| |
Tidal
modeling in the Adriatic Sea - MFSTEP annual report |
|
MFSTEP
- First Scientific Report (1st March, 2003 –
29th February, 2004) |
| |
| Partner
info |
|
| Subtask
info |
| N° |
9520 |
Title |
Inclusion
of tidal and atmospheric pressure forcing |
|
|
Abstract
Model results of the AREG tidal model, that is based on
Princeton Ocean Model (POM) architecture with sigma-coordinate
system, are presented together with the difficulties that
were encountered in running the model in 3D mode = 3. The
tidal model is almost sufficiently calibrated, with the
amplitude different from the observations for less than
2.2 cm and the phase for less than 29.5 0. Maximum difference
in phase occurred in a port that is the southern most one
along the eastern coast of the Adriatic Sea (Durres). |
Data and methods The AREG tidal model is based
on the concept of POM that is installed on a topographic
grid of 5 km x 5 km, provided by the project-coordinator
(INGV). A previous study of model response showed that the
AREG tidal model response depends mainly on the applied
topography (Fig. 1). |
|
Fig. 1. -
Study area with model topography. Note the open
boundary line (OBL) along the southern most grid
line. |
|
The majority of runs were performed in mode = 4, in which
temperature and salinity fields were not prognostic. Only
the final runs were in mode = 3 with constant temperature
(= 13 0C) and salinity (= 38 PSU). The resonance curve, obtained
from model results of the AREG model applied on the INGV topographic
grid, gave slightly lower values for first seiche period (21.2
h) and for the second seiche period (10.5 h), for about 0.4
h. It was decided, however, that even if the response of the
model would be better, from the point of view of the seiche
periods, by changing the model topography, the calibration
for each of seven major tidal constituents would not be shortened
and would have to follow the usual procedure, and that the
model topography could not be changed since the prognostic
AREG model is already in operation. The “spin-up”
time for the AREG tidal model was determined from the long
run of POM for the tidal constituents M2 and K1. We stated
that after 80 days the amplitude of M2 and K1 does not change
more than 10-3 m. Since in the analysis the AREG tidal model
run was performed over the first 270 days of 1999, the remaining
190 days were used for the analysis of the results. A homogeneous
roughness of topography was supposed, z0 = 0.01 m.
Firstly, the calibration of the AREG tidal model was
performed separately for every of seven principal tidal constituents,
when the model was driven with individual tidal constituents
along the OB line. However, in the last group of model runs
for calibration, the sea-surface along the OB line was prescribed
with all seven tidal constituents and the model results were
observed by harmonic analysis in 15 ports. A sufficient match
of model results with observations was achieved after four
model runs in succession (mode = 4). Finally, the model was
driven in mode = 3.
The amplitudes and phases of these constituents at the Open
Boundary Line (south of Otranto) were tuned according to a
comparison of observed and modelled amplitudes and phases
of the sea elevation in the port of Trieste. Fig. 2 represents
a typical distribution of amplitudes and phases along the
OB line of two major tidal constituents, M2 and K1, together
with the least squares fit of the second order, which simplified
the number of parameters that need to be read by the model. |
|
Fig. 2. - Typical
distribution of amplitudes (left scale) and phases
(right scale) of the M2 and K1 constituents along
the model OB line south of the Otranto strait, which
was applied during the model calibration, together
with the polynomial least squares fit of second
order, which reduced the number of parameters read
by the model. |
|
| Model sensitivity, however, was more helpful in defining
the strategy of model calibration. This analysis of the model
was conducted when the period of the SSE along the OBL was
set to be constant (equal to the period of a tidal constituent)
while the amplitude of SSE varied from one model run to another.
The power law of the growth of the amplitude of a single constituent
in the Gulf of Trieste with the amplitude of the same constituent
along the OB line is close to the linear one (the exponent
= 0.93 for the M2 constituent and 0.81 for the K1 constituent).
The tidal phase shift along the OB line was, however, determined
by the trial-and-error method. Tides in the Adriatic have
a dual nature. (Malacic and Viezzoli, 2000) They are composed
of gravity-topograpy waves, where the semidiurnal constituents
travel along the channel (a system of two Kelvin waves), while
the diurnals travel across it as a topography wave and have
the amplitude modulated along the channel axis. Therefore,
the model results for tidal phase were observed separately,
once for the ports along the eastern boundary, and then also
for those along the western boundary. For the semidiurnal
constituents we had to observe the phase separately, not just
for ports that were along the eastern or western boundary,
but we also had to pay attention to whether ports are located
southward or northward of the amphidromic point, which is
situated in the middle of the Adriatic, in the center of the
line that connects Ancona with Zadar. During four model runs
of 270 days with hourly data, SSE was analysed for 16 ports
around the Adriatic coastline where all seven tidal constituents
were used as a forcing with prescribed SSE along the OB line.
|
Results There were two planned deliverables that
needed to be accomplished. First is the table of model performance.
This is represented in Tab. 1 (constituent amplitudes) and
Tab. 2 (phases), in which a comparison of model results
with observations is performed. There is quite a serious
problem about the observations. Analysis of at least four
sources showed that the differences in phase could be as
large as 300 and in amplitude for several cm. A detailed
analysis of the observation results will be prepared for
the next scientific report. The problem is related to the
undocumented procedure about how, and on which data the
harmonic analysis was performed. As it looks, there could
be variations in observed harmonic constants among different
sources due to changes in the local topography, and the
annual data, which are usually accepted as a standard data
set, might not be sufficient due to significant year-to-year
variations of the stratification of the Adriatic basin (a
typical example is the summer situation of 2003, when there
was a huge lack of freshwater supply, mainly from the Po
river, which was far below 'climatological' river flux.
Therefore, we collected the most recent observation values,
although there are many ports where the analysis of measurements
is missing for several decades.
Tab. 1 shows that the modeled amplitudes are in reasonable
agreement with the observations. The port of Split is excluded
from the simple statistics, because this port is located
along the eastern coastline in mid-Adriatic behind islands,
and the model resolution is insufficient to model tides
in the sea between the islands and the town of Split. We
also noticed large barotropic currents through the 'model
strait' between islands, that are far different from the
reality. We see that the amplitude difference of each constituent,
averaged over 15 ports, differs from the observations by
no more than 1.3 cm, and that the maximum difference is
2.2 cm (port of Ravenna). As usual, model phases differ
from those observed for up to several tens of degrees, the
largest average difference is for the constituent P1 (12.80),
the amplitude of which is smaller than 6.0 cm (in Trieste).
This large average difference is mainly due to the port
of Durres (29.50), which is the southern most one along
the eastern coast of the Adriatic Sea. |
| |
|
OTR |
BRI |
MAN |
VIE |
ORT |
ANC |
PES |
RAV |
VEN |
TRI |
ROV |
DUB |
BAR |
DUR |
PAL |
SPL |
<> |
Max |
|
M2
|
Zo |
6.5 |
8.7 |
10.0 |
7.9 |
6.4 |
6.0 |
12.8 |
15.5 |
23.4 |
26.7 |
19.3 |
8.7 |
9.2 |
9.3 |
10.0 |
7.6 |
|
|
|
Zm |
8.1 |
9.5 |
10.4 |
9.4 |
5.5 |
6.8 |
12.7 |
17.7 |
24.0 |
26.7 |
19.6 |
9.9 |
10.0 |
9.8 |
8.3 |
14.8 |
|
|
|
|Zo-Zm| |
1.6 |
0.8 |
0.4 |
1.5 |
0.9 |
0.8 |
0.1 |
2.2 |
0.6 |
0.0 |
0.3 |
1.2 |
0.8 |
0.5 |
1.7 |
7.2 |
1.3 |
2.2 |
|
K2
|
Zo |
1.7 |
1.4 |
2.7 |
1.9 |
2.1 |
0.2 |
1.8 |
2.5 |
5.3 |
4.3 |
3.0 |
2.1 |
1.7 |
1.5 |
3.0 |
2.1 |
|
|
|
Zm |
1.3 |
1.6 |
1.8 |
1.7 |
1.1 |
1.0 |
2.1 |
2.9 |
4.1 |
4.6 |
3.3 |
1.7 |
1.7 |
1.7 |
1.5 |
4.1 |
|
|
|
|Zo-Zm| |
0.4 |
0.2 |
0.9 |
0.2 |
1.0 |
0.8 |
0.3 |
0.4 |
1.2 |
0.3 |
0.3 |
0.4 |
0.0 |
0.2 |
1.5 |
2.0 |
0.5 |
1.5 |
|
N2
|
Zo |
1.2 |
1.4 |
1.6 |
1.9 |
0.9 |
1.3 |
3.2 |
3.0 |
3.8 |
4.5 |
3.5 |
1.5 |
1.3 |
0.6 |
3.0 |
1.1 |
|
|
|
Zm |
1.4 |
1.6 |
1.8 |
1.6 |
0.8 |
1.3 |
2.3 |
3.1 |
4.2 |
4.6 |
3.4 |
1.7 |
1.7 |
1.7 |
1.4 |
1.9 |
|
|
|
|Zo-Zm| |
0.2 |
0.2 |
0.2 |
0.3 |
0.1 |
0.0 |
0.9 |
0.1 |
0.4 |
0.1 |
0.1 |
0.2 |
0.4 |
1.1 |
1.6 |
0.8 |
0.4 |
1.6 |
|
S2
|
Zo |
4.0 |
5.2 |
6.1 |
5.1 |
4.5 |
3.2 |
6.8 |
9.1 |
13.8 |
16.0 |
11.2 |
5.8 |
5.6 |
5.5 |
5.9 |
5.4 |
|
|
|
Zm |
4.5 |
5.6 |
6.3 |
5.8 |
3.9 |
3.5 |
7.1 |
10.2 |
14.2 |
16.0 |
11.5 |
6.0 |
6.0 |
5.9 |
5.3 |
10.7 |
|
|
|
|Zo-Zm| |
0.5 |
0.4 |
0.2 |
0.7 |
0.6 |
0.3 |
0.3 |
1.1 |
0.4 |
0.0 |
0.3 |
0.2 |
0.4 |
0.4 |
0.6 |
5.3 |
0.4 |
1.1 |
|
K1
|
Zo |
2.5 |
4.6 |
4.7 |
4.2 |
9.7 |
12.8 |
15.4 |
15.9 |
16.0 |
18.2 |
16.1 |
5.5 |
4.8 |
5.0 |
6.0 |
9.5 |
|
|
|
Zm |
4.3 |
5.9 |
5.8 |
6.3 |
10.1 |
13.6 |
15.3 |
16.4 |
17.7 |
18.1 |
16.8 |
6.4 |
6.3 |
6.2 |
7.9 |
12.2 |
|
|
|
|Zo-Zm| |
1.8 |
1.3 |
1.1 |
2.1 |
0.4 |
0.8 |
0.1 |
0.5 |
1.7 |
0.1 |
0.7 |
0.9 |
1.5 |
1.2 |
1.9 |
2.7 |
1.1 |
1.9 |
|
P1
|
Zo |
0.8 |
1.5 |
1.7 |
1.5 |
3.0 |
4.1 |
4.2 |
5.3 |
4.3 |
6.0 |
5.3 |
1.6 |
1.4 |
1.4 |
3.0 |
2.7 |
|
|
|
Zm |
1.5 |
2.0 |
1.9 |
2.1 |
3.4 |
4.5 |
5.1 |
5.5 |
6.0 |
6.1 |
5.6 |
2.2 |
2.1 |
2.1 |
2.6 |
3.5 |
|
|
|
|Zo-Zm| |
0.7 |
0.5 |
0.2 |
0.6 |
0.4 |
0.4 |
0.9 |
0.2 |
1.7 |
0.1 |
0.3 |
0.6 |
0.7 |
0.7 |
0.4 |
0.8 |
0.6 |
1.7 |
|
O1
|
Zo |
1.1 |
1.5 |
1.7 |
1.6 |
3.4 |
4.0 |
5.1 |
5.0 |
5.2 |
5.4 |
4.9 |
2.1 |
1.9 |
1.6 |
3.0 |
3.2 |
|
|
|
Zm |
1.8 |
2.2 |
2.1 |
2.2 |
3.3 |
4.2 |
4.7 |
5.0 |
5.3 |
5.4 |
5.1 |
2.4 |
2.3 |
2.3 |
2.7 |
4.3 |
|
|
|
|Zo-Zm| |
0.7 |
0.7 |
0.4 |
0.6 |
0.1 |
0.2 |
0.4 |
0.0 |
0.1 |
0.0 |
0.2 |
0.3 |
0.4 |
0.7 |
0.3 |
1.1 |
0.4 |
0.7 |
|
Tab.
1. - Modeled (Zm), observed (Zo) amplitudes and
their absolute difference for each of seven major
constituents in 16 ports along the Adriatic coastline,
where the ports of Otranto, Brindisi, Manfredonia,
Vieste, Ortona, Ancona, Pesaro, Ravena, Venezia,
Trieste, Rovinj, Dubrovnik, Bar, Durres, Palagruža
and Split are denoted with only first three letters
of their name. The average (< >) and maximum
value were calculated out from 15 ports, without
Split which has erroneous model results (see text).
Maximum differences of 15 port are in bold. |
|
| Distribution of amplitudes and phases are presented in Fig.
3 (semidiurnal constituents) and Fig. 4 (diurnal constituents).
We observe classical figures of semidiurnal tides, in which
the tidal wave rotates anticlockwise around the amphidromic
point which is positioned in the center of the connecting
line Ancona – Zadar, and where the amplitude is increasing
radially outwards from the amphidromic point. The strongest
is the M2 constituents, the second most important is the S2
constituent. Diurnal constituents all travel from the eastern
coastline towards the westen one, and the amplitude increases
northward. K1 is the strongest constituent. |
|
|
Fig. 3. - Horizontal
distribution of amplitudes (cm) and phases (0) for
the semidiurnal constituents. Phases increase in
an anticlockwise direction around the amphidromic
point while amplitudes increase radially outwards
from the amphidromic point. |
|
|
|
Fig 4. - The
same for the diurnal tidal constituents. The amplitude
increases towards the closed end of the Adriatic
Sea, while the phase increases from the eastern
coastline towards the western one. |
|
We may therefore conclude that the first part of the subtask
was completed, and that a complicated procedure of inverse
method (Janekovic et al., 2002) is not feasible since it does
not produce better results. The model results are similar
to those obtained recently by other authors (Cushman-Roisin
and Naimie, 2002; Janekovic et al., 2002).
In the end we have to point out huge problems that are related
to the 3 D fully prognostic model run in mode = 3 on the topography
for the Adriatic Sea. While we had no problems in running
the model in mode = 4, the model became singular when running
in mode = 3 (negative temperatures, huge velocities). The
singularity always starts near the sea-floor, and spreads
inside the basin, regardless of the OB conditions that we
applied for the barotropic and baroclinic velocity, while
we had to keep the prescribed sea-surface elevation. |
| |
|
OTR |
BRI |
MAN |
VIE |
ORT |
ANC |
PES |
RAV |
VEN |
TRI |
ROV |
DUB |
BAR |
DUR |
PAL |
SPL |
<> |
Max |
|
M2
|
go |
110.0 |
102.0 |
113.0 |
89.0 |
97.0 |
345.0 |
311.0 |
303.0 |
288.0 |
277.5 |
270.0 |
104.0 |
105.0 |
102.0 |
103.0 |
121.0 |
|
|
| gm |
102.7 |
103.2 |
99.6 |
97.0 |
88.1 |
320.6 |
304.8 |
295.7 |
286.1 |
277.5 |
270.7 |
102.2 |
101.2 |
99.0 |
102.9 |
124.6 |
|
|
| |go-gm| |
7.3 |
1.2 |
13.4 |
8.0 |
8.9 |
24.4 |
6.2 |
7.3 |
1.9 |
0.0 |
0.7 |
1.8 |
3.8 |
3.0 |
0.1 |
3.6 |
5.9 |
24.4 |
|
K2
|
go |
118.0 |
111.0 |
119.0 |
104.0 |
103.0 |
355.0 |
313.0 |
310.0 |
281.0 |
286.1 |
277.0 |
110.0 |
108.0 |
114.0 |
103.0 |
122.0 |
|
|
| gm |
105.7 |
105.9 |
101.8 |
99.7 |
93.3 |
329.1 |
309.6 |
299.5 |
289.5 |
280.5 |
273.7 |
103.8 |
102.7 |
100.2 |
104.7 |
129.8 |
|
|
| |go-gm| |
12.3 |
5.1 |
17.2 |
4.3 |
9.7 |
25.9 |
3.4 |
10.5 |
8.5 |
5.6 |
3.3 |
6.2 |
5.3 |
13.8 |
1.7 |
7.8 |
8.9 |
25.9 |
|
N2
|
go |
104.0 |
99.0 |
120.0 |
76.0 |
91.0 |
333.0 |
279.0 |
296.0 |
299.0 |
274.9 |
266.0 |
106.0 |
114.0 |
123.0 |
104.0 |
124.0 |
|
|
| gm |
100.4 |
101.5 |
98.0 |
94.9 |
85.4 |
314.9 |
301.9 |
293.7 |
284.8 |
276.4 |
269.7 |
101.5 |
100.5 |
98.3 |
102.2 |
135.2 |
|
|
| |go-gm| |
3.6 |
2.5 |
22.0 |
18.9 |
5.6 |
18.1 |
22.9 |
2.3 |
14.2 |
1.5 |
3.7 |
4.5 |
13.5 |
24.7 |
1.8 |
11.2 |
10.7 |
24.7 |
|
S2
|
go |
116.0 |
111.0 |
119.0 |
113.0 |
106.0 |
358.0 |
313.0 |
310.0 |
293.0 |
286.1 |
277.0 |
109.0 |
110.0 |
104.0 |
115.0 |
122.0 |
|
|
| gm |
111.3 |
111.7 |
108.5 |
106.8 |
100.5 |
334.6 |
315.0 |
305.1 |
295.1 |
286.1 |
278.8 |
109.7 |
108.6 |
106.0 |
111.3 |
130.2 |
|
|
| |go-gm| |
4.7 |
0.7 |
10.5 |
6.2 |
5.5 |
23.4 |
2.0 |
4.9 |
2.1 |
0.0 |
1.8 |
0.7 |
1.4 |
2.0 |
3.7 |
8.2 |
4.6 |
23.4 |
| K1
|
go |
83.0 |
69.0 |
78.0 |
80.0 |
88.0 |
93.0 |
84.0 |
82.0 |
79.0 |
71.1 |
71.0 |
60.0 |
57.0 |
48.0 |
71.0 |
55.0 |
|
|
| gm |
79.2 |
77.0 |
75.4 |
86.0 |
81.4 |
83.4 |
82.3 |
79.5 |
75.5 |
71.2 |
68.4 |
64.5 |
62.5 |
58.5 |
71.1 |
58.9 |
|
|
| |go-gm| |
3.8 |
8.0 |
2.6 |
6.0 |
6.6 |
9.6 |
1.7 |
2.5 |
3.5 |
0.1 |
2.6 |
4.5 |
5.5 |
10.5 |
0.1 |
3.9 |
4.5 |
10.5 |
|
P1
|
go |
72.0 |
69.0 |
66.0 |
66.0 |
84.0 |
95.0 |
56.0 |
82.0 |
56.0 |
71.1 |
71.0 |
51.0 |
33.0 |
27.0 |
48.0 |
47.0 |
|
|
| gm |
76.6 |
74.7 |
72.9 |
83.8 |
79.9 |
82.4 |
81.5 |
78.9 |
75.1 |
70.9 |
67.8 |
62.4 |
60.5 |
56.5 |
69.3 |
53.7 |
|
|
| |go-gm| |
4.6 |
5.7 |
6.9 |
17.8 |
4.1 |
12.6 |
25.5 |
3.1 |
19.1 |
0.2 |
3.2 |
11.4 |
27.5 |
29.5 |
21.3 |
6.7 |
12.8 |
29.5 |
|
O1
|
go |
58.0 |
57.0 |
49.0 |
84.0 |
67.0 |
80.0 |
84.0 |
67.0 |
70.0 |
61.1 |
56.0 |
40.0 |
63.0 |
48.0 |
58.0 |
36.0 |
|
|
| gm |
66.6 |
65.5 |
62.6 |
72.4 |
70.1 |
72.3 |
71.7 |
69.3 |
65.7 |
61.8 |
58.9 |
55.5 |
53.9 |
50.4 |
60.6 |
39.6 |
|
|
| |go-gm| |
8.6 |
8.5 |
13.6 |
11.6 |
3.1 |
7.7 |
12.3 |
2.3 |
4.3 |
0.7 |
2.9 |
15.5 |
9.1 |
2.4 |
2.6 |
3.6 |
7.0 |
15.5 |
|
Tab.
2. - Modeled (gm), observed (go) phase and their
absolute difference for each of seven major constituents
in 16 ports along the Adriatic coastline. The table
structure and calculations of averages and maximum
values are the same as those in Tab. 1.
|
|
| We made numerous unsuccessful attempts (over 80) to run
the model for the homogeneous sea, mostly using the super-computer.
These runs involved different OB conditions, among which we
introduced the upstream advection, zero gradient for temperature
and salinity, and radiation condition for the 'v' component
of velocity. In some attempts we also introduced a sponge
layer by prolongating the model southward, where in the prolongation
the coefficient of horizontal viscosity was set to 1000 m2/s,
which did not help. The model also did not run when it was
driven for the non-homogeneous sea and when the signal from
outside the model domain (provided by the project coordinator,
INGV) was passed inside the model domain via the usual nesting
procedure (experiments conducted by Dr. Hua Wang). We got
the model to run only with the following set of OB conditions: |
- prescribed sea-surface elevation ? at any time step
- radiation boundary condition for the barotropic velocity:
v = [g/h]1/2(?-?ob), where ?ob is the prescribed sea-surface
elevation
- zero gradient for temperature and salinity. There is
an upwind scheme to pass the temperature and salinity
signal from the first vertical plane next to the vertical
OB plane towards the model interior. However, we (Boris
Petelin) introduced the additional constraint that the
temperature and salinity in the second vertical plane
next to the boundary is also the same as those in the
boundary plane.
|
| In the near future we need to explore the effect of this
additional constraint near the OB plane. From the inspection
of failed model results it looks as if we were facing the
problem of pressure gradient terms in the sigma co-ordinate
system, which could lead to 'hydrostatic incostistency', if
the relative horizontal gradient of topography is larger than
the relative horizontal gradient of sea-surface elevation
(Mellor et al., 1994). While the prescription of how to avoid
the problem related to the horizontal density gradient is
written in this reference, we need to fix the problem of the
pressure gradient related to the sea-surface elevation. This
means that the resolution of the model should be decreased
and topography very much smoothed (we also performed this
last operation, yet it was unsuccessful). It was suggested
(Marco Zavatarelli, pers. comm.) to follow another, probably
promising path in modelling. First, run the model in mode
= 4 up to a date at which the run in mode = 3 would start,
at least for several months until the model stabilizes. Save
these instantaneous model results, and insert the sea-surface
elevation, together with the barotropic velocity as the initial
fields. In this way we would avoid huge horizontal pressure
gradients at the model start, when the sea-surface elevation
is zero in the model interior and different from zero along
the OB line. |
References
Cushman-Roisin, B. and Naimie, C.E., 2002. A 3D finite-element
model of the Adriatic tides. Journal of Marine Systems,
37(4): 279-297.
Janekovic, I., Bobanovic, J. and Kuzmic, M., 2002. The Adriatic
Sea M2 and K1 tides by 3D model and data assimilation. Estuarine,
Coastal and Shelf Science, 57(5-6): 873-885.
Malacic, V. and Viezzoli, D., 2000. Tides in the northern
Adriatic Sea - the Gulf of Trieste. IL Nuovo Cimento, 23
C(4): 365-382.
Mellor, G.L., Ezer, T. and Oey, L.-Y., 1994. The pressure
gradient conundrum of sigma coordinate ocean models. Journal
of Atmospheric and Oceanic Technology, 11: 1126-1134. |
Planned deliverable state |
|
|
| Del Number |
Description1 |
State2 |
Dissemination date |
| 1 |
Report with plots of distribution of SSE amplitude
and phase of M2 and K1 constituents, and the table
of model perfomances in Adriatic ports. |
completed |
29 February 2004 |
|
|
| 1 - Description: the nature of the deliverable (report,
software, hardware, etc.) and the place of dissemination.
This will be cross-checked with the management report. |
| 2 - State: related to the planned time, say if deliverable
is completed, not started, in progress or delayed with respect
to time table. This will be cross-checked with the management
report. |
|
|
|
