Resonant coupling of a traveling air pressure disturbance with the east Adriatic coastal waters

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2004jc002279, 2004 Resonant coupling of a traveling air pressure disturbance with the east Adriatic coastal waters Ivica Vilibić, 1 Nenad Domijan, 2 Mirko Orlić, 3 Nenad Leder, 2 and Miroslava Pasarić 3 Received 14 January 2004; revised 24 June 2004; accepted 22 July 2004; published 1 October [1] Exceptional sea level oscillations and strong current reversals, observed in the east Adriatic on 27 June 2003, are analyzed using available meteorological and tide-gauge measurements and numerical model results. It is shown that the variability in the atmosphere-sea system was characterized by high frequencies ( min 1 ) and sea level and current amplitudes surpassing 1 m and 1 m s 1, respectively. The event was related to the occurrence of a gravity disturbance in the atmosphere above the Adriatic. The disturbance traveled toward the east-southeast at a speed of 22 m s 1 and was resonantly coupled with a wave in the sea 50 m deep. The resulting forced wave was further amplified when entering funnel-shaped bays opened to it. There are indications that the forcing disturbance and its counterpart in the sea excited normal modes of the bays and harbors in the area. Moreover, nonlinear steepening of the forced wave seemingly occurred, resulting in the formation of high-frequency wave trains. This process, along with the generation of coastal seiches, could explain the observed and modeled differences between the spectra of coastal variability and the spectrum of forcing wave. INDEX TERMS: 4504 Oceanography: Physical: Air/sea interactions (0312); 4243 Oceanography: General: Marginal and semienclosed seas; 4556 Oceanography: Physical: Sea level variations; 4255 Oceanography: General: Numerical modeling; KEYWORDS: Adriatic Sea, atmospheric disturbance, resonance, seiche, modeling, flooding and damage Citation: Vilibić, I., N. Domijan, M. Orlić, N. Leder, and M. Pasarić (2004), Resonant coupling of a traveling air pressure disturbance with the east Adriatic coastal waters, J. Geophys. Res., 109,, doi: /2004jc Introduction 1 Institute of Oceanography and Fisheries, Split, Croatia. 2 Hydrographic Institute of the Republic of Croatia, Split, Croatia. 3 Andrija Mohorovičić Geophysical Institute, Faculty of Science, University of Zagreb, Zagreb, Croatia. Copyright 2004 by the American Geophysical Union /04/2004JC [2] On 27 June 2003 exceptional sea level oscillations and strong current reversals characterized by high frequencies ( min 1 ) were observed in several east Adriatic coastal basins. Particularly dramatic were reports coming from Stari Grad Bay on the island of Hvar and Mali Ston Bay sandwiched between mainland and Pelješac peninsula (Figure 1). According to the former reports, maximum sea-surface elevation amounted to 1.3 m, resulting in the flooding of seafront. The latter reports stressed the damage done to shellfish farms by swift currents. The phenomenon was strongly reminiscent of the flooding which occurred on 21 June 1978 in Vela Luka Bay on the island of Korčula (Figure 1) due to a wave having period close to 15 min and crest-to-trough height of about 6 m at the head of the bay. [3] Already after the 1978 event it was recognized that such pronounced motions are due to the resonant response of the sea to the forcing. Zore-Armanda [1979] and Hodžić [1979] interpreted the flooding in terms of a free progressive wave reaching Vela Luka Bay from the open sea and resonating with its normal modes. They differed in explanation of the origin of the open-sea wave: Zore-Armanda related it to a seismic event, Hodžić to an atmospheric disturbance. Orlić [1980], however, noted that the occurrence of sea level oscillations coincided with the passage of an atmospheric gravity disturbance above Vela Luka Bay. A forced progressive wave was thus assumed to form in front of the bay, its large amplitude being ascribed to the resonant coupling of the atmospheric disturbance with a gravity wave in the sea. It was further hypothesized that, after impinging on the bay, the forcing disturbance and its counterpart in the sea triggered the bay seiches. [4] The distinction should be made here between two types of resonance mentioned. In one case resonance is due to the frequency of the forcing being equal to the frequency of a normal mode in the sea. The other case occurs when both the frequency and wave number of the forcing equal the frequency and wave number of a wave in the sea or, in other words, when the velocities of the forcing and the wave are equal. Investigations of both types of resonance go back at least to G. B. Airy and his treatise on tides published in 1845 [Lamb, 1932; Proudman, 1953]. During the subsequent century the findings of tidal theorists were applied to the study of atmosphere-sea interaction. Modeling of the influence of air pressure waves on the sea and of the firsttype resonance was pioneered by Chrystal [1908], whereas an influential theoretical paper on the response of the sea to 1of12

2 Figure 1. Position and bathymetry of the eastern part of the middle Adriatic Sea. Circles denote meteorological stations (KO, Komiža; HV, Hvar; SP, Split; MA, Makarska; PL, Ploče; LA, Lastovo; and DU, Dubrovnik), whereas triangles mark tide-gauge stations (SU, Sućuraj; SP, PL, and DU). the air pressure forcing and on the second-type resonance was published by Proudman [1929]. The resonant processes they considered later became known as harbor resonance and Proudman resonance, respectively. As pointed out by Groen and Groves [1962], the nature of atmosphere-sea coupling depends on the relative extent of the atmospheric system acting on the sea and of the body of water affected: if the former is greater than the latter harbor resonance may be expected, in the opposite case Proudman resonance is possible. [5] Theoretical studies provided a basis for the interpretation and, later, numerical modeling of pronounced highfrequency oscillations of the sea and lake levels observed at various places around the world: English Channel [Douglas, 1929], Lake Michigan [Ewing et al., 1954; Donn and Ewing, 1956; Harris, 1957; Platzman, 1958, 1965; Irish, 1965], Lakes Huron and Erie [Donn, 1959], coastal waters off New York [Donn and McGuinness, 1960; Donn and Balachandran, 1969], Nagasaki Bay [Hibiya and Kajiura, 1982], Balearic Islands [Tintore et al., 1988; Monserrat et al., 1991; Gomis et al., 1993; Garcies et al., 1996; Rabinovich and Monserrat, 1998; Monserrat et al., 1998; Rabinovich et al., 1999], Sicily Strait [Candela et al., 1999], Buenos Aires coastal area [Dragani et al., 2002] and Newfoundland coast [Mercer et al., 2002]. According to the opinion prevailing in the papers cited, the effect of air pressure forcing dominates that of wind forcing. Proudman resonance was invoked in order to explain strong oscillations in all the basins mentioned. However, in two cases (Nagasaki Bay, Balearic Islands) it was recognized that both Proudman and harbor resonances were needed to interpret the observations in a satisfactory way. The combined effect was called double resonance by Rabinovich [1993]. A similar phenomenon was probably responsible for the exceptional sea level oscillations in the east Adriatic in 1978 and 2003 as well. [6] Studies of the 1978 event in the Adriatic were hampered by the available data, at the time collected by analog tide gauges and anemometers as well as by barographs of low sensitivity. The event of 2003 was recorded in a better way: although no data were taken in the two bays that were most affected, a network of high-sensitivity barographs, one of them digital, was operating in the vicinity, and several digital anemometers and tide gauges were at work in the area. The data originating from these instruments were already used in an analysis of some modest events [Vilibić and Mihanović, 2003], and will be utilized here in order to study the exceptional event of 27 June 2003 and to verify results of its numerical modeling. The data are described in the second section, as is the numerical model used to reproduce response of the east Adriatic coastal waters to the atmospheric forcing. Meteorological and oceanographic data are analyzed and compared in the third section. Numerical model results are verified against the field data in the fourth section, and are then used to consider processes in Stari Grad and Mali Ston Bays for which only visual observations are available. In the final, fifth section the present findings are summarized and are related to the results previously obtained for the Adriatic and other basins. 2. Data and Methods [7] The area investigated has a shape of triangle-like bay, opened to the west, with a number of islands oriented along the bay and channels stretching between them (Figure 1). The depth decreases almost uniformly from about 100 m at the western entrance of the bay to m in Mali Ston Bay, therefore cross-section areas are reduced by a decrease in both the transect width and depth. Consequently, it may be expected that any wave or disturbance propagating in the sea from the west to the east will be amplified at the bay head due to the topographical effect. 2of12

3 Figure 2. Model domain (every second grid line is displayed) together with the domains of the nested models (black squares and inserted figures). Speed and direction of the traveling air pressure disturbance are shown, too. [8] A number of meteorological and tide-gauge stations have been operating in June 2003 in the eastern part of the middle Adriatic Sea. The experimental setting is illustrated in Figure 1. Air pressure data have been digitally recorded only at Split (SP), with a resolution of 2 min and accuracy of ±0.05 hpa, whereas the rest of the stations (Komiža (KO), Hvar (HV), Makarska (MA), Lastovo (LA), Ploče (PL) and Dubrovnik (DU)) had analog chart-recording devices. Digital anemometers have been running at three meteorological stations (HV, MA and DU); they recorded wind gusts as well as wind speed and direction averaged over 10 min intervals, the latter with an accuracy of ±0.5 m s 1 and ±5, respectively. Sea-level heights have been recorded at four stations (SP, Sućuraj; SU, PL and DU) by digital tide gauges with a resolution of 1 min and accuracy of ±1 mm. [9] Hydrodynamic modeling was undertaken with the two-dimensional, nonlinear finite difference model 2DD developed by Black [1995]. An explicit leapfrog solution is applied to solve the two-dimensional momentum and @z fv ¼ gu ð u2 þ v 2 Þ 1=2 C 2 ðd þ zþ þ r agjwjw x rðd þ zþ þ þ fu gv ð u2 þ v 2 Þ 1=2 C 2 ðd þ zþ þ r agjwjw y rðd þ zþ þ A H r r @x ½ðd þ ðd þ zþv Š ¼ 0; ð3þ where t is time, u and v are vertically averaged velocities in the x and y directions, g is acceleration due to gravity (9.81 m s 2 ), z stands for sea level above a horizontal datum, d marks the water depth below the datum, f is the Coriolis parameter, r and r a are the water and air density, respectively, P denotes air pressure, W represents the wind speed at 10 m height above sea level, W x and W y are the x and y wind components, g is wind drag coefficient, and A H is horizontal eddy viscosity coefficient. Seabed frictional resistance C is given by C ¼ 18 log 10 ð0:37h=z 0 Þ; ð4þ where h is total water depth and z 0 is the roughness length (a level above the bed where velocity equals zero). We choose in our simulations A H to be 15 m 2 s 1 and z 0 to equal m. [10] Model domain covers the area where the flooding event took place (Figure 2), and incorporates an island at the southwestern corner in order to avoid singular point there. The bathymetry resolution is set to be 1 km, thus altogether there are grid cells. In this way all the major topographical features are resolved, but the resolution is still too coarse to properly represent the areas for which strongest flooding and greatest damages were reported. Hence two high-resolution domains, having 50 m square grid resolution, were created and nested into the basic model in order to enable more precise simulation of the motions in Stari Grad and Mali Ston Bays (Figure 2). The depths for 3of12

4 [12] The model forcing allowed for a moving air pressure disturbance only, the winds being weak during the event considered. Although digital air pressure data were available for a single, SP station, the traveling air pressure disturbance was well documented by the chart-recording barographs (see next section, Figures 3 and 4), indicating that the model could be forced in the following way: (1) speed and direction of the moving air pressure disturbance were set to be constant over the whole domain (Figure 2) with the values resulting from the measurements (22 m s 1 and 108, respectively), (2) time interval elapsed from the passage of air pressure front above each grid point was calculated, and (3) air pressure data were interpolated linearly in time at each grid point by using the SP values shifted in time according to the determined time interval. Figure 3. Time series of the air pressure measured on 27 June 2003 at SP with 2 min sampling interval, together with digitized barograph records originating from KO, HV, MA, LA, PL, and DU stations. In the lower part of the figure, wind speed and direction, averaged over 10 min intervals, are given for HV and MA stations. nested model grids were obtained by digitizing bathymetric survey sheets archived in the Hydrographic Institute of the Republic of Croatia, and therefore the model topography is considered to be of high quality. Simulations were carried out with time steps of 12 s (basic model) and 0.5 s (submodels) in order to satisfy the stability criterion for the grid sizes and depths considered. [11] Classical radiation boundary condition was imposed at the western and southern boundaries, in order to allow for leakage of energy out of the model domain. In addition, sponge procedure was applied to the sea levels near the boundaries [Black, 1995], as given by z i ¼ ðji i b j=nþ r ðz i z b Þþz b ; ð5þ where z i is the sea level at grid cell i, z b is the value at the boundary cell i b, N is the number of the cells in the sponge, and r is a constant. The value r = 0.1 provides for slow damping and minimal reflections. Nested models had no sponge at the boundaries; instead, sea level series from the major model were imposed there. 3. Observations [13] Late June 2003 was characterized by stable synoptic conditions over the middle Adriatic, as is usual for the early summer when the path of Atlantic cyclones is shifted to the north of Europe. Nevertheless, a high-frequency disturbance occurred in the atmosphere at the southern edge of a large cyclone, and passed over the investigated area in the early hours of 27 June. The disturbance had a sine-like shape (Figure 3), with two maxima of which the first one was more pronounced at the coastal (SP, MA, PL, DU) than at the island stations. A sudden change in the air pressure ranged up to 8 hpa, and the whole event lasted only 2 3 hours as the disturbance propagated toward the east and southeast. From the times of appearance of the first (Figure 4) and the second maximum at various stations, average propagation speed is estimated to be 22 m s 1, whereas average direction was approximately ESE, or more precisely, 108. In addition, weak and shortlasting winds were recorded at the meteorological stations during the event (Figure 3), having no significant impact on the sea surface. [14] Reaction of the sea to the moving air pressure disturbance was quite dramatic (Figure 5), despite the fact that winds, which are usually the dominant exciting force, were weak and the energy came directly from the air pressure oscillations. It may be expected that response of the sea to the forcing would resemble the inverse barometer effect, which has already been documented on hourly and daily scales in the Adriatic [e.g., Kasumović, 1958; Karabeg and Orlić, 1982]. However, the actual response was amplified following the atmospheric pressure disturbance from the western boundary toward Mali Ston Bay. Namely, direct response to the air pressure disturbance, somewhat obscured by local seiches at SP and PL, was about 3 times greater than the inverse barometer one at SU and 7 8 times greater at PL (see also the model verification in the next section). This strongly suggests that dynamic effect was at work and that it was responsible for the occurrence of Proudman resonance and enhancement of sea level variability. Shallow water equations, reproducing linear frictionless motions generated in an infinite nonrotating channel of constant width and depth by a traveling air pressure þ z z eþ ¼ 0 ð6þ 4of12

5 Figure 4. Arrival times (in hours) of the first air pressure maximum as extracted from digital and ¼ 0; where z e refers to the equilibrium sea level elevation implied by the inverse barometer effect, and the other symbols have been introduced before. The solution to these equations, subject to z e = F(x Ut), where U is the speed of atmospheric disturbance, is [Proudman, 1929] ð7þ seiches. Particularly pronounced is the 30 min seiche at PL (the station is located inside 2 km long complex embayment). During the event considered here the seiche at PL lasted almost 8 hours with the amplitude greater than 20 cm (Figure 5); the frictional and radiational decays were apparently weak, as were the winds at the time. A proof of the resonant excitation of seiches at PL can be found in the air pressure versus sea level cross spectrum (Figure 7): the phase shift at 30 min is close to 180, as already found in the Balearic Islands [Monserrat et al., 1991; Gomis et al., 1993; Garcies et al., 1996]. The amplitude of the fundamental, 30-min mode is about 60 times greater than would be expected from the simple inverse barometer effect; other normal modes are rather low, as is usually the case at station PL (I. Vilibić and H. Mihanović, personal communication, 2004). Thus a part of the sea level energy at high frequencies could probably be related to the traveling air pressure disturbance and its counterpart in the sea. Both were obviously characterized by continuous spectra, albeit red. While traveling toward the east-southeast they encountered various bays and harbors and could excite seiches through the well-known mechanism of harbor resonance. A significant increase of sea level energy at SP between 8 and 30 min (not all of which is seen in Figure 6 since it is truncated at the frequency of 0.1 min 1 ) has already been 1 z ¼ 1 U 2 Fx Ut =c2 ð Þ ð8þ U u ¼ dð1 U 2 =c 2 Fx ð UtÞ; ð9þ Þ where c =(gd) 1/2 is speed of free long waves in the sea. Thus, if U converges to c, sea levels and currents are dynamically amplified. The speed U equaled 22 m s 1 in our case, therefore one should expect dynamic amplification at depths of about 50 m. The area around SU is a plateau with depths between 45 and 55 m (Figure 1), and for that reason is a place where the appearance of Proudman resonance could be expected. The sea response to the air pressure disturbance was enlarged there, and even more so further eastward where it was probably additionally modified by the topographical properties of the area: at PL it was approximately 2 times larger than at SU. [15] Let us also consider power spectra of measured air pressure and sea level time series (Figure 6). The air pressure spectrum for SP does not contain significant peaks. Nevertheless, the shape of the spectrum indicates the nature of the air pressure disturbance. If one fits logarithmic function to and then removes it from the spectrum, a decaying cosine-like oscillating fraction of the air pressure energy becomes obvious. Such a spectral shape belongs to the time series that contain box function (so-called sinc function; see, e.g., Bracewell [1999]), and in our case the air pressure disturbance is product of sine and box functions, the latter setting the sine part to zero outside the disturbance. Sea-level power spectra reveal a large number of significant peaks, partially being a result of small bay and harbor Figure 5. High-frequency component of sea level time series at SP, SU, PL, and DU. Low-frequency oscillations were removed by using high-pass digital filter (with the cutoff period placed at 2 hours). 5of12

6 middle and inner basins, with a period of 5.1 min. The 17.7-min, fundamental mode of these basins is not so pronounced, having about 5 times lower amplitude and therefore being of minor importance for the sea level and current variations in the bay. Consequently, strong sea level oscillations should not be expected, but the currents in the constrictions could be considerable primarily as the result of the excitation of 5.1-min mode. [18] Next, a number of model runs were carried out in order to properly setup the basic model parameters and initial conditions such as the air pressure disturbance speed and propagation angle, bottom friction, boundary reflection, etc. (see details in section 2). All of them started about Figure 6. Power spectra of the air pressure measured at SP (upper SP spectrum) and of the sea level at SP, SU, PL, and DU, depicted for the frequencies lower than 0.1 min 1. The spectra were computed from time series collected between 24 and 30 June interpreted before in terms of Proudman resonance that occurs in front of SP harbor at depths of m and of further amplification of the waves when entering the harbor [Vilibić and Mihanović, 2003]. 4. Model Results [16] The model was first used to estimate normal modes of both Stari Grad and Mali Ston Bays. Seiches were generated by applying random sea level series at the open boundary of two submodels, as such time series are characterized by white spectrum. As a result, normal modes were resonantly driven inside the whole bays or some of their parts. Table 1 shows type and period of the most significant modes. [17] Fundamental mode of Stari Grad Bay has the period of 10.6 min, and is strongest at the head of the bay where the flooding occurred. The contribution, however, of the 8.3- and 6.1-min modes, of which the latter is fundamental one of the inner bay but also higher mode of the whole basin, is not negligible. Namely, both 8.3- and 6.1-min mode amplitudes equal between 55 and 65% of the 10.6-min mode amplitude at the bay head. Even more normal modes are found in Mali Ston Bay due to its complex topography. Strongest is the first mode of the Figure 7. Cross-spectrum between air pressure at SP and sea level at PL, computed for 27 June The air pressure data have been shifted by 60 min, the time estimated for the disturbance to travel from SP to PL; the sea level data have been subsampled with a 2 min time step. The cross spectrum has been calculated by smoothing and averaging over 11 half-overlapping Hanning windows, i.e., with 91 degrees of freedom. 6of12

7 Table 1. Period of Normal Modes of Stari Grad and Mali Ston Bays a Type of Normal Mode Period, min Stari Grad Bay Region Fundamental, whole bay Fundamental, SE part of the bay 8.33 Fundamental, inner bay 6.06 Mali Ston Bay Region Fundamental, middle and inner basins Fundamental, middle basin 8.01 Fundamental, inner basin 8.76 Higher, middle and inner basins 5.12 Higher, outer embayment 3.42 a For nomenclature, see Figures 11 and hours before the arrival of major air pressure disturbance (on 26 June, 1200 UTC). However, the final run (of which the results are presented here) was repeated starting 3 days before the event (on 24 June) in order to check the stability of the model. The results of the two final runs show no significant differences. Furthermore, the model was tuned by adjusting its results to the SP, SU and PL sea level data recorded with a 1 min resolution. The problem arose with the high-frequency oscillations related to the bay and harbor seiches, which are not well reproduced by our model having a 1 km resolution. Therefore both measured and modeled sea levels have been subjected to a band-pass filter (Z. Pasarić, manuscript in preparation, 2004), which allowed only the frequencies between min 1 (40 min) and min 1 (200 min) to pass through. The series thus obtained are shown in Figure 8. [19] The agreement between the observed and modeled sea levels is good at SU and PL, especially for the major wave that occurred between 0400 and 0700 UTC. To be precise, both the timing and amplitude are successfully reproduced, the latter, however, being slightly underestimated at PL due to the position of tide gauge: it is located in the narrow and shallow embayment, which is not resolved by the model bathymetry, and the air pressure related signal could be large there. Bigger problems arose at SP, as the model severely underestimated the measured signal; nevertheless, the timing of the event was again properly reproduced. A number of factors could be responsible for the underestimation: (1) tide gauge at SP, similarly to PL, is located in the shallow harbor where the signal is amplified due to topographic features not resolved by the model, (2) observed direction of the air pressure disturbance is more to the north over the SP area (direction of ) whereas the modeled direction is 108 over the whole domain, (3) bathymetry is too coarse to allow for Proudman resonance which is suspected by Vilibić and Mihanović [2003] to occur off the harbor, (4) western model boundary is close to SP and the boundary conditions may affect the area, and (5) although the winds were weak during the event and therefore not included in the model, they could probably modify some processes in the shallow coastal zone. [20] Once verified by the measurements in a greater part of its domain, the model is assumed to be adequate for reproducing large sea level oscillations in Stari Grad Bay and vigorous current reversals in Mali Ston Bay. Snapshots of the model results, covering passage of the major air pressure disturbance between 0500 and 0630 UTC, are given in Figure 9. The growth of the air pressure generated wave in the region is clearly visible between the snapshots (top to bottom), being dramatic in Mali Ston Bay. Besides the channeling effect due to the decrease in cross-shore area and in depth, Proudman resonance was at work at the depths of about 50 m, specifically at the plateau off SU, which is large enough to be properly represented by the model topography. After that, the wave hit Mali Ston Bay, with the maximum sea level displacements at its entrance of about 40 cm. These served as an input to the nested highresolution model of Mali Ston Bay, as did the sea level series computed for the mouth of Stari Grad Bay, both small-scale models being also forced by the moving air pressure disturbance as described in the second section. [21] Figure 10a shows modeled sea levels at some points inside Stari Grad Bay, namely at the head of the inner bay (P1), in front of it (P2) and near the mouth of the bay (P3, location of grid points is given in Figure 11). The difference between points P1 and P2, which are only 1300 m apart, is remarkable. Sea-level height reached only 30 cm at P2 and almost 120 cm at the head of the bay (P1), due to the harbor resonance and the decrease in width and depth of the inner basin from its mouth toward the head. Unfortunately, the computations of sea level could not be accurately Figure 8. Time series of measured and modeled sea levels filtered by a band-pass digital filter (having cutoff periods of 40 and 200 min). The data were collected on 27 June 2003 at stations SP, SU, and PL, and the modeled series were taken from a grid point closest to the position of each tidegauge station. 7of12

8 [22] The seiches were strongest at the head of the inner bay, as is documented by the sea level spectra (Figure 10b). At point P1 high energies are found at min 1 (10.3 min), min 1 (8.2 min), min 1 (6.0 min), min 1 (4.0 min), min 1 (3.5 min) and min 1 (3.1 min). The highest energy is found at the period of fundamental bay mode (Table 1) and also at the other modal peaks (8.2 and 6.0 min), leading to the straightforward conclusion that the harbor resonance was responsible for large sea level oscillations in the inner bay. A part of the high-frequency energy seems to be a result of nonlinear interaction of the progressive incoming wave and topography, probably being strongest near the mouth of Stari Grad Bay. In that part of the bay a bank having height of about 5 m is found, just at the depths of m where the resonance is expected to occur (Figure 2). The nonlinear effect can be deduced from the model snapshots of sea level during the event. Figure 11 documents sea-level distribution over the 6 min interval during which the highest sea levels were modeled for P1; the second image contains a wave-like feature traveling toward the inner basin with the maximum displacement of about cm and wavelength of about 800 m. Figure 9. Half-hour model snapshots of sea level heights at (a) 0500, (b) 0530, (c) 0600, and (d) 0630 UTC on 27 June 2003, which, according to the model, were caused by the air pressure disturbance passing over the east Adriatic archipelago. See color version of this figure at back of this issue. verified, as there were no measurements in the area. However, eyewitnesses reported maximum sea level heights reaching about 70 cm above the pier near the head of the harbor (inner basin), and this value is confirmed by the marks on a building located close to the harbor. During the event mean sea level (as determined from SP tide gauge) was positioned about cm below the pier, and therefore maximum sea-surface elevation can be roughly estimated to be about cm. It may be concluded that the high-resolution nested model of Stari Grad Bay properly quantified the flooding event, which occurred as a result of the amplification of the barometric sea level response off the bay (at the depths of about 50 m) and its further enlargement in the inner bay due to the topographic constraint and the resonant excitation of various normal modes. Figure 10. The results for Stari Grad Bay nested model: (a) time series of sea level heights obtained for points P1, P2, and P3 and (b) power spectra computed for points P1 and P3 (27 June 2003). The position of P1, P2, and P3 is shown in Figure 11. 8of12

9 Figure 11. Model snapshots of sea level distribution over Stari Grad Bay as modeled for (a) 0456, (b) 0459, and (c) 0502 UTC, 27 June [23] A different situation should be expected in Mali Ston Bay, due to its complex topography (Figure 2). Namely, the bay consists of three subbasins, of which the outer one is the deepest (depths m) and fully opened to the northwest. It is connected to the middle basin via narrow constriction with depths of m (at point S2). The middle basin decreases in depth (down to 12 m), especially in its northeast embayment. The inner basin has similar depths as the middle one (12 m), but the connection between them (point S1) is shallower than 5 m. Therefore one should expect that the system partially reflects the incoming air pressure-induced wave energy at the outer constriction, and that it supports strong currents there and also inside the shallow inner constriction. The computation of normal modes leads to the same conclusion, as fundamental mode is low compared to the higher ones, the modes defined by constrictions being strongest. [24] Sea-level snapshots during the event are displayed in Figure 12. It appears that a part of the incoming energy was trapped in an embayment positioned to the southwest of the outer constriction, but another part leaked to the middle basin and induced pronounced sea-level gradients in the inner constriction (see the second image), predominantly as a result of 5.1-min mode of the middle and inner basins. The seiches were excited in some embayments (e.g., at point Q3), yet the induced sea levels were generally not so high as in Stari Grad Bay. The obvious reason is topography, which did not allow for additional increase in sea level in the middle and inner basins, and supported higher normal modes instead of the fundamental one. For example, sealevel heights at Q1 and Q2 did not surpass 40 cm during the event (Figure 13a). However, high sea levels (up to 100 cm) are modeled for Q3, which is located at the head of the embayment opened to the incoming waves and having similar topographical characteristics (decrease in depth and transverse area toward the closed end) as Stari Grad Bay. [25] Along-shore current velocities at point S1 (Figure 13b) were strongest between 0630 and 0640 UTC, when the wave maximum arrived at the inner constriction. The velocity exceeded 120 cm s 1 and therefore the currents were able to damage the shellfish farms located in that part of Mali Ston Bay. Already before the currents reached their maximum at S2, with the speed of about 80 cm s 1, when both the maximum and minimum incoming wave entered the outer constriction (at 0600 and 0620 UTC, respectively). After the event, the currents returned to normal values (below 30 cm s 1 ). Spatial distribution of current speed maxima (Figure 14) clearly identifies constrictions as the places where strongest currents appeared during the event. The currents were strongest inside the inner constriction, where they reached 150 cm s 1 at some points, and nowhere did they fall below 80 cm s 1. Somewhat lower maximum currents are modeled inside the outer constriction, with the highest values close to 100 cm s 1 at its narrowest section. However, the currents were generally weak in the inner and middle basins, their speed being smaller than 40 cm s 1. The same result is obtained for the outer basin, except for its southwestern embayment where maximum currents reached 80 cm s 1 at some points, due to the seiches and nonlinear high-frequency oscillations (suggested also by sea levels computed for Q3, Figure 13a). Consequently, the largest impact of the air pressure induced wave on the shellfish farms in Mali Ston Bay is expected to occur within the inner constriction, then within the outer one, and finally at some points near the southwestern shore of the outer basin. 5. Summary and Discussion [26] The present analysis of pronounced sea-level oscillations and strong current reversals, observed on the morning of 27 June 2003 in the east Adriatic archipelago, proved beyond doubt that the phenomenon was related to an atmospheric gravity disturbance that passed at the time over the area. It appears that several processes contributed to the exceptional quality of the event: [27] 1. The atmospheric disturbance, whose speed was about 22 m s 1, was resonantly coupled with the gravity 9of12

10 Figure 12. Half-hour model snapshots of sea level heights as modeled for Mali Ston Bay at (a) 0600, (b) 0630, (c) 0700, and (d) 0730 UTC, 27 June wave in the sea 50 m deep. This effect, called Proudman resonance, resulted in the formation of a forced wave in the sea, which traveled toward the east-southeast along with the forcing wave. [28] 2. Since several bays in the area have funnelshaped form and are opened to the west, the forced wave was further amplified due to the imposed topographic constraint. [29] 3. While traveling over the archipelago, the forcing wave and its counterpart in the sea encountered many bays and harbors. Having broadband spectral characteristics, they excited normal modes of the coastal basins through the mechanism called harbor resonance. [30] 4. According to the model, nonlinear steepening of the forced wave sporadically occurred and high-frequency wave trains were formed. This process, along with the formation of coastal seiches, was probably responsible for the spectra of coastal variability being different than the spectrum of forcing wave. [31] The conclusions are listed in the order of our decreasing confidence in them. The Proudman resonance and topographic modification are supported by the data taken in and the modeling performed for the wider east Adriatic area and by a successful data-to-model comparison. The harbor resonance is also documented by both data and model, but no comparison was possible because the data were taken in the basin for which fine-scale bathymetry was not available whereas no instrumental observations were performed in the two bays in which the flooding event was most pronounced. As for the nonlinear effects, they are suggested primarily by modeling results. [32] It is of some interest to compare the 2003 event, which was particularly strong in Stari Grad and Mali Ston Bays, with the event of 1978, which was most pronounced in nearby Vela Luka Bay. Both were related to the occur- Figure 13. The results for Mali Ston Bay nested model: (a) time series of sea level heights obtained for points Q1, Q2, and Q3 and (b) along-shore current velocity time series at points S1 and S2 (27 June 2003). The position of Q1, Q2, Q3, S1, and S2 is shown in Figure of 12

11 Figure 14. The distribution of maximum current speed as modeled for Mali Ston Bay and the air pressure disturbance of 27 June suggests that the closest resemblance exists with the processes in Nagasaki Bay [Hibiya and Kajiura, 1982] and the Balearic Islands [Gomis et al., 1993; Garcies et al., 1996; Rabinovich and Monserrat, 1998; Rabinovich et al., 1999]. In particular, in all the places a combination of Proudman resonance in offshore waters and harbor resonance in various basins appears to be a necessary condition for the flooding. What, however, is distinctly different in the Adriatic as compared to the other two sites is the lack of measurements in the bays most affected and in the sea off them. It is to be hoped that such measurements will be soon organized in the Adriatic. Although it may not be expected that they will immediately capture an event as strong as that considered here, the time interval between it and the previous similar one being 25 years, they should enable more modest cases to be documented. Presuming that the strength of an event depends primarily on the degree of resonant tuning, even slightly off-resonant cases may help to understand the processes better and to improve their modeling. rence of gravity disturbances in the atmosphere. The disturbances traveled at exactly the same speed in both cases. Their directions of propagation, however, differed: in 1978 the disturbance traveled toward the northeast [Orlić, 1980]. Therefore the question is whether the direction influences response of a particular bay. A number of model runs have been performed, keeping the speed and shape of the measured air pressure disturbance constant but changing the inclination angle. A maximum of sea-level energy at the mouth of both Stari Grad and Vela Luka Bays was obtained for disturbances traveling at angles ranging between 50 (northeastward) to 130 (southeastward); for the other angles the energy rapidly decreased. Thus directions of propagation observed in the years 1978 and 2003 were suitable for generation of large oscillations in both bays. According to the model, however, the energy content off Stari Grad was about 5 times larger then off Vela Luka during the 2003 event (unfortunately, there is no possibility to perform similar analysis for the 1978 event because air pressure records of the time were not suitable for the purpose). Consequently, large sea-level oscillations in front of Stari Grad Bay and relatively small values off Vela Luka Bay in June 2003 presumably resulted from energy distribution of the air pressure disturbance. [33] Another interesting fact is that both events occurred in June. This resembles the finding according to which large sea-level oscillations in the Balearic Islands are observed every year between May and September [Monserrat et al., 1991]. Most probably, summertime conditions are favorable for the occurrence of atmospheric gravity waves in the wider Mediterranean area. It is less likely that a single atmospheric disturbance could influence the Adriatic after affecting the Balearic Islands. Whatever the nature of the connection, it would appear that a comparative study of atmospheric conditions in the two areas could be fruitful. It would help meteorologists to generalize on a phenomenon which is of no particular significance for the atmospheric processes but is oceanographically relevant. [34] Comparison of the atmosphere-sea coupling in the east Adriatic with similar phenomena observed elsewhere [35] Acknowledgments. Meteorological data were provided by the Hydrometeorological Institute of the Republic of Croatia. Suggestions provided by Alexander Rabinovich and an anonymous reviewer were very helpful. The work was supported by the Ministry of Science and Technology of the Republic of Croatia (grants , and project Adriatic ) as well as by the European Commission (fifth framework project European Sea Level Service Research Infrastructure, contract EVR1-CT ). References Black, K. P. (1995), The Numerical Hydrodynamic Model 3DD1 and Support Software, Occas. Rep. 19, 53 pp., Dept. of Earth Sci., Univ. of Waikato, Waikato, N. Z. Bracewell, R. N. (1999), Fourier Transform and Its Applications, 640 pp., McGraw-Hill, New York. Candela, J., S. Mazzola, C. Sammari, R. Limeburner, C. J. Lozano, B. Patti, and A. Bonnano (1999), The Mad Sea phenomenon in the Strait of Sicily, J. Phys. Oceanogr., 29, Chrystal, G. (1908), An investigation of the seiches of Loch Earn by the Scottish Lake Survey 5-Mathematical appendix on the effect of pressure disturbances upon the seiches in a uniform parabolic lake, Trans. 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12 Hodžić, M. (1979), Occurrences of exceptional sea-level oscillations in the Vela Luka Bay (in Croatian), Priroda, 68(2 3), Irish, S. M. (1965), The prediction of surges in the southern basin of Lake Michigan part II, Mon. Weather Rev., 93(5), Karabeg, M., and M. Orlić (1982), The influence of air pressure on sea level in the North Adriatic A frequency-domain approach, Acta Adriatica, 23(1/2), Kasumović, M. (1958), On the influence of air pressure and wind on the Adriatic sea level fluctuations (in Croatian), Hidrografski Godišnjak, 1956/57, Lamb, H. (1932), Hydrodynamics, 738 pp, Cambridge Univ. Press, New York. Mercer, D., J. Sheng, R. J. Greatbatch, and J. Bobanović (2002), Barotropic waves generated by storms moving rapidly over shallow water, J. Geophys. Res., 107(C10), 3152, doi: /2001jc Monserrat, S., A. Ibbetson, and A. J. Thorpe (1991), Atmospheric gravity waves and the Rissaga phenomenon, Q. J. R. Meteorol. Soc., 117, Monserrat, S., A. B. Rabinovich, and B. Casas (1998), On the reconstruction of the transfer function for atmospherically generated seiches, Geophys. Res. Lett., 25(12), Orlić, M. (1980), About a possible occurrence of the Proudman resonance in the Adriatic, Thalassia Jugoslavica, 16(1), Platzman, G. W. (1958), A numerical computation of the surge of 26 June 1954 on Lake Michigan, Geophysica, 6(1), Platzman, G. W. (1965), The prediction of surges in the southern basin of Lake Michigan part I, Mon. Weather Rev., 93(5), Proudman, J. (1929), The effects on the sea of changes in atmospheric pressure, Geophys. Suppl. Mon. Notices R. Astron. Soc., 2(4), Proudman, J. (1953), Dynamical Oceanography, 409 pp, John Wiley, Hoboken, N. J. Rabinovich, A. B. (1993), Long Ocean Gravity Waves: Trapping, Resonance and Leaking (in Russian), 325 pp., Gidrometeoizdat, St. Petersburg. Rabinovich, A. B., and S. Monserrat (1998), Generation of meteorological tsunamis (large amplitude seiches) near the Balearic and Kuril Islands, Nat. Hazards, 18, Rabinovich, A. B., S. Monserrat, and I. V. Fain (1999), Numerical modeling of extreme seiche oscillations in the region of the Balearic Islands, Oceanology, 39(1), Tintore, J., D. Gomis, S. Alonso, and D. P. Wang (1988), A theoretical study of large sea level oscillations in the western Mediterranean, J. Geophys. Res., 93(C9), 10,797 10,803. Vilibić, I., and H. Mihanović (2003), A study of resonant oscillations in the Split harbour (Adriatic Sea), Estuarine Coastal Shelf Sci., 56, Zore-Armanda, M. (1979), Destructive wave in the Adriatic, Rapp. P. V. Reun. Cons. Int. Explor. Sci. Mer Mediter., 25 26(7), N. Domijan and N. Leder, Hydrographic Institute of the Republic of Croatia, Zrinsko-Frankopanska 161, Split, Croatia. M. Orlić and M. Pasarić, Andrija Mohorovičić Geophysical Institute, Faculty of Science, University of Zagreb, Horvatovac bb, Zagreb, Croatia. I. Vilibić, Institute of Oceanography and Fisheries, Šetalište I. Meštrovića 63, Split, Croatia. (vilibic@izor.hr) 12 of 12

13 Figure 9. Half-hour model snapshots of sea level heights at (a) 0500, (b) 0530, (c) 0600, and (d) 0630 UTC on 27 June 2003, which, according to the model, were caused by the air pressure disturbance passing over the east Adriatic archipelago. 8of12