Atmospheric pressure variations and water mass exchange between the continental shelf and the Bay of Cadiz*

Transcription

1 SCI. MAR., 61 (3): SCIENTIA MARINA 1997 Atmospheric pressure variations and water mass exchange between the continental shelf and the Bay of Cadiz* MIGUEL BRUNO 1, BEATRIZ FRAGUELA 1, JOSE J. ALONSO 1, ANTONIO RUIZ 1 - CAÑAVATE, RAFAEL MAÑANES 1 and JUAN RICO 2 1 Facultad de Ciencias del Mar, Polígono del Río San Pedro s/n., Apartado 40, Puerto Real, Cádiz. España. 2 Instituto Hidrográfico de la Marina, Tolosa Latour s/n, Cádiz. España. SUMMARY: In this paper are analysed the low frequency fluctuations (less than 0.72 cycles/day) of current velocity series in the mouth of the Bay of Cadiz. From an Empirical Orthogonal Function (EOF) analysis of the data two low frequency oscillation modes are found: a first mode associated to the continental shelf dynamics and a second one to the inner Bay dynamics. In addition, the second mode is highly correlated with atmospheric pressure variations in the Bay which can be explained in terms of the quasi-static response of low frequency sea level in the inner Bay to atmospheric pressure variations. Key words: Shallow water bodies, low frequency oscillations, isostatic response, water mass exchange. RESUMEN: VARIACIONES DE PRESIÓN ATMOSFÉRICA E INTERCAMBIO DE MASAS DE AGUA ENTRE LA PLATAFORMA CONTINENTAL YLABAHÍA DE CÁDIZ..En este trabajo se analizan las fluctuaciones de frecuencia baja ( menos de 0.72 ciclos/día) de las corrientes en la boca de la Bahía de Cádiz. A partir de la descomposición en funciones empíricas ortogonales de las series de corrientes, se encuentran dos modos de oscilación: el primero de éllos asociado a la dinámica de la plataforma continental y el segundo asociado a la dinámica en el interior de la Bahía. Este segundo modo presenta además, una correlación significativamente alta con las variaciones de presión atmosférica, que puede ser explicada en función de la respuesta cuasiestática del nivel del mar en la Bahía a las variaciones de presión atmosférica. Palabras clave: Cuerpos de agua semicerrados, oscilaciones de baja frecuencia, respuesta estática, intercambio de masas de agua. INTRODUCTION *Received September 4, Accepted March 12, The ecological aspects of any semi-enclosed body of water (Bay, Gulf, Estuary) are conditioned to a certain extent by the exchange between the continental shelf and the inner waters (Smith, 1986). This exchange dynamics is controlled mainly by three different forcing agents (Valle Levinson, 1994): a) Astronomical Tide. b) Meteorology (wind and atmospheric pressure). c) River Outflow (in the estuarine case). ATMOSPHERIC PRESSURE AND WATER MASS EXCHANGE 379

2 FIG. 1. External Bay of Cadiz and location of currentmeters, water level record and meteorological station. Depths are expressed in meters. The net transport (nutrients, sediments, salinity, temperature and pollution) shows very different characteristics according to the forcing agent. With respect to the Astronomical Tide, the transport has an easily predictable periodic behaviour, while the meteorologically associated transport exhibits random characteristics. The tide associated water mass exchange time scale goes from 12 hours to larger scales, including fortnightly and monthly periods. The larger periods do not have a direct astronomical origin, being related to non-linear tidal interactions. This is the case, for example, with the semidiurnal and S 2 interaction that originates the fortnightly Msf, or the and N 2 interaction originating the monthly Mn (Parker, 1991). In addition, these interactions produce a net contribution to the mean current through the non-linear generation of residual currents. Periods in the meteorology-associated exchanges are larger than 24 hours. Generally speaking these exchanges are more important than the low frequency tidal exchanges (Weisberg, 1976; Wilson and Filadelfo, 1986 and Goodrich, 1988). In all of the works in which these exchanges have been studied the meteorological variability of the low frequency currents has been associated with the local wind stress or to Ekman Transport. In this paper the current low frequency signal (ω< 0.72 cycles/day) is studied at the mouth of the Bay of Cadiz. Empirical orthogonal function (EOF) analysis of the data shows a mode in the low frequency oscillation of the currents which is strongly related with the atmospheric pressure variations and it is suggested to be the main contributor to water mass net transport between the continental shelf and the Bay of Cadiz. In addition, the relationship of this mode with the atmospheric pressure seems to be explained by a quasi-static response of the sea level in the inner Bay to atmospheric pressure variations. It is then suggested that for the present case that mechanism is more important than the wind driven circulation found by a great number of authors to explain the exchange of water masses due to low frequency meteorological forcing. 380 BRUNO et al.

3 FIG. 2. Vectorial series of low frequency current velocity during the period from 8/2/92 to 22/3/92: a) currentmeter, b) currentmeter. Organisation is as follows: in the first section is described the geography of the region, data, and techniques used to obtain the low frequency signal from all available series: current, sea level and atmospheric pressure data. In the second section are analysed the low frequency current series of data by the EOF analysis. In the third section these results are discussed and a physical interpretation of the obtained mode is proposed. ATMOSPHERIC PRESSURE AND WATER MASS EXCHANGE 381

4 FIG. 3. Results from cross-spectral analysis between low frequency current velocity series of and currentmeter. The used band width was ω=0.125 cycles/day: a) coherence, dashed line means for 95% significant level for coherence values in accordance with Box and Jenkins (1970), b) phase lag, dashed lines denote 95% confidence intervals in accordance with Box and Jenkins (1970), c) percentage of variance explained by each frequency; (dashed line) and (solid line). Location of the study zone and data analysis procedure The Bay of Cadiz is located at the southern end of the Iberian Peninsula, between the latitudes 36º 30 and 36º 45 N and between the longitudes 6º 15 and 6º 30 W (figure 1). The experiment designed to study the low frequency flow originated at the mouth of the Bay consisted of the deployment of two current meters at 5m depth, one in the location (South) and the other in (North) (figure 1). During the experiment (February through March 1992) were available atmospheric pressure data from the National Institute of Meteorology (Spain), taken at Rota Naval Station, and tidal data from the Navy Hydrographic Institute (Spain) for Cadiz Harbour. The tidal series for the sea level in Cadiz Harbour are representative of the external Bay dynamics and are used to detect correlation with the current meter signal that is responding to the Bay dynamics. The locations of the stations are shown in figure 1. TABLE 1. Results of EOF analysis on low frequency velocity series from and currentmeters: a) percentage of variance explained by each of the modes in each current velocity series, b) eigenvector component values corresponding to each of the obtained modes. VARIABLES MODE 1 MODE 2 v v b) VARIABLES a 1 Ci a 2 Ci v v BRUNO et al.

5 FIG. 4. Hypothetical modes of the flow in the Cadiz Bay mouth; a) shelf mode b) inner Bay mode (local mode). To get the low frequency signal, all series were filtered using a low pass filter with the following procedure: A.- Current series ( and ) : The original data, sampled with 30 minutes intervals, were filtered using an A 2 A 2 A 3 filter (Godin, 1972) and after being subsampled in one hour intervals, an A 24 A 24 A 25 (Godin, 1972) filter was applied on the resulting series. That allowed the elimination of periods of less than 30 hours. The resultant speed component series u 1 (E-W), v 1 (S-N) and u 2 (E-W), v 2 (S-N) show current speed low frequency variations. B.- Atmospheric pressure and sea level series: As the data were sampled with one hour intervals, an A 24 A 24 A 25 filter was applied on them. The resulting series show the sea level and atmospheric pressure low frequency variation. Current data analysis In figures 2a and 2b can be seen low frequency vector series representations from the two currentmeters and. One of the most prominent characteristics in those figures is the North-South dominant direction for the flow in both stations. For this reason the current will be characterised only by the v(n-s) component in later analysis. Another important feature is that certain discrepancies between the series of both stations can be clearly seen even though the general lines are fairly similar. To analyse those discrepancies a cross spectral analysis between the v component series of both currentmeters was performed. The data of the first week were left out of the analysis as the discrepancies were very marked and did not represent the typical conditions for the whole of the recording period. ATMOSPHERIC PRESSURE AND WATER MASS EXCHANGE 383

6 FIG. 5. Time series during the experiment; a) mode 1, b) low frequency sea level, c) mode 2 and d) atmospheric pressure. The results are shown in figure 3. Though the distribution in percentage of the variance explained by each frequency is similar and the coherence values are significantly high, the phase shift at the frequency, where the maximum variance is located (0.11 cycles/day), shows a value that when translated to time, it supposes a time lag period about 7 hours. Taking into account that the time and the space scales of variation in the low frequencies are much larger than the distance separating both currentmeters, the phase shift shown by the signals of FIG. 6. Results from cross-spectral analysis among modes 1 and 2 with low frequency sea level series in the Cadiz Harbour. The used band width was ω=0.125 cycles/day: a) coherence between mode 1 and sea level (dotted line) and coherence between mode 2 and sea level (solid line), dashed line means for 95% significant level for coherence values in accordance with Box and Jenkins (1970), b) percentage of variance explained by each frequency; sea level (solid line), mode 1 (dotted line) and mode 2 (dashed line). the two currentmeters cannot be explained unless it is assumed that the Bay s internal dynamics interferes somewhat on the shelf s flow whose signal would be on phase in both currenmeters in case the mouth of the Bay were be closed. 384 BRUNO et al.

7 FIG 7. Results from cross-spectral analysis between atmospheric pressure at Rota Naval Station (given in mb) and low frequency sea level at Cadiz Harbour (given in cm). The used band width was ω=0.125 cycles/day: a) coherence, dashed line means for 95% significant level for coherence values in accordance with Box and Jenkins (1970), b) percentage of variance explained by each frequency; atmospheric pressure (solid line) and sea level (dotted line), c) transference function modulus and d) phase lag. dashed lines in c) and d) denote 95% confidence intervals in accordance with Box and Jenkins (1970). These considerations lead to some working hypothesis that will be verified later. We suppose that the flow close to the Bay mouth can be decomposed into two modes: a) One shelf mode resulting from a forcing whose scale is larger than the Bay scale. b) Another local mode resulting from a forcing associated to the inner Bay dynamics. The latter would be associated to the water mass inflow and outflow between the shelf and the inner Bay. The flow associated to both modes is described in figure 4. As can be seen, the shelf s mode flow is on phase in both currentmeters producing a zero net mass transport between the shelf and the inner Bay. The local mode flow, however, has a phase lag of 180 degrees between both currentmeters and describes a larger flow towards the North in one currentmeter while in the other the flow is larger towards the South, and viceversa. The second mode generates a non zero net mass transport between the shelf and the inner Bay, producing convergence or divergence in the latter. This convergence or divergence is then translated into sea level variations, and the local flow mode correlated with the sea level variation in the inner Bay. ATMOSPHERIC PRESSURE AND WATER MASS EXCHANGE 385

8 To verify the existence of these modes a EOF analysis on the v component of both currentmeters was performed. The results are discussed in the following section. EOF results in the current velocity low frequency series When the EOF analysis is applied, the current speed series (v-component),in each of the stations, can be expressed in the following form (Kundu et al, 1975; Wilson and Filadelfo, 1986; Candela et al, 1989; Ruíz-Cañavate, 1994): V (t) = a 1 M 1 (t) + a 2 (t) V (t) = a 1 M 1 (t) + a 2 (t) where v (t) y v (t) are the velocity series in each of the stations after subtracting the corresponding mean values, t is the time, and [a 1,a 1 ] and [a 2,a 2 ] are the eigenvector components associated to each of the eigenvalues λ 1 and λ 2 of the covariance matrix of the series v (t) and v (t). M 1 (t) and (t) in eqs. (1) and (2) are the time weights associated to each orthogonal mode that are obtained by M 1 (t) = a 1 v (t) + a 1 v (t) (t) = a 2 v (t) + a 2 v (t) In table 1 are presented the variance percentages explained by each of the modes in each current speed series (1a) and the eigenvector component values corresponding to each of the obtained modes (1b). The first mode shows positive values for the eigenvector components in both stations, and can therefore be associated to a situation like the one described in figure 4.a. In addition this mode explains the larger part of the current low frequency variance in both currentmeters. The second mode, which shows opposing sign values in the eigenvector components, seems to be associated to a situation like the one shown in figure 4.b. Although the variance percentages explained by this mode for each of the series is lower than the variance percentage explained by the first mode, it is important to note that these characteristics in the second mode could be implying net water mass exchanges between the shelf and the inner bay. This will be analysed in the following section. DISCUSSION AND CONCLUSIONS In figure 5 are presented the time weights corresponding to the first and second modes M 1 (t) and (t) and the sea level low frequency series taken in Cadiz Harbour. The time weights have been modified by the following: M 1 (t) is multiplied by ( a 1 + a 1 )/2 and (t) by ( a 2 + a 2 )/2. In presenting the modes in this way, the comparison of the magnitude of the current speed oscillations associated to each mode is made possible. The current value oscillations associated to mode one are larger than those corresponding to mode two, as was previously described. However, if we take into account the time series corresponding to the sea level low frequency oscillation in Cadiz Harbour, it can be seen that it is precisely the mode two that shows a larger similarity, as there exists a clear correspondence between the maxima and minima in both series. With respect to the opposing sign values in the eigenvector components; a 2 and a 2 (table 1b), a positive maximum value in mode 2 means a South component intensification in the currentmeter, and a North component intensification in the, identifying a water mass inflow towards the Bay. This inflow would be correlated with a rise in the sea level at Cadiz Harbour. A negative maximum in mode 2 means a North component intensification in the currentmeter, and a South component intensification in the, identifying a water mass outflow from the Bay. That outflow is correlated with a low in the sea level at Cadiz Harbour. The above comments are confirmed by the cross spectral analysis results between the time weights corresponding to both modes and the sea level series observed at Cadiz Harbour. In figure 6b is shown the variance percentage explained by each frequency for each of the three series, and in figure 6a, the existing coherence between modes 1 and 2 and the sea level series. The variance percentage explained by each frequency for both mode 1 and mode 2 shows similar distribution to the sea level series, with the maximum located around the eight-day period. However, the coherence between mode 2 and the sea level series shows significant values in frequencies where the higher part of the variance between both series (figure 6b) is located while the coherence between mode 1 and the sea level series shows coherence values clearly down to the significant level in frequencies where the sea level variance series exhibits very high values. 386 BRUNO et al.

9 All these results lead us to belive that mode 2 is indeed related to the dynamic situation illustrated by figure 4b and may responsible for the net water mass transport between the shelf and the Bay of Cadiz associated to the low frequency dynamics. Another interesting result is that the sea level variation in the Bay of Cadiz is essentially explained by a quasi-static response to the atmospheric pressure variations as can be seen from figure 5 and is further corroborated by the cross spectral analysis results between the atmospheric pressure series at Rota and the sea level series at Cadiz Harbour (figure 7). In figure 7b is presented the variance percentage distribution explained by each frequency for both series, and it can be seen that the distributions are similar showing a variance maximum in the same frequency ranges. In the frequency range where almost all the variance is concentrated, the coherence is close to one (figure 7a) and the phase lag between both series close to 180 degrees (figure 7d). These results along with the transfer function modulus value, with a close to one value ( ) (see figure 7c) confirm the existence of a quasi-static response similar to an inverted barometer response of the sea level with respect to the atmospheric pressure variations. At this point we can conclude that the response in the sea level to the atmospheric pressure variations in the inner Bay of Cadiz is responsible for the inflow and the outflow between the Bay and the shelf in periods between 30 hours and several months during the analysed time period. The isolation of this kind of response of low frequency currents to atmospheric pressure variations through the EOF analysis establishes that the response of the currents to satisfy a sea level quasi-static response to atmospheric pressure variations can be a very important mechanism (even more important than the exchange due to the wind stress) to explain the exchange of water masses between the continental shelves and semi-enclosed bodies whose spatial dimensions are similar to those of the Bay of Cadiz. REFERENCES Box, G.E.P. and G.M. Jenkins Time series analysis, forecasting and control. Holden day, Inc., San Francisco. Candela J., C.D. Winant and H. Bryden Meteorologically forced subinertial flows through the Strait of Gibraltar. J.Geophys.Res., 94: Godin G The Analysis of Tides. University of Toronto Press. Toronto. Goodrich D.M On meteorologically induced flushing in three U. S. East Coast estuaries. Estuarine, Coastal and Shelf Science, 26: Kundu, P.K., J.S. Allen and R.L. Smith Modal Decomposition of the Velocity Field Near Oregon Coast. J. Phys. Oceanogr., 5: Parker, B.B Tidal Hydrodynamics. Ed. Bruce B. Parker. New York. Ruiz-Cañavate A Flujos Barotrópicos de Marea en el Estrecho de Gibraltar. PHd. Thesis. Universidad de Cádiz. Smith, N.P Subtidal Exchanges Between Corpus Christi Bay and Texas Inner Shelf Waters. Lecture notes on Coastal and Estuarine Studies. Ed Van Kreeke. Springer Verlag, 16: Valle-Levinson A Observations of barotropic and baroclinic exchanges in the lower Chesapeake Bay. Continental Shelf Research, 15: Weisberg R.H The nontidal flow in the Providence River of Narragansett Bay: A stochastic approach to estuarine circulation. Journal of Physical Oceanography, 6: Wilson R.E. and R.J. Filadelfo Subtidal Current Variability in the Lower Hudson Stuary. Lecture Notes in Coastal and Estuarine Studies, 16: Scient. ed.: J.Font ATMOSPHERIC PRESSURE AND WATER MASS EXCHANGE 387