Linear and Nonlinear Signatures in the Planetary Wave Dynamics of an AGCM: Phase Space Tendencies

2005 ◽  
Vol 62 (6) ◽  
pp. 1792-1811 ◽  
Author(s):  
Grant Branstator ◽  
Judith Berner
Keyword(s):  
Phase Space ◽  
General Circulation ◽  
Planetary Wave ◽  
Gaussian White Noise ◽  
Circulation Model ◽  
Lag Time ◽  
Empirical Orthogonal Functions ◽  
Linear Component ◽  
Least Squares Fit ◽  
Linear And Nonlinear

Abstract To identify and quantify indications of linear and nonlinear planetary wave behavior, characteristics of a very long integration of an atmospheric general circulation model in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights, and the primary investigated characteristic is the state dependence of mean phase space tendencies. Defining the linear component of planetary wave tendencies as that part which can be captured by a least squares fit linear operator driven by additive Gaussian white noise, the study finds that there are distinct linear and nonlinear signatures. These signatures are especially easy to see in plots of mean tendencies projected onto phase space planes. For some planes the mean tendencies are highly linear, while for others there are strong departures from linearity. The results of the analysis are found to depend strongly on the lag time used to estimate tendencies with the linear component monotonically increasing with lag time. This is shown to result from the ergodicity of the system. Using the theory of Markov models it is possible to remove the lag-dependent component of the tendencies from the results. When this is done the projected mean dynamics in some planes is found to be almost exclusively nonlinear, while in others it is nearly linear. In the four-dimensional space the linear component of the dynamics is largely a reflection of a westward propagating Northern Hemisphere pattern concentrated over the Pacific and North America. The nonlinear signature can be approximated by two linear functions, each operating in a different region of phase space. One region is centered around a Pacific blocking pattern while the other is centered on a state with enhanced zonal symmetry. It is concluded that reduced models of the planetary waves should strive to include these state-dependent dynamics.

Linear and Nonlinear Signatures in the Planetary Wave Dynamics of an AGCM: Probability Density Functions

2007 ◽  
Vol 64 (1) ◽  
pp. 117-136 ◽  
Author(s):  
Judith Berner ◽  
Grant Branstator
Keyword(s):  
Phase Space ◽  
Probability Density ◽  
General Circulation ◽  
Planetary Wave ◽  
Circulation Model ◽  
Gaussian Mixture ◽  
Empirical Orthogonal Functions ◽  
Planetary Waves ◽  
Linear And Nonlinear ◽  
Non Gaussian

Abstract To identify and quantify indications of linear and nonlinear planetary wave behavior and their impact on the distribution of atmospheric states, characteristics of a very long integration of an atmospheric general circulation model (GCM) in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights. First it is established that nonlinear tendencies similar to those reported in an earlier study of the phase space behavior in this GCM have the potential to lead to non-Gaussian features in the probability density function (PDF) of planetary waves. Then using objective measures it is demonstrated that the model’s distribution of states has distinctive non-Gaussian features. These features are characterized in various subspaces of dimension as high as four. A key feature is the presence of three radial ridges of enhanced probability emanating from the mode, which is shifted away from the climatological mean. There is no evidence of multiple maxima in the full PDF, but the radial ridges lead to three distinct modes in the distribution of circulation patterns. It is demonstrated that these key aspects of non-Gaussianity are captured by a two-Gaussian mixture model fitted in four dimensions. The two circulation states at the centroids of the component Gaussians are very similar to those associated with two nonlinear features identified by Branstator and Berner in their analysis of the trajectories of the GCM. These two dynamical features are locally linear, so it is concluded that the behavior of planetary waves can be conceptualized as being approximately piecewise-linear, leading to a two-Gaussian mixture with three preferred patterns.

The Relationship between Statistically Linear and Nonlinear Feedbacks and Zonal-Mean Flow Variability in an Idealized Climate Model

2009 ◽  
Vol 66 (2) ◽  
pp. 353-372 ◽  
Author(s):  
Sergey Kravtsov ◽  
John E. Ten Hoeve ◽  
Steven B. Feldstein ◽  
Sukyoung Lee ◽  
Seok-Woo Son
Keyword(s):  
Phase Space ◽  
General Circulation ◽  
Climate Model ◽  
Circulation Model ◽  
Zonal Flow ◽  
Empirical Orthogonal Functions ◽  
Nonlinear Flow ◽  
Mean Flow ◽  
Orthogonal Functions ◽  
Flow Variability

Abstract Simulations using an idealized, atmospheric general circulation model (GCM) subjected to various thermal forcings are analyzed via a combination of probability density function (PDF) estimation and spectral analysis techniques. Seven different GCM runs are examined, each model run being characterized by different values in the strength of the tropical heating and high-latitude cooling. For each model run, it is shown that a linear stochastic model constructed in the phase space of the ten leading empirical orthogonal functions (EOFs) of the zonal-mean zonal flow provides an excellent statistical approximation to the simulated zonal flow variability, which includes zonal index fluctuations, and quasi-oscillatory, poleward, zonal-mean flow anomaly propagation. Statistically significant deviations from the above linear stochastic null hypothesis arise in the form of a few anomalously persistent, or statistically nonlinear, flow patterns, which occupy particular regions of the model’s phase space. Some of these nonlinear regimes occur during certain phases of the poleward propagation; however, such an association is, in general, weak. This indicates that the regimes and oscillations in the model may be governed by distinct dynamical mechanisms.

scholarly journals A Multivariate Empirical Orthogonal Function Method to Construct Nitrate Maps in the Southern Ocean

2018 ◽  
Vol 35 (7) ◽  
pp. 1505-1519 ◽  
Author(s):  
Yu-Chiao Liang ◽  
Matthew R. Mazloff ◽  
Isabella Rosso ◽  
Shih-Wei Fang ◽  
Jin-Yi Yu
Keyword(s):  
Southern Ocean ◽  
General Circulation ◽  
Model Simulation ◽  
Potential Temperature ◽  
Circulation Model ◽  
Empirical Orthogonal Functions ◽  
Cluster Method ◽  
Sampling Strategies ◽  
Data Sampling ◽  
Mean Square Errors

AbstractThe ability to construct nitrate maps in the Southern Ocean (SO) from sparse observations is important for marine biogeochemistry research, as it offers a geographical estimate of biological productivity. The goal of this study is to infer the skill of constructed SO nitrate maps using varying data sampling strategies. The mapping method uses multivariate empirical orthogonal functions (MEOFs) constructed from nitrate, salinity, and potential temperature (N-S-T) fields from a biogeochemical general circulation model simulation Synthetic N-S-T datasets are created by sampling modeled N-S-T fields in specific regions, determined either by random selection or by selecting regions over a certain threshold of nitrate temporal variances. The first 500 MEOF modes, determined by their capability to reconstruct the original N-S-T fields, are projected onto these synthetic N-S-T data to construct time-varying nitrate maps. Normalized root-mean-square errors (NRMSEs) are calculated between the constructed nitrate maps and the original modeled fields for different sampling strategies. The sampling strategy according to nitrate variances is shown to yield maps with lower NRMSEs than mapping adopting random sampling. A k-means cluster method that considers the N-S-T combined variances to identify key regions to insert data is most effective in reducing the mapping errors. These findings are further quantified by a series of mapping error analyses that also address the significance of data sampling density. The results provide a sampling framework to prioritize the deployment of biogeochemical Argo floats for constructing nitrate maps.

scholarly journals The Antarctic Oscillation Structure in an AOGCM with Interactive Stratospheric Ozone

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
S. Brand ◽  
K. Dethloff ◽  
D. Handorf
Keyword(s):  
General Circulation ◽  
Planetary Wave ◽  
Middle Atmosphere ◽  
Stratospheric Ozone ◽  
Circulation Model ◽  
Wave Activity ◽  
Antarctic Oscillation ◽  
Wave Dynamics ◽  
Hemisphere Winter ◽  
The Antarctic

Based on 150-year equilibrium simulations using the atmosphere-ocean-sea ice general circulation model (AOGCM) ECHO-GiSP, the southern hemisphere winter circulation is examined focusing on tropo-stratosphere coupling and wave dynamics. The model covers the troposphere and strato-mesosphere up to 80 km height and includes an interactive stratospheric chemistry. Compared to the reference simulation without interactive chemistry, the interactive simulation shows a weaker polar vortex in the middle atmosphere and is shifted towards the negative phase of the Antarctic Oscillation (AAO) in the troposphere. Differing from the northern hemisphere winter situation, the tropospheric planetary wave activity is weakened. A detailed analysis shows, that the modelled AAO zonal mean signal behaves antisymmetrically between troposphere and strato-mesosphere. This conclusion is supported by reanalysis data and a discussion of planetary wave dynamics in terms of Eliassen-Palm fluxes. Thereby, the tropospheric planetary wave activity appears to be controlled from the middle atmosphere.

scholarly journals Tropospheric Planetary Wave Dynamics and Mixture Modeling: Two Preferred Regimes and a Regime Shift

2007 ◽  
Vol 64 (10) ◽  
pp. 3521-3541 ◽  
Author(s):  
A. Hannachi
Keyword(s):  
General Circulation ◽  
Regime Shift ◽  
Planetary Wave ◽  
Clustering Algorithm ◽  
Spatial Clustering ◽  
Gaussian Mixture Models ◽  
Circulation Model ◽  
Gaussian Mixture ◽  
Stochastic Dynamical Systems ◽  
Wave Dynamics

Abstract Investigation of preferred structures of planetary wave dynamics is addressed using multivariate Gaussian mixture models. The number of components in the mixture is obtained using order statistics of the mixing proportions, hence avoiding previous difficulties related to sample sizes and independence issues. The method is first applied to a few low-order stochastic dynamical systems and data from a general circulation model. The method is next applied to winter daily 500-hPa heights from 1949 to 2003 over the Northern Hemisphere. A spatial clustering algorithm is first applied to the leading two principal components (PCs) and shows significant clustering. The clustering is particularly robust for the first half of the record and less for the second half. The mixture model is then used to identify the clusters. Two highly significant extratropical planetary-scale preferred structures are obtained within the first two to four EOF state space. The first pattern shows a Pacific–North American (PNA) pattern and a negative North Atlantic Oscillation (NAO), and the second pattern is nearly opposite to the first one. It is also observed that some subspaces show multivariate Gaussianity, compatible with linearity, whereas others show multivariate non-Gaussianity. The same analysis is also applied to two subperiods, before and after 1978, and shows a similar regime behavior, with a slight stronger support for the first subperiod. In addition a significant regime shift is also observed between the two periods as well as a change in the shape of the distribution. The patterns associated with the regime shifts reflect essentially a PNA pattern and an NAO pattern consistent with the observed global warming effect on climate and the observed shift in sea surface temperature around the mid-1970s.

scholarly journals Evolution of atmospheric connectivity in the 20th century

2014 ◽  
Vol 21 (4) ◽  
pp. 825-839 ◽  
Author(s):  
F. Arizmendi ◽  
A. C. Martí ◽  
M. Barreiro
Keyword(s):  
20Th Century ◽  
General Circulation ◽  
Circulation Model ◽  
Internal Variability ◽  
Western Pacific ◽  
Positive Trend ◽  
Central Pacific ◽  
Nonlinear Networks ◽  
The Pacific ◽  
Linear And Nonlinear

Abstract. We aim to study the evolution of the upper atmosphere connectivity over the 20th century as well as to distinguish the oceanically forced component from the atmospheric internal variability. For this purpose we build networks from two different reanalysis data sets using both linear and nonlinear statistical similarity measures to determine the existence of links between different regions of the world in the two halves of the last century. We furthermore use symbolic analysis to emphasize intra-seasonal, intra-annual and inter-annual timescales. Both linear and nonlinear networks have similar structures and evolution, showing that the most connected regions are in the tropics over the Pacific Ocean. Also, the Southern Hemisphere extratropics have more connectivity in the first half of the 20th century, particularly on intra-annual and intra-seasonal timescales. Changes over the Pacific main connectivity regions are analyzed in more detail. Both linear and nonlinear networks show that the central and western Pacific regions have decreasing connectivity from early 1900 up to about 1940, when it starts increasing again until the present. The inter-annual network shows a similar behavior. However, this is not true of other timescales. On intra-annual timescales the minimum connectivity is around 1956, with a negative (positive) trend before (after) that date for both the central and western Pacific. While this is also true of the central Pacific on intra-seasonal timescales, the western Pacific shows a positive trend during the entire 20th century. In order to separate the internal and forced connectivity networks and to study their evolution through time, an ensemble of atmospheric general circulation model outputs is used. The results suggest that the main connectivity patterns captured in the reanalysis networks are due to the oceanically forced component, particularly on inter-annual timescales. Moreover, the atmospheric internal variability seems to play an important role in determining the intra-seasonal timescale networks.

scholarly journals Transient teleconnection event at the onset of a planet-encircling dust storm on Mars

2009 ◽  
Vol 27 (9) ◽  
pp. 3663-3676 ◽  
Author(s):  
O. Martínez-Alvarado ◽  
L. Montabone ◽  
S. R. Lewis ◽  
I. M. Moroz ◽  
P. L. Read
Keyword(s):  
Dust Storm ◽  
General Circulation ◽  
Thermal Emission ◽  
Three Dimensional ◽  
Circulation Model ◽  
Empirical Orthogonal Functions ◽  
State Variables ◽  
Orthogonal Functions ◽  
Teleconnection Patterns ◽  
Pressure Surface

Abstract. We use proper orthogonal decomposition (POD) to study a transient teleconnection event at the onset of the 2001 planet-encircling dust storm on Mars, in terms of empirical orthogonal functions (EOFs). There are several differences between this and previous studies of atmospheric events using EOFs. First, instead of using a single variable such as surface pressure or geopotential height on a given pressure surface, we use a dataset describing the evolution in time of global and fully three-dimensional atmospheric fields such as horizontal velocity and temperature. These fields are produced by assimilating Thermal Emission Spectrometer observations from NASA's Mars Global Surveyor spacecraft into a Mars general circulation model. We use total atmospheric energy (TE) as a physically meaningful quantity which weights the state variables. Second, instead of adopting the EOFs to define teleconnection patterns as planetary-scale correlations that explain a large portion of long time-scale variability, we use EOFs to understand transient processes due to localised heating perturbations that have implications for the atmospheric circulation over distant regions. The localised perturbation is given by anomalous heating due to the enhanced presence of dust around the northern edge of the Hellas Planitia basin on Mars. We show that the localised disturbance is seemingly restricted to a small number (a few tens) of EOFs. These can be classified as low-order, transitional, or high-order EOFs according to the TE amount they explain throughout the event. Despite the global character of the EOFs, they show the capability of accounting for the localised effects of the perturbation via the presence of specific centres of action. We finally discuss possible applications for the study of terrestrial phenomena with similar characteristics.

scholarly journals The Origin of Nonlinear Signatures of Planetary Wave Dynamics: Mean Phase Space Tendencies and Contributions from Non-Gaussianity

2007 ◽  
Vol 64 (11) ◽  
pp. 3987-4003 ◽  
Author(s):  
Christian Franzke ◽  
Andrew J. Majda ◽  
Grant Branstator
Keyword(s):  
Phase Space ◽  
General Circulation ◽  
General Framework ◽  
Planetary Wave ◽  
Low Frequency ◽  
Planetary Waves ◽  
Small Deviations ◽  
Wave Dynamics ◽  
Gaussian Case ◽  
The Impact

Abstract Mean phase space tendencies are investigated to systematically identify the origin of nonlinear signatures and the dynamical significance of small deviations from Gaussianity of planetary low-frequency waves. A general framework for the systematic investigation of mean phase space tendencies in complex geophysical systems is derived. In the special case of purely Gaussian statistics, this theory predicts that the interactions among the planetary waves themselves are the source of the nonlinear signatures in phase space, whereas the unresolved waves contribute only an amplitude-independent forcing, and cannot contribute to any nonlinear signature. The predictions of the general framework are studied for a simple stochastic climate model. This toy model has statistics that are very close to being Gaussian and a strong nonlinear signature in the form of a double swirl in the mean phase space tendencies of its low-frequency variables, much like recently identified signatures of nonlinear planetary wave dynamics in prototype and comprehensive atmospheric general circulation models (GCMs). As predicted by the general framework for the Gaussian case, the double swirl results from nonlinear interactions of the low-frequency variables. Mean phase space tendencies in a reduced space of a prototype atmospheric GCM are also investigated. Analysis of the dynamics producing nonlinear signatures in these mean tendencies shows a complex interplay between waves resolved in the subspace and unresolved waves. The interactions among the resolved planetary waves themselves do not produce the nonlinear signature. It is the interaction with the unresolved waves that is responsible for the nonlinear dynamics. Comparing this result with the predictions of the general framework for the Gaussian case shows that the impact of the unresolved waves is due to their small deviations from Gaussianity. This suggests that the observed deviations from Gaussianity, even though small, are dynamically relevant.

scholarly journals Nonnormal Thermohaline Circulation Dynamics in a Coupled Ocean–Atmosphere GCM

2008 ◽  
Vol 38 (3) ◽  
pp. 588-604 ◽  
Author(s):  
Eli Tziperman ◽  
Laure Zanna ◽  
Cecile Penland
Keyword(s):  
North Atlantic ◽  
General Circulation ◽  
Thermohaline Circulation ◽  
Initial Perturbation ◽  
Circulation Model ◽  
Empirical Orthogonal Functions ◽  
Transient Growth ◽  
The North ◽  
The North Atlantic ◽  
Reduced Space

Abstract Using the GFDL coupled atmosphere–ocean general circulation model CM2.1, the transient amplification of thermohaline circulation (THC) anomalies due to its nonnormal dynamics is studied. A reduced space based on empirical orthogonal functions (EOFs) of temperature and salinity anomaly fields in the North Atlantic is constructed. Under the assumption that the dynamics of this reduced space is linear, the propagator of the system is then evaluated and the transient growth of THC anomalies analyzed. Although the linear dynamics are stable, such that any initial perturbation eventually decays, nonnormal effects are found to result in a significant transient growth of temperature, salinity, and THC anomalies. The growth time scale for these anomalies is between 5 and 10 yr, providing an estimate of the predictability time of the North Atlantic THC in this model. There are indications that these results are merely a lower bound on the nonnormality of THC dynamics in the present coupled GCM. This seems to suggest that such nonnormal effects should be seriously considered if the predictability of the THC is to be quantitatively evaluated from models or observations. The methodology presented here may be used to produce initial perturbations to the ocean state that may result in a stricter estimate of ocean and THC predictability than the common procedure of initializing with an identical ocean state and a perturbed atmosphere.

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