Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2018, Vol. 15, No. 7, pp. 15-23
Numerical solution of the problem of variational assimilation of the sea level on the liquid (open) boundary in the Baltic Sea hydrothermodynamics model
1 Marchuk Institute of Numerical Mathematics RAS, Moscow, Russia
Accepted: 29.10.2018
DOI: 10.21046/2070-7401-2018-15-7-15-23
This paper presents the results of a numerical solution of the problem of variational assimilation of the sea level on the liquid (open) part of the boundary in the Baltic Sea hydrothermodynamics model. By liquid boundaries of the water area boundaries between seas and oceans, boundaries passing through straits, estuaries, etc. are meant. The problem of imposing boundary conditions on liquid boundaries is an important problem of modern geophysics. One of the existing methods that can be applied to account for liquid boundaries in models is the use of variational assimilation of observations, including sea level. So, having the observations at certain moment, one can pose the inverse problem of restoring flows at the open boundary. The formulation of the problem of variational assimilation of the sea level at the open boundary is given in the paper, an iterative algorithm for solving the problem and some conclusions about the convergence of the algorithm and the solvability of the original problem are formulated. The results of applying the algorithm to the solution of the problem of the Baltic Sea hydrothermodynamics simulation and the questions of the availability of observational data are considered in detail. For the assimilation procedure, satellite altimetry data were used, as well as in-situ sea level observations.
Keywords: variational data assimilation, open boundaries, satellite altimetry, Baltic Sea, numerical methods, iterational algorithms, methods of adjoint equations, boundary conditions, mathematical model
Full textReferences:
- Agoshkov V. I., Metody optimal’nogo upravleniya i sopryazhennykh uravnenii v zadachakh matematicheskoi fiziki (Methods of optimal control and adjoint equations in problems of mathematical physics), Moscow: IVM RAN, 2016, 244 p.
- Kubryakov A. I., Primenenie tekhnologii vlozhennykh setok pri sozdanii sistemy monitoringa gidrofizicheskikh polei v pribrezhnykh raionakh Chernogo moray (Application of nested mesh technology for creation of a monitoring system for hydrophysical fields in the coastal regions of the Black Sea), Ekologicheskaya bezopasnost’ pribrezhnoi i shel’fovoi zon i kompleksnoe ispol’zovanie resursov shel’fa (Ecological safety of coastal and shelf zones and complex use of shelf resources). Sevastopol: NPC “EHKOSI-Gidrofizika”, 2004, Vol. 11, pp. 31–50.
- Lebedev S. A., Metodika obrabotki dannykh sputnikovoi al’timetrii dlya akvatorii Belogo, Barentseva i Karskogo morei (Processing method of satellite altimetry data for the White, Barents and Kara Seas), Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2016, Vol. 13, No. 6, pp. 203–223.
- Myslenkov S. A., Ispol’zovanie sputnikovoi al’timetrii dlya rascheta perenosa vod v Severnoi Atlantike (Using satellite altimetry to calculate the transport of waters in the North Atlantic), Trudy GU “Gidromettsentr Rossii”, 2011, Vol. 345, pp. 119–125.
- Chernov I. A., Tolstikov A. V., Chislennoe modelirovanie krupnomasshtabnoi dinamiki Belogo morya (Numerical modeling of a large-scale dynamics of the White Sea), Trudy Karel’skogo nauchnogo tsentra RAN, 2014, Vol. 4, pp. 137–142.
- Agoshkov V. I., Inverse problems of the mathematical theory of tides: boundary-function problem, Russian J. Numerical Analysis and Mathematical Modelling, 2005, Vol. 20, No. 1, pp. 1–18.
- Agoshkov V. I., Statement and study of some inverse problems in modelling of hydrophysical fields for water areas with ‘liquid’ boundaries, Russian J. Numerical Analysis and Mathematical Modelling, 2017, Vol. 32, No. 2, pp. 73–90.
- Agoshkov V. I., Sheloput T. O., The study and numerical solution of some inverse problems in simulation of hydrophysical fields in water areas with ‘liquid’ boundaries, Russian J. Numerical Analysis and Mathematical Modelling, 2017, Vol. 32, No. 3, pp. 147–164.
- Dementyeva E. V., Karepova E. D., Shaidurov V. V., Assimilation of observation data in the problem of surface wave propagation in a water area with an open boundary, Russian J. Numerical Analysis and Mathematical Modelling, 2014, Vol. 29, No. 1, pp. 13–23.
- Marchesiello P., McWilliams J. C., Shchepetkin A., Open boundary conditions for long-term integration of regional oceanic models, Ocean Modelling, 2001, Vol. 3, pp. 1–20.
- Ngodock H., Carrier M., Smith S., Martin P., Muscarella P., Jacobs G., Souopgui I., On the direct assimilation of along-track sea-surface height observations into a free-surface ocean model using a weak constraints four-dimensional variational (4D-Var) method, Quarterly J. Royal Meteorological Society, 2016, Vol. 142, pp. 1160–1170.
- Pujol M.-I., Faugère Y., Taburet G., Dupuy S., Pelloquin C., Ablain M., Picot N., DUACS DT2014: the new multi-mission altimeter data set reprocessed over 20 years, Ocean Science, 2016, Vol. 12, pp. 1067–1090.
- Zalesny V. B., Gusev A. V., Chernobay S. Yu., Aps R., Tamsalu R., Kujala P., Rytkӧnen J., The Baltic Sea circulation modelling and assessment of marine pollution, Russian J. Numerical Analysis and Mathematical Modelling, 2014, Vol. 29, No. 2. pp. 129–138.