Potential role of the quasi-biennial oscillation in the stratosphere-troposphere exchange as found in water vapor in general circulation model experiments

The tropical tropopause is considered to be the main region of upward transport of tropospheric air carrying water vapor and other tracers to the tropical stratosphere. The lower tropical stratosphere is also the region where the quasi-biennial oscillation (QBO) in the zonal wind is observed. The QBO is positioned in the region where the upward transport of tropospheric tracers to the overworld takes place. Hence the QBO can in principle modulate these transports by its secondary meridional circulation. This modulation is investigated in this study by an analysis of general circulation model (GCM) experiments with an assimilated QBO. The experiments show, first, that the temperature signal of the QBO modifies the specific humidity in the air transported upward and, second, that the secondary meridional circulation modulates the velocity of the upward transport. Thus during the eastward phase of the QBO the upward moving air is moister and the upward velocity is less than during the westward phase of the QBO. It was further found that the QBO period is too short to allow an equilibration of the moisture in the QBO region. This causes a QBO signal of the moisture which is considerably smaller than what could be obtained in the limiting case of indefinitely long QBO phases. This also allows a high sensitivity of the mean moisture over a QBO cycle to the El Niño-Southern Oscillation (ENSO) phenomena or major tropical volcanic eruptions. The interplay of sporadic volcanic eruptions, ENSO, and QBO can produce low-frequency variability in the water vapor content of the tropical stratosphere, which renders the isolation of the QBO signal in observational data of water vapor in the equatorial lower stratosphere difficult.

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.

The impacts of climate change on river flow regimes at the global scale

This paper presents an assessment of the impacts of climate change on a series of indicators of hydrological regimes across the global domain, using a global hydrological model run with climate scenarios constructed using pattern-scaling from 21 CMIP3 (Coupled Model Intercomparison Project Phase 3) climate models. Changes are compared with natural variability, with a significant change being defined as greater than the standard deviation of the hydrological indicator in the absence of climate change. Under an SRES (Special Report on Emissions Scenarios) A1b emissions scenario, substantial proportions of the land surface (excluding Greenland and Antarctica) would experience significant changes in hydrological behaviour by 2050; under one climate model scenario (Hadley Centre HadCM3), average annual runoff increases significantly over 47% of the land surface and decreases over 36%; only 17% therefore sees no significant change. There is considerable variability between regions, depending largely on projected changes in precipitation. Uncertainty in projected river flow regimes is dominated by variation in the spatial patterns of climate change between climate models (hydrological model uncertainty is not included). There is, however, a strong degree of consistency in the overall magnitude and direction of change. More than two-thirds of climate models project a significant increase in average annual runoff across almost a quarter of the land surface, and a significant decrease over 14%, with considerably higher degrees of consistency in some regions. Most climate models project increases in runoff in Canada and high-latitude eastern Europe and Siberia, and decreases in runoff in central Europe, around the Mediterranean, the Mashriq, central America and Brasil. There is some evidence that projecte change in runoff at the regional scale is not linear with change in global average temperature change. The effects of uncertainty in the rate of future emissions is relatively small

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.

Statistical–dynamical downscaling of present day and future precipitation regimes in the Aksu river catchment in Central Asia

A statistical–dynamical downscaling (SDD) approach is applied to determine present day and future high-resolution rainfall distributions in the catchment of the river Aksu at the southern slopes of the Tienshan Mountains, Central Asia. First, a circulation weather type (CWT) classification is employed to define typical lower atmospheric flow regimes from ERA-40 reanalysis data. Selected representatives of each CWT are dynamically downscaled with the regional climate model COSMO-CLM 4.8 at a horizontal grid resolution of 0.0625°, using the ERA-40 reanalysis data as boundary conditions. Finally, the simulated representatives are recombined to obtain a high-resolution rainfall climatology for present day climate. The methodology is also applied to ensemble simulations of three different scenarios of the global climate model ECHAM5/MPI-OM1 to derive projections of rainfall changes until 2100. Comparisons of downscaled seasonal and annual rainfall with observational data suggest that the statistical–dynamical approach is appropriate to capture the observed present-day precipitation climatology over the low lands and the first elevations of the Tienshan Mountains. On the other hand, a strong bias is found at higher altitudes, where precipitation is clearly underestimated by SDD. The application of SDD to the ECHAM5/MPI-OM1 ensemble reveals that precipitation changes by the end of the 21st century depend on the season. While for autumn an increase of seasonal precipitation is found for all simulations, a decrease in precipitation is obtained during winter for most parts of the Aksu catchment. The spread between different ECHAM5/MPI-OM1 ensemble members is strongest in spring, where trends of opposite sign are found. The largest changes in rainfall are simulated for the summer season, which also shows the most pronounced spatial heterogeneity. Most ECHAM5/MPI-OM1 realizations indicate a decrease of annual precipitation over large parts of the Tienshan, and an increase restricted to the southeast of the study area. These results provide a good basis for downscaling present-day and future rainfall distributions for hydrological purposes.

On the nature of large-scale mixing in the stratosphere and mesosphere

Studies of tracer transport in the stratosphere have shown that adiabatic quasi-horizontal tracer evolution is controlled primarily by the large-scale low-frequency component of the flow. This behavior is consistent with the concept of chaotic advection, wherein the Eulerian velocity field is spatially coherent and temporally quasi-regular on timescales over which the Lagrangian evolution is chaotic. In this study, winds from a middle atmosphere general circulation model (the Canadian Middle Atmosphere Model) are used to compare and contrast the nature of tracer evolution in the stratosphere and mesosphere. It is found that the concept of chaotic advection is relevant in the stratosphere but not in the mesosphere. The explanation for this behavior is the increased strength of gravity wave activity in the mesosphere as compared with the stratosphere, which leads to shallower kinetic energy spectra on synoptic scales and a much shorter Eulerian correlation time. The shallower kinetic energy spectra imply that tracer evolution in the mesosphere is spectrally local, in contrast with the spectrally nonlocal regime that prevails in the stratosphere. This means that tracer advection calculations in the mesosphere are controlled primarily by the gravity wave spectrum and are intrinsically resolution dependent.

A closer look at chaotic advection in the stratosphere: part II: statistical diagnostics

Statistical diagnostics of mixing and transport are computed for a numerical model of forced shallow-water flow on the sphere and a middle-atmosphere general circulation model. In particular, particle dispersion statistics, transport fluxes, Liapunov exponents (probability density functions and ensemble averages), and tracer concentration statistics are considered. It is shown that the behavior of the diagnostics is in accord with that of kinematic chaotic advection models so long as stochasticity is sufficiently weak. Comparisons with random-strain theory are made.

Chaotic mixing and transport in Rossby-wave critical layers

A simple, dynamically consistent model of mixing and transport in Rossby-wave critical layers is obtained from the well-known Stewartson–Warn–Warn (SWW) solution of Rossby-wave critical-layer theory. The SWW solution is thought to be a useful conceptual model of Rossby-wave breaking in the stratosphere. Chaotic advection in the model is a consequence of the interaction between a stationary and a transient Rossby wave. Mixing and transport are characterized separately with a number of quantitative diagnostics (e.g. mean-square dispersion, lobe dynamics, and spectral moments), and with particular emphasis on the dynamics of the tracer field itself. The parameter dependences of the diagnostics are examined: transport tends to increase monotonically with increasing perturbation amplitude whereas mixing does not. The robustness of the results is investigated by stochastically perturbing the transient-wave phase speed. The two-wave chaotic advection model is contrasted with a stochastic single-wave model. It is shown that the effects of chaotic advection cannot be captured by stochasticity alone.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

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.