NG32A-01 INVITED
The Phase-Space Approach to Low-Frequency Climate Variability: Particles and Waves, Model Hierarchies and Data Sets
Four decades ago, E. N. Lorenz provided some approximate limits to atmospheric predictability. The details---in space and time---of atmospheric flow fields are lost after about 10 days. Certain gross flow features, however, persist at times for longer and recur from time to time, giving hope for their extended prediction. Over the last two decades, numerous attempts have been made to describe, understand and predict these persistent and recurrent features. The attempts have involved, on the one hand, systematic improvements in numerical weather prediction (NWP) by increasing the spatial resolution and physical faithfulness in the detailed models used for this prediction. On the other hand, theoretical attempts motivated by the same goal have involved the study of the large-scale atmospheric motions' phase space and of its inhomogeneities. These "coarse-graining" studies have addressed observed as well as simulated atmospheric data sets. Two distinct approaches have been used in these studies: the episodic or intermittent and the oscillatory or periodic. The intermittency approach describes multiple-flow (or weather) regimes, their persistence and recurrence, and the Markov chain of transitions among them. The periodicity approach studies intraseasonal oscillations, with periods of 15--70 days, and their predictability. We review these two approaches, "particles" vs. "waves," in the quantum physics analogy alluded to in the title of this talk, discuss their complementarity, and outline unsolved problems. Considerable emphasis is also put on the complementarity between dynamical and statistical aspects of describing, understanding and predicting the state space structure of the atmosphere and oceans, across a hierarchy of models and in observations. Recent results point to the robustness of Markov chains of regimes across a hierarchy of models and in multi- annual, reanalysis-based data sets. Preferential exit directions from several regimes (i) confirm the importance of unstable fixed points as the dynamical origin of these regimes; and (ii) help extended prediction by advanced statistical algorithms. Combining such statistical predictions with the increased skill of state-of-the-art NWP models is an interesting challenge for nonlinear dynamicists, numerical modelers and data assimilators alike. http://www.atmos.ucla.edu/tcd/
NG32A-02
A delay differential model of ENSO variability: parametric instability and the distribution of extremes
We consider a Delay Differential Equation (DDE) model for El-Nino Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in the ENSO dynamics: delayed negative feedback and seasonal forcing. Descriptive and metric stability analyses of the model are performed in a complete 3D space of its physically relevant parameters. Existence of two regimes --- stable and unstable --- is reported. The domains of the regimes are separated by a sharp neutral curve in the parameter space. The detailed structure of the neutral curve become very complicated (possibly fractal), and individual trajectories within the unstable region become highly complex (possibly chaotic) as the atmosphere-ocean coupling increases. In the unstable regime, spontaneous transitions in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values occur, for purely periodic, seasonal forcing. This indicates (via the continuous dependence theorem) the existence of numerous unstable solutions responsible for the complex dynamics of the system. In the stable regime, only periodic solutions are found. Our results illustrate the role of the distinct parameters of ENSO variability, such as strength of seasonal forcing vs. atmosphere ocean coupling and propagation period of oceanic waves across the Tropical Pacific. The model reproduces, among other phenomena, the Devil's bleachers (caused by period locking) documented in other ENSO models, such as nonlinear PDEs and GCMs, as well as in certain observations. We expect such behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.
NG32A-03
First Passage Time (FPT) for Determining Large Ocean Model Predictability
First passage time (FPT) is used to evaluate large ocean (or atmosphere) model predictability. FPT is defined as the time period when the prediction error first exceeds a pre-determined criterion (i.e., the tolerance level). It depends not only on the instantaneous error growth, but also on the noise level, the initial error, and tolerance level. The model predictability skill is then represented by a single scalar, FPT. The longer the FPT, the higher the model predictability skill is. A theoretical framework on the base of the backward Fokker-Planck equation is developed to determine FPT. In this paper, we investigate error propagation near an unstable equilibrium state (classified as an unstable focus) for spatially uncorrelated and correlated finite-amplitude initial perturbations using short- (up to several weeks) and intermediate (up to two months) range forecast ensembles produced by a barotropic regional ocean model. An ensemble of initial perturbations is generated by the Latin Hypercube design strategy, and its optimal size is estimated through the Kullback - Liebler distance (the relative entropy). Although the ocean model is simple, the prediction error (PE) demonstrates non-trivial behavior similar to that existing in 3D ocean circulation models. In particular, in the limit of zero horizontal viscosity, the PE at first decays with time for all scales due to dissipation caused by nonlinear bottom friction, and then grows faster than [quasi]-exponentially. Statistics of a prediction time scale (i.e., FPT) quickly depart from Gaussian (the linear predictability regime) and becomes Weibullian (the non-linear predictability regime) as amplitude of initial perturbations grows. A transition from linear to non-linear predictability is clearly detected by the specific behavior of FPT variance. A new analytical formula for the model predictability horizon is introduced and applied to estimate the limit of predictability for the ocean model. References Chu, P.C., Ivanov, L.M., Margolina, T.M., Melnichenko, O.V., 2002. On probabilistic stability of an atmospheric model to various amplitude perturbations. J. Atmos. Sci. , 59, 2860-2873. Chu, P.C., L. Ivanov, L. Kantha, O. Melnichenko, and Y. Poberezhny, 2002. Power law decay in model predictability skill. Geophysical Research Letters, 29 (15), 10.1029/2002GLO14891 Chu, P.C., Ivanov, L. M., 2005. Statistical characteristics of irreversible predictability time in regional ocean models. Non. Proc. Geophys., 12, 1-10. Ivanov, L.M., and P.C. Chu, 2007. On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions. Dyn. Atmos. Oceans, in press. http://www.oc.nps.navy.mil/~chu
NG32A-04 INVITED
Systematic Identification of Metastable Regimes in Atmospheric Data Sets
A pronounced characteristic of the atmospheric circulation is its irregularity, visible in the daily change of the weather. Despite this chaotic behaviour it is well known that certain flow structures tend to occur over and over again. These recurring flow structures are commonly called atmospheric flow regimes and inspired a whole body of work. In this talk I will present a novel method which simultanously estimates possible metastable states, the Markov transition matrix for the switching between the metastable states and the corresponding local Principal Components. This methodology is based on combining Hidden Markov Models and Principal Component Analysis. If the Markov transition matrix possesses metastable (or quasi-persistent) states, we identify these as regimes. In this perspective, regimes can be present even though the observed data has a nearly Gaussian (unimodal) probability distribution. We apply this procedure to data from a model of barotropic flow over topography with a large scale mean flow. This model exhibits regime behaviour for sufficiently high topography. The regime structure and their dynamical significance will be discussed.
NG32A-05
Relating Regime Structure to Probability Distribution and Preferred Structure of Small Errors in a Large Atmospheric GCM
The probability distribution (pdf) of errors is followed in identical twin studies using the COLA T63 AGCM, integrated with observed SST for 15 recent winters. 30 integrations per winter (for 15 winters) are available with initial errors that are extremely small. The evolution of the pdf is tested for multi-modality, and the results interpreted in terms of clusters / regimes found in: (a) the set of 15x30 integrations mentioned, and (b) a larger ensemble of 55x15 integrations made with the same GCM using the same SSTs. The mapping of pdf evolution and clusters is also carried out for each winter separately, using the clusters found in the 55-member ensemble for the same winter alone. This technique yields information on the change in regimes caused by different boundary forcing (Straus and Molteni, 2004; Straus, Corti and Molteni, 2006). Analysis of the growing errors in terms of baroclinic and barotropic components allows for interpretation of the corresponding instabilities.
NG32A-06
Tracking the Spatiotemporal Evolution of Convective Instabilities in AMIP Simulations
Land-atmosphere interactions exhibit regionally the nonlinear dynamical behavior of self-organizing phenomena. A critical research need is to track and measure the complex space-time lifecycle of land-forced convective instabilities from their origin to the unfolding of clouds and the materialization of rainfall across the landscape. The co-moving Lyapunov Exponent characterizes the propagation of an initially localized perturbation in space- time from a physical dynamics perspective rather than relying on the statistics of specific realizations, and hence the deductive propagation velocity depicts a profile of the predictability horizon. Analysis of results of an application of this methodology to a 16-year long AMIP simulation is presented followed by discussion of how to translate our findings to improve model parameterizations.
NG32A-07
The Multi-Ensemble Approach: the NAEFS Example
The North American ensemble Forecasting System is the combination of two Ensemble Prediction Systems (EPS) coming from operational centers: Canadian Meteorological Centre (CMC) and National Centers for Environmental Prediction (NCEP). This system provides forecasts of up to two weeks and should improve the predictability skill of the probabilistic system, especially for the second week. First, a comparison between the two components of the NAEFS is performed for several atmospheric variables with `objective' verification tools developed at CMC (CRPS and reliability-resolution decomposition, reduced centered random variable, and confidence interval estimated by bootstrap methods). One observes that CMC system is more reliable, especially due to a better ensemble dispersion, while NCEP system has better probabilistic resolution. The NAEFS, compared to CMC and NCEP EPSs, shows significant improvements both in term of reliability and resolution. The predictability has been improved by one to two days in the second week. That improvement is not only due to the increased ensemble size in the EPS, from 20 members to 40 in the present case, but also to the combination of different models and initial condition perturbations. By randomly mixing members from CMC and NCEP systems in a 20-members EPS, an intrinsic skill improvement of the system is observed.
NG32A-08
Unstable Periodic Orbits and Predictability in a Large Atmospheric Dynamical System
The instability of periodic orbits in a two-layer quasi-geostrophic model has been studied to understand the structure of the chaotic attractors and the predictability of the system. As a step toward understanding the structure of the chaotic solutions of general circulation models, the two-layer model is studied for various spectral truncations by including many scales of motion. The model is selected to be large but still suitable to be studied as a dynamical system. The instability and bifurcations of periodic orbits for different spectral truncation levels and forcings have been studied, and multiple unstable periodic orbits have been found for certain forcings. The role of such unstable periodic orbits in determining the structure of the chaotic solutions and the growth and structure of errors are discussed. The change in the nature of the instability of the periodic solutions as the truncation level varies in the model is emphasized.