Studying the sensitivity of the optimal solution of the variational data assimilation problem for the Baltic Sea thermodynamics model

2015 ◽  
Vol 40 (6) ◽  
pp. 411-419 ◽  
Author(s):  
V. P. Shutyaev ◽  
E. I. Parmuzin
Author(s):  
François-Xavier Le Dimet ◽  
Victor Shutyaev ◽  
Eugene Parmuzin

AbstractThe problem of variational data assimilation for a model of ocean thermodynamics is formulated as an optimal control problem to find the boundary heat flux. The sensitivity of functionals of the optimal solution with respect to observations is studied. Computing the gradient of the functionals is reduced to the solution of a non-standard problem which is a coupled system involving direct and adjoint equations with mutually dependent boundary values. Solvability of the non-standard problem is studied based on the Hessian of the original cost function. An algorithm for computing the gradient of the response function related to the mean surface temperature is developed and justified. Numerical examples are presented for the Baltic Sea thermodynamics model.


2018 ◽  
Vol 25 (2) ◽  
pp. 429-439 ◽  
Author(s):  
Victor Shutyaev ◽  
Francois-Xavier Le Dimet ◽  
Eugene Parmuzin

Abstract. The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters of the model. The observation data, and hence the optimal solution, may contain uncertainties. A response function is considered as a functional of the optimal solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the observation data is studied. The gradient of the response function is related to the solution of a nonstandard problem involving the coupled system of direct and adjoint equations. The nonstandard problem is studied, based on the Hessian of the original cost function. An algorithm to compute the gradient of the response function with respect to observations is presented. A numerical example is given for the variational data assimilation problem related to sea surface temperature for the Baltic Sea thermodynamics model.


2016 ◽  
Vol 46 (3) ◽  
pp. 713-729 ◽  
Author(s):  
Weiwei Fu

AbstractA three-dimensional variational data assimilation (3DVAR) method is implemented in a coupled physical–biogeochemical (CPB) model in the Baltic Sea. This study carries out a 10-yr assimilation experiment with satellite sea surface temperature (SST) and observed in situ temperature (T) and salinity (S) profiles. The impact of the assimilation is assessed with the focus on how the biogeochemical model responds to the improved hydrodynamics. The assimilation of temperature and salinity data yields considerable improvements in the physical model. On a basin scale, the mean bias of SST, T, S, and mixed layer depth (MLD) is decreased by 0.18°C (57%), 0.31°C (49%), 0.34 psu (43%), and 1.8 m (43%), respectively. More importantly, the biogeochemical simulation is improved in response to the physical data assimilation. Compared with in situ observations, the mean biases of chlorophyll a (Chl), dissolved inorganic nitrogen (DIN) and phosphorus (DIP) are decreased by 0.09 mg m−3 (15.5%), 0.19 mmol m−3 (9%), and 0.15 mmol m−3 (23%). Physical data assimilation also improves the simulated variability of Chl, DIN, and DIP and their correlations with observation. Compared with satellite observations, the mean bias of surface chlorophyll is reduced by 0.10–0.32 mg m−3 especially in the Skagerrak–Kattegat area and Bornholm basin. The decrease of total Chl change is caused by different mechanisms for winter and summer. While the deepened mixed layer acts as a dilution factor in winter, strengthened stratification agrees well with the decrease of chlorophyll in summer. In the vertical, relatively large changes of DIN and DIP occur below 60 m, which corresponds to the mean permanent halocline depth (~60–80 m) of the Baltic Sea.


2018 ◽  
Author(s):  
Victor Shutyaev ◽  
Francois-Xavier Le Dimet ◽  
Eugene Parmuzin

Abstract. The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters of the model. The observation data, and hence the optimal solution, may contain uncertainties. A response function is considered as a functional of the optimal solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the observation data is studied. The gradient of the response function is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. The non-standard problem is studied, based on the Hessian of the original cost function. An algorithm to compute the gradient of the response function with respect to observations is presented. Numerical example is given for variational data assimilation problem related to sea surface temperature for the Baltic Sea thermodynamics model.


Boreas ◽  
2002 ◽  
Vol 31 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Christian Christiansen ◽  
Helmar Kunzendorf ◽  
Kay-Christian Emeis ◽  
Rudolf Endler ◽  
Ulrich Struck ◽  
...  

2003 ◽  
pp. 136-146
Author(s):  
K. Liuhto

Statistical data on reserves, production and exports of Russian oil are provided in the article. The author pays special attention to the expansion of opportunities of sea oil transportation by construction of new oil terminals in the North-West of the country and first of all the largest terminal in Murmansk. In his opinion, one of the main problems in this sphere is prevention of ecological accidents in the process of oil transportation through the Baltic sea ports.


Author(s):  
Angelina E. Shatalova ◽  
Uriy A. Kublitsky ◽  
Dmitry A. Subetto ◽  
Anna V. Ludikova ◽  
Alar Rosentau ◽  
...  

The study of paleogeography of lakes is an actual and important direction in modern science. As part of the study of lakes in the North-West of the Karelian Isthmus, this analysis will establish the dynamics of salinity of objects, which will allow to reconstruct changes in the level of the Baltic Sea in the Holocene.


Author(s):  
Małgorzata Leśniewska ◽  
Małgorzata Witak

Holocene diatom biostratigraphy of the SW Gulf of Gdańsk, Southern Baltic Sea (part III)The palaeoenvironmental changes of the south-western part of the Gulf of Gdańsk during the last 8,000 years, with reference to the stages of the Baltic Sea, were reconstructed. Diatom analyses of two cores taken from the shallower and deeper parts of the basin enabled the conclusion to be drawn that the microflora studied developed in the three Baltic phases: Mastogloia, Littorina and Post-Littorina. Moreover, the so-called anthropogenic assemblage was observed in subbottom sediments of the study area.


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