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.

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-Frequency Variability, Coherence Resonance, and Phase Selection in a Low-Order Model of the Wind-Driven Ocean Circulation

2011 ◽  
Vol 41 (9) ◽  
pp. 1585-1604 ◽  
Author(s):  
Stefano Pierini
Keyword(s):  
Ocean Circulation ◽  
Kuroshio Extension ◽  
Global Bifurcation ◽  
Low Frequency ◽  
Galerkin Projection ◽  
Coherence Resonance ◽  
Primitive Equation ◽  
Phase Selection ◽  
Low Frequency Variability ◽  
Low Order

Abstract In this paper, a low-order spectral quasigeostrophic (QG) model of the wind-driven ocean circulation is derived and used to analyze the low-order character of the intrinsic low-frequency variability of the midlatitude double-gyre ocean circulation and of the related coherence resonance and phase selection phenomena. The model includes an exponential in the basis functions that allows for westward intensification, retains only four modes in the Galerkin projection, is defined in a rectangular domain, and is forced by deterministic and stochastic winds, thus extending previous low-order QG ocean models. The solution under steady forcing is first obtained, and the results are also analyzed in terms of dynamical systems theory. A homoclinic bifurcation (with the wind amplitude chosen as the control parameter) leads to intrinsic decadal relaxation oscillations (ROs) similar in several respects to those obtained with primitive equation models. The system is then forced with an additional red noise wind, and, in a parameter range preceding the global bifurcation, a coherence resonance scenario very similar to the one found with a primitive equation model of the Kuroshio Extension is obtained: this suggests that such a phenomenon is of low-order character. To study the RO excitation mechanism, a method denoted as phase selection is proposed. The system is forced with additional fictitious periodic winds that produce an emergence of ROs yielding strong phase dependence with the periodic forcing. The subsequent analysis reveals the character of the wind forcing that is most likely to excite a RO. All the results are discussed within the general framework of climate dynamics.

scholarly journals Atmospheric Stability in a Generalized Barotropic Model

2005 ◽  
Vol 62 (2) ◽  
pp. 476-491 ◽  
Author(s):  
Christos M. Mitas ◽  
Walter A. Robinson
Keyword(s):  
Quantitative Description ◽  
Atmospheric Stability ◽  
Low Frequency ◽  
Initial Value ◽  
Modified Model ◽  
Barotropic Model ◽  
Upper Troposphere ◽  
Low Frequency Variability ◽  
Short Times ◽  
Better Than

Abstract An empirical modification of conventional barotropic dynamics is implemented to study the low-frequency variability (LFV) of the upper troposphere. Using the conservation of potential vorticity, generalized spectral barotropic operators that apply at single isentropic levels are constructed. In initial value calculations the empirical model shows improvement in skill compared to the conventional barotropic model, but it does not do significantly better than persistence. For short times, however, the empirically modified model shows a much closer resemblance to the observed streamfunction tendency. Overall, it is a significantly more accurate representation of the atmosphere than the conventional barotropic model. Normal, optimal, and singular modes of the modified model are calculated. The modes of the empirically modified model are more stable and more difficult to excite than those of the barotropic model. These results are consistent with previous studies that found barotropic dynamics deficient for the quantitative description of LFV. The singular modes of the modified operator have very similar patterns but explain less variance than those of the barotropic operator, which is consistent with the difficulty in detecting optimal patterns in observations. The modified barotropic operator is also more normal than the barotropic operator, and thus less variable.

scholarly journals Low-frequency variability and heat transport in a low-order nonlinear coupled ocean–atmosphere model

2015 ◽  
Vol 309 ◽  
pp. 71-85 ◽  
Author(s):  
Stéphane Vannitsem ◽  
Jonathan Demaeyer ◽  
Lesley De Cruz ◽  
Michael Ghil
Keyword(s):  
Heat Transport ◽  
Low Frequency ◽  
Low Frequency Variability ◽  
Ocean Atmosphere ◽  
Atmosphere Model ◽  
Low Order
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