Physical Oceanography, Vol.
MATHEMATICAL MODELING OF MARINE SYSTEMS
A PROCEDURE OF RECONSTRUCTION OF THE CLIMATIC SEASONAL
CIRCULATION IN THE BLACK SEA BASED ON THE ASSIMILATION
OF HYDROLOGICAL DATA IN THE MODEL
V. V. Knysh, S. G. Demyshev, and G. K. Korotaev
We propose a procedure of reconstruction of the continuous (in time) climatic annual behavior of
circulation in the Black Sea based on the successive assimilation of the climatic distributions of
temperature and salinity in the complete nonlinear model. We use monthly average arrays inter-
polated for each day of a year by expanding in harmonic functions of time. Various procedures
aimed at the assimilation of data are studied by taking into account the variance of measurement
errors. Our main attention is given to the analysis of qualitative and quantitative characteristics
of vertical motions in the sea depending on the quality of the data and parameters of the model.
The main version of calculations is illustrated by the maps of annual variability of the fields of
sea level, horizontal currents, and vertical velocity.
Although the problem of reconstruction of the climatic fields of currents in the Black Sea is studied in
numerous works [1–11], it remains quite important and urgent. This is explained by the following factors:
At present, the monthly climatic fields of temperature and salinity of the Black Sea reconstructed on the
basis of the archival experimental data are available from the literature [12, 13]. However, these arrays are
sometimes imperfect and incomplete due to the fact that, for some regions of the sea, the accumulated data of
observations are quite poor, their distributions are nonuniform, and the measurement errors are significant. As a
result, the climatic fields contain well-pronounced noises whose level increases at depths greater than
The imperfectness of the climatic arrays of temperature and salinity manifests itself especially clearly in recon-
structing the fields of geostrophic currents.
For the geostrophic velocities reconstructed according to the monthly climatic fields of temperature and
salinity, the level of noises is higher . Note that it is impossible to estimate the vertical velocity in the sea by
using these data.
The diagnostic method developed by A.
Sarkisyan for the numerical analysis of currents enables one to
avoid the necessity of introducing an arbitrarily specified zero surface but fails to suppress the noises present in
the climatic arrays. Therefore, in developing prognostic calculations on the basis of diagnostic methods, it was
proposed to use a procedure of reconstruction of climatic fields on the basis of adaptive calculations [5, 8, 11].
Within the framework of this procedure, the complete model of the dynamics of sea currents is integrated from
the initial conditions obtained by using diagnostic methods up to the completion of the stage of geostrophic
adaptation of the fields of currents, temperature, and salinity (density) accompanied by the filtration of noises.
The choice of the criteria of adaptation of fields in calculations of this sort is not evident. Therefore, the dura-
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
36–52, March–April, 2002. Original article submitted June 12, 2000.
88 0928–5105/02/1202–0088 $27.00 © 2002 Plenum Publishing Corporation