Physical Oceanography, Vol. 18, No. 4, 2008
THERMOHYDRODYNAMICS OF THE OCEAN
ASSIMILATION OF CLIMATIC DATA IN A MODEL OF CIRCULATION OF
WATERS IN THE BLACK SEA WITH REGARD FOR THE SPACE AND
TIME BEHAVIOR OF THE VARIANCES AND CROSS-COVARIANCE
FUNCTIONS OF FORECAST ERRORS
V. V. Knysh and N. V. Inyushina
We propose an improvement of the algorithm of joint assimilation of the data on climatic tempe-
rature, salinity, and altimetric sea level in a model of circulation. Unlike the previous works, the
variances of the forecast errors of temperature and salinity and the cross-covariance functions of
of the forecast errors of salinity-level and temperature-level depend on the dynamics of waters.
It is shown that the structure of the fields of cross-covariance functions in the upper mixed layer
is formed by the vertical turbulent diffusion of the variances of forecast errors of temperature and
salinity. At greater depths, these statistical characteristics are mainly determined by the vertical
advection. We compared the results of calculations with and without taking into account the dy-
namics of the statistical characteristics. The analysis of the influence of the dynamics of these
characteristics makes it possible to reconstruct the mutually adapted climatic fields of tempera-
ture, salinity, and horizontal and vertical current velocities in the Black Sea with the assimilation
of data in the numerical model in each time step.
In addition to the available arrays of climatic data on the temperature and salinity of waters in the Black Sea
, we can mention the appearance of a new climatic database of monthly average fields of dynamic sea level
. These fields and the corresponding fields of temperature and salinity were obtained as a result of the assi-
milation of the data of altimetry measurements for 1992–2003 in the model .
In , it is shown that, parallel with the climatic thermohaline fields, the climatic altimetry fields also con-
tain the data on the long-term variations of hydrophysical characteristics of the Black Sea. This is why a proce-
dure of joint assimilation of the climatic hydrological temperature and salinity fields and the fields of climatic al-
timetry level in a dynamic model of the sea was proposed in . It was assumed that the variances of the fore-
cast errors of temperature and salinity and the cross-covariance functions of the forecast errors of salinity-level
and temperature-level do not depend on the dynamics of the sea.
In the present work, we propose an improvement of the algorithm of joint assimilation of the data on clima-
tic temperature, salinity, and sea level in the model of circulation. Unlike , we take into account the depen-
dences of the variances of the forecast errors of temperature and salinity and the cross-covariance functions of
the forecast errors of salinity-level and temperature-level (appearing as sources in the transfer equations of heat
and salt diffusion) on the dynamics of the sea. The dynamics of the indicated statistical characteristics is taken
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
18–31, July–August, 2008. Original article submitted January 18, 2007;
revision submitted January 31, 2007.
0928-5105/08/1804–0179 © 2008 Springer Science+Business Media, Inc. 179