118
H.E.M. Meier and A. Höglund
Meier (2007) extended the approach to analyse different water masses of the
Baltic Sea. He calculated concentrations of passive tracers and associated age concentrations following (Delhez et al. 1999; Deleersnijder et al. 2001). At any time t
and location r, the concentration of a tracer C(t, r) would obey the following equation:
∂C
∂t
+ ∇ · (uC − K · ∇C) = 0,
(4.34)
where u is the water velocity and K denotes the diffusivity tensor. The age concentration α(t, r) of the water mass under study is the solution of the following
equation:
∂α
∂t
+ ∇ · (uα − K · ∇α) = C,
(4.35)
Finally, the age is then given as the ratio a(t, r) = α(t, r)/C(t, r). For further details
of the concept of age in marine modelling the reader is referred to Deleersnijder et al.
(2001).
Meier (2007) performed a simulation using the RCO model where various water
masses were marked with passive tracers and the associated age of the specific water
masses was calculated. The aim was to better understand the large-scale circulation
and related time scales.
In this approach the initial tracer and age concentrations were set to zero. At
the open boundary in the Kattegat the same radiation conditions as used within the
RCO model for temperature and salinity were utilized. In case of inflow, at the open
boundary the concentrations of the tracers and associated age were relaxed to zero,
with a time scale of one day. At the sea surface no-flux boundary conditions were
used.
Mean age (in years) for the last five years of a 96-year long simulation associated to tracers either marking inflowing saltier water at the Darss and Drogden
Sills (Fig. 4.5) or inflowing fresh water from all rivers (Fig. 4.6) has been evaluated
by Meier (2007). At the sea surface of the Bornholm Basin, Gotland Basin, Sea
of Bothnia, and Bay of Bothnia the mean age associated to inflowing water from
the Kattegat amounts to 26–30, 28–34, 34–38, and 38–42 years, respectively. The
largest mean sea surface age of more than 30 years associated to the fresh water
of the rivers is found in the Eastern Gotland Basin and Belt Sea. At the bottom the
mean age is largest in the Western Gotland Basin and amounts to more than 36 years.
In the Baltic Proper vertical gradients of age associated to the fresh water inflow are
smaller than in the case of inflowing saltier water from the Kattegat indicating an
efficient recirculation of fresh water in the Baltic Sea. Thus, studies of passive tracers and associated age help to understand the physical processes important for the
large-scale vertical circulation in the Baltic Sea.
The studies described above have in common that 3D artificial tracers (that is,
tracers that are free to move in any direction in the water column) with simplified
sources and sinks are utilized. In the following the tracer concept will be applied to
oil spills restricting the calculation of spread to only two dimensions in the surface
layer.
H.E.M. Meier and A. Höglund
Meier (2007) extended the approach to analyse different water masses of the
Baltic Sea. He calculated concentrations of passive tracers and associated age concentrations following (Delhez et al. 1999; Deleersnijder et al. 2001). At any time t
and location r, the concentration of a tracer C(t, r) would obey the following equation:
∂C
∂t
+ ∇ · (uC − K · ∇C) = 0,
(4.34)
where u is the water velocity and K denotes the diffusivity tensor. The age concentration α(t, r) of the water mass under study is the solution of the following
equation:
∂α
∂t
+ ∇ · (uα − K · ∇α) = C,
(4.35)
Finally, the age is then given as the ratio a(t, r) = α(t, r)/C(t, r). For further details
of the concept of age in marine modelling the reader is referred to Deleersnijder et al.
(2001).
Meier (2007) performed a simulation using the RCO model where various water
masses were marked with passive tracers and the associated age of the specific water
masses was calculated. The aim was to better understand the large-scale circulation
and related time scales.
In this approach the initial tracer and age concentrations were set to zero. At
the open boundary in the Kattegat the same radiation conditions as used within the
RCO model for temperature and salinity were utilized. In case of inflow, at the open
boundary the concentrations of the tracers and associated age were relaxed to zero,
with a time scale of one day. At the sea surface no-flux boundary conditions were
used.
Mean age (in years) for the last five years of a 96-year long simulation associated to tracers either marking inflowing saltier water at the Darss and Drogden
Sills (Fig. 4.5) or inflowing fresh water from all rivers (Fig. 4.6) has been evaluated
by Meier (2007). At the sea surface of the Bornholm Basin, Gotland Basin, Sea
of Bothnia, and Bay of Bothnia the mean age associated to inflowing water from
the Kattegat amounts to 26–30, 28–34, 34–38, and 38–42 years, respectively. The
largest mean sea surface age of more than 30 years associated to the fresh water
of the rivers is found in the Eastern Gotland Basin and Belt Sea. At the bottom the
mean age is largest in the Western Gotland Basin and amounts to more than 36 years.
In the Baltic Proper vertical gradients of age associated to the fresh water inflow are
smaller than in the case of inflowing saltier water from the Kattegat indicating an
efficient recirculation of fresh water in the Baltic Sea. Thus, studies of passive tracers and associated age help to understand the physical processes important for the
large-scale vertical circulation in the Baltic Sea.
The studies described above have in common that 3D artificial tracers (that is,
tracers that are free to move in any direction in the water column) with simplified
sources and sinks are utilized. In the following the tracer concept will be applied to
oil spills restricting the calculation of spread to only two dimensions in the surface
layer.