On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Wave-breaking characteristics of midlatitude blocking

In this article, Northern Hemisphere winter midlatitude blocking is analysed through its wave-breaking characteristics. Rossby wave breaking is identified as a key process in blocking occurrence, as it provides the mechanism for the meridional reversal pattern typical of blocking. Two indices are designed to detect the major properties of wave breaking, i.e. the orientation (cyclonic/anticyclonic–direction of breaking or DB index) and the relative contribution of air masses (warm/cold–relative intensity or RI index). The use of the DB index differentiates between the anticyclonic cases over Europe and Asia and the cyclonic events over the oceanic basins. One of the three regions displaying cyclonic type was found over the Atlantic Ocean, the other two being over the Pacific Ocean. The first of these is located over the western side of the Pacific and is dominated by warm air extrusions, whereas the second is placed northward of the exit region of the jet stream, where the meridional θ gradient is much weaker. Two European blocking types have been detected using the RI index, which separates out the cases dominated by warm and cold air masses. The latter cases in particular exhibited a well-structured dipole, with associated strong anomalies in both temperature and precipitation. Copyright © 2011 Royal Meteorological Society

Climate spectrum estimation in the presence of timescale errors.

We introduce an algorithm (called REDFITmc2) for spectrum estimation in the presence of timescale errors. It is based on the Lomb-Scargle periodogram for unevenly spaced time series, in combination with the Welch's Overlapped Segment Averaging procedure, bootstrap bias correction and persistence estimation. The timescale errors are modelled parametrically and included in the simulations for determining (1) the upper levels of the spectrum of the red-noise AR(1) alternative and (2) the uncertainty of the frequency of a spectral peak. Application of REDFITmc2 to ice core and stalagmite records of palaeoclimate allowed a more realistic evaluation of spectral peaks than when ignoring this source of uncertainty. The results support qualitatively the intuition that stronger effects on the spectrum estimate (decreased detectability and increased frequency uncertainty) occur for higher frequencies. The surplus information brought by algorithm REDFITmc2 is that those effects are quantified. Regarding timescale construction, not only the fixpoints, dating errors and the functional form of the age-depth model play a role. Also the joint distribution of all time points (serial correlation, stratigraphic order) determines spectrum estimation.

Is missing orographic gravity wave drag near 60°S the cause of the stratospheric zonal wind biases in chemistry–climate models?

Nearly all chemistry–climate models (CCMs) have a systematic bias of a delayed springtime breakdown of the Southern Hemisphere (SH) stratospheric polar vortex, implying insufficient stratospheric wave drag. In this study the Canadian Middle Atmosphere Model (CMAM) and the CMAM Data Assimilation System (CMAM-DAS) are used to investigate the cause of this bias. Zonal wind analysis increments from CMAMDAS reveal systematic negative values in the stratosphere near 608S in winter and early spring. These are interpreted as indicating a bias in the model physics, namely, missing gravity wave drag (GWD). The negative analysis increments remain at a nearly constant height during winter and descend as the vortex weakens, much like orographic GWD. This region is also where current orographic GWD parameterizations have a gap in wave drag, which is suggested to be unrealistic because of missing effects in those parameterizations. These findings motivate a pair of free-runningCMAMsimulations to assess the impact of extra orographicGWDat 608S. The control simulation exhibits the cold-pole bias and delayed vortex breakdown seen in the CCMs. In the simulation with extra GWD, the cold-pole bias is significantly reduced and the vortex breaks down earlier. Changes in resolved wave drag in the stratosphere also occur in response to the extra GWD, which reduce stratospheric SH polar-cap temperature biases in late spring and early summer. Reducing the dynamical biases, however, results in degraded Antarctic column ozone. This suggests that CCMs that obtain realistic column ozone in the presence of an overly strong and persistent vortex may be doing so through compensating errors.

A robust mechanism for strengthening of the Brewer–Dobson circulation in response to climate change: critical-layer control of subtropical wave breaking

Climate models consistently predict a strengthened Brewer–Dobson circulation in response to greenhouse gas (GHG)-induced climate change. Although the predicted circulation changes are clearly the result of changes in stratospheric wave drag, the mechanism behind the wave-drag changes remains unclear. Here, simulations from a chemistry–climate model are analyzed to show that the changes in resolved wave drag are largely explainable in terms of a simple and robust dynamical mechanism, namely changes in the location of critical layers within the subtropical lower stratosphere, which are known from observations to control the spatial distribution of Rossby wave breaking. In particular, the strengthening of the upper flanks of the subtropical jets that is robustly expected from GHG-induced tropospheric warming pushes the critical layers (and the associated regions of wave drag) upward, allowing more wave activity to penetrate into the subtropical lower stratosphere. Because the subtropics represent the critical region for wave driving of the Brewer–Dobson circulation, the circulation is thereby strengthened. Transient planetary-scale waves and synoptic-scale waves generated by baroclinic instability are both found to play a crucial role in this process. Changes in stationary planetary wave drag are not so important because they largely occur away from subtropical latitudes.

Extending Murty interferometry to the Terahertz part of the spectrum

We discuss some novel technologies that enable the implementation of shearing interferometry at the terahertz part of the spectrum. Possible applications include the direct measurement of lens parameters, the measurement of refractive index of materials that are transparent to terahertz frequencies, determination of homogeneity of samples, measurement of optical distortions and the non-contact evaluation of thermal expansion coefficient of materials buried inside media that are opaque to optical or infrared frequencies but transparent to THz frequencies. The introduction of a shear to a Gaussian free-space propagating terahertz beam in a controlled manner also makes possible a range of new encoding and optical signal processing modalities.

Climatology and Forcing of the Quasi-Biennial Oscillation in the MAECHAM5 Model

The quasi-biennial oscillation (QBO) in the equatorial zonal wind is an outstanding phenomenon of the atmosphere. The QBO is driven by a broad spectrum of waves excited in the tropical troposphere and modulates transport and mixing of chemical compounds in the whole middle atmosphere. Therefore, the simulation of the QBO in general circulation models and chemistry climate models is an important issue. Here, aspects of the climatology and forcing of a spontaneously occurring QBO in a middle-atmosphere model are evaluated, and its influence on the climate and variability of the tropical middle atmosphere is investigated. Westerly and easterly phases are considered separately, and 40-yr ECMWF Re-Analysis (ERA-40) data are used as a reference where appropriate. It is found that the simulated QBO is realistic in many details. Resolved large-scale waves are particularly important for the westerly phase, while parameterized gravity wave drag is more important for the easterly phase. Advective zonal wind tendencies are important for asymmetries between westerly and easterly phases, as found for the suppression of the easterly phase downward propagation. The simulation of the QBO improves the tropical upwelling and the atmospheric tape recorder compared to a model without a QBO. The semiannual oscillation is simulated realistically only if the QBO is represented. In sensitivity tests, it is found that the simulated QBO is strongly sensitive to changes in the gravity wave sources. The sensitivity to the tested range of horizontal resolutions is small. The stratospheric vertical resolution must be better than 1 km to simulate a realistic QBO.

Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization

The Canadian Middle Atmosphere Model is used to examine the sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. Momentum conservation requires that the parameterized gravity wave momentum flux at the top of the model be zero and corresponds to the physical boundary condition of no momentum flux at the top of the atmosphere. Allowing momentum flux to escape the model domain violates momentum conservation. Here the impact of momentum conservation in two sets of model simulations is investigated. In the first set, the simulation of present-day climate for two model-lid height configurations, 0.001 and 10 hPa, which are identical below 10 hPa, is considered. The impact of momentum conservation on the climate with the model lid at 0.001 hPa is minimal, which is expected because of the small amount of gravity wave momentum flux reaching 0.001 hPa. When the lid is lowered to 10 hPa and momentum is conserved, there is only a modest impact on the climate in the Northern Hemisphere; however, the Southern Hemisphere climate is more adversely affected by the deflection of resolved waves near the model lid. When momentum is not conserved in the 10-hPa model the climate is further degraded in both hemispheres, particularly in winter at high latitudes, and the impact of momentum conservation extends all the way to the surface. In the second set of simulations, the impact of momentum conservation and model-lid height on the modeled response to ozone depletion in the Southern Hemisphere is considered, and it is found that the response can display significant sensitivity to both factors. In particular, both the lower-stratospheric polar temperature and surface responses are significantly altered when the lid is lowered, with the effect being most severe when momentum is not conserved. The implications with regard to the current round of Intergovernmental Panel on Climate Change model projections are discussed.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

On the tropospheric response to anomalous stratospheric wave drag and radiative heating

Observational and numerical evidence suggest that variability in the extratropical stratospheric circulation has a demonstrable impact on tropospheric variability on intraseasonal time scales. In this study, it is demonstrated that the amplitude of the observed tropospheric response to vacillations in the stratospheric flow is quantitatively similar to the zonal-mean balanced response to the anomalous wave forcing at stratospheric levels. It is further demonstrated that the persistence of the tropospheric response is consistent with the impact of anomalous diabatic heating in the polar stratosphere as stratospheric temperatures relax to climatology. The results contradict previous studies that suggest that variations in stratospheric wave drag are too weak to account for the attendant changes in the tropospheric flow. However, the results also reveal that stratospheric processes alone cannot account for the observed meridional redistribution of momentum within the troposphere.

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.

The angular momentum constraint on climate sensitivity and downward influence in the middle atmosphere

It is shown that under reasonable assumptions, conservation of angular momentum provides a strong constraint on gravity wave drag feedbacks to radiative perturbations in the middle atmosphere. In the time mean, radiatively induced temperature perturbations above a given altitude z cannot induce changes in zonal mean wind and temperature below z through feedbacks in gravity wave drag alone (assuming an unchanged gravity wave source spectrum). Thus, despite the many uncertainties in the parameterization of gravity wave drag, the role of gravity wave drag in middle-atmosphere climate perturbations may be much more limited than its role in climate itself. This constraint limits the possibilities for downward influence from the mesosphere. In order for a gravity wave drag parameterization to respect the momentum constraint and avoid spurious downward influence, any nonzero parameterized momentum flux at a model lid must be deposited within the model domain, and there must be no zonal mean sponge layer. Examples are provided of how violation of these conditions leads to spurious downward influence. For planetary waves, the momentum constraint does not prohibit downward influence, but it limits the mechanisms by which it can occur: in the time mean, downward influence from a radiative perturbation can only arise through changes in reflection and meridional propagation properties of planetary waves.

Planetary-wave-induced transport in the stratosphere

In the stratosphere, chemical tracers are drawn systematically from the equator to the pole. This observed Brewer–Dobson circulation is driven by wave drag, which in the stratosphere arises mainly from the breaking and dissipation of planetary-scale Rossby waves. While the overall sense of the circulation follows from fundamental physical principles, a quantitative theoretical understanding of the connection between wave drag and Lagrangian transport is limited to linear, small-amplitude waves. However, planetary waves in the stratosphere generally grow to a large amplitude and break in a strongly nonlinear fashion. This paper addresses the connection between stratospheric wave drag and Lagrangian transport in the presence of strong nonlinearity, using a mechanistic three-dimensional primitive equations model together with offline particle advection. Attention is deliberately focused on a weak forcing regime, such that sudden warmings do not occur and a quasi-steady state is reached, in order to examine this question in the cleanest possible context. Wave drag is directly linked to the transformed Eulerian mean (TEM) circulation, which is often used as a surrogate for mean Lagrangian motion. The results show that the correspondence between the TEM and mean Lagrangian velocities is quantitatively excellent in regions of linear, nonbreaking waves (i.e., outside the surf zone), where streamlines are not closed. Within the surf zone, where streamlines are closed and meridional particle displacements are large, the agreement between the vertical components of the two velocity fields is still remarkably good, especially wherever particle paths are coherent so that diabatic dispersion is minimized. However, in this region the meridional mean Lagrangian velocity bears little relation to the meridional TEM velocity, and reflects more the kinematics of mixing within and across the edges of the surf zone. The results from the mechanistic model are compared with those from the Canadian Middle Atmosphere Model to test the robustness of the conclusions.

Extended Canadian middle atmosphere model: zonal-mean climatology and physical parameterizations

This paper describes the energetics and zonal-mean state of the upward extension of the Canadian Middle Atmosphere Model, which extends from the ground to ~210 km. The model includes realistic parameterizations of the major physical processes from the ground up to the lower thermosphere and exhibits a broad spectrum of geophysical variability. The rationale for the extended model is to examine the nature of the physical and dynamical processes in the mesosphere/lower thermosphere (MLT) region without the artificial effects of an imposed sponge layer which can modify the circulation in an unrealistic manner. The zonal-mean distributions of temperature and zonal wind are found to be in reasonable agreement with observations in most parts of the model domain below ~150 km. Analysis of the global-average energy and momentum budgets reveals a balance between solar extreme ultraviolet heating and molecular diffusion and a thermally direct viscous meridional circulation above 130 km, with the viscosity coming from molecular diffusion and ion drag. Below 70 km, radiative equilibrium prevails in the global mean. In the MLT region between ~70 and 120 km, many processes contribute to the global energy budget. At solstice, there is a thermally indirect meridional circulation driven mainly by parameterized nonorographic gravity-wave drag. This circulation provides a net global cooling of up to 25 K d^-1.

Wave-breaking characteristics of Northern Hemisphere winter blocking: a two-dimensional approach

This paper generalises and applies recently developed blocking diagnostics in a two- dimensional latitude-longitude context, which takes into consideration both mid- and high-latitude blocking. These diagnostics identify characteristics of the associated wave-breaking as seen in the potential temperature (θ) on the dynamical tropopause, in particular the cyclonic or anticyclonic Direction of wave-Breaking (DB index), and the Relative Intensity (RI index) of the air masses that contribute to blocking formation. The methodology is extended to a 2-D domain and a cluster technique is deployed to classify mid- and high-latitude blocking according to the wave-breaking characteristics. Mid-latitude blocking is observed over Europe and Asia, where the meridional gradient of θ is generally weak, whereas high-latitude blocking is mainly present over the oceans, to the north of the jet-stream, where the meridional gradient of θ is much stronger. They occur respectively on the equatorward and poleward flank of the jet- stream, where the horizontal shear ∂u/∂y is positive in the first case and negative in the second case. A regional analysis is also conducted. It is found that cold-anticyclonic and cyclonic blocking divert the storm-track respectively to the south and to the north over the East Atlantic and western Europe. Furthermore, warm-cyclonic blocking over the Pacific and cold-anticyclonic blocking over Europe are identified as the most persistent types and are associated with large amplitude anomalies in temperature and precipitation. Finally, the high-latitude, cyclonic events seem to correlate well with low- frequency modes of variability over the Pacific and Atlantic Ocean.