Multiscale Window Transform

2007 ◽  
Vol 6 (2) ◽  
pp. 437-467 ◽  
Author(s):  
X. San Liang ◽  
Donald G. M. Anderson
Keyword(s):  
Multiscale Window Transform

scholarly journals On the Seasonal Eddy Variability in the Kuroshio Extension

2018 ◽  
Vol 48 (8) ◽  
pp. 1675-1689 ◽  
Author(s):  
Yang Yang ◽  
X. San Liang
Keyword(s):  
Energy Transfer ◽  
Annual Cycle ◽  
Kuroshio Extension ◽  
Baroclinic Instability ◽  
Primary Energy ◽  
Seasonal Cycles ◽  
External Forcing ◽  
Energy Transfers ◽  
The Kuroshio ◽  
Multiscale Window Transform

AbstractUsing a recently developed tool, multiscale window transform (MWT), and the MWT-based canonical energy transfer theory, this study investigates the seasonal eddy variability in the Kuroshio Extension. Distinct seasonal cycles of eddy kinetic energy (EKE) are observed in the upstream and downstream regions of the Kuroshio Extension. In the upstream Kuroshio Extension, the EKE peaks in summer and reaches its minimum in winter over an annual cycle. By diagnosing the spatiotemporal structures of the canonical barotropic and baroclinic energy transfers, we found that internal processes due to mixed instabilities (i.e., both barotropic and baroclinic instabilities) are responsible for the seasonal eddy variability in this region. In the downstream Kuroshio Extension, the EKE exhibits a different annual cycle, peaking in spring and gradually decaying from summer to winter. Significant inverse barotropic energy transfer is found in this region throughout the year, leaving baroclinic instability the primary energy source for the regional seasonal eddy variability. Besides the internal redistribution, it is also evident that the external forcing may influence the Kuroshio Extension EKE seasonality—the EKE is found to be more damped by winds during winter than summer.

scholarly journals Canonical Transfer and Multiscale Energetics for Primitive and Quasigeostrophic Atmospheres

2016 ◽  
Vol 73 (11) ◽  
pp. 4439-4468 ◽  
Author(s):  
X. San Liang
Keyword(s):  
Multiple Scale ◽  
Pressure Work ◽  
The Past ◽  
Lie Bracket ◽  
Energy Transfers ◽  
Transport Kinetic ◽  
Work Done ◽  
Preliminary Application ◽  
Multiscale Window Transform ◽  
Canonical Transfer

Abstract The past years have seen the success of a novel and rigorous localized multiscale energetics formalism in a variety of ocean and engineering fluid applications. In a self-contained way, this study introduces it to the atmospheric dynamical diagnostics, with important theoretical updates and clarifications of some common misconceptions about multiscale energy. Multiscale equations are derived using a new analysis apparatus—namely, multiscale window transform—with respect to both the primitive equation and quasigeostrophic models. A reconstruction of the “atomic” energy fluxes on the multiple scale windows allows for a natural and unique separation of the in-scale transports and cross-scale transfers from the intertwined nonlinear processes. The resulting energy transfers bear a Lie bracket form, reminiscent of the Poisson bracket in Hamiltonian mechanics; hence, we would call them “canonical.” A canonical transfer process is a mere redistribution of energy among scale windows, without generating or destroying energy as a whole. By classification, a multiscale energetic cycle comprises available potential energy (APE) transport, kinetic energy (KE) transport, pressure work, buoyancy conversion, work done by external forcing and friction, and the cross-scale canonical transfers of APE and KE, which correspond respectively to the baroclinic and barotropic instabilities in geophysical fluid dynamics. A buoyancy conversion takes place in an individual window only, bridging the two types of energy, namely, KE and APE; it does not involve any processes among different scale windows and is hence basically not related to instabilities. This formalism is exemplified with a preliminary application to the study of the Madden–Julian oscillation.

scholarly journals Multiscale Dynamical Processes Underlying the Wintertime Atlantic Blockings

2017 ◽  
Vol 74 (11) ◽  
pp. 3815-3831 ◽  
Author(s):  
Jiwang Ma ◽  
X. San Liang
Keyword(s):  
Baroclinic Instability ◽  
Pressure Work ◽  
Warm Core ◽  
Synoptic Eddies ◽  
Two Phases ◽  
Blocking Event ◽  
Onset Phase ◽  
Vorticity Analysis ◽  
Multiscale Window Transform ◽  
Canonical Transfer

Abstract The wintertime atmospheric blocking over the Atlantic is investigated using a newly developed methodology—namely, localized multiscale energy and vorticity analysis (MS-EVA)—and the theory of canonical energy transfer. Through a multiscale window transform (MWT), the atmospheric fields from the ERA-40 data are reconstructed on three-scale ranges or scale windows: basic-flow window, blocking window, and synoptic window. The blocking event is obtained by compositing the wintertime blocking episodes, and a clear westward-retrograding signal is identified on the blocking window. Likewise, the local multiscale energetics following the signal are composited. It is found that a life cycle of the blocking-scale kinetic energy (KE) may be divided into three phases: onset phase, amplification phase, and decay phase. Different phases have different mechanisms in play. In general, pressure work and the canonical transfer from the synoptic eddies initiate the generation of the blocking, while the latter contributes to its amplification. The blocking decays as the system transports the KE away and as it converts the KE into available potential energy (APE) through buoyancy conversion. For the APE on the blocking window, its evolution experiences two maxima and, correspondingly, two phases can be distinguished. In the first maximum phase, the dominating mechanism is baroclinic instability; in the second, buoyancy conversion takes place. These are also the mechanisms that cause the warm core of the blocking in the troposphere.

scholarly journals Multiscale Interactive Processes Underlying the Heavy Rainstorm Associated with a Landfalling Atmospheric River

Atmosphere ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 29
Author(s):  
Zhuang Zhang ◽  
X. San Liang
Keyword(s):  
Multiscale Analysis ◽  
Heavy Precipitation ◽  
Stage I ◽  
Stage Ii ◽  
Background Flow ◽  
Atmospheric River ◽  
Analysis Methodology ◽  
Two Stages ◽  
Multiscale Window Transform ◽  
Canonical Transfer

The heavy precipitation in Northern California—brought about by a landfalling atmospheric river (AR) on 25–27 February 2019—is investigated for an understanding of the underlying dynamical processes. By the peaks in hourly accumulation, this rainstorm can be divided into two stages (Stage I and Stage II). Using a recently developed multiscale analysis methodology, i.e., multiscale window transform (MWT), and the MWT-based theory of canonical transfer, the original fields are reconstructed onto three scale windows, namely, the background flow, synoptic-scale and mesoscale windows, and the interactions among them are henceforth investigated. In both stages, the development of the precipitation is attributed to a vigorous buoyancy conversion and latent heating, and besides, the instability of the background flow. In Stage I, the instability is baroclinic, while in Stage II, it is barotropic. Interestingly, in Stage I, the mesoscale kinetic energy is transferred to the background flow where it is stored, and is released back in Stage II to the mesoscale window again, triggering intense precipitation.

scholarly journals On the Generation and Maintenance of the 2012/13 Sudden Stratospheric Warming

2017 ◽  
Vol 74 (10) ◽  
pp. 3209-3228 ◽  
Author(s):  
Fen Xu ◽  
X. San Liang
Keyword(s):  
Polar Region ◽  
Wave Interaction ◽  
Lower Atmosphere ◽  
Analysis Tool ◽  
Stratospheric Warming ◽  
Mean Flow ◽  
Sudden Stratospheric Warming ◽  
Three Stages ◽  
The Mean ◽  
Multiscale Window Transform

Abstract Using a newly developed analysis tool, multiscale window transform (MWT), and the MWT-based localized multiscale energetics analysis, the 2012/13 sudden stratospheric warming (SSW) is diagnosed for an understanding of the underlying dynamics. The fields are first reconstructed onto three scale windows: that is, mean window, sudden warming window or SSW window, and synoptic window. According to the reconstructions, the major warming period may be divided into three stages: namely, the stages of rapid warming, maintenance, and decay, each with different mechanisms. It is found that the explosive growth of temperature in the rapid warming stage (28 December–10 January) results from the collaboration of a strong poleward heat flux and canonical transfers through baroclinic instabilities in the polar region, which extract available potential energy (APE) from the mean-scale reservoir. In the course, a portion of the acquired APE is converted to and stored in the SSW-scale kinetic energy (KE), leading to a reversal of the polar night jet. In the stage of maintenance (11–25 January), the mechanism is completely different: First the previously converted energy stored in the SSW-scale KE is converted back, and, most importantly, in this time a strong barotropic instability happens over Alaska–Canada, which extracts the mean-scale KE to maintain the high temperature, while the mean-scale KE is mostly from the lower atmosphere, in conformity with the classical paradigm of mean flow–wave interaction with the upward-propagating planetary waves. This study provides an example that a warming may be generated in different stages through distinctly different mechanisms.

scholarly journals On the Inverse Relationship between the Boreal Wintertime Pacific Jet Strength and Storm-Track Intensity

2018 ◽  
Vol 31 (23) ◽  
pp. 9545-9564 ◽  
Author(s):  
Yuan-Bing Zhao ◽  
X. San Liang
Keyword(s):  
Inverse Relationship ◽  
Storm Track ◽  
Underlying Mechanism ◽  
Far North ◽  
Core Inverse ◽  
The Pacific ◽  
Resultant Effect ◽  
Diabatic Processes ◽  
Multiscale Window Transform ◽  
Canonical Transfer

Previous studies show that in boreal winters when the Pacific jet is extremely strong, the Pacific storm track is, however, unexpectedly weak. Using a recently developed technique, namely, the multiscale window transform (MWT), and the MWT-based localized multiscale energetics analysis, we investigate in this study the underlying mechanism of this counterintuitive phenomenon, based on ERA-40 data. It is found that most of the synoptic storms are generated at latitudes far north of the jet core, which lowers the relevance of the jet strength to the storm-track intensity, and the inverse relationship between the Pacific jet strength and storm-track intensity is mainly attributed to the internal dynamics. In the strong jet state, on one hand, the jet is narrow, and thus the jet winds at high latitudes are weak, resulting in weak baroclinic instabilities and hence reduced eddy growth rate; on the other hand, although baroclinic instabilities are strong at the jet core, inverse kinetic energy (KE) cascades are even stronger (by 43%). The resultant effect is that more eddy energy is transferred back to the background flow, leaving an overall weak storm track in a strong Pacific jet. In addition, diabatic processes are found to account for the inverse relationship: it is greatly weakened (by 25%) in the strong-core jet state. Apart from these, we also find that the role that barotropic canonical transfer plays in the inverse relationship is opposite to that in the formation of the midwinter minimum (MWM), another counterintuitive phenomenon in the Pacific storm track.

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