Andrey Kuleshov

An application of a data assimilation method based on the diffusion stochastic process theory using altimetry data in Atlantic

Abstract A data assimilation (DA) method based on the application of the diffusion stochastic process theory, particularly, of the Fokker-Planck equation, is considered. The method was introduced in the previous works; however, it is substantially modified and extended to the multivariate case in the current study. For the first time, the method is here applied to the assimilation of sea surface height anomalies (SSHA) into the Hybrid Coordinate Ocean Model (HYCOM) over the Atlantic Ocean. The impact of assimilation of SSHA is investigated and compared with the assimilation by an Ensemble Optimal Interpolation method (EnOI). The time series of the analyses produced by both assimilation methods are evaluated against the results from a free model run without assimilation. This study shows that the proposed assimilation technique has some advantages in comparison with EnOI analysis. Particularly, it is shown that it provides slightly smaller error and is computationally efficient. The method may be applied to assimilate other data such as observed sea surface temperature and vertical profiles of temperature and salinity.

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.

Thermomechanical Model of an Impermeable Porous Medium with a Chemically Active Filler

A self-consistent mathematical model describing the thermomechanical behavior of an elastic medium, which contains voids filled with a chemically active substance, is considered. The behavior of the medium is described by thermomechanical equations. Processes in the pores are described by a lumped model which allows for energy release, chemical reactions, and conditions of phase equilibrium. The model makes it possible to take into account an arbitrary number of components, which can be in solid and three mobile phases (liquid gaseous, liquid hydrocarbon, and aqueous phases). The distribution of components between phases is obtained using a thermodynamically consistent technique under assumption that any mobile component can be present in any mobile phase. In order to describe the thermodynamic behavior of the components with allowance for phase transitions, cubic equations of state are used, which are rather common in engineering practice. An algorithm based on a combination of domain decomposition method and physical splitting approach is proposed for the numerical solution of the model system of equations.

Numerical simulation of forest fire propagation based on modified two-dimensional model

A modified two-dimensional two-phase mathematical model of forest wildfires propagation is considered. The model is based on the averaging of three-dimensional equations of two-phase medium over the height of the forest fuel (FF) layer and it includes the (k‒ε)-turbulence model with additional turbulence production and dissipation terms in the forest layer and the Eddy Break-up Model for the combustion rate in the gas phase. The developed model can be used to carry out numerical simulation of the forest fire-front propagation under the conditions of a heterogeneous FF distribution, the presence of obstacles to the fire propagation, and the wind effects. This model can be used for real-time computation of the fire propagation, for expert assessments of emergency situations, and for assessments of the damage caused by forest fires.

Application of kinetic approach to porous medium flow simulation in environmental hydrology problems on high-performance computing systems

Abstract A kinetically-based system of equations for three-phase porous media flow simulation is considered. A simple case with the following assumptions is discussed: phase transitions are absent, phases do not dissolve and do not mix, the rock compressibility is negligible. Such systems are under consideration in applied problems when the pressure changes slightly and thermal processes are absent, for example, in environmental problems. The continuity equation is modified via introduction of the regularizing term and the second-order time derivative. Due to conversion to the hyperbolic type the corresponding difference equation stability is improved. An explicit algorithm is developed and adapted to high-performance computing systems. High parallelization efficiency is achieved on a classical cluster as well as on a hybrid cluster with graphics accelerators.