Physical Oceanography, Vol. 19, No. 6, 2009
THERMOHYDRODYNAMICS OF THE OCEAN
ASSIMILATION OF THE CLIMATIC HYDROLOGICAL DATA IN THE
-COORDINATE MODEL OF THE BLACK SEA BY THE ALGORITHM
OF ADAPTIVE STATISTICS
A. I. Mizyuk, V. V. Knysh, A. I. Kubryakov, and G. K. Korotaev
We realize the algorithm of adaptive statistics of forecasting errors for the assimilation of the cli-
matic fields of temperature and salinity in the
σ-coordinate model of the dynamics of the Black
Sea. The principal relations of this algorithm and its simplified version based on the Kalman fil-
ter are presented. The distinctive features of realization of the algorithm specified by the model
are discussed. We also present the results of comparison of the hydrophysical fields of the Black
Sea reconstructed according to the algorithm of adaptive statistics and a simplified scheme of as-
similation of the climatic data. It is shown that the dependence of sources in the transport equa-
tions (heat and salt diffusion) on the four-dimensional variances of forecasting errors and three-
dimensional measurement errors enables one to reconstruct the mutually adapted climatic param-
eters of the sea more exactly.
In a series of works published in recent years [1–4], various procedures aimed at the reconstruction of the
seasonal hydrophysical fields in the Black Sea on the basis of assimilation of the climatic temperature and sali-
nity fields in the model of circulation were proposed and realized. The analyses carried out in these works are
based on the numerical nonlinear model developed at the Marine Hydrophysical Institute (MHI) of the Ukrainian
National Academy of Sciences and described in detail in . As an important feature of the procedure of data
assimilation in the model, we can mention the fact that the sources proportional to the differences between the
climatic and model temperatures and salinities are included in the transport equations (of heat and salt diffusion,
respectively). The proportionality factors are either independent of the statistical characteristics of forecasting
errors (simplified algorithm of assimilation [1–3]) or depend on the three-dimensional variances of these errors
regarded as functions of time . In the latter case, not only rapid (geostrophic) adjustment of the hydrophysical
parameters of the sea is realized but also the adaptation of the statistics of errors to the data of observations. The
approach based on the optimal Kalman filtration  and used in  is called the algorithm of adaptive statistics.
Note that, up to now, the process of vertical mixing in the model presented in  is described by the Paca-
nowski–Philander parametrization of turbulent exchange updated in . The
σ-coordinate Princeton Ocean Mo-
del (POM) adapted to the conditions of the Black Sea  uses the turbulence level-2.5-closure model based on
the Rotta–Kolmogorov turbulence hypotheses and generalized by Mellor and Yamada  to give a more correct
description of the thermodynamics of upper layer of the sea. For this reason, in , the seasonal variations of the
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–22, November–December, 2009. Original article submitted August 14,
2008; revision submitted September 11, 2008.
0928-5105/09/1906–0339 © 2009 Springer Science+Business Media, Inc. 339