3. Current meter moorings

The flow in the Strait of Gibraltar shows great temporal and spatial variability. To obtain an accurate picture of the currents it is therefore necessary to complement measurements that were carried out at a given location for a longer period of time (current meter moorings, ship time stations) with measurements with good spatial resolution (ship-board measurements with ADCP and lowered ADCP).

The current meter mooring J (J. Candela, WHOI, and J. Rico, IHM) and the moorings from the pilot phase of CANIGO L (J.G. Lafuente, Univ. Malaga), and U (U. Send, IfM Kiel) were repeatedly deployed at the eastern entrance of the Strait between October 1994 and April 1998. The results of these measurements helped to design a mooring array for the intensive phase of CANIGO. It contained 7 current meter moorings I1, I2 (H. Bryden, SIO), N, C, S (J.G. Lafuente), and UN, US (U. Send) and was deployed at the same section from October 1997 to April 1998. The moorings were equipped with a total of 30 Aanderaa rotor current meters and one RDI acoustic current meter. The position of the moorings and the depth of the instruments is shown in Figure 1.1 and Figure 3.1.

	Figure 3.1: Array of the current meter moorings during the intensive phase of CANIGO.

4. Acoustic transmissions

Two methods of using high-frequency acoustic transmissions across the strait for transport integrals have been tested in collaboration with P. Worcester from SIO, San Diego. Along the path T1-T3, horizontal deflection of the sound by the currents was measured with a horizontal array, while reciprocal traveltime differences were analyzed along the diagonal path T1-T2 (Figure 1.1.). Figure 4.1 shows some of the acoustic ray paths across the strait between T1 and T2. At present, only the paths in the lower layer are used in order to obtain a horizontal integral of the flow. Figure 4.2 is a comparison of the horizontal phase differences at T3 with the averaged flow from the tidal inverse model for a few days. The tidal flow signal is clearly visible in the acoustic data, but a more quantitative agreement has not been achieved yet.

Figure 4.3 gives a similar comparison of the reciprocal traveltime data with the mean along-axis flow in the strait. The agreement here is very high, and it is not clear whether the remaining differences arise from the different cross sections used for the acoustic transmission and the inverse model, from an insufficient sampling of the acoustic instruments, or the residual currents not explained by the model.

	Figure 4.1: Some of the ray acoustic paths between the instruments deployed at T1 and T2.		Figure 4.2: Horizontal phase differences measured at T3 and averaged lower layer-flow from the inverse model.
	Figure 4.3: Reciprocal acoustic traveltime differences along T1-T2 (red) converted to along-axis mean lower-layer flow, compared to the sum of longeriodic flow (green) and average from the inverse model along the ray acoustic path (blue).

5. Inverse model

A tidal inverse model was developed to:

• obtain a detailed picture of the flow through the Strait of Gibraltar by combining measurements with good spatial sampling (ship-board measurements) and measurements with good temporal information (current meter moorings).
• describe the flow and the depth of the interface at the eastern entrance of the Strait as a function of time and 2-dimensional space
  
• to remove tidal currents from measurements to obtain steady and subinertial flow components.
  
• to calculate the volume transport through the Strait (under consideration of the movement of the interface).
  
• to check the acoustic measurements during the CANIGO-project.
  
• to understand the structure of flow to establish suitable longterm monitoring systems.

	Figure 5.1: The model boxes at the eastern entrance of the Strait of Gibraltar. The numbers in the boxes indicate the number of the used current speed data (a total of approximately 135.000 data).		Figure 5.2: The first and second EOF (56.5 % and 35.4% of the variance of the current speed) and the time-dependent vertical model functions (linear function, damped sine and cosine, 97.8% of variance). A 2nd order polynomial was used as horizontal function, and as constant vertical function a 4th order polynomial plus an exponential function was used. The temporal variablity was described with sines and cosines and the 7 most important tidal constituents.

5.1 Mean flow and tidal currents

Due to the strong tidal currents the vertical excursions of the moored current meters sometimes exceed 150 m. This was taken into account by determining the depth of the instruments with the pressure sensors. With this method high current speeds are assigned to deeper boxes and low current speeds to higher boxes. Because the data of the single boxes are therefore biased to higher or lower values, the tidal currents had to be removed before a mean value was calculated. The spatial gaps due to empty boxes were filled by using objective analysis.

	Figure 5.3: Mean current speed [cm/s] from the inverse model. The mean depth of the 38.0-Isohaline is shown by the dashed line.

The synoptical sections of the current speed calculated with the inverse model show the importance of the tidal currents in the Strait of Gibraltar (Figure 5.4). The figure shows a complete M2 tidal cycle during spring tide with a time difference of 2 h between the single sections.

Amplitude and phase of the dominant M2 tidal constituent show large differences between upper and lower layer (Figure 5.5). The mean phase shift between both layers is 75^o. Hence the M2 tide arrives in the upper layer 2.6 h earlier than in the lower layer.

	Figure 5.4: Synoptical sections of the current speed [cm/s] from the inverse model showing several phases of a M2 tidal cycle during spring tide. The time difference between the single sections is 2 h.		Figure 5.5: M2 tidal constituent at the eastern entrance of the Strait of Gibraltar. a) Amplitude [cm/s], b) phase [o].

5.2 Transport estimates

The estimate of the volume transport depends on the choice of the interface between Atlantic and Mediterranean water. To avoid the strong seasonal variations of temperature and hence density in the Strait, it is usually defined as an isohaline. When for example the chosen isohaline lies somewhere in the upper layer, the area of the cross section used for the calculations is smaller than it should be; the estimated transport is too small and the flow of the upper layer is partly ascribed to the lower layer. Since it is flowing into the opposite direction it also reduces the estimated lower layer transport. It is therefore assumed that the interface with which the transport calculations get maximal is the most appropriate one to use (Figure 5.6). The isohaline S=38.1 seems to be appropriate for this and is therefore used in this study for further calculations.

	Figure 5.6: Relation between the interface definition (isohaline) and the calculated volume transport of the upper layer respectively of the lower layer.

The volume transport through the eastern entrance of the Strait was calculated by combining:

• the inverse models for the current speed and for the depth of the interface:
  
• The volume transport below the 38.0-isohaline is estimated to 0.81+/-0.06 Sv for the upper layer and to -0.76+/- 0.06 Sv for the lower layer and are in good agreement with the measurements from H.L. Bryden et al. [1994] (0.72+-0.16 Sv, -0.68+-0.15 Sv) and the indirect estimates from H.L. Bryden and T.H. Kinder [1991] (0.92 Sv, -0.88 Sv).
  
• The correlation between the tidal fluctuations of the interface and the tidal currents reduces the volume transport at the eastern entrance by about 5%.
  

The error of the transport estimates, which results from an unsufficiently determined depth of the interface, is therefore much smaller in the east than at the Camarinal Sill, where the fluctuation of the interface account to about 50% of the volume transport (H.L. Bryden et al. [1994]).

6. Summary

• We have documented a rich temporal, horizontal and vertical structure of the flow in the Strait of Gibraltar, which is difficult to integrate with single moorings.
  
• The mean volume transport through the Strait was estimated with a tidal inverse model by combining measurements with good spatial sampling (ship-board measurements) and measurements with good temporal information (time-series over 4.5 a). The upper layer transport is 0.81 Sv and the lower layer transport -0.76 Sv, with an accuracy of 0.06 Sv.
• The tidal interface variablity accounts to about 5% of the volume transport through the Strait.
  
• The acoustic travel time differences show a good agreement with the averaged currents from the inverse model.
  
• Acoustic cross-strait transmissions hold a great potential for monitoring the volume transport, at least in the lower layer.
  
• Calculated Froude numbers and along strait sections with vmADCP give indications that the flow through the Strait of Gibraltar was hydraulically controlled in April 1996, but possibly not in October 1997.
  
• The behaviour and structures observed now help to optimize future measurements.

This work was supported by the EU/MAST-3 project CANIGO and by state and federal base funding of the IfM.

References

L. Armi and D.M. Farmer, Maximal two-layer exchange through a contraction with barotropic net flow, J. Fluid Mech. 164, pp. 27-51, 1986.

B. Baschek, Strömungsuntersuchungen in der Straße von Gibraltar, Diploma thesis, IfM Kiel, Germany, 1998.

B. Baschek, U. Send, J.G. Lafuente, and J. Candela, 2001: Transport estimates in the Strait of Gibraltar with a tidal inverse model. J. Geophys. Res., Vol. 106, No. C12, p. 31,033-31,044.

H.L. Bryden and T.H. Kinder, Steady two-layer exchange through the Strait of Gibraltar, Deep Sea Research 38, pp. 445-463, 1991.

H.L. Bryden et al.,Exchange through the Strait of Gibraltar,Progress of Oceanography 33, pp. 201-248, 1994.

D.M. Farmer and L. Armi, Maximal two-layer exchange over a sill and through a combination of a sill and a contraction with barotropic flow, J. Fluid Mech. 164,pp. 53-76, 1986.

C. Garrett, M. Bormans, and K. Thompson, Is the exchange through the Strait of Gibraltar maximal or submaximal?, in The physical oceanography of sea straits, edited by L.J. Pratt, pp. 271-294,Kluwer Academic Publishers. Dordrecht, 1990.

U. Send and B. Baschek, 2001: Intensive ship-board observations of the flow through the Strait of Gibraltar. J. Geophys. Res., Vol. 106, No. C12, pp. 31,017-31,032.

U. Send, P.F. Worcester, B.D. Cornuelle, C.O.Tiemann, and B. Baschek, 2002: Integral measurements of mass transport and heat content in the Strait of Gibraltar from acoustic transmissions. Deep Sea Res., part II, Vol. 49, No. 19, pp. 4069-4095.