Publications

2010
Strounine, K., Sergey Kravtsov, Dmitri Kondrashov, and Michael Ghil. 2010. “Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance.” Physica D: Nonlinear Phenomena 239 (3). Elsevier: 145–166. Abstract

Low-frequency variability (LFV) of the atmosphere refers to its behavior on time scales of 10–100 days, longer than the life cycle of a mid-latitude cyclone but shorter than a season. This behavior is still poorly understood and hard to predict. The present study compares various model reduction strategies that help in deriving simplified models of LFV. Three distinct strategies are applied here to reduce a fairly realistic, high-dimensional, quasi-geostrophic, 3-level (QG3) atmospheric model to lower dimensions: (i) an empirical–dynamical method, which retains only a few components in the projection of the full QG3 model equations onto a specified basis, and finds the linear deterministic and the stochastic corrections empirically as in Selten (1995) [5]; (ii) a purely dynamics-based technique, employing the stochastic mode reduction strategy of Majda et al. (2001) [62]; and (iii) a purely empirical, multi-level regression procedure, which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in Kravtsov et al. (2005) [3]. The empirical–dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi-level regression models; the extended Kalman filter was used for the parameter estimation. Overall, the reduced models perform better when more statistical information is used in the model construction. Thus, the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full QG3 model’s LFV, i.e. its autocorrelations and spectra, as well as the nonlinear properties, i.e. the persistent flow regimes that induce non-Gaussian features in the model’s probability density function. The empirical–dynamical models capture the basic statistical properties of the full model’s LFV, such as the variance and integral correlation time scales of the leading LFV modes, as well as some of the regime behavior features, but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes. Dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical–dynamical models, but do much less well on the full QG3 model’s nonlinear dynamics. These results are discussed in terms of their implications for a better understanding and prediction of LFV.

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Kondrashov, Dmitri, Sergey Kravtsov, and Michael Ghil. 2010. “Signatures of nonlinear dynamics in an idealized atmospheric model.” Journal of the Atmospheric Sciences 68 (1): 3–12.
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Zaliapin, Ilya, Efi Foufoula-Georgiou, and Michael Ghil. 2010. “Transport on river networks: A dynamic tree approach.” Journal of Geophysical Research: Earth Surface 115 (F2). Wiley Online Library.
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2009
Ni, Binbin, Yuri Shprits, Tsugunobu Nagai, Richard Thorne, Yue Chen, Dmitri Kondrashov, and Hee-jeong Kim. 2009. “Reanalyses of the radiation belt electron phase space density using nearly equatorial CRRES and polar-orbiting Akebono satellite observations.” Journal of Geophysical Research: Space Physics 114 (A5): n/a–n/a. Publisher's Version
Kravtsov, Sergey, Dmitri Kondrashov, and Michael Ghil. 2009. “Empirical model reduction and the modelling hierarchy in climate dynamics and the geosciences.” Stochastic physics and climate modelling. Cambridge University Press, Cambridge, 35–72. Abstract
Modern climate dynamics uses a two-fisted approach in attacking and solving the problems of atmospheric and oceanic flows. The two fists are: (i) observational analyses; and (ii) simulations of the geofluids, including the coupled atmosphere–ocean system, using a hierarchy of dynamical models. These models represent interactions between many processes that act on a broad range of spatial and time scales, from a few to tens of thousands of kilometers, and from diurnal to multidecadal, respectively. The evolution of virtual climates simulated by the most detailed and realistic models in the hierarchy is typically as difficult to interpret as that of the actual climate system, based on the available observations thereof. Highly simplified models of weather and climate, though, help gain a deeper understanding of a few isolated processes, as well as giving clues on how the interaction between these processes and the rest of the climate system may participate in shaping climate variability. Finally, models of intermediate complexity, which resolve well a subset of the climate system and parameterise the remainder of the processes or scales of motion, serve as a conduit between the models at the two ends of the hierarchy. We present here a methodology for constructing intermediate mod- els based almost entirely on the observed evolution of selected climate fields, without reference to dynamical equations that may govern this evolution; these models parameterise unresolved processes as multi- variate stochastic forcing. This methodology may be applied with equal success to actual observational data sets, as well as to data sets resulting from a high-end model simulation. We illustrate this methodology by its applications to: (i) observed and simulated low-frequency variability of atmospheric flows in the Northern Hemisphere; (ii) observed evo- lution of tropical sea-surface temperatures; and (iii) observed air–sea interaction in the Southern Ocean. Similar results have been obtained for (iv) radial-diffusion model simulations of Earth’s radiation belts, but are not included here because of space restrictions. In each case, the reduced stochastic model represents surprisingly well a variety of linear and nonlinear statistical properties of the resolved fields. Our methodology thus provides an efficient means of constructing reduced, numerically inexpensive climate models. These models can be thought of as stochastic–dynamic prototypes of more complex deterministic models, as in examples (i) and (iv), but work just as well in the situation when the actual governing equations are poorly known, as in (ii) and (iii). These models can serve as competitive prediction tools, as in (ii), or be included as stochastic parameterisations of certain processes within more complex climate models, as in (iii). Finally, the methodology can be applied, with some modifications, to geophysical problems outside climate dynamics, as illustrated by (iv).
Vivaldo, Gianna, Carla Taricco, Silvia Alessio, and Michael Ghil. 2009. “Accurate dating of the Gallipoli Terrace (Ionian Sea) sediments as a basis for reliable climate proxy series.” PAGES News 17 (1). PAGES International Project Office: 8–9.
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Simonnet, Eric, Henk A. Dijkstra, and Michael Ghil. 2009. “Bifurcation analysis of ocean, atmosphere, and climate models.” Handbook of numerical analysis, edited by R. Temam and J. Tribbia, 14: 187–229. Elsevier.
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Deremble, Bruno, Fabio D'Andrea, and Michael Ghil. 2009. “Fixed points, stable manifolds, weather regimes, and their predictability.” Chaos: An Interdisciplinary Journal of Nonlinear Science 19 (4). AIP Publishing: 043109. Publisher's Version
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Zhang, Yunyan, Bjorn Stevens, Brian Medeiros, and Michael Ghil. 2009. “Low-cloud fraction, lower-tropospheric stability, and large-scale divergence.” Journal of Climate 22 (18): 4827–4844.
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Taricco, Carla, Michael Ghil, Silvia Alessio, and Gianna Vivaldo. 2009. “Two millennia of climate variability in the Central Mediterranean.” Climate of the Past 5 (5). European Geosciences Union: 171–181. Abstract

This experimental work addresses the need for high-resolution, long and homogeneous climatic time series that facilitate the study of climate variability over time scales of decades to millennia. We present a high-resolution record of foraminiferal d18O from a Central-Mediterranean sediment core that covers the last two millennia. The record was analyzed using advanced spectral methods and shows highly significant oscillatory components with periods of roughly 600, 350, 200, 125 and 11 years. Over the last millennium, our data show several features related to known climatic periods, such as the Medieval Optimum, the Little Ice Age and a recent steep variation since the beginning of the Industrial Era. During the preceding millennium, the d18O series also reveals a surprising maximum at about 0 AD, suggesting low temperatures at that time. This feature contradicts widely held ideas about the Roman Classical Period; it is, therefore, discussed at some length, by reviewing the somewhat contradictory evidence about this period. We compare the d18O record with an alkenone-derived sea surface temperature time series, obtained from cores extracted in the same Central-Mediterranean area (Gallipoli Terrace, Ionian Sea), as well as with Italian and other European temperature reconstructions over the last centuries. Based on this comparison, we show that the long-term trend and the 200-y oscillation in the records are temperature driven and have a dominant role in describing temperature variations over the last two millennia.

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Bordi, Isabella, Klaus Fraedrich, Michael Ghil, and Alfonso Sutera. 2009. “Zonal flow regime changes in a GCM and in a simple quasigeostrophic model: The role of stratospheric dynamics.” Journal of the Atmospheric Sciences 66 (5): 1366–1383.
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2008
Hillerbrand, Rafaela, and Michael Ghil. 2008. “Anthropogenic climate change: Scientific uncertainties and moral dilemmas.” Physica D 237 (14-17): 2132–2138. Abstract

This paper considers the role of scientific expertise and moral reasoning in the decision making process involved in climate-change issues. It points to an unresolved moral dilemma that lies at the heart of this decision making, namely how to balance duties towards future generations against duties towards our contemporaries. At present, the prevailing moral and political discourses shy away from addressing this dilemma and evade responsibility by falsely drawing normative conclusions from the predictions of climate models alone. We argue that such moral dilemmas are best addressed in the framework of Expected Utility Theory. A crucial issue is to adequately incorporate into this framework the uncertainties associated with the predicted consequences of climate change on the well-being of future generations. The uncertainties that need to be considered include those usually associated with climate modeling and prediction, but also moral and general epistemic ones. This paper suggests a way to correctly incorporate all the relevant uncertainties into the decision making process.

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Ghil, Michael, Ilya Zaliapin, and Barbara Coluzzi. 2008. “Boolean delay equations: A simple way of looking at complex systems.” Physica D: Nonlinear Phenomena 237 (23). Elsevier: 2967–2986.
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Hallegatte, Stéphane, Michael Ghil, Patrice Dumas, and Jean-Charles Hourcade. 2008. “Business cycles, bifurcations and chaos in a neo-classical model with investment dynamics.” Journal of Economic Behavior & Organization 67 (1): 57–77. Abstract

This paper presents a non-equilibrium dynamic model (NEDyM) that introduces investment dynamics and non-equilibrium effects into a Solow growth model. NEDyM can reproduce several typical economic regimes and, for certain ranges of parameter values, exhibits endogenous business cycles with realistic characteristics. The cycles arise from the investment-profit instability and are constrained by the increase in labor costs and the inertia of production capacity. For other parameter ranges, the model exhibits chaotic behavior. These results show that complex variability in the economic system may be due to deterministic, intrinsic factors, even if the long-term equilibrium is neo-classical in nature.

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Ghil, Michael, Mickaël D. Chekroun, and Eric Simonnet. 2008. “Climate dynamics and fluid mechanics: Natural variability and related uncertainties.” Physica D 237: 2111–2126.
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Camargo, Suzana J., Andrew W. Robertson, Anthony G. Barnston, and Michael Ghil. 2008. “Clustering of eastern North Pacific tropical cyclone tracks: ENSO and MJO effects.” Geochemistry, Geophysics, Geosystems 9 (6). Wiley Online Library.
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Carrassi, Alberto, Michael Ghil, Anna Trevisan, and Francesco Uboldi. 2008. “Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system.” Chaos 18 (2). AIP: 023112. Abstract

We 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.

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Kondrashov, Dmitri, Chaojiao Sun, and Michael Ghil. 2008. “Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation.” Monthly Weather Review 136: 5062–5076. Abstract

The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

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Kravtsov, Sergey, W. K. Dewar, Michael Ghil, J. C. McWilliams, and Pavel S. Berloff. 2008. “A mechanistic model of mid-latitude decadal climate variability.” Physica D 237: 584–599.
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Hallegatte, Stéphane, and Michael Ghil. 2008. “Natural disasters impacting a macroeconomic model with endogenous dynamics.” Ecological Economics 68 (1-2): 582–592. Abstract

We investigate the macroeconomic response to natural disasters by using an endogenous business cycle (EnBC) model in which cyclical behavior arises from the investment-profit instability. Our model exhibits a larger response to natural disasters during expansions than during recessions. This apparently paradoxical result can be traced to the disasters amplifying pre-existing disequilibria during expansions, while the existence of unused resources during recessions damps the exogenous shocks. It thus appears that high-growth periods are also highly vulnerable to supply-side shocks. In our EnBC model, the average production loss due to a set of disasters distributed at random in time is highly sensitive to the dynamical characteristics of the impacted economy. Larger economic flexibility allows for a more efficient and rapid response to supply-side shocks and reduces production losses. On the other hand, too high a flexibility can lead to vulnerability phases that cause average production losses to soar. These results raise questions about the assessment of climate change damages or natural disaster losses that are based purely on long-term growth models.

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