scholarly journals Closures for Ensemble-Mean Linear Dynamics with Stochastic Basic Flows

2007 ◽  
Vol 64 (2) ◽  
pp. 497-514 ◽  
Author(s):  
F-F. Jin ◽  
L. Lin
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Basic Flow ◽  
External Forcing ◽  
Linear Dynamics ◽  
Ensemble Simulations ◽  
Synoptic Eddy ◽  
Low Frequency Variability ◽  
Ensemble Mean ◽  
Forced Responses

Abstract This paper demonstrates the validity of a second-order closure for the ensemble-mean dynamics using the approach of direct numerical ensemble simulations of a linear barotropic model with stochastic basic flows. For various configurations of the stochastic basic flow and external forcing, the deterministic solutions under the second-order closure capture, with remarkable accuracy, the ensemble means and the associated eddy covariance fields of forced responses simulated by a 500-member numerical ensemble. Thus, the second-order closure is found to be adequate for describing the ensemble-mean linear dynamics with stochastic basic flows. Moreover, simple analytical solutions based on the second-order closure also demonstrate that the stochastic component of a superrotational basic flow not only damps the ensemble-mean Rossby waves, but also enhances their eastward propagation. Various examples of ensemble-mean solutions all show the important role played by the stochastic synoptic eddy component of the basic flow in determining the ensemble-mean responses to external forcing. This study supports the notion that linear frameworks of ensemble-mean dynamics under second-order closure are useful tools for describing and understanding the dynamics of the synoptic eddy and the low-frequency flow (SELF) feedback and extratropical atmospheric low-frequency variability.

scholarly journals Eddy-Induced Instability for Low-Frequency Variability

2010 ◽  
Vol 67 (6) ◽  
pp. 1947-1964 ◽  
Author(s):  
F-F. Jin
Keyword(s):  
Dynamic Instability ◽  
Low Frequency ◽  
Basic Flow ◽  
Mean Flow ◽  
Eddy Activity ◽  
Planetary Scale ◽  
Synoptic Eddy ◽  
Low Frequency Variability ◽  
Eddy Structures ◽  
Scale Perturbation

Abstract Synoptic eddy–mean flow interaction has been recognized as one of the key sources for extratropical low-frequency variability. In this paper, the underlying dynamics of this interaction are examined from the perspective of a synoptic eddy-induced dynamic instability. To delineate this instability, a barotropic model is used that is linearized with respect to a stochastic basic flow prescribed with both climatologic-mean flow and synoptic eddy statistics. This linear model captures the dynamics of feedback between synoptic eddy and low-frequency flow through a dynamic closure that relates the anomalous eddy vorticity forcing to low-frequency flow anomalies. After reducing this dynamic closure to its fundamental components, this stability is elucidated with analytical results under the most idealized consideration of basic flow. It is shown that through systematic alteration of the synoptic eddy structures in the basic flow, a low-frequency planetary-scale perturbation generates anomalous eddy vorticity forcing positively proportional to the vorticity of the perturbation. Such a perturbation amplifies itself; the energy source for its growth comes from the reservoir residing in the basic synoptic eddy activity. Thus, the growth rate of the synoptic eddy-induced dynamic instability depends primarily on the kinetic energy level of the basic synoptic eddy activity. Moreover, this instability is scale selective with preference for zonal symmetric and asymmetric planetary-scale modes, whose meridional and zonal scales are roughly in the range of those of the observed leading low-frequency patterns. Analysis of this synoptic eddy-induced instability provides insight into the origin of extratropical low-frequency variability.

Dynamics of Synoptic Eddy and Low-Frequency Flow Interaction. Part I: A Linear Closure

2006 ◽  
Vol 63 (7) ◽  
pp. 1677-1694 ◽  
Author(s):  
F-F. Jin ◽  
L-L. Pan ◽  
M. Watanabe
Keyword(s):  
Atmospheric Circulation ◽  
Low Frequency ◽  
Equation Model ◽  
The Self ◽  
Quasi Equilibrium ◽  
Mean Flow ◽  
Linear Dynamic ◽  
Synoptic Eddy ◽  
Linear Framework ◽  
Low Frequency Variability

Abstract The interaction between synoptic eddy and low-frequency flow (SELF) has been recognized for decades to play an important role in the dynamics of the low-frequency variability of the atmospheric circulation. In this three-part study a linear framework with a stochastic basic flow capturing both the climatological mean flow and climatological measures of the synoptic eddy flow is proposed. Based on this linear framework, a set of linear dynamic equations is derived for the ensemble-mean eddy forcing that is generated by anomalous time-mean flows. By assuming that such dynamically determined eddy-forcing anomalies approximately represent the time-mean anomalies of the synoptic eddy forcing and by using a quasi-equilibrium approximation, an analytical nonlocal dynamical closure is obtained for the two-way SELF feedback. This linear closure, directly relating time-mean anomalies of the synoptic eddy forcing to the anomalous time–mean flow, becomes an internal part of a new linear dynamic system for anomalous time–mean flow that is referred to as the low-frequency variability of the atmospheric circulation in this paper. In Part I, the basic approach for the SELF closure is illustrated using a barotropic model. The SELF closure is tested through the comparison of the observed eddy-forcing patterns associated with the leading low-frequency modes with those derived using the SELF feedback closure. Examples are also given to illustrate an important role played by the SELF feedback in regulating the atmospheric responses to remote forcing. Further applications of the closure for understanding the dynamics of low-frequency modes as well as the extension of the closure to a multilevel primitive equation model will be given in Parts II and III, respectively.

scholarly journals On Time Scales of Intrinsic Oscillations in the Climate System

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 459
Author(s):  
Anastasios A. Tsonis ◽  
Geli Wang ◽  
Wenxu Lu ◽  
Sergey Kravtsov ◽  
Christopher Essex ◽  
...  
Keyword(s):  
Low Frequency ◽  
Milankovitch Cycles ◽  
Data Sets ◽  
External Forcing ◽  
Natural Oscillations ◽  
Climatic Oscillations ◽  
Slow Feature Analysis ◽  
Limited Length ◽  
Past Data ◽  
Cumulative Evidence

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~ 60 years to ~1000 years, from the longer time-scale periodicities (20,000 yr +) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.

scholarly journals Shift Detection in Hydrological Regimes and Pluriannual Low-Frequency Streamflow Forecasting Using the Hidden Markov Model

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 2058 ◽  
Author(s):  
Larissa Rolim ◽  
Francisco de Souza Filho
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Extreme Events ◽  
Hidden Markov ◽  
Low Frequency ◽  
Streamflow Forecasting ◽  
Hydrologic Time Series ◽  
Low Frequency Variability ◽  
The Impact

Improved water resource management relies on accurate analyses of the past dynamics of hydrological variables. The presence of low-frequency structures in hydrologic time series is an important feature. It can modify the probability of extreme events occurring in different time scales, which makes the risk associated with extreme events dynamic, changing from one decade to another. This article proposes a methodology capable of dynamically detecting and predicting low-frequency streamflow (16–32 years), which presented significance in the wavelet power spectrum. The Standardized Runoff Index (SRI), the Pruned Exact Linear Time (PELT) algorithm, the breaks for additive seasonal and trend (BFAST) method, and the hidden Markov model (HMM) were used to identify the shifts in low frequency. The HMM was also used to forecast the low frequency. As part of the results, the regime shifts detected by the BFAST approach are not entirely consistent with results from the other methods. A common shift occurs in the mid-1980s and can be attributed to the construction of the reservoir. Climate variability modulates the streamflow low-frequency variability, and anthropogenic activities and climate change can modify this modulation. The identification of shifts reveals the impact of low frequency in the streamflow time series, showing that the low-frequency variability conditions the flows of a given year.

scholarly journals A Chronology of El Niño Events from Primary Documentary Sources in Northern Peru*

2008 ◽  
Vol 21 (9) ◽  
pp. 1948-1962 ◽  
Author(s):  
R. Garcia-Herrera ◽  
D. Barriopedro ◽  
E. Hernández ◽  
H. F. Diaz ◽  
R. R. Garcia ◽  
...  
Keyword(s):  
El Niño ◽  
El Nino ◽  
Southern Oscillation ◽  
Low Frequency ◽  
Primary Sources ◽  
Proxy Data ◽  
Documentary Sources ◽  
Low Frequency Variability ◽  
Northern Peru

Abstract The authors present a chronology of El Niño (EN) events based on documentary records from northern Peru. The chronology, which covers the period 1550–1900, is constructed mainly from primary sources from the city of Trujillo (Peru), the Archivo General de Indias in Seville (Spain), and the Archivo General de la Nación in Lima (Peru), supplemented by a reassessment of documentary evidence included in previously published literature. The archive in Trujillo has never been systematically evaluated for information related to the occurrence of El Niño–Southern Oscillation (ENSO). Abundant rainfall and river discharge correlate well with EN events in the area around Trujillo, which is very dry during most other years. Thus, rain and flooding descriptors, together with reports of failure of the local fishery, are the main indicators of EN occurrence that the authors have searched for in the documents. A total of 59 EN years are identified in this work. This chronology is compared with the two main previous documentary EN chronologies and with ENSO indicators derived from proxy data other than documentary sources. Overall, the seventeenth century appears to be the least active EN period, while the 1620s, 1720s, 1810s, and 1870s are the most active decades. The results herein reveal long-term fluctuations in warm ENSO activity that compare reasonably well with low-frequency variability deduced from other proxy data.

Removing Spurious Low-Frequency Variability in Drifter Velocities

2013 ◽  
Vol 30 (2) ◽  
pp. 353-360 ◽  
Author(s):  
Rick Lumpkin ◽  
Semyon A. Grodsky ◽  
Luca Centurioni ◽  
Marie-Helene Rio ◽  
James A. Carton ◽  
...  
Keyword(s):  
Low Frequency ◽  
Original Data ◽  
Strain Sensors ◽  
Wind Forcing ◽  
Stokes Drift ◽  
Interannual Variations ◽  
Transmission Frequency ◽  
Low Frequency Variability ◽  
Frequency Variations ◽  
Drifting Buoys

Abstract Satellite-tracked drifting buoys of the Global Drifter Program have drogues, centered at 15-m depth, to minimize direct wind forcing and Stokes drift. Drogue presence has historically been determined from submergence or tether strain records. However, recent studies have revealed that a significant fraction of drifters believed to be drogued have actually lost their drogues, a problem that peaked in the mid-2000s before the majority of drifters in the global array switched from submergence to tether strain sensors. In this study, a methodology is applied to the data to automatically reanalyze drogue presence based on anomalous downwind ageostrophic motion. Results indicate that the downwind slip of undrogued drifters is approximately 50% higher than previously believed. The reanalyzed results no longer exhibit the dramatic and spurious interannual variations seen in the original data. These results, along with information from submergence/tether strain and transmission frequency variations, are now being used to conduct a systematic manual reevaluation of drogue presence for each drifter in the post-1992 dataset.

scholarly journals Handling Nonlinearity in an Ensemble Kalman Filter: Experiments with the Three-Variable Lorenz Model

2012 ◽  
Vol 140 (8) ◽  
pp. 2628-2646 ◽  
Author(s):  
Shu-Chih Yang ◽  
Eugenia Kalnay ◽  
Brian Hunt
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Linear Models ◽  
Low Frequency ◽  
Lorenz Model ◽  
Outer Loop ◽  
Nonlinear Growth ◽  
Ensemble Mean ◽  
Ensemble Transform Kalman Filter ◽  
The One

Abstract An ensemble Kalman filter (EnKF) is optimal only for linear models because it assumes Gaussian distributions. A new type of outer loop, different from the one used in 3D and 4D variational data assimilation (Var), is proposed for EnKF to improve its ability to handle nonlinear dynamics, especially for long assimilation windows. The idea of the “running in place” (RIP) algorithm is to increase the observation influence by reusing observations when there is strong nonlinear error growth, and thus improve the ensemble mean and perturbations within the local ensemble transform Kalman filter (LETKF) framework. The “quasi-outer-loop” (QOL) algorithm, proposed here as a simplified version of RIP, aims to improve the ensemble mean so that ensemble perturbations are centered at a more accurate state. The performances of LETKF–RIP and LETKF–QOL in the presence of nonlinearities are tested with the three-variable Lorenz model. Results show that RIP and QOL allow LETKF to use longer assimilation windows with significant improvement of the analysis accuracy during periods of high nonlinear growth. For low-frequency observations (every 25 time steps, leading to long assimilation windows), and using the optimal inflation, the standard LETKF RMS error is 0.68, whereas for QOL and RIP the RMS errors are 0.47 and 0.35, respectively. This can be compared to the best 4D-Var analysis error of 0.53, obtained by using both the optimal long assimilation windows (75 time steps) and quasi-static variational analysis.

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