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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.
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.
Abstract
Using a new analysis tool, namely, multiscale window transform (MWT), and the MWT-based theory of canonical transfer, this study investigates the spatiotemporal variations of the nonlinear interactions among the mean flows, interannual variabilities, quasi-annual fluctuations, and eddies in the global ocean. It is found that the canonical kinetic energy (KE) transfers are highly inhomogeneous in space, maximized in the western boundary current (WBC), Southern Ocean, and equatorial regions. In contrast to the equatorial and WBC regions where the temporal KE cascades are mainly forward, the Southern Ocean is the very place where coherent large-scale patterns of inverse KE cascade take place. The canonical transfers are also found to be highly variable in time. Specifically, in the Kuroshio Extension, the transfer from the mean flow to the interannual variability is in pace with the external winds from the eastern North Pacific; in the subtropical gyre, the mean flow-to-eddy transfer is responsible for the variability of the eddy kinetic energies (EKE) at both interannual and seasonal scales; in the tropics, the downscale transfers to the eddies from the other three scales all contribute to the interannual modulation of the EKE, and these transfers tend to decrease (increase) during El Niño (La Niña) events. In the Southern Ocean, the high-frequency eddies are found to feed KE to the low-frequency variability through temporal inverse cascade processes, which have been strengthened due to the enhanced eddy activities in the recent decade. Also discussed here is the relation between the seasonal EKE variability and the eddy–quasi-annual fluctuation interaction.
Abstract
Using a new analysis tool, namely, multiscale window transform (MWT), and the MWT-based theory of canonical transfer, this study investigates the spatiotemporal variations of the nonlinear interactions among the mean flows, interannual variabilities, quasi-annual fluctuations, and eddies in the global ocean. It is found that the canonical kinetic energy (KE) transfers are highly inhomogeneous in space, maximized in the western boundary current (WBC), Southern Ocean, and equatorial regions. In contrast to the equatorial and WBC regions where the temporal KE cascades are mainly forward, the Southern Ocean is the very place where coherent large-scale patterns of inverse KE cascade take place. The canonical transfers are also found to be highly variable in time. Specifically, in the Kuroshio Extension, the transfer from the mean flow to the interannual variability is in pace with the external winds from the eastern North Pacific; in the subtropical gyre, the mean flow-to-eddy transfer is responsible for the variability of the eddy kinetic energies (EKE) at both interannual and seasonal scales; in the tropics, the downscale transfers to the eddies from the other three scales all contribute to the interannual modulation of the EKE, and these transfers tend to decrease (increase) during El Niño (La Niña) events. In the Southern Ocean, the high-frequency eddies are found to feed KE to the low-frequency variability through temporal inverse cascade processes, which have been strengthened due to the enhanced eddy activities in the recent decade. Also discussed here is the relation between the seasonal EKE variability and the eddy–quasi-annual fluctuation interaction.
Abstract
Using a recently developed energetics diagnostic methodology, namely, the localized multiscale energy and vorticity analysis (MS-EVA), this study investigates the intricate nonlinear mutual interactions among the decadally modulating mean flow, the interannual fluctuations, and the transient eddies in the Kuroshio Extension region. It is found that the mean kinetic energy maximizes immediately east of the Izu–Ogasawara Ridge, while the transient eddy kinetic energy does not peak until 400 km away downstream. The interannual variabilities, which are dominated by a jet-trapped Rossby wave mode, provide an energy reservoir comparable to the other counterparts. In the upstream, strong localized barotropic and baroclinic transfers from the mean flow to the eddies are observed, whereas those from the interannual variabilities are not significant. Besides fueling the eddies, the unstable mean jet also releases energy to the interannual-scale processes. Between 144° and 154°E, both transfers from the mean flow and the interannual variabilities are important for the eddy development. Farther downstream, eddies are found to drive the mean flow on both the kinetic energy (KE) and available potential energy (APE) maps. They also provide KE to the interannual variabilities but obtain APE from the latter. The gained eddy APE is then converted to eddy KE through buoyancy conversion. Upscale energy transfers are observed in the northern and southern recirculation gyre (RG) regions. In these regions, the interannual–eddy interaction exhibits different scenarios: the eddies lose KE to the interannual processes in the northern RG region, while gaining KE in the southern RG region.
Abstract
Using a recently developed energetics diagnostic methodology, namely, the localized multiscale energy and vorticity analysis (MS-EVA), this study investigates the intricate nonlinear mutual interactions among the decadally modulating mean flow, the interannual fluctuations, and the transient eddies in the Kuroshio Extension region. It is found that the mean kinetic energy maximizes immediately east of the Izu–Ogasawara Ridge, while the transient eddy kinetic energy does not peak until 400 km away downstream. The interannual variabilities, which are dominated by a jet-trapped Rossby wave mode, provide an energy reservoir comparable to the other counterparts. In the upstream, strong localized barotropic and baroclinic transfers from the mean flow to the eddies are observed, whereas those from the interannual variabilities are not significant. Besides fueling the eddies, the unstable mean jet also releases energy to the interannual-scale processes. Between 144° and 154°E, both transfers from the mean flow and the interannual variabilities are important for the eddy development. Farther downstream, eddies are found to drive the mean flow on both the kinetic energy (KE) and available potential energy (APE) maps. They also provide KE to the interannual variabilities but obtain APE from the latter. The gained eddy APE is then converted to eddy KE through buoyancy conversion. Upscale energy transfers are observed in the northern and southern recirculation gyre (RG) regions. In these regions, the interannual–eddy interaction exhibits different scenarios: the eddies lose KE to the interannual processes in the northern RG region, while gaining KE in the southern RG region.
Abstract
Using 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.
Abstract
Using 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.
Abstract
The internal dynamical processes underlying the Kuroshio large meander are investigated using a recently developed analysis tool, multiscale window transform (MWT), and the MWT-based canonical transfer theory. Oceanic fields are reconstructed on a low-frequency mean flow window, a mesoscale eddy window, and a high-frequency synoptic window with reference to the three typical path states south of Japan, that is, the typical large meander (tLM), nearshore non-large meander (nNLM), and offshore non-large meander (oNLM) path states. The interactions between the scale windows are quantitatively evaluated in terms of canonical transfer, which bears a Lie bracket form and conserves energy in the space of scale. In general, baroclinic (barotropic) instability is strengthened (weakened) during the tLM state. For the first time we found a spatially coherent inverse cascade of kinetic energy (KE) from the synoptic eddies to the slowly varying mean flow; it occupies the whole large meander region but exists only in the tLM state. By the time-varying multiscale energetics, a typical large meander is preceded by a strong influx of mesoscale eddy energy from upstream with a cyclonic eddy, which subsequently triggers a strong inverse KE cascade from the mesoscale window to the mean flow window to build up the KE reservoir for the meander. Synoptic frontal eddies are episodically intensified due to the baroclinic instability of the meander, but they immediately feed back to the mean flow window through inverse KE cascade. These results highlight the important role played by inverse KE cascades in generating and maintaining the Kuroshio large meander.
Abstract
The internal dynamical processes underlying the Kuroshio large meander are investigated using a recently developed analysis tool, multiscale window transform (MWT), and the MWT-based canonical transfer theory. Oceanic fields are reconstructed on a low-frequency mean flow window, a mesoscale eddy window, and a high-frequency synoptic window with reference to the three typical path states south of Japan, that is, the typical large meander (tLM), nearshore non-large meander (nNLM), and offshore non-large meander (oNLM) path states. The interactions between the scale windows are quantitatively evaluated in terms of canonical transfer, which bears a Lie bracket form and conserves energy in the space of scale. In general, baroclinic (barotropic) instability is strengthened (weakened) during the tLM state. For the first time we found a spatially coherent inverse cascade of kinetic energy (KE) from the synoptic eddies to the slowly varying mean flow; it occupies the whole large meander region but exists only in the tLM state. By the time-varying multiscale energetics, a typical large meander is preceded by a strong influx of mesoscale eddy energy from upstream with a cyclonic eddy, which subsequently triggers a strong inverse KE cascade from the mesoscale window to the mean flow window to build up the KE reservoir for the meander. Synoptic frontal eddies are episodically intensified due to the baroclinic instability of the meander, but they immediately feed back to the mean flow window through inverse KE cascade. These results highlight the important role played by inverse KE cascades in generating and maintaining the Kuroshio large meander.
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.
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.
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.
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.
Abstract
The nonlinear multiscale dynamics of the Monterey Bay circulation during the Second Autonomous Ocean Sampling Network (AOSN-II) Experiment (August 2003) is investigated in an attempt to understand the complex processes underlying the highly variable ocean environment of the California coastal region. Using a recently developed methodology, the localized multiscale energy and vorticity analysis (MS-EVA) and the MS-EVA-based finite-amplitude hydrodynamic instability theory, the processes are reconstructed on three mutually exclusive time subspaces: a large-scale window, a mesoscale window, and a submesoscale window. The ocean is found to be most energetic in the upper layers, and the temporal mesoscale structures are mainly trapped above 200 m. Through exploring the nonlinear window–window interactions, it is found that the dynamics underlying the complex surface circulation is characterized by a well-organized, self-sustained bimodal instability structure: a Bay mode and a Point Sur mode, which are located near Monterey Bay and west of Point Sur, respectively. Both modes are of mixed types, but they are distinctly different in dynamics. The former is established when the wind relaxes, while the latter is directly driven by the wind. Either way, the wind instills energy into the ocean, which is stored within the large-scale window and then released to fuel temporal mesoscale processes. Upon wind relaxation, the generated mesoscale structures propagate northward along the coastline, in a form with dispersion properties similar to that of a free thermocline-trapped coastal-trapped wave. Between these two modes, a secondary instability is identified in the surface layer during 15–21 August, transferring energy to the temporal submesoscale window. Also studied is the deep-layer flow, which is unstable all the time throughout the experiment within the Bay and north of the deep canyon. It is observed that the deep temporal mesoscale flow within the Bay may derive its energy from the submesoscale window as well as from the large-scale window. This study provides a real ocean example of how secondary upwelling can be driven by winds through nonlinear instability and how winds may excite the ocean via an avenue distinctly different from the classical paradigms.
Abstract
The nonlinear multiscale dynamics of the Monterey Bay circulation during the Second Autonomous Ocean Sampling Network (AOSN-II) Experiment (August 2003) is investigated in an attempt to understand the complex processes underlying the highly variable ocean environment of the California coastal region. Using a recently developed methodology, the localized multiscale energy and vorticity analysis (MS-EVA) and the MS-EVA-based finite-amplitude hydrodynamic instability theory, the processes are reconstructed on three mutually exclusive time subspaces: a large-scale window, a mesoscale window, and a submesoscale window. The ocean is found to be most energetic in the upper layers, and the temporal mesoscale structures are mainly trapped above 200 m. Through exploring the nonlinear window–window interactions, it is found that the dynamics underlying the complex surface circulation is characterized by a well-organized, self-sustained bimodal instability structure: a Bay mode and a Point Sur mode, which are located near Monterey Bay and west of Point Sur, respectively. Both modes are of mixed types, but they are distinctly different in dynamics. The former is established when the wind relaxes, while the latter is directly driven by the wind. Either way, the wind instills energy into the ocean, which is stored within the large-scale window and then released to fuel temporal mesoscale processes. Upon wind relaxation, the generated mesoscale structures propagate northward along the coastline, in a form with dispersion properties similar to that of a free thermocline-trapped coastal-trapped wave. Between these two modes, a secondary instability is identified in the surface layer during 15–21 August, transferring energy to the temporal submesoscale window. Also studied is the deep-layer flow, which is unstable all the time throughout the experiment within the Bay and north of the deep canyon. It is observed that the deep temporal mesoscale flow within the Bay may derive its energy from the submesoscale window as well as from the large-scale window. This study provides a real ocean example of how secondary upwelling can be driven by winds through nonlinear instability and how winds may excite the ocean via an avenue distinctly different from the classical paradigms.
Abstract
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.
Abstract
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.
Abstract
This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Niño-3 SST data.
Abstract
This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Niño-3 SST data.
