Natalia Tuchkova

Comparison of methods for argo drifters data assimilation into a hydrodynamical model of the ocean

Different data assimilation methods such as an extended Kalman filter, the optimal interpolation method, and a method based on the Fokker-Planck equation applications are considered. Data from the ARGO drifters are assimilated into the HYCOM shallow water model (University of Miami, USA). Throughout the study, the schemes and methods of parallel computations with an MPI library are used. The results of the computations with assimilations are compared between themselves and with independent observations. The method based on the Fokker-Planck equation and the extended Kalman filter are preferable because they give better results than the optimal interpolation scheme. The various model characteristics of the ocean, such as the heat content fields and others, are analyzed after the data assimilation.

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

ABSTRACT An original data assimilation (DA) scheme with a general dynamics model is considered. It is shown that this scheme can be approximated by the stochastic diffusion process. The sufficient conditions to provide this approximation are formulated. Based on this algorithm a new DA method is developed. The method combines variational and statistical approaches commonly used in DA theory and minimizes the variance of the trajectory of a diffusion process in conjunction with a dynamics numerical model. In this sense the method is optimal in contrast to other DA approaches. The proposed scheme takes the model dynamics into account and in this way it differs from the well-known Kalman filter. Furthermore, the derived DA method can be applied to a very wide field of dynamical systems, for example, gas dynamics, fluid dynamics and other disciplines. However, the current study deals with oceanography and DA in oceanography specifically. Then the method is applied to the HYbrid Coordinate Ocean Model and assimilates satellite sea level anomaly data from the Archiving, Validating and Interpolating Satellite Oceanography Data over the Atlantic Ocean to correct the model state. Several numerical experiments have been performed. The experiments show that the method substantially changes the synoptic and mesoscale structure of ocean dynamics. Also, the distribution of the obtained result is estimated through the solution of the Fokker–Planck–Kolmogorov equation.

A correction method for dynamic model calculations using observational data and its application in oceanography

A new data assimilation method for the correction of model calculations is developed and applied. The method is based on the least resistance principle and uses the theory of diffusion-type stochastic processes and stochastic differential equations. Application of the method requires solving a system of linear equations that is derived from this principle. The system can be considered as a generalization of the well-known Kalman scheme taking the model’s dynamics into account. The method is applied to the numerical experiments with the HYbrid Coordinate Ocean Model (HYCOM) and Archiving, Validating, and Interpolating Satellite Ocean (AVISO) data for the Atlantic. The skill of the method is assessed using the results of the experiments. The model’s output is compared with the twin experiments, namely, the model calculations without assimilation, which confirms the consistency and robustness of the proposed method.

Numerical Realization of Hybrid Data Assimilation Algorithm in Ensemble Experiments with the MPIESM Coupled Model

Original data assimilation method is considered. This method is applied in conjunction with the coupled Max Planck Institute Earth System Model (MPIESM). The assimilation block and the interface with the MPIESM are realized on the “Lomonosov” supercomputer at the Lomonosov Moscow State University. Several experiments with and without assimilation of the sea level data and temperature-salinity profiles over the Equatorial Atlantic are conducted. The results of these experiments have been analyzed and discussed. In particular, it is shown that the ice concentration in Arctic zone of Russia fits better to the observations then in the reference experiments without assimilation.

A Generalized Solution of Eshelby and Eshelby Self‐Consistent Method for Gradient Models in Mechanics of Composites

We give a generalization of Eshelby integral representations for the gradient theory of elasticity. Gradient theory of the interphase layer and a particular gradient medium model whose properties are described by the harmonic equation are considered. For these models a generalization of the principle of Eshelby and integral representations (formulas) of Eshelby are given. Examples of application of the generalized Eshelby principle for determining the effective properties of composites with cohesion size effects and surface effects.