scholarly journals Low-Order Stochastic Mode Reduction for a Prototype Atmospheric GCM

2006 ◽  
Vol 63 (2) ◽  
pp. 457-479 ◽  
Author(s):  
Christian Franzke ◽  
Andrew J. Majda
Keyword(s):  
Stochastic Modeling ◽  
Multiplicative Noise ◽  
A Priori ◽  
Climate Modes ◽  
Systematic Strategy ◽  
Eddy Fluxes ◽  
Climate Drift ◽  
Stochastic Mode ◽  
Correction Terms ◽  
Low Order

Abstract This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a three-layer quasigeostrophic model. This model climate has reasonable approximations of the North Atlantic Oscillation (NAO) and Pacific–North America (PNA) patterns. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition in the total energy metric. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with 10 or less resolved modes capture the statistics of the original model very well, including the variances and temporal correlations with high pattern correlations of the transient eddy fluxes. A budget analysis establishes that the low-order stochastic models are highly nonlinear with significant contributions from both additive and multiplicative noise. This is in contrast to previous stochastic modeling studies. These studies a priori assume a linear model with additive noise and regression fit the resolved modes. The multiplicative noise comes from the advection of the resolved modes by the unresolved modes. The most straightforward low-order stochastic climate models experience climate drift that stems from the bare truncation dynamics. Even though the geographic correlation of the transient eddy fluxes is high, they are underestimated by a factor of about 2 in the a priori procedure and thus cannot completely overcome the large climate drift in the bare truncation. Also, variants of the reduced stochastic modeling procedure that experience no climate drift with good predictions of both the variances and time correlations are discussed. These reduced models without climate drift are developed by slowing down the dynamics of the bare truncation compared with the interactions with the unresolved modes and yield a minimal two-parameter regression fitting strategy for the climate modes. This study points to the need for better optimal basis functions that optimally capture the essential slow dynamics of the system to obtain further improvements for the reduced stochastic modeling procedure.

scholarly journals Low-Order Stochastic Mode Reduction for a Realistic Barotropic Model Climate

2005 ◽  
Vol 62 (6) ◽  
pp. 1722-1745 ◽  
Author(s):  
Christian Franzke ◽  
Andrew J. Majda ◽  
Eric Vanden-Eijnden
Keyword(s):  
Stochastic Models ◽  
Additive Noise ◽  
Low Frequency ◽  
Barotropic Model ◽  
Climate Modes ◽  
Low Frequency Variability ◽  
Systematic Strategy ◽  
Stochastic Mode ◽  
Correction Terms ◽  
Low Order

Abstract This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a realistic barotropic model climate. This barotropic model climate has reasonable approximations of the Arctic Oscillation (AO) and Pacific/North America (PNA) teleconnections as its two leading principal patterns of low-frequency variability. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with only four resolved modes capture the statistics of the original barotropic model modes quite well. A budget analysis establishes that the low-order stochastic models are dominated by linear dynamics and additive noise. The linear correction terms and the additive noise stem from the linear coupling between resolved and unresolved modes, and not from nonlinear interactions between resolved and unresolved modes as assumed in previous studies.

A priori tests of a stochastic mode reduction strategy

2002 ◽  
Vol 170 (3-4) ◽  
pp. 206-252 ◽  
Author(s):  
A. Majda ◽  
I. Timofeyev ◽  
E. Vanden-Eijnden
Keyword(s):  
A Priori ◽  
Reduction Strategy ◽  
Stochastic Mode

scholarly journals Empirical correction techniques: analysis and applications to chaotically driven low-order atmospheric models

2013 ◽  
Vol 20 (2) ◽  
pp. 199-206
Author(s):  
I. Trpevski ◽  
L. Basnarkov ◽  
D. Smilkov ◽  
L. Kocarev
Keyword(s):  
Linear Regression Method ◽  
Atmospheric Models ◽  
Time Intervals ◽  
Average Value ◽  
Climate Forecasting ◽  
Empirical Correction ◽  
Weather And Climate ◽  
Real World Applications ◽  
Correction Terms ◽  
Low Order

Abstract. Contemporary tools for reducing model error in weather and climate forecasting models include empirical correction techniques. In this paper we explore the use of such techniques on low-order atmospheric models. We first present an iterative linear regression method for model correction that works efficiently when the reference truth is sampled at large time intervals, which is typical for real world applications. Furthermore we investigate two recently proposed empirical correction techniques on Lorenz models with constant forcing while the reference truth is given by a Lorenz system driven with chaotic forcing. Both methods indicate that the largest increase in predictability comes from correction terms that are close to the average value of the chaotic forcing.

Enhanced detection through low-order stochastic modeling for guided-wave structural health monitoring

2011 ◽  
Vol 11 (2) ◽  
pp. 149-160 ◽  
Author(s):  
Eric B Flynn ◽  
Michael D Todd ◽  
Anthony J Croxford ◽  
Bruce W Drinkwater ◽  
Paul D Wilcox
Keyword(s):  
Structural Health Monitoring ◽  
Stochastic Modeling ◽  
Health Monitoring ◽  
Guided Wave ◽  
Structural Health ◽  
Low Order

scholarly journals A Diagnosis of Thickness Fluxes in an Eddy-Resolving Model

2007 ◽  
Vol 37 (3) ◽  
pp. 727-742 ◽  
Author(s):  
Carsten Eden ◽  
Richard J. Greatbatch ◽  
Jürgen Willebrand
Keyword(s):  
Large Scale ◽  
North Atlantic Ocean ◽  
A Priori ◽  
Baroclinic Instability ◽  
Optimization Technique ◽  
Subtropical Gyre ◽  
Equatorial Atlantic ◽  
The North ◽  
Eddy Fluxes ◽  
The Mean

Abstract Output from an eddy-resolving model of the North Atlantic Ocean is used to estimate values for the thickness diffusivity κ appropriate to the Gent and McWilliams parameterization. The effect of different choices of rotational eddy fluxes on the estimated κ is discussed. Using the raw fluxes (no rotational flux removed), large negative values (exceeding −5000 m2 s−1) of κ are diagnosed locally, particularly in the Gulf Stream region and in the equatorial Atlantic. Removing a rotational flux based either on the suggestion of Marshall and Shutts or the more general theory of Medvedev and Greatbatch leads to a reduction of the negative values, but they are still present. The regions where κ < 0 correspond to regions where eddies are acting to increase, rather than decrease (as in baroclinic instability) the mean available potential energy. In the subtropical gyre, κ ranges between 500 and 2000 m2 s−1, rapidly decreasing to zero below the thermocline in all cases. Rotational fluxes and κ are also estimated using an optimization technique. In this case, |κ| can be reduced or increased by construction, but the regions where κ < 0 are still present and the optimized rotational fluxes also remain similar to a priori values given by the theoretical considerations. A previously neglected component (ν) of the bolus velocity is associated with the horizontal flux of buoyancy along, rather than across, the mean buoyancy contours. The ν component of the bolus velocity is interpreted as a streamfunction for eddy-induced advection, rather than diffusion, of mean isopycnal layer thickness, showing up when the lateral eddy fluxes cannot be described by isotropic diffusion only. All estimates show a similar large-scale pattern for ν, implying westward advection of isopycnal thickness over much of the subtropical gyre. Comparing ν with a mean streamfunction shows that it is about 10% of the mean in midlatitudes and even larger than the mean in the Tropics.

P-wave tomographic model from local bulletin data for improved seismic location in and around Israel

2020 ◽  
Author(s):  
Lewis Schardong ◽  
Yochai Ben-Horin ◽  
Alon Ziv ◽  
Hillel Wust-Bloch ◽  
Yael Radzyner
Keyword(s):  
Eastern Mediterranean ◽  
A Priori ◽  
Warning System ◽  
Velocity Model ◽  
P Wave ◽  
Seismic Velocities ◽  
Fast Marching ◽  
Earthquake Early Warning System ◽  
Starting Model ◽  
Correction Terms

<p>For the past 40 years, the Geophysical Institute of Israel has been in charge of the recording, monitoring and relocating of local earthquakes. Due to the variety of data analysts and data sources, as well as several network upgrades, the resulting bulletin data has to be completed and homogenised, and station metadata needs to be tracked down, and sometimes corrected. For those reasons, as well as because of the lack of consensus on an accurate model for seismic velocities in the area, published source locations are often poorly constrained. We present a homogenised Israeli bulletin, including natural and man-made explosion data. We extract sets of seismic sources with location accuracy greater than 5 km (GT5), as well as GT0 explosions.</p><p>We select a set of events with the highest network coverage, comprising (1) natural earthquakes, (2) man-made quarry or mine blasts, (3) GT5 earthquakes or explosions, and (4) GT0 explosions. We relocate them altogether using the <em>BayesLoc</em> package, a Bayesian, hierarchical, multi-event locator which produces, after source relocation, event-, station- and phase-specific correction terms. We put different a priori constraints on the different categories of seismic events, allowing poorly constrained origin parameters to improve thanks to the more accurate GT locations. <em>BayesLoc</em> also produces traveltime correction terms that can be used to correct systematic errors in the dataset, as well as error estimates.</p><p>Eventually, we invert this homogenised local traveltime dataset in order to invert for a <em>P</em>-wave crustal velocity model of Israel and its surroundings. To do so, we use the <em>Fast Marching Tomography</em> package, which allows the representation of a wide variety of input structures (starting model and geometry of layer boundaries) and can take many different types of input data. We show preliminary inversion tests and results that are in good agreement with past local studies.</p><p>This crustal model of Israel is ultimately to be used as a starting model in a larger tomographic study of the Eastern Mediterranean and Middle East region, where the <em>Regional Seismic Travel Time</em> approach is to be expanded, in order to improve the CTBT’s capabilities in monitoring the regional seismicity. Eventually, such a velocity model could also be used to relocate the whole earthquake catalogue more accurately, and improve the Earthquake Early Warning System currently in development in Israel.</p>

Predicting the Real-Time Multivariate Madden–Julian Oscillation Index through a Low-Order Nonlinear Stochastic Model

2015 ◽  
Vol 143 (6) ◽  
pp. 2148-2169 ◽  
Author(s):  
Nan Chen ◽  
Andrew J. Majda
Keyword(s):  
Stochastic Model ◽  
Real Time ◽  
Stochastic Models ◽  
Multiplicative Noise ◽  
Hidden Variables ◽  
Ensemble Prediction ◽  
Madden Julian Oscillation ◽  
The Real ◽  
Nonlinear Stochastic Model ◽  
Low Order

Abstract A new low-order nonlinear stochastic model is developed to improve the predictability of the Real-time Multivariate Madden–Julian oscillation (MJO) index (RMM index), which is a combined measure of convection and circulation. A recent data-driven, physics-constrained, low-order stochastic modeling procedure is applied to the RMM index. The result is a four-dimensional nonlinear stochastic model for the two observed RMM variables and two hidden variables involving correlated multiplicative noise defined through energy-conserving nonlinear interaction. The special structure of the low-order model allows efficient data assimilation for the initialization of the hidden variables that facilitates the ensemble prediction algorithm. An information-theoretic framework is applied to the calibration of model parameters over a short training phase of 3 yr. This framework involves generalizations of the anomaly pattern correlation, the RMS error, and the information deficiency in the model forecast. The nonlinear stochastic models show skillful prediction for 30 days on average in these metrics. More importantly, the predictions succeed in capturing the amplitudes of the RMM index and the useful skill of forecasting strong MJO events is around 40 days. Furthermore, information barriers to prediction for linear models imply the necessity of the nonlinear interactions between the observed and hidden variables as well as the multiplicative noise in these low-order stochastic models.

scholarly journals Signatures of Nonlinear Dynamics in an Idealized Atmospheric Model

2011 ◽  
Vol 68 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Dmitri Kondrashov ◽  
Sergey Kravtsov ◽  
Michael Ghil
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Space ◽  
Model Reduction ◽  
Empirical Model ◽  
Multiplicative Noise ◽  
Atmospheric Model ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Functions ◽  
Low Order

Abstract Signatures of nonlinear dynamics are analyzed by studying the phase-space tendencies of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography. Nonlinear, stochastic, low-order prototypes of the full QG3 model are constructed in the phase space of this model’s empirical orthogonal functions using the empirical model reduction (EMR) approach. The phase-space tendencies of the EMR models closely match the full QG3 model’s tendencies. The component of these tendencies that is not linearly parameterizable is shown to be dominated by the interactions between “resolved” modes rather than by multiplicative “noise” associated with unresolved modes. The method of defining the leading resolved modes and the interactions between them plays a key role in understanding the nature of the QG3 model’s dynamics, whether linear or nonlinear, deterministic or stochastic.

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