3 Large-Scale Ocean Circulation: 4 a Dynamical Systems Approach (original) (raw)

XXXXXX 75 tal data that has been collected over the last century and 76 one half contributes, in turn, to a more and more 77 complete picture of the climate system's variability. 78 [3] The purpose of the present review paper is to describe 79 the role of the ocean circulation in this variability and to 80 emphasize that dynamical systems theory can contribute 81 substantially to understanding this role. The intended audi-82 ence and the way prospective readers can best benefit from 83 this review are highlighted in Box 1/Appendix A1. To 84 facilitate diverse routes through the paper, we have included 85 a glossary of the principal symbols in Table 1 and a list 86 acronyms in Table 2. 87 1.1. Climate Variability on Multiple Timescales 88 [4] An ''artist's rendering'' of climate variability on all 89 timescales is provided in Figure 1a. The first version of 90 Figure 1a was produced by Mitchell [1976], and many 91 versions thereof have circulated since. Figure 1a is meant 92 to summarize our knowledge of the spectral power S = S w , i.e., the amount of variability in a given frequency band, between w and w + Dw; here the frequency w is the inverse of the period of oscillation and Dw indicates a small increment. This power spectrum is not computed directly by spectral analysis from a time series of a given climatic quantity, such as (local or global) temperature; indeed, there is no single time series that is 10 7 years long and has a sampling interval of hours, as Figure 1a would suggest. Figure 1a includes, instead, information obtained by analyzing the spectral content of many different time series, for example, the spectrum (Figure 1b) of the 335-year long record of Central England Temperatures. This time series is the longest instrumentally measured record of any climatic variable. Given the lack of earlier instrumental records, one can easily imagine (but cannot easily confirm) that the higherfrequency spectral features might have changed, in amplitude, frequency, or both, over the course of climatic history. t1.1 TABLE 1. Glossary of Principal Symbols Symbol Definition Section t1.2 XXXXXX Dijkstra and Ghil: OCEAN CIRCULATION VARIABILITY 3 of 38 XXXXXX 206 eral spectral peaks of variability can be clearly related to 207 forcing mechanisms; others cannot. In fact, even if the 208 external forcing were constant in time, that is, if no 209 systematic changes in insolation or atmospheric composi-210 tion, such as trace gas or aerosol concentration, would 211 occur, the climate system would still display variability 212 on many timescales. This statement is clearly true for the 213 3-7 days synoptic variability of midlatitude weather, which 214 arises through baroclinic instability of the zonal winds, and 215 the ENSO variability in the equatorial Pacific, as discussed 216 above. Processes internal to the climate system can thus 217 give rise to spectral peaks that are not related directly to the 218 temporal variability of the forcing. It is the interaction of 219 this highly complex intrinsic variability with the relatively 220 small time-dependent variations in the forcing that is 221 recorded in the proxy records and instrumental data. 222 1.2. Role of the Ocean Circulation 223 [12] We focus in this review on the ocean circulation as a 224 source of internal climate variability. The ocean moderates 225 climate through its large thermal inertia, i.e., its capacity to 226 store and release heat and its poleward heat transport 227 through ocean currents. The exact importance of the latter 228 relative to atmospheric heat transport, though, is still a 229 matter of active debate [Seager et al., 2001]. The large-230 scale ocean circulation is driven both by momentum fluxes 231 as well as by fluxes of heat and freshwater at the ocean-232 atmosphere interface. The near-surface circulation is dom-233 inated by horizontal currents that are mainly driven by the 234 wind stress forcing, while the much slower motions of the 235 deep ocean are mainly induced by buoyancy differences. 236 [13] The circulation due to either forcing mechanism is 237 often described and analyzed separately for the sake of 238 simplicity. In fact, the wind-driven and thermohaline circu-239 lation together form a complex three-dimensional (3-D) 240 flow of different currents and water masses through the 241 global ocean. The simplest picture of the global ocean 242 circulation has been termed the ''ocean conveyor'' [Gordon, 243 1986; Broecker, 1991]; it corresponds to a two-layer view 244 where the vertical structure of the flow field is separated 245 into a shallow flow, above the permanent thermocline at 246 roughly 1000 m, and a deep flow between this thermocline 247 and the bottom (i.e., between a depth of roughly 1000 m and 248 4000 m); see Figure 2. The unit of volume flux in the ocean 249 is 1 Sv = 10 6 m 3 s À1 , and it equals approximately the total 250 flux of the world's major rivers. MacDonald and Wunsch 251 [1996] and Ganachaud and Wunsch [2000] have provided 252 an updated version of this schematic representation of the 253 ocean circulation. 254 [14] In the North Atlantic, for instance, the major current 255 is the Gulf Stream, an eastward jet that arises through the 256 merging of the two western boundary currents, the north-257 ward flowing Florida Current and the southward flowing 258 Labrador Current. In the North Atlantic's subpolar seas, 259 about 14 Sv of the upper ocean water carried northward by 260 the North Atlantic Drift, the northeastward extension of the 261 Gulf Stream, is converted to deepwater by cooling and 262 salinification. This North Atlantic Deep Water (NADW) XXXXXX Dijkstra and Ghil: OCEAN CIRCULATION VARIABILITY 4 of 38 XXXXXX 263 flows southward, crosses the equator, and joins the flows 264 in the Southern Ocean. The outflow from the North 265 Atlantic is compensated by water coming through the 266 Drake Passage (about 10 Sv) and water coming from the Indian Ocean through the Agulhas Current system (about 268 4 Sv). Part of the latter ''Agulhas leakage'' may originate 269 from Pacific water that flows through the Indonesian 270 Archipelago. We refer to earlier reviews [Gordon, 1986; 271 Schmitz, 1995; World Ocean Circulation Experiment 272 (WOCE), 2001] for more complete information on the 273 circulation in each major ocean basin as well as from one 274 basin to another. 275 [15] Changes in the ocean circulation can influence 276 climate substantially through their impact on both the 277 meridional and zonal heat transport. This can affect mean 278 global temperature and precipitation, as well as their distri-279 bution in space and time. Subtle changes in the North Atlantic surface circulation and their interactions with the 281 overlying atmosphere are thought to be involved in climate 282 variability on interannual and interdecadal timescales, as 283 observed in the instrumental record of the last century 284 [Martinson et al., 1995; Ghil, 2001]. Changes in the 285 circulation may also occur on a global scale, involving a 286 transition to different large-scale patterns. Such changes 287 may have been involved in the large-amplitude climate 288 variations of the past [Broecker et al., 1985]. 289 1.3. Modeling Hierarchy 290 411 Those fixed points for which eigenvalues with s r > 0 exist 412 are unstable, since the perturbations are exponentially 413 growing. Fixed points for which all eigenvalues have s r < 0 414 are linearly stable. 415 [27] Discretization of the systems of partial differential 416 equations (PDEs) that govern oceanic and other geophysical 417 flows [Gill, 1982; Pedlosky, 1987, 1996] leads to a system 418 of ODEs (1), with large n. In many cases the linearization 419 (3)-(5) yields solutions that are the classical linear waves of 420 geophysical fluid dynamics. These include neutrally stable 421 waves, like Rossby or Kelvin waves, or unstable ones, like 422 those associated with the barotropic or baroclinic instability 423 of ocean currents. 424 [28] If the number of solutions or their stability prop-425 erties change as a parameter is varied, a qualitative 426 change occurs in the behavior of the dynamical system: 427 The system is then said to undergo a bifurcation. The 428 points at which bifurcations occur are called bifurcation 429 points or critical points. A bifurcation diagram for a 430 particular system (1) is a graph in which the variation 431 of its solutions is displayed in the phase-parameter space. 432 Information on the most elementary bifurcations is pre-433 sented in Box 2/Appendix A2. 434 [29] Bifurcation theory goes beyond classical, linear 435 analysis in studying the nonlinear saturation of and inter-436 actions between linear instabilities. When the interaction