Physical Oceanography, Vol. 18, No. 1, 2008
ANALYSIS OF OBSERVATIONS AND METHODS FOR CALCULATING
HYDROPHYSICAL FIELDS IN THE OCEAN
ASSIMILATION OF CLIMATIC HYDROLOGICAL DATA IN A BLACK–SEA
MODEL BASED ON THE ALGORITHM OF ADAPTIVE STATISTICS OF
V. V. Knysh, S. G. Demyshev, N. V. Inyushina, and G. K. Korotaev
We propose an algorithm of adaptive statistics of prognostic errors aimed at the assimilation of
the climatic temperature and salinity fields in a model of dynamics of the sea. The algorithm is
used for the numerical solution of the proposed differential equations for the dispersions of prog-
nostic errors of temperature and salinity. The sources in the equations of advective diffusion of
heat and salt depend on the four-dimensional dispersions of prognostic errors and one-dimen-
sional (along the vertical coordinate) dispersions of measurement errors. The dispersions of
prognostic errors are corrected at the times of assimilation of the data. We perform the recon-
struction and analysis of the climatic fields of currents in the Black Sea. It is shown that the
structure of the fields of dispersions in the upper mixed layer is determined by the vertical diffu-
sion. Below this layer, the distribution of dispersions depends on the vertical advection. The al-
gorithm of adaptive statistics of prognostic errors allows us to reconstruct the improved mutually
adapted hydrophysical parameters with regard for the dynamics of the dispersions of errors.
In [1, 2], we proposed a method and reconstructed climatic currents in the Black Sea on the basis of assi-
milation of two different climatic arrays of temperature and salinity in a model of dynamics of the sea. The
simplified algorithm of assimilation used in the cited works can be described as follows: A source whose inten-
sity is proportional to the difference between the climatic and model temperature (salinity) is included in the
equation of advective heat (or salt) diffusion. The parameter of proportionality is specified by the inverse depen-
dence on the coefficient of relaxation and normalized dispersion of measurement errors (used as a measure of
these errors ). The indicated measure of errors is a priori chosen in the form of a nonlinear function of the
vertical coordinate independent of time. The climatic data are assimilated in each time step of the numerical mo-
del. As follows from the analysis of the numerical results, the role of the data of observations is, in this case,
overestimated and the reconstructed climatic fields are weakly compatible both with each other and with the ex-
ternal boundary conditions. This affects mostly the qualitative and quantitative characteristics of the vertical
velocity. Its fields contain small-scale alternating zones of downwelling and upwelling and, as follows from the
indirect estimates [4, 5], the values of the vertical velocity are overestimated .
A procedure of periodic assimilation of the data is proposed in . According to this procedure, the assi-
milation sources are computed and included in the equations at certain times. Between these times, the process
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
26–37, January–February, 2008.
Original article submitted June 29,
2006; revision submitted August 8, 2006.
14 0928-5105/08/1801–0014 © 2008 Springer Science+Business Media, Inc.