The background flow has been suspected for a long time to play a decisive role in determining the storm-tracks. The early studies of storm-tracks are attempts of relating the linear instability properties of different longitudinally varying basic flows to the structure of the storm tracks (e.g. Frederiksen, 1983; Pierrehumbert, 1984; Cai and Mak, 1990; Lee and Mak, 1995; Branstator, 1995). Some success in simulating the storm-tracks as a statistical feature can be achieved by using a linear model in which the basic flow is a suitably stabilized realistic time mean flow and the forcing consists of judiciously tuned stochastic perturbations (Whitaker and Sardeshmukh, 1998; Zhang and Held, private communication). The introduction of such a basic flow and forcing is meant to be a proxy of the neglected nonlinearity. What makes it possible in principle to reproduce the local variance distribution in a linear model is that the associated linear dynamical operator is nonnormal and has discrete modes. Most of the stochastic perturbation energy arising from nonmodal growth in a linear system, whether or not the basic flow is zonally varying, could be accumulated in the least damped modes (Farrell and Ioannou, 1996). To the extent that a background flow could be regarded as known a priori, such approach of modeling is successful and confirms the importance of the background flow and nonmodal linear instability process.

A self-contained dynamical account of the storm-tracks necessarily requires the use of a nonlinear model simply because the convergence of momentum and heat fluxes associated with the synoptic scale eddies in the storm-tracks are large and strongly influence the background flow itself. There have been several nonlinear storm-track models differing in the manner of how the external forcing is introduced. Whitaker and Dole (1995) simulate an idealized storm-track in a channel model using a relaxation forcing that has pronounced zonal inhomogeneity with a specified structure. Lee and Anderson (1996) treat storm tracks as a purely forced phenomenon in a barotropic model. Chang and Orlanski (1993) introduce a forcing in the form of a perpetual weak wave maker located upstream of a region of an initially uniform baroclinicity in a long channel domain. Although the amplified waves effectively neutralize the local background baroclinicity some distance downstream of the wave maker, the eddies can reach far downstream by dispersion. It should be noted that the location of strongest baroclinicity is effectively prescribed in those models.

The winter-mean (DJF) column-averaged net diabatic heating rate has strong zonal inhomogeneity, being positive in the storm-track regions and negative in the continental regions with values up to  ( Fig.1). It is calculated with the NCEP/NCAR Reanalysis data (Kalnay et al, 1996) by the residual method (courtesy of Ms Hailan Wang). Since synoptic scale eddies intrinsically tend to reduce their background baroclinicity by virtue of their heat flux divergence, a valid question is how the localized baroclinicity can be maintained in a time mean sense. On the basis of the response to a net diabatic heating field in a linear stationary wave model, Hoskins and Valdes (1990) suggest that the persistence of local baroclinicity might result from the condensational heating associated with the eddies in the storm tracks themselves. In that sense, the storm-tracks might be self-maintaining. Another process that could maintain the local baroclinicity in the storm track region associated with the planetary waves is orographic forcing. Lee and Mak (1996) show that the orographically modified flow driven by a forcing in the form of zonal relaxation of the temperature to the observed winter mean temperature alone could sustain fairly realistic storm-tracks in a fully nonlinear linear-balanced model under winter condition provided that the relaxation time is sufficiently short. Apart from condensational heating and orographic forcing, it warrants to also consider the surface sensible heat flux which can destabilize short shallow synoptic scale waves in a baroclinic zone (Fantini, 1995; Mak, 1998). The surface sensible heat flux is significant in winter at western N. Pacific and N. Atlantic where the SST is relatively high. It is therefore instructive to determine if a surface sensible heat flux also has a significant impact on the storm-tracks.

This is a follow-up investigation of Lee and Mak (1996) focusing on the role of the major diabatic heating/cooling processes in the storm-track dynamics. Treating the storm-tracks and their background flow as two integral parts of a nonlinear system, we attempt to simultaneously simulate both of them well in a simplest possible model setting. The objective is to clarify the relative importance among the orographic forcing, condensational heating and surface sensible heat flux in the context of storm-track maintenance by assessing the impacts of different combinations of those processes.

The numerical model for this study is presented in Secion 2. Section 3 first reports a comparison of the model high-frequency eddy statistics and the time-mean flow obtained from four distinct experiments. This is followed by analyses of the local energetics, wavepacket characteristics and wave-mean flow interaction in the most successful experiment. The paper ends with some concluding remarks in section 4.

2. Model and Analysis

We consider a primitive equation model consisting of the momentum, hydrostatic, thermodynamic, continuity and vertical velocity equations, written in a terrain following s-coordinate with standard notation as

(2-1)

(2-2)

(2-3)

(2-4)

(2-5)

The frictional force and thermal damping are denoted by  and  . The total diabatic heating is represented by Q. The boundary conditions for the vertical velocity in this formulation is

at s=0, 1 (2-6)

The orography is introduced through the boundary condition in the hydrostatic equation as

(2-7)

where H is the orographic height field.

Seven s-levels are arranged in the model to provide enhanced resolution near the surface in order to optimize the representation of shallow waves possibly destabilized by the surface heating process. The integer model levels are defined at {0.12, 0.36, 0.6, 0.755, 0.825, 0.895, 0.965} for all fields except for the vertical velocity which is defined on the staggered half-integer levels. The horizontal fields are spectrally represented by spherical harmonics with R-54 resolution so that short waves with wavelength down to ~ 1000 km would be adequately represented. We incorporate in the model a R-18 representation of the global orographic data from NCAR with an original resolution of 2.5^ox2.5^o .

The frictional force is written as

(2-8)

The first term stands for a surface drag with a vertical profile  and an empirical drag coefficient  . The second term is a biharmonic diffusion of momentum with a coefficient  . It facilitates an enstrophy cascade and prevents nonlinear aliasing from becoming problematic. The thermal damping is also treated as a biharmonic diffusion of temperature

(2-9)

Three diabatic heating processes are considered in this model : radiative, convective and surface heat flux. They are denoted at each level k as

(2-10)

Assuming that the storm track dynamics is primarily associated with the local midlatitude time-mean flow and in-situ thermal forcing, we restrict the self-induced surface and condensational heating to occur between 20^oN and 80^oN in the model . This restriction is compatible with the facts that both the observed precipitation and surface heat flux in winter are large primarily over the storm track regions and have virtually zero values over the continental regions (Otto-Bleisner and Johnson, 1982) .

The representation of the three diabatic processes is simplified to the greatest possible extent. Zonal inhomogeneity in the radiative heating is assumed to be relatively small. Thus, a zonally symmetric radiative forcing is introduced so that the zonal asymmetry in the circulation would only arise from the orography , surface heat flux and convective heating. The radiative heating rate at level k is expressed as a relaxation of the zonal mean component of the temperature field towards a reference field, viz.

(2-11)

where  is the time constant and T_EQ is a radiative equilibrium temperature with a functional form given by ( Held and Suarez, 1992)

(2-12)

where T_o=200 K, T_s=315 K, DT_y=60 K, Dq_z=10K, f_o=-10^o for f < 30^oN to represent the winter mean with the maximum temperature shifted to 10^oS. The temperature gradient for 30^o-90^oN is equal to that at 30^oN allowing for a monotonic decrease of temperature towards the pole.

The surface heating parameterization is a bulk aerodynamics formulation, viz.

(2-13)

The observed sea surface temperature (SST) is used as the model surface temperature in the oceanic regions, . The NMC SST data for the 1982-83 winter with a 2.5^ox2.5^o resolution are interpolated to the model grids. Surface heat flux is assumed zero at the land areas.

The greatest uncertainty is concerned with the calculation of the convective heating induced by the synoptic scale eddies. It is assumed to be proportional to the moisture convergence in the model as in a Kuo-scheme. To minimize the uncertainty, we use the winter mean specific humidity according to the NCEP/NCAR Reanalysis data as the model specific humidity instead of trying to determine it as a model variable in a moisture budget. It is indicated by a superscript "o". The total moisture convergence in a column would then only depend on the convergence of the flow field and surface evaporation, E, viz

(2-14)

together with

over the land grid points

over the oceanic grid points (2.15)

where  refers to specific humidity saturated at the surface temperature. The boundary moisture field at the oceanic grid points is assumed saturated at the boundary temperature where

(2-16)

with e_o=6.11 mb and T_o=273.15 K. The latent heat release by the cumulus ensemble is then given by

(2-17)

where  = 1 for M> 0 ; =0 for M < 0. The bottom and top levels of the model cloud layer are denoted as and  . Finally, the convective heating profile is evaluated on the basis of the Kuo scheme as

(2-18)

where the brackets indicate average over the cloud layer. The step function generates positive definite value when the layer CAPE is positive. The reference profile  is the pseudo-adiabat. It is saturated at the lowest model level temperature and is linearly extrapolated to the next level according to the pseudo-adiabatic lapse rate. This method is found to give very accurate temperature profiles as deduced from a skew-T plot.

The initial state has a zonal jet in linear-balance with a temperature equal to the prescribed zonal radiative equilibrium temperature. The interaction of the zonal flow with the orography, surface heat flux and condensational heating would quickly generate wave components in the flow. The model is integrated for 300 days. The model variables are sampled once every 12 hours. The time mean fields as well as the high frequency eddy statistics are evaluated with the model output from day 100 to day 300.

3. Results

Four experiments are designed with one or more processes suppressed at a time in order to assess the dynamical effects of such diabatic forcings on storm tracks and to ascertain the extent to which the observed storm tracks might be simulated under a simplest possible model condition. They are referred to as (i) FLAT, (ii) OROG, (iii) SURF and (iv) FULL. Experiment FLAT is done without orography in the model so that we can ascertain the extent to which the storm-tracks could be simulated in the absence of orographic forcing. In contrast, experiment OROG is done with orography and the radiative forcing only. The idea is to see how much of the storm-tracks might arise from the orographic forcing alone. Experiment SURF is done without condensational heating in order to isolate the additional impact by the surface sensible heat flux on the result of experiment OROG. Finally, experiment FULL is done with all processes operating in this model.

The values of the common parameters in these experiments were tuned to give best storm track simulation in the OROG experiment which will be also treated as a control run. The same parameter values are used in all four experiments, except of course for those that are either switched on or off. The complete set of parameter values used in this study are given in Table 1.
 

horizontal resolution	R54 spectral
time step	Dt=8 minutes
Robert filter parameter	a=0.1
biharmonic diffusion coefficient	n=4.6x1016 m4 s-1
surface drag coefficient	gd=6x10-6 m-1
radiative relaxation time	t=10 days
heat flux coefficient	gh=2.0x10-6 m-1
evaporation coefficient	Ce=3.0x10-3

Table 1

The time-mean flow and the high-frequency eddy statistics obtained in the four experiments will be compared among themselves as well as against observation . The detailed diagnoses of local energetics, wavepacket diagnostic and wave mean-flow interaction are presented only for the most successful experiment. All diagnoses are made on isobaric surfaces for convenience in making comparison with observation. Hence, the model fields are first linearly interpolated to isobaric levels {120, 360, 600, 755, 825, 895, 965} mb.

3.1 High-Frequency Eddy Statistics

The low-frequency (LF) component is first extracted from each total field with the use of a simple 21-point-moving-average filter^. The HF component is defined as the difference between a total field and the corresponding low-pass field. The standard deviation of such high-frequency windspeed at a selected level is then computed and used as a measure of the local synoptic eddy activity of the circulation.

An intercomparison of the distribution of this eddy statistic at the 360 mb model level for the four experiments is presented in Fig.2. For the FLAT case, the field has only very weak zonal inhomogeneity in midlatitude although the magnitude is fairly realistic ( ~ 22 , centering at about  , Fig.2a). Furthermore, the values over Pacific are slightly larger than those over Atlantic in contrast to observation. We conclude from this simulation that thermal forcing alone would not give rise to sufficiently localized storm-tracks in the absence of the actual orography.

For the OROG case, there is a fairly localized storm track in the Pacific sector but not so over the Atlantic (Fig.2b). The Pacific storm track has a maximum amplitude of 20 m s^-1 centered at . By contrast, the model Atlantic storm track is poorly-localized for it extends far into the European sector. The zonal extent of a storm track depends greatly on the deformation field of the background flow which would facilitate a transfer of eddy kinetic energy to the planetary scale background flow. The result implies that the deformation field of the planetary wave field in the OROG experiment, particularly in the Atlantic-Europe sector, is too weak in the absence of the other diabatic processes. A dry linear-balanced model under orographic influence alone turns out to be capable of simulating the Atlantic storm track better than a counterpart PE model probably because the additional vorticity forcing introduced in such a linear-balanced model gives rise to a stronger deformation (see Fig.6 in Lee and Mak, 1996).

In experiment SURF , the model yields two highly localized storm-tracks, although there are several deficiencies (Fig.2c). The central location of the Pacific storm track is too far to the east () and that of the Atlantic storm track is too far to the west (). The intensity of the two model storm tracks are comparable in contrast to observation. Furthermore, the intensity of the storm tracks is noticeably weaker, maximum about 18 m s^-1. We learn from this simulation that in conjunction with the orographic forcing, the surface heating per se would help localize the disturbances but would have a damping effect as previously reported in Branscombe et al (1989).

The model storm-tracks are best simulated in experiment FULL (Fig.2d). The intensity of the Pacific storm track is slightly weaker than that in the OROG case and its position is shifted back to about . By contrast, the intensity of the Atlantic storm track reaches about 20 m s^-1 and is actually stronger than that of the Pacific maximum by more than 2 m s^-1. Its position is now shifted further east to  , in better agreement with observation. The length of the Atlantic storm tracks is also more comparable to observation. Thus, the condensational heating is found to have an appreciable impact on the position, structure and intensity of the two storm tracks. All three diabatic processes together with the orographic forcing are demonstrated to be necessary and sufficient for realistically simulating the storm tracks.

The corresponding eddy statistics at the 965 mb model level are shown in Fig.3. The FLAT case again shows very weak localization in the eddy statistic over the Pacific and Atlantic sectors with a maximum value which reaches 11 m s^-1. For the OROG case, the near-surface windspeed is considerably weaker (8 m s^-1) and naturally has much larger zonal variability. The maximum at 965 mb is much enhanced by surface sensible heat flux in the SURF case as the maximum value reaches 11 m s^-1 . It is interesting to note that the surface variance is stronger even though the upper level variance is weaker than in the OROG case. This suggests that there are more shallow wave disturbances in the storm tracks induced by surface heating. The simulation in the FULL case is again most realistic with a maximum intensity of 12 m s^-1 in both the Atlantic and Pacific regions. The results suggest that weakening of the  over the continental areas is a significant aspect of the strong localization of the storm tracks.

Considering Fig.3d together with Fig.2d, we see that the strong low-level eddy intensity is far upstream of the strong upper level eddy intensity over Pacific. In contrast, the strong low level eddy intensity is effectively collocated with the strong upper level eddy intensity over Atlantic. It suggests that the heating in the Pacific induces shallow wave perturbations upstream which extend vertically and amplify at the upper level further downstream. This means that considerable disturbances in the model Atlantic storm track originate from the Pacific sector. Upon reaching the Atlantic jet region , they reintensify simultaneously at both upper and lower levels. The impact of the heating is therefore quite different in the two regions.

3.2 Time-Mean Statistics

The simulation of the time mean zonal velocity at the 360 mb level is worst in the FLAT experiment without orography and best in the FULL experiment as expected (Fig.4). The positions of the two upper level jet streams are quite well simulated in the FULL experiment (Fig.4d). The maximum velocity in the Pacific and Atlantic jets are 44 m s^-1 and 36 m s^-1 respectively, whereas the observed counterparts are 51 m s^-1 and 26 m s^-1 respectively. In other words, the simulated Atlantic jet is overestimated by almost 10 m s^-1 . This deficiency may arise from the use of a zonally homogeneous radiative forcing in the model.

More importantly is the finding from the intercomparison that the impacts of the diabatic heating on the storm tracks are highly correlated with the impacts on the time mean flow. For example, when the storm track becomes much better localized over the Atlantic as a result of the additional diabatic heating (Fig2b vs 2d) , so does the Atlantic time mean jet stream become much more localized over western Atlantic (Fig.4b vs 4d). Likewise, when the Pacific jet in the FULL case (Fig.4d) is shifted further to the west so does the Pacific storm track (Fig.2d). Similarly, as the Atlantic jet stream in the SURF case is weaker and shorter than that in the FULL case (Fig.4c and 4d), the Atlantic storm track is distinctly weaker and shorter (Fig.2c and 2d). In other words, unless the mutual influence between the storm tracks and the jet streams is properly captured in a model, both of them would not be well simulated. This result highlights the limitation of a linear theory of the storm-tracks in which the jet streams are presumed to be known a priori.

For brevity, we only present the result of the near surface (965 mb level) time mean zonal velocity for the FLAT and FULL cases (Fig.5). The simulation is worst in the FLAT case for it is excessively homogenous in the zonal direction (Fig.5a). For the FULL case, the jets are better localized with the maximum enhanced to 8 m s^-1 in both Atlantic and Pacific (Fig.5b). Such results agree fairly well with the counterpart observed field which also has localized jets of 11 m

s^{-1 in the Pacific and 9 m s-1 in the Atlantic .}

A comparison of the wave part of the simulated time mean streamfunction at 360 mb in the FLAT and FULL experiments is presented in Fig.6. The stationary wave field in the FLAT case is hardly detectable and that in the FULL case is most realistic. In particular, the wave associated with the Pacific jet is better simulated than that associated with the Atlantic jet. Moreover, the simulation in the SURF case is more realistic than that in the OROG case (not shown) suggesting that the surface heating also contributes significantly to the maintenance of the Pacific storm track.

The observed time-mean surface temperature is warmest over the north-western Atlantic and Pacific and has a strong gradient. Fig.7 shows a comparison of the 965 mb temperature field for the OROG and FULL experiments. In the OROG case where the SST is not imposed at the surface, the contours are nearly zonal and quite different from observation. The surface-atmosphere temperature difference in this case is very large due to the lack of a surface heat flux. The strong meridional temperature gradient indicates that the surface baroclinicity is maintained by the radiative relaxation. The isotherms of the 965 mb temperature field in the FULL experiment are parallel to the SST isotherms and are significantly more realistic. In particular, the strong difluence along the east-west contours is controlled by the SST field. Both fields are very similar suggesting that the surface heating strongly regulates the surface temperature. Nevertheless, the gradients are still weaker than observed along the ocean-continent boundaries. This may be due to the fact that the radiative relaxation forcing is zonal and thus does not adequately represent the strong high latitude winter radiative cooling over continental regions.

The low level intensity of a storm track is expected to be strongly dependent upon the time mean low level static stability . The distribution of  at 965 mb level in the OROG and FULL cases are shown in Fig.8 . The areas with values exceeding  are shaded to highlight the difference. It reveals that  over both Atlantic and Pacific Oceans is larger in the OROG case than in the FULL case by more than a factor of two. The significant reduction of the low level static stability in the FULL case is a natural consequence of the surface heat flux from the oceans. It accounts for the finding that the intensity of low level Pacific and Atlantic storm tracks is distinctly stronger in the FULL case than in the OROG case (Fig.3b vs 3d), although the intensity of eddy activity at the upper level is more comparable (Fig.2b vs 2d). We may conclude from this that the low level static stability influences the vertical partition of the eddy energy.

To further highlight the impact of the condensational heating and surface heat flux, we examine the difference between the zonal velocity at 360 mb for the FULL and OROG cases (Fig.9a). It shows positive values to the north and negative values to the south of the Pacific jet amounting to a northward shift of the jet when the additional heating is introduced. The same effect is found on the Atlantic jet. The difference between the temperature at 360 mb level for the FULL and OROG cases is shown in Fig.9b. We see that the additional heating results in a warming over the Pacific and over the eastern half of the Atlantic sector.

3.3 Local Energetics Analysis

A diagnosis of the local energetics would enable us to address the following questions. Which processes are mostly responsible for the localized energy in the storm track regions ? Is there a difference in the characteristic of the local energetics balance over the Pacific and Atlantic ? Is there evidence for a particular local instability process? Finally, what is the effect of heating on the local energetics balance? The formulation of time-mean local energetics not only depicts the role of energy generation by baroclinic conversion but also includes the time mean energy dispersion mediated by advective and ageostrophic geopotential fluxes. Such budget equation for the vertically-averaged local kinetic energy of the high-pass eddies can be written as

(3-3)

where the brackets and overbar represent a vertical average and time average, respectively. The four terms on the RHS stand for convergence of advective flux of KE, ageostrophic geopotential flux convergence, the effective baroclinic conversion rate including the dissipation and barotropic conversion respectively. They have the following explicit form

(3-4)

.

The E-vector of the eddies and D-vector of the time-mean difluence are defined as

(3-5)

. (3-6)

The terms involving triple products of the high frequency component are small.

The model results of the time-mean local kinetic energy processes in the FULL experiment are shown in Fig.10. In light of the distribution of the eddy activity in Fig.2, we see that the effective baroclinic generation process including the dissipation has a maximum value of 2.0x10^-3 J s^-1 at the upstream end of the Pacific storm track. This field is well localized near the time mean jets. The complimentary heat flux vectors are also plotted and the maximum value is ~ 40 K m s^-1 over the storm tracks similar to observation. The kinetic energy maximum is located downstream from the maximum of baroclinic generation in both the Pacific and Atlantic regions. Thus, the time tendency and amplitude of the kinetic energy are not collocated. The barotropic conversion rate has a maximum value of 7x10^-4 J s^-1 which is about 25% of the maximum baroclinic generation rate. The regions of positive and negative conversions and complementary E-vector fields are consistent with the expected energy exchange with the mean-flow over the storm track regions.

The process of KE flux divergence by the time mean flow redistributes some kinetic energy from the region of strong generation to the downstream region of each storm track in Pacific and Atlantic. The maximum value reaches 6x10^-4 J s^-1. There is also an extensive downstream transport from the Pacific to Atlantic region with the value largest over the storm track regions. We find generally small values for the ageostrophic geopotential flux convergence term . Although the ageostrophic geopotential flux associated with the individual wavepackets is important (Orlanski and Chang, 1993), its time mean distribution is small. This is not surprising since as disturbances propagate through a fixed point, there would be divergence as well as convergence of ageostrophic geopotential flux alternately passing through that point as well. They tend to cancel one another and give rise to a relatively small residual time mean value.

The spatial structure of these fields suggests that the time-mean eddy kinetic energy is primarily sustained by a net baroclinic generation. The downstream extension of the storm tracks is mostly due to the advection by the time-mean flow and secondarily due to ageostrophic geopotential flux. The local time-mean budget of the available potential energy does not offer extra insight and is therefore not presented for brevity.

Finally, it is instructive to examine the difference in the time-mean local baroclinic conversion rate between the FULL and OROG experiments associated with the additional diabatic heating. The baroclinic conversion rate is substantially enhanced in both Pacific and Atlantic sectors by about 1.0x10^-3 J s^-1 (Fig.11). This is nearly 50% of the value in the FULL experiment itself. Over the Pacific, the maximum value is located upstream of the upper level 360 mb storm track , but is collocated with the surface storm track. In contrast, the maximum value over the Atlantic is collocated with that of the storm track at both levels. It is interesting to note that the enhancement of the baroclinic generation rate in the Pacific sector does not lead to a substantial increase in the intensity of the Pacific storm track in the FULL case. The intensity in the Atlantic storm track on the other hand is increased by 4 m s^-1 . It suggests that the differential intensity between the Atlantic storm track and the Pacific storm track may be attributable to the impact of the diabatic heating. Under the influence of the self-induced diabatic heating, more disturbances from the Pacific sector could reach the Atlantic jet region and reamplify further downstream. In contrast, few disturbances of the Atlantic storm track survive in their propagation across the long stretch of land in Asia where the orography is particular high.

3.4 Heating rates

The surface heating field in the FULL experiment is strongly localized along the coastal regions in the western Pacific and Atlantic attaining 20 K day^-1 (Fig.12a). This heating rate is applied at the 0.965 and 0.895 model s-levels according to the prescribed surface heating profile. The structure and amplitude agree well with the vertical diffusion heating rate at the 1000 mb and 900 mb observational levels from the NCEP/NCAR reanalysis data set (Kalnay et al., 1996). As shown, the column-averaged model net diabatic heating reaches a maximum of 1.6 K day^-1 in the western Atlantic and Pacific with positive heating over the storm track regions (Fig.12b). The large values are found near the western part of the Atlantic and Pacific oceans reaching 4 K day^-1 The heating regions extend along the storm track regions as expected. The location of the positive heating regions agrees quite well with observation (see Fig.1), although the magnitude is under estimated by nearly 50%. The model condensational heating has a maximum value of 6 K day^-1 at 360 mb in the western Atlantic and Pacific (not shown). This represents the deep convective physics and is consistent with observed deep convective heating rates from the NCEP reanalysis data.

3.5 Statistical structure of the eddies

It is instructive to take a closer look at the evolution of the ensemble of eddies in the model storm tracks. Pertinent questions are : Can we identify the upstream Pacific region as a source region of shallow baroclinic waves which deepen downstream ? What are the heating effects on the wave structure? Is there a significant difference in the wave structure in Pacific and Atlantic regions?

The time evolution of the constituent disturbances in the storm tracks is depicted with a Hovmoller diagram of the squared high-pass meridional velocity averaged between 30^oN and 60^oN latitude , . Such plots of at the 360 mb and 965 mb levels from day 100 to day 300 in the FULL experiment are shown in Fig.13 with the same contour interval of 50 . The maximum value at the 360 mb is 2750  and that at 960 mb is 350 . We see that most individual wavepackets at the surface level originate near 120^oE. Many of them survive across Pacific and some even across Atlantic, but eventually decay over the long Asiatic land sector from 0^o to 120^oE . This suggests a picture of one globally coherent storm track system effectively starting from western Pacific. The upstream edge of the Pacific baroclinic generation occurs at 120^oE and is indicated by a solid line (Fig.13a). At the upper level, the edge of the wavepackets appears further downstream near 160^oE (Fig.13b). These results suggest that shallow waves seed the deep waves downstream in agreement with the conclusion of Hoskins et al (1983). Such scenario would be consistent with the difference in the locations of the upper and surface level maxima in the Pacific storm track. There is no clear gap in the wavepacket rays over the Rockie mountain at the 360 mb suggesting that many wavepackets continue to move to and reamplify in the Atlantic jet region.

The horizontal statistical structure of the eddies is presented in the format of one-point correlation maps for different lags. Each is constructed by temporal regression of a time series of the meridional velocity at a fixed spatial point relative to the counterpart time series with a specific lag at all other field points. Fig.14 shows such correlation maps for the 360 mb level in the FULL experiment using a reference point (180^oE, 45^oN) at the 965 mb level over the Pacific. The wavepackets form a statistical wave-train propagating effectively in the zonal direction along the poleward edge of the Pacific jet. The wave train structure in the OROG case is similar, although the envelope has a somewhat longer zonal extent. Fig.15 shows the correlation map at 360 mb level for a reference point (330^oE, 45^oN) in the Atlantic at 965 mb. One unique feature is that this wave-train is more strongly refracted equatorward at positive lag times implying that the wavepackets typically would not penetrate far into Europe. Also, the meridional scale of the carrier wave increases with lag indicating an `eddy straining' mechanism at work. The latter gives rise to a transfer of eddy energy to the time-mean flow. This is consistent with the orientation of the E-vector and barotropic conversion fields in Fig. 10.

3.6 Wave-Mean Flow Interaction

The feedback effects of the eddies on the local time mean flow stem from the horizontal convergence of the local time mean eddy vorticity flux and local time mean eddy heat flux. The upper level streamfunction tendency (360 mb) associated with the time mean eddy vorticity flux,  in the FULL experiment is shown in Fig.16a. The eddies are seen to strengthen the time mean planetary wave field. The low level (755mb) eddy heat flux tends to reduce the time mean baroclinicity with a convergence  giving rise to a warming (cooling) tendency to the north (south) of both Pacific and Atlantic storm tracks (Fig.16b). The maximum rate is about 3.5K day ^-1 . These model results are quite compatible with observation.

The impact of the condensational heating on the storm-tracks is also examined in terms of the time average local Eady baroclinic growth rate (s=0.31fL/N) as computed from the time-mean temperature field where  is the vertical shear and N is the Brunt Vaisala frequency (Hoskins and Valdes, 1990). Such measure in the FULL experiment is shown in Fig.17. Its distribution is found significantly different from that in the OROG experiment in both location and magnitude, particularly over the Atlantic region. In the FULL experiment, the maximum value in the Pacific region is about 1.0 day^-1. There is a localized maximum of 0.85 day^-1 off the east coast of North America and a separate highly localized maximum of 1.4 day^-1 east of Greenland. The poleward increase in Eady growth rate due to the condensational heating correlates well with the poleward shift in the surface 965 mb storm tracks.

4. Concluding Remarks

We have constructed a nonlinear storm-track model for the purpose of quantifying the importance of condensational heating and surface heat flux relative to that of the orographic forcing. It is found that while orographic forcing is essential for the strong localization of the storm tracks, it is not sufficient for simulating the storm tracks well. Incorporating a surface heat flux drives the surface temperature toward the SST field and thus sustains a stronger meridional temperature gradient upstream of each storm track. Moreover, it enhances the asymmetry of the time-mean jets and thereby improves the localization of the storm tracks. Best simulation is obtained in the FULL experiment in terms of the positions, localization and the asymmetry between the Pacific and Atlantic storm tracks. Suppression of disturbances over the continental areas is also an important aspect of the storm track localization. The success of a simulation is hinged upon how well the time-mean flow can be simultaneously simulated. Although condensational heating improves the localization and position of the local jet structure, the Pacific jet is still a little too weak and the Atlantic jet is considerably too strong compared to observation. The simulation is probably as good as one is entitled to expect from a highly simplified model such as this one.

Most eddy kinetic energy is generated baroclinically upstream of the storm tracks via local instability. The local barotropic process transfers some energy back to the mean flow. The average local energy redistribution is mainly attributable to the mean flow advection. Although the ageostrophic geopotential flux is important to the instantaneous development of the disturbances, it has a small time mean residual flux divergence. The seeding of the Atlantic storm tracks by disturbances from the Pacific gives rise to a stronger Atlantic storm track. The vast Asiatic land/orography area virtually attenuates all disturbances from the west.

The Hovmoller diagrams show that while the upper and lower level eddy activity over Atlantic are essentially collocated, there is a distinct difference in the initial locations of most eddies at the low and upper level over Pacific. The Atlantic and Pacific storm tracks may be viewed as parts of a global storm track complex. One-point correlation maps also show that the statistical wave train structure in the Pacific and Atlantic regions are noticeably different. The wave train is refracted more equatorward in the Atlantic.

Some deficiency of this model may stem from our restriction of the condensational heating and surface heat flux to the north of  and from the use of highly simplified representation of the diabatic processes. It would be more desirable in principle to use a more general heating scheme with an explicit moisture budget in the whole global domain. The additional tropical heating would induce a stronger extratropical stationary wave field which in conjunction with the orographic forcing may further improve the simulation of the two storm tracks.

Acknowledgment. This research is partly based on the doctoral thesis of MA and is supported by the National Science Foundation through Grant ATM-9615568.