I have completed the last of the five annexes for the revised Paleoceanography paper. Of course I am having some difficulty with the most telling comment from the editors, that is the significance, if any, of the conclusions drawn from the analysis. As a result, I may submit it to a more methods-based journal.
The most significant conclusion is the nature of dynamic change in all climate subsystems from the Early Quaternary to the Late Quaternary. All of the early Quaternary systems studied in this article show both limit cycles and Lyapunov-stable areas in their reconstructed phase space plots; whereas in the Late Quaternary we only observe Lyapunov-stable areas in the same plots.
It is possible to argue a topological similarity between the limit cycles and the LSAs, but their relation in phase space strongly implies different dynamics. Furthermore, the limit cycles are observed only in the Early Quaternary, where all records show a dominance by the 41 thousand year periodicity, whereas only LSAs are observed in the sections of the records dominated by 100-ky periodicity. The boundary between these two time periods is referred to as the Mid-Pleistocene transition (or by some authors, "revolution") and in the figures below is represented by the red box from about 1150 ka to 550 ka (by "ka" we mean thousands of years ago).
Ocean circulation (d13C data)
The d13C data refers to changes in the isotopic composition of 13C in the shells of microorganisms, which reflects variations in bottom water carbon chemistry; itself a reflection of global oceanic circulation. The record used in the figures above is from ODP sites 980 and 981, at a depth of about 2100 m. In the Raymo et al. (2004) paper, the differences in 13C between the Early and Late Quaternary were described in terms of cycle lengths (41 thousand-year cycles in the Early Quaternary vs. 100 thousand-year cycles in the Late Quaternary) and the apparent lack of variability between glacial and interglacial times in the Early Quaternary.
The PDP plots above show one other significant change--that of ocean dynamics. The change in dynamics between the Early and Late Quaternary is reflected in the change in geometry of the greatest probability density. The toroids we see in the Early and Mid Quaternary are reflective of stable cyclical behaviour. Those disappear in the Late Quaternary.
The regions of high probability in the Late Quaternary represent LSAs, and the presence of three distinct LSAs points to the existence of three separate metastable states. Distinctive metastable states in the context of oceanic circulation points to sudden changes in the organization of global circulation patterns, and this is an interpretation that has been proposed previously for the Late Quaternary (e.g., Broecker, 2000). Cyclicity in the 13C data is more difficult to interpret--it may be due to a series of gradual changes in the relative strengths of different currents over a period of time. Such gradual changes in oceanic circulation may be difficult to infer on the basis of one-dimensional data set projections.
Global ice volume
The deep-sea d18O data measure variations in deep water chemistry, specifically the variation in isotopic composition of seawater caused by the growth and decay of large (isotopically light) continental ice sheets. They are thus a proxy for global ice volume.
As noted for the oceanic circulation proxy, probability density plots of the 2-d phase space for the ice volume proxy show toroidal forms suggestive of limit cycle behaviour. There are no apparent toroids in either the Mid- or Late Quaternary. In the Late Pleistocene, we see four distinct probability peaks, each of which represents a stable ice volume.
In the early Quaternary, ice volume changed slowly, gradually, and in a repetitive fashion. By the mid- to Late Quaternary, ice volume changes occurred in the form of rapid, non-repetitive "jumps" from one volume to another as noted previously.
References:
Broecker, W., 2000. Was a change in thermohaline circulation responsible for the Little Ice Age? Proceedings of the National Academy of Sciences 97(4): 1339–1342.
Huybers, P., 2007. Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression. Quaternary Science Reviews, 26: 37-55.
Raymo, M. E., Oppo, D. W., Flower, B. P., Hodell, D. A., McManus, J. F., Venz, K. A., Kleiven, K. F., and McIntyre, K., 2004. Stability of North Atlantic water masses in face of pronounced climate variability during the Pleistocene. Paleoceanography, 19, PA2008, doi:10.1029/2003PA000921.
The most significant conclusion is the nature of dynamic change in all climate subsystems from the Early Quaternary to the Late Quaternary. All of the early Quaternary systems studied in this article show both limit cycles and Lyapunov-stable areas in their reconstructed phase space plots; whereas in the Late Quaternary we only observe Lyapunov-stable areas in the same plots.
It is possible to argue a topological similarity between the limit cycles and the LSAs, but their relation in phase space strongly implies different dynamics. Furthermore, the limit cycles are observed only in the Early Quaternary, where all records show a dominance by the 41 thousand year periodicity, whereas only LSAs are observed in the sections of the records dominated by 100-ky periodicity. The boundary between these two time periods is referred to as the Mid-Pleistocene transition (or by some authors, "revolution") and in the figures below is represented by the red box from about 1150 ka to 550 ka (by "ka" we mean thousands of years ago).
Ocean circulation (d13C data)
Probability density plots of the 2-D phase space of d13C data from
Raymo et al. (2004) for the Early Quaternary (above),
Mid Quaternary (middle) and Late Quaternary (bottom).
The d13C data refers to changes in the isotopic composition of 13C in the shells of microorganisms, which reflects variations in bottom water carbon chemistry; itself a reflection of global oceanic circulation. The record used in the figures above is from ODP sites 980 and 981, at a depth of about 2100 m. In the Raymo et al. (2004) paper, the differences in 13C between the Early and Late Quaternary were described in terms of cycle lengths (41 thousand-year cycles in the Early Quaternary vs. 100 thousand-year cycles in the Late Quaternary) and the apparent lack of variability between glacial and interglacial times in the Early Quaternary.
The PDP plots above show one other significant change--that of ocean dynamics. The change in dynamics between the Early and Late Quaternary is reflected in the change in geometry of the greatest probability density. The toroids we see in the Early and Mid Quaternary are reflective of stable cyclical behaviour. Those disappear in the Late Quaternary.
The regions of high probability in the Late Quaternary represent LSAs, and the presence of three distinct LSAs points to the existence of three separate metastable states. Distinctive metastable states in the context of oceanic circulation points to sudden changes in the organization of global circulation patterns, and this is an interpretation that has been proposed previously for the Late Quaternary (e.g., Broecker, 2000). Cyclicity in the 13C data is more difficult to interpret--it may be due to a series of gradual changes in the relative strengths of different currents over a period of time. Such gradual changes in oceanic circulation may be difficult to infer on the basis of one-dimensional data set projections.
Global ice volume
Probability density plots of the 2-D phase space of d18O data from
Huybers (2007) for the Early Quaternary (above),
Mid Quaternary (middle) and Late Quaternary (bottom).
The deep-sea d18O data measure variations in deep water chemistry, specifically the variation in isotopic composition of seawater caused by the growth and decay of large (isotopically light) continental ice sheets. They are thus a proxy for global ice volume.
As noted for the oceanic circulation proxy, probability density plots of the 2-d phase space for the ice volume proxy show toroidal forms suggestive of limit cycle behaviour. There are no apparent toroids in either the Mid- or Late Quaternary. In the Late Pleistocene, we see four distinct probability peaks, each of which represents a stable ice volume.
In the early Quaternary, ice volume changed slowly, gradually, and in a repetitive fashion. By the mid- to Late Quaternary, ice volume changes occurred in the form of rapid, non-repetitive "jumps" from one volume to another as noted previously.
References:
Broecker, W., 2000. Was a change in thermohaline circulation responsible for the Little Ice Age? Proceedings of the National Academy of Sciences 97(4): 1339–1342.
Huybers, P., 2007. Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression. Quaternary Science Reviews, 26: 37-55.
Raymo, M. E., Oppo, D. W., Flower, B. P., Hodell, D. A., McManus, J. F., Venz, K. A., Kleiven, K. F., and McIntyre, K., 2004. Stability of North Atlantic water masses in face of pronounced climate variability during the Pleistocene. Paleoceanography, 19, PA2008, doi:10.1029/2003PA000921.
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