mostly because of the significant difference between the potential and in situ
temperature and due to the fact that the grid resolution at the sea bottom is large
enough.
Conclusions
We emphasize the importance and significance of the DA strategy in the climate
research. By changing the initial conditions and setting them up with the DA
methods and different set of data it is possible to investigate the sensitivity of the
model and also the influence of the different regions on the initial data perturbations. It allows us to make the long- and medium range forecasts of different
parameters. It is important to note, that in these experiments it is necessary to keep
the balance between the input variables and conserve the integral mass and energy.
The data assimilation method is developed exactly for these purposes.
Acknowledgements This work was supported by the Russian Science Foundation: numerical
calculations were supported by project 14-11-00434.
References
1. Belyaev, K., Meyers, S., & O’Brien, J. J. (2000). Application of the Fokker-Planck equation
to data assimilation into hydrodynamical models. Journal of Mathematical Sciences, 99(4),
1393–1402.
2. Belyaev, K. P., Kuleshov, A. A., Tuchkova, N. P., & Tanajura, C. A. S. (2016). A correction
method for dynamic model calculations using observational data and its application in
oceanography. Mathematical Models and Computer Simulations, 8(4), 391–400.
3. Belyaev, K. P., Kuleshov, A. A., & Tanajura, C. A. S. (2016). An application of a data
assimilation method based on the diffusion stochastic process theory using altimetry data
in Atlantic. Russian Journal of Numerical Analysis and Mathematical Modelling, 31(3),
137–148.
4. Bryan, K. (1969). A numerical method for the study of the World Ocean. Journal of
Computational Physics, 3, 347–376.
5. Evensen, G. (2003). The ensemble Kalman filter: Theoretical formulation and practical
implementation. Ocean Dynamics, 53, 343–367.
6. Gandin, L. S. (1963). An objective analysis of hydrometeorologycal fields. Leningrad:
Gidrometizdat (in Russian).
7. Ghil, M., & Malnotte-Rizzoli, P. (1991). Data assimilation in meteorology and oceanography.
Advances in Geophysics, 33, 141–266.
8. Haak, H. (2004). Simulation of low-frequency climate variability in the north atlantic ocean
and the arctic, V.1. Max Planck Institute for Meteorology.
9. Kirtman, B., & Shukla, J. (2002). Interactive coupled ensemble: A new coupling strategy for
CGCMs. Geophysics Research Letters, 29(10), 245–272.
10. Marchuk, G. I., & Sarkisayn, A. S. (1988). Mathematical modeling of ocean circulation.
Moscow, Nauka (in Russian).
458
K. P. Belyaev et al.
temperature and due to the fact that the grid resolution at the sea bottom is large
enough.
Conclusions
We emphasize the importance and significance of the DA strategy in the climate
research. By changing the initial conditions and setting them up with the DA
methods and different set of data it is possible to investigate the sensitivity of the
model and also the influence of the different regions on the initial data perturbations. It allows us to make the long- and medium range forecasts of different
parameters. It is important to note, that in these experiments it is necessary to keep
the balance between the input variables and conserve the integral mass and energy.
The data assimilation method is developed exactly for these purposes.
Acknowledgements This work was supported by the Russian Science Foundation: numerical
calculations were supported by project 14-11-00434.
References
1. Belyaev, K., Meyers, S., & O’Brien, J. J. (2000). Application of the Fokker-Planck equation
to data assimilation into hydrodynamical models. Journal of Mathematical Sciences, 99(4),
1393–1402.
2. Belyaev, K. P., Kuleshov, A. A., Tuchkova, N. P., & Tanajura, C. A. S. (2016). A correction
method for dynamic model calculations using observational data and its application in
oceanography. Mathematical Models and Computer Simulations, 8(4), 391–400.
3. Belyaev, K. P., Kuleshov, A. A., & Tanajura, C. A. S. (2016). An application of a data
assimilation method based on the diffusion stochastic process theory using altimetry data
in Atlantic. Russian Journal of Numerical Analysis and Mathematical Modelling, 31(3),
137–148.
4. Bryan, K. (1969). A numerical method for the study of the World Ocean. Journal of
Computational Physics, 3, 347–376.
5. Evensen, G. (2003). The ensemble Kalman filter: Theoretical formulation and practical
implementation. Ocean Dynamics, 53, 343–367.
6. Gandin, L. S. (1963). An objective analysis of hydrometeorologycal fields. Leningrad:
Gidrometizdat (in Russian).
7. Ghil, M., & Malnotte-Rizzoli, P. (1991). Data assimilation in meteorology and oceanography.
Advances in Geophysics, 33, 141–266.
8. Haak, H. (2004). Simulation of low-frequency climate variability in the north atlantic ocean
and the arctic, V.1. Max Planck Institute for Meteorology.
9. Kirtman, B., & Shukla, J. (2002). Interactive coupled ensemble: A new coupling strategy for
CGCMs. Geophysics Research Letters, 29(10), 245–272.
10. Marchuk, G. I., & Sarkisayn, A. S. (1988). Mathematical modeling of ocean circulation.
Moscow, Nauka (in Russian).
458
K. P. Belyaev et al.