barotropic transport over the section may appear beyond the variability range of its
instantaneous values. This fact indicates that the total transport derived from the
barotropic transport deviation differs from the real values by unknown quantity,
which requires an assessment of the baroclinic transport variability.
In order to estimate quantitatively the distortions of the barotropic component of
the current, let us consider the level of the ocean surface ζ along the section line as a
function of two variables: time t and distance along section x; the positive direction
along the x axis corresponds to the direction of the section:
ζ = ζ x, t
ð Þ.
ð2Þ
The total differential of this function, dζ is written as:
dζ =
∂ζ
∂x
t
dx +
∂ζ
∂t
x
dt.
ð3Þ
We perform a transition from continuous function ζ to its approximation over the
section by the finite differences. Then, the total differential can be written as:
Δζ = ζ x i + 1 , t i + 1
ð
Þ− ζ x i , t i
ð
Þ,
ð4Þ
where the subscript corresponds to the station number. In this approach, each
station is assigned a single point in time and a single point in the ocean. However,
in the practice, the measurements at each station take a certain time interval and, in
addition, the drift of the vessel takes place during the station. The resulting variability of the level can be interpreted as a variation (determination error) of the
mentioned parameter at the station. This problem will be considered separately in
section “Error Estimates”.
In the representation of the level difference (and hence of the barotropic component of the current) between the stations according to formula (4), there is an
exact physical correspondence in time between the ocean level and the CTD profiles measured at these points. In this case, from the point of view of the contribution of the baroclinic and barotropic components of the current to the total
transport for a given pair of stations, we also obtain an exact physical relation
between these components. We note that because of the nonstationarity of the
current field and the fact that the measurements at different stations are made at
different moments of time, the calculated profiles of absolute geostrophic velocities
do not exist in reality, i.e. they are virtual. A similar method for calculating absolute
geostrophic currents was used in [9].
We add and subtract ζ x i + 0.5 , t i
ð
Þand ζ x i + 0.5 , t i + 1
ð
Þon the right side of formula
(4), which are the values of the level in the middle of the space between the i-th and
i + 1-st stations at the i-th and i + 1-st time moments, respectively. We obtain
368
R. Yu. Tarakanov
instantaneous values. This fact indicates that the total transport derived from the
barotropic transport deviation differs from the real values by unknown quantity,
which requires an assessment of the baroclinic transport variability.
In order to estimate quantitatively the distortions of the barotropic component of
the current, let us consider the level of the ocean surface ζ along the section line as a
function of two variables: time t and distance along section x; the positive direction
along the x axis corresponds to the direction of the section:
ζ = ζ x, t
ð Þ.
ð2Þ
The total differential of this function, dζ is written as:
dζ =
∂ζ
∂x
t
dx +
∂ζ
∂t
x
dt.
ð3Þ
We perform a transition from continuous function ζ to its approximation over the
section by the finite differences. Then, the total differential can be written as:
Δζ = ζ x i + 1 , t i + 1
ð
Þ− ζ x i , t i
ð
Þ,
ð4Þ
where the subscript corresponds to the station number. In this approach, each
station is assigned a single point in time and a single point in the ocean. However,
in the practice, the measurements at each station take a certain time interval and, in
addition, the drift of the vessel takes place during the station. The resulting variability of the level can be interpreted as a variation (determination error) of the
mentioned parameter at the station. This problem will be considered separately in
section “Error Estimates”.
In the representation of the level difference (and hence of the barotropic component of the current) between the stations according to formula (4), there is an
exact physical correspondence in time between the ocean level and the CTD profiles measured at these points. In this case, from the point of view of the contribution of the baroclinic and barotropic components of the current to the total
transport for a given pair of stations, we also obtain an exact physical relation
between these components. We note that because of the nonstationarity of the
current field and the fact that the measurements at different stations are made at
different moments of time, the calculated profiles of absolute geostrophic velocities
do not exist in reality, i.e. they are virtual. A similar method for calculating absolute
geostrophic currents was used in [9].
We add and subtract ζ x i + 0.5 , t i
ð
Þand ζ x i + 0.5 , t i + 1
ð
Þon the right side of formula
(4), which are the values of the level in the middle of the space between the i-th and
i + 1-st stations at the i-th and i + 1-st time moments, respectively. We obtain
368
R. Yu. Tarakanov