S. POUS ET AL.

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Table 3. Mean value of the differences between the model and the observed harmonic amplitudes H (in cm) and phase g (in

degrees).

M2 S2 K1 O1 N2 K2 P1

Averaged difference for the: H/g H/g H/g H/g H/g H/g H/g

11 gauges of Arabian Sea 4/5 2/4 3/4 2/3 1/9 0/6 1/4

31 gauges of the Persian Gulf 5/10 2/13 3/11 4/8 3/11 1/19 1/19

42 gauges (total) 5/9 2/11 3/10 3/6 2/11 1/14 1/10

average is taken over all tidal gauges in the gulf, in the

Arabian Sea or in the whole domain. Again, the model

results agree very well with the observations. The aver-

aged differences are on the order of a few centimeters for

the amplitude and a few degrees for the phase. Very

small errors are found in the Arabian Sea. The largest

errors are found for waves K2 and P1 in the Persian Gulf;

these errors can come from both the model and the

measurements.

Another element of the model which leads to precise

results is the accurate bathymetry in the Persian Gulf (see

also [11]). Navigation charts had originally been used to

provide the bottom depth in the gulf; but these charts

were not accurate enough (the gulf was too shallow) and

they led to a misrepresentation of the amphidromic

points. This was corrected by using the bathymetry pro-

vided by Proctor and complemented with ETOPO2. The

difference between the depth of the navigation charts and

that used finally in the model was about 10 m on averag e

over the gulf.

To show how important an accurate bathymetry is for

the model, we tested the influence of bottom topography

on tides in the idealized case of a rectangular basin with

an open strait at its eastern boundary; in that case, the

tide was prescribed at this strait with the same amplitude

and phase as in the real Persian Gulf.

Indeed, Defant [1] considered the reflection of Kelvin

waves in a semi-enclosed rectangular basin, and showed

that the natural period of waves in a basin comparable to

the Persian Gulf was 22 - 23 hours. Thus, with a diurnal

or semi-diurnal forcing, resonance oscillations can ap-

pear. When the forcing is a semi-diurnal wave, two am-

phidromic points should appear.

These two points are recovered in our simple basin

experiment when the average depth is 40 m but not when

it is 30 m. This shows that a proper b athymetry is critical

for a good representation of tides.

Finally, the nature of the tide in the Gulf varies de-

pending on the location. Table 2 provide the value of

ratio F defined as F = (K1 + O1)/(M2 + S2), which char-

acterizes the type (diurnal, semi-diurnal or mixed) of tide.

For F < 0.25 the tide is semi-diurnal; for 0.25 < F < 1.5,

the tide is semi-diurnal with diurnal inequality; for 1.5 <

F < 3.0, the tide is mixed; and finally, for F > 3.0, the

tide is diurnal. Figure 3 shows the value of factor F in

the Persian Gulf. The model correctly reproduces the

three types of tides (semi-diurnal, mixed and diurnal)

observed by John [12]. Figure 4 shows the time evolu-

tion of the free surface in the 2D model at three points

with different types of tides. Point A is located near the

diurnal amphidromic point; since the diurnal component

of the free surface elevation is zero at the amphidromic

point, the semi-diurnal component dominates the tidal

signal as observed. Conversely, point B is located near

the semi-diurnal amphidromic point so that the diurnal

component dominates. Finally, point C is not close to an

amphidromic point so that the tide is mixed at this point

as shown by Figure 4.

Figure 5(a) shows the maximal velocities of the tidal

current in the Persian Gulf over the year of simulation;

these current maxima do not necessarily occur at the

same time everywhere. Tidal currents can be fast nearly

everywhere in the Gulf; a striking feature is that such fast

currents do not specifically depe nd on the type of tide. In

particular, currents faster than 1 m/s are found in the

Straits of Hormuz and around islands. Eulerian residual

currents were then computed (because the mesh size is

too large to allow the computation of Lagrangian residual

currents) at a time of maximal diurnal and semi-diurnal

currents; this period was near day 165 of the simulation.

The currents were then averaged over a 20 day period

around that date (to filter the instantaneous tidal signal).

The residual currents are weak over the whole Gulf; ve-

locities do not exceed 2 cm/s (see Figure 5(b)). An anti-

cyclonic current pattern can be seen north of Qatar with

an intensification along the Iranian coast. Faster recircu-

lations are observed along the coasts, around islands and

in the Straits of Hormuz. These results agree with those

of a finite element model by [13].

4. Validation with Complementary Data

A complementary validation was performed using data

from the GOGP99 experiment at sea (see [14,15]). This

experiment was carried out in the Straits of Hormuz and

in the Gulf of Oman in October 1999. Figure 1(b) shows

the location of the moorings M1, M2 and D1 of this ex-

periment.

D1 is a Doppler current-meter; it was moored at 120 m

depth at the exit of the Straits of Hormuz. The Doppler