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- Author or Editor: Shyh-Chin Chen x

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## Abstract

Stationary planetary waves forced by orography and diabatic beating are studied using a quasi-geostrophic two-level model on a beta-plane. This study extends a previous one by Trenberth to include the effects of a baroclinic atmosphere with zonal mean wind shear. With the introduction of vertical shear, the temperature field is no longer locked onto the heating field and can become orthogonal so that even though the wave is thermally forced there may not be any generation or loss of energy by diabatic heating. The presence of both thermal and orographic forcing together violates the conditions of nonacceleration of the zonal mean flow. The induced changes in the zonal mean flow strongly depend upon the relative phase of the thermal and orographic forcing. With a specified diabatic heating field, the eddy fluxes and changes of zonal mean flow are not sensitive to the strength of the mean zonal wind shear. By increasing the wind shear, however, the vertically propagating waves become trapped. The trapped waves accelerate the zonal mean flow through an induced meridional circulation distinct from that of the propagating waves. The characteristics of the forced waves can be explained by the local index of refraction.

Results indicating important differences between the stationary planetary waves in the two hemispheres are 1) the higher total wave number in the Southern Hemisphere, which arises from the shorter meridional scale, so that the waves are trapped, and 2) interaction between thermal and orographic waves in the Northern Hemisphere which is less likely in the Southern Hemisphere.

The limitations of the two-level model with the traditional fixed upper boundary condition, ω = 0 at *p* = 0, in reproducing forced planetary waves is evaluated by testing the sensitivity of results to a modified radiation upper boundary condition. Distinct differences are found when the planetary waves can propagate vertically. Not only is the response of the planetary waves different in phase and magnitude but also the induced acceleration of the zonal mean flow can be completely opposite. Nevertheless, there is reasonable agreement when the planetary waves are trapped vertically so that the upper boundary conditions have minor impact.

## Abstract

Stationary planetary waves forced by orography and diabatic beating are studied using a quasi-geostrophic two-level model on a beta-plane. This study extends a previous one by Trenberth to include the effects of a baroclinic atmosphere with zonal mean wind shear. With the introduction of vertical shear, the temperature field is no longer locked onto the heating field and can become orthogonal so that even though the wave is thermally forced there may not be any generation or loss of energy by diabatic heating. The presence of both thermal and orographic forcing together violates the conditions of nonacceleration of the zonal mean flow. The induced changes in the zonal mean flow strongly depend upon the relative phase of the thermal and orographic forcing. With a specified diabatic heating field, the eddy fluxes and changes of zonal mean flow are not sensitive to the strength of the mean zonal wind shear. By increasing the wind shear, however, the vertically propagating waves become trapped. The trapped waves accelerate the zonal mean flow through an induced meridional circulation distinct from that of the propagating waves. The characteristics of the forced waves can be explained by the local index of refraction.

Results indicating important differences between the stationary planetary waves in the two hemispheres are 1) the higher total wave number in the Southern Hemisphere, which arises from the shorter meridional scale, so that the waves are trapped, and 2) interaction between thermal and orographic waves in the Northern Hemisphere which is less likely in the Southern Hemisphere.

The limitations of the two-level model with the traditional fixed upper boundary condition, ω = 0 at *p* = 0, in reproducing forced planetary waves is evaluated by testing the sensitivity of results to a modified radiation upper boundary condition. Distinct differences are found when the planetary waves can propagate vertically. Not only is the response of the planetary waves different in phase and magnitude but also the induced acceleration of the zonal mean flow can be completely opposite. Nevertheless, there is reasonable agreement when the planetary waves are trapped vertically so that the upper boundary conditions have minor impact.

## Abstract

A planetary wave model has been developed in which the orographic forcing at the lower boundary arising from the kinematically induced vertical motion is due to the *total* flow impinging on the mountains rather than just the zonal mean basic state component of the flow over the mountains used in previous models. Consequently, the effects of the vertical motions produced by the eddies at the lower boundary are included and are found to be as large, if not larger, than the zonal mean component. The model remains linear mathematically, but all the planetary waves become coupled through the lower boundary condition (LBC) and the model wave equations have to be solved for simultaneously. A contrast is drawn between the wave-coupled solutions and the solutions using the traditional lower boundary formulation in which the planetary waves are decoupled.

The model is symmetric about the equator and uses the linear balance set of equations on the sphere, with full spherical geometry and spherical harmonic function representation, truncated to include four zonal modes and up to mode 15 in the meridional direction. There are 11 levels in the vertical with the highest computational level at 5 mb. The model is linearized about a realistic observed January zonal-mean basic state and forced by the Northern Hemisphere orography and a wintertime calculated diabatic heating. In this paper, diabatic heating effects are not included and only the impact of the new LBC is examined in detail.

The wave-coupled LBC has significant impact on the forced planetary waves and consequently on the Eliassen-Palm fluxes. The most noticeable responses of the planetary waves at the boundary when the wave-coupled LBC is used are in the vicinity of the Himalayas. The boundary eddies set up perturbation easterlies that locally offset the imposed zonal mean westerlies by forcing the flow to go around the mountains. Thus the wave-coupled LBC allows the total flow at the lower boundary to circumvent the Himalayas, unlike the traditional LBC. The net impact is that the kinematic effects of the Himalayas alone form the basis for a quite realistic Siberian high and Aleutian low, and the resulting East Asian trough is close to the observed position. In contrast, the model with the traditional (wave-decoupled) LBC generates an unrealistic and too strong wave pattern. Consequently, it produces the lower-tropospheric heat flux maximum 15 degrees of latitude too far south and greatly overestimates the strength of the momentum flux near the subtropical tropopause, whereas the wave-coupled solution results in more realistic fluxes, both in amplitude and location. The results show that it is necessary to take account of the fact that the earth's orography is large and cannot be considered as a small perturbation, as in the traditional approach to the LBC.

## Abstract

A planetary wave model has been developed in which the orographic forcing at the lower boundary arising from the kinematically induced vertical motion is due to the *total* flow impinging on the mountains rather than just the zonal mean basic state component of the flow over the mountains used in previous models. Consequently, the effects of the vertical motions produced by the eddies at the lower boundary are included and are found to be as large, if not larger, than the zonal mean component. The model remains linear mathematically, but all the planetary waves become coupled through the lower boundary condition (LBC) and the model wave equations have to be solved for simultaneously. A contrast is drawn between the wave-coupled solutions and the solutions using the traditional lower boundary formulation in which the planetary waves are decoupled.

The model is symmetric about the equator and uses the linear balance set of equations on the sphere, with full spherical geometry and spherical harmonic function representation, truncated to include four zonal modes and up to mode 15 in the meridional direction. There are 11 levels in the vertical with the highest computational level at 5 mb. The model is linearized about a realistic observed January zonal-mean basic state and forced by the Northern Hemisphere orography and a wintertime calculated diabatic heating. In this paper, diabatic heating effects are not included and only the impact of the new LBC is examined in detail.

The wave-coupled LBC has significant impact on the forced planetary waves and consequently on the Eliassen-Palm fluxes. The most noticeable responses of the planetary waves at the boundary when the wave-coupled LBC is used are in the vicinity of the Himalayas. The boundary eddies set up perturbation easterlies that locally offset the imposed zonal mean westerlies by forcing the flow to go around the mountains. Thus the wave-coupled LBC allows the total flow at the lower boundary to circumvent the Himalayas, unlike the traditional LBC. The net impact is that the kinematic effects of the Himalayas alone form the basis for a quite realistic Siberian high and Aleutian low, and the resulting East Asian trough is close to the observed position. In contrast, the model with the traditional (wave-decoupled) LBC generates an unrealistic and too strong wave pattern. Consequently, it produces the lower-tropospheric heat flux maximum 15 degrees of latitude too far south and greatly overestimates the strength of the momentum flux near the subtropical tropopause, whereas the wave-coupled solution results in more realistic fluxes, both in amplitude and location. The results show that it is necessary to take account of the fact that the earth's orography is large and cannot be considered as a small perturbation, as in the traditional approach to the LBC.

## Abstract

A more complete and new formulation of the orographic forcing and new thermal forcings are included in a steady state model of the Northern Hemisphere planetary waves. When both forcings are included, the simulation produces excellent results which are compared in detail with observations. In particular, the Siberian high, the tropospheric East Asian trough and subtropical tropospheric East Asian jet stream maxima are well reproduced even though the forcing is primarily extratropical in origin.

The modes uses a lower boundary condition in which the orographic forcing is determined by the effects of the total flow, not just the zonal mean basic state. Consequently, the net orographic forcing changes when thermal forcing is added and the tow solution is not equal to the linear sum of the solutions with orographic and thermal forcings separately. The thermally induced orographic forcing is found to be very significant and, in the troposphere, there is strong interaction between the two forcings with both of roughly equal importance. However, the Iowa-latitude vertically propagating waves am deflected by the subtropical jet and absorbed in the low-latitude easterlies. Thus only the mid-high latitude planetary waves are important in the stratosphere which seems to be dominated by the thermally forced component.

The model is forced with new estimates of diabetic heating from several FGGE analyses. The sensitivity of the results to different heatings and their assumed vertical profile is examined. The amplitude of the lower-troposphere response is very sensitive to the vertical profile but there are much smaller changes at upper levels which are dominated by the remote response. Large differences in the response to the different diabatic heatings are found at high latitudes and over the Pacific Ocean. However, when orographic forcing is also included, these differences diminish indicating a smaller sensitivity to uncertainties in heating, and thus the orographic forcing is acting to constrain the total response. This is in marked contrast to the model results when the traditional lower-boundary condition (in which the waves are decoupled) is used since then the total response is entirely linear.

Wave 1 is too weak in the model and this is most likely mainly due to deficiencies in the thermal forcing. The model eddy fluxes of heat and momentum show excellent agreement with observations in location although the poleward heat flux is somewhat weak. These reveal noticeable improvements over the wave-decoupled model which produces too large a response with the lower-tropospheric heat flux too far south at 35°N in association with a degraded simulation of the Siberian high and East Asian trough, in particular.

## Abstract

A more complete and new formulation of the orographic forcing and new thermal forcings are included in a steady state model of the Northern Hemisphere planetary waves. When both forcings are included, the simulation produces excellent results which are compared in detail with observations. In particular, the Siberian high, the tropospheric East Asian trough and subtropical tropospheric East Asian jet stream maxima are well reproduced even though the forcing is primarily extratropical in origin.

The modes uses a lower boundary condition in which the orographic forcing is determined by the effects of the total flow, not just the zonal mean basic state. Consequently, the net orographic forcing changes when thermal forcing is added and the tow solution is not equal to the linear sum of the solutions with orographic and thermal forcings separately. The thermally induced orographic forcing is found to be very significant and, in the troposphere, there is strong interaction between the two forcings with both of roughly equal importance. However, the Iowa-latitude vertically propagating waves am deflected by the subtropical jet and absorbed in the low-latitude easterlies. Thus only the mid-high latitude planetary waves are important in the stratosphere which seems to be dominated by the thermally forced component.

The model is forced with new estimates of diabetic heating from several FGGE analyses. The sensitivity of the results to different heatings and their assumed vertical profile is examined. The amplitude of the lower-troposphere response is very sensitive to the vertical profile but there are much smaller changes at upper levels which are dominated by the remote response. Large differences in the response to the different diabatic heatings are found at high latitudes and over the Pacific Ocean. However, when orographic forcing is also included, these differences diminish indicating a smaller sensitivity to uncertainties in heating, and thus the orographic forcing is acting to constrain the total response. This is in marked contrast to the model results when the traditional lower-boundary condition (in which the waves are decoupled) is used since then the total response is entirely linear.

Wave 1 is too weak in the model and this is most likely mainly due to deficiencies in the thermal forcing. The model eddy fluxes of heat and momentum show excellent agreement with observations in location although the poleward heat flux is somewhat weak. These reveal noticeable improvements over the wave-decoupled model which produces too large a response with the lower-tropospheric heat flux too far south at 35°N in association with a degraded simulation of the Siberian high and East Asian trough, in particular.

## Abstract

Not available

## Abstract

Not available

## Abstract

An analysis is made of the planetary-scale response of the atmosphere to the kinematic effects of orographic forcing by, in particular, the Tibetan Plateau-Himalayan Mountain complex. Theoretical scaling arguments are used to deduce a critical mountain height *h _{c}
* beyond which the component of flow around will dominate that over the orography. The

*h*is proportional to the meridional scale of the orography and depends on latitude, For north–south scales appropriate for the Himalayas

_{c}*h*∼ 1.5 km which is much less than the actual height of 3706 m when resolved with tour zonal planetary waves, with the implication that the “around” component will dominate.

_{c}A steady-state planetary wave model which has a full kinematic nonlinear lower boundary condition is used to simulate the response to the eastern orography whose height has been multiplied by factors ranging from 0.1 to 2.0. Although the mountain configuration was fixed, the locations of the simulated perturbation highs and lows change substantially in such a way that the total flow increasingly adjusts to go around the high orography as the mountain heights are increased. This effect limits the total vertical motion induced by the orography and thus the amplitudes of the forced planetary waves increase at a rate much less than expected from linear theory. Neglected nonlinear terms in the model are shown to be relatively small in all cases. For shallow mountains the maximum response occurs at the latitude of the mountain (35°N) but both the maximum response and the maximum zonal mean poleward heat flux by the simulated waves are shifted poleward to ∼55°N for orography >1500 m high, consistent with the observed location of the wintertime stationary waves in the Northern Hemisphere. Overall, results support the expectations from scaling considerations and show that linear theory may be reasonably applied for Himalayan orography up to ∼1 km high when resolved on planetary scales, but the “around” component dominates the “over” component when the orography exceeds 1.5 km, as is the case in actuality. The around component should also dominate for the Greenland plateau and Antarctica but the effects are more equivocal for the Rockies which are only ∼1 km high when resolved with planetary scales while *h _{c}
* ∼ 1.5 km.

## Abstract

An analysis is made of the planetary-scale response of the atmosphere to the kinematic effects of orographic forcing by, in particular, the Tibetan Plateau-Himalayan Mountain complex. Theoretical scaling arguments are used to deduce a critical mountain height *h _{c}
* beyond which the component of flow around will dominate that over the orography. The

*h*is proportional to the meridional scale of the orography and depends on latitude, For north–south scales appropriate for the Himalayas

_{c}*h*∼ 1.5 km which is much less than the actual height of 3706 m when resolved with tour zonal planetary waves, with the implication that the “around” component will dominate.

_{c}A steady-state planetary wave model which has a full kinematic nonlinear lower boundary condition is used to simulate the response to the eastern orography whose height has been multiplied by factors ranging from 0.1 to 2.0. Although the mountain configuration was fixed, the locations of the simulated perturbation highs and lows change substantially in such a way that the total flow increasingly adjusts to go around the high orography as the mountain heights are increased. This effect limits the total vertical motion induced by the orography and thus the amplitudes of the forced planetary waves increase at a rate much less than expected from linear theory. Neglected nonlinear terms in the model are shown to be relatively small in all cases. For shallow mountains the maximum response occurs at the latitude of the mountain (35°N) but both the maximum response and the maximum zonal mean poleward heat flux by the simulated waves are shifted poleward to ∼55°N for orography >1500 m high, consistent with the observed location of the wintertime stationary waves in the Northern Hemisphere. Overall, results support the expectations from scaling considerations and show that linear theory may be reasonably applied for Himalayan orography up to ∼1 km high when resolved on planetary scales, but the “around” component dominates the “over” component when the orography exceeds 1.5 km, as is the case in actuality. The around component should also dominate for the Greenland plateau and Antarctica but the effects are more equivocal for the Rockies which are only ∼1 km high when resolved with planetary scales while *h _{c}
* ∼ 1.5 km.

## Abstract

It has been traditional in meteorology to divide the velocity field up into rotational and divergent components, but not the geopotential field. Yet any balance condition, such as the geostrophic relation or linear balance equation, is a diagnostic relation which states that not only can the balanced velocity field be computed from the geopotential field, but also that the geopotential can be derived from the velocity field. If the latter approach is adopted, then the difference between the observed and computed geopotential is the quantity we refer to as the divergent, or in some cases, ageostrophic, geopotential. In fact, for any balance set of equations, it is *essential* to partition the geopotential in such a way in order to derive an equivalent set of momentum equations.

The momentum equations equivalent to the linear balance set of equations are given. The linear balance equation is integrated to give a diagnostic relation between the rotational wind components and the gradient of the rotational geopotential plus an extra term which involves the gradient of the planetary vorticity advection potential (PVAP).

The partitioning of the velocity field into rotational and divergent parts **v** = **v**
_{
r
} + **v**
_{
d
} does not depend on any other field. Given **v**
_{
r
} and the associated streamfunction, we have computed Φ, from the linear balance equation. The difference Φ_{
d
} = Φ − Φ_{
r
} is of order Rossby number times Φ, has global scale dominated by wave 1, and tends to be a maximum near the equator. This partitioning depends upon the balance equation used. The different components of Φ have implications for how the observed Φ should and should not be used in diagnostic studies and provide a new interpretation as to what the ageostrophic component of the flow is. In particular, the ageostrophic wind is partitioned into the divergent wind plus contributions arising from the gradient of the PVAP and the gradient of the divergent geopotential rotated 90°.

The rotational and divergent geopotential fields and the PVAP have been computed from climatological mean January and July conditions. In addition for January, the tendencies due to the Coriolis form associated with the ageostrophic velocity are given and are shown to be related to the acceleration of jets in entrance regions and deceleration in exit regions of in excess of 30 m s^{−1}/day for the Northern Hemisphere. However, while all three terms contributing to the ageostrophic velocity are of roughly equal importance overall, the divergent wind is less important in jet entrance and exit regions and the gradients of the PVAP and Φ_{
d
} terms are dominant. This illustrates the kinematic nature of these acceleration terms and shows the balance that exists in the momentum budget, but provides little insight into the cause of the existence of the mean jets.

## Abstract

It has been traditional in meteorology to divide the velocity field up into rotational and divergent components, but not the geopotential field. Yet any balance condition, such as the geostrophic relation or linear balance equation, is a diagnostic relation which states that not only can the balanced velocity field be computed from the geopotential field, but also that the geopotential can be derived from the velocity field. If the latter approach is adopted, then the difference between the observed and computed geopotential is the quantity we refer to as the divergent, or in some cases, ageostrophic, geopotential. In fact, for any balance set of equations, it is *essential* to partition the geopotential in such a way in order to derive an equivalent set of momentum equations.

The momentum equations equivalent to the linear balance set of equations are given. The linear balance equation is integrated to give a diagnostic relation between the rotational wind components and the gradient of the rotational geopotential plus an extra term which involves the gradient of the planetary vorticity advection potential (PVAP).

The partitioning of the velocity field into rotational and divergent parts **v** = **v**
_{
r
} + **v**
_{
d
} does not depend on any other field. Given **v**
_{
r
} and the associated streamfunction, we have computed Φ, from the linear balance equation. The difference Φ_{
d
} = Φ − Φ_{
r
} is of order Rossby number times Φ, has global scale dominated by wave 1, and tends to be a maximum near the equator. This partitioning depends upon the balance equation used. The different components of Φ have implications for how the observed Φ should and should not be used in diagnostic studies and provide a new interpretation as to what the ageostrophic component of the flow is. In particular, the ageostrophic wind is partitioned into the divergent wind plus contributions arising from the gradient of the PVAP and the gradient of the divergent geopotential rotated 90°.

The rotational and divergent geopotential fields and the PVAP have been computed from climatological mean January and July conditions. In addition for January, the tendencies due to the Coriolis form associated with the ageostrophic velocity are given and are shown to be related to the acceleration of jets in entrance regions and deceleration in exit regions of in excess of 30 m s^{−1}/day for the Northern Hemisphere. However, while all three terms contributing to the ageostrophic velocity are of roughly equal importance overall, the divergent wind is less important in jet entrance and exit regions and the gradients of the PVAP and Φ_{
d
} terms are dominant. This illustrates the kinematic nature of these acceleration terms and shows the balance that exists in the momentum budget, but provides little insight into the cause of the existence of the mean jets.

## Abstract

Climatological and predictability features of a simplified moist general circulation model are described herein. The simplified model is driven by empirical forcings designed to eliminate systematic errors and maintain computational efficiency. Resulting perpetual January climatological features of forced variables such as the tropospheric heights and rotational winds, as well as unforced variables such as the velocity potential, compare well with the observations. Unforced temporal variations in the midlatitude 500-mb geopotential, as well as the tropical circulation's intraseasonal oscillation, are also simulated reasonably well.

Short-range persistence and predictability features of this model replicate geographical persistence and predictability features from simpler models and from numerical weather prediction. The streamfunction is highly persistent in the extratropics, less so in the tropical regions; similarly, the streamfunction is predicted better in midlatitude regions than in the tropics. By contrast, the velocity potential is more persistent in tropical regions but, like the streamfunction, is still predicted best in extratropical regions for short-range forecasts. At longer forecast ranges, the velocity potential is better predicted in the tropics than in midlatitudes. Interestingly, during prominent tropical intraseasonal oscillations, the model consistently demonstrates lower tropical forecasting skill. Predictions are more skillful during stagnant tropical periods.

## Abstract

Climatological and predictability features of a simplified moist general circulation model are described herein. The simplified model is driven by empirical forcings designed to eliminate systematic errors and maintain computational efficiency. Resulting perpetual January climatological features of forced variables such as the tropospheric heights and rotational winds, as well as unforced variables such as the velocity potential, compare well with the observations. Unforced temporal variations in the midlatitude 500-mb geopotential, as well as the tropical circulation's intraseasonal oscillation, are also simulated reasonably well.

Short-range persistence and predictability features of this model replicate geographical persistence and predictability features from simpler models and from numerical weather prediction. The streamfunction is highly persistent in the extratropics, less so in the tropical regions; similarly, the streamfunction is predicted better in midlatitude regions than in the tropics. By contrast, the velocity potential is more persistent in tropical regions but, like the streamfunction, is still predicted best in extratropical regions for short-range forecasts. At longer forecast ranges, the velocity potential is better predicted in the tropics than in midlatitudes. Interestingly, during prominent tropical intraseasonal oscillations, the model consistently demonstrates lower tropical forecasting skill. Predictions are more skillful during stagnant tropical periods.