Two Modes and Their Seasonal and Interannual Variation of the Baroclinic Waves/Storm Tracks over the Wintertime North Pacific

JIANG Yuxin and TAN Benkui

Department of Atmospheric and Oceanic Sciences,Peking University,Beijing 100871

Two Modes and Their Seasonal and Interannual Variation of the Baroclinic Waves/Storm Tracks over the Wintertime North Pacific

JIANG Yuxin and TAN Benkui?

Department of Atmospheric and Oceanic Sciences,Peking University,Beijing 100871

In this study,a newly developed method,termed moving empirical orthogonal function analysis(MEOF),is applied to the study of midlatitude baroclinic waves over the wintertime North Pacific from 1979 to 2009.It is shown that when the daily, high-pass filtered(2–10 days)meridional wind at 250 hPa is chosen as the variable of the MEOF analysis,typical features of baroclinic waves/storm tracks over the wintertime North Pacific can be well described by this method.It is found that the first two leading modes of the MEOF analysis,MEOF1 and MEOF2,assume quite different patterns.MEOF1 takes the form of a single wave train running in the east–west direction along 40?N,while MEOF2 is a double wave train pattern running in the east–west direction along 50?N and 30?N,respectively.The shift composites of various anomalous fields based on MEOF1 and MEOF2 assume typical baroclinic wave features.

MEOF1 represents a primary storm track pulsing with an intrinsic time scale of two days.It shows significant“midwinter suppression”and apparent interannual variability.It is stronger after the mid-1990s than before the mid-1990s.MEOF2 represents a double-branch storm track,also with an intrinsic time scale of approximately two days,running along 50?N and 30?N,respectively.It shows no apparent seasonal variation,but its interannual and decadal variation is quite clear.It oscillates with larger amplitude and longer periods after the mid-1990s than before the mid-1990s,and is heavily modulated by El Ni?no–Southern Oscillation(ENSO).

baroclinic waves,Pacific storm tracks,MEOF analysis,ENSO

1.Introduction

The North Pacific is one of the two major regions where baroclinic waves/storm tracks are very active.Therefore,the study of baroclinic waves/storm tracks over the North Pacific and their spatial and temporal variation has received much attention and remains a topic of extreme importance to the science and practice of weather and climate forecasting(e.g., Chang et al.,2002;Bader et al.,2011).

Previous studies show that the North Pacific storm track assumes apparent seasonality:it is strongest around November and weakest during midwinter(e.g.,Nakamura,1992). The mechanisms that lead to this midwinter suppression have also been extensively studied(Chang,2001;Nakamura and Sampe,2002;Harnik and Chang,2004;Penny et al.,2010). On time scales of one month or longer,Lau(1988),Chang and Fu(2002)and Wettstein and Wallace(2010)discovered that the first two modes of the Pacific storm track variability consist of a monopole that represents variability in the overall intensity of the storm track and a dipole that represents shifting of the climatological-mean storm track in the meridional direction.Chang et al.(2002)found that the Pacific storm track shifts equatorward during El Ni?no winters compared to La Ni?na winters.Seager et al.(2010)noticed that during El Ni?no events the warming of the eastern equatorial Pacific Ocean moves atmospheric convection eastward. Anomalous rising motion in the eastward-shifted convection region forces an upper-troposphere anticyclone.Anomalous westerly flow on the poleward flank at about 20?N of this upper-level anticyclone shifts both the subtropical jet and storm tracks equatorward.

Recently,the storm track response to the changing climate has attracted much attention from meteorologists,climatologists and other scientists,and many studies indicate that the Northern Hemisphere wintertime extratropical storm tracks shifted poleward and storm activity intensified in northern high latitudes during 1959–97(McCabe et al., 2001).Zhang et al.(2008)also found a northeastward shift of Arctic/North Atlantic Oscillation centers of action and a sudden jump to a dipolar leading pattern during 2001–05,which could be an integrative manifestation of the poleward shift ofstorm tracks.Some other studies have shown that the number of storms entering the Arctic has increased(Zhang et al., 2004;Sorteberg and Walsh,2008).Zhang et al.(2004)further found that storm activities have distinct regional characteristics across different geographic sectors.The North Atlantic storms show a similar trend to the whole of the Northern Hemisphere(Kushnir et al.,1997;Geng and Sugi,2001; Nie et al.,2008),while the North Pacific storms show an opposite trend;that is,intensifying and shifting southward (Chang and Fu,2002;Nakamura et al.,2002;Nie et al.,2008; Zhang et al.,2012).

The present study focuses on the baroclinic waves/storm tracks over the wintertime North Pacific and their temporal variability at various time scales,from intraseasonal to interannual and decadal.To this end,daily rather than monthly data are used.In addition,a newly developed method,termed moving empirical orthogonal function(MEOF)analysis(see section 2),is used in the present study,which is efficient for detecting the moving signals and their spatial and temporal variability,and provides a powerful tool for quantitatively describing both the baroclinic waves and the spatial and temporal variability of the storm tracks.

This paper is arranged as follows:Section 2 introduces the method and data used.The results are given in section 3, and this is followed by a summary of the study in section 4.

2.Data and methods

There are two main approaches,widely used in the literature,to producing diagnostics of storm tracks.The first approach examines storm tracks in a Eulerian framework in which the storm tracks are defined as the geographically localized maxima in the bandpass transient variance(Blackmon,1976;Blackmon et al.,1977).The main limitation of this approach is that,even though the filtered variance coincides with the major storm track regions,it can only provide a fairly general indication of the storm track activity,as it does not discriminate between cyclones and anticyclones,or give a measure of the number of the storms or their intensity. The second approach identifies individual storms in a Lagrangian framework and follows each storm from its cyclogenesis to its cyclolysis.This approach has developed from manual studies with weather charts(Petterssen,1956;Whittaker,1982)to computer-based automatic tracking algorithms with high-quality reanalysisdatasets(Murray and Simmonds, 1991;Serreze etal.,1993;Sinclair,1994;Hodges,1995;Graham and Diaz,2001;Hoskins and Hodges,2002;Zhang et al.,2004;Inatsu,2009;Mesquita et al.,2009).The automatic tracking algorithm identifies storms as local minima or maxima of parameters,such as sea-level pressure or relative vorticity,and links them together to form storm trajectories. The merit of this approach is that it can discriminate between cyclones and anticyclones,but it depends on the criteria chosen and differences can occur when different criteria are chosen.For details of the merits and limitations of these two approaches,readers are referred to Chang et al.(2002)and Hoskins and Hodges(2002).

To further reveal both the spatial and temporal variability of the storm tracks,the above two approaches are usually combined with EOF analysis(Lau,1988;Ulbrich and Christoph,1999;Norris,2000;Chang and Fu,2002;Nakamura et al.,2002;Harnik and Chang,2003;Wettstein and Wallace,2010;Chen et al.,2014).However,another obvious common limitation of the two approaches is that they do not provide a description of the structures of the baroclinic waves themselves.To overcome this drawback,a method based on point correlation was developed(Chang,1993),and applied to the meridional wind in the upper troposphere.Based on this method,the climatological structures of baroclinic waves,their downstream development and preferred regions of travel can be well described(Chang and Yu,1999).Compared to the EOF-based method,as expected,the one-pointcorrelation-based method is unable to conveniently describe the temporal variability,such as the seasonal or interannual variability,of storm tracks.

In this study,a newly developed method,termed moving EOF analysis(Jiang,2014),is used to study the baroclinic waves/storm tracks over the wintertime North Pacific.This method is basically similar to conventional EOF analysis,except that in order to accurately extract the moving signals,the spatial mode or modes are allowed to move(shift)in space. In MEOF analysis,there are three elements necessary for detecting the moving signals and their spatial and temporal variability:the spatial modes(denoted as MEOFs),the principle component time series(MPCs),and the shift functions.As a result,the MEOF can accurately describe the position,and therefore propagation velocity,of the moving signal,which conventional EOF fails to do(Jiang,2014).Here,we briefly describe the method,but for more details of the method and its advantages over the EOF,readers are referred to Jiang (2014).

where i and j represent the serial numbers of space and time, respectively.The objective function of conventional EOF analysis can be expressed as one designed to find a spatial mode uiand a principal component(PC)time series cj(for simplicity,the objective function only contains one mode), which satisfy:

subject to

The optimal uiis called EOF1 and cjis called PC1.These variables capture as much information(in the sense of an L2-norm)regarding Fijas possible.

The goal of MEOF analysis is to find a spatial mode ui,a time series cjand a shift function sjrepresenting forward/backward shifting of the spatial mode,which

subject to

The shift function sjcan also be regarded as the Lagrangian coordinate of the moving signal.This idea can be realized by performing the substitution i′=i?sj.Then,Eq.(3)can be rewritten as

subject to

If sjis already known,we can obtain uiand cjfrom Eqs. (2)and(4)by performing conventional EOF analysis on the matrix Fi+sj,j.Furthermore,if uiis already known,we can use Eq.(3)to solve sjand cjat each time step separately. Readers are referred to Jiang(2014)for details of the practical algorithm that solves ui,cjand sjusing Eq.(3)or Eq. (4),subject to periodic or even non-periodic boundary conditions.In this study,the MEOF modes are set to move along the zonal direction.The extended boundary condition is used,and the maximum shift allowed(smax)is set to 28,which corresponds to a movement of up to 70?east or west.This study uses the daily mean data from the National Centers for Environmental Prediction–Department of Energy (NCEP–DOE)Reanalysis 2(Kanamitsu et al.,2002)on 2.5?latitude–longitude grids in the winters of 1979–2009,where the winter season refers to November through March(NDJFM).We also tested the NCEP Climate Forecast System Reanalysis(CFSR)and the ERA-Interim reanalysis with different resolutions,and no apparent differences were found(Fig. S1–3).The variables examined include zonal and meridional wind,geopotential height,temperature,vertical velocity,and precipitation.The daily interpolated outgoing longwave radiation(OLR)data are provided by the NOAA/OAR/ESRL PSD(Liebmann and Smith,1996).The seasonal cycle is removed from all the variables by subtracting the first three harmonics of the annual cycle.Then,a 2–10-day band-pass Lanczos filter(Duchon,1979)is applied and,finally,the residual mean is removed.To examine the effect of El Ni?no–Southern Oscillation(ENSO)events on the baroclinic waves and storm tracks,the NOAA Extended Reconstructed Sea Surface Temperature(SST)V3b dataset(Smith et al.,2008) is used to calculate the winter season(NDJFM)mean interannual Ni?no3.4 index[SST averaged over(5?S–5?N,170?–120?W)].

3.Results

3.1.Baroclinic wave properties

As in Chang and Yu(1999),the meridional wind,rather than its variance,is used as the variable of the MEOF analysis.To correctly reflect the baroclinic wave features,the meridional wind is high-pass(2–10 days)filtered.MEOF analysis is performed over the domain(0?–90?N,120?E–105?W),and the square root of the cosine of latitude weighting is applied prior to the MEOF analysis.As shown in Fig. 1,the first two leading MEOF modes(MEOFs)assume apparent wave-like features.The first MEOF mode(MEOF1) is a single wave train–like pattern running across the central North Pacific,centered along 40?N(Fig.1a),which accounts for 32%of the total high-frequency variance.The wave train spans west–east by about 45?of longitude,corresponding to a wavelength of 3800 km.In contrast,the second MEOF mode(MEOF2)assumes a double wave train pattern(Fig. 1b).The northern branch of the wave train is located along 50?N and has a wavelength of 3900 km,while the southern branch is along 30?N and also has a wavelength of 3900 km. MEOF2 accounts for 12%of the total high-frequency variance.Figures 1c and d show the number of days when the centers of the two modes appear at a particular longitude,respectively.Clearly,the two modes are most active over the central North Pacific around 172?W,and gradually become inactive towards the east or west.

The phase velocity of the wave train–like anomalies can be calculated using the shift function sj.Figures 2a and b show the frequency distribution plot in(sj,sj+1?sj)space. An eastern movement with four to five grids each day can be identified.Taking 40?N as the central latitude of the two MEOF modes,the speed can be estimated using the formation

where Cjis the speed at time j,R the earth’s radius,φthe reference latitude and D the length of a day.Figures 2c and d are the local amplifications of Figs.2a and b,respectively. The phase speed of MEOF1 shows some variation from west to east,changing from approximately 12.5 m s?1to 8 m s?1.The phase speed of the second mode is slightly less, but shares the characteristics of MEOF1:faster in the west and slower in the east.

The above results show that the wave train–like anomalies revealed by MEOF1 and MEOF2 have only slight differences,characterized by a wavelength of approximately 4000 km and an average phase speed of 10 m s?1,which are typical features of baroclinic waves(Chang,1993).The baroclinic wave characteristics of MEOF1 and MEOF2 can also be clearly demonstrated by the shift composite maps of geopotential height,temperature and vertical velocity anomalies in the longitude–height cross sections through the wave train centers(Fig.3).These plots are obtained by shifting the centers of the MEOFs together,and then compositing.Figure 3 shows that the height perturbations have maximum amplitude at around 300 hPa,250 hPa,and 200 hPa for the wavetrains along 50?N,40?N,and 30?N,respectively.All height perturbations tilt westward with increasing height,and the vertical tilt appears slightly more pronounced for the waves in the upstream than in the downstream direction.In contrast,the temperature perturbations tilt towards the east with increasing height,except for the wave train at 30?N,where the temperature perturbation still tilts towards the west with increasing height in the upstream part of the wave train,and remains vertical with height in the downstream part.Furthermore,the temperature perturbation reaches its maximum at a lower height—approximately 500 hPa for the wave trains at 50?N and 40?N,and 400 hPa for the wave train at 30?N—and reverses its sign above the tropopause.The plot of vertical velocity shows maximum rising motion just ahead of the upper-level trough and descending motion just ahead of the ridge,with maximum vertical motion at 400 hPa,which corresponds to the maximum vertical omega velocity at 500 hPa(not shown).The wave features in the MEOFs are highly consistent with those estimated by Chang(1993).

In addition to height,meridional wind,temperature,and vertical velocity anomalous fields,MEOF1 and MEOF2 also leave their wave-like footprints in the OLR and precipitation anomalous fields,as shown in Fig.4,which provides strong evidence that baroclinic waves are the most powerful weather-bearing system in the midlatitudes.

3.2.Storm track features

From the above analysis,we know that the leading two MEOFs describe midlatitude baroclinic waves.Next,we show that the storm track properties,such as the seasonal and interannual variability,can also be derived from the two MEOFs and their time series.Given the fact that the standard deviation of high-pass filtered meridional wind can be used to define the storm track intensity(Blackmon et al., 1977),the MEOF-related storm track intensities can be obtained by applying the root-mean-square(RMS)to the MEOFs(Figs.5c and d).We term the MEOF1-related storm track the primary storm track,which is across the midlatitude North Pacific,and the MEOF2-related storm tracks the secondary storm tracks,which run along 50?N and 30?N,respectively.Comparing these two modes with the standard deviation(SD)of the 10-day high-pass filtered meridional wind for all winter days(Fig.5a),and the SD only for days when MPC2＞MPC1(Fig.5b),shows that the MEOF-related patterns strongly resemble the real-data SD patterns and can be used as the model modes of the storm track variability.(The intention of the condition MPC2＞MPC1 is to remove the influence of the primary storm track from the data so that the double wave train pattern can be clearly revealed).

In fact,the storm variability represented by MEOF1 describes pulsing of the storm track over the midlatitudes(Lau, 1988;Wettstein and Wallace,2010),while the MEOF2-related variability was previously unknown and is therefore discussed in more detail below.

3.3.Seasonal and interannual variability of storm tracks

In view of the fact that the two MEOFs represent the primary and secondary storm tracks,the two MPC time series in fact describe the daily evolution of the storm tracks,and the storm track variability of longer time scales can be derived from the two MPCs.To confirm this,we directly calculate the areal RMS of the storm track over the domain(20?–55?N, 170?E–120?W)(black rectangle in Fig.5a)with the daily high-pass filtered 250 hPa meridional wind(blue line in Fig. 6a),which is in good agreement with the MPC1 time series. The Pearson’s correlation coefficient between the two linesis as high as 0.81(p-value＜0.005).Figure 6b shows the MPC2 time series and the daily time series of the storm track with the MEOF1-represented storm track removed.Clearly, the two time series are also in remarkable agreement,with a correlation coefficient of 0.58(p-value＜0.005).Here,the relatively lower correlation for MEOF2 than MEOF1 may be due to the fact that MEOF2 is much weaker than MEOF1 (MEOF1 and MEOF2 account for 32%and 12%of the total high-frequency variance,respectively)and higher MEOFs also contribute a considerable amount of the variance.So, the two MEOF time series describe the daily evolution of the two kinds of storm track variability over the wintertime North Pacific well.

Next we examine the intrinsic time scale of the baroclinic waves/storm tracks.To this end,we compute the autocorrelation functions of the two MPC time series(Fig.7).The plot shows that the two MEOFs are fast-varying patterns.MPC1 and MPC2 in particular have e-folding decorrelation times of approximately two days,which is a typical time scale of baroclinic waves.

Based on the two MPC time series,the seasonal and interannual variability of storm tracks can be conveniently obtained(Fig.8).Figures 8a and b show the seasonal variability of the primary and secondary storm tracks,respectively,which are obtained simply by averaging the two MPC series for the same calendar day for the period 1979–2009. Clearly,the MPC1-related primary storm track has its minimum around January and February,which is known as the“midwinter suppression”(Nakamura,1992;Nakamura and Sampe,2002).The seasonality of the MPC2-related secondary storm tracks is not as apparent as the primary storm tracks,showing only a small peak during midwinter.This increase may be an intrinsic feature of the secondary storm tracks,or a result of the north–south shift of the primary storm track.

Figure 9 shows the interannual variability of the two MPC-related storm tracks,which is obtained by calculating the winter-season RMS of the two MPC time series,then,standardized.As shown in Fig.9a,the primary storm track assumes apparent interannual and decadal variation.It is much weaker prior to 1995 than after 1995,showing an upward trend for the period 1979–2009.

The MPC2-related storm tracks(Fig.9b)also assume apparent interannual variability.A most notable decadal change occurs in around the mid-1990s:the oscillation shows larger amplitude and longer periods after the mid-1990s than before the mid-1990s.

3.4.Modulation of ENSO

Next we examine the modulation of ENSO on the two modes of the storm track variability by calculating the correlation between the winter-mean MPCs and the winter-mean Ni?no3.4 index.The results show that the correlation between the first mode of the storm track variability is very weak, with a correlation coefficient of 0.07(p-value of 0.70),but the second mode of the storm track variability is highly modulated by ENSO,with a correlation coefficient of 0.64(Fig. 9b,p-value＜0.005),which is statistically significant at the 1%significance level.Further examination shows that this high correlation is mainly contributed by the MEOF2 over the eastern North Pacific.This result is consistent with a modeling study by Basu et al.(2013),who found that there are more numerous intense storms over southwest and northwestern North America when El Ni?no–like SST increases. Basu et al.(2013)’s result implies the coexistence of a storm track over the northeastern Pacific with the storm track over the southeastern Pacific during El Ni?no years.A theoretical study based on numerical modeling by Lee and Kim(2003) also supports this result.Their study also found that,in the presence of a subtropical jet of modest strength,baroclinic wave growth takes place primarily in the midlatitude baro-clinic zone,establishing a well-defined eddy-driven jet at midlatitude.

It is important to note that MEOF2-related baroclinic waves and storm tracks have received little attention previously.In fact,baroclinic waves in double wave train form can be frequently detected in the wintertime North Pacific.Figure 10 shows an example that appeared from 7 to 13 March 1988, during the 1987/88 ENSO event.On 8 March,a distinct double wave train pattern formed around the centralNorth Pacific region and propagated eastward.Then,it reached the coastline of North America on 10 March and weakened.At the same time,another double wave train–like pattern formed in the western North Pacific and propagated eastward.

4.Summary and conclusions

In this study,a newly developed method,MEOF analysis, is applied to the daily,high-pass filtered meridional wind at 250 hPa to study the midlatitude baroclinic waves and storm tracks in the wintertime North Pacific during 1979–2009.It is shown that MEOF analysis provides an efficient approach for the study of both the midlatitude baroclinic waves/storm tracks and their temporal variability at various time scales. The following conclusions have been reached:

(1)MEOF1 assumes a wave train–like pattern running across the midlatitude North Pacific,centered at 40?N.The shift composites of the variables,such as geopotential height, temperature,vertical velocity,precipitation and OLR anomalies,show that MEOF1 represents typical baroclinic waves.

(2)The MEOF1-represented storm track is the primary storm track in the wintertime midlatitude North Pacific,and pulses in intensity.The primary storm track has an intrinsic time scale of two days,experiences a“midwinter suppression”and decadal shift.It is stronger during the post-1995 period than the period prior to 1995.

(3)MEOF2 assumes a double wave train pattern running along 30?N and 50?N,respectively.The shift composites of the geopotential height,temperature,vertical velocity,precipitation and OLR anomalies show that the wave trains in MEOF2 also show typical baroclinic wave features.

(4)The MEOF2-represented storm track are the secondary storm tracks in the wintertime midlatitude North Pacific,which also have an intrinsic time scale of approximately two days.The secondary storm tracks show no apparent seasonality,but clear interannual and decadal variability.Like the primary storm track,the secondary storm tracks experience a decadal shift around the mid-1990s.They oscillate with larger amplitude and longer period during the post-1995 period than the period prior to 1995.The secondary storm tracks are heavily modulated by ENSO.

Acknowledgements.This research was supported by the National Natural Science Foundation of China(Grant Nos.41375060 and 41130962).We thank Professor Jiayou HUANG for his useful comments and suggestions.We would also like to thank the anonymous editor and the two reviewers for their helpful comments and suggestions,which led to improvements in the manuscript.

Electronic Supplementary Material:Supplementary material(Figs.S1–3)is available online at http://dx.doi.org/ 10.1007/s00376-015-4251-3.

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9 November 2014;revised 18 February 2015;accepted 9 March 2015)

?Corresponding author:TAN Benkui

Email:bktan@pku.edu.cn