Life-cycle simulations of shallow frontal waves and the impact of deformation strain

The life-cycle of shallow frontal waves and the impact of deformation strain on their development is investigated using the idealised version of the Met Office non-hydrostatic Unified Model which includes the same physics and dynamics as the operational forecast model. Frontal wave development occurs in two stages; first, a deformation strain is applied to a front and a positive potential vorticity (PV) strip forms, generated by latent heat release in the frontal updraft; second, as the deformation strain is reduced the PV strip breaks up into individual anomalies. The circulations associated with the PV anomalies cause shallow frontal waves to form. The structure of the simulated frontal waves is consistent with the conceptual model of a frontal cyclone. Deeper frontal waves are simulated if the stability of the atmosphere is reduced. Deformation strain rates of different strengths are applied to the PV strip to determine whether a deformation strain threshold exists above which frontal wave development is suppressed. An objective method of frontal wave activity is defined and frontal wave development was found to be suppressed by deformation strain rates $\ge 0.4\times10^{-5}\mbox{s}^{-1}$. This value compares well with observed deformation strain rate thresholds and the analytical solution for the minimum deformation strain rate needed to suppress barotropic frontal wave development. The deformation strain rate threshold is dependent on the strength of the PV strip with strong PV strips able to overcome stronger deformation strain rates (leading to frontal wave development) than weaker PV strips.

Ocean circulation and climate in an idealised Pangean OAGCM

An idealised Pangean configuration is integrated in a coupled ocean atmosphere general circulation model to investigate the form of the ocean circulation and its impacts on the large scale climate system. A vigorous, hemispherically symmetric overturning is found, driven by deep water formation at high latitudes. Whilst the peak mass transport is around 100Sv, a low vertical temperature gradient in the ocean means that the maximum heat transport is only 1.2PW. The geographical change in the coupled model is found to produce a global average warming of 2°C, despite an increase in global surface albedo. This occurs through changes in the atmospheric water vapour and cloud distributions. There is also reduction in the equator-pole temperature gradient, largely attributable to the same causes, avoiding the paradox of low meridional temperature gradients without increased polar heat transport.

On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

An ocean modelling and assimilation guide to using GOCE geoid products

We review the procedures and challenges that must be considered when using geoid data derived from the Gravity and steady-state Ocean Circulation Explorer (GOCE) mission in order to constrain the circulation and water mass representation in an ocean 5 general circulation model. It covers the combination of the geoid information with timemean sea level information derived from satellite altimeter data, to construct a mean dynamic topography (MDT), and considers how this complements the time-varying sea level anomaly, also available from the satellite altimeter. We particularly consider the compatibility of these different fields in their spatial scale content, their temporal rep10 resentation, and in their error covariances. These considerations are very important when the resulting data are to be used to estimate ocean circulation and its corresponding errors. We describe the further steps needed for assimilating the resulting dynamic topography information into an ocean circulation model using three different operational fore15 casting and data assimilation systems. We look at methods used for assimilating altimeter anomaly data in the absence of a suitable geoid, and then discuss different approaches which have been tried for assimilating the additional geoid information. We review the problems that have been encountered and the lessons learned in order the help future users. Finally we present some results from the use of GRACE geoid in20 formation in the operational oceanography community and discuss the future potential gains that may be obtained from a new GOCE geoid.

Solar signal propagation: the role of gravity waves and stratospheric sudden warmings

We use a troposphere‐stratosphere model of intermediate complexity to study the atmospheric response to an idealized solar forcing in the subtropical upper stratosphere during Northern Hemisphere (NH) early winter. We investigate two conditions that could influence poleward and downward propagation of the response: (1) the representation of gravity wave effects and (2) the presence/absence of stratospheric sudden warmings (SSWs). We also investigate how the perturbation influences the timing and frequency of SSWs. Differences in the poleward and downward propagation of the response within the stratosphere are found depending on whether Rayleigh friction (RF) or a gravity wave scheme (GWS) is used to represent gravity wave effects. These differences are likely related to differences in planetary wave activity in the GWS and RF versions, as planetary wave redistribution plays an important role in the downward and poleward propagation of stratospheric signals. There is also remarkable sensitivity in the tropospheric response to the representation of the gravity wave effects. It is most realistic for GWS. Further, tropospheric responses are systematically different dependent on the absence/presence of SSWs. When only years with SSWs are examined, the tropospheric signal appears to have descended from the stratosphere, while the signal in the troposphere appears disconnected from the stratosphere when years with SSWs are excluded. Different troposphere‐stratosphere coupling mechanisms therefore appear to be dominant for years with and without SSWs. The forcing does not affect the timing of SSWs, but does result in a higher occurrence frequency throughout NH winter. Quasi‐Biennial Oscillation effects were not included.

Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmosphere

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l_2/l_1 and of the corresponding dimensionless interface height l_1 H, for selected values of the dimensionless ridge width l_1 a and ratio of wind speeds in the two layers. When l_2/l_1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l_2/l_1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l_1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l_2/l_1 and slightly higher values of l_1 H than the propagating wave drag maxima. As l1a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l_2/l_1. These results are confirmed by numerical simulations for l_2/l_1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models.

Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere

During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.

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.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

The correlation of ULF waves and auroral intensity before, during and after substorm expansion phase onset

We present case studies of the evolution of magnetic wave amplitudes and auroral intensity through the late growth phase and the expansion phase of the substorm cycle. We present strong evidence that substorm-related auroral enhancements are clearly and demonstrably linked to ULF wave amplitudes observed at the same location. In most cases, we find that the highest correlations are observed when the magnetometer time series is advanced in time, indicating that the ULF wave amplitudes start to grow before measured auroral intensities, though interestingly this is not always the case. Further we discuss the four possible reasons that may be able to explain both the timing and the high correlations between these two phenomena, including: a simple coincidence, an artifact of instrumental effects, the response of the ionosphere to magnetic waves and auroral particle precipitation, and finally that ULF waves and auroral particle precipitation are physically linked. We discount coincidence and instrumental effects since in the studies presented here they are unlikely or in general will contribute negligible effects, and we find that the ionospheric response to waves and precipitation can explain some, but not all of the results contained within this paper. Specifically, ionospheric response to substorm waves and auroral precipitation cannot explain that the result that previous studies have shown, that onset of ULF wave activity and the onset of auroral particle precipitation occur at the same time and in the same location. This leaves the possibility that ULF waves and auroral particles are physically linked.

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field. Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ[identical with] (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ [identical with] (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences. The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to K Kβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [double less-than sign] κ for typical eddy length and velocity scales.