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main mechanism of decay, and the basic wave breaks down rapidly into an eddy field before it reaches the western boundary. By considering the parametric dependence of the ratio on latitude, possible only on the planetary scale, one could draw the conclusion that Z increases toward the high-latitude regions as the Coriolis parameter increases northward, which, as suggested by LaCasce and Pedlosky, is the reason for the confinement of wave patterns found in satellite measurements. This argument is
main mechanism of decay, and the basic wave breaks down rapidly into an eddy field before it reaches the western boundary. By considering the parametric dependence of the ratio on latitude, possible only on the planetary scale, one could draw the conclusion that Z increases toward the high-latitude regions as the Coriolis parameter increases northward, which, as suggested by LaCasce and Pedlosky, is the reason for the confinement of wave patterns found in satellite measurements. This argument is
, our analysis will show that split and displacement SSWs indeed have very distinct prewarming evolutions. However, in contrast to Charlton and Polvani (2007) and Bancala et al. (2012) , who focused on planetary waves in the region below 30 km (10 hPa), we extend our analysis upward to 55 km (0.5 hPa) and analyze the combined effects of both planetary waves and gravity waves on vortex preconditioning and the resonant excitation theory of SSWs. In doing so, we focus particular attention on split
, our analysis will show that split and displacement SSWs indeed have very distinct prewarming evolutions. However, in contrast to Charlton and Polvani (2007) and Bancala et al. (2012) , who focused on planetary waves in the region below 30 km (10 hPa), we extend our analysis upward to 55 km (0.5 hPa) and analyze the combined effects of both planetary waves and gravity waves on vortex preconditioning and the resonant excitation theory of SSWs. In doing so, we focus particular attention on split
relation for divergent barotropic planetary waves in a flat bottom polar basin. In related meteorological studies, Haurwitz (1975) and Bridger and Stevens (1980) use cylindrical polar coordinates to study freely propagating waves in a high-latitude atmosphere. The concept of the delta ( δ )-plane approximation for quasigeostrophic dynamics at high latitudes was developed by Harlander (2005) . Harlander (2005) demonstrates that the high-latitude δ -plane model can be consistently derived from
relation for divergent barotropic planetary waves in a flat bottom polar basin. In related meteorological studies, Haurwitz (1975) and Bridger and Stevens (1980) use cylindrical polar coordinates to study freely propagating waves in a high-latitude atmosphere. The concept of the delta ( δ )-plane approximation for quasigeostrophic dynamics at high latitudes was developed by Harlander (2005) . Harlander (2005) demonstrates that the high-latitude δ -plane model can be consistently derived from
climate, including the surface westerlies and the horizontal distribution of temperature. In the tropics, baroclinic instability is inhibited by weak rotation and small horizontal temperature gradients. Here, quasi-stationary equatorial planetary waves forced by the latent heat release from deep convection play a key role in the large-scale atmospheric circulation. Equatorial planetary waves are readily observed in the climatological-mean tropical circulation and are dominated by 1) an equatorially
climate, including the surface westerlies and the horizontal distribution of temperature. In the tropics, baroclinic instability is inhibited by weak rotation and small horizontal temperature gradients. Here, quasi-stationary equatorial planetary waves forced by the latent heat release from deep convection play a key role in the large-scale atmospheric circulation. Equatorial planetary waves are readily observed in the climatological-mean tropical circulation and are dominated by 1) an equatorially
resolve key processes at all relevant scales. Here we use an AGCM to explore one particular mechanism for remote soil moisture impacts on meteorological fields, a mechanism involving the phase locking of a planetary wave over a specific soil moisture pattern. We start in section 2 with a diagnostic analysis of AGCM simulations. This analysis provides the information needed to design specialty simulations ( section 3 ) that confirm the operation of the mechanism within the model. Supporting evidence
resolve key processes at all relevant scales. Here we use an AGCM to explore one particular mechanism for remote soil moisture impacts on meteorological fields, a mechanism involving the phase locking of a planetary wave over a specific soil moisture pattern. We start in section 2 with a diagnostic analysis of AGCM simulations. This analysis provides the information needed to design specialty simulations ( section 3 ) that confirm the operation of the mechanism within the model. Supporting evidence
possible cause of the instability is planetary wave (PW) forcing (PWF) (e.g., Baldwin and Holton 1988 ; Geer et al. 2013 ). More recently, the role of gravity wave (GW) forcing (GWF) 1 in the formation of the unstable condition is also a subject of focus (e.g., McLandress and McFarlane 1993 ; Norton and Thuburn 1996 ; Watanabe et al. 2009 ; Ern et al. 2011 ). It is well known that GWF in the upper mesosphere is important as a driving force of the residual mean circulation from the summer
possible cause of the instability is planetary wave (PW) forcing (PWF) (e.g., Baldwin and Holton 1988 ; Geer et al. 2013 ). More recently, the role of gravity wave (GW) forcing (GWF) 1 in the formation of the unstable condition is also a subject of focus (e.g., McLandress and McFarlane 1993 ; Norton and Thuburn 1996 ; Watanabe et al. 2009 ; Ern et al. 2011 ). It is well known that GWF in the upper mesosphere is important as a driving force of the residual mean circulation from the summer
EAWM was independent of the Siberian high. Since variability of the AO can significantly modulate the propagation of quasi-stationary planetary waves between the troposphere and the stratosphere ( Chen et al. 2000 , 2003 ; Chen and Huang 2005 ), Chen et al. (2005) examined the interannual AO–EAWM relationship from the perspective of the quasi-stationary planetary wave activity (PWA). They found that during the positive phase of the AO, more quasi-stationary planetary waves propagate from high
EAWM was independent of the Siberian high. Since variability of the AO can significantly modulate the propagation of quasi-stationary planetary waves between the troposphere and the stratosphere ( Chen et al. 2000 , 2003 ; Chen and Huang 2005 ), Chen et al. (2005) examined the interannual AO–EAWM relationship from the perspective of the quasi-stationary planetary wave activity (PWA). They found that during the positive phase of the AO, more quasi-stationary planetary waves propagate from high
, including a detailed comparison with previous approaches and an overview of the climatological wavenumber–frequency spectra in the extratropics. To investigate planetary wave interference effects, we will compare the structure of the standing waves and the climatological wave field. Last, we will compute the vertical and time-lagged coherences of the standing and traveling waves at selected Northern Hemisphere extratropical locations using correlation-coherence analysis ( Randel 1987 ). Section 4 will
, including a detailed comparison with previous approaches and an overview of the climatological wavenumber–frequency spectra in the extratropics. To investigate planetary wave interference effects, we will compare the structure of the standing waves and the climatological wave field. Last, we will compute the vertical and time-lagged coherences of the standing and traveling waves at selected Northern Hemisphere extratropical locations using correlation-coherence analysis ( Randel 1987 ). Section 4 will
1. Introduction Quasi-stationary Rossby waves have a pronounced influence on weather in the midlatitudes in both the Southern and Northern Hemisphere (SH and NH, respectively) and are often associated with extreme weather events ( Hoskins and Woollings 2015 ; Screen and Simmonds 2014 ; Coumou et al. 2014 ; Woollings 2010 ). Rossby or planetary waves are large-scale oscillations of the midlatitude flow resulting from the latitudinal dependency of the Coriolis effect combined with thermal or
1. Introduction Quasi-stationary Rossby waves have a pronounced influence on weather in the midlatitudes in both the Southern and Northern Hemisphere (SH and NH, respectively) and are often associated with extreme weather events ( Hoskins and Woollings 2015 ; Screen and Simmonds 2014 ; Coumou et al. 2014 ; Woollings 2010 ). Rossby or planetary waves are large-scale oscillations of the midlatitude flow resulting from the latitudinal dependency of the Coriolis effect combined with thermal or
1. Introduction Atmospheric waves play a central role in the middle atmospheric circulation. Planetary-scale Rossby waves (PWs) arising from large-scale topography and the land–sea thermal contrast predominate stratospheric phenomena, whereas in the upper stratosphere and mesosphere, smaller-scale gravity waves (GWs) forced by small-scale topography, convection, and jet/front systems play a key role ( Achatz et al. 2024 ; Andrews et al. 1987 ; Kim et al. 2003 ). While the relative
1. Introduction Atmospheric waves play a central role in the middle atmospheric circulation. Planetary-scale Rossby waves (PWs) arising from large-scale topography and the land–sea thermal contrast predominate stratospheric phenomena, whereas in the upper stratosphere and mesosphere, smaller-scale gravity waves (GWs) forced by small-scale topography, convection, and jet/front systems play a key role ( Achatz et al. 2024 ; Andrews et al. 1987 ; Kim et al. 2003 ). While the relative
