In this scheme, the total barotropic transport over the section is written as:
Q
′
alt = ∑
i = 1, n − 1
q alt x i + 0.5 , t i + 0.5
ð
Þ ≡ ∑
i = 1, n − 1
ζ x i + 1 , t i + 1
ð
Þ− ζ x i , t i
ð
Þ
ð
Þ
g i + 0.5 h ̄
i + 0.5
f i + 0.5
;
ð13Þ
the barotropic current, approximating ADCP measurements:
Q
′
adcp = Q
′
alt − Q t ,
ð14Þ
here Q t , as in the first scheme, is calculated from formula (10); the anomaly of the
total barotropic transport is:
ΔQ
′
alt t
ð Þ = ∑
i = 1, n − 1
Δq alt x i + 0.5 , t
ð
Þ≡ ∑
i = 1, n − 1
Δζ x i + 1 , t
ð
Þ− Δζ x i , t
ð Þ
ð
Þ
g i + 0.5 h ̄
i + 0.5
f i + 0.5
,
ð15Þ
where Δζ x i , t
ð Þ= ζ x i , t
ð Þ− ζ x i , t i
ð
Þ. The value of ΔQ
′
alt t
ð Þ does not depend on the
mean dynamic topography of the ocean. The range of values ΔQ
′
alt t
ð Þ determines
the variability of the total barotropic transport during the time of the section.
The anomalies of the total barotropic ΔQ
′
alt t
ð Þ, and the barotropic transports
ΔQ adcp t
ð Þ approximating the ADCP-measurements are related as:
ΔQ adcp t
ð Þ = ΔQ
′
alt t
ð Þ + Q t + ΔQ − ΔQ t
ð Þ,
ð16Þ
where variables
ΔQ = Q
′
alt t
ð Þ − Q adcp − Q t ,
ð17Þ
and
ΔQ t
ð Þ = Q
′
alt t
ð Þ − Q adcp t
ð Þ
ð18Þ
determine the quantitative difference between two finite difference schemes of the
representation of the section track in the course of measurements over the section
and for the instantaneous values of the transport in time, respectively. In this sense,
they are important characteristics in estimating the accuracy of the calculation.
Separately, these variables depend on the mean dynamic topography.
According to the previous theoretical justification, the calculations of the barotropic component of the current, barotropic transport, their temporal variability and
values characterizing the accuracy of calculations over individual sections presented
in Table 1 were performed. The data on SLA and ADT were interpolated linearly in
space along the tracks of the sections according to two schemes: to the points of the
stations and to the midpoints of the spaces between stations, and also in time for the
Influence of the Current Field Non-stationarity …
375
Q
′
alt = ∑
i = 1, n − 1
q alt x i + 0.5 , t i + 0.5
ð
Þ ≡ ∑
i = 1, n − 1
ζ x i + 1 , t i + 1
ð
Þ− ζ x i , t i
ð
Þ
ð
Þ
g i + 0.5 h ̄
i + 0.5
f i + 0.5
;
ð13Þ
the barotropic current, approximating ADCP measurements:
Q
′
adcp = Q
′
alt − Q t ,
ð14Þ
here Q t , as in the first scheme, is calculated from formula (10); the anomaly of the
total barotropic transport is:
ΔQ
′
alt t
ð Þ = ∑
i = 1, n − 1
Δq alt x i + 0.5 , t
ð
Þ≡ ∑
i = 1, n − 1
Δζ x i + 1 , t
ð
Þ− Δζ x i , t
ð Þ
ð
Þ
g i + 0.5 h ̄
i + 0.5
f i + 0.5
,
ð15Þ
where Δζ x i , t
ð Þ= ζ x i , t
ð Þ− ζ x i , t i
ð
Þ. The value of ΔQ
′
alt t
ð Þ does not depend on the
mean dynamic topography of the ocean. The range of values ΔQ
′
alt t
ð Þ determines
the variability of the total barotropic transport during the time of the section.
The anomalies of the total barotropic ΔQ
′
alt t
ð Þ, and the barotropic transports
ΔQ adcp t
ð Þ approximating the ADCP-measurements are related as:
ΔQ adcp t
ð Þ = ΔQ
′
alt t
ð Þ + Q t + ΔQ − ΔQ t
ð Þ,
ð16Þ
where variables
ΔQ = Q
′
alt t
ð Þ − Q adcp − Q t ,
ð17Þ
and
ΔQ t
ð Þ = Q
′
alt t
ð Þ − Q adcp t
ð Þ
ð18Þ
determine the quantitative difference between two finite difference schemes of the
representation of the section track in the course of measurements over the section
and for the instantaneous values of the transport in time, respectively. In this sense,
they are important characteristics in estimating the accuracy of the calculation.
Separately, these variables depend on the mean dynamic topography.
According to the previous theoretical justification, the calculations of the barotropic component of the current, barotropic transport, their temporal variability and
values characterizing the accuracy of calculations over individual sections presented
in Table 1 were performed. The data on SLA and ADT were interpolated linearly in
space along the tracks of the sections according to two schemes: to the points of the
stations and to the midpoints of the spaces between stations, and also in time for the
Influence of the Current Field Non-stationarity …
375