Ocean & coupled ocean

Speich, S, H Dijkstra, and M Ghil. 1995. “Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation.” Nonlinear Processes in Geophysics 2: 241–268. Abstract
Climate - the "coarse-gridded" state of the coupled ocean - atmosphere system - varies on many time and space scales. The challenge is to relate such variation to specific mechanisms and to produce verifiable quantitative explanations. In this paper, we study the oceanic component of the climate system and, in particular, the different circulation regimes of the mid-latitude win driven ocean on the interannual time scale. These circulations are dominated by two counterrotating, basis scale gyres: subtropical and subpolar. Numerical techniques of bifurcation theory are used to stud the multiplicity and stability of the steady-state solution of a wind-driven, double-gyre, reduced-gravity, shallow water model. Branches of stationary solutions and their linear stability are calculated systematically as parameter are varied. This is one of the first geophysical studies i which such techniques are applied to a dynamical system with tens of thousands of degrees of freedom. Multiple stationary solutions obtain as a result of nonlinear interactions between the two main recirculating cell (cyclonic and anticyclonic) of the large- scale double-gyre flow. These equilibria appear for realistic values of the forcing and dissipation parameters. They undergo Hop bifurcation and transition to aperiodic solutions eventually occurs. The periodic and chaotic behaviour is probably related to an increased number of vorticity cells interaction with each other. A preliminary comparison with observations of the Gulf Stream and Kuroshio Extensions suggests that the intern variability of our simulated mid-latitude ocean is a important factor in the observed interannual variability o these two current systems.
Jiang, Shi, Fei-fei Jin, and Michael Ghil. 1995. “Multiple Equilibria, Periodic, and Aperiodic Solutions in a Wind-Driven, Double-Gyre, Shallow-Water Model.” Journal of Physical Oceanography 25 (5). American Meteorological Society: 764–786. Abstract
A reduced-gravity shallow-water (SW) model is used to study the nonlinear behavior of western boundary currents (WBCs), with particular emphasis on multiple equilibria and low-frequency variations. When the meridionally symmetric wind stress is sufficiently strong, two steady solutions–nearly antisymmetric about the x axis–are achieved from different initial states. These results imply that 1) the inertial WBCs could overshoot either southward or northward along the western boundary, depending on their initial states; and thus, 2) the WBC separation and eastward jet could occur either north or south of the maximum wind stress line. The two equilibria arise via a perturbed pitchfork bifurcation, as the wind stress increases. A low-order, double-gyre, quasigeostrophic (QG) model is studied analytically to provide further insight into the physical nature of this bifurcation. In this model, the basic state is exactly antisymmetric when the wind stress is symmetric. The perturbations destroying the symmetry of the pitchfork bifurcation can arise, therefore. in the QG model only from the asymmetric components of the wind stress. In the SW model, the antisymmetry of the system's basic response to the symmetric forcing is destroyed already at arbitrarily low wind stress. The pitchfork bifurcation from this basic state to more complex states at high wind stress is accordingly perturbed in the absence of any forcing asymmetry. Periodic solutions arise by Hopf bifurcation from either steady-state branch of the SW model. A purely periodic solution is studied in detail. The subtropical and subpolar recirculations, separation, and eastward jet exhibit a perfectly periodic oscillation with a period of about 2.8 years. Outside the recirculation zones, the solutions are nearly steady. The alternating anomalies of the upper-layer thickness are periodically generated adjacent to the ridge of the first and strongest downstream meander and are then propagated and advected into the two WBC zones, by Rossby waves and the recirculating currents, respectively. These anomalies periodically change the pressure gradient field near the WBCs and maintain the periodic oscillation. Aperiodic solutions are also studied by either increasing wind forcing or decreasing the viscosity.
Unal, Yurdanur Sezginer, and Michael Ghil. 1995. “Interannual and interdecadal oscillation patterns in sea level.” Climate Dynamics 11 (5): 255–278. Abstract

Relative sea-level height (RSLH) data at 213 tide-gauge stations have been analyzed on a monthly and an annual basis to study interannual and interdecadal oscillations, respectively. The main tools of the study are singular spectrum analysis (SSA) and multi-channel SSA (M-SSA). Very-low-frequency variability of RSLH was filtered by SSA to estimate the linear trend at each station. Global sea-level rise, after postglacial rebound corrections, has been found to equal 1.62±0.38 mm/y, by averaging over 175 stations which have a trend consistent with the neighboring ones. We have identified two dominant time scales of El Niño-Southern Oscillation (ENSO) variability, quasi-biennial and low-frequency, in the RSLH data at almost all stations. However, the amplitudes of both ENSO signals are higher in the equatorial Pacific and along the west coast of North America. RSLH data were interpolated along ocean coasts by latitudinal intervals of 5 or 10 degrees, depending on station density. Interannual variability was then examined by M-SSA in five regions: eastern Pacific (25°S–55°N at 10° resolution), western Pacific (35°S–45°N at 10°), equatorial Pacific (123°E–169°W, 6 stations), eastern Atlantic (30°S, 0°, and 30°N–70°N at 5°) and western Atlantic (50°S–50°N at 10°). Throughout the Pacific, we have found three dominant spatio-temporal oscillatory patterns, associated with time scales of ENSO variability; their periods are 2, 2.5–3 and 4–6 y. In the eastern Pacific, the biennial mode and the 6-y low-frequency mode propagate poleward. There is a southward propagation of low-frequency modes in the western Pacific RSLH, between 35°N and 5°S, but no clear propagation in the latitudes further south. However, equatorward propagation of the biennial signal is very clear in the Southern Hemisphere. In the equatorial Pacific, both the quasi-quadrennial and quasi-biennial modes at 10°N propagate westward. Strong and weak El Niño years are evident in the sea-level time series reconstructed from the quasi-biennial and low-frequency modes. Interannual variability with periods of 3 and 4–8 y is detected in the Atlantic RSLH data. In the eastern Atlantic region, we have found slow propagation of both modes northward and southward, away from 40–45°N. Interdecadal oscillations were studied using 81 stations with sufficiently long and continuous records. Most of these have variability at 9–13 and some at 18 y. Two significant eigenmode pairs, corresponding to periods of 11.6 and 12.8 y, are found in the eastern and western Atlantic ocean at latitudes 40°N–70°N and 10°N–50°N, respectively.

Jiang, N., J. David Neelin, and Michael Ghil. 1995. “Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific.” Climate Dynamics 12: 101–112. Abstract

Evaluation of competing El Niño/Southern Oscillation (ENSO) theories requires one to identify separate spectral peaks in equatorial wind and sea-surface temperature (SST) time series. To sharpen this identification, we examine the seasonal-to-interannual variability of these fields by the data-adaptive method of multi-channel singular spectrum analysis (M-SSA). M-SSA is applied to the equatorial band (4°N-4°S), using 1950 1990 data from the Comprehensive Ocean and Atmosphere Data Set. Two major interannual oscillations are found in the equatorial SST and surface zonal wind fields, U. The main peak is centered at about 52-months; we refer to it as the quasi-quadrennial (QQ) mode. Quasi-biennial (QB) variability is split between two modes, with periods near 28 months and 24 months. A faster, 15-month oscillation has smaller amplitude. The QQ mode dominates the variance and has the most distinct spectral peak. In time-longitude reconstructions of this mode, the SST has the form of a standing oscillation in the eastern equatorial Pacific, while the U-field is dominated by a standing oscillation pattern in the western Pacific and exhibits also slight eastward propagation in the central and western Pacific. The locations of maximum anomalies in both QB modes are similar to those of the QQ mode. Slight westward migration in SST, across the eastern and central, and eastward propagation of U, across the western and central Pacific, are found. The significant wind anomaly covers a smaller region than for the QQ. The QQ and QB modes together represent the ENSO variability well and interfere constructively during major events. The sharper definition of the QQ spectral peak and its dominance are consistent with the “devil's staircase” interaction mechanism between the annual cycle and ENSO.

Ghil, Michael, and Paola Malanotte-Rizzoli. 1991. “Data assimilation in meteorology and oceanography.” Advances in Geophysics 33. Elsevier: 141–266.
Ghil, Michael. 1989. “Meteorological data assimilation for oceanographers. Part I: Description and theoretical framework.” Dynamics of Atmospheres and Oceans 13 (3-4). Elsevier: 171–218.
Ghil, Michael, and S. Childress. 1987. Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics. Springer-Verlag, New York/Berlin, 485.
Ghil, Michael, R. Benzi, and G. Parisi, ed. 1985. Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. North-Holland Publ. Co., Amsterdam/New York, 449.