scholarly journals Testing the Annular Mode Autocorrelation Time Scale in Simple Atmospheric General Circulation Models

2008 ◽  
Vol 136 (4) ◽  
pp. 1523-1536 ◽  
Author(s):  
Edwin P. Gerber ◽  
Sergey Voronin ◽  
Lorenzo M. Polvani
Keyword(s):  
Time Scale ◽  
General Circulation ◽  
Simple Procedure ◽  
Low Frequency ◽  
General Circulation Models ◽  
Low Frequencies ◽  
Annular Mode ◽  
Fluctuation Dissipation ◽  
Low Frequency Variability ◽  
Autocorrelation Time

Abstract A new diagnostic for measuring the ability of atmospheric models to reproduce realistic low-frequency variability is introduced in the context of Held and Suarez’s 1994 proposal for comparing the dynamics of different general circulation models. A simple procedure to compute τ, the e-folding time scale of the annular mode autocorrelation function, is presented. This quantity concisely quantifies the strength of low-frequency variability in a model and is easy to compute in practice. The sensitivity of τ to model numerics is then studied for two dry primitive equation models driven with the Held–Suarez forcings: one pseudospectral and the other finite volume. For both models, τ is found to be unrealistically large when the horizontal resolutions are low, such as those that are often used in studies in which long integrations are needed to analyze model variability on low frequencies. More surprising is that it is found that, for the pseudospectral model, τ is particularly sensitive to vertical resolution, especially with a triangular truncation at wavenumber 42 (a very common resolution choice). At sufficiently high resolution, the annular mode autocorrelation time scale τ in both models appears to converge around values of 20–25 days, suggesting the existence of an intrinsic time scale at which the extratropical jet vacillates in the Held and Suarez system. The importance of τ for computing the correct response of a model to climate change is explicitly demonstrated by perturbing the pseudospectral model with simple torques. The amplitude of the model’s response to external forcing increases as τ increases, as suggested by the fluctuation–dissipation theorem.

scholarly journals An Assessment of GCM Skill in Simulating Persistence across Multiple Time Scales

2011 ◽  
Vol 24 (14) ◽  
pp. 3609-3623 ◽  
Author(s):  
Fiona Johnson ◽  
Seth Westra ◽  
Ashish Sharma ◽  
Andrew J. Pitman
Keyword(s):  
Interannual Variability ◽  
General Circulation ◽  
Large Scale ◽  
Low Frequency ◽  
General Circulation Models ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Max Planck ◽  
Reservoir Storage ◽  
Low Frequency Variability

Abstract Climate change impact studies for water resource applications, such as the development of projections of reservoir yields or the assessment of likely frequency and amplitude of drought under a future climate, require that the year-to-year persistence in a range of hydrological variables such as catchment average rainfall be properly represented. This persistence is often attributable to low-frequency variability in the global sea surface temperature (SST) field and other large-scale climate variables through a complex sequence of teleconnections. To evaluate the capacity of general circulation models (GCMs) to accurately represent this low-frequency variability, a set of wavelet-based skill measures has been developed to compare GCM performance in representing interannual variability with the observed global SST data, as well as to assess the extent to which this variability is imparted in precipitation and surface pressure anomaly fields. A validation of the derived skill measures is performed using GCM precipitation as an input in a reservoir storage context, with the accuracy of reservoir storage estimates shown to be improved by using GCM outputs that correctly represent the observed low-frequency variability. Significant differences in the performance of different GCMs is demonstrated, suggesting that judicious selection of models is required if the climate impact assessment is sensitive to low-frequency variability. The two GCMs that were found to exhibit the most appropriate representation of global low-frequency variability for individual variables assessed were the Istituto Nazionale di Geofisica e Vulcanologia (INGV) ECHAM4 and L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4); when considering all three variables, the Max Planck Institute (MPI) ECHAM5 performed well. Importantly, models that represented interannual variability well for SST also performed well for the other two variables, while models that performed poorly for SST also had consistently low skill across the remaining variables.

scholarly journals Stochastic Parameterization Schemes for Use in Realistic Climate Models

2011 ◽  
Vol 68 (2) ◽  
pp. 284-299 ◽  
Author(s):  
Joel Culina ◽  
Sergey Kravtsov ◽  
Adam H. Monahan
Keyword(s):  
General Circulation ◽  
Ad Hoc ◽  
Climate Models ◽  
Low Frequency ◽  
General Circulation Models ◽  
Planetary Scale ◽  
Low Frequency Variability ◽  
Quasigeostrophic Model ◽  
Low Dimensional ◽  
O 10

Abstract Stochastic parameterizations of fast-evolving, subgrid-scale processes are increasingly being used in a range of models from conceptual models to general circulation models. However, stochastic terms are generally included in an ad hoc fashion. In this study, a systematic method—“Hasselmann’s method”—of stochastic parameterization is developed through the direct application of rigorously justified limit theorems that predict the effective slow dynamics in systems with coupled slow and fast variables. The multiple Hasselmann models form a hierarchy of models ordered by the time scales over which they are expected to provide good approximations to the slowly evolving variables. Adaptable, efficient algorithms for integrating these reduced models are developed that require minimal changes to the unreduced model. Hasselmann’s method is tested on an O(10 000)-dimensional (planetary and synoptic scale) quasigeostrophic model of atmospheric low-frequency variability. Low-dimensional deterministic and stochastic models in the planetary-scale modes alone are derived, which accurately generate the statistics of the corresponding modes of the unreduced model, including the statistical signatures of jet regime behavior. It is shown that deterministic nonlinearity through slow forcing averaged with respect to the fast modes distribution dominates over multiplicative noise in generating the regime behavior.

scholarly journals Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability*

2014 ◽  
Vol 44 (8) ◽  
pp. 2050-2069 ◽  
Author(s):  
Brian K. Arbic ◽  
Malte Müller ◽  
James G. Richman ◽  
Jay F. Shriver ◽  
Andrew J. Morten ◽  
...  
Keyword(s):  
High Resolution ◽  
Kinetic Energy ◽  
General Circulation Model ◽  
General Circulation ◽  
Low Frequency ◽  
Circulation Model ◽  
Satellite Altimeter ◽  
Low Frequencies ◽  
Low Frequency Variability ◽  
Geostrophic Turbulence

Abstract Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Low-Frequency Variability in a Turbulent Baroclinic Jet: Eddy–Mean Flow Interactions in a Two-Level Model

2010 ◽  
Vol 67 (2) ◽  
pp. 452-467 ◽  
Author(s):  
Joseph Bernstein ◽  
Brian Farrell
Keyword(s):  
Time Scale ◽  
General Circulation ◽  
Channel Model ◽  
Low Frequency ◽  
Circulation Model ◽  
Coupled System ◽  
Mean Flow ◽  
Low Frequency Variability ◽  
Flow Interactions ◽  
The Waves

Abstract The origin of low-frequency variability in the midlatitude jet is investigated using a two-level baroclinic channel model. The model state fields are separated into slow and fast components using intermediate time- scale averaging. In the equation for the fast variables the nonlinear wave–wave interactions are parameterized as a stochastic excitation. The slowly varying ensemble mean eddy fluxes obtained from the resulting stochastic turbulence model are coupled with the slowly varying mean flow dynamics. This forms a coupled set of deterministic equations on the slow time scale that governs the dynamics of the eddy–mean flow interaction. The equilibria of this coupled system are found as a function of the excitation strength, which controls the level of turbulence. At low levels of turbulence the equilibrated flow with zonally symmetric mean forcing remains zonally symmetric, but as excitation increases it undergoes zonal symmetry-breaking bifurcations. Time-dependent flows arising from these bifurcations take the form of westward-propagating wavelike structures resembling blocking patterns. Features of these waves are characteristic of blocking in both observations and atmospheric general circulation model simulations including retrogression, eddy variance concentrated upstream of the waves, and eddy momentum flux forcing the waves.

Frequency-Weighted Variable-Length Controllers Using Anytime Control Strategies

2011 ◽  
Author(s):  
Gundula B. Runge ◽  
Al Ferri ◽  
Bonnie Ferri
Keyword(s):  
Time Scale ◽  
Weighting Function ◽  
Control Strategies ◽  
Low Frequency ◽  
Low Frequencies ◽  
High Frequencies ◽  
Frequency Components ◽  
Computational Resources ◽  
Weighted Variable ◽  
Selection Of

This paper considers an anytime strategy to implement controllers that react to changing computational resources. The anytime controllers developed in this paper are suitable for cases when the time scale of switching is in the order of the task execution time, that is, on the time scale found commonly with sporadically missed deadlines. This paper extends the prior work by developing frequency-weighted anytime controllers. The selection of the weighting function is driven by the expectation of the situations that would require anytime operation. For example, if the anytime operation is due to occasional and isolated missed deadlines, then the weighting on high frequencies should be larger than that for low frequencies. Low frequency components will have a smaller change over one sample time, so failing to update these components for one sample period will have less effect than with the high frequency components. An example will be included that applies the anytime control strategy to a model of a DC motor with deadzone and saturation nonlinearities.

An applied mathematics perspective on stochastic modelling for climate

2008 ◽  
Vol 366 (1875) ◽  
pp. 2427-2453 ◽  
Author(s):  
Andrew J Majda ◽  
Christian Franzke ◽  
Boualem Khouider
Keyword(s):  
Stochastic Model ◽  
General Circulation ◽  
Applied Mathematics ◽  
Low Frequency ◽  
Lattice Models ◽  
Stochastic Modelling ◽  
General Circulation Models ◽  
Teleconnection Patterns ◽  
Slowing Down ◽  
Low Dimensional

Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.

UNIVERSAL MULTIFRACTAL CHARACTERIZATION AND SIMULATION OF SPEECH

1992 ◽  
Vol 02 (03) ◽  
pp. 715-719
Author(s):  
CHRIS LARNDER ◽  
NICOLAS DESAULNIERS-SOUCY ◽  
SHAUN LOVEJOY ◽  
DANIEL SCHERTZER ◽  
CLAUDE BRAUN ◽  
...  
Keyword(s):  
Time Scale ◽  
Scale Invariance ◽  
Characteristic Time ◽  
Low Frequency ◽  
Characteristic Time Scale ◽  
Low Frequencies ◽  
Universal Behavior ◽  
Nonlinear Mixing

In the 1970's it was found that; for low frequencies (<10 Hz), speech is scaling: it has no characteristic time scale. Now such scale invariance is associated with multiscaling statistics, and multifractal structures. Just as Gaussian noises frequently arise because they are generically produced by sums of many independent noise processes, scaling noises have an analogous universal behavior arising from nonlinear mixing of processes. We show that low frequency speech is consistent with these ideas, and use the measured parameters to produce stochastic speech simulations which are strikingly similar to real speech.

scholarly journals Superluminal Motion in CTA 102

1989 ◽  
Vol 134 ◽  
pp. 529-530
Author(s):  
Ann E. Wehrle
Keyword(s):  
Flux Density ◽  
High Speed ◽  
Low Frequency ◽  
Precise Determination ◽  
Flux Variation ◽  
Low Frequencies ◽  
Superluminal Motion ◽  
Low Frequency Variability ◽  
Expansion Speed

Sholomitskii (1965) discovered that the flux density of the quasar CTA 102 varies at low frequencies on a timescale of a few months. Low-frequency variability can be explained by “superluminal flux variation” (Romney et al. 1984): If the intrinsic brightness of a component moving in a relativistically beamed source varies by only a few percent, the observer sees its flux density change by a much larger factor δ3-α when the optically thin blob moves almost directly toward the observer. Such a relativistically beamed source is likely to exhibit superluminal motion if studied with sufficient resolution and sensitivity. Superluminal motion in CTA 102 was discovered by Bååth (1987) who concluded on the basis of maps made at three epochs at a frequency of 932 MHz that two components were separating at a rate of 0.65 milliarcseconds (mas) per year. Using a redshift z = 1.037 and H0 = 100 km s−1 Mpc−1, q0 = 0.5, this expansion speed corresponds to (18 ± 4)h−1c. The extraordinarily high speed led us to make VLBI images of the source at a higher frequency in order to increase the resolution and make a more precise determination of the speed.

An Eddy-Feedback Model for Propagating Annular Modes

2020 ◽  
Author(s):  
Sandro Lubis ◽  
Pedram Hassanzadeh
Keyword(s):  
Low Frequency ◽  
Wave Activity ◽  
Mean Flow ◽  
Wave Source ◽  
Annular Mode ◽  
Annular Modes ◽  
The North ◽  
Feedback Model ◽  
Low Frequency Variability ◽  
Extratropical Circulation

&lt;p&gt;Some types of extreme events&lt;span&gt; in the extratropics are often associated with anomalous jet behaviors. A well-known example is the annular mode, wherein its variation e.g., the meandering in the north-south direction of the jet, disrupts the normal eastward migration of troughs and ridges.&lt;/span&gt; &lt;span&gt;Since the seminal works of Lorenz and Hartmann, the annular mode has been mostly analyzed based on single EOF mode. However, a recent study showed that the first and second leading EOFs are strongly correlated at long lags and are manifestations of a single oscillatory decaying-mode. This means that the first and second leading EOF modes interact and exert feedbacks on each other. The purpose of this study is to develop an eddy-feedback model for the extratropical low-frequency variability that includes these cross-EOF feedbacks to better isolate the eddy momentum/heat flux changes with time- and/or zonal-mean flow. Our results show that, in the presence of the poleward-propagation regime, the first and second leading EOF modes interact and exert positive feedbacks at lags ~10 (~20) days about ~0.07 (~0.16) day&lt;/span&gt;&lt;span&gt;&lt;sup&gt;-1&lt;/sup&gt;&lt;/span&gt;&lt;span&gt; in the reanalysis (idealized GCM). This feedback is often ignored in the previous studies, and in fact, the magnitude is nearly double the feedback exerted by the single EOF mode. We found that this apparent positive eddy feedback is a result of the effect of jet pulsation (strengthening and weakening) in zonal flow variability (z&lt;/span&gt;&lt;span&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;&lt;span&gt;) on the eddy momentum flux due to the meandering in the north-south direction of the jet (m&lt;/span&gt;&lt;span&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt;&lt;span&gt;). A finite-amplitude eddy-mean flow interaction diagnostic has been performed to demonstrate the dynamics governing the positive feedback in the propagating regime of the annular modes. It is shown that the poleward propagation is caused by an orchestrated combination of equatorward propagation of wave activity (baroclinic process), nonlinear wave breaking (barotropic processes), and radiative relaxation. The latter two processes follow the first one, and as such, the meridional propagation of Rossby wave activity (likely generated by an enhanced baroclinic wave source at a low level) is the central mechanism. Finally, our model calculations suggest the rule of thumb that the propagating annular modes (i.e., when EOF1 and EOF2 together represent quasi-periodic poleward propagation of zonal-mean flow anomalies) exist if the ratio of the fractional variance and decorrelation time-scale of EOF2 to that of EOF1 exceeds 0.5 or the two leading PCs showing maximum correlations at larger lags. These criteria can be used to assess the predictability of preferred modes of extratropical circulation in GCMs. The present study advances and potentially transforms the state of our understanding of the low-frequency variability of the extratropical circulation.&lt;/span&gt;&lt;/p&gt;

Sign in / Sign up

Export Citation Format

Share Document