An optimal data assimilation method and its application to the numerical simulation of the ocean dynamics

Belyaev, Konstantin; Кулешов, А. А.; Tuchkova, N. P.; Tanajura, Clemente Augusto Souza

doi:10.1080/13873954.2017.1338300

Cited by 34 publications

(22 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…are the model fields (written in the form of a column bit vector in each grid point) after and before correction, i.e., the analysis and background fields, respectively; Y is the vector of observations, in our case, it is the temperature and salinity vector at the point of observation; K is the Kalman gain (the weighting matrix) whose meaning is to render information about the difference between the observed and model values, i.e., the errors of modeling, to the model itself including unobserved model parameters; Q is the model error covariance matrix determined only for the observed parameters (structurally, this is a positively definite symmetrical matrix); Λ and С are temporal trends, i.e., the time derivatives of model and observational parameters, respectively, written as column bit vectors at the grid points; H is the matrix of the linear projection operator from the phase space (set of values) of the model onto the phase space of observations, which interpolates the values of the model to the points of observations and exclude from consideration the unobserved model parameters; the upper index T designates the transposition of a vector and/or a matrix. The GKF method (1)-(3) is described in detail and theoretically substantiated in [15,16]. It is also shown in these papers that this method generalizes the known Kalman algorithm EnKF [12].…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…It is also shown in these papers that this method generalizes the known Kalman algorithm EnKF [12]. The values of the vector С and matrix Q are considered to be known and are determined, in particular, by the methods described in [15]. The advantages of this algorithm are as follows: it considers not only the difference between the model and observations, but also the temporal trend (the time derivative) in both the model and observation data.…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…One of such methods used in this study is the generalized Kalman filter (GKF) method developed by the authors. Its detailed description can be found in [15,16]. Below, we present a short description of this method, necessary to understand the matter of this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of the Meridional Heat and Mass Transport in the South Atlantic by Using the Joint Atmosphere and Ocean Circulation Model with Data Assimilation and Visualization Facilities

Belyaev¹,

Кулешов²,

Tuchkova³

2019

View full text Add to dashboard Cite

The joint ocean-Earth-atmosphere model of the Max Planck Institute for Meteorology with application of original data assimilation methods are used to estimate the meridional heat and mass flows. The CTD-sections of temperature and salinity across the Atlantic Ocean for 1991-1995 obtained in the course of the WOCE (The World Ocean Circulation Experiment) international experiment are used as observation data. The sections contain about 650 stations; each of them provides from 100 to 3000 measurements from the sea surface to the bottom. In our study both the control estimates for the velocities of currents and those with assimilation of the data of these experiments are obtained. Using visualization facilities, we have shown how data assimilation changes the model characteristics, including velocities of currents and temperature fields at different sea levels. The graphs demonstrate the influence of the change in the initial field after data assimilation on the results of the model calculations after 6 and 11 months of integration for both the observed model characteristics and those which are not observed directly. The Generalized Kalman Filter (GKF) method which coincides in a particular case with the classical Ensemble Kalman Filter (EnKF) is used as the data assimilation method. The results of calculations of the heat and mass flows are analyzed and compared with those of control calculations with no data assimilation. The calculations were performed on the supercomputers-Mistral‖ in DKRZ (Deutsches Klimarechenzentrum,

show abstract

Section: Data Assimilation Methodsmentioning

confidence: 99%

Section: Data Assimilation Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of the Meridional Heat and Mass Transport in the South Atlantic by Using the Joint Atmosphere and Ocean Circulation Model with Data Assimilation and Visualization Facilities

Belyaev¹,

Кулешов²,

Tuchkova³

2019

View full text Add to dashboard Cite

show abstract

“…ODA methods can be conditionally divided into variational methods based on minimizing a functional given [4][5][6][7], which are formulated as optimal control problems and the theory of conjugate equations, and dynamic-stochastic ones, based on probability theory and filtering methods [8][9][10][11]. The history of the variational method dates back to the 70s of the 20 th century, when Guriy.…”

Section: Introductionmentioning

confidence: 99%

Spatial-Temporal Variability of the Model Characteristics in the Southern Atlantic

Deinego¹,

Ansorge²,

Belyaev³

et al. 2019

PhO

View full text Add to dashboard Cite

The present article is aimed at studying spatial-temporal variability of some model characteristics, particularly, the sea level data in the Southern Atlantic. Methods and Results. The eigenvector decomposition method (called the Karhunen-Loeve decomposition) has been used as a main research technique. Variability of the eigenvectors and eigenvalues of the corresponding covariance matrices, and their distribution in time and space are represented. Application of the method to the problem of assimilating the observation data is shown, and physical sense of such assimilation is analyzed. The ocean hydrodynamics model developed in the Institute of Numerical Mathematics, Russian Academy of Sciences, was applied. The problem of dynamical-stochastic and hybrid assimilation of the sea level data is formulated. Spatial-temporal variability of the model sea level and the one observed in the Southern Atlantic were compared. The variability difference and similarity are analyzed. Conclusions. The correlation structure between the observed and model ocean level fields is considered. This can permit to assimilate the observational data using the obtained weight matrices. Such studies of the sought characteristics' correlation structures of surface temperature, currents, joint covariance etc. will make it possible to understand exactly how the observed values correct model calculations and to carry out observations in the manner most convenient for data assimilation. Climatic behavior of the structure of eigenvectors and eigenvalues is shown. The represented technique permits to model and to forecast the hydrodynamic processes in the Southern Atlantic in more details.

show abstract

“…Кроме указанных основных подходов АДН есть также и ряд гибридных методов, сочетающих оба вышеприведенных подхода. К этим методам можно, например, отнести авторскую схему АДН [19], в которой минимизируется функционал, построенный по динамико-стохастической схеме.…”

unclassified

Spatial-Temporal Variability of the Model Characteristics in the Southern Atlantic

Deinego¹,

Ansorge²,

Belyaev³

et al. 2019

MGZh

View full text Add to dashboard Cite

Цель. Изучение пространственно-временной изменчивости некоторых модельных характеристик, в частности поля уровня океана в Южной Атлантике,-цель настоящей работы. Методы и результаты. Основным методом исследования служит метод разложения аномалий уровня по естественным ортогональным составляющим (Karhunen-Loeve decomposition). Изучается изменчивость собственных чисел и векторов соответствующих ковариационных матриц, их распределение во времени и пространстве. Показывается, как данный метод может быть применен к ассимиляции наблюдаемых данных, и анализируется физический смысл этой ассимиляции. Рассматривается математическая модель гидродинамики океана, разработанная в Институте вычислительной математики РАН, сформулирована задача динамико-стохастической и гибридной ассимиляции данных уровня океана. Приведены результаты сравнений пространственно-временной изменчивости модельного и наблюдаемого уровня в Южной Атлантике. Проанализированы сходство и различие этой изменчивости. Выводы. Сделан анализ структуры взаимосвязи наблюдаемого и моделируемого полей уровня океана, что позволит в дальнейшем провести усвоение данных наблюдений с использованием полученных весовых матриц. Подобные исследования структур взаимосвязей характеристик для полей поверхностной температуры океана, поверхностных течений, совместных ковариационных связей и не только позволят понять, как именно наблюдаемые величины корректируют модельный расчет. Показан климатический ход собственных векторов и чисел, их временная и пространственная изменчивость. Данная методика позволит более детально моделировать и прогнозировать гидродинамические процессы в Южной Атлантике и проводить дальнейший анализ их природы. Ключевые слова: математическая модель, разложение по естественным ортогональным составляющим, динамико-стохастическая ассимиляция, Южная Атлантика. Благодарности: работа выполнена по заданию Министерства науки и высшего образования РФ № 0149-2019-0004, а также при частичной поддержке гранта РФФИ № 19-57-60001 (модельные расчеты). Работа И. Ансорг была поддержана грантом UID 118901 Национальным научным фондом Южно-Африканской Республики.

show abstract

An optimal data assimilation method and its application to the numerical simulation of the ocean dynamics

Cited by 34 publications

References 19 publications

Estimation of the Meridional Heat and Mass Transport in the South Atlantic by Using the Joint Atmosphere and Ocean Circulation Model with Data Assimilation and Visualization Facilities

Estimation of the Meridional Heat and Mass Transport in the South Atlantic by Using the Joint Atmosphere and Ocean Circulation Model with Data Assimilation and Visualization Facilities

Spatial-Temporal Variability of the Model Characteristics in the Southern Atlantic

Spatial-Temporal Variability of the Model Characteristics in the Southern Atlantic

Contact Info

Product

Resources

About