Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension

2010 ◽  
Vol 136 (647) ◽  
pp. 487-496 ◽  
Author(s):  
Anna Trevisan ◽  
Massimo D'Isidoro ◽  
Olivier Talagrand
Keyword(s):  
Variational Assimilation ◽  
Optimal Subspace ◽  
Unstable Subspace

CHAOS AND WEATHER FORECASTING: THE ROLE OF THE UNSTABLE SUBSPACE IN PREDICTABILITY AND STATE ESTIMATION PROBLEMS

2011 ◽  
Vol 21 (12) ◽  
pp. 3389-3415 ◽  
Author(s):  
ANNA TREVISAN ◽  
LUIGI PALATELLA
Keyword(s):  
Data Assimilation ◽  
Chaotic Systems ◽  
Weather Forecasting ◽  
Variational Assimilation ◽  
Forecasting Models ◽  
Operational Forecasting ◽  
Estimation Problems ◽  
Atmospheric Predictability ◽  
Unstable Subspace

In the first part of this paper, we review some important results on atmospheric predictability, from the pioneering work of Lorenz to recent results with operational forecasting models. Particular relevance is given to the connection between atmospheric predictability and the theory of Lyapunov exponents and vectors. In the second part, we briefly review the foundations of data assimilation methods and then we discuss recent results regarding the application of the tools typical of chaotic systems theory described in the first part to well established data assimilation algorithms, the Extended Kalman Filter (EKF) and Four Dimensional Variational Assimilation (4DVar). In particular, the Assimilation in the Unstable Space (AUS), specifically developed for application to chaotic systems, is described in detail.

Variational assimilation of observation data in the mathematical model of the Baltic Sea dynamics

2015 ◽  
Vol 30 (4) ◽  
Author(s):  
Valeriy I. Agoshkov ◽  
Eugene I. Parmuzin ◽  
Vladimir B. Zalesny ◽  
Victor P. Shutyaev ◽  
Natalia B. Zakharova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Heat Flux ◽  
Baltic Sea ◽  
Satellite Observation ◽  
Sea Surface ◽  
Observation Data ◽  
The Baltic Sea ◽  
Variational Assimilation ◽  
The Baltic ◽  
The Mathematical Model

AbstractA mathematical model of the dynamics of the Baltic Sea is considered. A problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satellite observation data, an algorithm solving the inverse problem of heat flux restoration on the interface of two media is proposed. The results of numerical experiments reconstructing the heat flux functions in the problem of variational assimilation of SST observation data are presented. The influence of SST assimilation on other hydrodynamic parameters of the model is considered.

Variational Assimilation of Geosat Data into an Eddy-resolving Model of the Gulf Stream Extension Area

1993 ◽  
Vol 23 (5) ◽  
pp. 925-953 ◽  
Author(s):  
Jens Schröter ◽  
Ulrike Seiler ◽  
Manfred Wenzel
Keyword(s):  
Gulf Stream ◽  
Variational Assimilation

scholarly journals Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case

2018 ◽  
Vol 25 (3) ◽  
pp. 565-587 ◽  
Author(s):  
Mohamed Jardak ◽  
Olivier Talagrand
Keyword(s):  
Probability Distribution ◽  
Simple Procedure ◽  
Linear Case ◽  
Bayesian Probability ◽  
Variational Assimilation ◽  
Non Linear ◽  
Abstract Data ◽  
Gaussian Case ◽  
Low Dimensional ◽  
Lorenz 96

Abstract. Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called here ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is studied in this two-part paper on the non-linear low-dimensional Lorenz-96 chaotic system, with the assimilation being performed by the standard variational procedure. In this first part, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The performances of the algorithm, considered either as a probabilistic or a deterministic estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for the ensemble Kalman filter (EnKF) and particle filter (PF), although at a higher cost. Globally similar results are obtained with the Kuramoto–Sivashinsky (K–S) equation.

scholarly journals Variational Assimilation of Land Surface Temperature within the ORCHIDEE Land Surface Model Version 1.2.6

2016 ◽  
Author(s):  
H. S. Benavides Pinjosovsky ◽  
S. Thiria ◽  
C. Ottlé ◽  
J. Brajard ◽  
F. Badran ◽  
...  
Keyword(s):  
Surface Temperature ◽  
Land Surface Temperature ◽  
Land Surface ◽  
Initial Conditions ◽  
Land Surface Model ◽  
Surface Model ◽  
Adjoint Model ◽  
Variational Assimilation ◽  
Internal Parameters

Abstract. The SECHIBA module of the ORCHIDEE land surface model describes the exchanges of water and energy between the surface and the atmosphere. In the present paper, the adjoint semi-generator software denoted YAO was used as a framework to implement a 4D-VAR assimilation method. The objective was to deliver the adjoint model of SECHIBA (SECHIBA-YAO) obtained with YAO to provide an opportunity for scientists and end users to perform their own assimilation. SECHIBA-YAO allows the control of the eleven most influent internal parameters of SECHIBA or of the initial conditions of the soil water content by observing the land surface temperature measured in situ or as it could be observed by remote sensing as brightness temperature. The paper presents the fundamental principles of the 4D-Var assimilation, the semi-generator software YAO and some experiments showing the accuracy of the adjoint code distributed. In addition, a distributed version is available when only the land surface temperature is observed.

scholarly journals A Constellation Space Dimensionality Reduced Sub-Optimal Receiver for Orthogonal STBC CPM Modulation in a MIMO Channel

10.14311/1107 ◽  
2009 ◽  
Vol 49 (2) ◽  
Author(s):  
M. Hekrdla
Keyword(s):  
Rayleigh Fading ◽  
Dimensional Subspace ◽  
Space Time ◽  
Mimo Channel ◽  
Optimal Receiver ◽  
Computational Performance ◽  
Awgn Channel ◽  
Serially Concatenated ◽  
Optimal Subspace ◽  
Subspace Search

We consider burst orthogonal space-time block coded (OSTBC) CPM modulation in a MIMO flat slow Rayleigh fading channel. The optimal receiver must process a multidimensional non-linear CPM signal on each antenna. This task imposes a high load on the receiver computational performance and increases its complexity. We analytically derive a suboptimal receiver with a reduced number of front end matched filters (MFs) corresponding to the CPM dimension. Our derivation is made fully in the constellation signal space, and the reduction is based on the linear orthogonal projection to the optimal subspace. Criterion optimality is a standard space-time rank and determinant criterion. The optimal arbitrary-dimensional subspace search leads to the eigenvector solution. We present the condition on a sufficient subspace dimension and interpret the meaning of the corresponding eigenvalues. It is shown that the determinant and rank criterion for OSTBC CPM is equivalent to the uncoded CPM Euclidean distance criterion. Hence the proposed receiver may be practical for uncoded CPM and foremost in a serially concatenated (SC) CPM system. All the derivations are supported by suitable error simulations for binary 2REC h= 1/2, but the procedure is generally valid for any CPM variant. We consider OSTBC CPM in a Rayleigh fading AWGN channel and SC CPM in an AWGN channel. 

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