Measuring the impact of observations on the predictability of the Kuroshio Extension in a shallow-water model

In this paper sequential importance sampling is used to assess the impact of observations on a ensemble prediction for the decadal path transitions of the Kuroshio Extension (KE). This particle filtering approach gives access to the probability density of the state vector, which allows us to determine the predictive power — an entropy based measure — of the ensemble prediction. The proposed set-up makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a post-processing step, the impact of different sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one-year. The method is applied in an identical-twin experiment for the Kuroshio Extension using a reduced-gravity shallow water model. We investigate the impact of assimilating velocity observations from different locations during the elongated and the contracted meandering state of the KE. Optimal observations location correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the first meander of the KE. During the contracted state of the KE it is located south of Japan, where the Kuroshio separates from the coast.

A global blended tropopause based on ERA data, Part I: Climatology

A new tropopause definition, based on a flow-dependent blending of the traditional thermal tropopause with one based on potential vorticity, has been developed. The benefits of such a blending algorithm are most apparent in regions with synoptic scale fluctuations between tropical and extratropical airmasses. The properties of the local airmass determine the relative contributions to the location of the blended tropopause, rather than this being determined by a specified function of latitude. Global climatologies of tropopause height, temperature, potential temperature and zonal wind, based on European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA) ERA-Interim data, are presented for the period 1989-2007. Features of the seasonal-mean tropopause are discussed on a global scale, alongside a focus on selected monthly climatologies for the two high latitude regions and the tropical belt. The height differences between climatologies based on ERA-Interim and ERA-40 data are also presented. Key spatial and temporal features seen in earlier climatologies, based mainly on the World Meteorological Organization thermal tropopause definition, are reproduced with the new definition. Tropopause temperatures are consistent with those from earlier climatologies, despite some differences in height in the extratropics.

A global blended tropopause based on ERA data, Part II: trends and tropical broadening

A new tropopause definition involving a flow-dependent blending of the traditional thermal tropopause with one based on potential vorticity has been developed and applied to the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalyses (ERA), ERA-40 and ERA-Interim. Global and regional trends in tropopause characteristics for annual and solsticial seasonal means are presented here, with emphasis on significant results for the newer ERA-Interim data for 1989-2007. The global-mean tropopause is rising at a rate of 47 m decade−1 , with pressure falling at 1.0 hPa decade−1 , and temperature falling at 0.18 K decade−1 . The Antarctic tropopause shows decreasing heights,warming,and increasing westerly winds. The Arctic tropopause also shows a warming, but with decreasing westerly winds. In the tropics the trends are small, but at the latitudes of the sub-tropical jets they are almost double the global values. It is found that these changes are mainly concentrated in the eastern hemisphere. Previous and new metrics for the rate of broadening of the tropics, based on both height and wind, give trends in the range 0.9◦ decade−1 to 2.2◦ decade−1 . For ERA-40 the global height and pressure trends for the period 1979-2001 are similar: 39 m decade−1 and -0.8 hPa decade−1. These values are smaller than those found from the thermal tropopause definition with this data set, as was used in most previous studies.

Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

The nature of Arctic polar vortices in chemistry-climate models

The structure of the Arctic stratospheric polar vortex in three chemistry–climate models (CCMs) taken from the CCMVal-2 intercomparison is examined using zonal mean and geometric-based methods. The geometric methods are employed by taking 2D moments of potential vorticity fields that are representative of the polar vortices in each of the models. This allows the vortex area, centroid location and ellipticity to be determined, as well as a measure of vortex filamentation. The first part of the study uses these diagnostics to examine how well the mean state, variability and extreme variability of the polar vortices are represented in CCMs compared to ERA-40 reanalysis data, and in particular for the UMUKCA-METO, NIWA-SOCOL and CCSR/NIES models. The second part of the study assesses how the vortices are predicted to change in terms of the frequency of sudden stratospheric warmings and their general structure over the period 1960–2100. In general, it is found that the vortices are climatologically too far poleward in the CCMs and produce too few large-scale filamentation events. Only a small increase is observed in the frequency of sudden stratospheric warming events from the mean of the CCMVal-2 models, but the distribution of extreme variability throughout the winter period is shown to change towards the end of the twentyfirst century.

Boundary-layer friction in midlatitude cyclone

Results from an idealized three-dimensional baroclinic life-cycle model are interpreted in a potential vorticity (PV) framework to identify the physical mechanisms by which frictional processes acting in the atmospheric boundary layer modify and reduce the baroclinic development of a midlatitude storm. Considering a life cycle where the only non-conservative process acting is boundary-layer friction, the rate of change of depth-averaged PV within the boundary layer is governed by frictional generation of PV and the flux of PV into the free troposphere. Frictional generation of PV has two contributions: Ekman generation, which is directly analogous to the well-known Ekman-pumping mechanism for barotropic vortices, and baroclinic generation, which depends on the turning of the wind in the boundary layer and low-level horizontal temperature gradients. It is usually assumed, at least implicitly, that an Ekman process of negative PV generation is the mechanism whereby friction reduces the strength and growth rates of baroclinic systems. Although there is evidence for this mechanism, it is shown that baroclinic generation of PV dominates, producing positive PV anomalies downstream of the low centre, close to developing warm and cold fronts. These PV anomalies are advected by the large-scale warm conveyor belt flow upwards and polewards, fluxed into the troposphere near the warm front, and then advected westwards relative to the system. The result is a thin band of positive PV in the lower troposphere above the surface low centre. This PV is shown to be associated with a positive static stability anomaly, which Rossby edge wave theory suggests reduces the strength of the coupling between the upper- and lower-level PV anomalies, thereby reducing the rate of baroclinic development. This mechanism, which is a result of the baroclinic dynamics in the frontal regions, is in marked contrast with simple barotropic spin-down ideas. Finally we note the implications of these frictionally generated PV anomalies for cyclone forecasting.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Tropical-extratropical interactions over Southern Africa: three cases of heavy summer season rainfall

The synoptic evolution of three tropical–extratropical (TE) interactions, each responsible for extreme rainfall events over southern Africa, is discussed in detail. Along with the consideration of previously studied events, common features of these heavy rainfall producing tropical temperate troughs (TTTs) over southern Africa are discussed. It is found that 2 days prior to an event, northeasterly moisture transports across Botswana, set up by the Angola low, are diverted farther south into the semiarid region of subtropical southern Africa. The TTTs reach full maturity as a TE cloud band, rooted in the central subcontinent, which is triggered by upper-level divergence along the leading edge of an upper-tropospheric westerly wave trough. Convection and rainfall within the cloud band is supported by poleward moisture transports with subtropical air rising as it leaves the continent and joins the midlatitude westerly flow. It is shown that these systems fit within a theoretical framework describing similar TE interactions found globally. Uplift forcing for the extreme rainfall of each event is investigated. Unsurprisingly, quasigeostrophic uplift is found to dominate in the midlatitudes with convective processes strongest in the subtropics. Rainfall in the semiarid interior of South Africa appears to be a result of quasigeostrophically triggered convection. Investigation of TTT formation in the context of planetary waves shows that early development is sometimes associated with previous anticyclonic wave breaking south of the subcontinent, with full maturity of TTTs occurring as a potential vorticity trough approaches the continent from the west. Sensitivity to upstream wave perturbations and effects on anticyclonic wave breaking in the South Indian Ocean are also observed.

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.

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

A unified theory of balance in the extratropics

Many physical systems exhibit dynamics with vastly different time scales. Often the different motions interact only weakly and the slow dynamics is naturally constrained to a subspace of phase space, in the vicinity of a slow manifold. In geophysical fluid dynamics this reduction in phase space is called balance. Classically, balance is understood by way of the Rossby number R or the Froude number F; either R ≪ 1 or F ≪ 1. We examined the shallow-water equations and Boussinesq equations on an f -plane and determined a dimensionless parameter _, small values of which imply a time-scale separation. In terms of R and F, ∈= RF/√(R^2+R^2 ) We then developed a unified theory of (extratropical) balance based on _ that includes all cases of small R and/or small F. The leading-order systems are ensured to be Hamiltonian and turn out to be governed by the quasi-geostrophic potential-vorticity equation. However, the height field is not necessarily in geostrophic balance, so the leading-order dynamics are more general than in quasi-geostrophy. Thus the quasi-geostrophic potential-vorticity equation (as distinct from the quasi-geostrophic dynamics) is valid more generally than its traditional derivation would suggest. In the case of the Boussinesq equations, we have found that balanced dynamics generally implies hydrostatic balance without any assumption on the aspect ratio; only when the Froude number is not small and it is the Rossby number that guarantees a timescale separation must we impose the requirement of a small aspect ratio to ensure hydrostatic balance.

Arctic ozone depletion in 2002–2003 measured by ASUR and comparison with POAM observations

We present ozone loss estimated from airborne measurements taken during January–February and March in the Arctic winter 2002/2003. The first half of the winter was characterized by unusually cold temperatures and the second half by a major stratospheric sudden warming around 15–18 January 2003. The potential vorticity maps show a vortex split in the lower stratosphere during the major warming (MW) in late January and during the minor warming in mid-February due to wave 1 amplification. However, the warming can be termed as a vortex displacement event as there was no vortex split during the MW period at 10 hPa. Very low temperatures, large areas of polar stratospheric clouds (PSCs), and high chlorine activation triggered significant ozone loss in the early winter, as the vortex moved to the midlatitude regions. The ozone depletion derived from the ASUR measurements sampled inside the vortex, in conjunction with the Mimosa-Chim model tracer, shows a maximum of 1.3 ± 0.2 ppmv at 450–500 K by late March. The partial column loss derived from the ASUR ozone profiles reaches up to 61 ± 4 DU in 400–550 K in the same period. The evolution of ozone and ozone loss assessed from the ASUR measurements is in very good agreement with POAM observations. The reduction in ozone estimated from the POAM measurements shows a similar maximum of 1.3 ± 0.2 ppmv at 400–500 K or 63 ± 4 DU in 400–550 K in late March. Our study reveals that the Arctic winter 2002/2003 was unique as it had three minor warmings and a MW, yet showed large loss in ozone. No such feature was observed in any other Arctic winter in the 1989–2010 period. In addition, an unusually large ozone loss in December, around 0.5 ± 0.2 ppmv at 450–500 K or 12 ± 1 DU in 400–550 K, was estimated for the first time in the Arctic. A careful and detailed diagnosis with all available published results for this winter exhibits an average ozone loss of 1.5 ± 0.3 ppmv at 450–500 K or 65 ± 5 DU in 400–550 K by the end of March, which exactly matches the ozone depletion derived from the ASUR, POAM and model data. The early ozone loss together with considerable loss afterwards put the warm Arctic winter 2002/2003 amongst the moderately cold winters in terms of the significance of the ozone loss.

Forecast, measurement, and modeling of an unprecedented polar ozone filament event over Mauna Loa Observatory, Hawaii

In mid-March 2005 the northern lower stratospheric polar vortex experienced a severe stretching episode, bringing a large polar filament far south of Alaska toward Hawaii. This meridional intrusion of rare extent, coinciding with the polar vortex final warming and breakdown, was followed by a zonal stretching in the wake of the easterly propagating subtropical main flow. This caused polar air to remain over Hawaii for several days before diluting into the subtropics. After being successfully forecasted to pass over Hawaii by the high-resolution potential vorticity advection model Modèle Isentrope du transport Méso-échelle de l'Ozone Stratosphérique par Advection (MIMOSA), the filament was observed on isentropic surfaces between 415 K and 455 K (17–20 km) by the Jet Propulsion Laboratory stratospheric ozone lidar measurements at Mauna Loa Observatory, Hawaii, between 16 and 19 March 2005. It was materialized as a thin layer of enhanced ozone peaking at 1.6 ppmv in a region where the climatological values usually average 1.0 ppmv. These values were compared to those obtained by the three-dimensional Chemistry-Transport Model MIMOSA-CHIM. Agreement between lidar and model was excellent, particularly in the similar appearance of the ozone peak near 435 K (18.5 km) on 16 March, and the persistence of this layer at higher isentropic levels for the following three days. Passive ozone, also modeled by MIMOSA-CHIM, was at about 3–4 ppmv inside the filament while above Hawaii. A detailed history of the modeled chemistry inside the filament suggests that the air mass was still polar ozone–depleted when passing over Hawaii. The filament quickly separated from the main vortex after its Hawaiian overpass. It never reconnected and, in less than 10 days, dispersed entirely in the subtropics

The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

Rossby number expansions, slaving principles, and balance dynamics

We consider the problem of constructing balance dynamics for rapidly rotating fluid systems. It is argued that the conventional Rossby number expansion—namely expanding all variables in a series in Rossby number—is secular for all but the simplest flows. In particular, the higher-order terms in the expansion grow exponentially on average, and for moderate values of the Rossby number the expansion is, at best, useful only for times of the order of the doubling times of the instabilities of the underlying quasi-geostrophic dynamics. Similar arguments apply in a wide class of problems involving a small parameter and sufficiently complex zeroth-order dynamics. A modified procedure is proposed which involves expanding only the fast modes of the system; this is equivalent to an asymptotic approximation of the slaving relation that relates the fast modes to the slow modes. The procedure is systematic and thus capable, at least in principle, of being carried to any order—unlike procedures based on truncations. We apply the procedure to construct higher-order balance approximations of the shallow-water equations. At the lowest order quasi-geostrophy emerges. At the next order the system incorporates gradient-wind balance, although the balance relations themselves involve only linear inversions and hence are easily applied. There is a large class of reduced systems associated with various choices for the slow variables, but the simplest ones appear to be those based on potential vorticity.