The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0

The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

Simulation of the diurnal cycle in a climate model and its evaluation using data from Meteosat 7

The representation of the diurnal cycle in the Hadley Centre climate model is evaluated using simulations of the infrared radiances observed by Meteosat 7. In both the window and water vapour channels, the standard version of the model with 19 levels produces a good simulation of the geographical distributions of the mean radiances and of the amplitude of the diurnal cycle. Increasing the vertical resolution to 30 levels leads to further improvements in the mean fields. The timing of the maximum and minimum radiances reveals significant model errors, however, which are sensitive to the frequency with which the radiation scheme is called. In most regions, these errors are consistent with well documented errors in the timing of convective precipitation, which peaks before noon in the model, in contrast to the observed peak in the late afternoon or evening. When the radiation scheme is called every model time step (half an hour), as opposed to every three hours in the standard version, the timing of the minimum radiance is improved for convective regions over central Africa, due to the creation of upper-level layer-cloud by detrainment from the convection scheme, which persists well after the convection itself has dissipated. However, this produces a decoupling between the timing of the diurnal cycles of precipitation and window channel radiance. The possibility is raised that a similar decoupling may occur in reality and the implications of this for the retrieval of the diurnal cycle of precipitation from infrared radiances are discussed.

A note on boundary layer friction in baroclinic cyclones

The interaction between extratropical cyclones and the underlying boundary layer has been a topic of recent discussion in papers by Adamson et al (2006) and Beare (2007). Their results emphasise different mechanisms through which the boundary layer dynamics may modify the growth of a baroclinic cyclone. By using different sea-surface temperature distributions and comparing the low-level winds, the differences are exposed and both of the proposed mechanisms appear to be acting within a single simulation.

Ice supersaturation in the ECMWF integrated forecast system

A parametrization for ice supersaturation is introduced into the ECMWF Integrated Forecast System (IFS), compatible with the cloud scheme that allows partial cloud coverage. It is based on the simple, but often justifiable, diagnostic assumption that the ice nucleation and subsequent depositional growth time-scales are short compared to the model time step, thus supersaturation is only permitted in the clear-sky portion of the grid cell. Results from model integrations using the new scheme are presented, which is demonstrated to increase upper-tropospheric humidity, decrease high-level cloud cover and, to a much lesser extent, cloud ice amounts, all as expected from simple arguments. Evaluation of the relative distribution of supersaturated humidity amounts shows good agreement with the observed climatology derived from in situ aircraft observations. With the new scheme, the global distribution of frequency of occurrence of supersaturated regions compares well with remotely sensed microwave limb sounder (MLS) data, with the most marked errors of underprediction occurring in regions where the model is known to underpredict deep convection. Finally, it is also demonstrated that the new scheme leads to improved predictions of permanent contrail cloud over southern England, which indirectly implies upper-tropospheric humidity fields are better represented for this region.

Evaluation of the use of radiosonde humidity data to predict the occurrence of persistent contrails

Regular visual observations of persistent contrails over Reading, UK, have been used to evaluate radiosonde measurements of temperature and humidity defining cold ice-supersaturated atmospheric regions which are assumed to be a necessary condition for persistent condensation trails (contrails) to form. Results show a good correlation between observations and predictions using data from Larkhill, 63 km from Reading. A statistical analysis of this result and the forecasts using data from four additional UK radiosonde stations are presented. The horizontal extent of supersaturated layers could be inferred from this to be several hundred kilometres. The necessity of bias corrections to radiosonde humidity measurements is discussed and an analysis of measured ice-supersaturated atmospheric layers in the troposphere is presented. It is found that ice supersaturation is more likely to occur in winter than in summer, with frequencies of 17.3% and 9.4%, respectively, which is mostly due to the layers being thicker in winter than in summer. The most probable height for them to occur is about 10 km.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. II: Changing ENSO regimes

Integrations of a fully-coupled climate model with and without flux adjustments in the equatorial oceans are performed under 2×CO2 conditions to explore in more detail the impact of increased greenhouse gas forcing on the monsoon-ENSO system. When flux adjustments are used to correct some systematic model biases, ENSO behaviour in the modelled future climate features distinct irregular and periodic (biennial) regimes. Comparison with the observed record yields some consistency with ENSO modes primarily based on air-sea interaction and those dependent on basinwide ocean wave dynamics. Simple theory is also used to draw analogies between the regimes and irregular (stochastically forced) and self-excited oscillations respectively. Periodic behaviour is also found in the Asian-Australian monsoon system, part of an overall biennial tendency of the model under these conditions related to strong monsoon forcing and increased coupling between the Indian and Pacific Oceans. The tropospheric biennial oscillation (TBO) thus serves as a useful descriptor for the coupled monsoon-ENSO system in this case. The presence of obvious regime changes in the monsoon-ENSO system on interdecadal timescales, when using flux adjustments, suggests there may be greater uncertainty in projections of future climate, although further modelling studies are required to confirm the realism and cause of such changes.