2013

Shprits, Yuri, Adam Kellerman, Dmitri Kondrashov, and Dmitriy Subbotin. 2013. “Application of a new data operator-splitting data assimilation technique to the 3-D VERB diffusion code and CRRES measurements.” Geophysical Research Letters 40 (19): 4998–5002. Publisher's Version

Kondrashov, Dmitri, Mickaël D. Chekroun, Andrew W. Robertson, and Michael Ghil. 2013. “Low-order stochastic model and ``past-noise forecasting" of the Madden-Julian oscillation.” Geophysical Research Letters 40: 5305–5310.

2011

Daae, M., Y. Y. Shprits, B. Ni, J. Koller, Dmitri Kondrashov, and Y. Chen. 2011. “Reanalysis of radiation belt electron phase space density using various boundary conditions and loss models.” Advances in Space Research 48 (8): 1327 - 1334. Publisher's Version

Kravtsov, Sergey, Dmitri Kondrashov, I. Kamenkovich, and Michael Ghil. 2011. “An empirical stochastic model of sea-surface temperatures and surface winds over the Southern Ocean.” Ocean Science 7 (6): 755–770. Publisher's Version Abstract

This study employs NASA's recent satellite measurements of sea-surface temperatures (SSTs) and sea-level winds (SLWs) with missing data filled-in by Singular Spectrum Analysis (SSA), to construct empirical models that capture both intrinsic and SST-dependent aspects of SLW variability. The model construction methodology uses a number of algorithmic innovations that are essential in providing stable estimates of the model's propagator. The best model tested herein is able to faithfully represent the time scales and spatial patterns of anomalies associated with a number of distinct processes. These processes range from the daily synoptic variability to interannual signals presumably associated with oceanic or coupled dynamics. Comparing the simulations of an SLW model forced by the observed SST anomalies with the simulations of an SLW-only model provides preliminary evidence for the ocean driving the atmosphere in the Southern Ocean region.

Ghil, Michael, P. Yiou, S. Hallegatte, B. D. Malamud, P. Naveau, A. Soloviev, P. Friederichs, et al. 2011. “Extreme events: dynamics, statistics and prediction.” Nonlinear Processes in Geophysics 18 (3): 295–350. Abstract

We review work on extreme events, their causes and consequences, by a group of Euro- pean and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deteministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.

Kondrashov, Dmitri, Michael Ghil, and Y. Shprits. 2011. “Lognormal Kalman filter for assimilating phase space density data in the radiation belts.” Space Weather 9 (11). Wiley Online Library.

PDFChekroun, Mickaël D., Dmitri Kondrashov, and Michael Ghil. 2011. “Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation.” Proceedings of the National Academy of Sciences 108 (29): 11766–11771. Abstract

Interannual and interdecadal prediction are major challenges of climate dynamics. In this article we develop a prediction method for climate processes that exhibit low-frequency variability (LFV). The method constructs a nonlinear stochastic model from past observations and estimates a path of the “weather” noise that drives this model over previous finite-time windows. The method has two steps: (i) select noise samples—or “snippets”—from the past noise, which have forced the system during short-time intervals that resemble the LFV phase just preceding the currently observed state; and (ii) use these snippets to drive the system from the current state into the future. The method is placed in the framework of pathwise linear-response theory and is then applied to an El Niño–Southern Oscillation (ENSO) model derived by the empirical model reduction (EMR) methodology; this nonlinear model has 40 coupled, slow, and fast variables. The domain of validity of this forecasting procedure depends on the nature of the system’s pathwise response; it is shown numerically that the ENSO model’s response is linear on interannual time scales. As a result, the method’s skill at a 6- to 16-month lead is highly competitive when compared with currently used dynamic and statistic prediction methods for the Niño-3 index and the global sea surface temperature field.

2010

Kravtsov, Sergey, Dmitri Kondrashov, and Michael Ghil. 2010. “Empirical model reduction and the modelling hierarchy in climate dynamics and the geosciences.” Stochastic physics and climate modeling. Cambridge University Press, Cambridge, edited by P. Williams and T. Palmer, 35–72. Cambridge University Press.

PDFKondrashov, Dmitri, Yuri Shprits, and Michael Ghil. 2010. “Gap Filling of Solar Wind Data by Singular Spectrum Analysis.” Geophysical Research Letters 37. CiteSeerX - Scientific Literature Digital Library and Search Engine [http://citeseerx.ist.psu.edu/oai2] (United States): L15101. Abstract

Observational data sets in space physics often contain instrumental and sampling errors, as well as large gaps. This is both an obstacle and an incentive for research, since continuous data sets are typically needed for model formulation and validation. For example, the latest global empirical models of Earth's magnetic field are crucial for many space weather applications, and require time continuous solar wind and interplanetary magnetic field (IMF) data; both of these data sets have large gaps before 1994. Singular spectrum analysis (SSA) reconstructs missing data by using an iteratively inferred, smooth “signal” that captures coherent modes, while “noise” is discarded. In this study, we apply SSA to fill in large gaps in solar wind and IMF data, by combining it with geomagnetic indices that are time continuous, and generalizing it to multivariate geophysical data consisting of gappy “driver” and continuous “response” records. The reconstruction error estimates provide information on the physics of co variability between particular solar wind parameters and geomagnetic indices.

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.

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.

PDF2009

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).

2008

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.

2007

Kondrashov, Dmitri, Y. Shprits, Michael Ghil, and R. Thorne. 2007. “A Kalman filter technique to estimate relativistic electron lifetimes in the outer radiation belt.” Journal of Geophysical Research: Space Physics 112 (A10). Wiley Online Library.

PDFKondrashov, Dmitri, Jie Shen, Richard Berk, Fabio D'Andrea, and Michael Ghil. 2007. “Predicting weather regime transitions in Northern Hemisphere datasets.” Climate Dynamics 29 (5). Springer: 535–551.

PDFShprits, Yuri, Dmitri Kondrashov, Yue Chen, Richard Thorne, Michael Ghil, Reiner Friedel, and Geoff Reeves. 2007. “Reanalysis of relativistic radiation belt electron fluxes using CRRES satellite data, a radial diffusion model, and a Kalman filter.” Journal of Geophysical Research: Space Physics 112 (A12). Wiley Online Library.

PDFKondrashov, Dmitri, and Michael Ghil. 2007. “Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets".” Nonlinear Processes in Geophysics 14 (1): 3–4.

PDF2006

Kondrashov, Dmitri, S. Kravtsov, and M. Ghil. 2006. “Empirical Mode Reduction in a Model of Extratropical Low-Frequency Variability.” Journal of the Atmospheric Sciences 63 (7): 1859-1877. Publisher's Version

Kondrashov, Dmitri, S Kravtsov, and M Ghil. 2006. “Empirical mode reduction in a model of extratropical low-frequency variability.” Journal of the Atmospheric Sciences 63 (7): 1859–1877. Abstract

This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model's phase space has a dimension of O(104). The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model's probability density function (PDF). In particular, the reduced model's PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog. An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model's deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model's multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.

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