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Model error and sequential data assimilation: a deterministic formulation
No full textData assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first‐order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short‐time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white‐noise assumption. The universal short‐time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Societ
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Treatment of the error due to unresolved scales in sequential data assimilation
No full textIn this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales
Short time augmented extended Kalman filter for soil analysis: A feasibility study
No full textData Assimilation, Soil physicsThis paper presents a soil analysis scheme based on an extended Kalman filter (EKF), the short time augmented extended Kalman filter (STAEKF), where the model parameters are estimated along with the system state. We use an off-line version of the interaction soil-biosphere-atmosphere model for the assimilation of screen-level temperature and relative humidity. The leaf area index, the albedo, and the minimum stomatal resistance are estimated with the STAEKF. Results show that the STAEKF gives encouraging results and indicate the benefit of the simultaneous estimation of the state and parameters in soil data assimilation. © 2012 Royal Meteorological Society
On Temporal Scale Separation in Coupled Data Assimilation with the Ensemble Kalman Filter
Get PDFData assimilation for systems possessing many scales of motions is a substantial methodological and technological challenge. Systems with these features are found in many areas of computational physics and are becoming common thanks to increased computational power allowing to resolve finer scales and to couple together several sub-components. Coupled data assimilation (CDA) distinctively appears as a main concern in numerical weather and climate prediction with major efforts put forward by meteo services worldwide. The core issue is the scale separation acting as a barrier that hampers the propagation of the information across model components (e.g. ocean and atmosphere). We provide a brief survey of CDA, and then focus on CDA using the ensemble Kalman filter (EnKF), a widely used Monte Carlo Gaussian method. Our goal is to elucidate the mechanisms behind information propagation across model components. We consider first a coupled system of equations with temporal scale difference, and deduce that: (i) cross components effects are strong from the slow to the fast scale, but, (ii) intra-component effects are much stronger in the fast scale. While observing the slow scale is desirable and benefits the fast, the latter must be observed with high frequency otherwise the error will grow up to affect the slow scale. Numerical experiments are performed using the atmosphere-ocean model, MAOOAM. Six configurations are considered, differing for the strength of the atmosphere-ocean coupling and/or the number of model modes. The performance of the EnKF depends on the model configuration, i.e. on its dynamical features. A comprehensive dynamical characterisation of the model configurations is provided by examining the Lyapunov spectrum, Kolmogorov entropy and Kaplan–Yorke attractor dimension. We also compute the covariant Lyapunov vectors and use them to explain how model instabilities act on different model’s modes according to the coupling strength. The experiments confirm the importance of observing the fast scale, but show also that, despite its slow temporal scale, frequent observations in the ocean are beneficial. The relation between the ensemble size, N, and the unstable subspace dimension, n, has been studied. Results largely ratify what known for uncoupled system: the condition N≥ n is necessary for the EnKF to work satisfactorily. Nevertheless the quasi-degeneracy of the Lyapunov spectrum of MAOOAM, with many near-zero exponents, is potentially the cause of the smooth gradual reduction of the analysis error observed for some model configurations, even when N> n. Future prospects for the EnKF in the context of coupled ocean-atmosphere systems are finally discussed
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State and parameter estimation with the extended Kalman filter: an alternative formulation of the model error dynamics
No full textAn alternative formulation of the extended Kalman filter for state and parameter estimation is presented, referred to as Short‐Time Augmented Extended Kalman Filter (ST‐AEKF). In this algorithm, the evolution of the model error generated by the uncertain parameters is described using a truncated short‐time Taylor expansion within the assimilation interval. This allows for a simplification of the forward propagation of the augmented error covariance matrix with respect to the classical state augmented approach. The algorithm is illustrated in the case of a scalar unstable dynamics and is then more extensively analyzed in the context of the Lorenz 36‐variable model. The results demonstrate the ability of the ST‐AEKF to provide accurate estimate of both the system's state and parameters with a skill comparable to that of the full state augmented approach and in some cases close to the EKF in a perfect model scenario. The performance of the filter is analyzed for different initial parametric errors and assimilation intervals, and for the estimates of one or more model parameters. The filter accuracy is sensitive to the nature of the estimated parameter but more importantly to the assimilation interval, a feature connected to the short‐time approximation on which the filter formulation relies. The conditions and the context of applications of the present approach are also discussed
The maximum likelihood ensemble filter performances in chaotic systems
No full textThe performance of the maximum likelihood ensemble filter (MLEF), is investigated in the context of generic systems featuring the essential ingredients of unstable dynamics and on a spatially extended system displaying chaos. The main objective is to clarify the response of the filter to different regimes of motion and highlighting features which may help its optimization in more realistic applications. It is found that, in view of the minimization procedure involved in the filter analysis update, the algorithm provides accurate estimates even in the presence of prominent non-linearities. Most importantly, the filter ensemble size can be designed in connection to the properties of the system attractor (Kaplan-Yorke dimension), thus facilitating the filter setup and limiting the computational cost by using an optimal ensemble. As a corollary, this latter finding indicates that the ensemble perturbations in the MLEF reflect the intrinsic system error dynamics rather than a sampling of realizations of an unknown error covariance. © 2009 The Authors Journal compilation © 2009 Blackwell Munksgaard
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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Deterministic treatment of model error in geophysical data assimilation
No full textThis chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first derive the equations for the model error dynamics in the general case, and then for the particular situation of parametric error. We show how this deterministic description of the model error can be incorporated in sequential and variational data assimilation procedures. A numerical comparison with standard methods is given using low-order dynamical systems, prototypes of atmospheric circulation, and a realistic soil model. The deterministic approach proves to be very competitive with only minor additional computational cost. Most importantly, it offers a new way to address the problem of accounting for model error in data assimilation that can easily be implemented in systems of increasing complexity and in the context of modern ensemble-based procedures
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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