Simulating the Seasonal Cycle of the Northern Hemisphere ... · idealized potential vorticity...

Simulating the Seasonal Cycle of the Northern Hemisphere Storm Tracks UsingIdealized Nonlinear Storm-Track Models

EDMUND K. M. CHANG

Institute for Terrestrial and Planetary Atmospheres, Marine Sciences Research Center, Stony Brook University,Stony Brook, New York

PABLO ZURITA-GOTOR*

UCAR Visiting Scientist Program, GFDL, Princeton, New Jersey

(Manuscript received 23 December 2005, in final form 27 October 2006)

ABSTRACT

In this study, an idealized nonlinear model is used to investigate whether dry dynamical factors alone aresufficient for explaining the observed seasonal modulation of the Northern Hemisphere storm tracks duringthe cool season. By construction, the model does an excellent job simulating the seasonal evolution of theclimatological stationary waves. Yet even under this realistic mean flow, the seasonal modulation in storm-track amplitude predicted by the model is deficient over both ocean basins. The model exhibits a strongersensitivity to the mean flow baroclinicity than observed, producing too-large midwinter eddy amplitudescompared to fall and spring. This is the case not only over the Pacific, where the observed midwinterminimum is barely apparent in the model simulations, but also over the Atlantic, where the October/Aprileddy amplitudes are also too weak when the January amplitude is tuned to be about right.

The nonlinear model generally produces stronger eddy amplitude with stronger baroclinicity, even in thepresence of concomitant stronger deformation due to the enhanced stationary wave. The same was foundto be the case in a simpler quasigeostrophic model, in which the eddy amplitude nearly always increases withbaroclinicity, and deformation only limits the maximum eddy amplitude when the baroclinicity is unreal-istically weak. Overall, these results suggest that it is unlikely that dry dynamical effects alone, such asdeformation, can fully explain the observed Pacific midwinter minimum in eddy amplitude.

It is argued that one should take into account the seasonal evolution of the impacts of diabatic heatingon baroclinic wave development in order to fully explain the seasonal cycle of the storm tracks. A set ofhighly idealized experiments that attempts to represent some of the impacts of moist heating is presentedin an appendix to suggest that deficiencies in the model-simulated seasonal cycle of both storm tracks maybe corrected when these effects, together with observed seasonal changes in mean flow structure, are takeninto account.

1. Introduction

It is well known that the storm tracks in the NorthernHemisphere (NH) exhibit different seasonal cycles(e.g., Nakamura 1992). The Atlantic storm-track activ-ity is most intense during midwinter, when the meridi-onal temperature gradient across the storm track is

strongest. On the other hand, the Pacific storm-trackactivity is most intense in late fall and exhibits a relativeminimum during midwinter and then a second peakduring early spring. It is worth noting that the meridi-onal temperature gradient across the Pacific stormtrack is also strongest during midwinter. This observednegative correlation between the Pacific storm-trackactivity and western Pacific baroclinicity is clearlysomething that one would like to understand.

While this so-called midwinter minimum (or midwin-ter suppression) of the Pacific storm track can be foundin GCM simulations (e.g., Christoph et al. 1997; Zhangand Held 1999), the mechanism that gives rise to thisphenomenon is still not well understood. Zhang and

* Current affiliation: Universidad Complutense, Madrid, Spain.

Corresponding author address: Dr. Edmund K. M. Chang,ITPA/MSRC, Stony Brook University, Stony Brook, NY 11794-5000.E-mail: [email protected]

JULY 2007 C H A N G A N D Z U R I T A - G O T O R 2309

DOI: 10.1175/JAS3957.1

© 2007 American Meteorological Society

JAS3957

Held (1999) successfully simulated the midwinter mini-mum using a linear stochastic storm-track model forcedby monthly mean flow taken from a GCM simulation.Their results suggest that the midwinter minimumcould be explained by the seasonal changes in the meanflow structure. However, an earlier attempt by Whi-taker and Sardeshmukh (1998) was unsuccessful. Todate, it is still not clear why the results of the two stud-ies differ, except perhaps that the model used by Zhangand Held (a 14-level primitive equation model) maybe more sophisticated than that used by Whitakerand Sardeshmukh [a two-level quasigeostrophic (qg)model].

Recently, Deng and Mak (2005) conducted idealizedmodeling studies in an attempt to interpret the midwin-ter minimum. They forced a two-level qg model usingidealized potential vorticity structures, namely, a regionof sharp potential vorticity gradient representing thestorm track environment, with a region of strongly dif-fluent flow downstream representing the storm-trackexit region. They found that when they increased theamplitude of the forcing, both the growth rate of themost unstable linear normal mode and the amplitude ofthe nonlinearly equilibrated storm track decrease sub-stantially, mainly due to the effect of strong eddy dis-sipation in the enhanced deformation field. They con-cluded that the midwinter minimum of the Pacificstorm track is due to the excessive amplitude of themidwinter deformation.

A caveat concerning the results of Deng and Mak(2005) is that their model storm tracks are not alwaysrealistic. The observed Pacific storm track has similarupstream seeding throughout the cool season (see, e.g.,Figs. 5a–g), with the interseasonal changes mainly inthe amplitude of the storm-track maximum. However,in Deng and Mak’s simulations, when the deformationis strong, the upstream seeding is substantially weaker,such that the ratio between the storm-track peak and itsupstream minimum is actually larger in their “midwin-ter” simulation, which is inconsistent with observations.Hence it is not clear whether the dynamics captured intheir simulations can actually explain the observed sea-sonal cycle.

Let us reconsider the results of Zhang and Held(1999). They constructed a linear stochastic model, us-ing stochastic forcing superposed on different basicstates representing the mean flow of the differentmonths. They found that if they use the same forcingfor the different months, they were able to obtain stron-ger storm tracks in fall and spring than in midwinter.

One of the weaknesses of linear storm-track modelsis that the amplitude of the model storm track is di-rectly proportional to the arbitrary amplitude of the

prescribed forcing. While one can argue that using thesame amplitude of forcing for the different months maybe a reasonable first start, there is no theoretical justi-fication that the amount of nonlinear scattering, whichis what the stochastic forcing represents, should neces-sarily be the same over the seasonal cycle. For example,while the storm-track amplitude over the Pacific, interms of upper tropospheric geopotential height vari-ance, is as strong in October/April as in midwinter, theobserved eddy heat flux in October/April is weakerthan that in midwinter.1 Based on this, one might arguethat the eddy source in October/April should be weakerthan that in midwinter.

In this study, an idealized nonlinear storm-trackmodel will be used in an attempt to simulate the sea-sonal cycle of the NH storm tracks. The model (de-scribed in section 2) generates realistic baroclinic waveand storm-track structure. Being nonlinear, the ampli-tude of the model storm track is determined internallyby nonlinear equilibration. In these aspects, the modelcan be regarded to be more sophisticated than thoseused in previous idealized studies.

In section 3, we will present results that suggest thatthe observed seasonal cycle of the NH storm track isunlikely to be entirely explained by dry dynamics alone.To show that our results are not peculiar to the specificmodel used, in section 4 we will discuss results from atwo-level qg model that support the insights gainedfrom the primitive equations experiments.

2. An idealized nonlinear storm-track model

The model is based on the dynamical core of theGeophysical Fluid Dynamics Laboratory (GFDL) glob-al spectral model (Held and Suarez 1994). The resolu-tion used in this study is T42 in the horizontal and 10evenly spaced sigma levels in the vertical. This resolu-tion should be sufficient for our purposes here, sinceZhang (1997) showed that the midwinter suppression ofthe Pacific storm track can be found in a nine-level, R30GCM seasonal run. Realistic orography, smoothed tomodel resolution, is imposed. A land–sea mask is used,with stronger surface friction over land. The friction isin the form of a drag quadratic in the wind speed and isequivalent to having a surface stress with CD � 0.0015

1 As shown in Nakamura (1992), the midwinter suppressionalso shows up in lower tropospheric heat flux. However, the sup-pression in terms of heat flux is not as pronounced as that in termsof geopotential height variance, such that in October and April,while Pacific eddy activity in terms of geopotential height varianceis nearly as large as that in midwinter, the eddy heat flux is weakerthan that in midwinter.

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(0.004) over ocean (land), with the stress decreasing to0 at the top of the first model layer, which represents10% of the atmospheric mass. Diabatic heating is rep-resented by Newtonian cooling, with a damping timescale of 30 days in the free atmosphere (� � 0.7), de-creasing to 2 days at the surface (� � 1). The only otherdamping is a highly scale selective diffusion (�8), with adamping time scale of 0.1 days on the highest wave-number.

The only forcing imposed is Newtonian damping to aradiative equilibrium temperature profile. For each ex-periment, the equilibrium temperature profile is itera-tively determined, such that at the end of the process,the model climate, as given by the time mean three-dimensional temperature distribution, is nearly identi-cal to a desired target temperature distribution. Theprocedure used to determine the equilibrium profile foreach experiment is summarized in appendix A. Moredetails concerning the model formulation can be foundin Chang (2006).

As discussed in Chang (2006), when the model cli-mate is forced to resemble the three-dimensional Janu-ary climatological temperature distribution [as given bythe 1982–94 mean taken from the National Centers forEnvironmental Prediction–National Center for Atmo-spheric Research (NCEP–NCAR) reanalysis data], themodel eddy activity is much too weak. Chang (2006)suggested that this is due to the fact that in this model,all diabatic forcings act to damp the eddies, whereas inthe atmosphere, diabatic heating due to latent heat re-lease can act to enhance eddy growth (e.g., Gutowski etal. 1992; Davis et al. 1993). As suggested by the resultsof Hayashi and Golder (1981), who compared dry andmoist development of baroclinic waves under the samezonal mean flow, eddy growth in the presence of latentheat release is enhanced not only by the eddy energygenerated by the latent heat release but also by the factthat baroclinic energy conversion is strongly enhancedin the presence of moisture. Chang (2006) suggestedthat such an enhancement of baroclinic energy genera-tion could be partially imitated by a reduction in thestatic stability. Chang (2006) showed that when themodel vertical potential temperature gradient is re-duced everywhere by 1.25 K km�1, realistic eddy am-plitudes can be obtained (see also Figs. 5d,k). In thisstudy, unless otherwise stated, we will use the samereduction in the static stability in our numerical experi-ments.

One may question whether reducing the static stabil-ity will lead to reduction in the eddy scale and result ineddies that are too small in the simulations. We esti-mated the average eddy scale (in terms of half wave-length) using one-point regression analysis applied to

300-hPa meridional velocity perturbations (Lim andWallace 1991) at 40°N near the date line. The scaleestimated from reanalysis is about 25° longitude, andthat estimated from our dry simulations without reduc-ing the static stability is about 29°, while for the simu-lations with static stability reduced by 1.25 K km�1, theeddy scale is estimated to be about 27°. Hence the eddyscale in our model simulations is not very sensitive tothe static stability and is quite close to that observed.This is consistent with the results of Frierson et al.(2006). Note that the eddy scale in a GCM simulation,which successfully simulated the midwinter suppression(Chang 2001), is about 29°; hence we do not think thatthe small difference in eddy scale between our modelsimulations and reanalysis is a critical flaw of the model.

Here we will first apply the model to examinewhether it can simulate strengthening/weakening of thePacific storm track. We have examined the observedinterannual variability of the January Pacific stormtrack in terms of 700-hPa poleward heat flux computedbased on a 24-h difference filter (see Wallace et al.1988) over the period 1979 to 1999. Out of these 21Januaries, the five years with the strongest eddy heatflux (HI years) were 1979, 1982, 1987, 1989, and 1990.The Pacific storm track was weakest during the Janu-aries of 1980, 1981, 1984, 1995, and 1998 (LO years).The differences between the HI and LO composites areshown in Fig. 1. In Fig. 1b, we see that the eddy heatflux at 700 hPa was clearly stronger in the Pacific duringthe HI years, and the Atlantic heat flux was also stron-ger (see Chang 2004). Another common measure ofstorm-track activity is the standard deviation of filtered500-hPa geopotential height (see Wallace et al. 1988).The composites for the HI and LO years are shown inFigs. 1c,d, respectively. We can see that both stormtracks were stronger during the HI years. The differ-ence in the observed mean flow structure is shown inFig. 1a. We can see an anticyclonic anomaly over thePacific, consistent with weakening and broadening ofthe Pacific jet2 [consistent with the results of Nakamuraet al. (2002) and Harnik and Chang (2004)].

Two sets of model runs have been conducted usingour idealized storm-track model. One set is forced toresemble the temperature structure of the HI compos-ite (taken from the NCEP–NCAR reanalysis but withstatic stability reduced as discussed above), while the

2 Note that while the strengthening of the Pacific storm trackwhen the Pacific jet is weak and broad in its interannual variationshas similarities to what happens during its seasonal march, previ-ous studies by Chang (2001) and Harnik and Chang (2004) havesuggested that the dynamics involved in these two phenomenamay be different.


other is forced to resemble the LO composite. The dif-ferences between the two experiments are shown inFigs. 1e,f. The pattern of the difference in time-mean500-hPa geopotential height (Fig. 1e) resembles ob-served (Fig. 1a) quite well, except the amplitude is a bitweak, especially over North America and the Atlantic.This is related to the fact that the iterative procedure isunable to converge to the exact desired temperaturedistribution due to strong internal climate variability(see discussions in appendix A and Chang 2006). Nev-ertheless, we can see the prominent anticyclonicanomaly over the Pacific, as well as the cyclonicanomaly over northern Eurasia.

Regarding the storm tracks, the model clearly simu-lates significantly stronger heat fluxes over the Pacificfor the HI experiment (Fig. 1f), and to a lesser extent,a stronger Atlantic storm track. The model storm track

in terms of standard deviation of filtered 500-hPa geo-potential height is also stronger for the HI experiment(Figs. 1g,h). Hence Fig. 1 confirms that the model cansimulate interannual change in the Pacific storm-trackactivity reasonably well. In addition, based on canonicalcorrelation analyses performed between mean flow andstorm-track anomalies, Chang (2006) showed that theobserved month-to-month storm-track/mean flow cova-riability is well simulated in the idealized model. Theseresults demonstrate that the idealized model performswell in simulating storm-track variability.

3. Simulation of the seasonal cycle

a. Structure of the mean flow

The observed seasonal cycle of the stationary wave(zonal asymmetrical part of the 500-hPa geopotential

FIG. 1. (a) Differences in 500-hPa mean geopotential height, between HI and LO Pacific storm-track Januaries (contour interval is30 m), from NCEP–NCAR reanalysis. (b) Same as in (a) but for 24-h filtered 700-hPa poleward heat flux [contour interval (CI) �10 K m s�1]. (c) Standard deviation of 24-h filtered 500-hPa geopotential height for HI years (CI � 20 m). (d) Same as in (c) but forLO years. (e)–(h) Same as in (a)–(d) but from idealized model simulations. Shaded regions indicate absolute values greater than 60 in(a),(e), greater than 10 in (b),(f), and greater than 100 in (c),(d),(g),(h).


height), based on the NCEP–NCAR reanalysis for theyears 1982 to 1994, is shown in Figs. 2a–g. We can seethat during the entire cool season (October throughApril), there is a trough centered near Japan, a ridgeover western North America, a trough over northeast-ern North America, and a ridge over eastern Atlanticextending into Europe. Over the season, there areslight shifts in the position of the centers, but the mostobvious change is in the stationary wave amplitude.The change in wave amplitude, as shown by RMS z�over the NH, is shown in Fig. 3b (solid line). We can seethat the amplitude of the NH stationary wave changesby about a factor of 2 between midfall/spring and mid-winter.

Figures 2h–n show how well our idealized modelsimulations can reproduce the observed stationarywave structure. These panels show results from sevendifferent experiments. In each experiment the modelclimate is iterated until the time-mean three-dimensional temperature distribution is close to thatobserved for that month (except that the stability isreduced; see discussions above). Quantitative compari-sons between the lhs and rhs panels are shown in Fig. 3.The pattern correlation between the stationary wavefor each month, over the NH between 20° and 70°N, isshown in Fig. 3a. The correlation is above 0.9 for No-vember through March and is about 0.88 in Octoberand 0.89 in April, when the stationary wave is weakest.As far as the amplitude is concerned, the model sta-tionary wave is slightly weaker than observed (Fig. 3b),but the seasonal cycle is clear. To put these results intoperspective, the agreement between our results and thereanalysis is much better than that between an Atmo-spheric Model Intercomparison Project (AMIP) run(for the same period considered) using the GFDL R30GCM (Broccoli and Manabe 1992) and the reanalysis(the pattern correlation for the GCM run lies between0.79 and 0.87). This is not entirely unexpected, since inour experiments we attempt to force the model tem-perature distribution to that observed, while nothinglike that is explicitly done in the GCM experiment.

In Fig. 3c, the seasonal progression of the zonal meantemperature difference between 21° and 69°N at 700hPa is plotted. This can be treated as a rough measureof how the zonal mean baroclinicity changes with time.The model simulations (dashed line) track the reanaly-sis (solid line) very well, with the difference betweenthe two lines being less than 0.25 K (less than 1% of thetotal temperature difference) for all months.

Since one of the hypotheses we want to examine iswhether seasonal changes in the deformation of themean flow alone might be enough to explain the sea-sonal cycle of the storm tracks, we need to first make

sure that the deformation is well simulated in our ex-periments. Following Cai and Mak (1990), the defor-mation vector is defined as follows:

D � ��U

�x�

�V

�y,�V

�x�

�U

�y�. �1a

In spherical coordinates, the deformation vector can bewritten as (e.g., Batchelor 1967, p. 601)

D � � 1a cos�

�U

��

1a

�V

��

V

atan�,

1a cos�

�V

��

1a

�U

��

�U

atan��. �1b

Here is the latitude, � is the longitude, and a is theradius of the earth. The two components of the vectorD, computed based on (1b) using NCEP–NCAR re-analysis data at 250 hPa for October and January, areshown in Figs. 4a–d, while those from the idealizedmodel simulation are shown in Figs. 4f–i. We can seethat the model simulates both components of the de-formation very well, with pattern correlation above 0.95over the entire NH, as well as over the eastern Pacific,and the RMS amplitude of both components are within7% of that observed. The model deformation for theother months (not shown) are also well simulated andshow the clear seasonal cycle of being weakest in Oc-tober/April and strongest in January/February.

b. Seasonal cycle of the eddies

The seasonal cycle of the Pacific and Atlantic stormtracks, in terms of standard deviation of 24-h filtered500-hPa geopotential height, as seen in the NCEP–NCAR reanalysis, for the years 1982–94, is shown inFigs. 5a–g. We can see that the Atlantic storm track hasa relatively simple seasonal cycle, strengthening fromOctober to January and then weakening after that. Forthe Pacific storm track, it is strongest in November andDecember, a bit weaker in March, even more so inJanuary, and weakest in February. The Pacific stormtrack in October and April is slightly weaker than inJanuary but stronger than in February. For the Pacificstorm track, there is also a seasonal shift in latitude,which can be seen clearly in Fig. 6a.

The seasonal cycle of the storm tracks, as simulatedby the idealized storm-track experiments, is shown inFigs. 5h–n and 6c,d. The model Atlantic storm track isclearly strongest in January and weakest in Octoberand April, in agreement with observations. However,the simulated amplitude of the seasonal cycle is muchlarger than that seen in the reanalysis, with the modelstorm tracks in October and April much weaker than


FIG. 2. (a)–(g) Evolution of the zonal asymmetrical part of the 500-hPa geopotential height (CI � 50 m) from the NCEP–NCARreanalysis. (h)–(n) Same as in (a)–(g) but from idealized model simulations. Shaded regions indicate absolute values greater than 100.


that in the other months (Fig. 6d), while in the reanaly-sis the differences are not as pronounced (Fig. 6b).

The simulated seasonal cycle of the Pacific stormtrack is even worse. The model storm track is strongestin December and January, slightly weaker in Novemberand March, even more so in February, but muchweaker in October and April. Instead of the midwinterminimum, there is a winter maximum (Fig. 6c). There isa hint of a relative minimum in February,3 but in themodel simulation, the February Pacific storm track issubstantially stronger than those in October and April,clearly inconsistent with what is observed. This failureoccurs even though we have achieved excellent simula-tion of the time-mean flow.

To verify that the dynamics of the eddies in our simu-lations are consistent with observed eddies, we havecomputed the eddy kinetic energy (EKE) budget for

the transient eddies (see Chang 2001 for details), bothfor all transients and for high-frequency (24 h filtered)transients. In the simulations, as in the reanalysis, ed-dies grow due to baroclinic conversion, with peak baro-clinic conversion over the two storm-track regions (notshown). Barotropic conversion, computed from re-analysis and the idealized model simulation for thehigh-frequency eddies for January, is shown in Figs.4e,j, respectively. We can see negative conversion overthe eastern portions of both storm tracks, with themodel barotropic conversion weaker than that com-puted from reanalysis, especially over the Atlantic.However, EKE in the model simulation (not shown) isalso weaker than that observed; hence the overall baro-tropic damping time scales for high-frequency eddies4

in the model simulation (8.2 days for NH and 3.3 daysover the eastern Pacific) are not very different fromthose computed based on reanalysis data (7.6 and 3.1days, respectively).

To test the robustness of our results, we conducted aseparate set of experiments without reducing the staticstability of the model climate (i.e., the target tempera-ture distributions are the actual climatological tempera-ture distribution of the different months). The resultsare summarized in Figs. 6e,f. Overall, the simulatedstorm-track amplitude is significantly weaker than ob-served. Nevertheless, the January maximum for the At-lantic storm track is simulated, but again, the stormtrack is clearly much too weak in October and April.For the Pacific storm track, the maximum for this setoccurs in December, with amplitude slightly larger thanin November, January, and February and significantlyso than in October and April, with the results showinga slight hint of a minimum in January. These resultsshow that our model results are not sensitive to thereduction of static stability employed in the simula-tions.

c. Discussions

Deng and Mak (2005) suggested that the midwinterminimum occurs mainly because of seasonal changes inthe deformation associated with the stationary waves;the stationary waves in midwinter are much strongerthan those during fall/spring, and the stronger deforma-tion strongly enhances barotropic dissipation such thatthe storm track is weaker when the stationary waveamplitude is strong, despite enhancement of baroclinic-ity near the jet core. Deng and Mak used analytical

3 The relative minimum in February shows up a bit clearer infiltered 300-hPa meridional velocity variance (not shown). How-ever, contrary to observations, even for that measure, the simu-lated storm track in October and April is weaker than that in theFebruary simulation.

4 For all transients, the respective barotropic damping timescales for model simulation are 25 and 7.9 days, while those fromreanalysis data are 22 and 6.2 days.

FIG. 3. (a) Pattern correlation between Figs. 2a–g and 2h–n. (b)Evolution of the amplitude of the stationary wave (m) at 500-hPalevel. (c) Evolution of the temperature difference (K) between21° and 69°N at 700-hPa level. In (b),(c), solid line is taken fromNCEP–NCAR reanalysis and dashed line from idealized modelsimulations.


forcing functions to represent what they regard as“plausible” forcings. Here we will use our model withmean flow structures close to those observed to testtheir hypothesis.

Two different sets of experiments have been per-formed to test this hypothesis. In the first set, the targettemperature structure of the January basic state ischanged, such that the zonal asymmetrical part is re-placed by that of October, but the zonal mean part

remains the same. Thus the zonal mean baroclinicity isnot changed, while the stationary wave amplitude isreduced. The stationary wave in this new experiment isshown in Fig. 7a. This should be compared with that ofthe standard January experiment (Fig. 2k). The stormtracks for this experiment are shown in Fig. 7b. We seethat with a decrease in the stationary wave amplitude,the amplitude of the Pacific storm track decreasesslightly, while that of the Atlantic storm track decreases

FIG. 4. (a) Stretching deformation (Dx; CI � 5 � 10�6 s�1) and (b) shearing deformation (Dy; CI � 1 � 10�6 s�1) at 250 hPa forOctober; (c),(d) Same as in (a),(b) but for January, and (e) vertically averaged barotropic conversion rate (CI � 10 m2 s�2 day�1) forJanuary computed based on NCEP–NCAR reanalysis data. (f)–(j) Same as in (a)–(e) but computed based on idealized modelsimulations. Shaded regions indicate absolute values greater than 1 � 10�5 in (a),(c),(f),(h), greater than 2 � 10�5 in (b),(d),(g),(i), andgreater than 10 in (e),(j).


FIG. 5. (a)–(g) Evolution of the standard deviation of the 24-h filtered 500-hPa geopotential height (CI � 20 m) from the NCEP–NCARreanalysis. (h)–(n) Same as in (a)–(g) but from idealized model simulations. Shaded regions indicate absolute values greater than 100.


substantially (cf. to Fig. 5k). We have performed similarexperiments by forcing to the zonal asymmetric tem-perature distributions of November, March, and April,and the results are similar.

In the second set of experiments, we first reduce theamplitude of the zonal asymmetrical part of the Janu-ary diabatic forcing [both c and Q in (A4)] by a factorof 0.5, and in another experiment, we increase the am-plitude of the asymmetric part by a factor of 2. In bothcases, the zonal mean diabatic forcing again stays thesame. The results of these two experiments are shownin Figs. 7c–f. The stationary wave (as well as the defor-mation, which is not shown) for the weaker forcing caseis clearly weaker (cf. Fig. 7c to Fig. 2k), while that forthe stronger forcing case is substantially stronger (Fig.7e), as expected. However, the two storm tracks areweaker in the weak forcing case (Fig. 7d) than in thestrong forcing case (Fig. 7f), even though in the strong

forcing case, the stationary wave amplitude (and defor-mation) is clearly much stronger than the observed cli-matological stationary wave amplitude for January(Fig. 2d).

One may wonder whether the results above are con-sistent with those shown in Fig. 1, which suggest thatthe storm track is stronger when there is an anomalousridge over the Pacific, or, in the words of Nakamura etal. (2002), when the winter monsoon is weak. However,note that the pattern correlation between the patternshown in Fig. 1a and the climatological stationary wave(Fig. 2d) is only �0.08 for the NH and �0.26 from 30°Eto the date line, showing that Fig. 1 does not correspondto a reduction in the climatological stationary wave am-plitude.

Another expectation is that when the stationary waveis strong, the heat transport by the stationary waveshould be stronger, hence necessitating less heat trans-

FIG. 6. (a) Seasonal cycle in the standard deviation of 24-h filtered 500-hPa geopotential height (CI � 10 m) forthe Pacific storm track (averaged between 120°E and 120°W) from NCEP–NCAR reanalysis. (b) Same as in (a)but for the Atlantic storm track (averaged between 90°W and 0°). (c),(d) Same as in (a),(b) but from idealizedmodel simulations. (e),(f) Same as in (c),(d) but from simulations without reduction in static stability. Shadedregions indicate absolute values greater than 100.


port by the transients. Indeed, when we diagnosed theheat transport in these two experiments and the Janu-ary control experiment, the heat transport by the sta-tionary wave is strongest in the strong stationary wavecase, and the total zonal mean transient heat transportfor that case is slightly weaker than in the other cases.However, the zonal mean high-pass-filtered transportturns out to be not weaker,5 and since it is now morezonally localized, the high-pass heat transport over thestorm tracks is stronger than in the two other cases.This applies not only to the 24-h difference filter, butalso when the eddies are defined using a 2–8-day filterafter Blackmon (1976).

Our results suggest that the midwinter minimum isunlikely to be simply explained by seasonal changes inthe mean flow structure. What other mechanisms cancontribute to this phenomenon? Nakamura (1992)speculated about a number of possible mechanisms, in-cluding wave saturation, excessive deformation, exces-sive advection, trapping of waves near the surface, theeffect of moisture, and change in upstream seeding.

Most of these, apart from the effects of moisture, aredynamical in nature and should be present in our non-linear storm-track model.

The fact that GCM runs, using similar resolutions asour experiments, can successfully simulate this seasonalcycle, while our model cannot, suggests that the failureprobably lies in the simplistic physical parameteriza-tions that we use. One such possibility has been dis-cussed in Chang (2001). Based on analyses of GCM andreanalysis data, Chang (2001) showed that over thewestern Pacific, the diabatic generation of transienteddy available potential energy (EAPE) is much stron-ger in October than in January. Results from the GCMsimulation suggested that this is due to two effects: totaldiabatic heating is stronger in October and the diabaticheating anomalies correlate better with temperatureanomalies in October than in January. Chang and Song(2006) examined the distribution of precipitationaround cyclones using reanalysis model-generated pre-cipitation, ship precipitation reports, and satellite-retrieved precipitation. Their results show that in mid-winter western Pacific cyclones a larger proportion ofthe precipitation occurs as convection in the cold airbehind cold fronts, thus reducing the correlation be-tween diabatic heating and temperature anomalies. For

5 In these experiments, the zonal mean low-frequency transportis weaker when the stationary wave is strong.

FIG. 7. (a) Zonally asymmetrical part of the 500-hPa geopotential height (CI � 50 m), and (b) standard deviation of the 24-h filtered500-hPa geopotential height perturbations (CI � 20 m) for experiment forced to January temperature distribution in the zonal meanbut October temperature distribution in the zonal asymmetrical part. (c),(d) Same as in (a),(b) but for experiment forced with half ofthe zonal asymmetrical forcing as the control January experiment. (e),(f) Same as in (c),(d) but for experiment forced with twice thezonal asymmetrical forcing as the control January experiment. Shaded regions indicate absolute values greater than 100.


the Atlantic, the results of Chang (2001) hinted thatdamping due to surface sensible heat flux is much stron-ger in midwinter than in spring/fall.

Diabatic generation of EAPE can be estimated fromthe reanalysis data as a residual in the EAPE budget(see Chang 2001; Chang et al. 2002). We have done thatfor the NCEP–NCAR and European Centre for Me-dium-Range Weather Forecasts (ECMWF) 15-yr re-analyses. The results, based on the NCEP–NCAR re-analysis for the years 1982–94, averaged over the NHbetween the surface and 100 hPa, is shown in Table 1.Diabatic effects include radiative heating, which gener-ally damps the eddies, but the amplitude is small. Sur-face sensible heat flux usually damps the eddiesstrongly within the planetary boundary layer, while la-tent heat release generally acts as a source of EAPE inthe free troposphere (see Fig. 8 in Chang et al. 2002),partially (or nearly entirely, for the cases of Octoberand April) canceling the damping effects of sensibleheating. The results shown in Table 1 show that hemi-sphere wide (row 1), throughout the cool season, totaldiabatic effects exert a net damping on the eddies, withthe damping most severe in February and weakest inOctober and April. These seasonal differences are notinsignificant: for reference, in January the hemisphericmean baroclinic conversion per unit mass is about 24m2 s�2 day�1 and the barotropic conversion is about�2.3 m2 s�2 day�1. Hence the amplitude of the seasonalcycle in diabatic effects comes out to be about 15% ofmean baroclinic conversion. Results based on the 15-yrECMWF Re-Analysis (ERA-15) data are similar. Forthe Atlantic, a similar seasonal cycle is found, withstrongest damping in February, while in the westernPacific diabatic generation is positive in fall and springand negative in winter. Nevertheless, all three rows inTable 1 show that there is a significant seasonal cycle inthe effects of diabatic heating, with strongest dampingin midwinter.

In our model, the only diabatic forcing is Newtoniancooling (physically mimicking the effects of radiationand surface sensible heat fluxes), which always acts todamp transient eddies. The same damping is used forall experiments (the NH mean diabatic damping timescales in our model runs all come out to be close to 7days); hence the seasonally changing role of diabaticheating is clearly not present in our model simulations.

In appendix B, we will present results from a series ofidealized experiments to illustrate what possible effectsthe seasonally varying role of diabatic generation ofEAPE may have on the seasonal cycle of the NH stormtracks.

4. Experiments using a quasigeostrophic model

The primitive equation experiments described abovesuggest that changes in the stationary wave cannot ac-count for the weakening of the Pacific storm track dur-ing midwinter. In our simulations, the enhancement ofthe stationary wave actually leads to an increase in eddyamplitude over both storm tracks, albeit more pro-nounced in the Atlantic. This stands in contrast with theresults of Deng and Mak (2005), who showed that en-hanced deformation with a stronger stationary wavecould weaken the eddies in an idealized model. How-ever, because these authors only examined two syn-thetic flows, which they associated with an early winterand a midwinter situation, it is unclear how robust theirresults really are. In particular, it is not clear whetherthe different behavior documented above is due to in-trinsic differences in the models, or whether the resultsthat they describe might be sensitive to the flow con-figuration. In this section we investigate this issue usinga two-layer qg model similar to theirs but consideringmore general forms of forcing. Of particular interest iswhether the storm tracks might be self limiting, in thesense that the deformation is internally generated in thepresence of enhanced baroclinicity, rather than exter-nally imposed as in Deng and Mak (2005).

For this purpose, we first consider the case in whichthe zonally varying forcing is purely baroclinic. Themodel that we use is the two-layer qg model describedin Zurita-Gotor and Chang (2005), and the parameterschosen are also the same as in their control run. Inparticular, the model solves the standard qg potentialvorticity (PV) equation over both layers:

�qn

�t� �J��n, qn �

��1n

�

�1 � �2 � �R

�2 �1

�M�n2�2�n

� ��6�n, �2

where qn � �2�n � (�1)n(�1 � �2)/�2 � �y stands forthe potential vorticity in the upper (n � 1) and lower

TABLE 1. Diabatic generation of transient EAPE per unit mass, averaged over 20°–70°N (m2 s�2 day�1).

Oct Nov Dec Jan Feb Mar Apr

NH �0.21 �1.87 �3.06 �3.71 �4.21 �2.16 �0.66Western Pacific �1.61 �1.00 �0.07 �0.80 �1.99 �0.85 �2.57Atlantic �2.04 �4.04 �6.80 �7.08 �7.84 �7.11 �4.48


(n � 2) layers, and �n is the corresponding streamfunc-tion. We take a radius of deformation (based on thelayer depth) � � 700 km, a typical midlatitude � � 1.6� 10�11 m�1 s�1, a channel length L � 32 � 103 km,and diabatic and frictional time scales � � 20 and �M �4 days, respectively. The baroclinic component of theflow is relaxed to the following “radiative equilibrium”profile:6

�R � Umax�1 � sin�2x�Ld��

dy� ��y, �3

where the zonal mean maximum wind Umax � 30 m s�1

and the meridional structure of the zonal mean thermalwind (d��/dy) � �exp(�y2/�2) is a Gaussian profilewith half-width � � 2200 km. The parameter � is usedto change the amplitude of the zonally asymmetricheating and must be sufficiently large to maintain thestationary wave against the mean flow advection. Asdiscussed by Zurita-Gotor and Chang (2005), this pro-cedure is roughly equivalent to forcing the wavenumberone component of the flow with a shorter time scale.

Since this study investigates the role of deformation,it is important to choose realistic horizontal scales forthe flow. With the above forcing the equilibrium jet hasa width of 4000 km, equivalent to 35° latitude, which isroughly consistent with observations. We have con-firmed that the results remain qualitatively the same ifthe baroclinic zone is narrowed or broadened. On theother hand, our channel length is comparable to that ofa midlatitude latitude circle, but the storm track mightstill be too elongated due to our choice of a wavenum-ber-1 forcing. However, simulations with a halved chan-nel produced again qualitatively similar results.

Figures 8a–c shows the equilibrium climate for � � 3,which is also the standard value chosen by Zurita-Gotor and Chang (2005). As discussed in that paper,this setting of � produces zonal contrasts in the equi-librium baroclinicity (Fig. 8b) and eddy amplitude (Fig.8c) that compare reasonably to observations. In thissection, the square root of transient eddy kinetic energyEKE � 1⁄2(u�2 � ��2) (where primes denote differencesfrom the time mean) is used as a proxy for the localeddy amplitude. Although a conserved quantity likepseudoenergy would be more appropriate, it is hard to

estimate this quantity in the absence of Lagrangian sta-tistics. As an alternative, we have considered the waveactivity proposed by Plumb (1986) but found the diag-nostics to be dominated by the spatial structure of themean flow PV gradient. We have used the EKE normin our discussion because it is directly affected by baro-tropic conversions and emphasizes deformation, butqualitatively similar results were found with other eddynorms. The conclusions presented below also holdwhen using a 24-h difference filter to remove the low-frequency variability. However, we chose to present un-filtered results because in some of our idealized runsthe filtered data are affected by changes in the charac-teristic eddy frequency due to changes in the advectionspeed (see, e.g., Burkhardt and James 2006).

Despite the semirealistic baroclinicity and EKE inFigs. 8b,c, the small meridional excursions of thestreamlines in Fig. 8a suggest that the deformation ofthe flow might be too weak, which is not surprisingbecause the forcing is purely baroclinic. To test whetherdeformation ever becomes important in limiting theeddy amplitude when the zonal baroclinicity contrast isenhanced, we have performed additional experimentschanging the value of � in (3). For example, Figs. 8d–fshow the equilibrium flow for � � 9. Although theupper-level deformation is enhanced relative to theprevious case, the eddy amplitude modulation stillseems to be controlled by the very strong zonal con-trasts in baroclinicity (note that the eddy amplitudepeaks just downstream of the baroclinicity maximum).Thus, the storm track would still be classified as “baro-clinic” in the terminology of Whitaker and Dole (1995).Most importantly, the maximum eddy amplitude is alsosignificantly larger than before. Figure 9a shows thatthis is generally the case as � is increased, consistentwith the primitive equation results.

To assess the robustness of these results, we haveinvestigated the sensitivity of the eddy amplitude on �when a uniform easterly component �U � �20 m s�1 isadded in both layers. As discussed by Zurita-Gotor andChang (2005), this makes the wave–mean flow interac-tion more local and favors stronger zonal contrasts ineddy amplitude. This would also be more consistentwith the local character of the midwinter equilibrium inDeng and Mak’s (2005) simulations, as indicated by thestrong eddy amplitude modulation in their Fig. 12. Inprinciple, we expect that slowing down the flow in thismanner should make the eddies more sensitive to de-formation (Whitaker and Dole 1995). However, we findthat the addition of the easterly component affects pri-marily the minimum eddy amplitude but much less sothe maximum eddy amplitude (Fig. 9b), consistent with

6 Note that there is a typo in Eq. (2) of Zurita-Gotor and Chang(2005), which lacks the d�/dy factor modulating the meridionalstructure of the asymmetric component in (3). This factor ensuresthat the asymmetric component of �R is small at the meridionalwalls—provided they are sufficiently far—and makes the netzonal transport independent of longitude.


the results of Zurita-Gotor and Chang (2005). As aresult, the maximum eddy amplitude still increases with� in this more local regime.

These results, together with those presented in pre-vious sections, cast some doubts on the hypothesis thatthe midwinter suppression could be due to enhancededdy-induced deformation in a more baroclinic envi-ronment. However, it is still possible that the midwinter

eddy amplitude might be limited by enhanced exter-nally forced deformation. To investigate this possibility,we have studied the sensitivity of the same zonal flowconsidered above to an imposed barotropic deforma-tion. Since it is awkward to relax vorticity, we havechosen instead to force this problem using the sameprocedure as Whitaker and Dole (1995) and Deng andMak (2005). In particular, we make �R zonally symmet-

FIG. 8. Equilibrium state for the baroclinic run with � � 3: (a) upper-level streamfunction; (b) temperature; and(c) upper-level eddy amplitude, measured as the square root of EKE (m s�1). (d)–(f) Same as in (a)–(c) but for thebaroclinic run with � � 9.


ric in (3) and add a forcing term J(�En, qEn) to (2); �En

and qEn define the target equilibrium state of �n and qn,respectively, that would be realized in the absence ofeddies. The asymmetric part of this equilibrium state,purely barotropic, has the same meridional structure asthe baroclinic forcing considered earlier. In both layers

�En � Umax sin�2x�L��d��

dy, �4

which produces again a net zonal transport indepen-dent of longitude in each layer when integrated be-tween the distant meridional walls. Combined with thezonal mean of (3), this definition implies that the slow-est upper-level zonal wind at midchannel is exactly zeroin the eddy-free state when � � 1.

With this type of forcing the upper-level stationarywave is significantly stronger than before. For instance,Figs. 10a–c shows the equilibrated state for � � 1, thelargest value considered. Although the time-meanzonal flow does not vanish at midchannel—as it wouldin the absence of eddies—it is still quite strongly modu-lated, with a minimum (maximum) value of 9.2 (60.8)m s�1. Yet despite this extreme modulation the storm-track amplitude (the maximum EKE) increases ratherthan decreases relative to the zonally symmetric run.The same is also observed for intermediate values of �,as shown in Fig. 11a. Even more strikingly, Table 2shows that the domain-integrated EKE changes re-markably little with � and is actually enhanced by 7.3%for � � 1 relative to the zonally symmetric problem.

Following Cai and Mak (1990), we have calculated

FIG. 9. (a) Eddy amplitude at midchannel for the baroclinic runs with the values of �indicated. (b) Same but with an added advective component �U � �20 m s�1. ZS stands forthe zonally symmetric run with � � 0.


the kinetic energy conversion from the mean flow intoeddies C(K, K�) � E · D, with D defined by (1) and

E � �12

�� 2 � u 2, �u � �. �5

Figure 12a shows the results for � � 1, normalized byU3

max/�. As can be seen, negative values dominate: re-lating the global integral of this conversion term to that

of EKE (see Table 2), one finds that barotropic pro-cesses destroy EKE in a characteristic time scale ofabout 26 days. However, when the same calculation isperformed for the zonally symmetric problem (� � 0),for which the domain-integrated �E · D� reduces simplyto �E · D� � ��u��U/�y�, we find that EKE is actuallydestroyed faster, in a time scale of 17 days. The reasonswhy the barotropic dissipation is reduced in the pres-

FIG. 10. Same as in Fig. 8 but for (a)–(c) the barotropic run with � � 1 and (d)–(f) Whitaker and Dole’sparameters. Note that the contour unit is different in (a) and (d) because Umax is different.


ence of the stationary wave become apparent when weseparate between the zonal and meridional contribu-tions to E · D, shown in Figs. 12b,c. The latter contri-bution is dominated by the standard barotropic conver-sion term u��U/�y, which accounts for 90% of the fullEyDy (not shown). As can be seen, it is this term that ismostly responsible for the dominant negative characterof the full E · D. The ExDx component is predominantly

positive and actually reduces the domain-integratedEKE destruction by roughly 40%. Table 2 shows that,to a lesser extent, this is also true for intermediate val-ues of �.

The previous results are surprising in that they seemto contradict the barotropic storm-track paradigm putforward, among others, by Whitaker and Dole (1995).To make sure that this is not due to any fault of our

TABLE 2. Eddy kinetic energy and barotropic conversions in the two-layer qg model.

RUN �EKE� �E · D� �Ex Dx� �Ey Dy� �Ex Dx�/�Ey Dy�

ZS (� � 0) 1.23 � 106 �0.817 �0.006 �0.811 0.6%� � 0.25 1.22 � 106 �0.831 0.003 �0.833 �0.3%� � 0.5 1.19 � 106 �0.903 0.052 �0.955 �5.5%� � 0.75 1.23 � 106 �0.802 0.189 �0.991 �19.1%� � 1 1.32 � 106 �0.583 0.418 �1.001 �41.8%

FIG. 11. (a) Eddy amplitude at midchannel for the barotropic runs with the values of �indicated. (b) Same as in (a) but with Whitaker and Dole’s parameters.


model, we have tried to reproduce their results in thebarotropic storm track limit. This can be accomplishedby using a slower but broader radiative equilibriumzonal jet (Umax � 16 m s�1; � � 2800 km) and slightlydifferent forcing time scales [15(5) days for heating(friction)]. In addition, our equilibrium meridionalstructure can be made similar to theirs (which is definedthrough a different functional form) replacing thed�/dy factor in (4) by a broad Gaussian with half-width�2 � 4500 km. Figures 10d–f show results from a simu-lation with � � 0.55, which is close to the value thatWhitaker and Dole used. These results are both inqualitative and quantitative agreement with theirs: notein particular the very weak zonal modulation in baro-

clinicity (Fig. 10e), in contrast with Fig. 10b, eventhough the asymmetric forcing was also purely barotro-pic in that case. Hence, it is unambiguous in this case toattribute the zonal modulation of eddy amplitude tobarotropic deformation, as argued by Whitaker andDole (1995). Given the role played by barotropic pro-cesses for this flow, it is interesting to explore the sen-sitivity of the EKE to the strength of the stationarywave. The results are shown in Fig. 11b. Now, both themaximum and domain-integrated EKE strongly de-crease with the amplitude of the stationary wave.

We have performed a sensitivity analysis to under-stand what makes this flow so different from the pre-vious example. We found that the main factor is the

FIG. 12. (a) EKE conversion C(K, K�) � E · D, (b) its zonal component ExDx, and (c) itsmeridional component EyDy for the barotropic run with � � 1. Values are normalized withU 3

max/�.


very small value of Umax used by Whitaker and Dole.Taking Umax � 32 m s�1 instead, and keeping the rest ofthe parameters unchanged, gives results that are moreconsistent with those shown in Figs. 10a–c (not shown).In that configuration, the EKE is still strongly modu-lated with �, but its maximum and domain-integratedvalues change little or even increase slightly. There arethree reasons why the eddies could be more sensitive todeformation with weaker Umax. First, baroclinic growthis weak. Second, the slow upper-level wind favors morelocal modes. Finally, as discussed by Whitaker andDole (1995), the waves are more likely to break in re-gions of high deformation.

The previous example shows that it is not impossibleto limit the eddy amplitude through barotropic defor-mation, as suggested by Deng and Mak (2005). How-ever, lacking a deeper understanding of the stability ofzonally varying flow, it is hard to predict a priori whatmakes a certain flow more or less sensitive to deforma-tion. In our model, this seems to require a set of pa-rameters that we believe unrealistic: the upper-levelwind and midlevel baroclinicity are very weak in Figs.10d,e, and the EKE is also much weaker than in obser-vations. In contrast, the simulations of Deng and Mak(2005) appear to have a much faster zonal wind.Though Deng and Mak show that the zonal modulationin baroclinicity in their model climates is reasonablecompared to the seasonal evolution in the Pacific, it isunclear whether their deformation is also realistic. Acursory inspection of their Fig. 12 suggests that thestorm-track termination might be too abrupt in theirmidwinter scenario, which may be taken as a hint of anexcessive deformation. In contrast, the break in eddyamplitude between the Pacific and Atlantic stormtracks is much more moderate in Fig. 5. Moreover,while the ratio between the minimum and maximumeddy amplitude along the storm-track axis changes intheir runs from roughly 80% to 50% (0.5/0.62 to 0.2/0.4)between the early winter and midwinter scenarios, thisparameter does not exhibit a clear seasonal cycle inFig. 5.

5. Summary and conclusions

In this study, an attempt has been made to simulatethe seasonal cycle of the NH cool season storm tracksusing idealized nonlinear storm-track models. A primi-tive equation dry dynamical core model is forced withfixed radiative forcing, with the heat sources and sinksarranged (using an iterative procedure outlined in ap-pendix A) such that the model climate, in terms of thesimulated mean temperature distribution, resemblesthe observed climatological temperature distribution

for the different months in the cool season, except thatin some of our experiments the static stability of themodel climate has been reduced to enhance eddygrowth in the absence of diabatic generation of EAPEdue to moist processes.

Using this procedure, we obtain an excellent simula-tion of the seasonal cycle of the climatological monthlymean flow. However, our simulation of the seasonalcycle of the storm tracks turns out to be deficient (Figs.5 and 6). In agreement with observations, the modelAtlantic storm track exhibits a single peak in January.However, its simulated amplitude in October and Aprilis much too weak. For the Pacific storm track, the ob-served storm track peaks in November/December andMarch and has a relative minimum in February, withthe February storm-track activity weaker than those inOctober and April. The simulated Pacific storm trackpeaks in December/January, with a nearly indiscerniblerelative minimum in February. In addition, the simu-lated storm track for October and April is much weakerthan that for February, in contrast to what is observed.

Our model results suggest that changes in the struc-ture of the monthly mean flow alone are insufficient tofully account for the observed seasonal cycle in storm-track activity. We note that a recent study by Deng andMak (2005) suggested that the increase in the ampli-tude of stationary wave in winter, as compared to falland spring, could lead to enhancement in the deforma-tion, thus giving rise to the observed decrease in mid-winter storm-track activity. We have conducted sensi-tivity experiments by changing the amplitude of thestationary wave forcing, and our results suggest that anincrease in the amplitude of the stationary wave forcingoften leads to enhancement (instead of reduction) inboth the Pacific and Atlantic storm-track activity.

To further explore the sensitivity of storm-track am-plitude to the strength of the stationary wave forcing,several sets of experiments have been conducted usinga two-level qg model. These results confirm the resultsfrom the primitive equation model that increasing thebaroclinic stationary wave forcing (through increasingthe amplitude of zonally asymmetrical diabatic heatingand cooling) generally leads to an increase in the storm-track amplitude. Even though the deformation in theflow increases with the increase in the forcing, its effectsare not sufficient to counteract those of the increase inlocal baroclinicity. We have also tested whether an in-crease in externally imposed barotropic forcing couldgive rise to a decrease in the storm-track amplitude.However, our results show that if the zonal mean baro-clinicity is close to that observed, even purely barotro-pic stationary wave forcing gives rise to significantmodulation in the baroclinic stationary wave ampli-


tude. Because of that, the peak amplitude of the stormtrack is still not significantly decreased even under verystrong barotropic stationary wave forcing. Only whenthe zonal mean baroclinicity is much weaker than thatobserved does barotropic wave forcing act to apprecia-bly reduce the amplitude of the model storm track.

We are not suggesting that changes in mean flowstructure do not impact storm-track amplitudes. Previ-ous studies (Harnik and Chang 2004; Nakamura et al.2002) have suggested that changes in mean flow struc-ture can affect the degree of midwinter suppression. Inaddition, our results do suggest a slight decrease in Pa-cific storm-track amplitude when the model mean flowis forced to resemble that observed in midwinter (seeFigs. 6c,e).

Comparing our model results to those observed, it isapparent that changes in the zonal mean dry barocli-nicity have much greater impacts on the model storm-track amplitude than those observed. If changes in thestructure of the stationary waves, which are well simu-lated by our model, are unable to counteract thechanges in baroclinicity, what else could do that? Not-ing that the seasonal cycle of the storm tracks can bewell simulated by GCMs, we propose that the defi-ciency in our model simulations probably arise from thesimplistic model physics used in our model simulations.Diagnosing the seasonal cycle in eddy energetics, wefind that there is a significant seasonal cycle in diabaticgeneration of EAPE, with diabatic forcing acting as aweak sink of EAPE in October and April but becominga significant sink during midwinter. An ad hoc attemptis made to illustrate this effect in our model by varyingthe degree of reduction in the static stability of themodel climate (see appendix B), with the largest reduc-tion applied to October and April when the diabaticdamping is weakest, and the smallest reduction appliedto February when the diabatic damping is strongest.After the inclusion of this effect, our model is able toreproduce the observed storm-track seasonal cyclemuch better.

We are not implying here that we have successfully“explained” the midwinter suppression. Our main con-clusion is that our results suggest that the midwintersuppression is unlikely to be completely explained bydry dynamics alone. The observed mean flow is gener-ated by the balance between diabatic forcing, stationarywave transports, and eddy transports due to moist ed-dies. It is well known that given the same mean flow,moist eddies are much more active than dry eddies(e.g., Hayashi and Golder 1981). On the other hand,other studies (e.g., Williams 1988) have also shown thatgiven the same external forcings, the meridional tem-perature gradient in a dry simulation is much stronger

than that in a moist simulation, giving rise to similareddy amplitudes in a dry and moist atmosphere undersimilar radiative forcings but with very different basicflows in the two cases. Hence in the presence of a sig-nificant seasonal cycle in the effects of diabatic heatingon eddies as found in the reanalysis (and GCM) data, itis not surprising that dry dynamics alone, applied to theobserved mean flow (which has been generated bymoist eddies), is unable to fully explain the seasonalcycle.

Even if we are able to explain the seasonal cycle inthe storm-track amplitude given the mean flow struc-ture, we have not really completely solved the mysteryof the midwinter suppression. Reexamining Fig. 3c, it isclear that the zonal mean temperature gradient in themidtroposphere does not change much between No-vember and March. A complete explanation of the sea-sonal cycle of the storm tracks will also need to accountfor the reason why the zonal mean temperature gradi-ent appears to be so insensitive to the seasonal changesin radiative forcing from late fall through early spring.

Acknowledgments. E. C. would like to thank Dr. I.Held for providing the GFDL dynamical core, whichwas adapted into the nonlinear storm-track model. Theauthors thank the anonymous reviewers for helpfulcomments. E.C. was supported by NSF GrantATM0296076 and NOAA Grant NA16GP2540. P. Z.-G.was supported by the Visiting Scientist Program at theNOAA/Geophysical Fluid Dynamics Laboratory ad-ministered by the University Corporation for Atmo-spheric Research.

APPENDIX A

Iterative Procedure for NonlinearStorm-Track Model

The nonlinear storm-track model is built upon thedynamical core of the spectral climate model developedat the Geophysical Fluid Dynamics Laboratory (Heldand Suarez 1994). Details of the model formulation canbe found in Chang (2006). Here we summarize the it-erative procedure used to obtain the diabatic heatingthat forces the model.

Diabatic forcings are represented by Newtoniancooling toward a radiative equilibrium potential tem-perature profile ( E). With this parameterization, thefirst law of thermodynamics can be written as

D�

Dt� �

� � �E

�� 8�, �A1

where � is the radiative time scale, taken to be 30 daysin the free atmosphere (� � 0.7) and decreasing to 2


days at the surface (� � 1). The variable E can be splitinto two parts as follows:

�E � �C � �Q. �A2

Here C can be viewed as the desired model climate.For illustrative purposes only, the model variables canbe partitioned into a time-mean part and a transientpart (note that no such partition is done in the actualmodel), that is,

� � � � � ; u � u � u ; etc. �A3

Substituting (A3) and (A2) into (A1), taking the timemean, and ignoring diffusion, we get

��

�t� � · u� � � · u��

� � �C

�� Q. �A4

When � C , Q is the only diabatic forcing in themodel and can be regarded as the climatological meannet diabatic heating rate.

In (A4), it can be seen that for the model climate ( )to be close to the one desired ( C), the heating Q mustbalance mean and eddy heat transports in the model.Since these transports are not known a priori, the exactform of Q is not known at the outset. To get to a de-sirable Q, an iteration is started with a first guess, sayQ0, and the model is run. In general, the model climate 0 will be different from C. A new Q, Q1, is then com-puted, using

QN � QN�1 �23

�N�1 � �C

�, N � 1, 2, 3, . . . ,

�A5

with the factor 2/3 in (A5) introduced to avoid over-corrections. A new run is then made with the new Q,and the procedure is repeated until the globally aver-aged RMS difference between TN and TC is less than0.7 K (TN and TC are the temperature distributionscorresponding to N and C). Due to the strong internalvariability in the model climate, we have found that inpractice it is difficult to achieve better agreement be-tween model and target temperature structures.

As discussed in Chang (2006), when the model isforced to the observed January climatological tempera-ture distribution, the eddy variances are found to bemuch weaker than observed (see also Figs. 6e,f). Thestudy of Hayashi and Golder (1981) showed that con-densational heating not only acts as a source of EAPE,but, more importantly, it acts to strongly enhance baro-clinic energy conversion. One way of mimicking part ofthis effect is by reducing the static stability of the at-mosphere. Instead of using the observed temperature

profile as the target climate, a profile with reducedstatic stability is imposed as follows:

�C � �obs�x, y, p � Az�p, �A6

where z(p) is the average geopotential height of thepressure surface. Chang (2006) found that a value of1.25 K km�1 for A provides realistic amplitudes of eddyfluxes for January. This value is used for the experi-ments shown in Figs. 1–5, 6c,d, and 7.

APPENDIX B

Experiments with Seasonally Varying Reduction inStatic Stability

In section 3c, we showed that there is a seasonal cyclein the diabatic generation of EAPE, with diabatic ef-fects being highly damping during the midwinter and

FIG. B1. (a) Same as in Fig. 5h but with the static stabilityreduced by 2 K km�1. (b) Same as in (a) but for January. (c) Sameas in (a) but for April.

TABLE B1. Reduction in static stability (K km�1) used for thedifferent months.

Oct Nov Dec Jan Feb Mar Apr

2.0 1.6 1.4 1.25 1.0 1.6 2.0


much less so (or even weakly positive) during springand fall. Here, we attempt to qualitatively illustrate itspossible effects on baroclinic generation by changingthe static stability of the mean climate. As discussed inappendix A, in order to obtain realistic eddy ampli-tudes in January, we need to decrease the static stabilityin our model by 1.25 K km�1. To represent the strongereffects of moist heating in October, we reduce the staticstability of the model climate even further. Fig. B1shows the storm-track distribution for October, Janu-ary, and April when the static stability is decreased by2 K km�1. The model storm tracks for October andApril are clearly stronger than those in the originalsimulations (Figs. 5h,n) and are now closer to the in-tensity observed. Obviously, if we use the same reduc-tion for January (Fig. B1b), the model January stormtracks will also become stronger and will stay muchstronger than those for October and April.

To illustrate the seasonally changing role of diabaticheating, we impose different reduction of the static sta-bility for the different months. The values range from 2K km�1 for October and April to a low of 1 K km�1 forFebruary. The values used for all the individual monthsare shown in Table B1. These values are motivated bythe results shown in Table 1, with minimum reductionin static stability (for February) corresponding tostrongest diabatic damping. The seasonal cycle of thePacific and Atlantic storm tracks in this set of experi-ments is shown in Fig. B2. The evolution seen in Fig. B2is clearly in much better agreement with the seasonalcycle seen in the reanalysis (Figs. 6a,b) than the originalsets of experiments (Figs. 6c–f). The Pacific storm tracknow has a clear minimum in February, and the Atlanticstorm track is no longer excessively weak in Octoberand April. These results suggest that the seasonal cyclesof both the Pacific and Atlantic storm tracks may besuccessfully simulated if we impose both the seasonalchanges in the mean flow structure, as well as model the

effect of the seasonally varying impacts of diabaticheating on the eddies. Clearly, these experiments arehighly idealized and do not capture all the effects ofmoisture on storm tracks. Experiments with more real-istic treatment of diabatic effects should be conductedto further pursue this point.

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