The study and numerical solution of the problem of heat and salinity transfer assuming ‘liquid’ boundaries

2016 ◽  
Vol 31 (2) ◽  
Author(s):  
Valery I. Agoshkov ◽  
Tatiana O. Sheloput
Keyword(s):  
Optimal Control Problems ◽  
Iterative Solution ◽  
Water Area ◽  
Control Problems ◽  
Observation Data ◽  
Physical Processes ◽  
The Baltic Sea ◽  
Variational Assimilation ◽  
Geophysical Hydrodynamics ◽  
The Baltic

AbstractThe problem of simulation of physical processes in water areas with ‘liquid’ boundaries is well known in geophysical hydrodynamics. In this paper we consider a problem of heat and salinity propagation as an example of approaches solving such problems and consisting in application of methods of variational assimilation of observation data. Using well known techniques of study and solution of inverse problems and optimal control problems, we propose an iterative solution algorithm, obtain conditions for existence of the solution, for unique and dense solvability of the problem, and for convergence of the iterative algorithm, The paper also presents results of numerical implementation of this algorithm in application to the water area of the Baltic sea.

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 with covariance matrices of observation data errors for the model of the Baltic Sea dynamics

2018 ◽  
Vol 33 (3) ◽  
pp. 149-160 ◽  
Author(s):  
Valery I. Agoshkov ◽  
Eugene I. Parmuzin ◽  
Natalia B. Zakharova ◽  
Victor P. Shutyaev
Keyword(s):  
Heat Flux ◽  
Baltic Sea ◽  
Satellite Observation ◽  
Covariance Matrices ◽  
Sea Surface ◽  
Observation Data ◽  
The Baltic Sea ◽  
Variational Assimilation ◽  
Data Errors ◽  
The Baltic

Abstract The mathematical model of the Baltic Sea dynamics developed at the Institute of Numerical Mathematics of RAS is considered. The problem of variational assimilation of average daily data for the sea surface temperature (SST) is formulated and studied with the use of covariance matrices of observation data errors. Based on variational assimilation of satellite observation data, we propose an algorithm for solving the inverse problem of the heat flux reconstruction on the sea surface. The results of numerical experiments on reconstruction of the heat flux function are presented for the problem of variational assimilation of observation SST data.

scholarly journals Assessment of a physical-biogeochemical coupled model system for operational service in the Baltic Sea

Ocean Science ◽  
2012 ◽  
Vol 8 (4) ◽  
pp. 683-701 ◽  
Author(s):  
Z. Wan ◽  
J. She ◽  
M. Maar ◽  
L. Jonasson ◽  
J. Baasch-Larsen
Keyword(s):  
Baltic Sea ◽  
Inorganic Nitrogen ◽  
Biogeochemical Model ◽  
Observation Data ◽  
Model Assessment ◽  
Model Errors ◽  
The Baltic Sea ◽  
Statistical Measures ◽  
The Baltic ◽  
Operational Service

Abstract. Thanks to the abundant observation data, we are able to deploy the traditional point-to-point comparison and statistical measures in combination with a comprehensive model validation scheme to assess the skills of the biogeochemical model ERGOM in providing an operational service for the Baltic Sea. The model assessment concludes that the operational products can resolve the main observed seasonal features for phytoplankton biomass, dissolved inorganic nitrogen, dissolved inorganic phosphorus and dissolved oxygen in euphotic layers as well as their vertical profiles. This assessment reflects that the model errors of the operational system at the current stage are mainly caused by insufficient light penetration, excessive organic particle export downward, insufficient regional adaptation and some from improper initialization. This study highlights the importance of applying multiple schemes in order to assess model skills rigidly and identify main causes for major model errors.

scholarly journals Hydrological and hydrochemical underpinnings of primary production and division of the Russian sector in the Gdansk basin of the Baltic sea

2019 ◽  
Vol 59 (1) ◽  
pp. 56-71
Author(s):  
E. A. Kudryavtseva ◽  
S. V. Aleksandrov
Keyword(s):  
Primary Production ◽  
Baltic Sea ◽  
Marine Environment ◽  
Bottom Topography ◽  
Water Area ◽  
Nutrient Concentrations ◽  
The Baltic Sea ◽  
Environment Temperature ◽  
Russian Sector ◽  
The Baltic

The distribution patterns of absolute and specific values of primary production in the upper 10-m layer depending on the physical and chemical condition of the marine environment (temperature, salinity, depth, bottom topography and configuration of the coastline, and nutrient concentrations) were distinguished in the Russian sector in the Gdansk Basin of the Baltic Sea based on long-term research data (2003–2015). Based on the results, the considered water area was divided into five regions: Cape Taran, the base of the Curonian Spit, the plateau of Rybachy, the open sea, and the Gdansk Bay (northeastern part). These regions are characterized by higher correlations of primary production and parameters of the marine environment compared to regression analysis for the regions distinguished by bathymetry. Primary production is the most closely correlated with temperature over the entire water area and with nutrients concentrations in seaward regions.

scholarly journals Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

2020 ◽  
Vol 146 (2) ◽  
pp. 335-368
Author(s):  
Owe Axelsson ◽  
János Karátson
Keyword(s):  
Optimal Control ◽  
Rate Of Convergence ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Control Problems ◽  
Block Form ◽  
Solution Methods ◽  
Preconditioned Matrix ◽  
Iterative Solution Methods

Abstract Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties, such as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

scholarly journals Sensitivity of oxygen dynamics in the water column of the Baltic Sea to external forcing

Ocean Science ◽  
2010 ◽  
Vol 6 (2) ◽  
pp. 461-474 ◽  
Author(s):  
S. Miladinova ◽  
A. Stips
Keyword(s):  
Baltic Sea ◽  
Transport Model ◽  
Meteorological Data ◽  
Biogeochemical Model ◽  
Physical Factors ◽  
Observation Data ◽  
Intermediate Water ◽  
The Baltic Sea ◽  
The Baltic ◽  
Oxygen Dynamics

Abstract. A 1-D biogeochemical/physical model of marine systems has been applied to study the oxygen cycle in four stations of different sub-basins of the Baltic Sea, namely, in the Gotland Deep, Bornholm, Arkona and Fladen. The model consists of the biogeochemical model of Neumann et al. (2002) coupled with the 1-D General Ocean Turbulence Model (GOTM). The model has been forced with meteorological data from the ECMWF reanalysis project for the period 1998–2003, producing a six year hindcast which is validated with datasets from the Baltic Environmental Database (BED) for the same period. The vertical profiles of temperature and salinity are relaxed towards both profiles provided by 3-D simulations of General Estuarine Transport Model (GETM) and observed profiles from BED. Modifications in the parameterisation of the air-sea oxygen fluxes have led to a significant improvement of the model results in the surface and intermediate water layers. The largest mismatch with observations is found in simulating the oxygen dynamics in the Baltic Sea bottom waters. The model results demonstrate the good capability of the model to predict the time-evolution of the physical and biogeochemical variables at all different stations. Comparative analysis of the modelled oxygen concentrations with respect to observation data is performed to distinguish the relative importance of several factors on the seasonal, interannual and long-term variations of oxygen. It is found that natural physical factors, like the magnitude of the vertical turbulent mixing, wind speed and the variation of temperature and salinity fields are the major factors controlling the oxygen dynamics in the Baltic Sea. The influence of limiting nutrients is less pronounced, at least under the nutrient flux parameterisation assumed in the model.

Assessment of biogenous load on the Gulf of Finland exerted from the Russian territory

2020 ◽  
Author(s):  
Nikolai Voronov ◽  
Nataly Victorova ◽  
Dmitry Shilov
Keyword(s):  
Baltic Sea ◽  
Point Sources ◽  
Gulf Of Finland ◽  
Observation Data ◽  
The Baltic Sea ◽  
Russian Territory ◽  
Catchment Areas ◽  
The Baltic ◽  
Bodies Of Water ◽  
The Gulf Of Finland

<p>The purpose of the essay was analysis and evaluation of the load generated by pollutants in the Russian part of the catchment area directly entering the Baltic Sea, as well as consideration of pro-rata contribution of all sources in the formation of factual biogenous load at the catchment areas of rivers flowing into the Gulf of Finland.</p><p>The assessment of biogenous load was made on the basis of observation data, statistical reporting data, mathematical modelling data and additional monitoring data for bodies of water in previously uncontrolled areas. To assess the amount of biogenous input from uncontrolled tributaries of the Gulf of Finland, field observations of the discharge and concentration of pollutants over a number of past years were analyzed and generalized.</p><p>It is noted that there has been a tendency towards reduction of pollutants for a number of substances in the last decade, as shown by the analysis. It is demonstrated that a significant decrease is due to reduced load from point sources that discharge pollutants directly to the Baltic Sea and its bays. Some proposals are presented for improving the Russian system of monitoring the load exerted on water bodies.</p>

scholarly journals Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 3-6 ◽  
Author(s):  
John W. Pearson ◽  
Martin Stoll ◽  
Andrew J. Wathen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Time Dependent ◽  
Control Problems

On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems

2010 ◽  
Vol 10 (3) ◽  
pp. 283-301 ◽  
Author(s):  
E. Laitinen ◽  
A. Lapin ◽  
S. Lapin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Function ◽  
Elliptic Boundary ◽  
Iterative Algorithms ◽  
Iterative Solution ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Finite Dimensional ◽  
The Right

AbstractIterative methods for finite-dimensional inclusions which arise in applying a finite-element or a finite-difference method to approximate state-constrained optimal control problems have been investigated. Specifically, problems of control on the right- hand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergence for the iterative algorithms based on the finding of the control function or Lagrange multipliers are proved.

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