Simulation of water circulation in the Baltic
Sea for selected months form April to November
(Symulacja cyrkulacji wód Baltyku dla
wybranych misiecy od kwietnia do listopada),
Rozprawy i Monografie IO PAN, 1998, 8, 1- 165, (in Polish)
Though simplified, this set of typical mean 'states'
of the model describes with sufficient accuracy the spatial structural
patterns of water movements in the Baltic Sea, thereby enabling non - modellers,
e.g. ecologists, geochimists or biologists, to apply the results of mathematical
models, not yet described in oceanographic literature. As the monograph
was conceived as a kind of atlas, the results of computations are presented
in the form
of charts and diagrams. The description of
the model itself and of the investigations performed its use was restricted
to an indispensable minimum.
Following a general introduction, the first chapter outlines the aims and scope of study, and the second provides the theoretical basis of the diagnostic model i.e. equations, boundary conditions and methods of solution. Chapter three describes the methods of estimating of physical model parameters and the forcing functions fields, that is to say, wind and density fields considered as climatic, long - term mean for each month. Making up the bulk of the work, chapter four includes the results of model computations. In chapter five the validation of computations is commented on with respect to the results of field studies written up in the oceanological literature. The monograph concludes with the some final comments on the results.
The model is based on the linearized set of steady equations of motion for horizontal components of current vector and continuity equation, with vertical eddy viscosity coefficient (assumed constant with z- axis), written with the hydrostatic and Boussinesq approximations (section 2.1).
The horizontal current velocity components are calculated from the analytical Ekman - type solution (section 2.2). The vertical component of the current velocity vector is estimated with the aid (help) of model based on the equation for the z-th vorticity component of the water shear stress (section 2.3).
The sea level,essential in estimation of the current
velocity vector components, is calculated from the numerical solution of
the set of equal to non - stationary equations for mass transport and sea
level (section 2.4). The finite - difference H - N scheme of Hansen with
the space and time steps equal to h_{x} = 7,5', h_{y} = 5' and \tau =
60 sec, respectively, was applied (section 2.5). In numerical calculations
the Baltic Sea was assumed as closed basin without taking into account
the river inflows.
The wind stress and baroclinic stress, expressing
the joint effects of spatial heterogenity of sea water density and
bottom
relief, stand as forcing functions for water
circulation (chapter 3). In figs. 3.2 - 3.9 the fields of wind velocity
vectors (calculated
with the aid of the model of gradient wind) for
each months are shown and respectively, in figs. A1.1 - A1.8 and A2.1 -
A2.8 (Appendix 1 and 2), the fields of baroclinic stress vectors are depicted.
The results of numerical calculations for selected
months have been presented in the form of schematic charts with isolines
of stream function for mass transport Psi (figs. 4.1 - 4.8), vectors of
mean - depth currents (figs. 4.9 - 4.16),
isolines of sea level (figs. 4.17 - 4.24) and
with vectors of horizontal currents at the sea surface (figs. 4.25 - 4.32),
and
at the depths of 20 m (figs. 4.33 - 4.40) and
of 40 m (figs. 4.41 - 4.48).
The fields with isolines of the vertical vector
velocity component at the selected depths: 30 m (figs. 4.49 - 4.56) and
50 m
(figs. 4.57 - 4.64) and the distributions of
the vertical velocity along five vertical longitudinal sections (figs.
4.66 - 4.70)
in some of the Baltic Proper (location of longitudinal
sections - see fig. 4.65) complete the picture of the water circulation
in the sea.
Cyclonic gyres - like structures prevail in the
fields of horizontal flow characteristics and their location are related
to the deepest regions of the sea - baltic deeps. Intensity and location
of the gyres changes from month to month but some specific tendency for
each seasons, especially, for spring and autumn months, when the variability
and amplitudes flows are the highest, may be observed. "Seasonality" of
variability of the water circulation parameters are closely correlated
with the spatial and temporal
variability of the fields of the forcing functions.
The results of calculations confirmed the results
of the previous investigations of water circulation in the Baltic (Sarkisyan
et al., 1975; Kowalik and Staskiewicz, 1976; Simons, 1978; Kielmann, 1981;
Funkquist and Gidhagen, 1984; Staskiewicz, 1988; Kullas and Tamsalu, 1975;
Mälkki and Tamsalu, 1985), concern on the
important role of the baroclinic of sea water and the bottom topography
(JEBAT - the Joint Effect of Baroclinicity and Topography of the sea bottom,
(Sarkisyan, 1977a,b)) in forming climaic, seasonal wind and density - driven
flows in the Baltic Sea Wind force play minor role and its influence on
circulations can be seen only for the autumn months, when the wind velocities
approach their maximal values.
Confrontation of the results of modelling, made
only qualitatively for the case of horizontal currents, because of lack
of the results of the
in situ measurements, confirmed that the model
patterns of water circulation in the Baltic Sea are in general agreement
with the known schemas of the
layout of the surface current vectors so in the
Baltic itself as in its Gulfs (section 5.1). Quantative verification of
the results of calculations of the sea level zeta (based on paper
of Lazarenko (1961), section 5.2, tab. 10 and figs. 5.4 - 5.14) showed
good agreements so in values of zeta as in seasonal variability of
that flow characteristic, so essential in the estimating the current velocity
components, at the greater number of the mareographic stations of the Baltic
Sea.
The charts of the flow characteristics, presented
in the work, indicate that for each months in the vicinity of the baltic
Deeps
the clusters of closed cyclonic (anticyclonic)
gyres in the horizontal current fields can be seen. These spatial patterns
are easily correlated with
the distributions of upwelling (downwelling)
regions in the fields of the vertical current velocity component.
In these gyre - like structures conditions are
created in which chemical, biological or geological substances can accumulate
more readily, by
comparison with adjacent water regions. This
may, in following, intensify activity of biological processes or form zones
with imperceptible
concentration of oxygen or with occurance of
hydrogen sulphide). Location of the spatial distributions of clusters (patterns)
of so - called "dead - zones" (low concentration
of oxygen or zones with occurance of hydrogen sulphide) in the deepest
areas of the Baltic Sea
(Melvasalo et al. 1981; Andersin and Sandler,
1988; Trzosinska, 1994) are nearly identical with the areas of the "permanent"
upwelling
(downwelling) observed at the charts of the isolines
of the vertical current velocity component w.
Results of field investigations on the coastal
upwellings, frequently observed in different parts of the Baltic Sea (tab.
12, fig. 5.25)
may provide useful information to confirm qualitatively
validation of the diagnostic model. The location of the zones of upwellings
are
similar to the location of the regions with clusters
of the extremal values of vertical velocity in the coastal zones of the
model Baltic Sea basin (fig. 5.17 - 5.24).
Thus it seems reasonable to conclude, that the
presented in the paper "atlas" collection of typical mean "states" of the
water dynamics for selected months may be useful for elucidating the hydrological
background necessary to diagnose the state of the Baltic Sea marine environment
on seasonal time scale, especially in stagnation periods.
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