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- Author or Editor: Maarten H. P. Ambaum x
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Abstract
A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960–2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality.
The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960–70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude.
As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.
Abstract
A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960–2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality.
The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960–70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude.
As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.
Abstract
A large fraction of papers in the climate literature includes erroneous uses of significance tests. A Bayesian analysis is presented to highlight the meaning of significance tests and why typical misuse occurs. The significance statistic is not a quantitative measure of how confident one can be of the “reality” of a given result. It is concluded that a significance test very rarely provides useful quantitative information.
Abstract
A large fraction of papers in the climate literature includes erroneous uses of significance tests. A Bayesian analysis is presented to highlight the meaning of significance tests and why typical misuse occurs. The significance statistic is not a quantitative measure of how confident one can be of the “reality” of a given result. It is concluded that a significance test very rarely provides useful quantitative information.
Abstract
Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.
Abstract
Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.
Abstract
The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.
Abstract
The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.
Abstract
An isentropic potential vorticity (PV) budget analysis is employed to examine the role of synoptic transients, advection, and nonconservative processes as forcings for the evolution of the low-frequency PV anomalies locally and those associated with the North Atlantic Oscillation (NAO) and the Pacific–North American (PNA) pattern. Specifically, the rate of change of the low-frequency PV is expressed as a sum of tendencies due to divergence of eddy transport, advection by the low-frequency flow (hereafter referred to as advection), and the residual nonconservative processes. The balance between the variances and covariances of these terms is illustrated using a novel vector representation.
It is shown that for most locations, as well as for the PNA pattern, the PV variability is dominantly driven by advection. The eddy forcing explains a small amount of the tendency variance. For the NAO, the role of synoptic eddy fluxes is found to be stronger, explaining on average 15% of the NAO tendency variance. Previous studies have not assessed quantitively how the various forcings balance the tendency. Thus, such studies may have overestimated the role of eddy fluxes for the evolution of teleconnections by examining, for example, composites and regressions that indicate maintenance, rather than evolution driven by the eddies. The authors confirm this contrasting view by showing that during persistent blocking (negative NAO) episodes the eddy driving is relatively stronger.
Abstract
An isentropic potential vorticity (PV) budget analysis is employed to examine the role of synoptic transients, advection, and nonconservative processes as forcings for the evolution of the low-frequency PV anomalies locally and those associated with the North Atlantic Oscillation (NAO) and the Pacific–North American (PNA) pattern. Specifically, the rate of change of the low-frequency PV is expressed as a sum of tendencies due to divergence of eddy transport, advection by the low-frequency flow (hereafter referred to as advection), and the residual nonconservative processes. The balance between the variances and covariances of these terms is illustrated using a novel vector representation.
It is shown that for most locations, as well as for the PNA pattern, the PV variability is dominantly driven by advection. The eddy forcing explains a small amount of the tendency variance. For the NAO, the role of synoptic eddy fluxes is found to be stronger, explaining on average 15% of the NAO tendency variance. Previous studies have not assessed quantitively how the various forcings balance the tendency. Thus, such studies may have overestimated the role of eddy fluxes for the evolution of teleconnections by examining, for example, composites and regressions that indicate maintenance, rather than evolution driven by the eddies. The authors confirm this contrasting view by showing that during persistent blocking (negative NAO) episodes the eddy driving is relatively stronger.
Abstract
The contributions of different time scales to extratropical teleconnections are examined. By applying empirical orthogonal functions and correlation analyses to reanalysis data, it is shown that eddies with periods shorter than 10 days have no linear contribution to teleconnectivity. Instead, synoptic variability follows wavelike patterns along the storm tracks, interpreted as propagating baroclinic disturbances. In agreement with preceding studies, it is found that teleconnections such as the North Atlantic Oscillation (NAO) and the Pacific–North America (PNA) pattern occur only at low frequencies, typically for periods more than 20 days. Low-frequency potential vorticity variability is shown to follow patterns analogous to known teleconnections but with shapes that differ considerably from them. It is concluded that the role, if any, of synoptic eddies in determining and forcing teleconnections needs to be sought in nonlinear interactions with the slower transients. The present results demonstrate that daily variability of teleconnection indices cannot be interpreted in terms of the teleconnection patterns, only the slow part of the variability.
Abstract
The contributions of different time scales to extratropical teleconnections are examined. By applying empirical orthogonal functions and correlation analyses to reanalysis data, it is shown that eddies with periods shorter than 10 days have no linear contribution to teleconnectivity. Instead, synoptic variability follows wavelike patterns along the storm tracks, interpreted as propagating baroclinic disturbances. In agreement with preceding studies, it is found that teleconnections such as the North Atlantic Oscillation (NAO) and the Pacific–North America (PNA) pattern occur only at low frequencies, typically for periods more than 20 days. Low-frequency potential vorticity variability is shown to follow patterns analogous to known teleconnections but with shapes that differ considerably from them. It is concluded that the role, if any, of synoptic eddies in determining and forcing teleconnections needs to be sought in nonlinear interactions with the slower transients. The present results demonstrate that daily variability of teleconnection indices cannot be interpreted in terms of the teleconnection patterns, only the slow part of the variability.
Abstract
Using monthly mean data, daily data, and theoretical arguments, relationships between surface pressure variations associated with the North Atlantic Oscillation (NAO), tropopause height, and the strength of the stratospheric vortex are established. An increase in the NAO index leads to a stronger stratospheric vortex, about 4 days later, as a result of increased equatorward refraction of upward-propagating Rossby waves. At tropopause level the effects of the enhanced NAO index and stratospheric polar vortex are opposite, resulting in a lower tropopause over Iceland and a higher tropopause over the Arctic. The raising of the Arctic tropopause leads to a stretching and spinup of the tropospheric column and is therefore associated with a lowering of the surface pressure near the North Pole. For monthly mean data it is found that a standard deviation increase in the NAO index is associated with a 10% increase in the strength of the stratospheric vortex, as measured by potential vorticity at 500 K. A simple theoretical model predicts that this is associated with about 300-m elevation of the Arctic tropopause, as is observed, and a 5-hPa lowering of the surface pressure at the North Pole. The effects of the spinup of the tropospheric column may project on the NAO pattern so that the stratosphere acts as an integrator of the NAO index.
Abstract
Using monthly mean data, daily data, and theoretical arguments, relationships between surface pressure variations associated with the North Atlantic Oscillation (NAO), tropopause height, and the strength of the stratospheric vortex are established. An increase in the NAO index leads to a stronger stratospheric vortex, about 4 days later, as a result of increased equatorward refraction of upward-propagating Rossby waves. At tropopause level the effects of the enhanced NAO index and stratospheric polar vortex are opposite, resulting in a lower tropopause over Iceland and a higher tropopause over the Arctic. The raising of the Arctic tropopause leads to a stretching and spinup of the tropospheric column and is therefore associated with a lowering of the surface pressure near the North Pole. For monthly mean data it is found that a standard deviation increase in the NAO index is associated with a 10% increase in the strength of the stratospheric vortex, as measured by potential vorticity at 500 K. A simple theoretical model predicts that this is associated with about 300-m elevation of the Arctic tropopause, as is observed, and a 5-hPa lowering of the surface pressure at the North Pole. The effects of the spinup of the tropospheric column may project on the NAO pattern so that the stratosphere acts as an integrator of the NAO index.
Abstract
This article describes a novel algorithmic development extending the contour advective semi-Lagrangian model to include nonconservative effects. The Lagrangian contour representation of finescale tracer fields, such as potential vorticity, allows for conservative, nondiffusive treatment of sharp gradients allowing very high numerical Reynolds numbers. It has been widely employed in accurate geostrophic turbulence and tracer advection simulations. In the present, diabatic version of the model the constraint of conservative dynamics is overcome by including a parallel Eulerian field that absorbs the nonconservative (diabatic) tendencies. The diabatic buildup in this Eulerian field is limited through regular, controlled transfers of this field to the contour representation. This transfer is done with a fast newly developed contouring algorithm. This model has been implemented for several idealized geometries. In this paper a single-layer doubly periodic geometry is used to demonstrate the validity of the model. The present model converges faster than the analogous semi-Lagrangian models at increased resolutions. At the same nominal spatial resolution the new model is 40 times faster than the analogous semi-Lagrangian model. Results of an orographically forced idealized storm track show nontrivial dependency of storm-track statistics on resolution and on the numerical model employed. If this result is more generally applicable, this may have important consequences for future high-resolution climate modeling.
Abstract
This article describes a novel algorithmic development extending the contour advective semi-Lagrangian model to include nonconservative effects. The Lagrangian contour representation of finescale tracer fields, such as potential vorticity, allows for conservative, nondiffusive treatment of sharp gradients allowing very high numerical Reynolds numbers. It has been widely employed in accurate geostrophic turbulence and tracer advection simulations. In the present, diabatic version of the model the constraint of conservative dynamics is overcome by including a parallel Eulerian field that absorbs the nonconservative (diabatic) tendencies. The diabatic buildup in this Eulerian field is limited through regular, controlled transfers of this field to the contour representation. This transfer is done with a fast newly developed contouring algorithm. This model has been implemented for several idealized geometries. In this paper a single-layer doubly periodic geometry is used to demonstrate the validity of the model. The present model converges faster than the analogous semi-Lagrangian models at increased resolutions. At the same nominal spatial resolution the new model is 40 times faster than the analogous semi-Lagrangian model. Results of an orographically forced idealized storm track show nontrivial dependency of storm-track statistics on resolution and on the numerical model employed. If this result is more generally applicable, this may have important consequences for future high-resolution climate modeling.
Abstract
It is shown that a quantitative relation exists between the stratospheric polar cap potential vorticity and the 100-hPa eddy heat flux. A difference in potential vorticity between years is found to be linearly related to the flux difference integrated over time, taking into account a decrease in relaxation time scale with height in the atmosphere.
This relation (the PV–flux relation) is then applied to the 100-hPa flux difference between 2008/09 and the climatology (1989–2008) to obtain a prediction of the polar cap potential vorticity difference between the 2008/09 winter and the climatology. A prediction of the 2008/09 polar cap potential vorticity is obtained by adding this potential vorticity difference to the climatological potential vorticity. The observed polar cap potential vorticity for 2008/09 shows a large and abrupt change in the potential vorticity in midwinter, related to the occurrence of a major sudden stratospheric warming in January 2009; this is also captured by the potential vorticity predicted from the 100-hPa flux and the PV–flux relation.
The results of the mean PV–flux relation show that, on average, about 50% of the interannual variability in the state of the Northern Hemisphere stratosphere is determined by the variations in the 100-hPa heat flux. This explained variance can be as large as 80% for more severe events, as demonstrated for the 2009 major warming.
Abstract
It is shown that a quantitative relation exists between the stratospheric polar cap potential vorticity and the 100-hPa eddy heat flux. A difference in potential vorticity between years is found to be linearly related to the flux difference integrated over time, taking into account a decrease in relaxation time scale with height in the atmosphere.
This relation (the PV–flux relation) is then applied to the 100-hPa flux difference between 2008/09 and the climatology (1989–2008) to obtain a prediction of the polar cap potential vorticity difference between the 2008/09 winter and the climatology. A prediction of the 2008/09 polar cap potential vorticity is obtained by adding this potential vorticity difference to the climatological potential vorticity. The observed polar cap potential vorticity for 2008/09 shows a large and abrupt change in the potential vorticity in midwinter, related to the occurrence of a major sudden stratospheric warming in January 2009; this is also captured by the potential vorticity predicted from the 100-hPa flux and the PV–flux relation.
The results of the mean PV–flux relation show that, on average, about 50% of the interannual variability in the state of the Northern Hemisphere stratosphere is determined by the variations in the 100-hPa heat flux. This explained variance can be as large as 80% for more severe events, as demonstrated for the 2009 major warming.
Abstract
The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.
Abstract
The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.
