Wind induced oscillator dynamics in the Black Sea revealed by Lagrangian drifters

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L13609, doi: /2007gl030263, 2007 Wind induced oscillator dynamics in the Black Sea revealed by Lagrangian drifters Leonid M. Ivanov, 1,2,3 Oleg V. Melnichenko, 4,5 Curtis A. Collins, 2 Valery N. Eremeev, 5 and Sergey V. Motyzhev 5 Received 4 April 2007; revised 2 May 2007; accepted 1 June 2007; published 12 July [1] Lagrangian drifter observations of the Black Sea circulation between 2002 and 2003 show six transitions between two meta-stable states representing single gyre structures centered in either the western or eastern sub-basin of the Black Sea, respectively. The major mechanisms driving such an oscillator dynamics are Ekman pumping for the eastern sub-basin, and most likely a resonance excitation for the western sub-basin. The sea strongly amplifies the wind responses of 120-day periodicity. Data analysis demonstrates that two-gyre structure ( Knipovich spectacles ) was a transient between the states. Residence time for the sea to occupy either state is mainly determined by the instability of the gyres, wind variability and, probably, variations in the pycnocline. This behavior is a manifestation of a bimodal dynamical regime which affects the long-term (climatic), large-scale transport and mixing of bio-geochemical substances. Citation: Ivanov, L. M., O. V. Melnichenko, C. A. Collins, V. N. Eremeev, and S. V. Motyzhev (2007), Wind induced oscillator dynamics in the Black Sea revealed by Lagrangian drifters, Geophys. Res. Lett., 34, L13609, doi: /2007gl Introduction [2] The Black Sea circulation system is believed to be dominated by a strong counterclockwise Rim Current with speeds up to m/s and cross-frontal scales O(40 km), a series of clockwise eddies between the Rim Current and the coastline, and cyclonic gyres occupying the interior of eastern and western sub-basins (Figure 1a). The eastern and western gyres evolve continuously by interactions with each other, as well as with the Rim Current. The Black Sea currents are also known to be dominated by seasonal changes at both basin and meso-scales [Filippov, 1968; Blatov et al., 1984; Korotaev et al., 2003]. The phase of current variability is determined by the seasonal cycle of the wind stress curl, and currents are strongest approximately three months after wind amplification. The Rim Current is strongest in winter-spring seasons. Winter circulation 1 Department of Mathematics, University of Southern California, Los Angeles, California, USA. 2 Department of Oceanography, Naval Postgraduate School, Monterey, California, USA. 3 Moss Landing Marine Laboratories, San Jose State University, San Jose, California, USA. 4 International Pacific Research Center, School of Ocean and Earth Science Technology, University of Hawaii, Honolulu, Hawaii, USA. 5 Marine Environmental Informational Technologies Department, Marine Hydrophysical Institute, Sevastopol, Ukraine. Copyright 2007 by the American Geophysical Union /07/2007GL consists of gyres in both eastern and western sub-basins but in spring the Rim Current encircles the entire sea along the continental slope. The currents weaken significantly during summer and in the fall the Rim Current usually breaks into a series of eddies. [3] This paper re-examines the picture of Black Sea circulation described above. Trajectories of Lagrangian drifters deployed in the Black Sea between 2001 and 2003 to measure the surface circulation were analyzed. Results reveal significant refinements to Black Sea circulation, including (1) a new mechanism for excitation of the western cyclonic gyre due to variations of wind and (2) a bi-modal dynamical regime dominated by time scales of four and twelve months. 2. Drifter Data [4] Trajectories from satellite-tracked drifters deployed in the Black Sea between 1999 and 2003 [Poulain et al., 2005] were used. Most drifters were Surface Velocity Program (SVP) drifters drogued at a nominal depth of 15 m. Positions were determined 8 10 times each day with an accuracy better than 1 km. These data allow reconstruction of the near-surface circulation directly without use of a numerical ocean model. Analysis focused on drifter data for since the majority of observations were concentrated in this period. Statistical methods were then used to study the relationship between the circulation and winds. [5] Trajectories of all drifters deployed between 1999 and 2003 are shown in Figure 1b. Although a visual inspection of Figure 1b supports the large-scale circulation pattern shown in Figure 1a, it is not possible to see how drifters were distributed in the western and eastern sub-basins with time. This was noted by Poulain et al. [2005] who were unable to confirm the separation of the Rim Current into separate cyclonic gyres in the western and eastern sub-basins. [6] Another transport feature of drifter trajectories was long-term correlation of drifter motions. Most drifters moved steadily in the Rim Current around the Black Sea and transited slowly from these paths to shorter closed streamlines which corresponded to sub-basin scale gyres and anti-cyclonic eddies (Figure 2a); this indicated the coherent character of the Rim and sub-basin currents and their dominance of the total transport. There was little crossstream movement of the drifters as they moved around the Black Sea in the Rim Current; this is shown in Figure 2b by bars which measure the across Rim Current distance of an array of six drifters at launch, a distance which effectively constrained the downstream trajectories. The long-term correlation and lack of cross stream motion indicate that L of6

2 Figure 1. Black Sea circulation. (a) After Korotaev et al. [2003]. The Rim Current is indicated by black curves. Two branches of the Rim Current are shown in the western part of the Black Sea. The western and eastern gyres are shown by dashed lines. Arrows show subbasin and mesoscale eddies which are usually associated with names of near by cities or geographical regions. (b) Trajectories of all drifters deployed in the Black Sea between 1999 and 2003 [Poulain et al., 2005]. Total number of drifter-years is about The drifters reveal the general basin and sub-basin cyclonic circulation and anticyclonic eddies, such as the Sevastopol and Batumi eddies. drifter motions were strongly affected by long-lived basin scale circulation structures and that large-scale transport and mixing in the Black Sea are as important as mesoscale mixing. 3. Methodology [7] The technique of Eremeev et al. [1992] was used to extract long-lived structures, such as Rossby waves, basin and sub-basin scale gyres, etc. from the Black Sea drifters. This technique has been tested [Chu et al., 2003a, 2003b] and used to reconstruct long Rossby waves in the Tropical North Atlantic from Argo subsurface float data [Chu et al., 2007]. Fifty-four large-scale circulation snapshots were reconstructed each 10 days for a 1.5-year time period from January 2002 to July [8] Following Eremeev et al. [1992], the near-surface circulation (u, v) of the Black Sea was represented as a weighted sum ux; ð y; tþ ¼ XK a k ðþr t y y k ðx; yþ; vx; ð y; tþ ¼ XK a k ðþr t x y k ðx; yþ; ð1þ where (r x, r the weighting functions (spectral coefficients) a k (k = 1,..., K) were estimated from observations, and y k are the basis functions (modes) calculated by r 2 y k ¼ l k y k ; y k j G ¼ 0; ð2þ where r 2 = r x r x + r y r y is the plane Laplace operator, l k are eigenvalues and G is the Black Sea coastline. [9] Six low-order modes are shown in Figure 3. They represent the elementary circulations that may potentially be excited in the Black Sea. Spatial structure of the modes is determined by basin geometry and does not depend on the processes affecting the circulation. [10] The weighting functions a k should minimize the sum of squared residuals between drifter and model (defined by equation (1)) velocities at float locations. Then y k calculated from equation (2) and a k were used to reconstruct the circulation at any point in the Black Sea including spatial gaps in the data using equation (1). The optimal (in least square sense) solution specified by the choice of K was selected to minimize the mean angle between the direction of drifters and their counterparts (synthetic particles deployed in the reconstructed circulation field). The reconstructed circulation patterns were not sensitive relative to specificities of the reconstruction procedure. They were robust for the Figure 2. (a) Effects of transition from long to shorter streamlines. (b) Small divergence of drifter trajectories downstream from launch. Black arrows show the directions of drifter motions. Black points are the launch position of the drifters. The bar shows the cross-stream spacing of the drifters at launch and is placed at several positions along the trajectories. 2of6

3 Figure 3. Stream functions of normalized modes computed on 15 km 15 km spatial grid. Mode number is indicated in the right upper corner of each panel. Negative values are indicated with dashed lines. given data and weakly dependent on the number of modes (K) in the spectral decomposition (1) for K greater than 10. Contributions of meso-scale eddy motions cannot be explicitly resolved, so they were filtered from the reconstructed fields by the choosing K < Meta-Stable States and Transient Dynamics [11] The reconstruction reveals the existence of metastable states (forced modes) of Black Sea circulation. These states represent one-gyre circulations centered in either the eastern (Figure 4a) or western (Figure 4b) sub-basins of the Black Sea. A one-gyre structure is clearly detected by the ratio of the mean kinetic energies for the western he 1 i and eastern he 2 i sub-basins of the Black Sea: h = he 1 i/he 2 i. The western (eastern) gyre corresponds to h >1(h <1). [12] Three (four) eastern (western) gyres existed during the time period between January 1, 2002 and July 1, 2003 (Figure 5a). The recurrence feature of the meta-stable states was clear. The western gyre circulations had the minimum number of degrees of freedom due to minimum spectral entropy S (Figure 5a), which is a measure of the spatial complexity of the circulation. The entropy must be 0 when the kinetic energy (KE) of the circulation was entirely in one mode or 1 when the energy was uniformly distributed among all modes [Aubry et al., 1991]. The spectral entropy is computed by XK 1 S ¼ ðlog KÞ p k log p k ; p k ¼ a 2 XK k =a; a ¼ a 2 k ; [13] Residence time in each meta-stable state depends on seasonal fluctuations of wind and, probably, seasonal variations of the pycnocline (we are not able to determine the contribution of each of these variations using only drifter observations). Residence time was estimated as the ð3þ time between two consecutive crossings of the ratio h of some threshold and did not exceed 1 month. [14] The eastern gyre was highly unstable and when decaying it probably radiated Rossby waves which propagated to the northwest. These waves appear as subbasin cyclonic eddies (wave packets) propagating with speeds of about 3 km/day. This agrees with the results of numerical modeling [Rachev and Stanev, 1997] and the analysis of satellite altimetry [Korotaev et al., 2001]. [15] The western gyre seemed to be baroclinically unstable and its periphery meanders near the Danube Fan, most likely generating sub-basin eddies such as the Sevastopol anti-cyclonic eddy. Original drifter trajectories showed a contribution from sub-basin and mesoscale eddy activity. Largest anti-cyclonic eddies (for example, the Batumi eddy) were observed in the reconstructed fields but smaller mesoscale eddy scale motions were filtered as discussed above. [16] The ratio h varied in time (Figure 5a) with two dominant periods: one year and about 120 days (the natural synoptic period). This agrees with Eremeev et al. [1992], Rachev and Stanev [1997], Korotaev et al. [2001], and others, who have estimated the natural synoptic period of the Black Sea as 120 days. [17] Due to the short observation sampling (18 months), the one-year oscillation period is assumed to be known a priori. Only a phase, which indicates the start of the seasonal cycle within the observation period, is determined by the Chu et al. [2007] method. This procedure estimates contributions of the one-year oscillation to each harmonic a k (t) and h(t). [18] The well-known two-gyre picture ( Knipovich spectacles ) was clearly observed for h 1 (Figure 4c). It existed when the eastern (western) gyre was decaying but a structured circulation in eastern (western) sub-basin still had not yet dissipated, and the western (eastern) gyre had begun to amplify at the same time. Therefore the spectacles were a manifestation of the transient dynamics 3of6

4 Figure 4. Snapshots of stream function scaled by multiplier m 2 /s for meta-stable states in (a) February 2002, (b) April 2002, and (c) Knipovich spectacles in June Contour interval is 0.2. of the Black Sea. A two-gyre circulation, in general, had maximum spectral entropy (Figure 5a). 5. What Drives the Circulation? [19] Korotaev et al. [2003], Stanev [2005], and others have hypothesized that the wind stress curl mainly affects the Black Sea circulation and the cyclonic gyres in the eastern and western sub-basins may be generated by instability of the Rim Current. To understand correlations between the wind stress curl and near-surface circulation at basin scales, the spectral approach discussed above was also applied to QuikSCAT winds with spatial resolution of (for details, see the scatterometer web site: Correlations between different circulation modes and their counterparts for the wind stress curl were then analyzed through the behavior of the spectral coefficients a k (t) and f k (t), where f k (t) = RR rot z (t)y k dxdy, t =(t x, t y ) is the wind W stress, and the integration is made over the basin area W. [20] The traditional wavelet analysis based on the Morletwavelet applied to the QuikSCAT wind observed between 2000 and 2004 showed that the annual, semi-annual and 120-day harmonics dominated the wind signal. Although the reconstructed circulation was represented by a 25 mode decomposition (1), depending on season, the first 5 8 modes contained up to 85% of the energy and determined the basin-scale dynamics of the Black Sea circulation. [21] The first mode (k = 1) represented the cyclonic gyre centered in the western sub-basin (Figure 3) and contained more than 40% energy of the reconstructed signal independently of season. Since the maxima of f 1 (t) and a 1 (t) were generally observed at the same time (the shift observed in Figure 5b is less than one month), a resonance mechanism of mode excitation due to variable wind forcing and buoyancy flux was assumed. The wavelet analysis showed that ratio of the kinetic energies of the annual oscillation to the 120 day oscillation was 0.15 for the atmosphere but was 3.14 for the Black Sea. Consequently, the Black Sea strongly amplified the wind responses at the 120-day period. A linear resonance between the western gyre and Rossby waves due to the eastern gyre instability may be responsible for this amplification of the wind response. [22] It is unlikely that the western gyre is a manifestation of Ekman transport because (1) hydrography observations do not show a shallow water cyclonic cell in the western sub-basin of the Black Sea [Blatov et al., 1984], and (2) Ekman drift velocities at 15 m depth estimated from QuikSCAT wind and Ekman spiral for constant vertical viscosity n z [Pedlosky, 1987] were considerably smaller than drifter velocities. For maximum magnitudes of wind stress of Pa (computed from the wind) and reasonable values of n z between and m 2 /s (estimated by Afanasyev et al. [2002] for the Black Sea through comparison of in-situ observations and different Ekman spiral models), the drift velocity does not exceed 0.12 m/s. The maximum velocity in the western gyre estimated from the drifter observations is about 0.40 m/s. More sophisticated models of Ekman boundary layer with variable vertical viscosity change the direction of drift velocity at 15 m but they also reduce its magnitude [Pedlosky, 1987]. In this case drift velocities will also be considerably less than 0.40 m/s even if n z is as large as m 2 /s near the sea surface. [23] Our calculations show that Ekman pumping was the dominant mechanism for excitation of the second mode (k = 2) (Figure 3). The strongest currents corresponding to this mode were observed approximately two-three months after intensification of the wind stress curl (Figure 5c). The second mode may contain up to 40% of the kinetic energy of the reconstructed signal, but this mode was always weaker than the first. [24] The mode with k = 3 (Figure 3) weakly contributed to one-gyre circulations. This mode was the most intensive 4of6

5 Figure 5. (a) Transition of the Black Sea circulation between two meta-stable states. A, one-gyre circulation centered in the eastern sub-basin; B, one-gyre circulation centered in the western sub-basin. Black and white dots are the ratio h and the spectral entropy S, respectively. Behavior of the (b) first, (c) second, (d) third, (e) fourth and (f) fifth modes. a k, black dots; f k, white dots. a k and f k are the coefficients of the spectral decompositions for the stream function and wind stress curl, respectively. in winter (up to 6 7% of the KE of the reconstructed signal) and negligible for other months (Figure 5d). [25] Two other modes with k = 4 and k = 5 (Figure 3) dominated in January March, July August and November December (Figures 5e and 5f). Mode k = 5 followed the annual cycle of river discharge with maxima in June and October. The winter-spring and late fall peaks in the mode amplitudes were probably caused by a hierarchy of different physical mechanisms including a resonance excitation and Ekman pumping. The drifter observations were not long enough to allow any of these mechanisms to be accepted or rejected. 6. Climate Aspects [26] Large-scale cyclonic circulation forms a zone of divergence (ZD) of surface waters. The ZD interacts with a coastal zone (CZ) which consists of a number of mesoscale anticyclonic eddies. These interactions play a fundamental role in the hydrography and ecology of the coastal waters [Ovchinnikov et al., 1994]. The drifter-based calculations reveal the oscillator behavior of ZD structure, and variability of boundary between ZD and CZ because one and two-gyre circulations alternate with each other. The temporal variability of the boundary may induce chaotic advection of bio-geochemical substances across this boundary [Wiggins, 2005]. Acceleration of the mean coastward transport should also be observed after averaging horizontal substance fluxes over a time period, which is considerably longer than one year because of the oscillator dynamical regime [Moffatt, 1983]. Both these effects improve water exchange between the ZD and CZ, and intensify vertical circulation in cyclonic gyres. That should stimulate the ventilation of the Black Sea pycnocline in the climatic sense. These climatic aspects will be analyzed in a separate paper. [27] Acknowledgments. L. Ivanov and C. Collins were supported by NSF award OCE The authors would like to thank Dr. S. Ryanzhin and an anonymous reviewer for helpful comments. References Afanasyev, Y. D., A. G. Kostianoy, A. G. Zatsepin, and P.-M. Poulain (2002), Analysis of velocity field in the eastern Black Sea from satellite data during the Black Sea 99 experiment, J. Geophys. Res., 107(C8), 3098, doi: /2000jc Aubry, N., R. Guyonnet, and R. Lima (1991), Spatio-temporal analysis of complex signals: Theory and applications, J. Stat. Phys., 64(3 4), Blatov, A. S., N. P. Bulgakov, V. A. Ivanov, A. N. Kosarev, and V. S. Tuzhilkin (1984), Variability of the Black Sea Hydrophysical Fields (in Russian), 239 pp., Hydrometizdat, St. Petersburg, Russia. Chu, P. C., L. M. Ivanov, T. P. Korzhova, T. M. Margolina, and O. V. Melnichenko (2003a), Analysis of sparse and noisy ocean current data using flow decomposition: 1. Theory, J. Atmos. Oceanic Technol., 20, Chu, P. C., L. M. Ivanov, T. P. Korzhova, T. M. Margolina, and O. V. Melnichenko (2003b), Analysis of sparse and noisy ocean current data 5of6

6 using flow decomposition: 2. Applications to Eulerian and Lagrangian data, J. Atmos. Oceanic Technol., 20, Chu, P. C., L. M. Ivanov, O. V. Melnichenko, and N. C. Wells (2007), On long baroclinic Rossby waves in the tropical North Atlantic observed from profiling floats, J. Geophys. Res., 112, C05032, doi: / 2006JC Eremeev, V. N., L. M. Ivanov, A. D. Kirwan Jr., O. V. Melnichenko, S. V. Kochergin, and R. R. Stanichnaya (1992), Reconstruction of oceanic flow characteristics from quasi-lagrangian data: 2. Characteristics of the largescale circulation in the Black Sea, J. Geophys. Res., 97, Filippov, D. M. (1968), Circulation and Structure of Waters in the Black Sea (in Russian), 136 pp., Nauka, Moscow. Korotaev, G. K., O. A. Saenko, and C. J. Koblinsky (2001), Satellite altimetry observations of the Black Sea level, J. Geophys. Res., 106, Korotaev, G., T. Oguz, A. Nikiforov, and C. Koblinsky (2003), Seasonal, interannual, and mesoscale variability of the Black Sea upper layer circulation derived from altimeter data, J. Geophys. Res., 108(C4), 3122, doi: /2002jc Moffatt, H. K. (1983), Transport effects associated with turbulence with particular attention to the influence of helicity, Rep. Prog. Phys., 46, Ovchinnikov, I. M., V. B. Titov, V. G. Krivosheya, and Y. I. Popov (1994), Major fluid dynamical processes and their role in the ecology of waters of the Black Sea, Oceanology, Engl. Transl., 33(6), Pedlosky, J. (1987), Geophysical Fluid Dynamics, 625 pp., Springer, New York. Poulain, P.-M., R. Barbanti, S. Motyzhev, and A. Zatsepin (2005), Statistical description of the Black Sea near-surface circulation using drifters in , Deep Sea Res., Part I, 52, Rachev, N. H., and E. V. Stanev (1997), Eddy processes in semi-closed seas: A case study for the Black Sea, J. Phys. Oceanogr., 27, Stanev, E. V. (2005), Understanding Black Sea dynamics: An overview of recent numerical modeling, Oceanography, 18(2), Wiggins, S. (2005), The dynamical systems approach to Lagrangian transport in oceanic flows, Annu. Rev. Fluid Mech., 37, C. A. Collins, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, Monterey, CA 93940, USA. V. N. Eremeev, O. V. Melnichenko, and S. V. Motyzhev, Marine Environmental Informational Technologies Department, Marine Hydrophysical Institute, 2 Kapitanskaya Street, Sevastopol 99011, Ukraine. L. M. Ivanov, Department of Mathematics, University of Southern California, 1042 W. 36th Place, Los Angeles, CA 90089, USA. (lmivanov@nps.edu) 6of6