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

2010 ◽  
Vol 67 (9) ◽  
pp. 2701-2716 ◽  
Author(s):  
Noboru Nakamura ◽  
Da Zhu
Keyword(s):  
Potential Vorticity ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Diffusive Flux ◽  
Mean Flow ◽  
Amplitude Wave ◽  
Flow Modification ◽  
Flow Interaction ◽  
Beta Plane ◽  
Finite Amplitude Wave Activity

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.

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

2010 ◽  
Vol 67 (12) ◽  
pp. 3967-3983 ◽  
Author(s):  
Noboru Nakamura ◽  
Abraham Solomon
Keyword(s):  
Zonal Wind ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
The Arctic ◽  
Surface Boundary ◽  
Mean Flow ◽  
Amplitude Wave ◽  
Finite Amplitude Wave Activity ◽  
Mean State

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.

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

2011 ◽  
Vol 68 (11) ◽  
pp. 2783-2799 ◽  
Author(s):  
Noboru Nakamura ◽  
Abraham Solomon
Keyword(s):  
General Circulation ◽  
Equation System ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
Mean Flow ◽  
Negative Wave ◽  
Amplitude Wave ◽  
Upper Troposphere ◽  
Finite Amplitude Wave Activity

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.

scholarly journals Role of Finite-Amplitude Rossby Waves and Nonconservative Processes in Downward Migration of Extratropical Flow Anomalies

2018 ◽  
Vol 75 (5) ◽  
pp. 1385-1401 ◽  
Author(s):  
Sandro W. Lubis ◽  
Clare S. Y. Huang ◽  
Noboru Nakamura ◽  
Nour-Eddine Omrani ◽  
Martin Jucker
Keyword(s):  
Finite Amplitude ◽  
Wave Activity ◽  
Mean Flow ◽  
Amplitude Wave ◽  
Wave Forcing ◽  
The Mean ◽  
Finite Amplitude Wave Activity ◽  
Tropospheric Wind ◽  
Stratospheric Variability

There is growing evidence that stratospheric variability exerts a noticeable imprint on tropospheric weather and climate. Despite clear evidence of these impacts, the principal mechanism whereby stratospheric variability influences tropospheric circulation has remained elusive. Here, the authors introduce a novel approach, based on the theory of finite-amplitude wave activity, for quantifying the role of adiabatic and nonconservative effects on the mean flow that shape the downward coupling from the stratosphere to the troposphere during stratospheric vortex weakening (SVW) events. The advantage of using this theory is that eddy effects (at finite amplitude) on the mean flow can be more readily distinguished from nonconservative effects. The results show (in confirmation of previous work) that the downward migration of extratropical wind anomalies is largely attributable to dynamical adjustments induced by fluctuating finite-amplitude wave forcing. The nonconservative effects, on the other hand, contribute to maintaining the downward signals in the recovery stage within the stratosphere, hinting at the importance of mixing and diabatic heating. The analysis further indicates that variations in stratospheric finite-amplitude wave forcing are too weak to account for the attendant changes and shapes in the tropospheric flow. It is suggested that the indirect effect of tropospheric finite-amplitude wave activity through the residual displacements is needed to amplify and prolong the tropospheric wind responses over several weeks. The results also reveal that the local tropospheric wave activity over the North Pacific and North Atlantic sectors plays a significant role in shaping the high-latitude tropospheric wind response to SVW events.

Local Finite-Amplitude Wave Activity as a Diagnostic for Rossby Wave Packets

2018 ◽  
Vol 146 (12) ◽  
pp. 4099-4114 ◽  
Author(s):  
Paolo Ghinassi ◽  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Rossby Wave ◽  
Model Simulation ◽  
Wave Packets ◽  
Meridional Wind ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Amplitude Wave ◽  
High Impact Weather ◽  
Finite Amplitude Wave Activity ◽  
Isentropic Coordinates

AbstractUpper-tropospheric Rossby wave packets (RWPs) are important dynamical features, because they are often associated with weather systems and sometimes act as precursors to high-impact weather. The present work introduces a novel diagnostic to identify RWPs and to quantify their amplitude. It is based on the local finite-amplitude wave activity (LWA) of Huang and Nakamura, which is generalized to the primitive equations in isentropic coordinates. The new diagnostic is applied to a specific episode containing large-amplitude RWPs and compared with a more traditional diagnostic based on the envelope of the meridional wind. In this case, LWA provides a more coherent picture of the RWPs and their zonal propagation. This difference in performance is demonstrated more explicitly in the framework of an idealized barotropic model simulation, where LWA is able to follow an RWP into its fully nonlinear stage, including cutoff formation and wave breaking, while the envelope diagnostic yields reduced amplitudes in such situations.

scholarly journals How waviness in the circulation changes surface ozone: a viewpoint using local finite-amplitude wave activity

2019 ◽  
Author(s):  
Wenxiu Sun ◽  
Peter Hess ◽  
Gang Chen ◽  
Simone Tilmes
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Surface Ozone ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Amplitude Wave ◽  
Local Flow ◽  
Finite Amplitude Wave Activity ◽  
The U.S

Abstract. Local finite-amplitude wave activity (LWA) measures the waviness of the local flow. In this work we relate the anticyclonic part of LWA, AWA (Anticyclonic Wave Activity), to surface ozone in summertime over the U.S. on interannual to decadal scales. Interannual covariance between AWA diagnosed from the European Centre for Medium-Range Weather Forecast Era-Interim reanalysis and ozone measured at EPA Clean Air Status and Trends Network (CASTNET) stations are analyzed using Maximum Covariance Analysis (MCA). The first two modes in the MCA analysis explain 84 % of the covariance between the AWA and MDA8 (Maximum Daily 8h-Average ozone). Over most of the U.S. we find a significant relationship between ozone at any specific location and AWA over the analysis domain (24° N–53° N, and 130° W–65° W) using a linear regression model. This relationship is diagnosed (i) using reanalysis meteorology and measured ozone from CASTNET, or (ii) using meteorology and ozone simulated by the Community Atmospheric Model version 4 with chemistry (CAM4-chem) within the Community Earth System Model (CESM1). Using the linear regression model we find that meteorological biases in AWA in CAM4-chem, as compared to the reanalysis meteorology, induces ozone changes between −4 and +8 ppb in CAM4-chem. Future changes (circa 2100) in AWA are diagnosed in four different climate change simulations in CAM4-chem, simulations which differ in their initial conditions and in one case in their reactive species emissions. All future simulations have enhanced AWA over the U.S., with the maximum enhancement in the southwest. As diagnosed using the linear regression model the future change in AWA is predicted to cause a corresponding change in ozone ranging up to 6 ppb. The location of this change depends on subtle features of the change in AWA. In many locations this change explains the magnitude and the sign of the overall simulated future ozone change.

scholarly journals Toward the Dynamical Convergence on the Jet Stream in Aquaplanet AGCMs

2015 ◽  
Vol 28 (17) ◽  
pp. 6763-6782 ◽  
Author(s):  
Jian Lu ◽  
Gang Chen ◽  
L. Ruby Leung ◽  
D. Alex Burrows ◽  
Qing Yang ◽  
...  
Keyword(s):  
Wave Breaking ◽  
Effective Diffusivity ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Jet Stream ◽  
Mean Flow ◽  
A Value ◽  
Poleward Shift ◽  
Finite Amplitude Wave Activity ◽  
Large Peclet Number

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.

Covariation of Finite-Amplitude Wave Activity and the Zonal-Mean Flow in the Midlatitude Troposphere. Part II: Eddy Forcing Spectra and the Periodic Behavior in the Southern Hemisphere Summer

2016 ◽  
Vol 73 (12) ◽  
pp. 4731-4752 ◽  
Author(s):  
Lei Wang ◽  
Noboru Nakamura
Keyword(s):  
Heat Flux ◽  
Southern Hemisphere ◽  
Austral Summer ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Amplitude Wave ◽  
Periodic Behavior ◽  
Eddy Heat Flux ◽  
Finite Amplitude Wave Activity ◽  
Mean State

Abstract Previously, in Part I of this study, the authors used latitude-by-latitude budgets of the vertically integrated finite-amplitude wave activity (FAWA) to describe the covariation of the zonal-mean state and eddy amplitude. In the austral summer within 40°–55°S, FAWA exhibits a marked 20–30-day periodicity driven mainly by the low-level meridional eddy heat flux, consistent with the recently identified baroclinic annular mode (BAM). The present article examines the spectra of eddy heat flux that produce the periodic behavior in the Southern Hemisphere storm track. Analysis of the ERA-Interim product reveals that the 20–30-day periodicity in raw FAWA and eddy heat flux is particularly robust during the warm season. A dry GCM is shown to reproduce qualitatively BAM-like eddy heat flux spectra if the zonal-mean state resembles that of the austral summer and if the surface thermal damping is sufficiently strong. The observed eddy heat flux cospectra in summer contain a few dominant frequencies for each of the energy-containing zonal wavenumbers (4–6). The corresponding Fourier modes are heat transporting but neutral, with slightly different meridional structures. As these modes travel at different phase speeds they interfere with each other and produce an amplitude modulation to the eddy heat flux with a periodicity consistent with the BAM. The meridionally confined baroclinic zone in the mean state of the austral summer provides a waveguide that directs the mode propagation and interference along the latitude circle. However, the processes that give rise to the quasi-discrete Fourier modes remain to be identified.

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