thestandard deviation do not capture all the features describedin sections 5 and 6. Their values are strongly affected byspecific features of the PV distribution, in particular thedifferent range of values above and below the tropopause.Therefore the skewness Cs and the variation (also referred to

as ‘‘normalized standard deviation’’) Cv are introduced hereto further illuminate the geographical characteristics of thePDF structures (with s denoting the standard deviation andN denoting the sample size):

Cs ¼1

N

XNt¼1

PV� PV

s

� �3

Cv ¼s

PV:

The skewness Cs describes the asymmetry of the PDF. For anormal variable the skewness is zero, and distributions witha longer upper tail are said to be positively (right) skewed.Accordingly, it is strongly positive within the troposphere(Figure 9). The highest values are associated with PVbelow 0.8 PVU and a low (but not zero) frequency ofpositive anomalies. The region of high skewness exhibitsa surprisingly strong zonal symmetry. Along the climato-logical tropopause the skewness decreases to zero since thetropospheric and stratospheric values build a bimodal (andsymmetric) PDF (see Figure 7a). North of it, in particularnorth of the troughs, the skewness exhibits moderatenegative values. An inspection of local PV PDFs reveals alack of strong positive values and more tropospheric values(e.g., north of 50�N in Figure 8a and less pronounced inFigure 7a).[39] For July the asymmetry between the climatological

troposphere and stratosphere is weaker but still pronounced.A higher number of strong positive values and fewertropospheric values can be found in the local PDFs (as,e.g., north of 70�N in Figure 7b) resulting in less anomalousskewness within the stratosphere.[40] The variation (Cv) shows the variability relative to

PV (Figure 10). The meridional shift of the maxima in thestandard deviation away from the tropopause toward higherPV mean values is compensated for by the distribution ofthe variation: The variability within the troposphere isweighted much stronger. In winter the maxima are locatedsouth of the ridges along the 0.8-PVU PV mean isoline. Theregion at the end of the storm tracks with strong Rossbywave breaking exhibits the highest values.[41] The July maxima are found more upstream, with an

extension toward the subtropics over both the Atlantic andPacific. The structure is similar to the PA distribution, butthe calculation is not very robust in the region of very lowPV values, i.e., toward the subtropics, and thus causes highspatial variability in this region. The overall difference in

Figure 8. Same as Figure 7 but along 130�E for January and July.


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magnitude of the standard deviation disappears between thewinter and summer. Therefore the larger standard deviationin July than in January (see Figure 4) is caused not by astronger relative variability but by a shift toward higher PVvalues.

7. Strong Positive Anomalies

[42] Precursors of surface cyclogenesis can often beidentified by anomalous high PV values of the order of4–6 PVU in midlatitudes. They are identified here as strongpositive anomalies (SPA) within the climatological strato-sphere. Here we employ a special anomaly selection thresh-old to directly identify SPA.[43] It is unclear to what extent these anomalies contrib-

ute to the standard deviation. Moreover, SPAs are to be

expected mainly within the climatological stratosphere; theanalysis need not be constrained to the climatologicaltroposphere as it was for the PA frequency.[44] The previous technique (see section 4) used to

establish the threshold value for PA within the tropo-sphere is now used to define SPA within the stratosphere(illustrated in Figure 11). As reference a PV value of4.8 PVU is chosen (see the value of 2 PVU in section 4).The threshold PV value dPVSPA is selected to identifyanomalies such that the area enclosed by the 4.8 PVU +dPV contour deviates by d = 10% of the hemisphericarea, from the area enclosed by the 4.8-PVU contour.This procedure results in threshold values of dPVJan

SPA =1.8 PVU for January and dPVJul

SPA = 2.8 PVU for July.[45] The resulting structures (Figure 12) are very similar

to the standard deviation and NA distribution both for

Figure 9. Same as Figure 4 but for skewness (shaded area).

Figure 10. Same as Figure 4 but for normalized standard deviation (shaded area).


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January and July as shown in Figures 4 and 6, respec-tively. In particular, the Pacific maxima consist again oftwo relative maxima, one over western North Americaand a weaker one over the central North Pacific. Both inJanuary and July the differences between the Atlantic andPacific maximum are similar for SPA and for NA.However, the detailed structure of the storm tracks revealssome differences: (1) The SPA Atlantic maximum extendsfarther eastward into the Eurasian continent than the NAmaximum and (2) during July the SPA maxima are moreconfined.[46] The magnitudes, locations, and patterns of the strato-

spheric NA and SPA frequency are found to be very similar.Thus the storm tracks can also be seen as regions of highfrequency of anticyclonic anomalies. With the thresholdvalues being different for positive and negative anomalies,

the amplitude of the frequencies is in the same order ofmagnitude.

8. Synthesis and Further Comments

[47] The combination of conventional statistical mea-sures, inspection of climatological and local PDFs of PV,and a subjective positive and negative anomaly identifica-tion technique was employed to study PV variability nearthe extratropical tropopause. The PV distribution is studiedon isentropic surfaces that are selected for each January andJuly separately. This enables direct consideration of inter-seasonal and interannual variability.[48] In January the region of lowest variability is located

upstream of the Pacific storm track and thereby separatesthe track from that over Asia. In contrast, the Atlanticstorm track is linked upstream to the Pacific stormtrack.[49] Indeed, the Pacific storm track differs significantly

from the Atlantic one. It is less confined and can besubdivided into three regions. Region 1 is upstream, overeastern Asia, with extremely low variability and strongzonally aligned PV gradients. Region 2 is downstream,over the central Pacific, and the PV gradients are reducedon the stratospheric side. Close to the tropopause, a sec-ondary maximum can be identified in all fields describingthe stratospheric variability. Region 3 is the climatologicalridge farther downstream over western North America andis associated with maximal variability within both theclimatological stratosphere and the troposphere. The struc-ture observed for the Pacific storm track can be related to aseparation between several regions of Rossby wave devel-opment and breaking. An indication for such a separation isalso found by Hoskins and Hodges [2002], who determinethe genesis region of cyclones ending over western NorthAmerica. The genesis region they find is collocated with the

Figure 11. Same as Figure 5 but with labels for strongpositive anomalies. See text for further explanations.

Figure 12. Frequency of strong positive anomalies (shaded area) and monthly averaged PV as isolines(0.2, 0.8, 2, 4, 6, and 8 PVU) for (a) January and (b) July from 1979 to 1993.


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region identified as secondary maximum of variability overthe North Pacific in the present study.[50] For the Atlantic storm track the spatial subdivision

is not so apparent. The trough over eastern America ismore pronounced and exhibits stronger meridional PVgradients. Downstream over the central North Atlanticthe ridge is less strong than its Pacific counterpart. Themaximum in variability extends from the American eastcoast across the Atlantic and into eastern Europe andeven Siberia. It is significantly broader within the clima-tological stratosphere than its Pacific counterpart. On thetropospheric side the maximum (of positive variability)is located slightly downstream toward Europe and theMediterranean.[51] The July hemisphere features shorter storm tracks

with a weaker meridional and zonal variability within thestratosphere. The minimum of variability along the tropo-pause is not located over eastern Asia but over centralSiberia. Also, the Pacific maximum is shifted significantlyfrom western North America to the central North Pacific,and both maxima are now collocated over the oceans. Thestronger baroclinicity due to the land-sea contrast in winteris said to have a particularly strong impact on winteratmospheric variability [Hoskins and Valdes, 1990]. How-ever, the anomaly frequency distribution exhibits a strongerasymmetry between the land and ocean domains in July atupper levels. The weaker meridional temperature gradientat the surface and the corresponding weaker thermal windat upper levels could result in more localized wave activity.The westward shift of high variability compared to winterand the related localization of strongest wave activity overthe oceans are also reflected in the contour length stretchingrates in these sectors [Scott and Cammas, 2002]. Thisindicates that the observed anomaly frequency maxima aredirectly linked to increased isentropic mixing across thetropopause.[52] Within the climatological troposphere, regions of

high PA frequency and weaker PV mean and standarddeviation extend into the subtropics. As indicated in Figure1b, the selected isentropes are located above 500 hPa in thezonal mean. Indeed, an inspection of individual eventsreveals that these PV anomalies are not located in the lowerparts of the troposphere but at upper levels around 200 hPaand are thus not related to diabatic effects but rather topossible subtropical Rossby wave breaking.[53] The origin and path of the anomalies cannot be

captured by the method employed in this study. For thePacific a strong monsoon anticyclone could contribute tothe advection of anomalies from the western Pacific towardthe subtropical central Pacific. Over the Atlantic, there is nosimilar anticyclone documented in summer, but the PVmean and the PA frequency indicate an analogous structureof Rossby wave breaking.[54] Subtropical Rossby wave breaking over the oceans

was also identified along the tropopause at 350 K by Posteland Hitchman [1999]. They find that the maxima arelocated slightly more to the west in the regions of thesubtropical Atlantic and Pacific during summer, and theirPacific maximum is twice as strong as the Atlantic one. Thisdifference could be related to their method: Meridionallyaligned structures in the form of streamers would not becaptured.

[55] A small ridge in the PV mean north of China isaccompanied by a weak local maximum in NA, SPA, andvariance. Therefore the overlap of tropospheric and strato-spheric PV values in this region could be a signature ofenhanced Rossby wave breaking. Negative PV cutoffs havebeen observed in this region and were attributed to theAsian summer monsoon [Popovic and Plumb, 2001]. How-ever, the center of monsoon activity is located significantlymore to the south. The observed feature could also be asignature of variability on higher isentropes.[56] The local PDFs of PV exhibit a wide heterogeneity.

The strong interseasonal variability within the stratosphereand the fundamental difference between the tropospheric andstratospheric PDF structure complicate the derivation anduse of physically meaningful quantities for statistics. Forexample, the bimodal structure in the storm track regionsis not symmetric. This results in negative anomaliesdominating positive anomalies. Nevertheless, the strato-spheric variability structure is represented very well by thestandard deviation. On the tropospheric side, however,features such as the subtropical extension over the oceansare not clearly discernible. It is shown that the local PDFs arestrongly non-Gaussian, in particular within the lowermoststratosphere. Thus the interpretation of local fields ofPV standard deviation, skewness, or variation has to becarried out very carefully by also considering the corre-sponding PDF structure directly or employing additionalmeasures.[57] The results also have implications for the determi-

nation of a background PV mean state, as it is necessary forPV inversion [Kleinschmidt, 1950; Hoskins et al., 1985]. Astrong zonal asymmetry is found in January (that is morepronounced than the conventional December–Februarydepiction) and a significantly different structure in July.Therefore it is of advantage to assess a spatially andseasonally confined background mean state. Also, verifica-tion metrics based on PV must be handled with care in thetropopause region.

[58] Acknowledgments. The authors would like to thank CorneliaB. Schwierz for fruitful discussions and for motivating several aspects ofthis study. Credit also goes to Heini Wernli for helpful contributions of botha technical and a scientific nature.

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��H. C. Davies, Institute for Atmospheric and Climate Science, ETH,

ETH-Hoenggerberg HPP, CH-8093 Zurich, Switzerland. (huw.davies@env. ethz.ch)M. A. Liniger, Climate Services, Federal Office of Meteorology and

Climatology, Krahbuhlstr. 58, CH-8044 Zurich, Switzerland. ([email protected])


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seasonal differences in extratropical potential vorticity variability at tropopause levels

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