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Abstract
A hemispheric solution is obtained for the topographically forced stationary linear perturbations in a two-layer primitive equation model of the atmosphere. Results are discussed for January conditions. Additionally, the linear theory of stationary perturbations in a quasi-geostrophic two-layer model with β-plane approximation is presented which shows that three types of standing waves may be excited by the topography. The structure of these waves and the conditions under which they appear are discussed. Furthermore, the influence of the surface friction and the vertical shear stress on these waves is studied.
This quasi-geostrophic theory is applied to the January case. It turns out that the topography induces so-called ultralong waves without a horizontal node in the frictionless model atmosphere. Cold troughs develop at both levels over the major mountain chains such as the Himalayas and the Rocky Mountains. The standing waves in northern latitudes seem to be forced by the orography in middle and southern latitudes.
The incorporation of surface friction and vertical shear stress into the model causes a strong eastward displacement of the standing waves and weak transports of heat and momentum.
Abstract
A hemispheric solution is obtained for the topographically forced stationary linear perturbations in a two-layer primitive equation model of the atmosphere. Results are discussed for January conditions. Additionally, the linear theory of stationary perturbations in a quasi-geostrophic two-layer model with β-plane approximation is presented which shows that three types of standing waves may be excited by the topography. The structure of these waves and the conditions under which they appear are discussed. Furthermore, the influence of the surface friction and the vertical shear stress on these waves is studied.
This quasi-geostrophic theory is applied to the January case. It turns out that the topography induces so-called ultralong waves without a horizontal node in the frictionless model atmosphere. Cold troughs develop at both levels over the major mountain chains such as the Himalayas and the Rocky Mountains. The standing waves in northern latitudes seem to be forced by the orography in middle and southern latitudes.
The incorporation of surface friction and vertical shear stress into the model causes a strong eastward displacement of the standing waves and weak transports of heat and momentum.
Abstract
A linear, hemispheric, two-level model which is based on the primitive equations is used to study the steady-state response of the atmosphere to sea surface temperature anomalies (SSTA's). First it is shown by comparison with analytical theories that the model's vertical resolution is not too coarse for such a study. Then the model's response to an idealized heat source in middle latitudes is examined, and it is demonstrated that the main features of the response can be explained in terms of a simple quasi-geostrophic theory.
The model is applied to SSTA cases off Newfoundland where statistically significant observations are available. The verification of the model's results against these observations is generally favorable downstream of the SSTA, i.e., the observed low (high) at the surface downstream of a warm (cold) pool is simulated. However, the linear theory predicts a weak surface high upstream of a positive SSTA which has no statistically significant counterpart in the observations. The model is able to reproduce approximately the blocking situation over Europe during the period 1958–60 when the observed SSTA in the Atlantic is prescribed. Realistic pressure and flow patterns in the tropics are obtained for an SSTA in the eastern equatorial Pacific and for an SSTA in the tropical Atlantic. In the first case the influence of SSTA's in the tropics on the mid-latitude circulation turns out to be negligible. This result is not supported by the observations. The SSTA in the Atlantic, however, causes a rather strong response at midlatitudes which is similar to that found in experiments with general circulations models where the same SSTA has been prescribed. The influence of the tropical mean basic wind field and of the grid spacing on the midlatitude response is discussed. Finally, it is shown that the linear model must fail when the SSTA is the result of atmospheric circulation anomalies.
Abstract
A linear, hemispheric, two-level model which is based on the primitive equations is used to study the steady-state response of the atmosphere to sea surface temperature anomalies (SSTA's). First it is shown by comparison with analytical theories that the model's vertical resolution is not too coarse for such a study. Then the model's response to an idealized heat source in middle latitudes is examined, and it is demonstrated that the main features of the response can be explained in terms of a simple quasi-geostrophic theory.
The model is applied to SSTA cases off Newfoundland where statistically significant observations are available. The verification of the model's results against these observations is generally favorable downstream of the SSTA, i.e., the observed low (high) at the surface downstream of a warm (cold) pool is simulated. However, the linear theory predicts a weak surface high upstream of a positive SSTA which has no statistically significant counterpart in the observations. The model is able to reproduce approximately the blocking situation over Europe during the period 1958–60 when the observed SSTA in the Atlantic is prescribed. Realistic pressure and flow patterns in the tropics are obtained for an SSTA in the eastern equatorial Pacific and for an SSTA in the tropical Atlantic. In the first case the influence of SSTA's in the tropics on the mid-latitude circulation turns out to be negligible. This result is not supported by the observations. The SSTA in the Atlantic, however, causes a rather strong response at midlatitudes which is similar to that found in experiments with general circulations models where the same SSTA has been prescribed. The influence of the tropical mean basic wind field and of the grid spacing on the midlatitude response is discussed. Finally, it is shown that the linear model must fail when the SSTA is the result of atmospheric circulation anomalies.
Abstract
An axisymmetric model of the flow over Antarctica is used to study the circulation induced by cooling of the air at the slopes of the continent. It is found that the resulting circulation with southeasterly surface winds and westerlies in the free troposphere agrees qualitatively quite well with the observed circulation. The profiles of wind and temperature obtained above the slope are compared to the results from a simple one-dimensional model of flow over sloping terrain. The agreement is quite good near the surface but not at upper levels. The reasons for this discrepancy are discussed. It is found that the two-dimensional flow does not settle down to a satisfactory steady state. It is argued that the surface easterlies at the slopes of Antarctica provide a source of westerly angular momentum. In the atmosphere, three-dimensional eddies can export momentum to lower latitudes, whereas the flow in the model cannot dispose of the momentum. This points to the limitations of the two-dimensional approach.
Abstract
An axisymmetric model of the flow over Antarctica is used to study the circulation induced by cooling of the air at the slopes of the continent. It is found that the resulting circulation with southeasterly surface winds and westerlies in the free troposphere agrees qualitatively quite well with the observed circulation. The profiles of wind and temperature obtained above the slope are compared to the results from a simple one-dimensional model of flow over sloping terrain. The agreement is quite good near the surface but not at upper levels. The reasons for this discrepancy are discussed. It is found that the two-dimensional flow does not settle down to a satisfactory steady state. It is argued that the surface easterlies at the slopes of Antarctica provide a source of westerly angular momentum. In the atmosphere, three-dimensional eddies can export momentum to lower latitudes, whereas the flow in the model cannot dispose of the momentum. This points to the limitations of the two-dimensional approach.
Abstract
We consider forced quasi-stationary Rossby waves in background flows with realistic variability in time and space. Long-term integrations of the nonlinear barotropic vorticity equation for deviations from background flow are carried out where a forcing term provides sources and sinks of vorticity for the deviations. The background flow is specified according to daily flow observations at 300 hPa. Mean deviation patterns for individual months and for the total period on record (18 months) are computed and compared to the results of more conventional linear and nonlinear computations where a zonal background flow is essentially fixed in time. It is the purpose of this paper to estimate the impact of the variability of the background flow in computations of quasi-stationary Rossby waves. For how long must a forcing act to make the application of linear theories to the response promising? Results are sensitive to the choice of the surface friction parameter C and eddy diffusivity D. For C = 1/(10 days), D = 1 × 105 m2 s−1 there are considerable discrepancies of computed monthly means and the corresponding solutions for fixed background flow. There is good agreement, however, if averages over the complete period of integration are compared. This suggests that conventional linear theories can be applied to climatological stationary waves. The variability of the background flow cannot be neglected, however, if events of only a few months duration are considered.
Abstract
We consider forced quasi-stationary Rossby waves in background flows with realistic variability in time and space. Long-term integrations of the nonlinear barotropic vorticity equation for deviations from background flow are carried out where a forcing term provides sources and sinks of vorticity for the deviations. The background flow is specified according to daily flow observations at 300 hPa. Mean deviation patterns for individual months and for the total period on record (18 months) are computed and compared to the results of more conventional linear and nonlinear computations where a zonal background flow is essentially fixed in time. It is the purpose of this paper to estimate the impact of the variability of the background flow in computations of quasi-stationary Rossby waves. For how long must a forcing act to make the application of linear theories to the response promising? Results are sensitive to the choice of the surface friction parameter C and eddy diffusivity D. For C = 1/(10 days), D = 1 × 105 m2 s−1 there are considerable discrepancies of computed monthly means and the corresponding solutions for fixed background flow. There is good agreement, however, if averages over the complete period of integration are compared. This suggests that conventional linear theories can be applied to climatological stationary waves. The variability of the background flow cannot be neglected, however, if events of only a few months duration are considered.
Abstract
A novel technique is used to test theories of Alpine lee cyclogenesis. An “idealized” reference simulation of a cyclogenetic event is performed with a channel flow model. Recent theories of Speranza et al., Pierrehumbert, and Smith are tested by modifying the reference experiment to meet the main assumptions of the respective theories. None of the proposed theories is found capable of explaining the cyclogenetic process in the reference experiment. Prospects of future theories are discussed.
Abstract
A novel technique is used to test theories of Alpine lee cyclogenesis. An “idealized” reference simulation of a cyclogenetic event is performed with a channel flow model. Recent theories of Speranza et al., Pierrehumbert, and Smith are tested by modifying the reference experiment to meet the main assumptions of the respective theories. None of the proposed theories is found capable of explaining the cyclogenetic process in the reference experiment. Prospects of future theories are discussed.
Abstract
A wave–mean flow model of dry channel flow is used to investigate the processes that determine the height HT and the slope of the extratropical tropopause. Without baroclinic waves, differential radiative heating and a convective adjustment mechanism cooperate to establish a well-defined tropopause and a mean zonal wind with almost constant vertical shear. This reference state is neutrally stratified in the troposphere and, therefore, baroclinically unstable. It is shown that the meridional and vertical heat transports by the unstable linear eigenmodes induce a rise of the tropopause in the northern part of the channel, whereas there is little change of HT in the south. These predictions of the linear theory are verified by aid of the nonlinear model. Changes of HT are restricted to the jet region if a jet is enforced.
Abstract
A wave–mean flow model of dry channel flow is used to investigate the processes that determine the height HT and the slope of the extratropical tropopause. Without baroclinic waves, differential radiative heating and a convective adjustment mechanism cooperate to establish a well-defined tropopause and a mean zonal wind with almost constant vertical shear. This reference state is neutrally stratified in the troposphere and, therefore, baroclinically unstable. It is shown that the meridional and vertical heat transports by the unstable linear eigenmodes induce a rise of the tropopause in the northern part of the channel, whereas there is little change of HT in the south. These predictions of the linear theory are verified by aid of the nonlinear model. Changes of HT are restricted to the jet region if a jet is enforced.
Abstract
It is proposed that the nonlinear interaction of forced waves and slowly moving free waves May lead to the development of blocking highs under favorable conditions. This idea is tested numerically for three types of quasi-geostrophic inviscid channel flow with low spectral resolution in the zonal direction where the forcing is provided by orography. First, barotropic channel flow without wave-mean flow interaction and a constant mean velocity u¯ is considered. The forcing induces standing waves, whereas the phase speed c of the free waves is given by the Rossby formula. A booking high develops when u¯ is chosen to make c≈0 for some of those waves which can interact with the forced standing waves. Blocking does not occur without forcing. Next, the model is extended to include wave-mean flow interaction. Blocking highs with realistic lifetimes develop when u¯ is appropriately chosen initially. The meridional profile of u¯ shows a double let when the block is fully developed. As a third step baroclinicity is admitted (two-level model). Blocking highs develop even under these more general conditions and show a strong preference for certain positions with respect to the orography. It is concluded that the proposed mechanism is capable of producing flow patterns in the channel which show good similarity to observed cases of blocking. However, the model used so far is so simple that it remains open as to whether the blocking mechanism tested in the model may be held responsible for blocking activity in the atmosphere.
Abstract
It is proposed that the nonlinear interaction of forced waves and slowly moving free waves May lead to the development of blocking highs under favorable conditions. This idea is tested numerically for three types of quasi-geostrophic inviscid channel flow with low spectral resolution in the zonal direction where the forcing is provided by orography. First, barotropic channel flow without wave-mean flow interaction and a constant mean velocity u¯ is considered. The forcing induces standing waves, whereas the phase speed c of the free waves is given by the Rossby formula. A booking high develops when u¯ is chosen to make c≈0 for some of those waves which can interact with the forced standing waves. Blocking does not occur without forcing. Next, the model is extended to include wave-mean flow interaction. Blocking highs with realistic lifetimes develop when u¯ is appropriately chosen initially. The meridional profile of u¯ shows a double let when the block is fully developed. As a third step baroclinicity is admitted (two-level model). Blocking highs develop even under these more general conditions and show a strong preference for certain positions with respect to the orography. It is concluded that the proposed mechanism is capable of producing flow patterns in the channel which show good similarity to observed cases of blocking. However, the model used so far is so simple that it remains open as to whether the blocking mechanism tested in the model may be held responsible for blocking activity in the atmosphere.
Abstract
The dynamic climatology of a simple model of barotropic stochastically forced β-plane flow over topography is studied. Except for the forcing, the model is similar to the three-component systems studied by Charney and DeVore (1979) and Hart (1979). In certain regions of parameter space there are two stable equilibria, a high-index flow with strong zonal winds and a low-index flow with a pronounced wave component. A random forcing is added in order to incorporate crudely the impact of the truncated flow modes on those retained in the model.
The Fokker-Planck equation for this system is solved numerically and the steady-state probability distribution of the system is evaluated. It is found that the probability density distribution has maxima at the equilibria but that there also is a finite probability for intermediate states. This situation corresponds to that in the atmosphere where certain types of circulation like a high-index flow are met more frequently than others. It is also found that the predictability of the flow system studied depends strongly on the location of the initial state in phase space.
Abstract
The dynamic climatology of a simple model of barotropic stochastically forced β-plane flow over topography is studied. Except for the forcing, the model is similar to the three-component systems studied by Charney and DeVore (1979) and Hart (1979). In certain regions of parameter space there are two stable equilibria, a high-index flow with strong zonal winds and a low-index flow with a pronounced wave component. A random forcing is added in order to incorporate crudely the impact of the truncated flow modes on those retained in the model.
The Fokker-Planck equation for this system is solved numerically and the steady-state probability distribution of the system is evaluated. It is found that the probability density distribution has maxima at the equilibria but that there also is a finite probability for intermediate states. This situation corresponds to that in the atmosphere where certain types of circulation like a high-index flow are met more frequently than others. It is also found that the predictability of the flow system studied depends strongly on the location of the initial state in phase space.
Abstract
The role of valley winds in the diurnal circulation of large-scale mountain massifs like the Tibetan Plateau is investigated. We consider a circular plateau with radial valleys leading to the surrounding lowlands. A low-resolution grid point model is used to compute the diurnal circulation above the plateau and in the valleys. The circulation is driven by the diurnal variation of the surface temperature.
The model produces valley winds and a diurnal circulation above the plateau in qualitative agreement with observations. The inflow towards the plateau in the valleys is strongest in the afternoon. There is nocturnal outflow. During the day, a low pressure system with a corresponding cyclonic circulation around the massif resides at the plateau and we find high pressure well above it. At night it is the reverse. It is demonstrated that the valley winds contribute significantly to the fluxes of mass and moisture in the plateau's diurnal circulation. Linear calculations for a neutrally stratified atmosphere and narrow valleys show that it is mainly the elevation of the sources and sinks of heat at the plateau which is responsible for the circulation.
Abstract
The role of valley winds in the diurnal circulation of large-scale mountain massifs like the Tibetan Plateau is investigated. We consider a circular plateau with radial valleys leading to the surrounding lowlands. A low-resolution grid point model is used to compute the diurnal circulation above the plateau and in the valleys. The circulation is driven by the diurnal variation of the surface temperature.
The model produces valley winds and a diurnal circulation above the plateau in qualitative agreement with observations. The inflow towards the plateau in the valleys is strongest in the afternoon. There is nocturnal outflow. During the day, a low pressure system with a corresponding cyclonic circulation around the massif resides at the plateau and we find high pressure well above it. At night it is the reverse. It is demonstrated that the valley winds contribute significantly to the fluxes of mass and moisture in the plateau's diurnal circulation. Linear calculations for a neutrally stratified atmosphere and narrow valleys show that it is mainly the elevation of the sources and sinks of heat at the plateau which is responsible for the circulation.
