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    (a) Differences in 500-hPa mean geopotential height, between HI and LO Pacific storm-track Januaries (contour interval is 30 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 for LO 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).

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    (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.

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    (a) Pattern correlation between Figs. 2a–g and 2h–n. (b) Evolution of the amplitude of the stationary wave (m) at 500-hPa level. (c) Evolution of the temperature difference (K) between 21° and 69°N at 700-hPa level. In (b),(c), solid line is taken from NCEP–NCAR reanalysis and dashed line from idealized model simulations.

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    (a) Stretching deformation (Dx; CI = 5 × 10−6 s−1) and (b) shearing deformation (Dy; CI = 1 × 10−6 s−1) at 250 hPa for October; (c),(d) Same as in (a),(b) but for January, and (e) vertically averaged barotropic conversion rate (CI = 10 m2 s−2 day−1) for January computed based on NCEP–NCAR reanalysis data. (f)–(j) Same as in (a)–(e) but computed based on idealized model simulations. 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), and greater than 10 in (e),(j).

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    (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.

  • View in gallery

    (a) Seasonal cycle in the standard deviation of 24-h filtered 500-hPa geopotential height (CI = 10 m) for the 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 idealized model simulations. (e),(f) Same as in (c),(d) but from simulations without reduction in static stability. Shaded regions indicate absolute values greater than 100.

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

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    Equilibrium state for the baroclinic run with α = 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 the baroclinic run with α = 9.

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    (a) Eddy amplitude at midchannel for the baroclinic runs with the values of α indicated. (b) Same but with an added advective component ΔU = −20 m s−1. ZS stands for the zonally symmetric run with α = 0.

  • View in gallery

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

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

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    (a) EKE conversion C(K, K′) = E · D, (b) its zonal component ExDx, and (c) its meridional component EyDy for the barotropic run with α = 1. Values are normalized with U3max/λ.

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    Fig. B1. (a) Same as in Fig. 5h but with the static stability reduced by 2 K km−1. (b) Same as in (a) but for January. (c) Same as in (a) but for April.

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    Fig. B2. (a),(b) Same as in Figs. 6c,d but from simulations with reduction in static stability that varies according to Table B1.

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

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  • 1 Institute for Terrestrial and Planetary Atmospheres, Marine Sciences Research Center, Stony Brook University, Stony Brook, New York
  • | 2 UCAR Visiting Scientist Program, GFDL, Princeton, New Jersey
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Abstract

In this study, an idealized nonlinear model is used to investigate whether dry dynamical factors alone are sufficient for explaining the observed seasonal modulation of the Northern Hemisphere storm tracks during the cool season. By construction, the model does an excellent job simulating the seasonal evolution of the climatological 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 stronger sensitivity to the mean flow baroclinicity than observed, producing too-large midwinter eddy amplitudes compared to fall and spring. This is the case not only over the Pacific, where the observed midwinter minimum is barely apparent in the model simulations, but also over the Atlantic, where the October/April eddy 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 the presence of concomitant stronger deformation due to the enhanced stationary wave. The same was found to be the case in a simpler quasigeostrophic model, in which the eddy amplitude nearly always increases with baroclinicity, and deformation only limits the maximum eddy amplitude when the baroclinicity is unrealistically weak. Overall, these results suggest that it is unlikely that dry dynamical effects alone, such as deformation, 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 heating on baroclinic wave development in order to fully explain the seasonal cycle of the storm tracks. A set of highly idealized experiments that attempts to represent some of the impacts of moist heating is presented in an appendix to suggest that deficiencies in the model-simulated seasonal cycle of both storm tracks may be corrected when these effects, together with observed seasonal changes in mean flow structure, are taken into account.

* Current affiliation: Universidad Complutense, Madrid, Spain

Corresponding author address: Dr. Edmund K. M. Chang, ITPA/MSRC, Stony Brook University, Stony Brook, NY 11794-5000. Email: kmchang@notes.cc.sunysb.edu

Abstract

In this study, an idealized nonlinear model is used to investigate whether dry dynamical factors alone are sufficient for explaining the observed seasonal modulation of the Northern Hemisphere storm tracks during the cool season. By construction, the model does an excellent job simulating the seasonal evolution of the climatological 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 stronger sensitivity to the mean flow baroclinicity than observed, producing too-large midwinter eddy amplitudes compared to fall and spring. This is the case not only over the Pacific, where the observed midwinter minimum is barely apparent in the model simulations, but also over the Atlantic, where the October/April eddy 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 the presence of concomitant stronger deformation due to the enhanced stationary wave. The same was found to be the case in a simpler quasigeostrophic model, in which the eddy amplitude nearly always increases with baroclinicity, and deformation only limits the maximum eddy amplitude when the baroclinicity is unrealistically weak. Overall, these results suggest that it is unlikely that dry dynamical effects alone, such as deformation, 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 heating on baroclinic wave development in order to fully explain the seasonal cycle of the storm tracks. A set of highly idealized experiments that attempts to represent some of the impacts of moist heating is presented in an appendix to suggest that deficiencies in the model-simulated seasonal cycle of both storm tracks may be corrected when these effects, together with observed seasonal changes in mean flow structure, are taken into account.

* Current affiliation: Universidad Complutense, Madrid, Spain

Corresponding author address: Dr. Edmund K. M. Chang, ITPA/MSRC, Stony Brook University, Stony Brook, NY 11794-5000. Email: kmchang@notes.cc.sunysb.edu

1. Introduction

It is well known that the storm tracks in the Northern Hemisphere (NH) exhibit different seasonal cycles (e.g., Nakamura 1992). The Atlantic storm-track activity is most intense during midwinter, when the meridional temperature gradient across the storm track is strongest. On the other hand, the Pacific storm-track activity is most intense in late fall and exhibits a relative minimum during midwinter and then a second peak during early spring. It is worth noting that the meridional temperature gradient across the Pacific storm track is also strongest during midwinter. This observed negative correlation between the Pacific storm-track activity and western Pacific baroclinicity is clearly something that one would like to understand.

While this so-called midwinter minimum (or midwinter suppression) of the Pacific storm track can be found in GCM simulations (e.g., Christoph et al. 1997; Zhang and Held 1999), the mechanism that gives rise to this phenomenon is still not well understood. Zhang and Held (1999) successfully simulated the midwinter minimum using a linear stochastic storm-track model forced by monthly mean flow taken from a GCM simulation. Their results suggest that the midwinter minimum could be explained by the seasonal changes in the mean flow structure. However, an earlier attempt by Whitaker and Sardeshmukh (1998) was unsuccessful. To date, it is still not clear why the results of the two studies differ, except perhaps that the model used by Zhang and Held (a 14-level primitive equation model) may be more sophisticated than that used by Whitaker and Sardeshmukh [a two-level quasigeostrophic (qg) model].

Recently, Deng and Mak (2005) conducted idealized modeling studies in an attempt to interpret the midwinter minimum. They forced a two-level qg model using idealized potential vorticity structures, namely, a region of sharp potential vorticity gradient representing the storm track environment, with a region of strongly diffluent flow downstream representing the storm-track exit region. They found that when they increased the amplitude of the forcing, both the growth rate of the most unstable linear normal mode and the amplitude of the nonlinearly equilibrated storm track decrease substantially, mainly due to the effect of strong eddy dissipation in the enhanced deformation field. They concluded that the midwinter minimum of the Pacific storm track is due to the excessive amplitude of the midwinter deformation.

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

Let us reconsider the results of Zhang and Held (1999). They constructed a linear stochastic model, using stochastic forcing superposed on different basic states representing the mean flow of the different months. They found that if they use the same forcing for the different months, they were able to obtain stronger storm tracks in fall and spring than in midwinter.

One of the weaknesses of linear storm-track models is that the amplitude of the model storm track is directly proportional to the arbitrary amplitude of the prescribed forcing. While one can argue that using the same amplitude of forcing for the different months may be a reasonable first start, there is no theoretical justification that the amount of nonlinear scattering, which is what the stochastic forcing represents, should necessarily be the same over the seasonal cycle. For example, while the storm-track amplitude over the Pacific, in terms of upper tropospheric geopotential height variance, is as strong in October/April as in midwinter, the observed eddy heat flux in October/April is weaker than that in midwinter.1 Based on this, one might argue that the eddy source in October/April should be weaker than that in midwinter.

In this study, an idealized nonlinear storm-track model will be used in an attempt to simulate the seasonal cycle of the NH storm tracks. The model (described in section 2) generates realistic baroclinic wave and storm-track structure. Being nonlinear, the amplitude of the model storm track is determined internally by nonlinear equilibration. In these aspects, the model can be regarded to be more sophisticated than those used in previous idealized studies.

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

2. An idealized nonlinear storm-track model

The model is based on the dynamical core of the Geophysical Fluid Dynamics Laboratory (GFDL) global spectral model (Held and Suarez 1994). The resolution used in this study is T42 in the horizontal and 10 evenly spaced sigma levels in the vertical. This resolution should be sufficient for our purposes here, since Zhang (1997) showed that the midwinter suppression of the Pacific storm track can be found in a nine-level, R30 GCM seasonal run. Realistic orography, smoothed to model resolution, is imposed. A land–sea mask is used, with stronger surface friction over land. The friction is in the form of a drag quadratic in the wind speed and is equivalent to having a surface stress with CD = 0.0015 (0.004) over ocean (land), with the stress decreasing to 0 at the top of the first model layer, which represents 10% of the atmospheric mass. Diabatic heating is represented by Newtonian cooling, with a damping time scale of 30 days in the free atmosphere (σ < 0.7), decreasing to 2 days at the surface (σ = 1). The only other damping is a highly scale selective diffusion (∇8), with a damping time scale of 0.1 days on the highest wavenumber.

The only forcing imposed is Newtonian damping to a radiative equilibrium temperature profile. For each experiment, the equilibrium temperature profile is iteratively determined, such that at the end of the process, the model climate, as given by the time mean three-dimensional temperature distribution, is nearly identical to a desired target temperature distribution. The procedure used to determine the equilibrium profile for each experiment is summarized in appendix A. More details concerning the model formulation can be found in Chang (2006).

As discussed in Chang (2006), when the model climate is forced to resemble the three-dimensional January climatological temperature distribution [as given by the 1982–94 mean taken from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data], the model 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 in the atmosphere, diabatic heating due to latent heat release can act to enhance eddy growth (e.g., Gutowski et al. 1992; Davis et al. 1993). As suggested by the results of Hayashi and Golder (1981), who compared dry and moist development of baroclinic waves under the same zonal mean flow, eddy growth in the presence of latent heat release is enhanced not only by the eddy energy generated by the latent heat release but also by the fact that baroclinic energy conversion is strongly enhanced in the presence of moisture. Chang (2006) suggested that such an enhancement of baroclinic energy generation could be partially imitated by a reduction in the static stability. Chang (2006) showed that when the model vertical potential temperature gradient is reduced everywhere by 1.25 K km−1, realistic eddy amplitudes can be obtained (see also Figs. 5d,k). In this study, unless otherwise stated, we will use the same reduction in the static stability in our numerical experiments.

One may question whether reducing the static stability will lead to reduction in the eddy scale and result in eddies that are too small in the simulations. We estimated the average eddy scale (in terms of half wavelength) using one-point regression analysis applied to 300-hPa meridional velocity perturbations (Lim and Wallace 1991) at 40°N near the date line. The scale estimated from reanalysis is about 25° longitude, and that estimated from our dry simulations without reducing the static stability is about 29°, while for the simulations with static stability reduced by 1.25 K km−1, the eddy scale is estimated to be about 27°. Hence the eddy scale in our model simulations is not very sensitive to the 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 that the small difference in eddy scale between our model simulations and reanalysis is a critical flaw of the model.

Here we will first apply the model to examine whether it can simulate strengthening/weakening of the Pacific storm track. We have examined the observed interannual variability of the January Pacific storm track in terms of 700-hPa poleward heat flux computed based on a 24-h difference filter (see Wallace et al. 1988) over the period 1979 to 1999. Out of these 21 Januaries, the five years with the strongest eddy heat flux (HI years) were 1979, 1982, 1987, 1989, and 1990. The Pacific storm track was weakest during the Januaries of 1980, 1981, 1984, 1995, and 1998 (LO years). The differences between the HI and LO composites are shown in Fig. 1. In Fig. 1b, we see that the eddy heat flux at 700 hPa was clearly stronger in the Pacific during the HI years, and the Atlantic heat flux was also stronger (see Chang 2004). Another common measure of storm-track activity is the standard deviation of filtered 500-hPa geopotential height (see Wallace et al. 1988). The composites for the HI and LO years are shown in Figs. 1c,d, respectively. We can see that both storm tracks were stronger during the HI years. The difference in the observed mean flow structure is shown in Fig. 1a. We can see an anticyclonic anomaly over the Pacific, consistent with weakening and broadening of the Pacific jet2 [consistent with the results of Nakamura et al. (2002) and Harnik and Chang (2004)].

Two sets of model runs have been conducted using our idealized storm-track model. One set is forced to resemble the temperature structure of the HI composite (taken from the NCEP–NCAR reanalysis but with static stability reduced as discussed above), while the other is forced to resemble the LO composite. The differences between the two experiments are shown in Figs. 1e,f. The pattern of the difference in time-mean 500-hPa geopotential height (Fig. 1e) resembles observed (Fig. 1a) quite well, except the amplitude is a bit weak, especially over North America and the Atlantic. This is related to the fact that the iterative procedure is unable to converge to the exact desired temperature distribution due to strong internal climate variability (see discussions in appendix A and Chang 2006). Nevertheless, we can see the prominent anticyclonic anomaly over the Pacific, as well as the cyclonic anomaly over northern Eurasia.

Regarding the storm tracks, the model clearly simulates significantly stronger heat fluxes over the Pacific for 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 geopotential height is also stronger for the HI experiment (Figs. 1g,h). Hence Fig. 1 confirms that the model can simulate interannual change in the Pacific storm-track activity reasonably well. In addition, based on canonical correlation analyses performed between mean flow and storm-track anomalies, Chang (2006) showed that the observed month-to-month storm-track/mean flow covariability is well simulated in the idealized model. These results demonstrate that the idealized model performs well 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 height), based on the NCEP–NCAR reanalysis for the years 1982 to 1994, is shown in Figs. 2a–g. We can see that during the entire cool season (October through April), there is a trough centered near Japan, a ridge over western North America, a trough over northeastern North America, and a ridge over eastern Atlantic extending into Europe. Over the season, there are slight shifts in the position of the centers, but the most obvious 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 see that the amplitude of the NH stationary wave changes by about a factor of 2 between midfall/spring and midwinter.

Figures 2h–n show how well our idealized model simulations can reproduce the observed stationary wave structure. These panels show results from seven different experiments. In each experiment the model climate is iterated until the time-mean three-dimensional temperature distribution is close to that observed for that month (except that the stability is reduced; see discussions above). Quantitative comparisons between the lhs and rhs panels are shown in Fig. 3. The pattern correlation between the stationary wave for each month, over the NH between 20° and 70°N, is shown in Fig. 3a. The correlation is above 0.9 for November through March and is about 0.88 in October and 0.89 in April, when the stationary wave is weakest. As far as the amplitude is concerned, the model stationary wave is slightly weaker than observed (Fig. 3b), but the seasonal cycle is clear. To put these results into perspective, the agreement between our results and the reanalysis is much better than that between an Atmospheric Model Intercomparison Project (AMIP) run (for the same period considered) using the GFDL R30 GCM (Broccoli and Manabe 1992) and the reanalysis (the pattern correlation for the GCM run lies between 0.79 and 0.87). This is not entirely unexpected, since in our experiments we attempt to force the model temperature distribution to that observed, while nothing like that is explicitly done in the GCM experiment.

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

Since one of the hypotheses we want to examine is whether seasonal changes in the deformation of the mean flow alone might be enough to explain the seasonal cycle of the storm tracks, we need to first make sure that the deformation is well simulated in our experiments. Following Cai and Mak (1990), the deformation vector is defined as follows:
i1520-0469-64-7-2309-e1a
In spherical coordinates, the deformation vector can be written as (e.g., Batchelor 1967, p. 601)
i1520-0469-64-7-2309-e1b
Here ϕ is the latitude, λ is the longitude, and a is the radius of the earth. The two components of the vector D, computed based on (1b) using NCEP–NCAR reanalysis data at 250 hPa for October and January, are shown in Figs. 4a–d, while those from the idealized model simulation are shown in Figs. 4f–i. We can see that the model simulates both components of the deformation very well, with pattern correlation above 0.95 over the entire NH, as well as over the eastern Pacific, and the RMS amplitude of both components are within 7% of that observed. The model deformation for the other months (not shown) are also well simulated and show the clear seasonal cycle of being weakest in October/April and strongest in January/February.

b. Seasonal cycle of the eddies

The seasonal cycle of the Pacific and Atlantic storm tracks, in terms of standard deviation of 24-h filtered 500-hPa geopotential height, as seen in the NCEP–NCAR reanalysis, for the years 1982–94, is shown in Figs. 5a–g. We can see that the Atlantic storm track has a relatively simple seasonal cycle, strengthening from October to January and then weakening after that. For the Pacific storm track, it is strongest in November and December, a bit weaker in March, even more so in January, and weakest in February. The Pacific storm track in October and April is slightly weaker than in January but stronger than in February. For the Pacific storm 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 simulated by the idealized storm-track experiments, is shown in Figs. 5h–n and 6c,d. The model Atlantic storm track is clearly strongest in January and weakest in October and April, in agreement with observations. However, the simulated amplitude of the seasonal cycle is much larger than that seen in the reanalysis, with the model storm tracks in October and April much weaker than that in the other months (Fig. 6d), while in the reanalysis the differences are not as pronounced (Fig. 6b).

The simulated seasonal cycle of the Pacific storm track is even worse. The model storm track is strongest in December and January, slightly weaker in November and March, even more so in February, but much weaker in October and April. Instead of the midwinter minimum, there is a winter maximum (Fig. 6c). There is a hint of a relative minimum in February,3 but in the model simulation, the February Pacific storm track is substantially stronger than those in October and April, clearly inconsistent with what is observed. This failure occurs even though we have achieved excellent simulation of the time-mean flow.

To verify that the dynamics of the eddies in our simulations are consistent with observed eddies, we have computed the eddy kinetic energy (EKE) budget for the transient eddies (see Chang 2001 for details), both for all transients and for high-frequency (24 h filtered) transients. In the simulations, as in the reanalysis, eddies grow due to baroclinic conversion, with peak baroclinic conversion over the two storm-track regions (not shown). Barotropic conversion, computed from reanalysis and the idealized model simulation for the high-frequency eddies for January, is shown in Figs. 4e,j, respectively. We can see negative conversion over the eastern portions of both storm tracks, with the model barotropic conversion weaker than that computed from reanalysis, especially over the Atlantic. However, EKE in the model simulation (not shown) is also weaker than that observed; hence the overall barotropic damping time scales for high-frequency eddies4 in the model simulation (8.2 days for NH and 3.3 days over the eastern Pacific) are not very different from those computed based on reanalysis data (7.6 and 3.1 days, respectively).

To test the robustness of our results, we conducted a separate set of experiments without reducing the static stability of the model climate (i.e., the target temperature distributions are the actual climatological temperature distribution of the different months). The results are summarized in Figs. 6e,f. Overall, the simulated storm-track amplitude is significantly weaker than observed. Nevertheless, the January maximum for the Atlantic storm track is simulated, but again, the storm track is clearly much too weak in October and April. For the Pacific storm track, the maximum for this set occurs in December, with amplitude slightly larger than in November, January, and February and significantly so than in October and April, with the results showing a slight hint of a minimum in January. These results show that our model results are not sensitive to the reduction of static stability employed in the simulations.

c. Discussions

Deng and Mak (2005) suggested that the midwinter minimum occurs mainly because of seasonal changes in the deformation associated with the stationary waves; the stationary waves in midwinter are much stronger than those during fall/spring, and the stronger deformation strongly enhances barotropic dissipation such that the storm track is weaker when the stationary wave amplitude is strong, despite enhancement of baroclinicity near the jet core. Deng and Mak used analytical forcing functions to represent what they regard as “plausible” forcings. Here we will use our model with mean flow structures close to those observed to test their hypothesis.

Two different sets of experiments have been performed to test this hypothesis. In the first set, the target temperature structure of the January basic state is changed, such that the zonal asymmetrical part is replaced by that of October, but the zonal mean part remains the same. Thus the zonal mean baroclinicity is not changed, while the stationary wave amplitude is reduced. The stationary wave in this new experiment is shown in Fig. 7a. This should be compared with that of the standard January experiment (Fig. 2k). The storm tracks for this experiment are shown in Fig. 7b. We see that with a decrease in the stationary wave amplitude, the amplitude of the Pacific storm track decreases slightly, while that of the Atlantic storm track decreases substantially (cf. to Fig. 5k). We have performed similar experiments by forcing to the zonal asymmetric temperature distributions of November, March, and April, and the results are similar.

In the second set of experiments, we first reduce the amplitude of the zonal asymmetrical part of the January diabatic forcing [both θc and Q in (A4)] by a factor of 0.5, and in another experiment, we increase the amplitude of the asymmetric part by a factor of 2. In both cases, the zonal mean diabatic forcing again stays the same. The results of these two experiments are shown in Figs. 7c–f. The stationary wave (as well as the deformation, which is not shown) for the weaker forcing case is clearly weaker (cf. Fig. 7c to Fig. 2k), while that for the stronger forcing case is substantially stronger (Fig. 7e), as expected. However, the two storm tracks are weaker in the weak forcing case (Fig. 7d) than in the strong forcing case (Fig. 7f), even though in the strong forcing case, the stationary wave amplitude (and deformation) is clearly much stronger than the observed climatological stationary wave amplitude for January (Fig. 2d).

One may wonder whether the results above are consistent with those shown in Fig. 1, which suggest that the storm track is stronger when there is an anomalous ridge over the Pacific, or, in the words of Nakamura et al. (2002), when the winter monsoon is weak. However, note that the pattern correlation between the pattern shown in Fig. 1a and the climatological stationary wave (Fig. 2d) is only −0.08 for the NH and −0.26 from 30°E to the date line, showing that Fig. 1 does not correspond to a reduction in the climatological stationary wave amplitude.

Another expectation is that when the stationary wave is strong, the heat transport by the stationary wave should be stronger, hence necessitating less heat transport by the transients. Indeed, when we diagnosed the heat transport in these two experiments and the January control experiment, the heat transport by the stationary wave is strongest in the strong stationary wave case, and the total zonal mean transient heat transport for that case is slightly weaker than in the other cases. However, the zonal mean high-pass-filtered transport turns out to be not weaker,5 and since it is now more zonally localized, the high-pass heat transport over the storm tracks is stronger than in the two other cases. This applies not only to the 24-h difference filter, but also when the eddies are defined using a 2–8-day filter after Blackmon (1976).

Our results suggest that the midwinter minimum is unlikely to be simply explained by seasonal changes in the mean flow structure. What other mechanisms can contribute to this phenomenon? Nakamura (1992) speculated about a number of possible mechanisms, including wave saturation, excessive deformation, excessive advection, trapping of waves near the surface, the effect of moisture, and change in upstream seeding. Most of these, apart from the effects of moisture, are dynamical in nature and should be present in our nonlinear storm-track model.

The fact that GCM runs, using similar resolutions as our experiments, can successfully simulate this seasonal cycle, while our model cannot, suggests that the failure probably lies in the simplistic physical parameterizations that we use. One such possibility has been discussed in Chang (2001). Based on analyses of GCM and reanalysis data, Chang (2001) showed that over the western Pacific, the diabatic generation of transient eddy available potential energy (EAPE) is much stronger in October than in January. Results from the GCM simulation suggested that this is due to two effects: total diabatic heating is stronger in October and the diabatic heating anomalies correlate better with temperature anomalies in October than in January. Chang and Song (2006) examined the distribution of precipitation around cyclones using reanalysis model-generated precipitation, ship precipitation reports, and satellite-retrieved precipitation. Their results show that in midwinter western Pacific cyclones a larger proportion of the precipitation occurs as convection in the cold air behind cold fronts, thus reducing the correlation between diabatic heating and temperature anomalies. For the Atlantic, the results of Chang (2001) hinted that damping due to surface sensible heat flux is much stronger in midwinter than in spring/fall.

Diabatic generation of EAPE can be estimated from the reanalysis data as a residual in the EAPE budget (see Chang 2001; Chang et al. 2002). We have done that for the NCEP–NCAR and European Centre for Medium-Range Weather Forecasts (ECMWF) 15-yr reanalyses. The results, based on the NCEP–NCAR reanalysis for the years 1982–94, averaged over the NH between the surface and 100 hPa, is shown in Table 1. Diabatic effects include radiative heating, which generally damps the eddies, but the amplitude is small. Surface sensible heat flux usually damps the eddies strongly within the planetary boundary layer, while latent heat release generally acts as a source of EAPE in the free troposphere (see Fig. 8 in Chang et al. 2002), partially (or nearly entirely, for the cases of October and April) canceling the damping effects of sensible heating. The results shown in Table 1 show that hemisphere wide (row 1), throughout the cool season, total diabatic effects exert a net damping on the eddies, with the damping most severe in February and weakest in October and April. These seasonal differences are not insignificant: for reference, in January the hemispheric mean baroclinic conversion per unit mass is about 24 m2 s−2 day−1 and the barotropic conversion is about −2.3 m2 s−2 day−1. Hence the amplitude of the seasonal cycle in diabatic effects comes out to be about 15% of mean baroclinic conversion. Results based on the 15-yr ECMWF Re-Analysis (ERA-15) data are similar. For the Atlantic, a similar seasonal cycle is found, with strongest damping in February, while in the western Pacific diabatic generation is positive in fall and spring and negative in winter. Nevertheless, all three rows in Table 1 show that there is a significant seasonal cycle in the effects of diabatic heating, with strongest damping in midwinter.

In our model, the only diabatic forcing is Newtonian cooling (physically mimicking the effects of radiation and surface sensible heat fluxes), which always acts to damp transient eddies. The same damping is used for all experiments (the NH mean diabatic damping time scales in our model runs all come out to be close to 7 days); hence the seasonally changing role of diabatic heating is clearly not present in our model simulations. In appendix B, we will present results from a series of idealized experiments to illustrate what possible effects the seasonally varying role of diabatic generation of EAPE may have on the seasonal cycle of the NH storm tracks.

4. Experiments using a quasigeostrophic model

The primitive equation experiments described above suggest that changes in the stationary wave cannot account for the weakening of the Pacific storm track during midwinter. In our simulations, the enhancement of the stationary wave actually leads to an increase in eddy amplitude over both storm tracks, albeit more pronounced in the Atlantic. This stands in contrast with the results of Deng and Mak (2005), who showed that enhanced deformation with a stronger stationary wave could weaken the eddies in an idealized model. However, because these authors only examined two synthetic flows, which they associated with an early winter and a midwinter situation, it is unclear how robust their results really are. In particular, it is not clear whether the different behavior documented above is due to intrinsic differences in the models, or whether the results that they describe might be sensitive to the flow configuration. In this section we investigate this issue using a two-layer qg model similar to theirs but considering more general forms of forcing. Of particular interest is whether the storm tracks might be self limiting, in the sense that the deformation is internally generated in the presence of enhanced baroclinicity, rather than externally imposed as in Deng and Mak (2005).

For this purpose, we first consider the case in which the zonally varying forcing is purely baroclinic. The model that we use is the two-layer qg model described in Zurita-Gotor and Chang (2005), and the parameters chosen are also the same as in their control run. In particular, the model solves the standard qg potential vorticity (PV) equation over both layers:
i1520-0469-64-7-2309-e2
where qn = ∇2ψn + (−1)n(ψ1ψ2)/λ2 + βy stands for the potential vorticity in the upper (n = 1) and lower (n = 2) layers, and ψn is the corresponding streamfunction. We take a radius of deformation (based on the layer depth) λ = 700 km, a typical midlatitude β = 1.6 × 10−11 m−1 s−1, a channel length L = 32 × 103 km, and diabatic and frictional time scales τ = 20 and τM = 4 days, respectively. The baroclinic component of the flow is relaxed to the following “radiative equilibrium” profile:6
i1520-0469-64-7-2309-e3
where the zonal mean maximum wind Umax = 30 m s−1 and the meridional structure of the zonal mean thermal wind () = −exp(−y2/σ2) is a Gaussian profile with half-width σ = 2200 km. The parameter α is used to change the amplitude of the zonally asymmetric heating and must be sufficiently large to maintain the stationary wave against the mean flow advection. As discussed by Zurita-Gotor and Chang (2005), this procedure is roughly equivalent to forcing the wavenumber one 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 for the flow. With the above forcing the equilibrium jet has a width of 4000 km, equivalent to 35° latitude, which is roughly consistent with observations. We have confirmed that the results remain qualitatively the same if the baroclinic zone is narrowed or broadened. On the other hand, our channel length is comparable to that of a midlatitude latitude circle, but the storm track might still be too elongated due to our choice of a wavenumber-1 forcing. However, simulations with a halved channel produced again qualitatively similar results.

Figures 8a–c shows the equilibrium climate for α = 3, which is also the standard value chosen by Zurita-Gotor and Chang (2005). As discussed in that paper, this setting of α produces zonal contrasts in the equilibrium baroclinicity (Fig. 8b) and eddy amplitude (Fig. 8c) that compare reasonably to observations. In this section, the square root of transient eddy kinetic energy EKE = ½() (where primes denote differences from the time mean) is used as a proxy for the local eddy amplitude. Although a conserved quantity like pseudoenergy would be more appropriate, it is hard to estimate this quantity in the absence of Lagrangian statistics. As an alternative, we have considered the wave activity proposed by Plumb (1986) but found the diagnostics to be dominated by the spatial structure of the mean flow PV gradient. We have used the EKE norm in our discussion because it is directly affected by barotropic conversions and emphasizes deformation, but qualitatively similar results were found with other eddy norms. The conclusions presented below also hold when using a 24-h difference filter to remove the low-frequency variability. However, we chose to present unfiltered results because in some of our idealized runs the filtered data are affected by changes in the characteristic eddy frequency due to changes in the advection speed (see, e.g., Burkhardt and James 2006).

Despite the semirealistic baroclinicity and EKE in Figs. 8b,c, the small meridional excursions of the streamlines in Fig. 8a suggest that the deformation of the flow might be too weak, which is not surprising because the forcing is purely baroclinic. To test whether deformation ever becomes important in limiting the eddy amplitude when the zonal baroclinicity contrast is enhanced, we have performed additional experiments changing the value of α in (3). For example, Figs. 8d–f show the equilibrium flow for α = 9. Although the upper-level deformation is enhanced relative to the previous case, the eddy amplitude modulation still seems to be controlled by the very strong zonal contrasts in baroclinicity (note that the eddy amplitude peaks just downstream of the baroclinicity maximum). Thus, the storm track would still be classified as “baroclinic” in the terminology of Whitaker and Dole (1995). Most importantly, the maximum eddy amplitude is also significantly larger than before. Figure 9a shows that this is generally the case as α is increased, consistent with the primitive equation results.

To assess the robustness of these results, we have investigated the sensitivity of the eddy amplitude on α when a uniform easterly component ΔU = −20 m s−1 is added in both layers. As discussed by Zurita-Gotor and Chang (2005), this makes the wave–mean flow interaction more local and favors stronger zonal contrasts in eddy amplitude. This would also be more consistent with the local character of the midwinter equilibrium in Deng and Mak’s (2005) simulations, as indicated by the strong eddy amplitude modulation in their Fig. 12. In principle, we expect that slowing down the flow in this manner should make the eddies more sensitive to deformation (Whitaker and Dole 1995). However, we find that the addition of the easterly component affects primarily the minimum eddy amplitude but much less so the maximum eddy amplitude (Fig. 9b), consistent with the results of Zurita-Gotor and Chang (2005). As a result, the maximum eddy amplitude still increases with α in this more local regime.

These results, together with those presented in previous sections, cast some doubts on the hypothesis that the midwinter suppression could be due to enhanced eddy-induced deformation in a more baroclinic environment. However, it is still possible that the midwinter eddy amplitude might be limited by enhanced externally forced deformation. To investigate this possibility, we have studied the sensitivity of the same zonal flow considered above to an imposed barotropic deformation. Since it is awkward to relax vorticity, we have chosen instead to force this problem using the same procedure as Whitaker and Dole (1995) and Deng and Mak (2005). In particular, we make ψR zonally symmetric in (3) and add a forcing term J(ψEn, qEn) to (2); ψEn and qEn define the target equilibrium state of ψn and qn, respectively, that would be realized in the absence of eddies. The asymmetric part of this equilibrium state, purely barotropic, has the same meridional structure as the baroclinic forcing considered earlier. In both layers
i1520-0469-64-7-2309-e4
which produces again a net zonal transport independent of longitude in each layer when integrated between the distant meridional walls. Combined with the zonal mean of (3), this definition implies that the slowest upper-level zonal wind at midchannel is exactly zero in the eddy-free state when α = 1.

With this type of forcing the upper-level stationary wave is significantly stronger than before. For instance, Figs. 10a–c shows the equilibrated state for α = 1, the largest value considered. Although the time-mean zonal flow does not vanish at midchannel—as it would in the absence of eddies—it is still quite strongly modulated, 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 rather than decreases relative to the zonally symmetric run. The same is also observed for intermediate values of α, as shown in Fig. 11a. Even more strikingly, Table 2 shows that the domain-integrated EKE changes remarkably little with α and is actually enhanced by 7.3% for α = 1 relative to the zonally symmetric problem.

Following Cai and Mak (1990), we have calculated the kinetic energy conversion from the mean flow into eddies C(K, K′) = E · D, with D defined by (1) and
i1520-0469-64-7-2309-e5
Figure 12a shows the results for α = 1, normalized by U3max/λ. As can be seen, negative values dominate: relating the global integral of this conversion term to that of EKE (see Table 2), one finds that barotropic processes destroy EKE in a characteristic time scale of about 26 days. However, when the same calculation is performed for the zonally symmetric problem (α = 0), for which the domain-integrated 〈E · D〉 reduces simply to 〈E · D〉 = −〈U/∂y〉, we find that EKE is actually destroyed faster, in a time scale of 17 days. The reasons why the barotropic dissipation is reduced in the presence of the stationary wave become apparent when we separate between the zonal and meridional contributions to E · D, shown in Figs. 12b,c. The latter contribution is dominated by the standard barotropic conversion term U/∂y, which accounts for 90% of the full EyDy (not shown). As can be seen, it is this term that is mostly responsible for the dominant negative character of the full E · D. The ExDx component is predominantly positive and actually reduces the domain-integrated EKE destruction by roughly 40%. Table 2 shows that, to a lesser extent, this is also true for intermediate values of α.

The previous results are surprising in that they seem to contradict the barotropic storm-track paradigm put forward, among others, by Whitaker and Dole (1995). To make sure that this is not due to any fault of our model, we have tried to reproduce their results in the barotropic storm track limit. This can be accomplished by using a slower but broader radiative equilibrium zonal jet (Umax = 16 m s−1; σ = 2800 km) and slightly different forcing time scales [15(5) days for heating (friction)]. In addition, our equilibrium meridional structure can be made similar to theirs (which is defined through a different functional form) replacing the /dy factor in (4) by a broad Gaussian with half-width σ2 = 4500 km. Figures 10d–f show results from a simulation with α = 0.55, which is close to the value that Whitaker and Dole used. These results are both in qualitative and quantitative agreement with theirs: note in particular the very weak zonal modulation in baroclinicity (Fig. 10e), in contrast with Fig. 10b, even though the asymmetric forcing was also purely barotropic in that case. Hence, it is unambiguous in this case to attribute the zonal modulation of eddy amplitude to barotropic deformation, as argued by Whitaker and Dole (1995). Given the role played by barotropic processes for this flow, it is interesting to explore the sensitivity of the EKE to the strength of the stationary wave. The results are shown in Fig. 11b. Now, both the maximum and domain-integrated EKE strongly decrease with the amplitude of the stationary wave.

We have performed a sensitivity analysis to understand what makes this flow so different from the previous example. We found that the main factor is the very small value of Umax used by Whitaker and Dole. Taking Umax = 32 m s−1 instead, and keeping the rest of the parameters unchanged, gives results that are more consistent with those shown in Figs. 10a–c (not shown). In that configuration, the EKE is still strongly modulated with α, but its maximum and domain-integrated values change little or even increase slightly. There are three reasons why the eddies could be more sensitive to deformation with weaker Umax. First, baroclinic growth is weak. Second, the slow upper-level wind favors more local modes. Finally, as discussed by Whitaker and Dole (1995), the waves are more likely to break in regions of high deformation.

The previous example shows that it is not impossible to limit the eddy amplitude through barotropic deformation, as suggested by Deng and Mak (2005). However, lacking a deeper understanding of the stability of zonally varying flow, it is hard to predict a priori what makes a certain flow more or less sensitive to deformation. In our model, this seems to require a set of parameters that we believe unrealistic: the upper-level wind and midlevel baroclinicity are very weak in Figs. 10d,e, and the EKE is also much weaker than in observations. 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 modulation in baroclinicity in their model climates is reasonable compared to the seasonal evolution in the Pacific, it is unclear whether their deformation is also realistic. A cursory inspection of their Fig. 12 suggests that the storm-track termination might be too abrupt in their midwinter scenario, which may be taken as a hint of an excessive deformation. In contrast, the break in eddy amplitude between the Pacific and Atlantic storm tracks is much more moderate in Fig. 5. Moreover, while the ratio between the minimum and maximum eddy amplitude along the storm-track axis changes in their runs from roughly 80% to 50% (0.5/0.62 to 0.2/0.4) between the early winter and midwinter scenarios, this parameter does not exhibit a clear seasonal cycle in Fig. 5.

5. Summary and conclusions

In this study, an attempt has been made to simulate the seasonal cycle of the NH cool season storm tracks using idealized nonlinear storm-track models. A primitive equation dry dynamical core model is forced with fixed radiative forcing, with the heat sources and sinks arranged (using an iterative procedure outlined in appendix A) such that the model climate, in terms of the simulated mean temperature distribution, resembles the observed climatological temperature distribution for the different months in the cool season, except that in some of our experiments the static stability of the model climate has been reduced to enhance eddy growth in the absence of diabatic generation of EAPE due to moist processes.

Using this procedure, we obtain an excellent simulation of the seasonal cycle of the climatological monthly mean flow. However, our simulation of the seasonal cycle of the storm tracks turns out to be deficient (Figs. 5 and 6). In agreement with observations, the model Atlantic storm track exhibits a single peak in January. However, its simulated amplitude in October and April is much too weak. For the Pacific storm track, the observed storm track peaks in November/December and March and has a relative minimum in February, with the February storm-track activity weaker than those in October and April. The simulated Pacific storm track peaks in December/January, with a nearly indiscernible relative minimum in February. In addition, the simulated storm track for October and April is much weaker than that for February, in contrast to what is observed.

Our model results suggest that changes in the structure of the monthly mean flow alone are insufficient to fully account for the observed seasonal cycle in storm-track activity. We note that a recent study by Deng and Mak (2005) suggested that the increase in the amplitude of stationary wave in winter, as compared to fall and spring, could lead to enhancement in the deformation, thus giving rise to the observed decrease in midwinter storm-track activity. We have conducted sensitivity experiments by changing the amplitude of the stationary wave forcing, and our results suggest that an increase in the amplitude of the stationary wave forcing often leads to enhancement (instead of reduction) in both the Pacific and Atlantic storm-track activity.

To further explore the sensitivity of storm-track amplitude to the strength of the stationary wave forcing, several sets of experiments have been conducted using a two-level qg model. These results confirm the results from the primitive equation model that increasing the baroclinic stationary wave forcing (through increasing the amplitude of zonally asymmetrical diabatic heating and cooling) generally leads to an increase in the storm-track amplitude. Even though the deformation in the flow increases with the increase in the forcing, its effects are not sufficient to counteract those of the increase in local baroclinicity. We have also tested whether an increase in externally imposed barotropic forcing could give rise to a decrease in the storm-track amplitude. However, our results show that if the zonal mean baroclinicity is close to that observed, even purely barotropic stationary wave forcing gives rise to significant modulation in the baroclinic stationary wave amplitude. Because of that, the peak amplitude of the storm track is still not significantly decreased even under very strong barotropic stationary wave forcing. Only when the zonal mean baroclinicity is much weaker than that observed does barotropic wave forcing act to appreciably reduce the amplitude of the model storm track.

We are not suggesting that changes in mean flow structure do not impact storm-track amplitudes. Previous studies (Harnik and Chang 2004; Nakamura et al. 2002) have suggested that changes in mean flow structure can affect the degree of midwinter suppression. In addition, our results do suggest a slight decrease in Pacific storm-track amplitude when the model mean flow is forced to resemble that observed in midwinter (see Figs. 6c,e).

Comparing our model results to those observed, it is apparent that changes in the zonal mean dry baroclinicity have much greater impacts on the model storm-track amplitude than those observed. If changes in the structure of the stationary waves, which are well simulated by our model, are unable to counteract the changes in baroclinicity, what else could do that? Noting that the seasonal cycle of the storm tracks can be well simulated by GCMs, we propose that the deficiency in our model simulations probably arise from the simplistic model physics used in our model simulations. Diagnosing the seasonal cycle in eddy energetics, we find that there is a significant seasonal cycle in diabatic generation of EAPE, with diabatic forcing acting as a weak sink of EAPE in October and April but becoming a significant sink during midwinter. An ad hoc attempt is made to illustrate this effect in our model by varying the degree of reduction in the static stability of the model climate (see appendix B), with the largest reduction applied to October and April when the diabatic damping is weakest, and the smallest reduction applied to February when the diabatic damping is strongest. After the inclusion of this effect, our model is able to reproduce the observed storm-track seasonal cycle much better.

We are not implying here that we have successfully “explained” the midwinter suppression. Our main conclusion is that our results suggest that the midwinter suppression is unlikely to be completely explained by dry dynamics alone. The observed mean flow is generated by the balance between diabatic forcing, stationary wave transports, and eddy transports due to moist eddies. 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 that given the same external forcings, the meridional temperature gradient in a dry simulation is much stronger than that in a moist simulation, giving rise to similar eddy amplitudes in a dry and moist atmosphere under similar radiative forcings but with very different basic flows in the two cases. Hence in the presence of a significant seasonal cycle in the effects of diabatic heating on eddies as found in the reanalysis (and GCM) data, it is not surprising that dry dynamics alone, applied to the observed mean flow (which has been generated by moist eddies), is unable to fully explain the seasonal cycle.

Even if we are able to explain the seasonal cycle in the storm-track amplitude given the mean flow structure, we have not really completely solved the mystery of the midwinter suppression. Reexamining Fig. 3c, it is clear that the zonal mean temperature gradient in the midtroposphere does not change much between November and March. A complete explanation of the seasonal cycle of the storm tracks will also need to account for the reason why the zonal mean temperature gradient appears to be so insensitive to the seasonal changes in radiative forcing from late fall through early spring.

Acknowledgments

E. C. would like to thank Dr. I. Held for providing the GFDL dynamical core, which was adapted into the nonlinear storm-track model. The authors thank the anonymous reviewers for helpful comments. E.C. was supported by NSF Grant ATM0296076 and NOAA Grant NA16GP2540. P. Z.-G. was supported by the Visiting Scientist Program at the NOAA/Geophysical Fluid Dynamics Laboratory administered by the University Corporation for Atmospheric Research.

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APPENDIX A

Iterative Procedure for Nonlinear Storm-Track Model

The nonlinear storm-track model is built upon the dynamical core of the spectral climate model developed at the Geophysical Fluid Dynamics Laboratory (Held and Suarez 1994). Details of the model formulation can be found in Chang (2006). Here we summarize the iterative procedure used to obtain the diabatic heating that forces the model.

Diabatic forcings are represented by Newtonian cooling toward a radiative equilibrium potential temperature profile (θE). With this parameterization, the first law of thermodynamics can be written as
i1520-0469-64-7-2309-ea1
where τ is the radiative time scale, taken to be 30 days in the free atmosphere (σ < 0.7) and decreasing to 2 days at the surface (σ = 1). The variable θE can be split into two parts as follows:
i1520-0469-64-7-2309-ea2
Here θC can be viewed as the desired model climate. For illustrative purposes only, the model variables can be partitioned into a time-mean part and a transient part (note that no such partition is done in the actual model), that is,
i1520-0469-64-7-2309-ea3
Substituting (A3) and (A2) into (A1), taking the time mean, and ignoring diffusion, we get
i1520-0469-64-7-2309-ea4
When θθC, Q is the only diabatic forcing in the model and can be regarded as the climatological mean net diabatic heating rate.
In (A4), it can be seen that for the model climate (θ) to be close to the one desired (θC), the heating Q must balance mean and eddy heat transports in the model. Since these transports are not known a priori, the exact form of Q is not known at the outset. To get to a desirable Q, an iteration is started with a first guess, say Q0, and the model is run. In general, the model climate θ0 will be different from θC. A new Q, Q1, is then computed, using
i1520-0469-64-7-2309-ea5
with the factor 2/3 in (A5) introduced to avoid overcorrections. A new run is then made with the new Q, and the procedure is repeated until the globally averaged RMS difference between TN and TC is less than 0.7 K (TN and TC are the temperature distributions corresponding to θN and θC). Due to the strong internal variability in the model climate, we have found that in practice it is difficult to achieve better agreement between model and target temperature structures.
As discussed in Chang (2006), when the model is forced to the observed January climatological temperature distribution, the eddy variances are found to be much weaker than observed (see also Figs. 6e,f). The study of Hayashi and Golder (1981) showed that condensational heating not only acts as a source of EAPE, but, more importantly, it acts to strongly enhance baroclinic energy conversion. One way of mimicking part of this effect is by reducing the static stability of the atmosphere. Instead of using the observed temperature profile as the target climate, a profile with reduced static stability is imposed as follows:
i1520-0469-64-7-2309-ea6
where z(p) is the average geopotential height of the pressure surface. Chang (2006) found that a value of 1.25 K km−1 for A provides realistic amplitudes of eddy fluxes for January. This value is used for the experiments shown in Figs. 1 –5, 6c,d and 7.

APPENDIX B

Experiments with Seasonally Varying Reduction in Static Stability

In section 3c, we showed that there is a seasonal cycle in the diabatic generation of EAPE, with diabatic effects being highly damping during the midwinter and much less so (or even weakly positive) during spring and fall. Here, we attempt to qualitatively illustrate its possible effects on baroclinic generation by changing the static stability of the mean climate. As discussed in appendix A, in order to obtain realistic eddy amplitudes in January, we need to decrease the static stability in our model by 1.25 K km−1. To represent the stronger effects of moist heating in October, we reduce the static stability of the model climate even further. Fig. B1 shows the storm-track distribution for October, January, and April when the static stability is decreased by 2 K km−1. The model storm tracks for October and April are clearly stronger than those in the original simulations (Figs. 5h,n) and are now closer to the intensity observed. Obviously, if we use the same reduction for January (Fig. B1b), the model January storm tracks will also become stronger and will stay much stronger than those for October and April.

To illustrate the seasonally changing role of diabatic heating, we impose different reduction of the static stability for the different months. The values range from 2 K km−1 for October and April to a low of 1 K km−1 for February. The values used for all the individual months are shown in Table B1. These values are motivated by the results shown in Table 1, with minimum reduction in static stability (for February) corresponding to strongest diabatic damping. The seasonal cycle of the Pacific and Atlantic storm tracks in this set of experiments is shown in Fig. B2. The evolution seen in Fig. B2 is clearly in much better agreement with the seasonal cycle seen in the reanalysis (Figs. 6a,b) than the original sets of experiments (Figs. 6c–f). The Pacific storm track now has a clear minimum in February, and the Atlantic storm track is no longer excessively weak in October and April. These results suggest that the seasonal cycles of both the Pacific and Atlantic storm tracks may be successfully simulated if we impose both the seasonal changes in the mean flow structure, as well as model the effect of the seasonally varying impacts of diabatic heating on the eddies. Clearly, these experiments are highly idealized and do not capture all the effects of moisture on storm tracks. Experiments with more realistic treatment of diabatic effects should be conducted to further pursue this point.

Fig. 1.
Fig. 1.

(a) Differences in 500-hPa mean geopotential height, between HI and LO Pacific storm-track Januaries (contour interval is 30 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 for LO 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).

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 2.
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.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 3.
Fig. 3.

(a) Pattern correlation between Figs. 2a–g and 2h–n. (b) Evolution of the amplitude of the stationary wave (m) at 500-hPa level. (c) Evolution of the temperature difference (K) between 21° and 69°N at 700-hPa level. In (b),(c), solid line is taken from NCEP–NCAR reanalysis and dashed line from idealized model simulations.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 4.
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 for October; (c),(d) Same as in (a),(b) but for January, and (e) vertically averaged barotropic conversion rate (CI = 10 m2 s−2 day−1) for January computed based on NCEP–NCAR reanalysis data. (f)–(j) Same as in (a)–(e) but computed based on idealized model simulations. 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), and greater than 10 in (e),(j).

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 5.
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.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 6.
Fig. 6.

(a) Seasonal cycle in the standard deviation of 24-h filtered 500-hPa geopotential height (CI = 10 m) for the 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 idealized model simulations. (e),(f) Same as in (c),(d) but from simulations without reduction in static stability. Shaded regions indicate absolute values greater than 100.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 7.
Fig. 7.

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

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 8.
Fig. 8.

Equilibrium state for the baroclinic run with α = 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 the baroclinic run with α = 9.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 9.
Fig. 9.

(a) Eddy amplitude at midchannel for the baroclinic runs with the values of α indicated. (b) Same but with an added advective component ΔU = −20 m s−1. ZS stands for the zonally symmetric run with α = 0.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 10.
Fig. 10.

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

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 11.
Fig. 11.

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

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Fig. 12.
Fig. 12.

(a) EKE conversion C(K, K′) = E · D, (b) its zonal component ExDx, and (c) its meridional component EyDy for the barotropic run with α = 1. Values are normalized with U3max/λ.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

i1520-0469-64-7-2309-fb01

Fig. B1. (a) Same as in Fig. 5h but with the static stability reduced by 2 K km−1. (b) Same as in (a) but for January. (c) Same as in (a) but for April.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

i1520-0469-64-7-2309-fb02

Fig. B2. (a),(b) Same as in Figs. 6c,d but from simulations with reduction in static stability that varies according to Table B1.

Citation: Journal of the Atmospheric Sciences 64, 7; 10.1175/JAS3957.1

Table 1.

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

Table 1.
Table 2.

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

Table 2.

Table B1. Reduction in static stability (K km−1) used for the different months.

i1520-0469-64-7-2309-tb01

1

As shown in Nakamura (1992), the midwinter suppression also shows up in lower tropospheric heat flux. However, the suppression in terms of heat flux is not as pronounced as that in terms of geopotential height variance, such that in October and April, while Pacific eddy activity in terms of geopotential height variance is nearly as large as that in midwinter, the eddy heat flux is weaker than that in midwinter.

2

Note that while the strengthening of the Pacific storm track when the Pacific jet is weak and broad in its interannual variations has similarities to what happens during its seasonal march, previous studies by Chang (2001) and Harnik and Chang (2004) have suggested that the dynamics involved in these two phenomena may be different.

3

The relative minimum in February shows up a bit clearer in filtered 300-hPa meridional velocity variance (not shown). However, contrary to observations, even for that measure, the simulated storm track in October and April is weaker than that in the February simulation.

4

For all transients, the respective barotropic damping time scales for model simulation are 25 and 7.9 days, while those from reanalysis data are 22 and 6.2 days.

5

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

6

Note that there is a typo in Eq. (2) of Zurita-Gotor and Chang (2005), which lacks the /dy factor modulating the meridional structure of the asymmetric component in (3). This factor ensures that the asymmetric component of ψR is small at the meridional walls—provided they are sufficiently far—and makes the net zonal transport independent of longitude.

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