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- Author or Editor: Klaus-Peter Hoinka x

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## Abstract

The relation of pressure torques and mountain torques is investigated on the basis of observations for the polar caps, two midlatitude and two subtropical belts, and a tropical belt by evaluating the lagged covariances of these torques for various isentropic surfaces. It is only in the polar domains and the northern midlatitude belts that the transfer of angular momentum to and from the earth at the mountains is associated with pressure torques acting in the same sense. The situation is more complicated in all other belts. The covariances decline with increasing potential temperature (height). The role of both torques in the angular momentum budget of a belt is discussed.

## Abstract

The relation of pressure torques and mountain torques is investigated on the basis of observations for the polar caps, two midlatitude and two subtropical belts, and a tropical belt by evaluating the lagged covariances of these torques for various isentropic surfaces. It is only in the polar domains and the northern midlatitude belts that the transfer of angular momentum to and from the earth at the mountains is associated with pressure torques acting in the same sense. The situation is more complicated in all other belts. The covariances decline with increasing potential temperature (height). The role of both torques in the angular momentum budget of a belt is discussed.

## Abstract

The interaction of large-scale wave systems with the Tibetan Plateau (TP) is investigated by regressing pressure, potential temperature, winds, precipitation, and selected fluxes in winter onto the three components *T*
_{o}
*
_{i}
* of this massif’s mountain torque on the basis of the 40-yr ECMWF reanalysis (ERA-40) data. Events with respect to the equatorial “Greenwich” axis of the global angular momentum exhibit by far the largest torques (

*T*

_{o1,}), which essentially represent north–south pressure differences across the TP. The axial torque

*T*

_{o3}peaks when the surface pressure is high at the eastern slope of the TP. The torque

*T*

_{o2}with respect to the 90°E axis is closely related to

*T*

_{o3}with

*T*

_{o2}∼ −

*T*

_{o3}. The maximum (minimum) of

*T*

_{o1}tends to occur about 1 day earlier than the minimum (maximum) of

*T*

_{o2}. All torque events are initiated by equivalent barotropic perturbations moving eastward along the northern rim of the TP. In general, the initial depression, for example, forms a southward-protruding extension at the eastern slope of the TP and a new high grows near Japan. Later, the perturbation near Japan moves eastward in

*T*

_{o2}events but extends northward in

*T*

_{o1}events. These flow developments cannot be explained by theories of topographic instability. The observed vertical motion at the lee slope is at best partly consistent with theories of linear quasigeostrophic wave motion along mountain slopes. These findings lead the authors to test the eventual usefulness of linear theories by fitting the linear terms of a novel statistical equation for the potential temperature

*θ*to the observed changes of

*θ*and the torque to the observations. This test indicates that the evolving regression patterns of

*θ*can be explained by linear terms at least in specific domains. In turn, pressure tendency regressions at a selected level can be calculated on the basis of the linear

*θ*tendencies above that level. The formation of the lee trough appears to be mainly caused by horizontal warm-air advection along the slopes, but changes of the potential temperature above the height of the TP also contribute significantly to the pressure changes in the lee. Cold-air advection aloft strengthens the Japan high. “Turbulent” transports appear to be mainly responsible for the decay of the perturbations but data accuracy problems impede the analysis. In particular, the noisiness of the vertical motion fields affects the skill of the linear calculations.

## Abstract

The interaction of large-scale wave systems with the Tibetan Plateau (TP) is investigated by regressing pressure, potential temperature, winds, precipitation, and selected fluxes in winter onto the three components *T*
_{o}
*
_{i}
* of this massif’s mountain torque on the basis of the 40-yr ECMWF reanalysis (ERA-40) data. Events with respect to the equatorial “Greenwich” axis of the global angular momentum exhibit by far the largest torques (

*T*

_{o1,}), which essentially represent north–south pressure differences across the TP. The axial torque

*T*

_{o3}peaks when the surface pressure is high at the eastern slope of the TP. The torque

*T*

_{o2}with respect to the 90°E axis is closely related to

*T*

_{o3}with

*T*

_{o2}∼ −

*T*

_{o3}. The maximum (minimum) of

*T*

_{o1}tends to occur about 1 day earlier than the minimum (maximum) of

*T*

_{o2}. All torque events are initiated by equivalent barotropic perturbations moving eastward along the northern rim of the TP. In general, the initial depression, for example, forms a southward-protruding extension at the eastern slope of the TP and a new high grows near Japan. Later, the perturbation near Japan moves eastward in

*T*

_{o2}events but extends northward in

*T*

_{o1}events. These flow developments cannot be explained by theories of topographic instability. The observed vertical motion at the lee slope is at best partly consistent with theories of linear quasigeostrophic wave motion along mountain slopes. These findings lead the authors to test the eventual usefulness of linear theories by fitting the linear terms of a novel statistical equation for the potential temperature

*θ*to the observed changes of

*θ*and the torque to the observations. This test indicates that the evolving regression patterns of

*θ*can be explained by linear terms at least in specific domains. In turn, pressure tendency regressions at a selected level can be calculated on the basis of the linear

*θ*tendencies above that level. The formation of the lee trough appears to be mainly caused by horizontal warm-air advection along the slopes, but changes of the potential temperature above the height of the TP also contribute significantly to the pressure changes in the lee. Cold-air advection aloft strengthens the Japan high. “Turbulent” transports appear to be mainly responsible for the decay of the perturbations but data accuracy problems impede the analysis. In particular, the noisiness of the vertical motion fields affects the skill of the linear calculations.

## Abstract

Transfer of axial angular momentum across isentropic surfaces due to adiabatic processes is performed by pressure torques. These torques are evaluated from observations for selected latitude belts and isentropic surfaces, focusing attention on regional contributions. It is found that downward time mean contributions culminate in the storm tracks except above and near major mountain massifs where even upward transfers may be found. Variations of these torques in time are short lived with a decay time of 1–2 days. Height perturbations of isentropic surfaces are presented for torque events. The torque patterns are compared to analyses of the more conventional vertical momentum transports in the *z* system.

## Abstract

Transfer of axial angular momentum across isentropic surfaces due to adiabatic processes is performed by pressure torques. These torques are evaluated from observations for selected latitude belts and isentropic surfaces, focusing attention on regional contributions. It is found that downward time mean contributions culminate in the storm tracks except above and near major mountain massifs where even upward transfers may be found. Variations of these torques in time are short lived with a decay time of 1–2 days. Height perturbations of isentropic surfaces are presented for torque events. The torque patterns are compared to analyses of the more conventional vertical momentum transports in the *z* system.

## Abstract

Given the budget equation for the global axial angular momentum *M,* the related covariance equations are derived. These equations allow one to study the response of the global angular momentum to the forcing by mountain and friction torques in a statistical framework. ECMWF reanalysis (ERA) data are used to evaluate the terms of these equations and to assess their relative importance. Moreover, a new test of the quality of these data is provided this way.

The decay of the autocovariance function of *M* with increasing lag *τ* is slow and almost linear for 20 < *τ* < 280 days. That of the friction torque *T*
_{
f
} is exponential with a decay rate of ∼5 days. The autocovariance of the mountain torque *T*
_{
o
} decays even faster. The torque *T*
_{
g
} due to the gravity wave drag is more persistent than the mountain torque. When inserting the observed covariance functions in the respective equations, it is found that the mountain torque is generally more important than *T*
_{
f
}. The contribution by *T*
_{
g
} is small. The cross covariance of *T*
_{
o
} and *T*
_{
f
} is a major contributor in the covariance equations of these torques. However, both torques act on *M* as if they were almost independent. All covariance equations are satisfied quite well, particularly for the covariance of *T*
_{
g
} and *M.* A regressive model for *M,*
*T*
_{
o
}, and *T*
_{
f
} is presented.

## Abstract

Given the budget equation for the global axial angular momentum *M,* the related covariance equations are derived. These equations allow one to study the response of the global angular momentum to the forcing by mountain and friction torques in a statistical framework. ECMWF reanalysis (ERA) data are used to evaluate the terms of these equations and to assess their relative importance. Moreover, a new test of the quality of these data is provided this way.

The decay of the autocovariance function of *M* with increasing lag *τ* is slow and almost linear for 20 < *τ* < 280 days. That of the friction torque *T*
_{
f
} is exponential with a decay rate of ∼5 days. The autocovariance of the mountain torque *T*
_{
o
} decays even faster. The torque *T*
_{
g
} due to the gravity wave drag is more persistent than the mountain torque. When inserting the observed covariance functions in the respective equations, it is found that the mountain torque is generally more important than *T*
_{
f
}. The contribution by *T*
_{
g
} is small. The cross covariance of *T*
_{
o
} and *T*
_{
f
} is a major contributor in the covariance equations of these torques. However, both torques act on *M* as if they were almost independent. All covariance equations are satisfied quite well, particularly for the covariance of *T*
_{
g
} and *M.* A regressive model for *M,*
*T*
_{
o
}, and *T*
_{
f
} is presented.

## Abstract

The horizontally averaged global angular momentum *μ* at a certain height reacts only to the vertical divergence of the angular momentum flux at least above the crest height of the earth's orography. The flux is tied to the torques at the surface. Data are used to evaluate the flux and the response of *μ* to the torques. It is shown that the accuracy of the data is sufficient for an investigation of this interaction.

It is found that the horizontally averaged angular momentum in the upper troposphere and lower stratosphere tends to be negative before an event of positive friction torque. Downward transports of negative angular momentum from these layers allow the angular momentum to further decrease near the ground, even shortly before the event although the friction torque is positive at that time. The impact of the mountains during this process is demonstrated. The ensuing positive response to the friction torque is felt throughout the troposphere. The final decay of this reaction involves downward transports of *μ* with typical velocities of ∼1–2 km day^{−1}.

The angular momentum in the lower troposphere tends to be negative before an event of positive mountain torque. There is a short burst of rapid upward transport of positive angular momentum during the event itself, which reaches the stratosphere within 1–2 days. A phase of decay follows with slow downward transport of positive angular momentum.

## Abstract

The horizontally averaged global angular momentum *μ* at a certain height reacts only to the vertical divergence of the angular momentum flux at least above the crest height of the earth's orography. The flux is tied to the torques at the surface. Data are used to evaluate the flux and the response of *μ* to the torques. It is shown that the accuracy of the data is sufficient for an investigation of this interaction.

It is found that the horizontally averaged angular momentum in the upper troposphere and lower stratosphere tends to be negative before an event of positive friction torque. Downward transports of negative angular momentum from these layers allow the angular momentum to further decrease near the ground, even shortly before the event although the friction torque is positive at that time. The impact of the mountains during this process is demonstrated. The ensuing positive response to the friction torque is felt throughout the troposphere. The final decay of this reaction involves downward transports of *μ* with typical velocities of ∼1–2 km day^{−1}.

The angular momentum in the lower troposphere tends to be negative before an event of positive mountain torque. There is a short burst of rapid upward transport of positive angular momentum during the event itself, which reaches the stratosphere within 1–2 days. A phase of decay follows with slow downward transport of positive angular momentum.

## Abstract

This paper describes some laboratory experiments with two-dimensional stratified flow over isolated topography, in which a novel configuration simulating a radiating upper boundary condition is employed. Several experimental tests show that the upper boundary is quite effective in absorbing energy. The properties of flow over five different obstacle shapes were obtained for a merge of values of the parameter *Nh*/*U*(*h* is obstacle height, *N* Brunt-Väisälä frequency and *U* towing velocity) from 0 to 4 (approximately). The main results of the study are 1) for 0 ≤ *Nh*/*U* ≤ 0.5 (±0.2), the flow is consistent with linear theory and Longs model; 2) for 0.5 ≲ *Nh*/*U* ≲ 2.0, upstream columnar disturbances are found which apparently propagate arbitrarily far upstream in an inviscid system. 3) overturning and rotors in the lee wave field occur for *Nh*/*U* ∼ 1.5; and 4) for *Nh*/*U* ∼ 2.0, blocked fluid is present upstream, and in some cases is also apparent downstream. This upstream blocking is due to the super-position of the propagating columnar disturbances; it will similarly extend arbitrarily far upstream given sufficient time.

## Abstract

This paper describes some laboratory experiments with two-dimensional stratified flow over isolated topography, in which a novel configuration simulating a radiating upper boundary condition is employed. Several experimental tests show that the upper boundary is quite effective in absorbing energy. The properties of flow over five different obstacle shapes were obtained for a merge of values of the parameter *Nh*/*U*(*h* is obstacle height, *N* Brunt-Väisälä frequency and *U* towing velocity) from 0 to 4 (approximately). The main results of the study are 1) for 0 ≤ *Nh*/*U* ≤ 0.5 (±0.2), the flow is consistent with linear theory and Longs model; 2) for 0.5 ≲ *Nh*/*U* ≲ 2.0, upstream columnar disturbances are found which apparently propagate arbitrarily far upstream in an inviscid system. 3) overturning and rotors in the lee wave field occur for *Nh*/*U* ∼ 1.5; and 4) for *Nh*/*U* ∼ 2.0, blocked fluid is present upstream, and in some cases is also apparent downstream. This upstream blocking is due to the super-position of the propagating columnar disturbances; it will similarly extend arbitrarily far upstream given sufficient time.

## Abstract

Given the distribution of one atmospheric variable, that of nearly all others can be derived in balanced flow. In particular, potential vorticity inversion (PVI) selects potential vorticity (PV) to derive pressure, winds, and potential temperature *θ*. Potential temperature inversion (PTI) starts from available *θ* fields to derive pressure, winds, and PV. While PVI has been applied extensively, PTI has hardly been used as a research tool although the related technical steps are well known and simpler than those needed in PVI. Two idealized examples of PTI and PVI are compared. The 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) datasets are used to determine typical anomalies of PV and *θ* in the North Atlantic storm-track region. Statistical forms of PVI and PTI are applied to these anomalies. The inversions are equivalent but the results of PTI are generally easier to understand than those of PVI. The issues of attribution and piecewise inversion are discussed.

## Abstract

Given the distribution of one atmospheric variable, that of nearly all others can be derived in balanced flow. In particular, potential vorticity inversion (PVI) selects potential vorticity (PV) to derive pressure, winds, and potential temperature *θ*. Potential temperature inversion (PTI) starts from available *θ* fields to derive pressure, winds, and PV. While PVI has been applied extensively, PTI has hardly been used as a research tool although the related technical steps are well known and simpler than those needed in PVI. Two idealized examples of PTI and PVI are compared. The 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) datasets are used to determine typical anomalies of PV and *θ* in the North Atlantic storm-track region. Statistical forms of PVI and PTI are applied to these anomalies. The inversions are equivalent but the results of PTI are generally easier to understand than those of PVI. The issues of attribution and piecewise inversion are discussed.

## Abstract

The axial angular momentum (AAM) budget of zonal atmospheric annuli extending from the surface to a given height and over meridional belts is discussed within the framework of conventional and transformed Eulerian mean (TEM) theory. Conventionally, it is only fluxes of AAM through the boundaries and/or torques at the surface that are able to change the AAM of an annulus. TEM theory introduces new torques in the budget related to the vertically integrated Eliassen–Palm flux divergence and also new AAM fluxes of the residual difference circulation. Some of these torques are displayed for various annuli. In particular, the application of TEM theory generates a large positive torque at tropospheric upper boundaries in the global case. This torque is much larger than the global mountain and friction torques but is cancelled exactly by the new vertical AAM fluxes through the upper boundary. It is concluded that the TEM approach complicates the analysis of AAM budgets but does not provide additional insight. Isentropic pressure torques are believed to be similar to the TEM torques at the upper boundary of an annulus. The isentropic pressure torques are evaluated from data and found to differ in several respects from the TEM torques.

## Abstract

The axial angular momentum (AAM) budget of zonal atmospheric annuli extending from the surface to a given height and over meridional belts is discussed within the framework of conventional and transformed Eulerian mean (TEM) theory. Conventionally, it is only fluxes of AAM through the boundaries and/or torques at the surface that are able to change the AAM of an annulus. TEM theory introduces new torques in the budget related to the vertically integrated Eliassen–Palm flux divergence and also new AAM fluxes of the residual difference circulation. Some of these torques are displayed for various annuli. In particular, the application of TEM theory generates a large positive torque at tropospheric upper boundaries in the global case. This torque is much larger than the global mountain and friction torques but is cancelled exactly by the new vertical AAM fluxes through the upper boundary. It is concluded that the TEM approach complicates the analysis of AAM budgets but does not provide additional insight. Isentropic pressure torques are believed to be similar to the TEM torques at the upper boundary of an annulus. The isentropic pressure torques are evaluated from data and found to differ in several respects from the TEM torques.

## Abstract

The wave forcing of the atmospheric mean flow in isentropic coordinates has been investigated intensively in the past with the divergence of the Eliassen–Palm flux playing a dominating role. These concepts are reviewed briefly and it is pointed out that angular momentum is attractive in this context because the wave driving can be written in the form of a flux divergence. This helps to evaluate the wave forcing in other coordinate systems with a different separation of waves and mean flow. The following coordinates are chosen: (*λ*, *φ*, *z*), (*λ*, *φ*, *θ*), and (*λ*, *θ*, *z*). To be consistent, only one type of zonal averaging should be used. Mass-weighted averaging is applied in the isentropic standard case and simple averaging is applied in the others. The wave driving is presented for all three systems. It has to balance essentially the mean-flow part of the “Coriolis term” in the angular momentum budget in (*φ*, *z*) and (*θ*, *z*) coordinates but not in the (*φ*, *θ*) system where the form drag is a mean-flow term and, therefore, the forcing pattern differs from what has been published so far.

## Abstract

The wave forcing of the atmospheric mean flow in isentropic coordinates has been investigated intensively in the past with the divergence of the Eliassen–Palm flux playing a dominating role. These concepts are reviewed briefly and it is pointed out that angular momentum is attractive in this context because the wave driving can be written in the form of a flux divergence. This helps to evaluate the wave forcing in other coordinate systems with a different separation of waves and mean flow. The following coordinates are chosen: (*λ*, *φ*, *z*), (*λ*, *φ*, *θ*), and (*λ*, *θ*, *z*). To be consistent, only one type of zonal averaging should be used. Mass-weighted averaging is applied in the isentropic standard case and simple averaging is applied in the others. The wave driving is presented for all three systems. It has to balance essentially the mean-flow part of the “Coriolis term” in the angular momentum budget in (*φ*, *z*) and (*θ*, *z*) coordinates but not in the (*φ*, *θ*) system where the form drag is a mean-flow term and, therefore, the forcing pattern differs from what has been published so far.

## Abstract

The concept of downward control proposes a mechanism for the impact of the stratospheric circulation on the troposphere. Momentum forcing at upper-stratospheric levels induces a meridional circulation that eventually reaches the surface. So far, a lack of sufficiently accurate data hindered an observational test of this downward propagation. The concept is extended in this paper by looking at the effect of angular momentum forcing in prescribed regions in the lower stratosphere on the tropospheric circulation. In that case, the European Centre for Medium-Range Weather Forecasts Reanalysis Project (ERA) data can be used to investigate the atmospheric response to forcing in a prescribed domain. It is found that these forcing events are quite short lived and that angular momentum flux convergence in the prescribed domain is highly correlated with convergence outside this forcing area. Typically, these fields of convergence and also divergence extend to the surface in a quasibarotropic manner outside the Tropics. This structure of the forcing is not compatible with the assumptions of the downward control concept. The observed related meridional circulation therefore differs widely from that predicted. In particular, there is no obvious descent of the circulation to the ground. Even so, such forcing events are accompanied by an intensive exchange of angular momentum between stratosphere and troposphere. The confinement of the forcing to the selected forcing domain is reasonably strict in the Tropics. A relatively narrow tongue of angular momentum is growing at the equator underneath the forcing area. Frictional torques play a role in this development. Altogether, the forcing events as selected involve a strong angular momentum exchange between stratosphere and troposphere but are not suited for a test of the downward control concept. Alternatives are discussed.

## Abstract

The concept of downward control proposes a mechanism for the impact of the stratospheric circulation on the troposphere. Momentum forcing at upper-stratospheric levels induces a meridional circulation that eventually reaches the surface. So far, a lack of sufficiently accurate data hindered an observational test of this downward propagation. The concept is extended in this paper by looking at the effect of angular momentum forcing in prescribed regions in the lower stratosphere on the tropospheric circulation. In that case, the European Centre for Medium-Range Weather Forecasts Reanalysis Project (ERA) data can be used to investigate the atmospheric response to forcing in a prescribed domain. It is found that these forcing events are quite short lived and that angular momentum flux convergence in the prescribed domain is highly correlated with convergence outside this forcing area. Typically, these fields of convergence and also divergence extend to the surface in a quasibarotropic manner outside the Tropics. This structure of the forcing is not compatible with the assumptions of the downward control concept. The observed related meridional circulation therefore differs widely from that predicted. In particular, there is no obvious descent of the circulation to the ground. Even so, such forcing events are accompanied by an intensive exchange of angular momentum between stratosphere and troposphere. The confinement of the forcing to the selected forcing domain is reasonably strict in the Tropics. A relatively narrow tongue of angular momentum is growing at the equator underneath the forcing area. Frictional torques play a role in this development. Altogether, the forcing events as selected involve a strong angular momentum exchange between stratosphere and troposphere but are not suited for a test of the downward control concept. Alternatives are discussed.