399 research outputs found
Hilbert problems for the geosciences in the 21st century
No full textThe scientific problems posed by the Earth's fluid envelope, and its atmosphere, oceans, and the land surface that interacts with them are central to major socio-economic and political concerns as we move into the 21st century. It is natural, therefore, that a certain impatience should prevail in attempting to solve these problems. The point of this review paper is that one should proceed with all diligence, but not excessive haste: "festina lente," as the Romans said two thousand years ago, i.e. "hurry in a measured way." The paper traces the necessary progress through the solutions to the ten problems: 1. What is the coarse-grained structure of low-frequency atmospheric variability, and what is the connection between its episodic and oscillatory description? 2. What can we predict beyond one week, for how long, and by what methods? 3. What are the respective roles of intrinsic ocean variability, coupled ocean-atmosphere modes, and atmospheric forcing in seasonal-to-interannual variability? 4. What are the implications of the answer to the previous problem for climate prediction on this time scale? 5. How does the oceans' thermohaline circulation change on interdecadal and longer time scales, and what is the role of the atmosphere and sea ice in such changes? 6. What is the role of chemical cycles and biological changes in affecting climate on slow time scales, and how are they affected, in turn, by climate variations? 7. Does the answer to the question above give us some trigger points for climate control? 8. What can we learn about these problems from the atmospheres and oceans of other planets and their satellites? Correspondence to: M. Ghil ([email protected]) 9. Given the answer to the questions so far, what is the role of humans in modifying the clim..
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AAM The Movie – 7’56” video
No full textThis video is a supplement to Chapter 6,
Ghil, M., A. Groth, D. Kondrashov, and A. W. Robertson, 2018: Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view, in
The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction, A. W. Robertson and F. Vitart (Eds.), Elsevier.
It provides substantial evidence for the generation of 40–50-day atmospheric variability in the Northern Hemisphere (NH) mid-latitudes as a result of an oscillatory instability in the flow of the prevailing westerlies over large-scale topography.
History
The video was originally prepared as part of the research published in the Journal of Atmospheric Sciences, in a set of two papers:
1. Marcus, S. L., M. Ghil, and J. O. Dickey, 1994: The extratropical 40–50-day oscillation in the UCLA general circulation model. Part I: Atmospheric angular momentum. J. Atmos. Sci., 51, 1431–1446.
2. Marcus, S. L., M. Ghil, and J. O. Dickey, 1996: The extratropical 40-day oscillation in the UCLA general circulation model. Part II: Spatial structure. J. Atmos. Sci., 53, 1993–2014.
The video could not be published in the mid-1990s, at a time when the journals of the American Meteorological Society did not allow the inclusion of multimedia supplements. Its scientific value is still considerable today, and the video is published here with the explicit consent of its original authors, M. Ghil, S. L. Marcus, J. O. Dickey and C. L. Keppenne.
The video was produced by the Audiovisual Services Office of the Jet Propulsion Laboratory in 1991. Full credits appear at the end of the video, and its contents are described below.
Description
To test the theory of NH extratropical oscillations developed in simpler models, Marcus et al. (1994, 1996) studied a 3-year perpetual-January simulation that had been performed with a version of the UCLA general circulation model (GCM) in which no self-sustained Madden-Julian Oscillation (MJO) was apparent in the tropics. A robust 40-day oscillation in atmospheric angular momentum (AAM) was found to arise in the model's NH mid-latitudes when standard topography is present. Three shorter runs with no topography produced no intraseasonal oscillation; this result is consistent with a topographic origin for the NH extratropical oscillation in the standard model. The spatial structure of the circulation anomalies associated with the model's extratropical oscillation is shown in the present video, as displayed in several model-simulated fields, namely 500-hPa geopotential heights, 250-hPa streamfunction, and surface pressure torques.
The oscillation is dominated by a standing wavenumber-2 pattern, which undergoes a predominantly barotropic, tilted-trough vacillation. High values of AAM are associated with low 500-hPa heights over the northeast Pacific and the North Atlantic oceans, and vice versa. These flow patterns resemble the configurations seen in the Charney and DeVore (1979) simple model, shown as Fig. 1b in the main text of Ch. 6 above. The NE–SW-tilting and NW–SE-tilting phases in the video's 500-hPa fields are strongly reminiscent of the extremes and intermediate phases of the 40-day oscillation that arises by Hopf bifurcation from the blocked equilibrium in the Legras and Ghil (1985) model; see discussion of Ghil et al. (2003, Fig. 3).
References
Charney, J. G., and J. G. DeVore, 1979: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci., 36, 1205–1216.
Ghil, M., D. Kondrashov, F. Lott, and A. W. Robertson, 2003: Intraseasonal oscillations in the mid-latitudes: observations, theory and GCM results. In: Proc. ECMWF/CLIVAR Workshop on Simulation and Prediction of Intra-Seasonal Variability with Emphasis on the MJO, 3–6 Nov. 2003, ECMWF, Reading, UK. 35–53.
Legras, B., and M. Ghil, 1985: Persistent anomalies, blocking and variations in atmospheric predictability. J. Atmos. Sci., 42, 433–471
Geophysical flows as dynamical systems: the influence of Hide's experiments
No full textMichael Ghil, Peter L Read and Leonard A Smith recount the many and various ways that Raymond Hide has influenced their life and work in geophysical fluid dynamics, meteorology, climatology and planetary sciences, as well as in developing the study of dynamical systems in general
Estimating model evidence using data assimilation
No full textWe review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual model–which corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurred–and a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensemble-DA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble four-dimensional variational smoother (En-4D-Var), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated time-dependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz three-variable convection model (L63), and (ii) the Lorenz 40-variable midlatitude atmospheric dynamics model (L95). The numerical results of these three DA-based methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DA-based methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution
Reply to Roe and Baker's comment on "Another look at climate sensitivity" by Zaliapin and Ghil (2010)
No full textG. H. Roe and M. B. Baker (hereafter R&B) claim that analysis of a global linear approximation to the climate system allows one to conclude that the quest for reliable climate predictions is futile. We insist that this quest is important and requires a proper understanding of the roles of both linear and nonlinear methods in climate dynamics
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Data assimilation as a nonlinear dynamical systems problem : stability and convergence of the prediction-assimilation system
No full textWe study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method
Endogenous Business Cycles and the Economic Response to Exogenous Shocks
No full textIn this paper, we investigate the macroeconomic response to exogenous shocks, namely natural disasters and stochastic productivity shocks. To do so, we make use of an endogenous business cycle model in which cyclical behavior arises from the investment–profit instability; the amplitude of this instability is constrained by the increase in labor costs and the inertia of production capacity and thus results in a finite-amplitude business cycle. This model is found to exhibit a larger response to natural disasters during expansions than during recessions, because the exogenous shock amplifies pre-existing disequilibria when occurring during expansions, while the existence of unused resources during recessions allows for damping the shock. Our model also shows a higher output variability in response to stochastic productivity shocks during expansions than during recessions. This finding is at odds with the classical real-cycle theory, but it is supported by the analysis of quarterly U.S. Gross Domestic Product series; the latter series exhibits, on average, a variability that is 2.6 times larger during expansions than during recessions.Business cycles, Natural disasters, Productivity shocks, Output variability
Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system
No full textWe study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method. © 2008 American Institute of Physics
Comment on "Another look at climate sensitivity" by Zaliapin and Ghil (2010)
No full textAbstract. Zaliapin and Ghil (hereafter, ZG) claim that the linearity of the climate feedback model in Roe and Baker (2007) (hereafter, RB) invalidates our derivation of the well-known skewed shapes of published probability distributions (pdfs) of climate sensitivity. We show here that linearity is fully justified. Nonlinearity could be of some importance only if the focus is on exotic and improbable events, which appear to be the focus of ZG, instead of the sensitivity pdfs, which were the focus of RB.
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Unified Notation for Data Assimilation: Operational, Sequential and Variational
No full textThe need for unified notation in atmospheric and oceanic data assimilation arises from the field's rapid theoretical expansion and the desire to translate it into practical applications. Self-consistent notation is proposed that bridges sequential and variational methods, on the one hand, and operational usage, on the other. Over various other mottoes for this risky endeavor, the authors selected: "When I use a word," Humpty Dumpty said, in rather a scornful voice tone, "it means just what I choose it to mean --- neither more nor less." Lewis Carroll, 1871. 1 J. Met. Soc. Japan, Special Issue on "Data Assimilation in Meteorology and Oceanography: Theory and Practice." Vol. 75, No. 1B, pp. 181--189, 1997. 2 Corresponding author. 3 Current affiliation: CNES, 2, place Maurice Quentin, 75039 Paris Cedex 01, France. 1 J. Met. Soc. Japan, (1997), K. Ide, P. Courtier, M. Ghil and A.C. Lorenc 2 1. Introduction and motivation Model-based assimilation of observations, or data assimilati..
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