Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

High-latitude influence of the quasi-biennial oscillation

The interannual variability of the stratospheric winter polar vortex is correlated with the phase of the quasi-biennial oscillation (QBO) of tropical stratospheric winds. This dynamical coupling between high and low latitudes, often referred to as the Holton–Tan effect, has been the subject of numerous observational and modelling studies, yet important questions regarding its mechanism remain unanswered. In particular it remains unclear which vertical levels of the QBO exert the strongest influence on the winter polar vortex, and how QBO–vortex coupling interacts with the effects of other sources of atmospheric interannual variability such as the 11-year solar cycle or the El Nino Southern Oscillation. As stratosphere-resolving general circulation models begin to resolve the QBO and represent its teleconnections with other parts of the climate system, it seems timely to summarize what is currently known about the QBO’s high-latitude influence. In this review article, we offer a synthesis of the modelling and observational analyses of QBO–vortex coupling that have appeared in the literature, and update the observational record.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: III. Quasi-instantaneous convection responses in the Cowley-Lockwood paradigm

Using a numerical implementation of the Cowley and Lockwood (1992) model of flow excitation in the magnetosphere–ionosphere (MI) system, we show that both an expanding (on a _12-min timescale) and a quasiinstantaneous response in ionospheric convection to the onset of magnetopause reconnection can be accommodated by the Cowley–Lockwood conceptual framework. This model has a key feature of time dependence, necessarily considering the history of the coupled MI system. We show that a residual flow, driven by prior magnetopause reconnection, can produce a quasi-instantaneous global ionospheric convection response; perturbations from an equilibrium state may also be present from tail reconnection, which will superpose constructively to give a similar effect. On the other hand, when the MI system is relatively free of pre-existing flow, we can most clearly see the expanding nature of the response. As the open-closed field line boundary will frequently be in motion from such prior reconnection (both at the dayside magnetopause and in the cross-tail current sheet), it is expected that there will usually be some level of combined response to dayside reconnection.

The characteristics of the magnetopause reconnection X-line deduced from low-altitude satellite observations of cusp ions

We present an analysis of a “quasi-steady” cusp ion dispersion signature observed at low altitudes. We reconstruct the field-parallel part of the Cowley-D ion distribution function, injected into the open LLBL in the vicinity of the reconnection X-line. From this we find the field-parallel magnetosheath flow at the X-line was only 20 ± 60 km s−1, placing the reconnection site close to the flow streamline which is perpendicular to the magnetosheath field. Using interplanetary data and assuming the subsolar magnetopause is in pressure balance, we derive a wealth of information about the X-line, including: the density, flow, magnetic field and Alfvén speed of the magnetosheath; the magnetic shear across the X-line; the de-Hoffman Teller speed with which field lines emerge from the X-line; the magnetospheric field; and the ion transmission factor across the magnetopause. The results indicate that some heating takes place near the X-line as the ions cross the magnetopause, and that sheath densities may be reduced in a plasma depletion layer. We also compute the reconnection rate. Despite its quasi-steady appearance on an ion spectrogram, this cusp is found to reveal a large pulse of enhanced reconnection rate.

On the quasi-periodic nature of magnetopause flux transfer events

The recurrence rate of flux transfer events (FTEs) observed near the dayside magnetopause is discussed. A survey of magnetopause observations by the ISEE satellites shows that the distribution of the intervals between FTE signatures has a mode value of 3 min, but is highly skewed, having upper and lower decile values of 1.5 min and 18.5 min, respectively. The mean value is found to be 8 min, consistent with previous surveys of magnetopause data. The recurrence of quasi-periodic events in the dayside auroral ionosphere is frequently used as evidence for an association with magnetopause FTEs, and the distribution of their repetition intervals should be matched to that presented here if such an association is to be confirmed. A survey of 1 year's 15-s data on the interplanetary magnetic field (IMF) suggests that the derived distribution could arise from fluctuations in the IMF Bz component, rather than from a natural oscillation frequency of the magnetosphere-ionosphere system.

Observations at the magnetopause and in the auroral ionosphere of momentum transfer from the solar wind

Recent radar studies of field-perpendicular flows in the auroral ionosphere, in conjunction with observations of the interplanetary medium immediately upstream of the Earth's bow shock, have revealed direct control of dayside convection by the Bz component of the interplanetary magnetic field (IMF). The ionospheric flows begin to respond to both northward and southward turnings of the IMF impinging upon the magnetopause after a delay of only a few minutes in the early afternoon sector, rising to about 15 minutes nearer dawn and dusk. In both the polar cap and the auroral oval, the subsequent rise and decay times are of order 5–10 minutes. We conclude there is very little convection “flywheel” effect in the dayside polar ionosphere and that only newly-opened flux tubes impart significant momentum to the ionosphere, in a relatively narrow region immediately poleward of the cusp. These findings concerning the effects of quasi-steady reconnection have important implications for any ionospheric signatures of transient reconnection which should be considerably shorter-lived than thought hitherto. In order to demonstrate the difficulty of uniquely identifying a Flux Transfer Event (FTE) in ground-based magnetometer data, we present observations of an impulsive signature, identical with that expected for an FTE if data from only one station is studied, following an observed magnetopause compression when the IMF was purely northward. We also report new radar observations of a viscous-like interaction, consistent with an origin on the flanks of the magnetotail and contributing an estimated 15–30kV to the total cross-cap potential during quiet periods.

Field-perpendicular and field-aligned plasma flows observed by EISCAT during a prolonged period of northward IMF

The effect of a prolonged period of strongly northward Interplanetary Magnetic Field (IMF) on the high-latitude F-region is studied using data from the EISCAT Common Programme Zero mode of operation on 11–12 August 1982. The analysis of the raw autocorrelation functions is kept to the directly derived parameters Ne, Te, Ti and velocity, and limits are defined for the errors introduced by assumptions about ion composition and by changes in the transmitted power and system constant. Simple data-cleaning criteria are employed to eliminate problems due to coherent signals and large background noise levels. The observed variations in plasma densities, temperatures and velocities are interpreted in terms of supporting data from ISEE-3 and local riometers and magnetometers. Both field-aligned and field-perpendicular plasma flows at Tromsø showed effects of the northward IMF: convection was slow and irregular and field-aligned flow profiles were characteristic of steady-state polar wind outflow with flux of order 1012 m−2 s−1. This period followed a strongly southward IMF which had triggered a substorm. The substorm gave enhanced convection, with a swing to equatorward flow and large (5 × 1012 m−2 s−1), steady-state field-aligned fluxes, leading to the possibility of O+ escape into the magnetosphere. The apparent influence of the IMF over both field-perpendicular and field-aligned flows is explained in terms of the cross-cap potential difference and the location of the auroral oval.

Origin and impact of initialisation shocks in coupled atmosphere-ocean forecasts

Current methods for initialising coupled atmosphere-ocean forecasts often rely on the use of separate atmosphere and ocean analyses, the combination of which can leave the coupled system imbalanced at the beginning of the forecast, potentially accelerating the development of errors. Using a series of experiments with the European Centre for Medium-range Weather Forecasts coupled system, the magnitude and extent of these so-called initialisation shocks is quantified, and their impact on forecast skill measured. It is found that forecasts initialised by separate ocean and atmospheric analyses do exhibit initialisation shocks in lower atmospheric temperature, when compared to forecasts initialised using a coupled data assimilation method. These shocks result in as much as a doubling of root-mean-square error on the first day of the forecast in some regions, and in increases that are sustained for the duration of the 10-day forecasts performed here. However, the impacts of this choice of initialisation on forecast skill, assessed using independent datasets, were found to be negligible, at least over the limited period studied. Larger initialisation shocks are found to follow a change in either the atmospheric or ocean model component between the analysis and forecast phases: changes in the ocean component can lead to sea surface temperature shocks of more than 0.5K in some equatorial regions during the first day of the forecast. Implications for the development of coupled forecast systems, particularly with respect to coupled data assimilation methods, are discussed.