Finite-amplitude Wave Activity Research Articles

Local Finite-Amplitude Wave Activity as a Diagnostic of Anomalous Weather Events

Abstract Finite-amplitude Rossby wave activity (FAWA) proposed by Nakamura and Zhu measures the waviness of quasigeostrophic potential vorticity (PV) contours and the associated modification of the zonal-mean zonal circulation, but it does not distinguish longitudinally localized weather anomalies, such as atmospheric blocking. In this article, FAWA is generalized to local wave activity (LWA) to diagnose eddy–mean flow interaction on the regional scale. LWA quantifies longitude-by-longitude contributions to FAWA following the meridional displacement of PV from the circle of equivalent latitude. The zonal average of LWA recovers FAWA. The budget of LWA is governed by the zonal advection of LWA and the radiation stress of Rossby waves. The utility of the diagnostic is tested with a barotropic vorticity equation on a sphere and meteorological reanalysis data. Compared with the previously derived Eulerian impulse-Casimir wave activity, LWA tends to be less filamentary and emphasizes large isolated vortices involving reversals of meridional gradient of potential vorticity. A pronounced Northern Hemisphere blocking episode in late October 2012 is well captured by a high-amplitude, near-stationary LWA. These analyses reveal that the nonacceleration relation holds approximately over regional scales: the growth of phase-averaged LWA and the deceleration of local zonal wind are highly correlated. However, marked departure from the exact nonacceleration relation is also observed during the analyzed blocking event, suggesting that the contributions from nonadiabatic processes to the blocking development are significant.

Covariation of finite‐amplitude wave activity and the zonal mean flow in the midlatitude troposphere: 1. Theory and application to the Southern Hemisphere summer

AbstractTropospheric eddy‐mean flow interaction is formulated in terms of the vertically integrated budget of finite‐amplitude wave activity (FAWA). At each latitude the dynamics is governed by three coupled equations for the interior and surface FAWA and barotropic zonal mean zonal flow. In midlatitude austral summer, the budget reveals a largely adiabatic, antiphase covariation of FAWA and the mean flow. A marked periodicity is found for FAWA around 20–30 days, but not the mean flow, consistent with the recently discovered baroclinic annular mode. The difference in the spectra of FAWA and the mean flow arises from (i) distinct spectra of low‐level meridional eddy heat flux and the barotropic eddy momentum flux convergence and (ii) a strong thermal damping of surface wave activity: the latter makes the FAWA respond largely to the low‐level meridional eddy heat flux at low frequencies, whereas the zonal mean flow responds to the momentum flux convergence whose spectrum is broader and occupies higher frequencies.

Toward the Dynamical Convergence on the Jet Stream in Aquaplanet AGCMs

Abstract Systematic sensitivity of the jet position and intensity to horizontal model resolution is identified in several aquaplanet AGCMs, with the coarser resolution producing a more equatorward eddy-driven jet and a stronger upper-tropospheric jet intensity. As the resolution of the models increases to 50 km or finer, the jet position and intensity show signs of convergence within each model group. The mechanism for this convergence behavior is investigated using a hybrid Eulerian–Lagrangian finite-amplitude wave activity budget developed for the upper-tropospheric absolute vorticity. The results suggest that the poleward shift of the eddy-driven jet with higher resolution can be attributed to the smaller effective diffusivity of the model in the midlatitudes that allows more wave activity to survive the dissipation and to reach the subtropical critical latitude for wave breaking. The enhanced subtropical wave breaking and associated irreversible vorticity mixing act to maintain a more poleward peak of the vorticity gradient, and thus a more poleward jet. Being overdissipative, the coarse-resolution AGCMs misrepresent the nuanced nonlinear aspect of the midlatitude eddy–mean flow interaction, giving rise to the equatorward bias of the eddy-driven jet. In accordance with the asymptotic behavior of effective diffusivity of Batchelor turbulence in the large Peclet number limit, the upper-tropospheric effective diffusivity of the aquaplanet AGCMs displays signs of convergence in the midlatitude toward a value of approximately 107 m2 s−1 for the ∇2 diffusion. This provides a dynamical underpinning for the convergence of the jet stream observed in these AGCMs at high resolution.

Effective Isentropic Diffusivity of Tropospheric Transport

Abstract Tropospheric transport can be described qualitatively by the slow mean diabatic circulation and rapid isentropic mixing, yet a quantitative understanding of the transport circulation is complicated, as nearly half of the isentropic surfaces in the troposphere frequently intersect the ground. A theoretical framework for the effective isentropic diffusivity of tropospheric transport is presented. Compared with previous isentropic analysis of effective diffusivity, a new diagnostic is introduced to quantify the eddy diffusivity of the near-surface isentropic flow. This diagnostic also links the effective eddy diffusivity directly to a diffusive closure of eddy fluxes through a finite-amplitude wave activity equation. The theory is examined in a dry primitive equation model on the sphere. It is found that the upper troposphere is characterized by a diffusivity minimum at the jet’s center with enhanced mixing at the jet’s flanks and that the lower troposphere is dominated by stronger mixing throughout the baroclinic zone. This structure of isentropic diffusivity is generally consistent with the diffusivity obtained from the geostrophic component of the flow. Furthermore, the isentropic diffusivity agrees broadly with the tracer equivalent length obtained from either a spectral diffusion scheme or a semi-Lagrangian advection scheme, indicating that the effective diffusivity of tropospheric transport is largely dictated by large-scale stirring rather than details of the small-scale diffusion acting on the tracers.

The Role of Subtropical Irreversible PV Mixing in the Zonal Mean Circulation Response to Global Warming–Like Thermal Forcing

Abstract The atmospheric circulation response to the global warming–like tropical upper tropospheric heating is revisited using a dry atmospheric general circulation model (AGCM) in light of new diagnostics based on the concept of finite-amplitude wave activity (FAWA) on equivalent latitude. For a given tropical heating profile, the linear Wentzel–Kramers–Brillouin (WKB) wave refraction analysis sometimes gives a very different and even opposite prediction of the eddy momentum flux response to that of the actual full model simulation, exposing the limitation of the traditional linear approach in understanding the full dynamics of the atmospheric response under global warming. The implementation of the FAWA diagnostics reveals that in response to the upper tropospheric heating, effective diffusivity—a measure of the mixing efficiency—increases and advances upward and poleward in the subtropics and the resultant enhancement and the poleward encroachment of eddy potential vorticity mixing leads to a poleward displaced potential vorticity (PV) gradient peak in the upper troposphere. The anomalous eddy PV flux, in balance with the PV dissipation, gives rise to a poleward shift in the eddy-driven jet and eddy-driven mean meridional circulation. Sensitivity experiments show that these irreversible dissipation processes in the upper troposphere are robust, regardless of the width of the tropical heating.

Delineating the Eddy–Zonal Flow Interaction in the Atmospheric Circulation Response to Climate Forcing: Uniform SST Warming in an Idealized Aquaplanet Model

Abstract The mechanisms of the atmospheric response to climate forcing are analyzed using an example of uniform SST warming in an idealized aquaplanet model. A 200-member ensemble of experiments is conducted with an instantaneous uniform SST warming. The zonal mean circulation changes display a rapid poleward shift in the midlatitude eddy-driven westerlies and the edge of the Hadley cell circulation and a slow equatorward contraction of the circulation in the deep tropics. The shift of the poleward edge of the Hadley cell is predominantly controlled by the eddy momentum flux. It also shifts the eddy-driven westerlies against the surface friction, at a rate much faster than the expectation from the natural variability of the eddy-driven jet (i.e., the e-folding time scale of the annular mode), with much less feedback between the eddies and zonal flow. The transient eddy–zonal flow interactions are delineated using a newly developed finite-amplitude wave activity diagnostic of Nakamura. Applying it to the transient ensemble response to uniform SST warming reveals that the eddy-driven westerlies are shifted poleward by permitting more upward wave propagation in the middle and upper troposphere rather than reducing the lower-tropospheric baroclinicity. The increased upward wave propagation is attributed to a reduction in eddy dissipation of wave activity as a result of a weaker meridional potential vorticity (PV) gradient. The reduction allows more waves to propagate away from the latitudes of baroclinic generation, which, in turn, leads to more poleward momentum flux and a poleward shift of eddy-driven winds and Hadley cell edge.

An exact Lagrangian-mean wave activity for finite-amplitude disturbances to barotropic flow on a sphere

AbstractThe finite-amplitude Rossby wave activity introduced recently by Nakamura and co-workers measures disturbances in terms of the areal displacement of potential vorticity (PV) from zonal symmetry and possesses exact Eliassen–Palm and non-acceleration theorems. This article investigates both theoretically and numerically how this wave activity, denoted ${A}^{\ensuremath{\ast} } $, relates to previously defined quantities such as the generalized Lagrangian-mean (GLM) pseudomomentum density and the impulse-Casimir (IC) wave activity in the context of barotropic flow on a sphere. It is shown that under the barotropic constraint both the new and GLM formalisms derive the non-acceleration theorem from the conservation of Kelvin’s circulation, but the two differ in the way the circulation is partitioned into a mean flow and wave activity/pseudomomentum density. The new wave activity differs from the (negative of) GLM pseudomomentum density by the Stokes correction to angular momentum density, which is not negligible even in the small-amplitude limit. In contrast, ${A}^{\ensuremath{\ast} } $ converges to the IC wave activity and the familiar linear pseudomomentum density in the conservative small-amplitude limit, provided that their reference states are identical. Both the GLM pseudomomentum density and the zonal-mean IC wave activity may be cast in a flux conservation form in equivalent latitude, which may then be related to an exact Eliassen–Palm theorem through a gauge transformation. However, of the three wave activity forms, only ${A}^{\ensuremath{\ast} } $ satisfies an exact non-acceleration theorem for the zonal-mean zonal wind $\bar {u} $. A simple jet forcing experiment is used to examine the quantitative differences among these diagnostics. In this experiment, ${A}^{\ensuremath{\ast} } $ and the IC wave activity behave similarly in the domain average; however, they differ substantially in the local profiles, the former being more closely related to the flow modification. Despite their close conceptual relationship, the GLM pseudomomentum fails to capture the meridional structure of ${A}^{\ensuremath{\ast} } $ because the Stokes correction term dominates the former. This demonstrates various advantages of ${A}^{\ensuremath{\ast} } $ as a diagnostic of eddy–mean flow interaction.

Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part II: Analysis in the Isentropic Coordinate

Abstract The finite-amplitude wave activity diagnostic developed for quasigeostrophic (QG) flows in Part I is extended to the global primitive equation system in the isentropic coordinate. The Rossby wave activity density A is proportional to Kelvin’s circulation around the wavy potential vorticity (PV) contour minus that around the zonal circle that encloses the same isentropic mass. A quasi-conservative, eddy-free reference state flow uREF is constructed from the observed Kelvin’s circulation by zonalizing the PV contours conservatively while enforcing gradient balance. The departure of the observed zonal-mean flow of the atmosphere from the reference state is defined as the net adjustment by the eddies. Then Δu is further partitioned into the direct eddy drag −A and the residual impulse ΔuR consistent with the time-integrated transformed Eulerian mean (TEM) zonal-wind equation. The analyzed climatological-mean wave activity in the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) is similar to that in Part I. The net adjustment Δu is mainly due to the direct eddy drag (Δu ≈ −A) in the winter polar stratosphere and can reach approximately −60 m s−1 in the Northern Hemisphere. In the extratropical troposphere Δu is a small residual (ΔuR ≈ A), yet it clearly reveals a 5–6 m s−1 eddy driving of the Southern Hemisphere jet as well as a 7–8 m s−1 eddy drag in the subtropical upper troposphere of both hemispheres. The local maxima in wave activity in the equatorial upper troposphere and the extratropical lower stratosphere found in Part I are undetected, while negative wave activity is found where the isentropes intersect the ground. As in the QG case, uREF exhibits significantly less transient and interannual variability than , implying a better signal-to-noise ratio as a climate variable.

Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part I: Quasigeostrophic Theory and Analysis

Abstract A diagnostic relationship between finite-amplitude wave activity and the associated adiabatic adjustments to the zonal-mean zonal wind and temperature is developed in the quasigeostrophic (QG) framework and is applied to a 23-yr segment (1979–2001) of the 40-yr ECMWF Re-Analysis (ERA-40) data. Wave activity is defined in terms of an instantaneous areal displacement of QG potential vorticity (PV) from zonal symmetry. Unlike previous forms, the tendency of wave activity equals exactly the negative of the eddy PV flux (Eliassen–Palm flux divergence) in the conservative limit, even at finite amplitude. This allows one to integrate the transformed Eulerian mean (TEM) theory in time and quantify the departure (adiabatic adjustment) of the zonal-mean state from an eddy-free reference state in terms of the observed wave activity. The structure of wave activity identifies synoptic eddies in the extratropics and planetary waves in the high latitudes of winter-to-spring stratosphere. In addition, a thin layer of high wave activity is found at the top of the lowermost stratosphere (∼17 km) in the summer extratropics. The reference state is constructed by “zonalizing” the PV contours conservatively (preserving area) on the isobaric surface and by inverting the resultant PV gradient for the mean flow. The adjustment associated with wave activity depends on the assumed surface boundary condition for the reference state. With a no-slip condition, the observed zonal-mean temperature is on average ∼33 (90) K higher than the reference state in the troposphere (stratosphere) of the Arctic winter, while the zonal-mean zonal wind is ∼30 m s−1 slower in the upper stratosphere. Since the reference state filters out the advective eddy–mean flow interaction, it fluctuates less than the zonal-mean state, potentially improving the signal-to-noise ratio for climate diagnosis.

Finite-Amplitude Wave Activity and Diffusive Flux of Potential Vorticity in Eddy–Mean Flow Interaction

Abstract An exact diagnostic formalism for finite-amplitude eddy–mean flow interaction is developed for barotropic and quasigeostrophic baroclinic flows on the beta plane. Based on the advection–diffusion–reaction equation for potential vorticity (PV), the formalism quantifies both advective and diffusive contributions to the mean flow modification by eddies, of which the latter is the focus of the present article. The present theory adopts a hybrid Eulerian–Lagrangian-mean description of the flow and defines finite-amplitude wave activity in terms of the areal displacement of PV contours from zonal symmetry. Unlike previous formalisms, wave activity is readily calculable from data and the local Eliassen–Palm relation does not involve cubic or higher-order terms in eddy amplitude. This leads to a natural finite-amplitude extension to the local nonacceleration theorem, as well as the global stability theorems, in the inviscid and unforced limit. The formalism incorporates mixing with effective diffusivity of PV, and the diffusive flux of PV is shown to be a sink of wave activity. The relationship between the advective and diffusive fluxes of PV and its implications for parameterization are discussed in the context of wave activity budget. If all momentum associated with wave activity were returned to the zonal-mean flow, a balanced eddy-free flow would ensue. It is shown that this hypothetical flow uREF is unaffected by the advective PV flux and is driven solely by the diffusive PV flux and forcing. For this reason, uREF, rather than the zonal-mean flow, is proposed as a diagnostic for the diffusive mean-flow modification. The formalism is applied to a freely decaying beta-plane turbulence to evaluate the contribution of the diffusive PV flux to the jet formation.