scholarly journals Resonant Wave Interactions in the Equatorial Waveguide

2008 ◽  
Vol 65 (11) ◽  
pp. 3398-3418 ◽  
Author(s):  
Carlos F. M. Raupp ◽  
Pedro L. Silva Dias ◽  
Esteban G. Tabak ◽  
Paul Milewski
Keyword(s):  
Time Scales ◽  
Gravity Waves ◽  
Resonance Condition ◽  
Low Frequency ◽  
Vertical Direction ◽  
Present Theory ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Resonant Triads ◽  
Initial Mode

Abstract Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial β-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface–gravity waves in deep water and capillary–gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby–gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(ɛ) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

scholarly journals Biosphere-atmosphere exchange of CO<sub>2</sub> in relation to climate: a cross-biome analysis across multiple time scales

2009 ◽  
Vol 6 (10) ◽  
pp. 2297-2312 ◽  
Author(s):  
P. C. Stoy ◽  
A. D. Richardson ◽  
D. D. Baldocchi ◽  
G. G. Katul ◽  
J. Stanovick ◽  
...  
Keyword(s):  
Eddy Covariance ◽  
Time Scales ◽  
Ecosystem Respiration ◽  
Climatic Variability ◽  
Low Frequency ◽  
Net Ecosystem Exchange ◽  
Ecosystem Model ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Terrestrial Carbon

Abstract. The net ecosystem exchange of CO2 (NEE) varies at time scales from seconds to years and longer via the response of its components, gross ecosystem productivity (GEP) and ecosystem respiration (RE), to physical and biological drivers. Quantifying the relationship between flux and climate at multiple time scales is necessary for a comprehensive understanding of the role of climate in the terrestrial carbon cycle. Orthonormal wavelet transformation (OWT) can quantify the strength of the interactions between gappy eddy covariance flux and micrometeorological measurements at multiple frequencies while expressing time series variance in few energetic wavelet coefficients, offering a low-dimensional view of the response of terrestrial carbon flux to climatic variability. The variability of NEE, GEP and RE, and their co-variability with dominant climatic drivers, are explored with nearly one thousand site-years of data from the FLUXNET global dataset consisting of 253 eddy covariance research sites. The NEE and GEP wavelet spectra were similar among plant functional types (PFT) at weekly and shorter time scales, but significant divergence appeared among PFT at the biweekly and longer time scales, at which NEE and GEP were relatively less variable than climate. The RE spectra rarely differed among PFT across time scales as expected. On average, RE spectra had greater low frequency (monthly to interannual) variability than NEE, GEP and climate. CANOAK ecosystem model simulations demonstrate that "multi-annual" spectral peaks in flux may emerge at low (4+ years) time scales. Biological responses to climate and other internal system dynamics, rather than direct ecosystem response to climate, provide the likely explanation for observed multi-annual variability, but data records must be lengthened and measurements of ecosystem state must be made, and made available, to disentangle the mechanisms responsible for low frequency patterns in ecosystem CO2 exchange.

scholarly journals Multi-time scale data assimilation for atmosphere–ocean state estimates

2015 ◽  
Vol 11 (4) ◽  
pp. 3729-3757 ◽  
Author(s):  
N. Steiger ◽  
G. Hakim
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Time Scales ◽  
Time Scale ◽  
Low Frequency ◽  
Climate System ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Proxy Data ◽  
Frequency Components

Abstract. Paleoclimate proxy data span seasonal to millennial time scales, and Earth's climate system has both high- and low-frequency components. Yet it is currently unclear how best to incorporate multiple time scales of proxy data into a single reconstruction framework and to also capture both high- and low-frequency components of reconstructed variables. Here we present a data assimilation algorithm that can explicitly incorporate proxy data at arbitrary time scales. Through a series of pseudoproxy experiments, we find that atmosphere–ocean states are most skilfully reconstructed by incorporating proxies across multiple time scales compared to using proxies at short (annual) or long (~ decadal) time scales alone. Additionally, reconstructions that incorporate long time-scale pseudoproxies improve the low-frequency components of the reconstructions relative to using only high-resolution pseudoproxies. We argue that this is because time averaging high-resolution observations improves their covariance relationship with the slowly-varying components of the coupled-climate system, which the data assimilation algorithm can exploit. These results are insensitive to the choice of climate model, despite the model variables having very different spectral characteristics. Our results also suggest that it may be possible to reconstruct features of the oceanic meridional overturning circulation based solely on atmospheric surface temperature proxies.

scholarly journals Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

2009 ◽  
Vol 66 (10) ◽  
pp. 3165-3183 ◽  
Author(s):  
Carlos F. M. Raupp ◽  
Pedro L. Silva Dias
Keyword(s):  
Heat Source ◽  
Gravity Waves ◽  
The Other ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Frequency Wave ◽  
Resonant Interactions ◽  
Energy Exchanges ◽  
Resonant Triads ◽  
Stationary Component

Abstract Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial β-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(ɛ)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby–gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(ɛ) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby–gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an “accelerator” for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

scholarly journals Biosphere-atmosphere exchange of CO<sub>2</sub> in relation to climate: a cross-biome analysis across multiple time scales

2009 ◽  
Vol 6 (2) ◽  
pp. 4095-4141 ◽  
Author(s):  
P. C. Stoy ◽  
A. D. Richardson ◽  
D. D. Baldocchi ◽  
G. G. Katul ◽  
J. Stanovick ◽  
...  
Keyword(s):  
Time Scales ◽  
Ecosystem Respiration ◽  
Climatic Variability ◽  
Low Frequency ◽  
Net Ecosystem Exchange ◽  
Ecosystem Model ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multiple Frequencies ◽  
Low Dimensional

Abstract. The biosphere-atmosphere flux of CO2 responds to climatic variability at time scales from seconds to years and longer. Quantifying the strength of the interaction between the flux and climate variables at multiple frequencies is necessary to begin understanding the climatic controls on the dynamics of the terrestrial carbon cycle. Orthonormal wavelet transformation (OWT) can quantify the interaction between flux and microclimate at multiple frequencies while expressing time series variance in few energetic wavelet coefficients, offering a low-dimensional view of the measured climate-flux interaction. The variability of the net ecosystem exchange of CO2 (NEE), gross ecosystem productivity (GEP) and ecosystem respiration (RE), and their co-variability with dominant climatic drivers, are explored with a global dataset consisting of 253 eddy covariance research sites. Results demonstrate that the NEE and GEP wavelet spectra are similar amongst plant functional types (PFT) at weekly and shorter time scales, but significant divergence appeared among PFT at the biweekly and longer time scales, at which NEE and GEP are relatively less variable than climate. The RE spectra rarely differ among PFT across time scales. On average, RE spectra had greater low frequency (monthly to interannual) variability than NEE, GEP and climate. The low frequency Fourier coefficients of eight sites with more than eight years of data were compared against CANOAK ecosystem model simulations. Both measurements and theory demonstrate that "multi-annual" spectral peaks in flux may emerge at low (4+ years) time scales. Biological responses to climate and other internal system dynamics provide the likely explanation for observed multi-annual variability, but data records must be lengthened and measurements of ecosystem state must be made, and made available, to disentangle the mechanisms responsible for these patterns.

SOME REMARKS ON THE MULTIPLE TIME SCALES OF DIFFUSION IN MINERALS AND MELTS

2018 ◽  
Author(s):  
Yan Liang ◽  
◽  
Daniele J. Cherniak ◽  
Chenguang Sun
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Are We Doing ‘Systems’ Research? An Assessment of Methods for Climate Change Adaptation to Hydrohazards in a Complex World

2019 ◽  
Vol 11 (4) ◽  
pp. 1163 ◽  
Author(s):  
Melissa Bedinger ◽  
Lindsay Beevers ◽  
Lila Collet ◽  
Annie Visser
Keyword(s):  
Climate Change ◽  
Human Nature ◽  
Climate Change Adaptation ◽  
Time Scales ◽  
Spatial Scales ◽  
Local Context ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Systems Research

Climate change is a product of the Anthropocene, and the human–nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for ‘systems’ research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human–nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human–nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom–up and top–down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human–nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.

scholarly journals A multistate model incorporating estimation of excess hazards and multiple time scales

2021 ◽  
Vol 40 (9) ◽  
pp. 2139-2154
Author(s):  
Caroline E. Weibull ◽  
Paul C. Lambert ◽  
Sandra Eloranta ◽  
Therese M. L. Andersson ◽  
Paul W. Dickman ◽  
...  
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multistate Model
Sign in / Sign up

Export Citation Format

Share Document