Physics and Chemistry of the Earth 34 (2009) 948–970

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Physics and Chemistry of the Earth

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Sea level variability and the ‘Milghuba’ seiche oscillations in the northern coast of Malta, Central Mediterranean

Aldo Drago *

Physical Oceanography Unit, IOI-Malta Operational Centre, University of Malta, Msida MSD2080, Birkirkara, Malta article info abstract

Article history: The characteristics of the water level variations in the northern coastal area of Malta are studied by a set Received 8 March 2009 of densely sampled data collected in the period 1993–1996 (43 months) at a permanent coastal sea level Accepted 12 October 2009 installation in Mellieha Bay. These measurements constitute the first digitised sea level recordings in the Maltese Islands and were collected as part of a research programme that produced a long time series of simultaneous water level and meteorological parameters in the Central Mediterranean. Keywords: Tidal oscillations reach a maximum range of only 20.6 cm on average and are predominantly semi- Sea level oscillations diurnal. Important non-tidal signals are however found to span the whole spectral range of frequencies. Tides Seiche oscillations in the form of large amplitude sea level fluctuations, known locally as the ‘milghuba’, Shelf resonances Seiche carry substantial energy in the range of long wave frequencies (0.2–2 cph) and often mask completely the Power spectra tidal signal. These coastal seiches are believed to be the expression of shelf scale resonances; in the Bay numerous embayments on the northern coastline of the Maltese Islands, these seiches are greatly ampli- fied and have associated swift alternating currents that are useful for the mixing and exchange of the water body in the embayments with the adjoining open sea areas, but can constitute a nuisance to nav- igation especially at harbour entrances. In the synoptic and sub-synoptic time scales, variations in atmo- spheric pressure associated with mesoscale meteorological phenomena produce a predominant effect on the sea level, but the response of the sea is non-isostatic and carries the signature of oceanographic con- ditions in the region as well as that of non-local forcing resulting from intra-basin differences. Strong sea- sonal non-eustatic fluctuations in the mean sea level are characterised by a high sea level in December and is typically followed by a sharp fall to a minimum in February/March. This seasonal variability is a manifestation of the adjustments in the mass balance of the whole Mediterranean basin. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The Sicilian Channel is a large and dynamically active area connecting the eastern and western Mediterranean sub-basins. The quest to improve predictions of the residual circulation and The general flow in the Channel is mainly driven by the slow to refine the skill of ocean forecasting numerical models in dealing (vertical) Mediterranean thermohaline basin scale circulation. with mesoscale activity containing energy at the synoptic time The region is known to contain a number of significant hydrody- scale, has in recent years accentuated the challenge to understand namical processes and phenomena that span the full spectrum of the interaction of the sea with the atmosphere. This consideration temporal and spatial scales (Grancini and Michelato, 1987; Manz- is indeed crucial for the Mediterranean Sea where the tide is gen- ella et al., 1990; Moretti et al., 1993). The mesoscale processes erally weak and the tidal circulation is greatly surpassed by the are triggered by the synoptic scale atmospheric forcing. The heat meteorologically forced motions. In the particular case of the and momentum fluxes at the air–sea interface represent the Sicilian Channel, the synoptic variability and the mesoscale phe- dominant factor in the mixing and pre-conditioning of the Med- nomena constitute very important components of the total flow iterranean Atlantic Water (MAW) on its way to the eastern (Lermusiaux and Robinson, 2001). The signatures of these phe- Mediterranean. nomena are captured by the sea level signals which carry a high le- The highly irregular bottom topography of the Channel takes vel of variability at the synoptic, seasonal and interannual scales the form of a submarine ridge which connects in the east and west (Robinson, 1999), and as in the rest of the Mediterranean represent to the respective Mediterranean basins only through a system of an energetic part of the sea level spectrum. narrow sills. This ridge restrains the exchange between the two Mediterranean basins and has a controlling function, in addition

* Tel./fax: +356 2144 0972. to that at the Strait of Gibraltar, on the adjustment of the sea level E-mail address: [email protected] in the Mediterranean to meteorological forcing. The ridge is

1474-7065/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2009.10.002 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 949 characterised by a long-shaped NW–SE basin cutting deep into the 1972) especially when measured, as in the case of Malta, at a loca- continental shelf (Fig. 1). The average depth of this intermediate tion away from the continental mainland. basin is in the order of 500 m. Owing to the nature of its different The overall objective of this work is to make a detailed analysis behaviour with respect to the main basins, it is generally consid- of the sea level measurements collected in Malta. The aim is to ered as a third basin: the Central Mediterranean basin. In contrast identify and quantify the tidal and non-tidal signals composing to the rest of the Mediterranean, the continental margins in the the sea level spectrum in the vicinity of the islands, and study their Channel are rather wide and shallow. On the African coast the shelf occurrence and variability in relation to the adjustment of the area covers more than a third of the areal extent of the Strait with Mediterranean Sea to meteorological forcing and to other pertinent water depths less than 30 m in the Gulf of Gabes. Along the south- oceanographic processes. Section 2 describes the datasets and the ern coast of Sicily the shelf takes the form of two disconnected and data processing techniques used in this paper; it also gives a gen- relatively shallow (<200 m) banks. The Maltese Archipelago, con- eral overview of the sea level characteristics on the basis of the en- sisting of a group of small islands aligned in a NW–SE direction, ergy distribution between different frequency bands obtained from is located close to the southeastern margin of the Sicilian shelf. spectral analysis, and with a focus on the tidal component. This is The islands are thus located at an oceanographically strategic posi- followed in Section 3 by a more detailed analysis of the short per- tion in the middle of the exchange flow through the Channel, and iod and large amplitude coastal seiches. It is interesting to note act like a permanent station close to the shelf break. that one of the first scientific studies on seiches by Sir George Airy A set of densely sampled sea level, barometric pressure and wind (1878) refers precisely to the Grand Harbour in Malta. Since then vector recordings were collected at two stations on the northern the seiche phenomenon in Malta remained unstudied and this coastal perimeter of Malta. These datasets constitute the basis of work forms part of a renewed effort to study these high frequency this study and were acquired through the Physical Oceanography sea level oscillations in this part of the Mediterranean (Drago, Unit of the IOI-Malta Operational Centre of the University of Malta. 1999, 2001, 2007). The subsequent sections deal more specifically On the merit of the position of the island within the Sicilian Chan- with the other sea level components – meteorological and sea- nel, the datasets are particularly important to understand the role sonal. The final section discusses the results and poses questions of the Channel in controlling the exchange between the two major for further research. basins of the Mediterranean Sea. With an internal Rossby radius of just a few tens of kilometres on the shelf areas, mesoscale phenom- ena in the Channel are impossible to detect and follow unless a de- 2. Materials and methods tailed observation set is available in both time and space. Under such circumstances, sea level measurements become of great rele- Densely sampled sea-level data (at the variable rate of 30 or 60 vance as an indicator of the general dynamics of the sea (Wunsch, samples per hour) have been collected at a permanent tide gauge

Fig. 1. The Central Mediterranean showing the main isobaths and sea level stations used for tidal constituents in Table 2. The insert in the figure shows the seabed topography of the Siculo–Maltese continental shelf and the location of the stations deployed for this study. Gabes = GB; Zarzos = ZA; Lampedusa = LP; JANUS SG = SG; Porto Empidocle = PE; Capo Passero = CP; Sfax = SX; Pantelleria = PA; Mazara del Vallo = MZ; Tripoli = TR; Malta = GR. 950 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

installation positioned at the head of Mellieha Bay which is a small in the first step. A Doodson Xo filter (IOC-UNESCO, 1985) with 27 embayment on the northwestern coast of Malta (indicated by ML weighting factors and a half-gain at 0.39 cycles/h is subsequently in the insert in Fig. 1). The data set used for this study is that col- used to obtain the hourly values. The mean sea level (MSL) is de- lected in the period June 1993–December 1996. An Endeco Type rived by applying the A24A24A25/(242 25) tide-killing filter 1029/1150 differential pressure tide gauge is used and is situated (Godin, 1972) to the hourly data; this filter has a half-gain at a per- inside a small stilling well connected to the sea. The pressure iod of 2 days and thus retains only the longer period variations of transducer is located in a subsurface case and is awakened every the signal. Daily and monthly averages are calculated by taking sampling interval for a total of 49 s in order to filter waves. The the simple arithmetical mean of MSL over 24 h or 1 month, instrument measures absolute pressure; atmospheric pressure is respectively. compensated by means of a vented tube which passes through Tidal harmonic analysis is made by means of a least square pro- the topcase unit and terminates inside an environmental isolator cedure using TIRA, a software developed at the Proudman Oceano- in the form of a small exposed PVC tube with a bladder. graphic Laboratory in Bidston, Birkenhead, UK, (Murray, 1964). Meteorological parameters are also measured by Aanderaa sen- TIRA allows analysis even in the presence of gaps. A few short gaps sors at a nearby automatic weather station in Ramla tal-Bir (MT in in the original data set, each smaller than 1 day, are thus interpo- the insert in Fig. 1) which is situated on the coastal strip overlook- lated by using predicted values. Residuals prior to and after a data ing the South Comino Channel. The sensors are positioned in an gap are linearly interpolated and used to estimate and add the non- unobstructed location at a height of 20 m from mean sea level. tidal component to the predicted elevation during gaps. In order to The data set consists of wind speed and direction, air pressure isolate the non-tidal higher frequency component in the data, the and temperature, relative humidity and net atmospheric solar radi- predicted tides are subtracted from the original records and further ation each measured at 1 or 2 min intervals, in the period April analysis is then performed on the residual series. 1994–December 1996. These data sets represent the first long term The sea level and meteorological data are also used to calculate digitised measurements of hydro-meteorological parameters in energy distributions and power spectra. 50% overlapping segments Malta. Air pressure data are expressed in millibars and corrected are taken in each case. Trend and mean are removed and a Kaiser- to mean sea level. Bessel window (Harris, 1978) applied to each segment. The tapered Short analogue records of hourly sea-level data in the Grand segments are then subjected to Fast Fourier Transform (FFT) anal- Harbour and of 3-h sampled air pressure at Luqa are provided by ysis to calculate the spectra by using the Welch method. In the case the Hydrographic Office of the Malta Maritime Authority, and by of spectra obtained from an average over a long series, the influ- the local Meteorological Office, respectively. Upon digitisation, ence of transient effects is suppressed and the results thus deter- these data sets are used in addition to the above data sets. mine the general phenomenology in the region of the measuring Observations at the shelf scale level are provided from the ded- station. icated Malta Channel Experiment. The Malta Channel is the stretch of sea separating the Maltese Islands from the southern coast of 2.1. General data analysis Sicily (refer to the insert in Fig. 1). These observations consist of a series of simultaneous sea level measurements at two locations Water level records from Mellieha Bay demonstrate that the across the Malta Channel. The data comprise simultaneous bottom tide is mainly semi-diurnal and with low amplitude. The range pressure recordings at Qawra station outside Mellieha Bay for spring tides is on average 0.206 m, and is reduced to 4.6 cm (depth = 30 m; position = 35° 59.350N; 14° 25.810E), at Pozzallo on during neap tides. Fig. 2 is a typical data series of 2-min sampled the southern coast of Sicily (depth = 18 m; position = 36° 42.210N; water levels covering the period from mid-September to mid-Octo- 14° 50.120E) and at the Mellieha coastal station (refer to locations ber 1995. The most remarkable feature in the trace is the presence QW, PZ and ML, respectively, in the insert in Fig. 1). Pozzallo sta- of a band of high frequency signals with periods ranging from sev- tion is approximately to the north of Qawra station at a separation eral hours to as low as a few minutes. The long term measurements of about 100 km across the whole shelf area. These measurements presented in this work constitute the first digitised data set that span a period of 20 days (8:50 GMT 10th September to 11:54 GMT permit the scientific study of these non-tidal short period sea level 30th September 1996) and were collected during the Malta Channel fluctuations which are the expression of a coastal seiche, known by Experiment carried out in co-operation with the Italian CNR local fishermen as the ‘milghuba’.1 This phenomenon has now been Institute at Mazara del Vallo, Sicily. Bottom pressure fluctuations observed to occur all along the northern coast of the Maltese archi- (in mb) are translated into sea level variations (in cm) by direct pelago and manifests itself with very short resonating periods of equivalence. Atmospheric pressure at MSL is added to coastal the order of 20 min in the adjacent coastal embayments. Analysis sea-level data to obtain adjusted sea levels. of the full data set shows that weak seiching is present uninter- Furthermore an ENDECO/YSI tethered-type current meter is rupted and appears like a background ‘noise’ on the tidal records. used to measure seiche-induced subsurface currents in Mellieha During random sporadic events the seiche oscillations can however Bay. The instrument is deployed within the embayment at a station become greatly enhanced and mask completely the astronomical located at 35° 58.80N, 14° 22.80E where the total depth is 28 m (re- signal. It is interesting to note that reference to similar sea level fer to Fig. 8). Measurements consist of the vector averaged sea cur- variations (known as the ‘Marrubbio’) on the southern coast of rent and temperature sampled every 2 min at 13 m from the Sicily is found in the Italian ‘Portolano’ for ship navigation. Their surface and cover the period 16:04 GMT 25th July–07:52 GMT occurrence is reported to be most frequent in May or June in asso- 30th July 1994. Sea level is also measured every 2 min at the coast- ciation to south easterly winds, and their crest-to-trough ampli- al station situated at the head of the embayment. Meteorological tudes can reach as high as 1.5 m. Literature on the ‘Marrubbio’ is parameters, including wind, surface pressure and air temperature very scarce with the most relevant publication being that by Col- are measured at the nearby Ramla tal-Bir station. ucci and Michelato (1976) who quote typical periods of 14.6 min Finite Impulse Response filters are used on the original data (main peak), 33.6 and 48 min (secondary peaks) in Porto Empido- time series in two steps and with decimation to first produce a cle where the maximum seiche amplitude is however reported to 10-min series and subsequently hourly averaged values in the sec- reach only 35 cm. Similar short period oscillations are known to ond step. A cosine filter with nine weighting factors, pass-band ending at 0.156 cycles/data interval (99% gain) and stop-band 1 The term ‘milghuba’ comes from the Maltese verb ‘laghab’ which means ‘play’. starting at 0.326 cycles/sampling interval (1% gain) is employed The terminology refers to the ‘play of the sea’. A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 951 occur in other places including the Mediterranean where they have ual (observed minus predicted) water level fluctuations, together been extensively studied in Ciutadella Harbour, Menorca in the with the corresponding inverted barometric pressure for the peri- Balearic Islands (Rabinovich and Monserrat, 1996, 1998; Monserrat od covering 18 March–10th May, 1995. The smooth curve drawn et al., 2006; Vilibic et al., 2008). upon the observed data gives the variation of MSL and shows the The longer period signals are better studied from the filtered presence of long-period oscillations due to both long-period tidal hourly values. Fig. 3 presents a representative record of observed, constituents and meteorological influences. These signals have a predicted (sum of tidal periodic variations) and non-periodic resid- periodicity of several days and are related to the large-scale cyclic

Fig. 2. Time series of sea level in Mellieha Bay (14th September–14th October 1995).

Fig. 3. Time series of (a) the observed tide and mean sea level, (b) the predicted astronomical tide and (c) the residual sea elevation in Mellieha Bay for the period 18th March–10th May 1995; (d) is the inverted atmospheric pressure at MSL for the same period. 952 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 atmospheric patterns in the region. The meteorological origin of plotted for the observed (Fig. 5c) and the residual (Fig. 5d) data. these long-period variations is evidenced by the very consistent in- The sea level variations are dominated by energy inputs from the verse relation between MSL and barometric pressure (Fig. 3). low frequency signals and the semi-diurnal tidal components (Fig. 4), with a secondary contribution from the diurnal fluctua- 2.2. Spectral analysis and energy distribution tions. In the tidal frequency range, fluctuations are dominated by energy inputs of semi-diurnal frequency with weaker contribu- The characteristics of the sea level signals are best studied by tions from diurnal signals. Comparison between the two tidal en- spectral analytic techniques. Fig. 4a and b is a normalised power ergy density peaks yields a ratio of amplitudes of the order of spectral density plot of the full 2-min sampled data set from 1/6/93 1:7 which agrees well with results from harmonic analysis of to 2/1/97 plotted on a linear scale. Since the spectrum is obtained coastal tidal records. The peaks towards the higher frequency ends from an average over a long series, the influence of transient effects of the tidal range refer to the 1/3- and 1/4-diurnal contributions. is suppressed and the results thus determine the phenomenology The energy distribution at different frequencies is expressed as of the sea surface vertical movement in the region of this station. a percentage of the total energy in the records (Table 1). These per- The Kaiser-Bessel spectral windows with 50% overlap are chosen centages quantify the dominance of the low frequency inputs, pre- to be 217 records for the lower frequency range (Fig. 4a) and 214 sumably of large scale meteorological origin, which contribute for records for the higher frequencies (Fig. 4b). The different window 57.3% of the total energy in Mellieha Bay. Tidal energy inputs sizes permit an optimal resolution for the long-period and short- (35.8%) mainly result from the semi-diurnal component (32.7%). period components, respectively. The linear spectral plot gives a The high frequency (>4.8 cpd) inputs, due to the coastal seiches, better visualisation of the relative distribution of energy. The contribute only 6.6%. This figure is an average of seiche energy over corresponding logarithmic plots in Fig. 5a–e display the same char- the whole time span covered by the data series and greatly under- acteristics, but the components with smaller energy inputs are estimates the real energy carried by the large amplitude seiches enhanced. In Fig. 5a an additional frequency averaging is per- which are transient events lasting only for relatively short periods formed to smooth the spectral estimates at the higher frequencies. of time (from a few hours to a couple of days). A full characterisa- In this case the degrees of freedom are 22 and 110 for the lower tion of different kinds of seiches experienced in Mellieha Bay, and and higher frequency ends, respectively, of the spectrum. their relative power spectral signatures is given in Drago (1999). The analysis is performed on three main frequency bands: (1) During the summer months, in particular July and August, the the low frequency (long-period) band (LB) in the range 0–0.8 cpd seiche is very sharp, with a duration that can often be as short as (T (h) >30); (2) the tidal frequency band (TB) in the range 0.8–4.8 a few cycles. The associated sea level fluctuations have a tsunami- cpd (30 > T (h) > 5); (3) the long wave frequency (short-period) like nature, starting with an abrupt and large impulse that subse- band (SB) in the range 4.8 cpd and upwards (T (h) < 5). The term quently decays after a few oscillations. Seiches during this time of ‘long wave’ is here associated to sea level fluctuations with periods year are particularly strong. On several occasions, seiche heights intermediate between those of the long swell and of the astronom- close to 1 m have been recorded. One of the strongest is that on ical tide. These spectra for these three frequency bands are drawn 22nd August 1996 with an excursion in sea level of 1.3 m. In other separately (Fig. 5b–e) for better visualisation. The tidal band is periods of the year the seiche height does not generally reach these

Fig. 4. Normalised power spectra on a linear scale calculated from 2-min sampled sea levels in Mellieha Bay (1/6/93–2/1/97): (a) the 95% confidence factors, for 22 degrees of 2 freedom are (Bmin = 0.52; Bmax = 2.5); the spectrum normalisation factor is 0.2048 m /cpd, (b) the 95% confidence factors, for 176 degrees of freedom are (Bmin = 0.85; 2 Bmax = 1.3). The spectrum normalisation factor is 0.1572 m /cph. A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 953

Fig. 5. (a) Normalised power spectrum on a logarithmic scale calculated from 2-min sampled sea levels in Mellieha Bay (1/6/93–2/1/97). Up to f = 3 cpd, the spectrum is calculated with 22 degrees of freedom and 95% confidence factors Bmin = 0.52 and Bmax = 2.5). For f > 3 cpd, the spectrum is calculated with 110 degrees of freedom and 95% 2 confidence factors Bmin = 0.78 and Bmax = 1.35). The normalising factor is 0.2048 m /cpd. Normalised power spectrum on a logarithmic scale for (b) the low frequency band; (c) the tidal band from observed sea levels. Normalised power spectrum on a logarithmic scale for (b) the low frequency band; (c) the tidal band from observed sea levels. The 2 spectrum is calculated with 22 degrees of freedom and the 95% confidence factors are (Bmin = 0.52; Bmax = 2.5); the normalising factor is 0.2048 m /cpd. Normalised power spectrum on a logarithmic scale for (d) the tidal band from residual levels, and (e) the short period band. In (d), the spectrum is calculated with 22 degrees of freedom and the 2 95% confidence factors are (Bmin = 0.52; Bmax = 2.5); the normalising factor is 0.2048 m /cpd. In (e) the spectrum is calculated with 110 degrees of freedom and the 95% 2 confidence factors are (Bmin = 0.78; Bmax = 1.35); the normalisation factor is 0.1572 m /cph.

extremes. The seiches are however much more persistent, lasting seiche events. The seiche then develops as a succession of random even for days on some occasions. The cumulative seiche energy is intensifications which follow closely one another resulting in a ser- thus much higher. A short buildup period generally preceeds these ies of bursts of large amplitude fluctuations. 954 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

Fig. 5 (continued)

2.3. The tidal constituents the tide in the region is thus generally small (Defant, 1961). The phase and amplitude of the four main tidal harmonic constituents The general tidal pattern for the Mediterranean Sea as a whole for the main ports in the Central Mediterranean (Table 2) are based gives nodal locations in the Strait of Sicily, and the magnitude of upon values from Mosetti and Purga (1989), Molines (1991) and Tsimplis et al. (1995). The values are in most cases derived from Table 1 short series of tide gauge data. The constituents for Mazara del Percentage energy distribution in Mellieha Bay. Vallo, the island of Pantelleria, the island of Lampedusa and an Frequency band % offshore mooring (indicated by SG in Fig. 1) situated at approxi- mately 20 nautical miles in the NNE of Linosa Island are taken from Low frequency (<0.8 cpd) 57.3 Diurnal (0.8–1.2 cpd) 3.0 9 months of bottom pressure measurements carried out during the Semi-diurnal (1.8–2.2 cpd) 32.7 JANUS Experiment (Astraldi et al., 1987). The known longest Quarter diurnal (3.8–4.2 cpd) 0.06 historical sea-level data set in the region refers to the Grand High frequency (>4.2 cpd) 6.6 Harbour (GR in Fig. 1) in Malta; these chart records are kept at Other 0.36 the British Hydrographic Office and cover the period 1876–1926.

Table 2 Harmonic constants for the Central Mediterranean Sea. Amplitudes in centimetres; phases in degrees, relative to UT.

Station Latitude Longitude M2 (cm/deg) S2 (cm/deg) K1 (cm/deg) O1 (cm/deg) Mean spring range Mean neap range Form number Gabes 33°530 10°070 51.1 36.4 2.5 0.5 175 29.4 0.034 79 107 349 81 Sfax 34°440 10°460 41.6 26.7 1.8 0.8 136.6 29.8 0.038 76 103 4 82 Zarzis 33°300 11°070 21.9 15.3 2.0 0.9 74.4 13.2 0.078 77 103 31 102 Pantelleria 36°470 12°000 1.6 1.9 1.3 1.4 7.0 0.6 0.771 31 42 184 Lampedusa 35°300 12°300 6.6 4.2 0.9 0.7 21.6 4.8 0.148 45 58 3 Mazara del Vallo 37°380 12°350 4.3 1.8 3.5 1.6 12.2 5.0 0.836 161 151 114 74 JANUS SG 36°100 12°590 4.8 3.1 0.5 0.9 15.8 3.4 0.177 50 57 78 Tripoli 32°540 13°120 11.1 5.4 2.0 0.6 33.0 11.4 0.158 60 75 13 121 Porto Empidocle 37°150 13°300 4.5 3.3 1.8 1.4 15.6 2.4 0.410 78 77 91 76 Malta 35°540 14°310 6.3 4.0 1.0 0.8 20.6 4.6 0.175 47 57 19 55 Capo Passero 36°410 15°090 6.7 3.5 1.9 0.9 20.4 6.4 0.275 62 67 52 46 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 955

In general there is a discrepancy in the phases of the constituents uent is M2, but the contribution of the solar radiation tidal input is quoted by various sources and calculated from one or more years high (S2 is 62.4% of M2), which is typical of the Mediterranean. The of this data from the Grand Harbour; the values in Table 2 are those tide is predominantly semi-diurnal (Form number = 0.15) and the based on an analysis of 13 months of data from May 1990 to May main diurnal constituents K1,O1 and P1 are relatively weaker in 1991 (Drago, 1992). Besides the tabulated values, other important the region of the Maltese Islands compared to the Sicilian shore constituents in this port are N2 (1.1 cm; 48°) and K2 (1.3 cm; 47°). to the North. These diurnal constituents cause the minor diurnal The tidal oscillations in the Strait of Sicily are dominated by the inequalities. semi-diurnal constituents with supplementary contributions from These results for Mellieha Bay are in good agreement with the the diurnal constituents especially on the North African coast. M2, values for the Grand Harbour in Table 2. The two locations are very S2,K2,N2,K1 and O1 are the only components greater than 1 cm close to one another and the differences, particularly in the phase, (Purga et al., 1979). The higher frequency components are reported are probably more related to temporal changes. Changes in the to be less than 1 mm on the Sicilian coast (Mosetti et al., 1983). tidal constituents between different locations can also however Notwithstanding their small size, the tides in this region denote occur due to the presence of continental shelf waves which are a behaviour of particular interest. They are greatly connected with known to propagate in the area. Besides producing an anomalous the hydrodynamics of the whole Mediterranean Sea and their intensification of the tidal currents, these continental shelf waves development is related to the influence of tidal co-oscillations. are responsible for the appearance of small-scale variations in The basin morphology has also important effects and the relatively the harmonic constants (Rabinovich and Zhukov, 1984). shallow bathymetry on the African shelf results in an amplification In the case of the Grand Harbour data, an analysis on separate of the tide. The syzigial excursions in the Gulf of Gabes reach months (May 1990–May 1991) is also performed. From 29-day ti-

216 cm (Mosetti and Purga, 1989). The M2 tide alone has a remark- dal analysis of successive months, Drago and Ferraro (1996) show able amplitude of 51 cm in Gabes (Molines, 1991). that there is considerable variability in both the amplitudes and

The diurnal tides are everywhere small and without nodes in phase of the main constituents, especially N2,K1 and O1. For these the Strait (Manzella et al., 1988). The amplitude of K1 is uniform constituents, the standard deviation is of the order of 20% in the with values of 3.1 cm at Gabes and 2.1 cm at Cape Passero. On amplitude, and 23% in the phase. For M2 and S2 the variation is the other hand the influence of the rotation of the earth causes much less but not negligible. In the case of M2, the amplitude fluc- strong transverse (North–South) oscillations that transform the tuates in the range 58–67 mm, and the phase in the range 42–53°. nodal lines of the semi-diurnal components in the region into amp- This variation can be attributed to the relative contributions of the hidromies contra solem. On the basis of semi-empiric consider- equilibrium forcing and the tidal wave through Gibraltar in the ations, Sterneck (1915) had prognosticated an M2 amphidromic propagation of the tide in the Mediterranean. A high-resolution, point close to Pantelleria even before tidal coastal data could pro- two-dimensional model of the whole basin (Tsimplis et al., 1995) vide a confirmation by means of field measurements. Numerical has revealed that the incoming wave through the Strait of Gibraltar simulations of the barotropic tide (Mosetti and Purga, 1989 and is important in tuning the tides in the whole Mediterranean Sea. In Molines, 1991) have recently succeeded to reproduce these tidal the Strait of Sicily the forcing at Gibraltar causes a wandering of the features and to elaborate on the associated hydrodynamics. M2 amphidrome to the eastern part of Sicily and gives rise to dou- Table 3 compares the amplitudes and phases of the harmonic ble amphidromes in the propagation of both K1 and O1 in the area constituents (with H > 1 mm) in Mellieha Bay. The tidal analysis between Malta and Sicily. Comparison of the constituents at differ- is performed on the hourly sea-level data (from June 1993 to ent ports (refer Table 2) needs therefore to be reconsidered espe- December 1996) on the basis of 61 constituents. The main constit- cially in those cases where the analysis is based on data sets of different length and different year or month. From the values in Table 2 it is however clear that for all the principal constituents the change in phase across the eastern side of the Central Mediter- Table 3 ranean region is much more gradual with respect to the west. This Tidal Harmonic constituents in Mellieha Bay with phases relative to GMT. is in agreement with tidal model results. The phase differences be- Harmonic constituent H/cm g/deg tween Malta and the nearby Sicilian ports to the north suggest a Sa 8.85 201 relative spatial concentration of phase contours over the shallow Ssa 1.45 152 continental shelf. Mn 0.55 185 Mf 1.22 337 Msf 0.21 067 Q1 0.27 056 3. Characterisation of the seiches RO1 0.10 134 O1 0.78 056 The broad ‘hump’ in the frequency range of 1–10 cph in the chil 0.17 253 pil 0.30 149 power spectrum (Fig. 5a and e) reveals a very interesting selective P1 0.26 051 enhancement of a band of short-period signals in Mellieha Bay that S1 0.58 281 explains the nature of its seiche oscillations. In this amplification K1 0.70 053 process the response of the embayment is not restricted to the PSI1 0.27 057 eigenperiods of its water body, but covers a wide range of frequen- 2N2 0.11 082 MU2 0.18 092 cies whose energy inputs are considerably increased above the N2 0.93 064 background values. The characteristic eigenoscillations stand out nu2 0.19 064 as well-pronounced peaks upon this overall amplified response M2 6.04 055 of the embayment. In particular, three sharp maxima with respec- L2 0.30 056 tive periods of 25.1, 21.2 and 16.8 min (corresponding to 2.4, 2.8 T2 0.15 081 S2 3.77 062 and 3.6 cph) feature in the rather intricate spectrum. K2 1.15 065 Higher frequency maxima with frequencies above 4 cph are an M3 0.10 169 expression of the higher order bay modes. It is important to ascer- M4 0.15 271 tain that this spectral structure in not contaminated by aliased sig- MS4 0.16 316 nals. The energy density computed at a frequency f can have 956 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

Fig. 6. Cross-spectral analysis of 2-min sampled water level observations at Qawra station (MALTA) and Pozzallo station (SICILY in the period (08h50) 10th September to

(11h54) 30th September 1996. Power spectral density in (a) is calculated over 54 degrees of freedom with a 95% confidence factor of 3.3 dB (Bmin = 0.7; Bmax = 1.5). The 95% confidence level for the coherence estimate is 0.11.

contributions from aliased frequencies f ±2mNf with m =1,2,3, fractional areas are not as fixed as in the case of a cul-de-sac or etc. But the sampling interval (Nyquist frequency Nf of 30 cph) in small bay that is suddenly terminated. The other two peaks with this case is sufficiently small to rule out effects due to aliasing. slightly longer periods represent oscillations involving the shelf Contributions of the energy densities in the sea level at frequencies area immediately adjacent to the bay. of 60, 90, 120, ...cph are in fact known to be too small to be of any The SB band (Fig. 5e) also presents a series of sharp, well-de- importance. The measured peaks of energy are thus real. fined and equally energetic peaks on its lower frequency end. The case of Mellieha Bay is particularly interesting. Its wide en- The main maxima have periods of 3.7, 2.2, 1.7, 1.1 h, and 58, 46, trance increases the number and variety of the observed seiche 34.3, 29.5 and 27.7 min. These peaks are probably related to shelf modes. Furthermore, movement of its water body is coupled to oscillations in the Malta Channel. an adjacent embayment and the bathymetry at its wide open The long wave structure of sea level oscillations in the region is mouth is complicated by a shallow bank offshore. Seiches are also typically characterised by (a) forced motions, (b) free long waves amplified by a shoaling effect on the shallow sand bank at its head. propagating along the shelf, and (c) eigenoscillations of individual The main peak at 16.8 min is verified by numerical computation coastal areas including embayments and inlets. The bay oscilla- (Drago, 1999) to be related to the Helmholtz mode of the bay tions are treated elsewhere (Drago, 1999), and are found to con- and corresponds to a Merian along-axis extent that exceeds the ac- cern signals with periods lower than 20 min. Long waves with tual physical dimensions of the bay. The volume of the excited longer periods are however also persistent and rise above the back- water body is thus dictated by the bathymetry outside and in the ground levels during seiching events. Their periods normally range immediate vicinity of the bay. At times water level records in the from 20 min to a few hours. Main signals with periods 3.7, 2.2, 1.7, bay take the form of quite regular oscillations, especially during 1.1 h, and 58, 46, 34.3, 29.5, 27.7, 25.1, 21.2 min were identified periods when excursions are strong; at other times the seiching from the general spectral analysis. The bays are shallow coastal is irregular and is characteristic of a coastal configuration in which indentations with shapes that do not permit natural resonant peri- A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 957

Fig. 7. Theoretical spectrum for a straight ledge (width = 100 km; shelf depth = 100 m; c2 = 5) in the case of normal incidence.

these two peaks, the coherence rises to high levels. The phase is re- versed back to zero at 1.16 cph. At each of these phase reversals the coherency dips to zero. These phase reversals between 0° and 180° are indicative of the occurrence of standing waves on the shelf. These results can be tentatively explained by considering the shelf to be very simplistically represented by a straight steep coast with uniform bathymetry alongshore (y-axis) and a step cross-

shore (x-axis) profile with constant width L, depth H1 on the shelf and H2 on the deep sea side. One possible long wave motion on this continental shelf model is a system of leaky waves normal to the shore (Snodgrass et al., 1962) with an antinode at the shore and Fig. 8. Bathymetry of Mellieha Bay and positioning of instruments. a node at the shelf edge. In the case of waves incident normally

from the deeper ocean with an associated spectrum So(f), the spec- 2 2 trum at the shoreline (x =0) is a (f)So(f), where a (f) = [1 + ods to match these values. This shows that these oscillations must 2 2 2 2 p tan (2pfL/c1)]/[1 + c tan (2pfL/c1)] and c = c2/c1, c1 = (gH1), necessarily concern a larger water body. p c2 = (gH2). The spectrum at an offshore position (x = X < L)on 2 2 the shelf is a (f)cos (2pfX/c1)S(f). Taking a typical value for the 3.1. Results of the Malta Channel experiment shelf width L = 100 km and a mean depth H1 = 100 m, the theoret- ical spectra on the Sicilian coast (solid) and on the northern coast This section treats the findings from the simultaneous sea level of Malta (dotted; with position of the island taken at X = 0.75 L) measurements at two locations across the Malta Channel, the for normal incidence (from the south) are shown in Fig. 7 with val- stretch of sea on the continental shelf area linking the Maltese Is- ues normalised to S(f) = 1. The signals are in phase up to A (0.37 lands to the southern shores of Sicily. These measurements were cph), become in antiphase from A to B (1.11 cph), and return in conducted to identify the shelf scale components of the seiches. phase from B to C (1.85 cph). The coherence (not shown) follows The similarity and temporal coincidence of the bottom pressure a negative delta function, falling to zero with a very narrow trough recordings at Pozzallo (PZ) and Malta (QW) in Fig. 6 is an indication centred on the frequencies at each phase reversal, and is equally that the lower frequency long wave oscillations are not related to high on both sides. Successive spectral peaks on the Sicilian coast the local topography at the respective stations, but are instead an have also the same amplitude and occur at To = 3.55 h and To/3 = expression of the larger scale movements of the water body over 1.18 h. These periods compare well to the peaks X and Y in the the continental shelf. The cross-spectral analysis between the observed spectra (Fig. 6). It is also possible to account for the two records shows that the principal signals at the two stations second phase reversal which coincides to that observed at 1.16 are identical, with energies being on average an order of magni- cph. Some remarkable differences are however noted. The ob- tude higher in Pozzallo throughout the range of frequencies served fundamental mode is weaker than the first resonance mode. 0.4 < f < 1.1 cph. The analysis shows two main sudden variations The observed dips in coherence are smeared into troughs, and the in phase and coherence. The records are consistently in phase coherence remains low beyond 1.2 cph. The first phase reversal is and highly coherent for f < 0.7 cph. In this range of frequencies expected at a third of this frequency (f = 0.37 cph) whereas it actu- the energy spectrum carries a broad peak centred at 0.285 cph ally occurs at a much higher frequency (f = 0.78 cph). The observed (T = 3.5 h) followed by sharper and stronger peaks at T = 2.2, 1.7, fundamental peaks in Malta and Sicily have also equal amplitudes 1.45 h. At 0.78 cph the phase changes abruptly and the signals be- which again does not agree with theory. For other angles of inci- come in antiphase between 0.8 and 1.1 cph. The strongest energy dence (h – 0), the resonance peaks and anti-resonances shift to p peak (with T = 1.1 h) at Pozzallo is registered in this frequency higher frequencies by a factor (1 c2sin2h) and the amplifica- range. It is accompanied by a weaker peak at T = 58 min. At both tion at the coast is reduced. In the extreme case of glancing inci- 958 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

Fig. 9. Current stick plot of subsurface sea currents observed in Mellieha Bay at a depth of 11 m from the water surface.

dence (h = 0) this amounts to a shift of 12% in frequency which still with two of the observed spectral peaks. Pozzallo and Qawra sta- does not account for the differences between theory and observa- tions are on the same side of the ridge, but their longitudinal coor- tions, especially with regard to the fundamental mode. This mode dinates differ by 24.310 which amounts to an east–west separation thus appears to be greatly modified by the shape and limited lati- of about 36 km. This explains the phase relationship of the oscilla- tudinal extent of the shelf. The failure of the coherence to recover tions at the two stations which are in phase for mode T1, but in after the second phase reversal also suggests that the presence of antiphase for mode T2. multiple stationary modes is important. These modes apparently The shelf itself can also in its totality be considered as a sub- carry an appreciable fraction of in-phase energy even after most merged ridge extending normal to the borderland. In this case if of the energy is out of phase. we take Ho = 100 m and a = 60 km, we obtain a second mode peri- The simplified model above does not thus fully apply to the od of 1.724 h which again compares well with the observed peak at shelf area between Malta and Sicily on account of the shelf’s com- T = 1.7 h. The signal at T = 1.45 h is probably related to a co-oscilla- plicated bathymetry and its very abrupt termination on the east. A tion of the plateau (averaging a depth of 150 m) on the western multi-directional distribution of incident energy from the deeper flank of the shelf with the Central Mediterranean basin. ocean may indeed partly explain the smearing of the features in the observed spectra and coherence, but the anomalous character- 3.2. Seiche-induced currents in Mellieha Bay istics pertaining to the gravest mode should be sought in the effect produced by the coastal configuration of the northern borderland This section deals with the strong oscillating currents that can and the irregular shape of the shelf. A three-dimensional numerical be triggered by seiches especially in semi-enclosed basins like har- modelling approach would be necessary to resolve these bours and coastal embayments. High frequency, large amplitude characteristics. sea level fluctuations can have associated horizontal motions that Other important intermediate energy peaks (at T = 2.2, 1.7, can be a damage potential on moored vessels. Ship loading/unload- 1.45 h and 58 min) are not explained by the above model. These ing operations can be delayed or even potentially hazardous. Con- signals are apparently related to latitudinal stationary modes on stricted flow at harbour entrances also results in strong reversible the shelf. These modes are attributed to the trapping of long wave currents that can be detrimental to navigation. energy on the shelf area as a whole as well as in localised areas Taking the example of the Grand Harbour, with a narrow open- along isolated features on the sea bed. One such feature is the ing to the adjacent sea, we can estimate the magnitude of this crescentic submarine ridge which runs close to the eastern and seiche-induced flow. If the profile of the uninodal standing wave southern perimeter of the shelf. This inner shelf ridge can act as oscillation is taken to be sinusoidal with wavelength k and swing a waveguide for long waves. height H, then the volume of water that must flow in half a period The depth profile normal to the ridge axis can be taken to be across a vertical line through the nodal point at the mouth of the p 2 2 parabolic according to H = Ho (1 + x /a ), where Ho is the mini- harbour is Hk/2p. The time average horizontal velocity is ob- mum water depth at the centre of the ridge (x = 0); at a distance tained on dividing by the time T/2 of one half period and the aver- p x = a from the ridge axis the depth is H / 2. The lower frequency age cross-sectional area, namely the depth d. On using the shallow op mode has a period given by T = 6.95(a/ gH )(Defant, 1961, page water wave propagation relation, the maximum velocity at the nodal 1 o p 235) and consists of anti-phasic oscillations on opposite sides of point is then given by Vmax = p < V >/2=Hk/(2Td) = (H/2) (g/d), the ridge, with a node over the ridge. On each separate side of where d is the average depth of the basin. the ridge, the oscillations remain in phase with the amplitude Taking H = 0.25 m, d = 18 m as typical values for the Grand Har- reaching a maximum at a distance x 2a. The next mode is short- bour, and assuming the constriction at the harbour mouth to be p er, with a period given by T2 = 3.24(a/ gHo), and consists of sym- half the extent of the average harbour width, then the actual value 1 metrical oscillations with an antinode over the ridge, nodes at of Vmax is expected to be 0.37 m s . x ±a and antinodes at x ±2a. Taking H = 50 m and a =25km The horizontal particle excursion at the harbour mouth is given o p as typical values for the inner shelf ridge, the corresponding modes by T/2 = Hk/2pd =(HT/2p) (g/d) 41 m. By proportion the have periods T1 = 2.179 h and T2 = 1.016 h which compare well excursion at the middle of the harbour is expected to be 20 m. Thus A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 959 although the maximum velocity is not excessively high, the large dicular to the bay axis. The current component plots in Fig. 10 horizontal motion could create difficulties. show clearly the onset of the current fluctuations in coincidence with the sea level oscillations on the 26th July. The seiche currents 3.2.1. Observation of seiche currents are predominantly rectilinear and orientated along the bay axis. Direct observations of seiche-induced subsurface currents have Their component across the bay is less important although it is been conducted in Mellieha Bay by means of an ENDECO/YSI teth- not completely negligible. ered-type current meter positioned inside the embayment (refer In order to better study the seiche currents it is important to to Fig. 8) such as to mainly pick the influence from the main mode isolate them from the background component. This is done by high of bay oscillation. The current meter measures the total current pass filtering each of the resolved current component time series. A which consists of a background current upon which the seiche-in- Vercelli filter with 48 weighting coefficients and a cut-off period of duced currents are superimposed. The background current is pre- 34 min is used. The recombination of the high pass filtered compo- dominantly established by wind-induced effects as well as by the nents returns the seiche current vectors. interaction of the bay circulation with the open sea. In general this background circulation predominates and completely masks the 3.2.2. Estimation of seiche-generated currents from sea-level data seiche currents. During strong seiching events the associated move- The 1D model described in Appendix 2 is applied to the obser- ment of the oscillating water body in the bay can however produce vations in the period 12:00 GMT–15:00 GMT 26th July 1994. To is significant currents. In the case of Mellieha Bay these seiche currents obtained from an inspection of the average period of the water le- have the same frequency of the sea level oscillations (with a period vel oscillations during this period. The value To = 16.8 min is of around 20 min) and can usually be easily detected as very rapid adopted. The average depth is taken to be 20 m while the total fluctuations in the current stick plots. The stick plot in Fig. 9 shows depth at the current meter station is taken as D = 28 m.p Theffiffiffiffi  sea le- an example when the seiche currents become important and the To gd dgðtÞ vel time series is used to obtain 2-min values of 2pD dt . current switches direction very rapidly in a matter of a few minutes. o o These values are compared with the filtered along-axis current These currents are aligned in parallel to the bay axis along a NE–SW observations. The correlation estimated is found to be very high direction and are therefore an expression of the sloshing water (r = 0.865) which shows the efficiency of the model. A regression movement in the bay. The current vectors in one half-cycle are not pffiffiffiffi  To gd dgðtÞ analysis between U and 2 D dt gives the optimal value of parallel to those in the next half cycle since a background current p o o across the bay is superimposed during this particular interval. sinðpao=2Þ as 1/1.96. This implies that ao = 0.34 and hence that The incidence of these high frequency currents can be followed L = xo/0.34. This result confirms that the seiche oscillations are from the along- and cross-bay axis components of the currents. not confined to the interior of Mellieha Bay, but that they actually These components are obtained by resolving the current vectors involve a much larger water body which extends well beyond the along orthogonal directions N65°E and S25°E parallel and perpen- promontaries of the bay. This water body is about three times the

Fig. 10. Time series plot of water elevation in Mellieha Bay, and of subsurface current components resolved along/across the bay axis. 960 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

Fig. 11. Comparison of observed and calculated along-axis current components in Mellieha Bay. size of the bay and includes the deeper basin between the mouth of continental platform. An associated vertical oscillation of the ther- the bay and the White Bank to the northeast of the bay. mocline in the form of an internal tide has been quantified to have Fig. 11 compares the depth-averaged along-axis seiche current a crest-to-trough amplitude of the order of 8 m (Drago, 1997). component derived by the above model (with ao set equal to From CTD casts taken during the same survey, the density profiles 0.34) to the observed high pass filtered currents. The correspon- show that the seasonal pycnocline has a sharp gradient between 10 dence confirms the validity of the model which can thus be used and 30 m depth and acts as a clear interface between the surface to predict seiche currents from observations of sea level on the mixed layer and the deeper layer. Taking the mean relative density coast. In particular it is interesting to note that moderate seiche difference between these upper and lower layers to be 0.3% 3 3 amplitudes of just 15 cm can generate quite strong seiche currents (q1ðupperÞ1024:5Kg m ; q2ðlowerÞ1027:5kg m ), the free which peak up to 10 cm s1. This shows the potential hazard of surface displacement accompanying this internal tide is estimated these seiche-induced currents even in the case of a wide mouthed to have a semi-amplitude of the order of 1.2 cm. embayment such as Mellieha Bay. The variability of the diurnal residual energy over the whole period of measurements (June 1993–December 1996) is studied from a series of spectra calculated in each of successive 3-month 4. Other oscillations of non-tidal origin half-overlapping periods. The energy carried in the frequency range of 0.978–1.022 cpd is calculated for each spectral estimate. Spectral analysis of the residual sea-level data allows the sepa- The relevant plot against time (Fig. 12) shows a consistent pattern rate study of the non-tidal oscillations. The analysis is performed with peak energy during the periods spanning mid-October–mid- by two alternative computations of energy spectra for (1) the January and mid-April–mid-July, respectively. This intra-seasonal whole time series (Fig. 5d), and (2) 27 successive 50% overlapped variability of the diurnal signal is probably linked to dynamical 3-month periods in order to reveal any seasonal variability. The processes that have a correlated temporal repeatability; there is most important result is a strong diurnal residual energy that cov- as yet no sufficiently long hydrodynamical datasets to confirm this ers a relatively broad band of spectral frequencies centred at 1 cpd. relationship. The variability of the semi-diurnal residual energy This signal is probably related to the signature of baroclinic mo- calculated over the frequency range 0.48–0.52 cpd is less pro- tions on the continental shelf. Measurements made during a phys- nounced. In particular, the semi-diurnal residual can predominate ical oceanographic survey carried out in the NW coastal area of over the diurnal residual during late winter and early spring. Malta in summer 1992 have in fact revealed the presence of diur- nal subsurface flows in the vicinity of the islands. These diurnal 4.1. Variability in the low frequency range and relation to atmospheric baroclinic currents are believed to be the expression of a topo- forcing graphically trapped wave that takes the form of an internal Kel- vin-like waveform in the deeper sea away from the shelf break The subtidal sea level signals are well resolved in the LB spectral and is accompanied by shelf wave modes propagating over the band (Fig. 5b) by utilising a long window size of 65,536 records A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 961

Fig. 12. Variability of the (a) diurnal (solid) and (b) semi-diurnal (dotted) residual energy calculated for successive 3-month half-overlapping.

Fig. 13. Time series of (a) residual sea level in Mellieha Bay; (b) inverted barometric pressure fluctuations at MSL; (c) and (d) along/cross-shore components of wind at Ramla station for the period mid-November 1995–mid-July 1996 (Residual sea level is measured relative to MSL; the positive along-shore wind component corresponds to a wind from S55°E; the positive cross-shore wind component corresponds to a wind from N35°E.). 962 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

(182 days:01 h:04 min). The sea-level is found to have significant vel displays the presence of variability at different time scales. Sea variability in the 1.2–15 days period (periods from tidal to several level variations at a time scale of 1 month have the largest ampli- weeks). This is very typical of the whole Mediterranean basin tudes and can reach peak-to-trough values of up to 0.35 m. Higher where the sea level variability in the low frequency range repre- frequency oscillations at time scales of several days (synoptic var- sents an energetic part of the sea level spectrum. iability) appear on both the sea level and pressure time series, and Besides the effect of the tides and oceanographic factors such as are predominant during the winter months. These oscillations are water density and currents (both geostrophic and ageostrophic), related to natural periods of occurrence of cyclones in the region. the influence of meteorology determines a great part of the synop- Variations in the atmospheric pressure can reach up to 18 mbar tic variability in the sea level. In the Mediterranean, sea level vari- at high frequencies, and are accompanied by equivalent variations ations at time scales from 1 to 10 days have been shown to be in sea surface height. Both high and low frequency sea level oscil- primarily due to surface pressure changes related to synoptic lations in fact bear a distinct visual correlation with the inverted atmospheric pressure disturbances (Kasumovic, 1958; Mosetti, barometric pressure and extreme values of sea level are very well 1971; Papa, 1978; Godin and Trotti, 1975). Sea level variations at associated with extreme values of inverted pressure. It is also clear time scales from 10 days to several weeks have been explained that the sea level and atmospheric pressure variance differs sea- as being due to atmospheric planetary waves (Orlic, 1983; Lascara- sonally. The sea level signal shows however a greater variability tos and Gacic, 1990). The contribution of the wind is also impor- than that implied by a simple barometric effect. tant, both with regard to its dynamic effects as well as to its The two wind components are taken to correspond to a wind effect on rate of evaporations and the difference in air–sea vector from directions 35° (positive cross-shore component) and temperature. 125° (positive along-shore component) with respect to north. The comparative plot of the residual sea level and meteorolog- These components are roughly coincident to a wind directed along ical time series (Fig. 13) presents some very interesting first hand the axis of Mellieha Bay and parallel to the northern foreshore information in this part of the Mediterranean. The residual sea le- coastline of the island, respectively. The mean wind magnitude is

Fig. 14. General spectra for (a) residual sea elevation in Mellieha Bay, and (b) MSL atmospheric pressure and (c and d) wind components at Ramla tal-Bir. The 95% confidence factor, for 24 degrees of freedom is 5.0 dB (Bmin = 0.6; Bmax = 1.9). Data used consists of hourly values from 18/11/95–11/8/96. A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 963

1.15 m s1 from the west (N87°W). The wind data are character- day). This behaviour has been reported in other studies based on ised by frequent clockwise rotations of the wind direction which coastal data (Palumbo and Mazzarella, 1982; Pasaric and Orlic, is indicative of the passage of fronts over the area. During the 1992; Tsimplis and Vlakhis, 1994) and is probably due to signals, occurrence of these pressure lows, the wind vector can typically such as from steric effects and wind, which can be correlated with rotate by 90° and subsequently attenuate very rapidly, or even un- atmospheric pressure. For periods higher than 25 days, Le Traon dergo a complete reversal without losing in strength. and Gauzelin (1997) have also found an over-isostatic response The comparison is further investigated by means of auto- and of the satellite-derived mean sea level to the ECMWF model anal- cross-spectra of the data series which were computed from hourly ysis mean atmospheric pressure calculated over the whole values, after linear detrending and mean removal, by means of 13 Mediterranean. 50%-overlapping consecutive segments of 1024 points each. All the In the lower synoptic frequency range (0.05 < f < 0.3 cpd) the spectra (Fig. 14) show the ‘red’ shift of energy that is characteristic pressure variance is higher than that of the residual sea level. of geophysical processes. The prominent peak in the atmospheric The phase relationship remains less than 180° and a maximum de- pressure spectrum at the frequency of 2 cpd is due to the semi- lay of 70° in the response of the sea level is registered at a fre- diurnal atmospheric tides. The diurnal maximum is less pro- quency slightly higher than 0.1 cpd. The response is thus well nounced. At the higher frequencies, the atmospheric spectrum fol- under-isostatic, and the equivalent sea level fluctuations are only lows an x2.2 power law that is in good agreement with about half the value expected for a perfect inverse barometer re- observations by Rabinovich and Monserrat (1996) and Kovalev sponse. On the other hand the response is very close to isostatic et al. (1991) (x2.3), and only slightly steeper than that described in the upper synoptic frequency range (0.3 < f < 0.5 cpd). For this by Herron et al. (1969) (x2.0). The spectrum has however a dis- band of frequencies the sea level is highly correlated to pressure, tinctive steeper gradient in the higher synoptic frequency range and responds in antiphase to pressure with an average gain of 0.7. (0.2–1 cpd) where it follows an x3.2 power law decay. The pres- For further higher frequencies (f > 0.5 cpd) the coherence is in sure and wind spectra, especially the NS component, exhibit a dis- general low except for a number of discrete frequencies. In partic- tinct flattening at periods greater than about 5 days. The sea level ular, the sea level signals close to the diurnal frequency are uncor- spectrum has no such bounding limit on power at the lower fre- related to barometric pressure, which indicates that their origin quencies and the spectrum has an almost constant slope for the full has to be sought from other oceanographic influences. range of frequencies. As a matter of fact, the prevalence of the sea level spectrum over that of atmospheric pressure results in the power in sea level rising much more rapidly than that of pressure at periods longer than about 12 days, and in an increased diver- gence between the two spectra at the higher frequencies. At plan- etary time scales (several weeks), the sea level variance is thus roughly seven times higher than that of pressure. As expected the seasonal signal of the atmospheric pressure is less than that of the sea level since the latter carries other forcings especially from steric effects. At the synoptic time scale (0.05–0.5 cpd) the variances are equal at the lower frequency end, with variance in pressure become more important with increasing frequency. The comparative plot of spectra on a semi-logarithmic scale (Fig. 15) shows that signals with frequencies higher than 0.5 cpd represent only a negligible fraction of the total variance in both residual sea level and atmospheric pressure. The wind spectra exhibit a predominance of the EW component over the NS component in the synoptic frequency range (3:1) and especially for the lower frequencies (12:1).

4.2. Barometer factor from spectrum analysis

The significant dependence of sea level variability on atmo- spheric pressure in the synoptic and planetary wave scales is evi- denced by the fairly high coherence between the residual sea level and atmospheric pressure fluctuations at these frequencies (Fig. 16a and b). Coherence levels have an average of 0.7 for the re- sponse at frequencies lower than 0.5 cpd (T > 2 days). Coherence has a value of 0.6 for the lower frequencies, drops to 0.4 for fre- quencies centred on 0.14 cpd (T approx. = 7 days), and rises again to values close to 0.8 in the frequency range of 0.3–0.5 cpd (2 < T < 3 cpd) on average. The gain (barometer factor) and phase relationship bear a very similar dependence on frequency so that the response can be broadly classified into three bands of frequency. In the lower frequency planetary wave time scale (f < 0.05 cpd) the response is over-isostatic with a gain of about 1.5, and a lag of atmospheric pressure with respect to sea level a few tens of de- Fig. 15. Comparison spectra with semi-logarithmic scales for (a) residual sea grees less than 180°; This phase relationship is equivalent to that elevation in Mellieha Bay (solid), and (b) MSL atmospheric pressure at Ramla tal-Bir of an atmospheric pressure leading the inverted sea level by a (dotted). The 95% confidence factor, for 24 degrees of freedom is 5.0 dB (Bmin = 0.6; few tens of degrees (i.e. an approximate phase difference of 1 Bmax = 1.9). Data used consists of hourly values from 18/11/95 to 11/8/96. 964 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970

4.3. Seasonal changes in mean sea level and is often influenced by local effects such as of temperature and spells of strong winds whose incidence can vary from year to The seasonal variation in the mean sea level in Mellieha Bay is year (Goldsmith, 1990). Indeed this renders eustatic sea level studied by 43 monthly averages of sea-level data covering the per- determinations more difficult to detect. In general, seasonality in iod June 1993–December 1996. The seasonal signal in the sea level the west is less regular, and is not as sharp as in the southeastern is seen to be quite strong (Fig. 17) and is actually larger than the Mediterranean. Satellite altimetric missions such as from the ERS-1 daily variation. The magnitude of these sea level seasonal changes and Topex/Poseidon platforms, have since 1992 provided a new is in the order of tens of centimetres and therefore greatly exceeds technology to monitor sea level change, and permit variations to in size other effects on the sea level such as of climate change.. be followed not only in time but also in space by providing a 2D Such seasonality is typical of the whole Mediterranean Sea where, view of the variability that has revealed considerable geographical on the basis observations from sea level stations, seasonal signals differences worldwide and in the Mediterranean. Analysis of sea are found to account on average for approximately 20% of the total levels derived from TOPEX/POSEIDON satellite altimetry data dur- sea level variance (Marcos and Tsimplis, 2007). Besides the spatial ing 1993–1994 show that the mean level variations in the western variability across the Mediterranean (Emery et al., 1988), the sea- and eastern Mediterranean basins are about the same in magni- sonal signal is characterised by a strong temporal variability with tude, but have a phase lag which varies with time (Larnicol et al., changes in amplitude and phase from year to year, and this is 1995; Jorge del Rio et al., 2007). mainly attributed to changes in water temperature (Marcos and In the case of Mellieha Bay the records (Figs. 17 and 18a) show Tsimplis, 2007). The range, pattern and regularity of the seasonal that a sea level maximum generally occurs in October while a min- signal varies widely for different locations in the Mediterranean imum occurs in March. The sharp lowering in the mean sea level

Fig. 16. (a) and (b) Coherence and phase for residual sea level and atmospheric pressure at MSL; (c) amplitude of the barometer factor as a function of frequency. The data set covers the period mid-November 1995–mid-September 1996. The phase indicates the lead of sea level with respect to the pressure. The dashed line indicates the level above which the coherence is significant at the 95% confidence level. With 24 degrees of freedom this is equal to 0.22. A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 965

the extreme levels is in the order of tens of centimetres. The three years are however not fully alike. Both the size and phase of the fluctuations as well as the occurrence of fast variations (such as the sharp rise in sea level in May 1996) are indicative of consider- able interannual variability. A comparison with 13 months of sea- level data covering the period May 1990–May 1991 and obtained at a sea level station in the Grand Harbour (only within a few kilo- metres of distance from Mellieha Bay) further confirms that the seasonality is not very regular (Fig. 19a). During 1990/1991 the rise to maximum sea level in October is more gradual, while the min- imum in 1991 occurs in January rather than March. There seems thus to be a sensible phase shift in the seasonal signal with respect to the period 1995/1996. This implies that in the case of local sea level variations with the longer time scales and with cycles in the order of tens of years, studies need to be based on longer time series of data so as to enable inferences on statistical averages that are better representative of the predominant seasonal signals. The seasonal signal is also present, though less energetic, in the atmospheric pressure (Figs. 18b and 19b). After applying the IB correction the mean sea level still retains a large part of its variabil- Fig. 17. Monthly mean sea level in Mellieha Bay as a function of time (June 1993– ity and hence other factors besides the barotropic effect of baro- December 1996). metric pressure are responsible for the sea level variations at this scale. On the basis of 44 years of model data from the HIPPOCAS after October is interrupted by a second maximum in December/ project Gomis et al. (2008) attribute only a small contribution January while the increase after March is temporarily halted by a (2 cm amplitude) to the observed sea level seasonal cycle from secondary minimum in late spring. The maximum range between the atmospheric pressure forcing; the temporal offset with respect

Fig. 18. (a) Monthly mean sea level in Mellieha Bay as a function of time with (dotted) and without (solid) the inverse barometer correction; (b) monthly MSL atmospheric pressure at Ramla station (period covered is December 1995–December 1996). 966 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 to the steric cycle results in an overall reduction in the amplitude cycle of mean sea level in terms of a mass balance that takes into of the annual cycle. Seasonal winds and the piling of water onshore account local evaporation and precipitation rates and Atlantic as a result of storm surges can greatly contribute to the seasonal water inflow. In their modal analysis of the contribution of atmo- sea level variations (Goldsmith and Gilboa, 1987). Other processes spheric pressure forcing to sea level variability in the Mediterra- influencing sea levels include currents (Pirazzoli, 1987; Thompson nean Sea, Gomis et al. (2008) relate a basin-wide EOF (explaining and Pugh, 1986) and shelf waves (Huthnance, 1986). Palumbo and 66% of the variance) to the existence of a related flow exchange Mazzarella (1982) have determined on various time scales the at the Strait of Gibraltar. meteorological as well as the hydrographic and oceanic factors that The response of the Mediterranean mean sea level to variations can explain the seasonal cycle in the mean sea level. Sea water in the difference between evaporation and precipitation (E–P) in temperature and baroclinic phenomena such as steric effects the basin thus appears to be linked to the exchange at the seasonal which are related to the volume dilation and contraction of the scale at the straits. In the case of a barotropic adjustment to (E–P) sea surface layer in response to changes in heat fluxes are also variations, the basin has a very rapid response (gravity waves take important factors contributing to the seasonal oscillation. Using less than a day to cross the whole Mediterranean) and the sea level an ECMWF climatology of net surface heat fluxes for the Mediter- is thus practically unaffected. On the other hand, when variations ranean, it is found that steric effects produce changes in the mean in (E–P) give rise to baroclinic processes, such as during the forma- sea level that have the right phase compared to observations, but tion of deep waters and Levantine Intermediate Water that are which are only about half in size to the actual variations (Larnicol triggered by strong winter cooling and evaporation conditions, et al., 1995). On the seasonal timescale, the Mediterranean is thus the associated vigorous vertical mixing processes are slower and probably not in mass balance. In order to account for this discrep- an associated signature in the mean sea level is expected. These ba- ancy it seems necessary to hypothesize variations in the inflow and sin properties affect the nature of the exchange at the Strait of outflow at the Strait of Gibraltar. Ovchinnikov (1974) suggests that Gibraltar between the Mediterranean Sea and the Atlantic Ocean. seasonal fluctuations in the inflow at the Strait could well be in On the basis of existing evidence, Garrett et al. (1990a) conclude antiphase to the fluctuations in the outflow, thus resulting in a that the hydraulically controlled flow in the Strait of Gibraltar is net barotropic flow and an associated expression in terms of mean very close to the state of maximal exchange, but do not exclude sea level variations. On the basis of measurements made in the Bay a switching to a marginally sub-maximal state during the second of Naples, Palumbo and Mazzarella (1985) explain the seasonal half of the year. Evidence supporting this seasonal pattern also

Fig. 19. (a) Monthly mean sea level in the Grand Harbour as a function of time with (dotted) and without (solid) the inverse barometer correction; (b) monthly MSL atmospheric pressure at Luqa (period covered is May 1990–May 1991). A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 967 comes from the drop in the mean sea level along the strait from Ca- nected role but to be indeed dynamically and mutually linked to diz to Malaga, which is found to change during the year becoming one another. For example, the sea level drop across the straits more enhanced during sub-maximal exchange conditions (Garrett may not simply be consequential of the state of flow, but may actu- et al., 1990b). ally act as a forcing agent that dictates, possibly together with a During sub-maximal exchange the density difference between number of other factors, the transition between marginally sub- the inflow and outflow is large; the budgets of the sea require only maximal and maximal exchange strait flows. a slow exchange and the outflow is likely to be restricted to a thin layer above the bottom of the sill. If the sea becomes more mixed, the hydraulically controlled outflow becomes less dense; budgets 5. Discussion and conclusion will require greater flow rates and the outflow will occupy a thick- er bottom layer in the strait; the exchange becomes maximal. The The sea level and its variability in the Sicilian Channel is far seasonal flips between the two states could thus be a consequence from fully studied. Long data sets are generally lacking especially of wintertime replenishment of dense Mediterranean water fol- on the African coast. Storm surges and sea level seasonal fluctua- lowed by summertime draining of this water by the outflow. Dur- tions in this region of the Mediterranean have not been previously ing sub-maximal exchange rapid baroclinic adjustment through studied. The work presented in this paper has served to improve the strait to basin (E–P) variations is possible and no effect on the knowledge on the full spectrum of sea level signals in the re- the mean sea level is expected. On the other hand, the suppressed gion of the Maltese Islands, a key location in the Central adjustment during maximal flow produces a direct response of the Mediterranean. mean sea level to changes in (E–P). The analysis of densely sampled meteo-marine observations Unfortunately knowledge on the seasonal variations in (E–P) in collected in the region of Mellieha Bay on the northwestern area the Mediterranean is too scarce to confirm these suppositions. of Malta demonstrates that the tidal amplitude in the vicinity of Whether the flow at Gibraltar is maximal or sub-maximal is still the Maltese Islands is small. The mean spring tidal range is an open question. It is however certain that this simplified picture 20.6 cm and is reduced to 4.6 cm during neap tide. Water level considering the Mediterranean as a single basin will have to be variations are dominated by energy inputs from long-period oscil- modified in order to include the more complex intra-basin interac- lations of non-tidal origin. The annual Sa (365.3 days) and semi-an- tion between the eastern and western Mediterranean through the nual Ssa (182.6 days) components are rather strong. Although Strait of Sicily. The mean sea level variations observed in Malta are variations in atmospheric pressure associated with mesoscale found to be practically unrelated to the wind climate. The wind meteorological phenomena produce a predominant effect on the does not in fact have any significant seasonal character, being dom- sea level in the synoptic and sub-synoptic time scales, the response inated by the westerly winds practically throughout the year. A of the sea is non-isostatic. The response of the sea level on the great part of the seasonality is thus believed to be non-local in nat- atmospheric pressure is thus a complex one being determined by ure and to predominantly carry the signals deriving from differ- both local and non-local effects. The smaller extent of the sea ences of meteo-marine parameters in the two basins. It is the and the closer proximity of the land in the Central Mediterranean intra-basin changes that in fact dictate the seasonality in the flow area give rise to distinctive weather patterns that pertain to the re- through the Strait of Sicily. gion and which directly affect the sea elevation. But the main influ- Taking the example of the atmospheric pressure field, very dif- ence is determined by the general synoptic situation over the ferent behaviours are observed between the two basins. From data whole Mediterranean basin, with geostrophic gradients being pro- reported by the Koninklijk Netherlands Meteorological Institute duced in the Sicilian Channel by different pressure regimes be- (1957) and by the Meteorological Office in London (1964), the wes- tween the western and eastern Mediterranean basins. Besides tern basin is characterised by a minimum in April. This is followed meteorlogical forcing other factors are expected to contribute to by a rise until July, with the pressure remaining practically con- its variability mainly depending on effects derived from the influ- stant until January when it starts to decline again until April. The ence by the general circulation and from mesoscale eddies propa- range is on average 6 m bars. In the eastern basin a deeper mini- gating on the Sicilian shelf. mum occurs at mid-July and is followed by a sharp rise until It is not easy to identify the physical processes responsible for November. The range is about 10 mbar. The pressure remains such a response. It would certainly be necessary to obtain simulta- approximately at the same levels during winter, with a maximum neous measurements at other sea level stations, particularly in the in January, after which it begins to fall until mid-July. With respect Central Mediterranean area, in order to assess the dependence of to these two characterisations, the observations in Malta (Figs. 18b the response on the geographical position. Only then can one iden- and 19b) show that the atmospheric pressure field has a marked tify the extent to which discrepancies from the inverse barometer interannual variability and follows a mixed behaviour as the two effect can be related to local effects as compared to the dependence pressure regimes are, respectively, pushed eastwards or westwards on the larger scale dynamics of the Strait of Sicily acting as a con- over the Central Mediterranean. This will have a local effect on the nection between the two major basins of the Mediterranean Sea. sea level, but most importantly the difference in pressure over the Short period oscillations with periodicities that are in agree- two basins will govern the flow through the Strait of Sicily and thus ment to the theoretical natural periods of Mellieha Bay are also ob- produce other indirect non-local effects on the sea level. These con- served. They are attributed to coastal seiche motions that are siderations render the measurements in Malta particularly impor- triggered in cascade manner by open sea modes in the nearshore tant. Simultaneous observations at a number of locations in this shelf areas, and on a larger spatial scale by resonances over the part of the Mediterranean can certainly reveal key aspects on the Sicilian continental shelf. The large amplitude sea level oscillations exchange between the two basins. observed on the northern coast of Malta in the long wave fre- A hydraulic control may also pertain to the flow in the Strait of quency band contain substantial energy in the range of frequencies Sicily. This can indeed be dictated by discrepancies in the mass bal- 0.2–2 cph. The lower frequency signals are associated to longitudi- ance of the respective basins and may not necessarily have the nal, latitudinal and mixed stationary modes that develop on the same state of flow as that in the Strait of Gibraltar. It can be envis- highly irregular shaped continental shelf. The presence of these aged that the exchange condition through the two straits may in modes suggests that the Sicilian coast is a good reflector to these fact be different. Different factors that have a control on the strait long waves. Their wavelengths are comparable to the shelf extent exchange may moreover be expected to not simply play a discon- which thus modifies their characteristics from a simple quarter- 968 A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 wave resonant effect. It is inferred that the observed waves are not case of a plane coast with a linear sloping bathymetry d(x)=ax, only ones that cross the shelf from the deep sea, but that compara- the leaky waves normal to the coast are described by the expres- ble energy is presented in trapped waves associated to bathymetric sion (Lamb, 1932): features on the shelf. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The higher frequency coastal seiches are characterised not only 2 gðx; xÞ¼AJoðvÞ¼AJo 4x x=ga by eigenmodes pertaining to inlets and bays on the coastal perim- eter, but also by long period modes in the adjacent open sea areas where x ¼ 2p=T is the angular frequency, A is the amplitude at the outside the embayments. This is particularly evident in the pres- coast, J is the zeroth order Bessel function of the first kind and g is ence of coastal shallows, reefs or banks such as in the case of Mel- o the acceleration due to gravity. The function J has zeros when its lieha Bay. The bays are in double resonance with the adjacent o argument v = 2.405, 5.520, 8.654, etc. and maxima at v = 3.832, nearshore areas; the open coastal sea is on its own count in double K M 7.016, 10.174, etc. At any offshore position, distant X from the coast, resonance with the offshore deeper shelf area. It is thus inferred p standing waves with frequencies x = v (ga/4X) thus exist for that the observed long period wave field in coastal areas is not sim- K K which J = 0 represents a nodal line parallel to the coastline. At fre- ply restricted to those oscillations directly related to the deeper o p quencies x = v (ga/4X) antinodes are obtained. The theoretical shelf, but that comparable energy is also present in the form of sta- M M spectral energy distribution for this linear slope model (propor- tionary coastal waves that are excited in the nearshore and inner tional to J2 thus consists of peaks at frequencies x and troughs shore areas either directly by local atmospheric disturbances or o M at x . indirectly through the forcing by deeper sea waves. Both mecha- K In the case of trapped modes the energy is channelled by the nisms involve a cascading effect from larger to smaller horizontal bathymetry and remains on the shelf. The waves propagate in a scales. direction parallel to the coast and energy is totally internally re- Seasonal changes in the mean sea level show a major minimum flected at the continental slope. For a straight continental shelf of in March and a major maximum towards the last months of the uniform width and constant depth falling vertically at the shelf year. Besides the usual steric and direct meteorological effects, this edge to a flat bottomed ocean, amplitudes decrease exponentially variability is attributed to adjustments in the mass balance of the seawards. Only certain angles of incidence are permissible. At whole Mediterranean basin. glancing incidence, a lower cut-off frequency occurs in each mode corresponding approximately to periods of infinity, T/2, T/4, T/6, p Acknowledgements etc. where T =4L/ (gh), and the waves are thus non-dispersive. Their offshore wavelengths have the same scale as their offshore The authors wish to thank Mr. A. Xuereb and Mr. J. Bianco of the wavelengths. For a given frequency and bottom slope the along- Hydrographic Office at the Malta Maritime Authority, and Major J. shore wavelengths have a discrete spectrum, so that only certain Mifsud and Capt. A. Gauci, ex-Chief Meteorologists at the Meteoro- wavelengths are permitted. For a wave of a given frequency on a logical Office in Luqa, for kindly making available the sea level data continental shelf with no longshore variations, trapped modes al- in the Grand Harbour and the atmospheric pressure records in ways have shorter alongshore wavelengths compared to those of Luqa, respectively. Thanks also go to Dr. Alexander Rabinovich of leaky modes. This may not however apply in the case of a more the Russian Academy of Sciences for his numerous suggestions complicated bathymetry with both cross-shore and alongshore and advice. variations. Moreover if the depth at a distance from the coast tends to a constant value, the trapped modes leak some energy to infin- ity, although the consequent rate of decay may be exceedingly Appendix 1. General description of long waves on a continental slow (Longuet-Higgins, 1967). With a real bathymetry the transi- shelf tion between leaky and trapped modes is thus much more tenuous than the idealised case. The typical lengths of these lower frequency long waves are in The initial energy of these long period shelf oscillations may be the order of tens of kilometres and are compatible to the character- absorbed by radiation of the same frequency incident from the istic widths of continental shelves. The constructive interference adjacent deeper sea areas. It may alternatively be derived from a between incident waves of appropriate dimensions from the dee- sharp pulse such as due to a travelling pressure disturbance. In per ocean with waves reflected from the coast can thus lead to the case of the Maltese shelf area, there is evidence (Drago, standing wave patterns corresponding to the well-known leaky 1999) in favour of the dependence of long waves in the sea on pres- modes and trapped modes (also called edge waves) of waveguide sure fluctuations in the atmosphere. The passage of a pressure dis- theory (Munk et al., 1964). These oscillations can develop on the turbance is responsible for the resonance generation of shelf continental shelf as well as in more restricted coastal areas pro- modes (Kulikov and Shevchenko, 1992); it can also generate a vided that appropriate bottom slope conditions apply. whole range of more localised sea level signals in the medium Leaky modes re-radiate energy into the deep sea. Along a coast range of frequencies. The periods of these shelf oscillations are with uniform alongshore bathymetry their alongshore wave- dependent on both the period range in the pressure wave spectrum lengths are usually long in comparison with the offshore wave- as well as on the bottom relief. lengths. For a particular frequency they have a continuous spectrum of alongshore wavelengths. Any angle of approach is pos- sible, that for normal incidence corresponding to a standing wave Appendix 2. 1D model to estimate seiche-generated currents system normal to the shore. An antinode is required at the shore from sea-level data and a node at the shelf edge. In the case of a shelf with constant alongshore characteristics, width L and a monotonic depth profile Seiche-induced currents in a rectangular open ended embay- d(x), where x is the distanceR normal to the coast, the fundamental ment can be related to the sea level oscillations inside the bay by period is given by T ¼ 4 L pdxffiffiffiffi. Other possible modes are given by means of a simple 1D model. Suppose that the sea level g is 0 gd the odd harmonics T/3, T/5, etc. For other angles of incidence the measured by a coastal gauge at the head of the bay (origin O in resonant frequencies become slightly higher and the amplification Fig. 20). These sea level oscillations follow the movement of the is less. Leaky waves do not however necessarily require a shelf sloshing water in and out of the embayment. The proposed one- break and can occur over smaller areas and close to shore. In the dimensional model estimates the along-axis barotropic currents A. Drago / Physics and Chemistry of the Earth 34 (2009) 948–970 969 associated to this movement. Currents in the along-axis direction References are calculated at X at distance xo from O. The bay is assumed to have constant width. The distance x from the origin O is measured Astraldi, M., Galli, C., Gasparini, C., Lazzoni, E., Manzella, G.M.R., 1987. The Janus Experiment, Istituto Dinamica Grandi Masse, S.O. Technical Report TR140, 40pp. along the ‘talweg’; the depth D is taken to be the crossectional Colucci, P., Michelato, A., 1976. An approach to the study of the ‘Marrubbio’ average orthogonal to the ‘talweg’. phenomenon. Bollettino di Geofisica Teorica ed Applicata 13 (69), 3–10. Suppose that the water body is oscillating at its gravest mode Defant, A., 1961. Physical Oceanography, vol. 2. Pergamon Press, Oxford. Drago, A.F., 1992. Tide Tables 1993. Grand Harbour, Malta, 46pp. with period To. The position of the displacement node which marks Drago, A.F., Ferraro, S., 1996. Oscillazioni del livello del mare nel Porto di Malta. In: the boundary between the water body in the bay and the open sea Proceedings of the XI Congress of the Italian Association of Limnology and is not known a priori. The position of X with respect to this bound- Oceanography, Sorrento, 1994, pp. 235–246. ary is thus described by a non-dimensional distance a = x /L, Drago, A.F., 1997. Hydrographic measurements in the north western coastal area of o o Malta. Xjenza, Journal of the Malta Chamber of Scientists 2 (1), 6–14. where L is the hypothetical distance of the open boundary from O. Drago, A.F., 1999, A study on the sea level variations and the ‘Milghuba’ The elevation along the bay axis is also assumed to follow a phenomenon in the coastal waters of the Maltese Islands. Ph.D Thesis, School sinusoidal profile with a maximum amplitude at the head and zero of Ocean and Earth Science, University of Southampton. Drago, A.F., 2001. Sea level variations in Mellieha Bay, Malta. Rapport Commission displacement at the open boundary. The elevation g at O is an Internationale mer Méditerranée 36, 95. expression of the instantaneous displacement of the vertical oscil- Drago, A.F., 2007. Numerical modeling of coastal seiches in Malta. Physics and lation at O. If the free surface along the bay is assumed to retain a Chemistry of the Earth 33 (3–4), 260–275. Emery, K.O., Aubrey, D.G., Goldsmith, V., 1988. Coastal neo-tectonics of the sinusoidal profile in time, the instantaneous displacement at any Mediterranean from tide gauge records. Marine Geology 81, 41–52. position a (=x/L) will be given by y(a, t)=g(t)cos(pa/2). Garrett, C., Bormans, A., Thompson, K., 1990a. Is the exchange through the Strait of Gibraltar maximal or sub-maximal? In: Pratt, L.J. 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