Climate Dynamics

, Volume 36, Issue 7, pp 1221–1237

Climatology of summer midtropospheric perturbations in the US northern plains. Part II: large-scale effects of the Rocky Mountains on genesis

Authors

    • Department of Geological and Atmospheric SciencesIowa State University
    • Utah Climate CenterUtah State University
  • Tsing-Chang Chen
    • Department of Geological and Atmospheric SciencesIowa State University
  • Eugene S. Takle
    • Department of Geological and Atmospheric SciencesIowa State University
    • Department of AgronomyIowa State University
Article

DOI: 10.1007/s00382-010-0765-7

Cite this article as:
Wang, S., Chen, T. & Takle, E.S. Clim Dyn (2011) 36: 1221. doi:10.1007/s00382-010-0765-7

Abstract

Propagating convective storms across the US northern plains are often coupled with preexisting midtropospheric perturbations (MPs) initiated over the Rocky Mountains. A companion study (Part I) notes that such MPs occur most commonly at 12 UTC (early morning) and 00 UTC (late afternoon). Using a regional reanalysis and a general circulation model (GCM), this study investigates how such a bimodal distribution of the MP frequency is formed. The results point to two possible mechanisms working together while each has a different timing in terms of maximum effect. The diurnal evolutions between the midtropospheric flows over the Rockies and over the Great Plains are nearly out-of-phase due to inertial oscillation. During the nighttime, the westerly flows at 700–500 mb over the Rockies intensify while flows at the same level over the Great Plains turn easterly. These two flows converge over the eastern Rockies and induce cyclonic vorticity through vortex stretching. After sunrise, the convergence dissipates and the cyclonic vorticity is redistributed by horizontal vorticity advection, moving it downstream. This process creates a climatological zonally propagating vorticity signal which, in turn, facilitates the early-morning MP genesis at 12 UTC. The analysis also reveals marked dynamic instability conducive to subsynoptic-scale disturbances in the midtroposphere over the Rockies. Strong meridional temperature gradients appear over the north-facing slopes of the Rockies due to terrain heating to the south and the presence of cooler air to the north. This feature, along with persistent vertical shear, creates a Charney–Stern type of instability (i.e. sign changes of the meridional potential vorticity gradient). Meanwhile, the development of terrain boundary layer reduces the Rossby deformation radius which, subsequently, enhances the likelihood for baroclinic short waves. Such effects are most pronounced in the late afternoon and therefore are supportive to the MP genesis around 00 UTC. Examination of GCM experiments with and without orography further supports the critical role of the Rocky Mountains and its associated boundary layer impacts on the formation of MPs.

Keywords

Midtropospheric perturbationShort waveBaroclinic instabilityMCSBoundary layer

1 Introduction

The role of the Rocky Mountains on cold-season weather disturbances has been extensively studied (e.g., Karyampudi et al. 1995; Poulos et al. 2000; Steenburgh and Blazek 2001), particularly the lee cyclogenesis as reviewed in Hobbs et al. (1996). In comparison, the effect of the Rockies on summer weather disturbances is not so well documented. A majority of summer convective storms develop near the eastern slopes of the Rockies in the afternoon and then move eastward. Their initiation, growth and propagation across the northern plains are attributed to the consecutive processes of diurnal heating over terrain and moisture supply by the nocturnal low-level jet (LLJ) (e.g., Wallace 1975; McCorcle 1988; Nicolini et al. 1993; Stensrud 1996; Wang and Chen 2009). Among such storms, those occurring under the northwesterly flow often travel a long distance following a regular propagation pattern (Johns 1982; Johns and Hirt 1987). These characteristics were found coincident with corridors of propagating rainfall over the central United States (Carbone et al. 2002; Tuttle and Davis 2006; Jiang et al. 2006; Carbone and Tuttle 2008).

Long-lived, progressive mesoscale convective systems (MCSs) often accompany preexisting subsynoptic-scale (~1,000 km) perturbations embedded in the midtropospheric northwesterlies (Maddox et al. 1979; Bosart and Sanders 1981; Changnon and Kunkel 1999; Doswell and Bosart 2001; Knievel and Johnson 2002). Such midtropospheric perturbations (MPs) are occasionally a result of residual synoptic waves coming from the northeastern Pacific Ocean (Trier et al. 2006), but a majority of them emanate from the Rocky Mountains (Wang et al. 2009a, b). Using a regional reanalysis dataset, Wang et al. (2009a, hereafter Part I) conducted a climatological study of these MPs during the warm seasons (May–September) from 1997 to 2006. They showed that MPs have a high frequency in July and August, when the North American anticyclone fully develops forming prevailing northwesterly flow over the northern plains. The areal frequency of MPs (Fig. 1a; see Part I for case definition) depicts a northwest–southeast oriented band from the Rockies to the Ohio Valley, coincident with the prime track of severe weather outbreaks under northwesterly flow (Johns 1982).
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Fig. 1

a Summer (July–August) mean 600-mb streamlines superimposed with the occurrence frequency of MPs (dots showing the 3-h position) and topography (shadings). b Diurnal frequency of MPs based on the time of genesis, obtained from Part I. The growth rate of unstable waves (solid curve) and the error bar for different wavelengths (400–1,600 km), as well as the 600-mb vortex stretching (dotted curve), is superimposed on (b). Variables used for the growth rate and vortex stretching are obtained from the MP genesis domain outlined by a box in (a)

Part I noted that the diurnal frequency of MP geneses reveals a bimodal distribution with a primary peak at 12 UTC (early morning) and a secondary peak at 00Z (late afternoon) (Fig. 1b histogram). Despite an intuitive suspicion that the perturbations may be better resolved by the assimilation system at operational rawinsonde times, this timing preference coincides with the early-morning stable boundary layer and the late-afternoon convective boundary layer over the Rockies (Banta and Cotton 1981; Banta 1984; Stull 1988). This, in turn, implies a link with the planetary boundary layer (PBL) evolution. The PBL of the Rocky Mountains extends well into the midtroposphere (Stensrud 1993; Jiang et al. 2007) and can modulate the flow characteristics there (Lieman and Alpert 1993). The interaction between the daytime mixed layer and the mountain wind system can trigger convective clouds and impose instability on the mid-level flow (Banta 1984, 1986). Moreover, the PBL evolution over the Rockies changes the continental diurnal thermal processes and alters the mid-level flow direction between night and day (Helfand and Schubert 1995). A similar process regulates near-surface pressure gradients around the terrain and helps form the Great Plains LLJ (Paegle and Rasch 1973; Paegle and McLawhorn 1983; Jiang et al. 2007). These previous findings underline the influence of PBL over the Rockies on the atmospheric circulation in different scales.

Early works (e.g., Eady 1949; Kuo 1953; Phillips 1954; Staley and Gall 1977) have predicted the occurrence of baroclinic short waves in areas with low static stability and vertical shear. When the lapse rate is near-adiabatic and the zonal wind increases with height (i.e. westerly shear), the wavelength of growing baroclinic waves can decrease to shorter than 500 km (Wiin-Nielsen 1989). Unstable baroclinic waves in the subsynoptic scale (1,000 km or smaller) are likely to occur when either surface friction (Satyamurty 1983) or ageostrophic effects (Aranson 1963; Satyamurty et al. 1982) are present, though short-wave instability can also be induced by low static stability or large vertical shear alone (Staley 1989). Because near-adiabatic lapse rate, large vertical shear, surface friction and ageostrophic forcing are common in the PBL over terrain, unstable short waves that fit the MP profile seem likely.

Based on the climatological study of MPs in Part I, we take a diagnostic approach to examine the impact of the Rocky Mountains and the associated PBL on the MP genesis. The analysis is conducted using the North American Regional Reanalysis (NARR) data and a general circulation model (GCM). The NARR features 32-km spatial and 3-hourly temporal resolutions (Mesinger et al. 2006). Analytical solution is not performed here, due to the wide range of assumptions that are unlikely to be applicable in an observational study. We adopt a comparative method instead. In view of the high frequency of MPs in July and August (Part I), the analysis focuses on these 2 months (referred to as summer) from 1997 to 2006. The summer circulation is examined in Sect. 2 with an emphasis on its midtropospheric properties over the Rocky Mountains. The diurnal wind variations near and above the Rockies and their impact on MP geneses are diagnosed in Sect. 3. Possible instability factors leading to unstable short waves are discussed in Sect. 4. To supplement the diagnostic, in Sect. 5 we analyze two numerical experiments (with and without terrain) performed by a GCM. Summary and suggestions are given in Sect. 6.

2 Basic state of the midtroposphere over the Rocky Mountains

It is known that the diurnal evolution of midtropospheric (i.e. between 700 and 500 mb) winds over the Rocky Mountains is opposite to that over the Great Plains. This is because daytime terrain heating produces inflow at low levels and outflow at mid-levels through a “thermal chimney” near the foothills, while nighttime cooling reverses the circulation. The thermal chimney leads to midtropospheric divergence (convergence) over the eastern slope of the Rockies in response to the daytime upslope convergence (nighttime downslope divergence), as was found in Helfand and Schubert (1995) and Jiang et al. (2007). Such a thermally induced circulation may create vortex stretching which subsequently induces cyclonic vorticity. To inspect this possibility, the 3-h evolution of vorticity tendency at 600 mb due to stretching of absolute vorticity, \( - (f + \zeta )\nabla \cdot V \), is shown in Fig. 1b (dotted line; averaged in the MP genesis region as outlined in Fig. 1a). A marked diurnal cycle of \( - (f + \zeta )\nabla \cdot V \) is revealed showing an early-morning maximum, coincident with the peak MP frequency at 12 UTC. Since vortex stretching is generally proportional to horizontal convergence, this result agrees with the finding of Helfand and Schubert (1995) that the midtropospheric flows converge in the night and diverge in the day over the eastern Rockies.

Beginning in late June, a quasi-stationary anticyclone develops over the Rocky Mountains following the onset of the North American Monsoon (Higgins et al. 1997; Barlow et al. 1998), as shown in Fig. 2 by the vertical sections of eddy streamfunction across 43°N. The anticyclone extends deeply downward to just over the mountains and forms a seemingly stable flow regime in the midtroposphere. However, during the daytime strong surface heating forms a near adiabatic temperature profile over the Rockies reaching 600 mb (Fig. 2a), accompanied by large vertical shear at the top of the PBL (Fig. 2b) owing to vertical mixing and terrain drag (Banta 1984, 1986). At night, static stability restores (Fig. 2c) but vertical shear remains strong above the terrain surface (Fig. 2d). In view of the persistent westerly shear in the midtroposphere, baroclinic instability becomes possible as the terrain drag acts to restore vertical shear and maintains instability (Gutowski 1985; Robinson 2000). Such restoration of baroclinic instability by friction/drag is specifically important to the equilibration of short Charney waves (Zurita-Gotor and Lindzen 2004) and, therefore, may be important to MPs.
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Fig. 2

Longitude-height sections across 43°N of the summer mean eddy streamfunction (contours) superimposed with static stability (∂θV/∂p) at (a) 00 UTC and (c) 12 UTC, and vertical wind shear (−∂u/∂p) at (b) 00 UTC and (d) 12 UTC. Terrain is shaded in black. The data are July–August climatology for 1997–2006 from the NARR

To examine this factor, we compute the instantaneous growth rate for normal mode baroclinic instability using a simple two-layer model provided in Holton (2004).1 Parameters used in this computation include the mean 600-mb zonal wind speed, basic state thermal wind between 700 and 200 mb (i.e. pressure interval 500 mb), and the observed values of static stability at 600 mb, all of which are averaged over the MP genesis region as outlined in Fig. 1a. Zonal wavelengths are prescribed from 400 to 1,600 km with a 200 km increment. As shown in Fig. 1b, the growth rate (solid line; for exponential growth) reveals a clear diurnal pattern with a late-afternoon peak, coincident with the 00 UTC maximum of the MP frequency and the fact that low static stability reduces the cutoff wavelength for smaller disturbances (e.g., Aranson 1963; Wiin-Nielsen 1989). In Part I we showed that the growth rate of the first two examples of MPs in July 2005 is about 1.0 day−1, a number comparable with this estimated maximum growth rate at 00 UTC. A recent study (Wang et al. 2009b; their Fig. 10) showed that the average growth rate of MPs is about 0.3 day−1, which is also in good agreement with the daily-mean growth rate of 0.32 day−1 as suggested from Fig. 1b. Though a two-layer model may not be sufficient to represent the complex atmospheric conditions over broad terrain, this exercise provides clues that unstable waves are more likely to occur over the Rockies in daytime conditions than at night.

While the growth rate increase and the wavelength decrease coincide with the 00 UTC peak of MP geneses, the midtropospheric conditions in the early morning (09–12 UTC) are unfavorable for any short-wave instability; this does not support the maximum frequency of MPs at 12 UTC. Likewise, negative vorticity tendency at 00 UTC does not favor the late-afternoon geneses of MPs. In other words, the results in Fig. 1b imply that the bimodal distribution of the MP frequency may be a combined effect from those two: vorticity generation in the early morning and dynamic instability in the late afternoon. In the following section we will examine the vorticity generation process. The instability mechanism will be explored in Sect. 4.

3 The climatological propagating mode

3.1 Diurnal variation of the midtropospheric flows

Part I pointed out that the MP frequency collocates with a climatological zonally propagating vertical vorticity signal (hereinafter, climatological propagating mode) initiated over the Rockies in the early morning, while the MP genesis and movement appear to be modulated by this climatological propagating mode (Fig. 3c; adopted from Part I). It was inferred from Fig. 1b that the formation mechanism of this mode is associated with the mid-level vorticity generation. To verify, Fig. 3a and b show the Hovmöller diagrams of the anomalous 600-mb zonal winds (Δu) and meridional winds (Δv), respectively, with their daily mean removed, superimposed with the turbulent kinetic energy (TKE). The TKE exhibits a late afternoon (21–00 UTC) maximum over the Rockies (between 105°W and 120°W). Likely, the extraction of kinetic energy from the westerly flow by the TKE causes the reduction in wind speed during the afternoon and the corresponding increase in the night. Over the Great Plains (105–95°W), Δv reveals a diurnal variation alternating between southerly around 15 UTC and northerly around 03 UTC (Fig. 3b).
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Fig. 3

Hovmöller diagrams along 43°N of 600-mb (a) zonal wind and (b) meridional wind anomalies (with the daily mean removed; contour) superimposed with the TKE (shadings), and (c) departure of 600-mb vorticity from the daily mean (Δζ; positive values shaded) superimposed with departure of 3-hourly MP frequency (ΔNF; thick lines) adopted from Part I. In (c) areas of positive ΔNF are hatched to indicate the preferred propagation pattern of MPs. The 24-h cycle is repeated in all panels for a better illustration

Such variations of the midtropospheric winds correspond with the concurrent “return flow” of the LLJ. The return flow was named in describing the phenomenon of mid-level northerly wind that is opposite to the nocturnal LLJ (Hering and Borden 1962). During midnight at the peak of the LLJ, the return flow is northerly as opposite to the southerly jet (in the sense of anomaly). Similar to the LLJ, the return flow features a clockwise rotation in wind direction due to inertial oscillation (Helfand and Schubert 1995), but the phase of this rotation is opposite to the typical diurnal rotation of the LLJ (Jiang et al. 2007). For instance, at 09 UTC when the LLJ anomaly is pointing northeastward, the mid-level flow anomaly is pointing southwestward. For convenience we use the term “return flow” throughout the text, although this term does not always mean northerly wind.

During 12–18 UTC, the westerly anomalies across the Rockies (Fig. 3a) meet the southerly anomalies over the Great Plains (Fig. 3b). The superposition of these two flows appears to create cyclonic vorticity between them around 105°W (Fig. 3c; shadings). This early-morning generation of cyclonic vorticity coincides with the primary peak of the MP diurnal frequency at 12 UTC (Fig. 1b). After its formation, the cyclonic vorticity signal moves eastward at a constant speed of 15 m s−1, similar to that of MPs and summer convective episodes (Carbone et al. 2002; Tuttle and Davis 2006). At such speed, the cyclonic vorticity signal would be positioned in the Ohio Valley when a new cyclonic vorticity signal appears over the eastern Rockies the next morning. The existing and newly generated cyclonic vorticity signals form a wave train across the central-eastern United States.

Because vorticity itself is essentially white noise and may contain irrelevant signals, we use streamfunction (ψ = \( \nabla^{ - 2} \zeta \)) to illustrate the kinematic structure of this climatological propagating mode. Applying Fourier analysis, the streamfunction anomaly (i.e. daily mean removed) is spatially filtered with the short wave regime of zonal wavenumbers 10–61, denoted as ΔψS, based on the 103 km-scale of MPs. The horizontal distribution of 600-mb ΔψS (Fig. 4a) and the vertical section of ΔψS across 43°N (Fig. 4b) at every 6 h depict a well organized wave train moving eastward. The vertical development of this wave train is restricted at heights below 400 mb with stronger amplitudes over the Rockies than the Midwest, signaling that the wave train weakens while moving toward the East Coast. This ΔψS wave train also features a westward tilting (i.e. baroclinic) structure near the Rockies and a barotropic structure over the plains. The baroclinic structure has implications for the MP genesis mechanism, which will be addressed in Sect. 4.
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Fig. 4

Departures of shortwave-regime streamfunction (ΔψS) from the daily mean at (a) 600 mb and (b) latitude-height section across 43°N at (top to bottom) 12, 18, 00, and 06 UTC. Zero contours are omitted. Terrain is shaded in (a) gray and (b) black. The center position of the short-wave train is lined up by dashed lines

3.2 Formation of the climatological propagating mode

The formation sequence of this climatological propagating mode is shown in Fig. 5a by the 600-mb wind anomalies from 12 to 18 UTC (daily mean removed). At 12 UTC, cyclonic vorticity develops along the northeastern Rockies associated with the substantial convergence between westerlies over the Rockies and southeaster lies over the Great Plains. At 15 UTC, this cyclonic vorticity amplifies and begins to move away from the Rockies, following the diurnal rotation of the mid-level flows. At 18 UTC, the lee-side convergence dissipates and the cyclonic vorticity signal moves further east and slightly weakens. Then, according to Fig. 4, this cyclonic vorticity signal continues to migrate eastward with decreasing magnitude.
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Fig. 5

a Departures of 600-mb wind vectors and vertical vorticity (contours) from their daily means at (top to bottom) 12, 15, and 18 UTC. Zero contours of vorticity are omitted while unit vector is given in the bottom. Terrain is lightlyshaded. b Time-height profiles of wind anomalies at 100°W, 40°N (109°W, 40°N) from the daily mean superimposed with meridional (zonal) wind speed as shadings at the top (bottom)

In order to depict the evolution of flows linking to the formation of this climatological propagating mode, time-height profiles of the diurnal wind anomalies over the Great Plains (at 100°W, 40°N) and the Rockies (at 109°W, 40°N) are shown in Fig. 5b. At 06–09 UTC, the LLJ and the return flow are represented by low-level southerlies and mid-level northerlies over the Great Plains. It is apparent that the wind directions of both the LLJ and the return flow exhibit a clockwise rotation throughout the day, but as previously mentioned their rotations are out-of-phase. Over the Rockies, the cross-mountain flow also features a clockwise rotation owing to inertial oscillation (Helfand and Schubert 1995), with the maximum variation taking place between 700 and 500 mb.

The dynamic process leading to the climatological propagating mode is diagnosed based on the horizontal vorticity budget analysis. Because the MP genesis level is near the PBL top where temperature gradients are strong, the solenoidal term in the vorticity equation could be important. Strong vertical shear (cf. Fig. 2) may also lead to a tilting effect on vorticity. To determine the importance of each forcing term relative to vorticity tendency, the magnitude of individual terms is compared with the magnitude of vorticity tendency; these are absolute values averaged within a 2° × 2° domain over the maximum center of vorticity tendency at 12 and 18 UTC, as shown in Table 1. It appears that neither the tilting term nor the solenoidal term is sufficiently large to impact vorticity tendency, as they contribute less than 5% to vorticity tendency. Results in Table 1 provide a justification to scale the vorticity budget equation as,
$$ \zeta_{t} \left( { = {\frac{\partial \zeta }{\partial t}}} \right) \approx - V \cdot \nabla (\zeta + f) - (f + \zeta )\nabla \cdot V, $$
(1)
with conventional symbols. These terms are shown in Fig. 6.
Table 1

Ratio between the magnitude (i.e. absolute value) of each forcing term in the vorticity budget equation and that of vorticity tendency at 12 and 18 UTC

 

12 UTC

(%)

18 UTC

(%)

\( | - V \cdot \nabla (\zeta + f)| \)/\( |\zeta_{t} | \)

8

94

\( | - (\zeta + f)\nabla \cdot V| \)/\( |\zeta_{t} | \)

91

5

\( \left| { - \left( {{\frac{{\partial w^{*} }}{\partial x}}{\frac{\partial v}{\partial z}} - {\frac{\partial w}{\partial y}}{\frac{\partial u}{\partial z}}} \right)} \right| \)/\( |\zeta_{t} | \)

4

2

\( |{\frac{1}{{\rho^{2} }}}({\frac{\partial \rho }{\partial x}}{\frac{\partial p}{\partial y}} - {\frac{\partial \rho }{\partial y}}{\frac{\partial p}{\partial x}})| \)/\( |\zeta_{t} | \)

1

3

* w is computed by the kinematic method

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Fig. 6

Same as Fig. 5 except superimposed with anomalies of (a) vorticity tendency (ζt; contours), (b) vortex stretching [−(f + ζ)∇·V], and (c) horizontal vorticity advection [−V·∇(f + ζ)] at 12 UTC (daily mean removed). (d)–(f) Same as (a)–(c) but for 18 UTC

At 12 UTC, strong positive vorticity tendency appears between the westerly anomalies over the Rockies and the southeasterly anomalies over the Great Plains (Fig. 6a). The vorticity tendency pattern is nearly identical to vortex stretching (Fig. 6b), indicating that positive vorticity tendency over the lee of the Rockies is primarily generated by vortex stretching. Vorticity advection is very weak at this moment (Fig. 6c). Since vortex stretching by vorticity (\( - \zeta \nabla \cdot V \); not shown) contributes to only about 5% of the variance, the marked vortex stretching in Fig. 6b is approximated as \( - f\nabla \cdot V \). Thus, the lee side vorticity generation in the early morning is closely related to the mid-level convergence, consistent with Fig. 1b. The formation of this climatological propagating mode also echoes the observation by Davis et al. (2002) that mid-level “dry vortices” (i.e. mesoscale vortices unassociated with convective storms) are often initiated over the eastern Rockies.

At 18 UTC, vorticity tendency evolves into a negative-positive dipole sandwiching the cyclonic vorticity signal (Fig. 6d). The effect of vortex stretching now almost vanishes (Fig. 6e), so positive vorticity tendency is mostly formed by horizontal vorticity advection (Fig. 6f), which then drives the cyclonic vorticity signal eastward. Such a mechanism continues until the cyclonic vorticity signal dissipates (not shown). The lack of vortex stretching also prevents the climatological propagating mode from growing over the plains. These features altogether suggest that the vorticity dynamics of this climatological propagating mode can be depicted as
$$ \zeta_{t} \approx - f\nabla \cdot V\;{\text{during the genesis stage}}, $$
(2)
and
$$ \zeta_{t} \approx - V \cdot \nabla (\zeta + f)\;{\text{during the propagation stage}}. \, $$
(3)
Converting vorticity tendency in Eq. (2) to streamfunction tendency yields
$$ \psi_{t} = \nabla^{ - 2} \left( {{\frac{\partial \zeta }{\partial t}}} \right) \approx \nabla^{ - 2} ( - f\nabla \cdot V_{D} ) , $$
(4)
where VD is divergent winds. Equation 4 shows that rotational (i.e. geostrophic) flows are generated by divergent (i.e. ageostrophic) flows, thereby linking the climatological propagating mode to inertial oscillation—the same mechanism that plays an important part in the Great Plains LLJ (Blackadar 1957) as well as the return flow (Helfand and Schubert 1995).

How is the seemingly weak vorticity magnitude of the climatological propagating mode (~10−6 s−1) related to the much stronger vorticity of some individual MPs (>10−5 s−1)? Wang et al. (2009b) pointed out that MPs often stimulate MCSs which feed back to induce and/or intensify mid-level vorticity (e.g., Zhang and Fritsch 1988; Hertenstein and Schubert 1991; Zhang 1992). Such a process occurs most frequently about 18–24 h after the MP genesis when the associated convective storms are often rapidly developing. This feature concurs with the developing nocturnal convection (Part I). One may question if the climatological propagating mode is merely the long term average of individual MPs; to examine, we reconstruct a “non-MP” composite of the 600-mb vorticity anomalies, following Fig. 3c but removing all the MP days identified in Part I. The result (not shown) reveals a similarly apparent, yet slightly weak propagating signal initiated from the lee-side convergence area and moving eastward, with the same speed as that revealed in Fig. 3c. This further supports the propagating vorticity signal as a climatological feature and that it modulates the activity of individual MPs.

Another remaining question is that the early-morning acceleration of zonal winds over the Rockies may not be simply explained by the loss of kinetic energy due to the TKE development. Previous studies analyzing the LLJ formation (e.g., Bonner and Paegle 1970) suggested that the stable nocturnal inversion layer over sloping terrain leads to the supergeostrophic wind atop the boundary layer and, in turn, results in the nocturnal jet core. Given the prevailing westerly flow in the midtroposphere, such a process may contribute to the nighttime acceleration of the cross-mountain westerlies. This claim is examined by comparing the magnitude of the diurnal wind anomalies with that of the supergeostrophic wind. Figure 7a shows the meridional section of static stability and zonal wind at 12 UTC across 107°W (with the daily mean removed). Large static stability following the topography indicates a shallow stable layer, while westerly anomalies form immediately above this stable layer. The supergeostrophic winds in the zonal direction, revealed by actual winds minus the geostrophic winds (u − ug), are shown in Fig. 7b. Over the Rockies, westerly (easterly) anomalies of u − ug are distributed above (within) the boundary layer. This relation reverses over regions south of 35°N where the background flow is easterly. The flow patterns in Fig. 7a and b are consistent, suggesting that the early-morning westerly anomalies above the terrain are linked to the supergeostrophic wind.
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Fig. 7

Meridional cross-sections of the departure of static stability (shadings) from the daily mean across 107°W at 12 UTC superimposed with (a) zonal wind anomalies (Δu) and (b) zonal wind minus geostrophic wind (u − ug; contours). Zero contours are omitted. Terrain is shaded in black and the MP genesis area is indicated in the bottom

4 Instability in the midtroposphere

We have shown that the preferred 12 UTC geneses of MPs are likely facilitated by the robust cyclonic vorticity generation of the climatological propagating mode developed in the early morning. What contributes to the other preferred geneses around 00 UTC is unclear. Recall from Sect. 2 and Fig. 1b that the midtroposphere above the Rockies becomes dynamically unstable in the late afternoon. This potential mechanism is investigated here.

4.1 Climatology

The inferred dynamic instability over the Rockies is first examined through the Rossby deformation radius2 (LR), which depicts the length scale at which rotational effects become decisive (i.e. so perturbations can grow). We compute the 3 hourly LR across 43°N at 600 mb (Fig. 8a) and 300 mb (Fig. 8c). In the midtroposphere, LR is much reduced over the Rockies from the typical 1,000 km radius, reaching 300 km at 00 UTC and 700 km at 12 UTC. This fluctuation range of LR echoes the observation by Wiin-Nielsen (1989; his Fig. 9) that unstable wavelengths smaller than 400 km with the e-folding time within 1 day can occur when the lapse rate nears adiabatic in a moderate shear environment. Such lapse rate and shear are common in the MP genesis region over the Rockies (cf. Fig. 2a, b). The decrease in LR not only reduces the horizontal scale for eddy transport but also lowers the critical shear (βLR2), causing the supercriticality (ξ ≡ US/βLR2, where US is vertical shear) to exceed 1 over the Rockies (Fig. 8b). It is known that ξ above unity can enhance eddy energy generation (Stone 1972; Held and Larichev 1996) and therefore is favorable for short waves. In comparison, LR (Fig. 8c) and ξ (Fig. 8d) in the free atmosphere remain at their typical values and are much less variable, except for the slight depression in LR (rise in ξ) near 100°W depicting the unstable lee area. This contrast of LR and ξ between the middle and upper troposphere further reveals the unstable midtropospheric environment over the Rockies.
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Fig. 8

Rossby deformation radius (LR) at (a) 600 mb and (c) 300 mb and the supercriticality (ξ) at (b) 600 mb and (d) 300 mb across 43°N at every 3 h. The scales of LR and ξ are given to the right. The values at 00 UTC (12 UTC) are indicated by thick dotted lines (thick solid lines). Terrain is shaded in gray with the scale (in meter) given to the left for comparison

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Fig. 9

Latitude-height sections of \( \partial \bar{q}/\partial y \) (contours) and \( \partial \theta /\partial y \) (shadings) across 107°W at (a) 00 UTC, (b) 06 UTC, (c) 12 UTC and (d) 18 UTC. Terrain is shaded in black and contour intervals are given at the bottom. The MP genesis region is indicated between 39°N and 50°N

The majority of MP geneses occur close to the north-facing slopes of the Rockies (i.e. 40°–50°N), as indicated in Fig. 1a. During summer, the terrain heating to the south of this region generates a pronounced meridional gradient of potential temperature (\( \partial \theta /\partial y \)) in the midtroposphere. Strong negative \( \partial \theta /\partial y \) is present throughout the day (Fig. 9a–d; shadings) but is more pronounced at 00 UTC than 12 UTC, which is an obvious consequence of the diurnal solar heating over terrain. This sloping region, known as the “Wyoming wind corridor” (Martner and Marwitz 1981), is also characterized by prevailing westerlies associated with large vertical shear. Vertical shear is important to baroclinic instability in the quasi- (or semi-) geostrophic balance. The cause of vertical wind shear in this case is likely surface friction leading to Ekman damping. Common perception sees Ekman damping as limiting the range of unstable wavenumbers and reducing the growth rate. However, many studies (e.g., Lin and Pierrehumbert 1988; Valdes and Hoskins 1988; Moore and Montgomery 2004) have found that boundary layer friction cannot eliminate baroclinic instability. In some occasions boundary layer friction actually favors baroclinic short waves (e.g., Wiin-Nielsen 1989; Zurita-Gotor and Lindzen 2004). Regardless, there is little doubt that the combination of thermal gradient and vertical shear creates instability and promotes the release of available potential energy for pressure perturbations.

Such conditions are perceived from the Charney–Stern barotropic–baroclinic instability (Charney and Stern 1962) in which the meridional gradient of pseudo-potential vorticity (\( \partial \bar{q}/\partial y \)) changes sign, i.e.,
$$ {\frac{{\partial \bar{q}}}{\partial y}} = {\frac{\partial }{\partial y}}(\bar{\zeta } + f) + {\frac{\partial }{\partial p}}\left({\frac{{pf_{0}^{2} }}{R\sigma }}{\frac{{\partial \bar{u}}}{\partial p}}\right) $$
(5)
where f0 is the Coriolis parameter and σ is the static stability (σ = \( {\frac{{\bar{T}}}{{\bar{\theta }}}}{\frac{{\partial \bar{\theta }}}{\partial p}} \)), while the rest are conventional symbols. The overbar indicates an average with respect to time (long-term mean) and longitude (115°–100°W). The Charney–Stern instability has been linked to the genesis of midtropospheric short waves, such as the African easterly wave with a wavelength of 1,500–3,000 km (e.g., Burpee 1972; Thorncroft and Hoskins 1994a, b) and the East Asian monsoonal disturbance with a ~1,200 km wavelength (Chen et al. 2007; Wang and Chen 2008). In order to have such instability, \( \partial \bar{q}/\partial y \) has to be negative somewhere in the midtroposphere over the Rocky Mountains.
The meridional cross-sections of \( \partial \bar{q}/\partial y \) every 6 h (Fig. 9a–d; contours) reveal persistent sign reversals between 800–500 mb throughout the day with negative gradients distributed over the MP genesis region (40°–50°N). Similar to \( \partial \theta /\partial y \), negative \( \partial \bar{q}/\partial y \) is also more pronounced at 00 UTC than 12 UTC. This diurnal fluctuation corresponds to that of LR and ξ (Fig. 8), as the condition of ξ > 1 tends to induce negative \( \partial \bar{q}/\partial y \) at lower levels (Bretherton 1966) while sign reversals of \( \partial \bar{q}/\partial y \) often occur in flows with negative meridional gradients of potential temperature (Held 2007). It appears that the persistent negative \( \partial \theta /\partial y \) helps maintain the mid-level baroclinicity. To examine, we recalculate \( \partial \bar{q}/\partial y \) based on two scenarios at 00 UTC:
  1. 1.
    \( \partial \bar{u}/\partial z = 0 \) by vertically averaging the zonal winds between 900 and 500 mb, which eliminates vertical shear, while retaining the actual potential temperature profile (Fig. 10a). Note the extremely low static stability in the MP genesis region as indicated by the upright θ profile. Negative \( \partial \bar{q}/\partial y \) (Fig. 10b) is as pronounced as that in Fig. 9a, suggesting that the meridional temperature gradient has a major impact on this Charney–Stern instability.
    https://static-content.springer.com/image/art%3A10.1007%2Fs00382-010-0765-7/MediaObjects/382_2010_765_Fig10_HTML.gif
    Fig. 10

    Latitude-height sections of zonal wind (shadings) and potential temperature (θ; contours) across 107°W at 00 UTC with (a) ∂u/∂z = 0 and real θ scenario, and (c) ∂θ/∂y = 0 and real u scenario (see text). The cross-sections of \( \partial \bar{q}/\partial y \) computed from the conditions in (a) and (c) are given in (b) and (d), respectively. The contour intervals are given above (a) and (b)

     
  2. 2.

    \( \partial \bar{\theta }/\partial y = 0 \) by meridionally averaging the temperature profile between 15°N and 65°N, which eliminates the meridional temperature gradient and redistributes static stability, while retaining the actual zonal wind profile (Fig. 10c). Compared with Fig. 9a, areas of negative \( \partial \bar{q}/\partial y \) are much reduced (Fig. 10d) and appear to resemble the 12 UTC situation (Fig. 9c) in which \( \partial \theta /\partial y \) is relatively weak. This suggests a secondary role of vertical shear in the instability.

     

The diagnostic here reveals the decisive effect of the mid-level meridional temperature gradient on the Charney–Stern instability, consistent with Held (2007).

4.2 Case composite

To further investigate if the genesis of individual MPs is also related to the Charney–Stern instability, we perform a composite analysis at each MP genesis using cases over the 1997–2006 period as identified in Part I. The composite is made by aligning the first appearance of MPs with their average genesis position which, subsequently, creates a “MP-relative composite” following Figs. 810 of Part I. For MP geneses that occur at 00 UTC (Fig. 11a; genesis area indicated by a thick box), the meridional sections of \( \partial \bar{q}/\partial y \) across the composite genesis region (~107°W) reveal robust negative gradients with clear sign changes in the midtroposphere. At 12 UTC (Fig. 11b), sign changes of \( \partial \bar{q}/\partial y \) are less apparent corresponding to the much weaker negative gradients. Regardless, at both time steps the composite MP geneses occur precisely in the sign change area of \( \partial \bar{q}/\partial y \); this supports their link with the Charney–Stern instability. Furthermore, the variation in \( \partial \bar{q}/\partial y \) suggests its relation with the diurnal evolution of static stability and meridional temperature gradients, which are consistent with the diagnostic in Fig. 10.
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Fig. 11

Latitude-height cross-sections of \( \partial \bar{q}/\partial y \) (shadings) and vortex stretching (− f ∇·V; contours) computed from the MP-relative composite during geneses (see text) at (a) 00 UTC and (b) 12 UTC. The composite MP genesis (~107°W) is outlined by a thick black box and indicated by an arrow. The contour interval is 2 × 10−10 s−2. c and d Vertical profiles of the mean-flow Richardson number (Ri; solid line) and the growth rate (dashed line) computed from the two-layer model at 00 and 12 UTC, respectively, averaged within a 4° × 4° domain centered at the composite MP genesis. Note that the growth rate with respect to each pressure level is a result of the static stability setting at that particular level, rather than an actual profile

One may argue that the terrain boundary layer should be dissipative for MPs, as the PBL can prevent baroclinic adjustment for mesoscale eddies due to dissipation by turbulence and vertical mixing (e.g., Swanson and Pierrehumbert 1997; Stone and Nemet 1996). To address this foreseeable objection, we compute the mean-flow Richardson number [\( Ri = {\frac{{g/\theta_{v} (\partial \theta_{v} /\partial z)}}{{(\partial u_{g} /\partial z)^{2} }}} \)]. It is known that a decrease in Ri reduces the e-folding time (i.e. enhances the growth rate) for baroclinic waves. When Ri is less than 1, the likelihood for baroclinic instability and exponentially growing momentum of mesoscale eddies drastically increases (e.g., Held and Larichev 1996). On the other hand, Ri also needs to be larger than 0.25 for isolation from the turbulence regime (Stone 1966; Holton 2004). As shown by the vertical profile of Ri at 00 UTC in the composite (Fig. 11c; averaged within a 4° × 4° domain surrounding the composite genesis), Ri remains smaller than 0.25 below 650 mb and increases rapidly to exceed 1 at 450 mb. Below 650 mb mesoscale eddies will be dissipated by turbulence and vertical mixing. Above 450 mb the atmosphere becomes too stable for such eddies. In other words, only the layer between 650 and 450 mb is suitable for MP-like disturbances. Ri at 12 UTC (Fig. 11d) exhibits similar characteristics.

Also shown in Fig. 11c and d is the instantaneous growth rate of unstable waves computed from the two layer model as used for Fig. 1b. Here we give a fixed wavelength of 1,000 km with various static stability settings as those measured at each pressure level over the MP genesis area. The rest of the parameters (i.e. wind speed, thermal wind, etc.) follow those used in Fig. 1b. Again this is a crude representation of baroclinic instability over terrain, but such a simple model helps substantiate the impact of different static stability at different levels on wave growth. At 00 UTC, the growth rate is larger than 0.5 day−1 above 550 mb. If we use this 0.5 day−1 growth rate as threshold, given that the MP lifecycle is 48 h, then the layer between 550 mb and the terrain surface is where growing eddies are most likely to occur. After taking into account the turbulence regime determined by Ri (i.e. Ri < 0.25), one obtains an “optimal” layer of 650–550 mb in which mesoscale eddies can effectively grow, as indicated by the shaded area in Fig. 11c. This estimated genesis level coincides with the observation in Part I that the maximum amplitude of MPs occurs around 600 mb. In summary, MPs tend to develop at a level far enough above the turbulent PBL so eddy kinetic energy is not dissipated by turbulence, yet low enough so shorter waves can survive underneath the longer-wave instability (cf. Fig. 8).

Meanwhile, vortex stretching (\( - f\nabla \cdot V \)) in the midtroposphere over the MP genesis area is weak at 00 UTC (Fig. 11a) but becomes pronounced at 12 UTC (Fig. 11b), supporting the early-morning vorticity generation. Due to the consistently small growth rate resulting from large static stability in the early morning (cf. Fig. 1b), an optimal layer for growing eddies cannot be identified for 12 UTC (Fig. 11d). In this case, the apparent vortex stretching leading to mid-level cyclonic vorticity, as discussed in Sect. 3, may be the primary forcing mechanism for MPs. Therefore, MP geneses around 00 UTC (late afternoon) are more likely linked to the dynamic instability, while geneses at 12 UTC (early morning) are more closely related to the climatological propagating mode. Their combined effects correlate greatly with the bimodal frequencies of the MP genesis peaking at 00 and 12 UTC.

The pronounced sign change of \( \partial \bar{q}/\partial y \) coexisted with small Rossby radius in the late afternoon suggests a combined terrain and PBL modulation on subsynoptic-scale instability. Such modulation remains to be theoretically proven, as it requires careful examination of the forcing-dissipation problem of the baroclinic equilibrium to obtain analytical solutions for the wavelength and growth rate. A similar problem was recently revisited by Zurita-Gotor and Lindzen (2006); however, the diurnally varying PBL and mesoscale instability over terrain, as encountered in this study, are proving to be more complicated than the assumptions made in their idealized model. The inclusion of terrain and diurnal PBL variation in the forcing-dissipation problem is beyond existing instability theories (Chris Snyder, personal communication). What we have shown may be regarded as oblique evidence, but the correlation between these two forcing mechanisms and the MP genesis is strong and deserves further investigation.

It is worth noting some differences between MP geneses in the 12 UTC “convergence group” and the 00 UTC “baroclinic group”. The first difference is about intensity. MP geneses occurring at 12 UTC tend to have a stronger vorticity core than those at 00 UTC, as revealed in the case-relative composite analysis similar to Fig. 11 (not shown). This feature echoes the robustness of the mid-level convergence and the fact that the 12 UTC group of MPs has the largest population. The second difference is about initial location. The distribution of the 12 UTC geneses covers a broader area including the lee side of the Rockies, whereas the 00 UTC geneses occur further to the west of the Front Range, as can be observed in the MP frequency anomalies in Fig. 3c. However, as stated earlier, in an observational study it is not possible to physically separate MP geneses from the two groups, so such differences are suggestive rather than conclusive. Nonetheless, once convection is initiated and MPs move away from the Rockies, there are no noticeable differences between MPs initiated at 00Z and 12Z.

5 GCM experiments

To evaluate the impact of terrain on the MP formation, an atmospheric general circulation model (AGCM) is adopted. This AGCM was developed by the Geophysical Fluid Dynamics Laboratory (GFDL) Global Atmospheric Model Development Team (2004). The GFDL AGCM has a horizontal resolution of 1.25° longitude × 1.0° latitude with 24 vertical levels and incorporates diurnal changes in radiative transfer. Jiang et al. (2007) conducted two experiments using this AGCM to study the Great Plains LLJ: (1) control experiment using the global orography with default settings of physical parameters, and (2) no mountain (NOMT) experiment replacing the global topography by a flat land surface. Both experiments were run for 5 years with hourly output. The AGCM outputs analyzed in this study are the same as those used in Jiang et al. (2007). Here, the climatological diurnal cycle and mean circulations were extracted from July and August of each 5-year simulation.

Given the differences in spatial resolutions and model characteristics between the NARR and the AGCM, it is impractical to compare the absolute frequency of MPs from these two datasets. Thus, we estimate the MP activity by the root-mean-square (RMS) of 3 hourly relative vorticity at 600 mb. Since the average life cycle of MPs is 48 h (Part I), relative vorticity is filtered (ζ′) with a 6–48 h passband using the Butterworth bandpass filter in order to retain the MP characteristics and filter out synoptic waves. Furthermore, to avoid the contamination of synoptic disturbances propagating from higher latitudes, we only calculate the RMS of ζ′ south of the summer jet stream (~50°N). The observed and simulated 600-mb geopotential height and the RMS of ζ′ are shown in Fig. 12. In the NARR, an elongated band of large ζ′ activity emanates from the Rockies across the northern plains following the north–south baroclinicity zone (Fig. 12a; inferred from the strong meridional gradients of geopotential height). Despite some localized features of the ζ′ activity over terrain, this band structure of ζ′ agrees with the general track of MPs (Fig. 1a).
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Fig. 12

a Summer mean 600-mb geopotential height (contours) superimposed with the root-mean-square of relative vorticity filtered with a 6–48 h passband. The contour interval is 15 m. Terrain is indicated by dotted areas. (b) Same as (a) but for the control AGCM experiment. (c) Same as (b) but for the NOMT experiment

The summer anticyclone in the control experiment (Fig. 12b) is broader in the zonal direction and slightly narrower in the meridional direction, compared to the NARR. These features are accompanied by stronger pressure gradients to the north of the anticyclone. Despite such differences, the midtropospheric circulation is reasonably simulated. The RMS of ζ′ in the control experiment also reveals a band structure extending from the Rockies toward the East Coast, similar to that in the NARR. The eastward extension of the ζ′ activity relative to the NARR is likely due to the stronger anticyclone over the central plains causing stronger westerly flow. The AGCM has a relatively coarse spatial resolution but a finer temporal (i.e. hourly) resolution than the NARR, so it is not surprising that MPs can be simulated in the AGCM. In the NOMT experiment (Fig. 12c), however, the midtropospheric anticyclone is substantially weaker and the zonal flows across the Rockies become very strong. No trace of any ζ′ activity is found over the location of the (missing) Rockies and the central plains. Such a contrast speaks for the critical role of the Rocky Mountains to MPs.

Following Fig. 9a, the meridional sections of \( \partial \bar{q}/\partial y \) and \( \partial \theta /\partial y \) at 00 UTC are shown in Fig. 13a. In the control experiment, the distinct sign changes of \( \partial \bar{q}/\partial y \) overlapping with strong negative \( \partial \theta /\partial y \) are both reasonably simulated, although the magnitude of \( \partial \theta /\partial y \) is noticeably stronger than the observed. Without the topography (Fig. 13b), \( \partial \theta /\partial y \) becomes much weaker and closer to the surface while negative \( \partial \bar{q}/\partial y \) disappears from the midtroposphere. This result supports the argument in Sect. 4 that MP geneses around 00 UTC are linked to the Charney–Stern instability induced through the mid-level meridional temperature gradient and vertical westerly shear.
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Fig. 13

(a) and (b) Same as Fig. 9a but for the AGCM simulations in the control and NOMT experiments, respectively. (c) and (d) Same as Fig. 5a at 12 UTC but for the control and NOMT experiments, respectively

Following Fig. 5a, the simulated 600-mb anomalous winds and vorticity at 12 UTC are shown in Fig. 13c (daily mean removed). The AGCM captures the early-morning cyclonic vorticity over the eastern and northeastern foothills of the Rockies (Fig. 13c), as well as the convergence between the cross-mountain westerly flow and the easterly “return flow” (and the subsequent vortex stretching; not shown). In the NOMT experiment (Fig. 13d), however, the 600-mb anomalous winds are much weaker without any localized features or signals of cyclonic vorticity west of 100°W that may facilitate the MP development. In their study, Jiang et al. (2007) noted that both the LLJ and the mid-level return flow vanish in the NOMT experiment due to the absence of diurnal pressure gradient force and the lack of vertical diffusion. Their finding helps explain the lack of substantial diurnal variability in the mid-level circulation when orography is removed from the simulations. This, in turn, eliminates the vorticity generation mechanism for MPs.

6 Summary and discussion

Summer progressive MCSs often occur in association with preexisting MPs in northwesterly flow. In Part I we showed that MPs are initiated over the Rocky Mountains at a preferred genesis level of 600 mb. The MP genesis frequency reveals a bimodal distribution with a primary peak at 12 UTC (early morning) and a secondary peak at 00 UTC (late afternoon). MPs occurring around 12 UTC tend to follow a climatological zonally propagating vorticity signal that develops over the eastern Rockies and moves across the northern plains. Extended from Part I, this study examines the formation mechanism and the unique timing of MP geneses using 10 years of the NARR data for July and August. The results suggest that the bimodal distribution of the MP frequency may form by two separate mechanisms working together while each has a different timing in terms of maximum effect.

The early-morning genesis is linked to the lee side vorticity generation in the midtroposphere induced by accelerated westerly flow over the Rockies and easterly anomalies over the Great Plains. These two flows, both driven by inertial oscillation, converge during midnight and create vortex stretching over the eastern Rockies leading to cyclonic vorticity tendency. After sunrise, these two flows evolve into opposite directions so vortex stretching diminishes, while the newly created cyclonic vorticity is redistributed downstream through horizontal advection, forming the climatological propagating mode. MPs occurring around 12 UTC coincide well with this climatological propagating mode.

The NARR data also reveal a Charney–Stern type of instability characterizing the midtroposphere over the Rocky Mountains. Over the north-facing slopes of the Rockies (40°–50°N), the heated terrain to the south and the relatively cool air to the north together form strong meridional temperature gradients and, along with persistent vertical shear, create negative meridional gradients of potential vorticity and sign changes nearby. In the meantime the development of PBL reduces the Rossby deformation radius due to low static stability. Both effects reach their maximum intensity in the late afternoon (00 UTC). MPs occurring around 00 UTC are highly correlated with the robust sign changes of meridional gradients of potential vorticity, suggestive of their association with the Charney–Stern instability. Moreover, MP geneses are found to occur near the top of PBL (600 mb), rather than within the PBL, so mesoscale instability can survive the dissipative convective/mixing layer above the Rocky Mountains.

The reasons why such dynamic instability is present over the Rocky Mountains are manifold and defy easy explanation, since the PBL prevents mixed barotropic–baroclinic adjustment for eddies. The results presented here provide a large-scale perspective on the unstable environment favorable for short-wave perturbations in the MP spectrum. In order to sufficiently explain the specific wavelength and the growth rate of MPs in relation to any instability, analytical solutions are needed. However, such an approach must consider the forcing-dissipation problem of baroclinic equilibrium, which involves balancing surface friction that restores the baroclinicity, surface processes that prevent baroclinic adjustment, and factors other than the local thermal damping. This forcing-dissipation problem of baroclinic equilibrium remains challenging today.

Footnotes
1

The two-layer model was modified from the Matlab program “twolayer_model_2A.m” provided with Chapter 8 of Holton (2004).

 
2

LR ≡ NH/f0 for a continuously stratified fluid, where N is Brunt-Väisälä frequency, H is scale height and f0 is the Coriolis parameter.

 

Acknowledgments

We are grateful to Xianan Jiang at Joint Institute for Regional Earth System Science and Engineering, UCLA for kindly providing the GFDL AGCM simulations. We thank the anonymous reviewers for the valuable comments which greatly improved the manuscript. Editorial assistance by Marty Booth and Adam Clark is highly appreciated. This work was initiated under the Iowa State University Baker Endowment Fund 497-41-39-15-3803. Partial financial support for EST was supplied by a grant from the National Science Foundation (BCS0618823).

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© Springer-Verlag 2010