340
T. Soomere
and from Lahemaa to Paldiski along the southern coast of the gulf. On the contrary,
an intense exchange of water with the offshore is typical for Narva Bay and NE
coast of Estonia.
The areas with relatively large particle age are located, as expected, far from the
coasts and islands. Their spatial distribution (Fig. 10.4) mirrors the properties of a
similar distribution for the probabilities such as a rich internal structure and a certain
asymmetry in the North-South direction. The distribution of the particle age in areas
with a ij > 6 days is obviously smoothed to some extent owing to the use of 10-day
long time windows. The largest values of particle age and the smallest probabilities
are located in areas considerably shifted to the north from the geometrical axis of
the gulf in the narrowest part of the gulf between Tallinn and Helsinki. These areas
do not necessarily coincide with domains that have the longest distance to the coast.
This implicitly reflects the anisotropy of the surface currents and signifies that the
entire approach leads to nontrivial results for the Gulf of Finland.
10.5.5 Dependence on Spatial Resolution
The discussed properties obviously depend on the ability of the circulation model
to represent the geometry and bathymetry of the basin and to resolve mesoscale
motions. The dependence of the distributions of probabilities and of the particle age
on the model resolution was studied using the OAAS model with spatial resolutions
of 2, 1 and 0.5 nm and otherwise identical setup, forcing and boundary conditions.
The number of sea points in the calculation area was 2270 for the 2 nm model, 8810
for the 1 nm model and 31,838 for the 0.5 nm model (Andrejev et al. 2010).
The temporal behaviour of the mean probability P (k) and particle age A(k) for
particular time windows, and their cumulative values ¯
P (n) and ¯
A(n) was very similar for all horizontal resolutions (Fig. 10.5). The time series of P (k) and A(k) are
highly correlated (for example, r = 0.98 for the 1 nm and 0.5 nm simulations) and
have small bias, mean and root-mean-square deviation, and also a very low level of
spread. The standard deviations for the pointwise values from the average values of
P (k) and A(k) are almost the same for different resolutions (Andrejev et al. 2011).
This suggests that the variations in these fields with respect to the mean values have,
on average, a similar structure.
The estimates of the asymptotic values ¯
P (N max ) and ¯
A(N max ) are practically
insensitive to the resolution of the ocean model. Therefore, these quantities are to
some extent similar to certain scalar fields such as salinity and temperature that are
also well represented by eddy-permitting models starting from a 1 nm resolution.
The resolution of the ocean model affects to some extent the 2D maps of the
probability p ij and particle age a ij (Fig. 10.6). The overall appearance of these
maps, the location of the isolines and the areas of low probabilities and high particle
age largely coincide for all resolutions. The largest differences between the relevant
maps at the resolutions of 1 nm and 0.5 nm are in the size of the areas of the smallest
T. Soomere
and from Lahemaa to Paldiski along the southern coast of the gulf. On the contrary,
an intense exchange of water with the offshore is typical for Narva Bay and NE
coast of Estonia.
The areas with relatively large particle age are located, as expected, far from the
coasts and islands. Their spatial distribution (Fig. 10.4) mirrors the properties of a
similar distribution for the probabilities such as a rich internal structure and a certain
asymmetry in the North-South direction. The distribution of the particle age in areas
with a ij > 6 days is obviously smoothed to some extent owing to the use of 10-day
long time windows. The largest values of particle age and the smallest probabilities
are located in areas considerably shifted to the north from the geometrical axis of
the gulf in the narrowest part of the gulf between Tallinn and Helsinki. These areas
do not necessarily coincide with domains that have the longest distance to the coast.
This implicitly reflects the anisotropy of the surface currents and signifies that the
entire approach leads to nontrivial results for the Gulf of Finland.
10.5.5 Dependence on Spatial Resolution
The discussed properties obviously depend on the ability of the circulation model
to represent the geometry and bathymetry of the basin and to resolve mesoscale
motions. The dependence of the distributions of probabilities and of the particle age
on the model resolution was studied using the OAAS model with spatial resolutions
of 2, 1 and 0.5 nm and otherwise identical setup, forcing and boundary conditions.
The number of sea points in the calculation area was 2270 for the 2 nm model, 8810
for the 1 nm model and 31,838 for the 0.5 nm model (Andrejev et al. 2010).
The temporal behaviour of the mean probability P (k) and particle age A(k) for
particular time windows, and their cumulative values ¯
P (n) and ¯
A(n) was very similar for all horizontal resolutions (Fig. 10.5). The time series of P (k) and A(k) are
highly correlated (for example, r = 0.98 for the 1 nm and 0.5 nm simulations) and
have small bias, mean and root-mean-square deviation, and also a very low level of
spread. The standard deviations for the pointwise values from the average values of
P (k) and A(k) are almost the same for different resolutions (Andrejev et al. 2011).
This suggests that the variations in these fields with respect to the mean values have,
on average, a similar structure.
The estimates of the asymptotic values ¯
P (N max ) and ¯
A(N max ) are practically
insensitive to the resolution of the ocean model. Therefore, these quantities are to
some extent similar to certain scalar fields such as salinity and temperature that are
also well represented by eddy-permitting models starting from a 1 nm resolution.
The resolution of the ocean model affects to some extent the 2D maps of the
probability p ij and particle age a ij (Fig. 10.6). The overall appearance of these
maps, the location of the isolines and the areas of low probabilities and high particle
age largely coincide for all resolutions. The largest differences between the relevant
maps at the resolutions of 1 nm and 0.5 nm are in the size of the areas of the smallest