The ECMWF Ensemble Prediction System: Looking Back (more than) 25 Years and Projecting Forward 25 Years

This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast system. In particular, the reasons for the development of singular vectors and stochastic physics - particular features of the ECMWF Ensemble Prediction System - are discussed. The author speculates about the development and use of ensemble prediction in the next 25 years.Comment: Submitted to Special Issue of the Quarterly Journal of the Royal Meteorological Society: 25 years of ensemble predictio

On the use of simple dynamical systems for climate predictions: A Bayesian prediction of the next glacial inception

Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on complicated aspects of atmosphere and ocean dynamics, skillful prediction also requires a phenomenological approach, particularly for very slow processes, such as glacial-interglacial cycles. Phenomenological models are often represented as low-order dynamical systems. These are tractable, and a rich source of insights about climate dynamics, but they also ignore large bodies of information on the climate system, and their parameters are generally not operationally defined. Consequently, if they are to be used to predict actual climate system behaviour, then we must take very careful account of the uncertainty introduced by their limitations. In this paper we consider the problem of the timing of the next glacial inception, about which there is on-going debate. Our model is the three-dimensional stochastic system of Saltzman and Maasch (1991), and our inference takes place within a Bayesian framework that allows both for the limitations of the model as a description of the propagation of the climate state vector, and for parametric uncertainty. Our inference takes the form of a data assimilation with unknown static parameters, which we perform with a variant on a Sequential Monte Carlo technique (`particle filter'). Provisional results indicate peak glacial conditions in 60,000 years.Comment: superseeds the arXiv:0809.0632 (which was published in European Reviews). The Bayesian section has been significantly expanded. The present version has gone scientific peer review and has been published in European Physics Special Topics. (typo in DOI and in Table 1 (psi -> theta) corrected on 25th August 2009

Random fluctuation leads to forbidden escape of particles

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.Comment: 6 pages, 6 figures - Up to date with corrections suggested by referee

Revision of TR-09-25: A Hybrid Variational/Ensemble Filter Approach to Data Assimilation

Two families of methods are widely used in data assimilation: the four dimensional variational (4D-Var) approach, and the ensemble Kalman filter (EnKF) approach. The two families have been developed largely through parallel research efforts. Each method has its advantages and disadvantages. It is of interest to develop hybrid data assimilation algorithms that can combine the relative strengths of the two approaches. This paper proposes a subspace approach to investigate the theoretical equivalence between the suboptimal 4D-Var method (where only a small number of optimization iterations are performed) and the practical EnKF method (where only a small number of ensemble members are used) in a linear Gaussian setting. The analysis motivates a new hybrid algorithm: the optimization directions obtained from a short window 4D-Var run are used to construct the EnKF initial ensemble. The proposed hybrid method is computationally less expensive than a full 4D-Var, as only short assimilation windows are considered. The hybrid method has the potential to perform better than the regular EnKF due to its look-ahead property. Numerical results show that the proposed hybrid ensemble filter method performs better than the regular EnKF method for both linear and nonlinear test problems

Control of Systems With Slow Actuators Using Time Scale Separation

This paper addresses the problem of controlling a nonlinear plant with a slow actuator using singular perturbation method. For the known plant-actuator cascaded system the proposed scheme achieves tracking of a given reference model with considerably less control demand than would otherwise result when using conventional design techniques. This is the consequence of excluding the small parameter from the actuator dynamics via time scale separation. The resulting tracking error is within the order of this small parameter. For the unknown system the adaptive counterpart is developed based on the prediction model, which is driven towards the reference model by the control design. It is proven that the prediction model tracks the reference model with an error proportional to the small parameter, while the prediction error converges to zero. The resulting closed-loop system with all prediction models and adaptive laws remains stable. The benefits of the approach are demonstrated in simulation studies and compared to conventional control approaches

Methods and advances in the study of aeroelasticity with uncertainties

AbstractUncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncertainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the μ method. It covers the numerical calculation algorithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation

Lectures on Holographic Space Time

Summary of three talks on the Holographic Space Time models of early universe cosmology, particle physics, and the asymptotically de Sitter final state of our universe.Comment: LaTex2e. 32 page