Atmospherically Forced Exchange through the Bab el Mandeb Strait

Transcription

1 JULY 2012 J O H N S A N D S O F I A N O S 1143 Atmospherically Forced Exchange through the Bab el Mandeb Strait WILLIAM E. JOHNS Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida SARANTIS S. SOFIANOS Division of Environmental Physics, University of Athens, Athens, Greece (Manuscript received 1 September 2011, in final form 4 January 2012) ABSTRACT The exchange between the Red Sea and the Indian Ocean on synoptic time scales (days to weeks) is investigated using moored current meter data collected in the strait of Bab el Mandeb from June 1995 to November Transport variations through the strait on these time scales can reach amplitudes of up to 0.6 Sv (1 Sv [ 10 6 m 3 s 21 ), or nearly twice as large as the mean rate of exchange through the strait driven by annual evaporation over the Red Sea. The synoptic transport variability appears to be driven by two primary forcing mechanisms: 1) local wind stress variability over the strait and 2) variation in the large-scale barometric pressure over the Red Sea. Simple models of the forced response are developed and are shown to reproduce the essential features of the observations. The response to barometric pressure forcing over the Red Sea is fundamentally barotropic, whereas the response to along-strait winds is barotropic at high frequencies and tends toward a two-layer exchange at low frequencies. The responses to both types of forcing show enhanced amplitude at the Helmholtz resonance frequency for the Red Sea, which occurs at a period of about 5 days. A linear two-layer model, incorporating both types of forcing and a reasonable frictional parameterization, is shown to account for about 70% of the observed transport variance within the strait. 1. Introduction Straits have attracted a great deal of study from the oceanographic community because the exchange and mixing processes occurring in them can have significant impacts on large areas of the surrounding ocean. In the case of semi-enclosed seas, they can often control the stratification and circulation of the entire basin (Stern 1972; Whitehead et al. 1974; Gill 1977; Garrett and Toulany 1982; Bryden and Stommel 1984; Pratt and Lundberg 1991). One of the most important straits in the World Ocean is the Bab el Mandeb strait located at the southern end of the Red Sea, connecting it with the Gulf of Aden and through this with the Indian Ocean. It is a vital link in the commercial waterway connecting the Atlantic and Indian Oceans through the Suez Canal and Corresponding author address: William E. Johns, Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, 4600 Rickenbacker Causeway, Miami, FL bjohns@rsmas.miami.edu Strait of Gibraltar. The Bab el Mandeb is a narrow and shallow channel with its shallowest point located at the northern end of the strait (the Hanish Sill; about 160 m deep) and the narrowest point at the southern end of the strait (the Perim Narrows), where the width is approximately 25 km and the depth is about 220 m (Fig. 1). The history of its modern study dates back over 80 yr (Vercelli 1931); however, it remains considerably less well studied than many other key straits (e.g., the Strait of Gibraltar). The Red Sea experiences strong atmospheric forcing from both wind stress and surface heat and freshwater fluxes. Because of the extensive evaporation (about 2myr 21 ) and negligible precipitation and river runoff, the basic form of exchange at the Bab el Mandeb is of the inverse estuarine type, with a fresh inflow to the sea overlying an outflow of high-salinity water (39.7 psu at the strait), the so-called Red Sea Outflow Water (RSOW). During summer (June September), influenced by the monsoon winds (Patzert 1974) and possibly by the annual cycle of the buoyancy forcing over the Red Sea, the exchange takes place in a three-layer pattern, with a shallow surface outflow, an intermediate inflow of DOI: /JPO-D Ó 2012 American Meteorological Society

2 1144 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 42 FIG. 1. Map of the Bab el Mandeb strait study area. Stars indicate the locations of moorings deployed at the Perim Narrows and Hanish Sill, in the southern and northern parts of the strait, respectively. The location of the tide and meteorological station at the west side of the Hanish Sill is indicated. relatively fresh and cold Gulf of Aden Water (GAW), and a much weaker RSOW outflow. Although this seasonal exchange pattern has been established for a long time (Vercelli 1931; Siedler 1968; Maillard and Soliman 1986), only recently have long-term observations in the strait unambiguously revealed the strength of the exchange flow and its annual cycle (Murray and Johns 1997; Sofianos et al. 2002). In addition to the seasonal variability, the exchange experiences strong fluctuations at shorter time scales, including tidal (dominantly semidiurnal) and synoptic time scales ranging from a few days to several weeks. Although the tidal exchange is important and quite complicated, because the strait connects basins with different tidal regimes (Jarosz et al. 2005a,b), the focus in this paper is on the variability at synoptic time scales. Lacombe and Richez (1982), investigating the variability of the flow and stratification in the Strait of Gibraltar, proposed that the two mechanisms affecting the flow at these time scales are the local wind and the atmospheric pressure over the Mediterranean Sea. The latter affects the sea level in the basin through the inverted barometer effect. Crepon (1965) found a considerable correlation between the atmospheric pressure in the western Mediterranean and the flow through Gibraltar but unexpectedly found them to be out of phase in contradiction with mass conservation. Garrett (1983) and Garrett and Majaess (1984) attempted to explain this paradox using a two-basin (eastern and western Mediterranean) model with geostrophic control (Garrett and Toulany 1982) at the two connecting straits (Gibraltar and Sicily) forced by eastward-propagating atmospheric pressure systems. They found that the phase difference between the flow through Gibraltar and the sea level in the western Mediterranean (or negative atmospheric pressure) becomes small, but this is accompanied by a noninverse barometer response of the sea level in the eastern Mediterranean. Candela et al. (1989) used the same two-basin configuration, but without rotational effects, in a linear model forced by the mean atmospheric pressure over the Mediterranean Sea. Assuming linear friction of the form 2lu, their model produced transport variations through Gibraltar that agreed quite well with observations, explaining about 58% of the total transport variance at synoptic time scales. Two characteristic resonant (Helmholtz) frequencies emerged from the model, related to the size of the basins and the geometrical characteristics of the straits. The effect of the local wind in the above cases was mostly neglected, although its importance is accepted widely, because the magnitude of the wind speed inside straits is often considerable because of orographic focusing. The effect of local winds in association with geostrophic control was investigated for the Bass Strait (Middleton and Viera 1991; Hannah 1992) and was found to be important. A number of other studies have also shown the importance of local winds in generating transport fluctuations in straits [e.g., Toulany et al. (1987) for the Strait of Belle Isle and Lee and Williams (1988) for the Straits of Florida]. However, the above cases are different from the case of the Red Sea or the Mediterranean, because these straits connect two relatively open bodies of water rather than opening into a semi-enclosed sea. In the latter case, the sea level variations in the sea and the flow through the strait are closely linked by mass conservation; in the former case, they are not. Also, in most of the studied cases the flow fluctuations forced by winds are considered to be fundamentally barotropic, either by assumption or because of the shallow depth of the strait, which is a situation that we show is not valid for the Bab el Mandeb. In this paper, we develop a linear model that accounts for the effects of both barometric pressure fluctuations and local wind stress on the strait exchange. The model builds on the work of Candela et al. (1989) and extends it to two layers to include the effects of the local wind stress. It is shown, in fact, that the wind stress is the dominant forcing mechanism driving exchange fluctuations in the Bab el Mandeb on these time scales and that the response to wind forcing is rather interesting and

3 JULY 2012 J O H N S A N D S O F I A N O S 1145 FIG. 3. The transport-per-unit-depth profile at the Perim Narrows section, after low-pass filtering with a 60-day filter to emphasize the seasonal exchange pattern through the strait (units: 10 4 m 2 s 21 ). Positive transports correspond to inflow to the Red Sea from the Gulf of Aden. The masked-out area (black bar) corresponds to the period when moorings were serviced midway through the experiment. FIG. 2. Topography and instrumentation at the Perim cross section, where the transport measurements used in the paper are derived. more complicated than the response to barometric pressure forcing. Nevertheless, we show that a simple two-layer analytical model is capable of explaining the characteristics of the combined forced response. The paper proceeds as follows: In the next section (section 2), the flow observations in the strait and the local wind and atmospheric pressure measurements that are used to form forcing functions for the model are described. The characteristics of the flow and transport fluctuations in the strait and their relationships to the forcing functions are illustrated in section 3. The model is described in section 4 and its results are compared with the observations in section 5. Section 6 discusses the limitations of the model and possible effects of remote forcing and stratification. Section 7 provides the summary and conclusions. Sill (Fig. 1). The field measurements are described fully in Murray and Johns (1997) and Sofianos et al. (2002). Because the most complete coverage of the velocity field was achieved at the Perim Narrows section (Fig. 2), the transport estimates that are used here were derived from this array. Transports through the strait were calculated by combining all current measurements in the cross section and extrapolating the flow linearly to the surface and sidewalls of the channel. Details of the transport calculations are given in Sofianos et al. (2002), where the seasonal exchange patterns and transports are described. Fluctuations with tidal periods are eliminated using a 40-h Butterworth low-pass filter and resampling the results at 12-h intervals. The transport profile for the Perim Narrows is presented in Fig. 3, where it has been further filtered with a 60-day low-pass filter to emphasize the seasonal cycle, and in Fig. 4, where the full synoptic variability is shown. The transport profile is given by the lateral integral, at each depth, of the along-strait velocity across the width of the channel, 2. Data The observations that are used here were obtained from a long-term (18 months) deployment of current meter and acoustic Doppler current profiler (ADCP) moorings in the Bab el Mandeb, located at the Hanish Sill and Perim Narrows (Fig. 1). The mooring arrays were deployed in two 9-month settings, from June 1995 to March 1996 and from March to December In addition to the current measurements, pressure gauges were deployed at several locations around the strait, and a meteorological station was deployed for the full length of the experiment at a location near the Hanish Q(z) 5 ð W(z) 0 u(x, z) dx. The horizontal structure of the fluctuations is relatively uniform across the channel and the main structure is in the vertical. Therefore, most of our analysis is focused on the vertical structure of the fluctuations. The basic seasonal cycle of the exchange, two layers in winter (October May) and three layers in summer (June September), is clearly revealed in Fig. 3. Superimposed on this seasonal cycle are energetic fluctuations on shorter time scales (Fig. 4). These fluctuations exhibit largest amplitudes in the upper layers of the strait, but

4 1146 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42 FIG. 4. As in Fig. 3, but for the anomaly of the transport-per-unit-depth profile (the observed profile minus the 60-day low-pass-filtered profile), illustrating the vertical structure of the synoptic fluctuations (units: 104 m2 s21). there are also frequent occurrences of subsurface maxima near m. The relationship between the surface and subsurface transport fluctuations is highly variable and has a strong frequency dependence, as we will describe further in following sections. Atmospheric pressure data for the period of the Bab el Mandeb observations come from six coastal meteorological stations around the perimeter of the Red Sea that are available from the National Climatic Data Center (Fig. 5a). The available stations are concentrated in the northern FIG. 5. (a) Atmospheric pressure time series at the six meteorological stations in the Red Sea, running from the northernmost station at the top to the southernmost at the bottom (see Fig. 5b for station locations). (b) Location of the meteorological stations and the spatial patterns of first two EOFs of atmospheric pressure variations over the Red Sea.

5 JULY 2012 J O H N S A N D S O F I A N O S 1147 scales take place during winter with the exception of a few very strong summer events when reversals of the wind field take place. 3. Results FIG. 6. Time series of (a) the mean atmospheric pressure over the Red Sea and (b) the along-strait winds at the Hanish Sill that form the two main forcing functions used to model the exchange through the strait. The seasonal cycles (sum of first and second annual harmonic) are shown by the bold curves. Red Sea and are sparse in the south. The patterns of atmospheric pressure variability were examined with a principal component (EOF) analysis, whose spatial weights are plotted in Fig. 5b. The first EOF mode explains 83.4% of the variance and represents a covarying pattern where the atmospheric pressure from all stations is in phase. The second EOF (explaining 10.4% of the variance) has a zero node at 268N close to the northern end of the basin. Since the dominant fluctuations of the atmospheric pressure are of the covarying type, the mean atmospheric pressure over the Red Sea was computed, using the station measurements weighted by the area of the basin that each one represents. This time series is plotted in Fig. 6a and is used as one of the forcing functions for the model. The other important mechanism for forcing the synoptic variability of the flow in Bab el Mandeb is the local wind stress. Because of the presence of mountains on the two sides of the strait, the low-level winds are orographically steered along the axis of the strait and the across-axis component of the wind is typically an order of magnitude weaker. Local winds in the strait were obtained from an anemometer station installed on a small island on the western side of the strait, near the Hanish Sill (Fig. 1), for the duration of the experiment. The component parallel to the main axis of the strait is plotted in Fig. 6b. A strong annual cycle is present with south-southeast winds during winter and northnorthwest winds during summer. The winter winds are stronger than the summer winds, with average values of 8 and 4 m s 21, respectively. Around this seasonal pattern strong variability is present with typical time scales from a few days to a few weeks and amplitudes of 5 10 m s 21. The strongest fluctuations on synoptic time The time series of exchange through the strait in different layers and of the total net transport through the strait are plotted in Fig. 7, where positive values represent fluxes into the Red Sea. The exchange magnitude reaches typical values of 0.6 Sv (1 Sv [ 10 6 m 3 s 21 ) during the winter two-layer regime and 0.3 Sv in summer, when the three-layer regime is active and the intermediate inflow is balanced by the sum of the surface and deep outflows. To compensate for the freshwater loss to the atmosphere, a small net volume flux into the basin of about 0.03 Sv is expected on the annual mean. The mean residual transport through the strait estimated from the observations is 0.03 Sv, which supports the accuracy of the transport calculations. A striking feature of Fig. 7 is the large-amplitude variability of the transport through the strait that occurs at high frequencies, which can achieve amplitudes of up to 1 Sv. Fluctuations in the net transport on these shorter time scales are comparable in magnitude to the total inflow/outflow exchange through the strait. If one uses the annual-mean outflow of high-salinity Red Sea water as a measure of the overall strength of the exchange, which is about 0.36 Sv based on these observations (Sofianos et al. 2002), the high-frequency fluctuations can reach magnitudes of 2 3 times this value. Thus, they can significantly alter the instantaneous exchange pattern in the strait. To establish the structure of this higher-frequency variability, an EOF analysis was performed on the transport profile in the strait (Fig. 8). The first EOF of the daily transport profiles explains 87% of variance, whereas the second mode explains 7%. Also shown in Fig. 8 are the EOFs obtained after filtering the transport profile time series with a 2 60-day bandpass filter. This is done to exclude the influence of the seasonal cycle on the vertical mode structures and is more relevant to the synoptic band, which is of central interest here. The first mode again explains a large fraction of the variance (72%), whereas the second mode explains 22%. Both of the first modes present a pattern of opposite flow between the surface and deeper parts of the strait, with a zero crossing at about 70 m for the synoptic band. Thus, fluctuations of a two-layer type are expected account for much of the variability observed in the strait. The second EOF is more of a barotropic type with maximum amplitude at a depth of 120 m.

6 1148 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 42 FIG. 7. (a) The observed transports through the strait, broken into the surface-layer, intermediate-layer, and deep outflow transports. The intermediate inflow layer only exists in summer when the surface flow is outward into the Gulf of Aden and the deep outflow is weak. (b) The net transport through the strait [sum of all the layers in (a)], with the seasonal cycle and mean residual (of 0.03 Sv) shown. A feature not revealed by this analysis is that the vertical structure of the fluctuations is highly frequency dependent even within the synoptic band. Figure 9 shows a similar EOF analysis carried out in the frequency domain, where results are broken down into four separate frequency bands in the 2 30-day period range. The frequency-domain approach allows progressive phase variations in the vertical to be determined instead of just correlated (or anticorrelated) variability at zero time lag as in the regular time-domain EOFs. In each of these bands, the first EOF explains typically 70% 80% of the variance, except for the shortest period band (2 4 days), where the first EOF explains only 63%. The distinctive feature of these EOFs is the vertical phase change from the surface to the deeper layers. The sense of the phase variation is that the lower-layer flow lags the surface-layer flow, and this phase lag increases from about 308 for the shortest periods (2 4 days) to about 1308 for the longer periods (10 30 days). The spectrum of the net transport Q n through the strait shows maximum variance in the synoptic band from about 3 10 days, with a peak near 5 6 days (Fig. 10). The relationship of the transport to the forcing fields is investigated in Fig. 11 in terms of cross-spectra with the Red Sea atmospheric pressure P a and along-strait wind stress t x. To maximize the statistical confidence in the results, the cross-spectra are derived by breaking the full 540-day time series into a large number of individual segments with lengths of 36 days, which are then windowed with a Hanning window in the time domain and overlapped by 50%. The resulting spectral estimates are then ensemble averaged, spanning the synoptic band from periods of 2 to 36 days. FIG. 8. The first two EOFs of the transport profile in the strait, including the EOFs obtained from the full 40-h low-pass data (labeled as unfiltered) and after filtering the variability with a 2 60-day bandpass filter.

7 JULY 2012 J O H N S A N D S O F I A N O S 1149 FIG. 10. The spectrum of the net transport through the strait, plotted in variance-conserving form. A clear peak is present near a frequency of 0.2 cpd, (periodicity of ;5 days). FIG. 9. Frequency-domain EOFs of the transport profile variability in the strait, corresponding to different frequency bands, indicated by the associated range of periodicities. An increasing phase lag between the surface and bottom layers is seen for longer periodicities. The transport is significantly coherent with both P a and t x for periods longer than about 3 days (Figs. 11a,b) and shows the largest coherence with t x. The transport shows a peak in gain (amplitude response) to wind forcing near a period of 6 days, (Fig. 11d), whereas the response to atmospheric pressure forcing has several small peaks in the synoptic band (Fig. 11c). The phase relationships both show a smooth behavior with phase decreasing approximately linearly with frequency. The phase of the transport response is such that it lags P a at low frequencies (i.e., inflow through the strait lags high P a over the Red Sea) but then changes to leading P a at higher frequencies, above a period of ;6 days (Fig. 11e). The expected relationship for a simple inverse barometer response of the Red Sea, in which rising P a over the Red Sea would lead to lowering sea level and an export of water through the strait, is a phase lag of 2908 (2708) between Q n and P a. Only at the lower frequencies does this approximately hold; the response is fundamentally different than this at periods shorter than about 6 days. Similarly, the response to wind stress forcing shows an opposite phase relationship for periods longer or shorter than about 5 days, with the transport leading the wind stress at longer periods and lagging it at shorter periods. The expected relationship for a simple inviscid response of the flow to wind stress would be for the transport to lag the wind stress by 908, which occurs only at the shortest periods. Thus, both types of forced response show robust and interesting behaviors and suggest that dynamics more complicated than the simple considerations described above must be taken into account to explain the observed relationships. 4. An analytical model of the forced exchange To explain some of the variability observed at the strait, a simple linear model of the response of the strait to the local wind and changes of the atmospheric pressure over the Red Sea is developed here. The basic variables and constants used are shown in the schematic of Fig. 12, and their values are presented in Table 1. Several assumptions and simplifications are used in the basic equations describing the model. The present approach is two dimensional, so that the rotational effect is neglected and no geostrophic control is implied. This is not an unreasonable approximation, because the external Rossby radius of deformation R d is O(1300 km) and the internal R d is O(35 km), which is close to the average width of the strait and larger than the strait width at its narrowest point, the Perim Narrows. The sea level inside the basin is taken to be uniform. Long gravity waves propagate very rapidly and can

8 1150 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 42 FIG. 11. (a),(c),(e) Coherence, gain, and phase of the net transport Q n response to atmospheric pressure P a forcing and (b),(d),(f) the corresponding Q n response to wind stress t x forcing. Note that the y-axis label of (d), Gain (Sv/Pa), refers to wind stress in units of Pascals (Pa) and does not have any relationship to atmospheric pressure. The 95% significance limits for the coherence are shown in (a),(b). [Note that negative phases in (e) have had 3608 added to them to avoid a jump in the phase relationship at 61808; phases between 1808 and 3608 therefore correspond to negative phases of to 08, respectively.) adjust the sea level in the Red Sea on time scales much shorter than the synoptic time scales considered here. Outside the basin, the sea surface is assumed to respond isostatically to the atmospheric pressure forcing, so that the sum of P a and 2rgh is constant at the outer entrance of the strait (and here taken as zero for simplicity). Changes of the sea level outside the strait induced by wind set up in the Gulf of Aden can also play a role in the exchange, although Garrett (1983) suggests that this effect is less important than atmospheric pressure in inducing flows through straits. Here, this effect will be neglected and we will revisit this problem in a later section. An important difference of this model with previous approaches is not only the introduction of the local winds but also the assumption that the effect of the wind is felt only in an upper layer of thickness H 1. Therefore, we adopt a two-layer model where the wind stress is distributed as a body force over the upper layer, which is taken to have a thickness H m, the depth of the zero crossing of the most energetic EOF. This layer does TABLE 1. Numerical values and description of the parameters used in the analytical model. FIG. 12. Schematic of the model used for the forced synoptic exchange through the Bab el Mandeb; all variables are defined in the text. Parameter Description Value surface area of the Red Sea m 2 A S cross-sectional area of Bab el Mandeb m 2 A 1 cross-sectional area of the upper layer m 2 A 2 cross-sectional area of the lower layer m 2 L S length of the strait 270 km H 1 depth of upper layer 70 m r mean density of seawater 1027 kg m 23

9 JULY 2012 J O H N S A N D S O F I A N O S 1151 not necessarily coincide with surface layer of the inverse estuarine exchange. Under these assumptions the governing equations are u 1 t u 2 t 52 1 r 1 P 1 x 1 t x H 1 r 1 2 l 1 u 1 (1.1) 52 1 r 2 P 2 x 2 l 2 u 2 (1.2) h t 2 h i 5 A 1 u t A 1 (1.3) RS h i t 5 A 2 u 2 (1.4) P 1 5 P a 1 gr 1 (h 2 z) (1.5) P 2 5 P a 1 gr 1 h 1 g9r 2 (h i 2 H 1 ) 2 gr 2 z, (1.6) where u 1 and u 2 represent the velocity of the surface and lower layer, respectively; is the surface area of the Red Sea; and h and h i are the sea level and depth of the layer interface in the basin. Here, A 1 and A 2 are the cross-sectional areas of the two layers and these sum to the total cross-sectional area of the strait (A 1 1 A 2 5 A S ), taken as the average value somewhere in the middle of the channel. Friction is represented by the linear forms l 1 and l 2, following Candela et al. (1989) and Middleton and Viera (1991), although the values they use differed by almost an order of magnitude. In general, l 1 6¼ l 2 and friction in the lower layer is expected to be larger than that in the surface layer. In the set of solutions presented here and the comparison of the results with the observations, a single value l 1 5 l 2 5 l is used in order to reduce the number of parameters involved in the discussion. As before, P a and t x are the forcing functions of the atmospheric pressure fluctuations and the wind stress parallel to axis of the strait, respectively. The model Eqs. (1.1) (1.6) are written in a general form that includes the possibility of different densities r 1 and r 2 in the two layers, in which case any difference in the interface depth h i between the Red Sea and Gulf of Aden would lead to a baroclinic pressure gradient through the strait. However, for most of this paper we will focus exclusively on the barotropic problem in which r 1 5 r 2 5 r 0, and thus P 1 5 P 2 and the pressure gradient through the strait in both layers is related only to P a and the sea surface elevation h. The reasons for this are described in more detail in the discussion section but are briefly mentioned here before proceeding. First, unlike the rapid equilibration of the sea surface elevation that can occur in the Red Sea because of the fast propagation of external gravity waves, internal gravity waves are much slower and it cannot be assumed that the interface depth in the Red Sea will come into equilibrium on the synoptic time scales of interest here. Second, internal gravity waves may not be able to freely travel through the strait because of possible hydraulic control in the strait (Pratt et al. 1999, 2000). Both of these factors would need to be taken into account to properly model the evolution of the baroclinic pressure gradient and would require a much more complex model than developed here, which is left for future work. However, more importantly, we find that baroclinic effects are likely to have only a small impact on the synoptic time scales considered here and show that the barotropic model is capable of explaining most of the observed variability in the strait exchange on these time scales. It should be emphasized that, even with the choice of r 1 5 r 2 and a vertically uniform pressure gradient, the upper and lower layers will still respond differently because the upper layer is forced by both the along-strait pressure gradient and the wind stress, whereas the lower layer is forced only by the along-strait pressure gradient. Note also that, when t x 5 0, the momentum equations become symmetric and the response to P a forcing alone can be represented by an equivalent single-layer problem. Taking both P a and t x to behave as e ivt and seeking solutions of u 1, u 2, and h of the same form, with / x / 1/L S, where L S is the length of the strait, we obtain solutions that are presented in their complete form in the appendix. It is instructive to first consider the inviscid limit of the solution. For l 1 5 l 2 5 0, elimination of u 1 and u 2 in favor of h leads to the simple second-order equation 2 h t 2 1 v2 0 h 52 A S rl S P a 1 A 1 rl S t x, (2) which represents that of a forced harmonic oscillator with v 0 5 (ga S /L S ) 1/2, corresponding to the Helmholtz resonance frequency for the geometrical characteristics of the Red Sea and Bab el Mandeb system. The most uncertain parameter included in v 0 is the length of the strait L S, which is not necessarily the distance between the sill and the narrows but extends north and south of this point to include the whole shallow channel. The behavior of the transport and sea level observations suggests that the effective value of L S is around 270 km. This corresponds to a channel length extending from the mouth of the strait at the Gulf of Aden, some 60 km seaward of the Perim Narrows, to a point about 40 km north of the Hanish Sill, where the water depth begins to increase substantially into the Red Sea. The resulting v 0 is s 21, corresponding to a Helmholtz oscillation period of 5.2 days. The solution

10 1152 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 42 to Eq. (2) is well known and consists of a resonant response at v 0 that is in phase with the forcing, a reduced response at v, v 0 that is still in phase with the forcing, and at v. v 0 a reduced response that is out of phase with the forcing. Therefore, in the inviscid limit the sea level in the Red Sea would be expected to fall with rising atmospheric pressure at frequencies below the Helmholtz frequency (in the same sense as for an inverse barometer response) but to covary with atmospheric pressure at v. v 0 (i.e., high atmospheric pressure forces high sea level). For wind stress forcing, the inviscid response is a co-oscillation of t x and h (wind stress into the Red Sea causes high sea level) for v, v 0 and an antiphase oscillation for v. v 0. An interesting consequence of this result is that, at frequencies below v 0, the sea level variation in the Red Sea tends to oppose the wind stress in driving the net upper-layer flow through the strait, as can be seen from the upper-layer momentum Eq. (1.1) in the case where P a 5 0 and thus P 1 h. Because the solutions are a linear addition of the effect of the wind and the atmospheric pressure forcing, we can examine the influence of each forcing mechanism separately. The inviscid solutions for the net transport (Q h 5 Q 1 1 Q 2 )forcedbyp a ; for the upper-layer transport (Q 1 5 A 1 3 u 1 ), lower-layer transport (Q 2 5 A 2 3 u 2 ), and net transport (Q h 5 Q 1 1 Q 2 ) forced by the local wind stress; and for the sea level h inside the basin forced by the local wind stress are shown in Figs , respectively. The inviscid responses all show an abrupt change in phase at the Helmholtz frequency. At low frequencies, the P a leads transport by 908 and is out of phase with the sea level anomaly in the basin, as is expected for a response of the inverse barometer kind (Fig. 13). At frequencies greater than v 0, the response is changed and the atmospheric pressure forcing lags the transport by 908 and it is in phase with h. The response of the transport to the local wind stress (Fig. 14) is far more complicated because, as noted above, the upper layer feels both the wind stress and the changes of the sea level inside the basin, whereas the lower layer feels only the gradient in h. At low frequencies, t x and h are in phase, tending to force the two layers in opposite directions. At frequencies higher than the Helmholtz resonance frequency, they are out of phase and work together to force a barotropic type of response. The most complicated phase pattern is the one relating the wind stress and the upper-layer transport (Figs. 14c,d). There are two frequencies of abrupt phase change, at v 0 and v 02, where the latter is the equivalent Helmholtz frequency for the lower layer and is related to the ability of the lower layer to drain water from the basin (see the appendix). Between these two frequencies, at v cpd (period of 5.2 days) and v cpd (period of FIG. 13. (a) Gain and (b) phase of the net transport Q n through the strait in response to P a, comparing the model solution (light curves; for the inviscid limit and two frictional parameters) with the observations (bold). 7.4 days), h dominates and opposes t x, causing an acceleration of the upper-layer flow in the direction opposite to the wind stress. Friction can limit the strength of the flow through the strait but can also influence the frequency of maximum response. Solutions for different l corresponding to plausible levels of friction (see below) are shown in the same figures. The introduction of friction reduces the amplitude of the resonant response and generally smooths all of the phase patterns. Each of the gain functions still exhibit a peak at the Helmholtz resonance frequency v 0, except for the lower-layer transport in the strongest friction case (Fig. 14e), where a distinct resonance peak is no longer present. The upper- and lower-layer transports in Fig. 14 also have a second peak at v / 0, but because they are out of phase they do not contribute to a net transport. The abrupt phase changes at v 0 and v 02 in the inviscid surface-layer response to the wind stress forcing are also largely eliminated when friction is added. 5. Comparison with the observations The solutions presented above in the frequency domain can be compared with the corresponding gain and phase relations of the observations. Following Candela et al. (1989), a reasonable value for l can be obtained from l 5 C D U/H, where C D is the drag coefficient, U is the characteristic flow velocity, and H is the hydraulic

11 JULY 2012 J O H N S A N D S O F I A N O S 1153 FIG. 14. Gain and phase of (a),(b) the net transport Q n through the strait; (c),(d) the upperlayer transport Q 1 ; and (e),(f) the lower-layer transport Q 2, in response to t x, for the model solution (for the inviscid limit and two frictional parameters) compared with the observations. depth (cross-sectional area over width). With C D , U m s 21,andH m, we obtain l s 21. The values used in Figs correspond to this value and a value of half this magnitude, which seem to be the most appropriate values with respect to the observations. The most obvious result from the comparisons shown in Figs is that the wind-driven solution fits much better to the observations than that due to P a forcing. Furthermore, the effect of the wind is more important. Taking into account the magnitude of the fluctuations and the gain response of the transport at intermediate frequencies, the wind-induced response is 3 4 times larger than that of the atmospheric pressure. One of the issues in comparing the observations to the model is that a pure response to either type of forcing may be difficult to isolate if there is any correlation between the forcing functions. However, the wind stress and the atmospheric pressure over the Red Sea are weakly correlated (the correlation coefficient is 20.18), which suggests the observed responses can be examined separately. Nevertheless, because there is an active response to both kinds of forcing within the same basic frequency band, this should tend to result in decreased coherence of the identified response to either type of forcing. One might therefore expect the coherences observed in Fig. 11 to actually be larger if only one type of forcing were present. It should be emphasized that the data used to represent the sea surface elevation in the Red Sea in Fig. 15 are actually the data from the pressure gauge located at the west side of the Hanish Sill. Unfortunately, there are no available data for the sea level variability inside the basin on submonthly time scales during the period of observations. Therefore, the Hanish Sill record provides the closest approximation to the Red Sea sea level that is available to us. The data from all the pressure gauges inside the strait are in phase, but the response increases to the north, which is related to the Red Sea s sea level response to atmospheric forcing. However, although there is good agreement between the Hanish sea level observations and the model for the wind-driven solution, the corresponding solution for the atmospheric pressure forcing (not shown) does not seem to describe the observations. Two factors may contribute to this discrepancy: first, the Hanish site is still in the northern part of the strait in the area of the direct influence of the local wind field and most likely cannot represent the sea level anomaly of the whole basin; second, the sea level response to atmospheric pressure forcing is the weaker of the two responses and may be partly obscured by the wind-forced response.

12 1154 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 42 amplitude response of the transports suggests a smaller valueoffrictionthan s 21, whereas the phase responses suggest a larger value $ s 21.Despite these differences, the overall nature of the responses agrees well with the model, and it seems clear that the model captures a significant part of the fundamental dynamics. Neglected processes that could contribute to some of the above discrepancies are noted in the next section. Using the parameters discussed before (Table 1) and using an intermediate value of friction l s 21, we can produce a model of the transport in the time domain to compare with the observations. The results of this model are plotted in Fig. 16 for the net transport through the strait. There is a very good agreement, and the correlation coefficient between the predicted and observed transport is 0.84 (or the model explains 70% of the observed variance). This is a remarkable result, considering the simplicity of the model and the fact that no particular tuning has been done, such as choosing different values of friction for the upper and lower layers. FIG. 15. As in Fig. 13, but for the response of the sea level in the Red Sea h to the wind stress at the strait t x. Other notable differences between the observations and model predictions include the fact that the amplitude responses are generally greater than predicted at both the high and low ends of the spectrum, away from the Helmholtz frequency. In addition, no single value of friction seems to be consistent with all of the observed responses. For example, in Fig. 13 the phase relationships are suggestive of relatively low friction at high frequencies and high friction at low frequencies. Similarly, in Fig. 14 the 6. Discussion The fundamentally new contribution of this study to the problem of transport through semi-enclosed sea straits is the use of a two-layer formulation, coupled with a strong mass constraint within the marginal sea, to model the net exchange forced by a wind stress at the surface of the strait. Several studies, notably that of Candela et al. (1989), have considered the problem of transport fluctuations driven by atmospheric pressure forcing over semienclosed seas, but this leads to only a vertically uniform transport response. The interesting aspect of the FIG. 16. Time series of model-predicted (red) and observed (blue) net transport through the strait for the time period of the Bab el Mandeb observations.

13 JULY 2012 J O H N S A N D S O F I A N O S 1155 wind-driven problem is that the forced sea level response inside the marginal sea, which follows the Helmholtz equation, can act to either enhance or suppress the upperlayer wind-driven transport through the strait depending on the frequency of the forcing. The resulting transport response has a rich and complex behavior with some nonintuitive characteristics. We have used here a constant upper-layer thickness of 70 m in the model, which appears to be the most appropriate value for Bab el Mandeb based on the structure of the first EOF of the transport profile (Fig. 8). Presumably, the thickness of this layer is dictated by the depth to which the wind energy is mixed in the strait, and indeed the typical mixed layer depths in the strait during winter are on the order of 70 m and can reach as high as 90 m during very strong forcing events. During summer the mixed layer depth is typically much shallower, on the order of m, and it can be seen in Fig. 4 that the thickness of the upper-layer flow is normally restricted to 50 m or less during this season. Therefore, a shallower upper layer is probably more appropriate for the summer period; obviously, the depth of the upper-layer response will depend to some extent on the intensity of each forcing event. Another question regarding the vertical structure of the response is why the assumed uniform lower-layer flow often seems to have a maximum near m (Fig. 4). In part, this can be explained by frictional effects, which will be strongest near the bottom. Also, there is a geometrical effect due to the topography of the deep channel, which narrows significantly below 150 m (Fig. 2). This will lead to a middepth maximum of the transport profile, even in the case of a uniform lower-layer velocity. A factor that may be important in affecting the transport through the strait that is not considered in the model is the role of remote forcing in the Gulf of Aden. This forcing can have several forms, including local wind setup effects outside the strait or coastally trapped waves traveling to the strait from the northern part of the Gulf of Aden. The local wind setup at the western end of the Gulf of Aden is potentially the most interesting within the framework of our model study, because it can be assumed to be approximately in phase with the wind field inside the strait. Winds blowing toward the Red Sea will tend to pile up water outside the entrance of the channel, raising the sea level, and, conversely, will lower the sea level during periods when the wind blows toward the exit of the Red Sea. This effect will tend to produce stronger flows through the strait than predicted by the model, both at low frequencies, where it will reduce the adverse pressure gradient competing against the winds, and at high frequencies, where it will enhance the pressure drop into the Red Sea. The closest sea level station outside of the strait that is available to examine this effect is located in Aden (12.648N, E or 35 km from the Perim Narrows). The correlation between the strait winds and the sea level from this pressure gauge is relatively weak at synoptic time scales (correlation coefficient of 0.35), but the regression slope between them is approximately 20 cm Pa 21. This value is 25% 50% of the amplitude response of the sea level inside the Red Sea to the along-strait wind forcing, which has magnitudes of cm Pa 21 over most of the synoptic band (Fig. 15). Thus, the remote sea level setup in the Gulf of Aden has the potential to be quantitatively important to the observed response and may help explain why the model generally underestimates the transport response to the along-strait wind forcing, particularly at frequencies away from the Helmholtz peak. However, the weak correlation between the Aden sea level and the winds in the strait suggests that it is not straightforward to model this effect. The model solutions described herein have also assumed a homogeneous ocean, where the penetration of the wind is confined in a surface layer, but the pressure gradient through the strait does not vary with depth. As noted previously, if one includes two distinct layers of different densities, r 1 and r 2, the interface separating the two layers can oscillate too and a baroclinic pressure gradient can develop. Treatment of this within our simple model framework is complicated by two factors. First, the internal gravity waves that can adjust the interface inside the Red Sea are much slower than the long surface gravity waves. Therefore a complete adjustment may not occur at higher frequencies. Taking values of g9 (reduced gravity) of ms 22 and upper-layer thickness in the Red Sea of m gives an internal wave speed (g9h) 1/2 of 1 2 m s 21, meaning that the time required for an internal wave to transit the 1500-km length of the Red Sea would be O(8 16 days). Second, the outer interface condition in the Gulf of Aden may not be felt by the Red Sea if the lower-layer outflow from the strait is sufficient to arrest first-mode internal waves propagating from the Gulf. Pratt et al. (2000) investigated this for the Bab el Mandeb by solving for the phase speeds of first- and second-mode internal waves using a modified Taylor Goldstein equation with realistic topography, stratification, and shear in the strait. They found that the first internal mode was marginally critical during parts of the year (the winter season with strong mean lower-layer outflow), suggesting that free baroclinic wave communication through the strait could be limited. Modeling these effects realistically in the Red Sea and Bab el Mandeb strait would require a much more complex model than we have used. However, it can be shown by a simple order of magnitude

14 1156 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 42 calculation that displacements of the interface depth in the Red Sea caused by the variations in transport through the strait would be very small on the time scales considered here. From Eq. (1.4), the interface displacement in the Red Sea forced by a 1-Sv lower-layer flow through the strait lasting for 5 days would be only about 1 m and would cause only a minor perturbation in the lower-layer pressure gradient related to sea surface elevation changes. If the complications regarding internal wave propagation through the system are ignored, and the sea level and the interface between the layers inside the Red Sea are both assumed to respond uniformly, it is possible to obtain solutions to (1.1) (1.6) that include the effects of a baroclinic along-strait pressure gradient. These solutions are now very complicated, but some preliminary conclusions can be drawn from the simpler inviscid limit. The relation between h i and h for the case of only wind forcing (neglecting atmospheric pressure variations) is h i 5 v2 02 v 2 2 v902 2 h; v sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g9a 2, L S so that for frequencies greater than v9 02 the surface and interface displacement are in phase and the pressure gradient in both layers is primarily controlled by the sea level perturbation, as in the case described in the previous sections. During events of very low frequencies, they are out of phase. Also at frequencies around v9 02 the fluctuations of the interface become much greater than those at sea level. However, because v9 02 corresponds to a periodicity of $100 days, for reasonable values of g9, at this limit one is no longer dealing with synoptic time scales. In the frequency band examined here, which is associated with meteorological forcing, the solutions discussed in the previous sections seem an appropriate approximation of the response of the strait. 7. Summary We have developed a simple model that can reproduce the transport variability observed in the Bab el Mandeb in response to local wind stress forcing at the strait and atmospheric pressure forcing over the Red Sea. The Helmholtz response of the Red Sea is fundamental to the dynamics of both types of response. The Helmholtz resonance period for the Red Sea Bab el Mandeb system is about 5 days, and an elevated transport response through the strait is observed near this period. The model can explain 70% of the observed variance and, if only the winter season (October May) is considered when the atmospheric forcing is much stronger, this value rises to almost 80%. The wind seems to be the more important forcing mechanism in the case of Bab el Mandeb and the correlation between observations and winddriven model solutions is much better. This can be attributed to the strength of the wind fluctuations and the orographic effect in combination with the small width of the channel. The flow variability at synoptic time scales can be important for the dynamics of the Bab el Mandeb Red Sea system. It can modify the mixing in the strait and possibly affect hydraulic control mechanisms in the strait. Pratt et al. (2000) found that during certain periods of the year the flow is close to criticality, and synoptic fluctuations of the type described here can potentially make this kind of control intermittent. This is especially true when they result in the upper and lower layers being accelerated in opposite directions, as occurs at lower frequencies for the wind-driven fluctuations. More elaborate models can investigate the influence of parameters neglected in the model described here, like the rotational effect when layers of different density are allowed and the internal R d becomes critically close to the width of the strait. The choice of a constant l simplifies our derivation, but the investigation of other forms of friction may improve the performance of similar models. Furthermore, the role of the different forms of remote forcing that can influence the variability in the strait should be investigated. Finally, it should be possible for ocean general circulation models that incorporate synoptic meteorological forcing and sufficiently high horizontal resolution to capture the types of responses observed here and to provide a more detailed picture of the dynamics governing the synoptic exchange through the strait. Acknowledgments. Funding for this research was provided by the Office of Naval Research under Contract N with the University of Miami. We acknowledge the skillful support provided by the Ocean Technology Group of the Rosenstiel School of Marine and Atmospheric Science, University of Miami, and the Field Support Group of Louisiana State University s Coastal Studies Institute, in acquiring the field observations. APPENDIX Model Solutions The solutions to the set of equations derived in section 4 of the paper are given here, in terms of response