753 research outputs found

    Application of Differential Transform Method for El Nino Southern Oscillation (ENSO) Model with compared Adomian Decomposition and Variational Iteration Methods

    Full text link
    We consider two nonlinear El Nino Southern Oscillation (ENSO) model to obtain approximate solutions with differential transform method for the first time. Efficiency, accuracy and error rates of solutions are compared with analytic solution, variational iteration and adomian decomposition solutions on the given tables and figures.Comment: 12 pages, 10 figure

    Techniques of linear prediction, with application to oceanic and atmospheric fields in the tropical Pacific

    No full text
    The problem of constructing optimal linear prediction models by multivariance regression methods is reviewed. It is well known that as the number of predictors in a model is increased, the skill of the prediction grows, but the statistical significance generally decreases. For predictions using a large number of candidate predictors, strategies are therefore needed to determine optimal prediction models which properly balance the competing requirements of skill and significance. The popular methods of coefficient screening or stepwise regression represent a posteriori predictor selection methods and therefore cannot be used to recover statistically significant models by truncation if the complete model, including all predictors, is statistically insignificant. Higher significance can be achieved only by a priori reduction of the predictor set. To determine the maximum number of predictors which may be meaningfully incorporated in a model, a model hierarchy can be used in which a series of best fit prediction models is constructed for a (prior defined) nested sequence of predictor sets, the sequence being terminated when the significance level either falls below a prescribed limit or reaches a maximum value. The method requires a reliable assessment of model significance. This is characterized by a quadratic statistic which is defined independently of the model skill or artificial skill. As an example, the method is applied to the prediction of sea surface temperature anomalies at Christmas Island (representative of sea surface temperatures in the central equatorial Pacific) and variations of the central and east Pacific Hadley circulation (characterized by the second empirical orthogonal function (EOF) of the meridional component of the trade wind anomaly field) using a general multiple‐time‐lag prediction matrix. The ordering of the predictors is based on an EOF sequence, defined formally as orthogonal variables in the composite space of all (normalized) predictors, irrespective of their different physical dimensions, time lag, and geographic position. The choice of a large set of 20 predictors at 12 time lags yields significant predictability only for forecast periods of 3 to 5 months. However, a prior reduction of the predictor set to 4 predictors at 10 time lags leads to 95% significant predictions with skill values of the order of 0.4 to 0.7 up to 6 or 8 months. For infinitely long time series the construction of optimal prediction models reduces essentially to the problem of linear system identification. However, the model hierarchies normally considered for the simulation of general linear systems differ in structure from the model hierarchies which appear to be most suitable for constructing pure prediction models. Thus the truncation imposed by statistical significance requirements can result in rather different models for the two cases. The relation between optimal prediction models and linear dynamical models is illustrated by the prediction of east‐west sea level changes in the equatorial Pacific from wind field anomalies. It is shown that the optimal empirical prediction is statistically consistent in this case with both the first‐order relaxation and damped oscillator models recently proposed by McWilliams and Gent (but with somewhat different model parameters than suggested by the authors). Thus the data do not allow a distinction between the two physical models; the simplest acceptable model is the first‐order damped response. Finally, the problem of estimating forecast skill is discussed. It is usually stated that the forecast skill is smaller than the true skill, which in turn is smaller than the hindcast skill, by an amount which in both cases is approximately equal to the artificial skill. However, this result applies to the mean skills averaged over the ensemble of all possible hindcast data sets, given the true model. Under the more appropriate side condition of a given hindcast data set and an unknown true model, the estimation of the forecast skill represents a problem of statistical inference and is dependent on the assumed prior probability distribution of true models. The Bayesian hypothesis of a uniform prior distribution yields an average forecast skill equal to the hindcast skill, but other (equally acceptable) assumptions yield lower forecast skills more compatible with the usual hindcast‐averaged expressio

    A Convenient Adomian-Pade Technique for the Nonlinear Oscillator Equation

    Get PDF
    Very recently, the convenient way to calculate the Adomian series was suggested. This paper combines this technique and the Pade approximation to develop some new iteration schemes. Then, the combined method is applied to nonlinear models and the residual functions illustrate the accuracies and conveniences

    Conceptual models of the climate : 2001 program of studies in geophysical fluid dynamics

    Get PDF
    In 2001, the Geophysical Fluid Dynamics Summer Study Program grappled with Conceptual Models of the Climate. Eli Tziperman (Weizman Institute), Paola Cessi (Scripps Institution of Oceanography) and Ray Pierre- Humbert (University of Chicago) provided the principal lectures. This introduction gave us all a glimpse into the complex problem of the climate, both in the present, past and future, and even on other planets. As always, the next weeks of the program were filled with many seminars from the visitors, and culminated in the fellow's reports

    The Laplace-Adomian-Pade Technique for the ENSO Model

    Get PDF
    The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation

    2000 days of SMOS at the Barcelona Expert Centre: a tribute to the work of Jordi Font

    Get PDF
    Soil Moisture and Ocean Salinity (SMOS) is the first satellite mission capable of measuring sea surface salinity and soil moisture from space. Its novel instrument (the L-band radiometer MIRAS) has required the development of new algorithms to process SMOS data, a challenging task due to many processing issues and the difficulties inherent in a new technology. In the wake of SMOS, a new community of users has grown, requesting new products and applications, and extending the interest in this novel brand of satellite services. This paper reviews the role played by the Barcelona Expert Centre under the direction of Jordi Font, SMOS co-principal investigator. The main scientific activities and achievements and the future directions are discussed, highlighting the importance of the oceanographic applications of the mission.Peer ReviewedPostprint (published version

    Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part II: Stochastic Hopf Bifurcation

    Get PDF
    The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via decomposition formulas in terms of RP resonances. Stochastic analysis techniques relying on the theory of Markov semigroups for the study of the RP spectrum and a rigorous reduction method is presented in Part I. This framework is here applied to study a stochastic Hopf bifurcation in view of characterizing the statistical properties of nonlinear oscillators perturbed by noise, depending on their stability. In light of the H\"ormander theorem, it is first shown that the geometry of the unperturbed limit cycle, in particular its isochrons, is essential to understand the effect of noise and the phenomenon of phase diffusion. In addition, it is shown that the spectrum has a spectral gap, even at the bifurcation point, and that correlations decay exponentially fast. Explicit small-noise expansions of the RP eigenvalues and eigenfunctions are then obtained, away from the bifurcation point, based on the knowledge of the linearized deterministic dynamics and the characteristics of the noise. These formulas allow one to understand how the interaction of the noise with the deterministic dynamics affect the decay of correlations. Numerical results complement the study of the RP spectrum at the bifurcation, revealing useful scaling laws. The analysis of the Markov semigroup for stochastic bifurcations is thus promising in providing a complementary approach to the more geometric random dynamical system approach. This approach is not limited to low-dimensional systems and the reduction method presented in part I is applied to a stochastic model relevant to climate dynamics in part III
    • 

    corecore