One approach to studying the dynamics of complex systems is to reconstruct phase space portraits of the original time series. The reconstructed phase space reveals the topological structure of attractors (if present) although their geometric shapes are distorted.
Today I present to you reconstructed phase space portraits, using the time-delay method, from some longer Arctic sea ice records, found here and here (pdf). The last record I looked at went back to 1979. The one below begins at 1972.
As in the earlier article, I have used a two-year lag.
There are some interesting differences we note with the slightly longer record. First of all, there appears to be a behavioural change at about 1989, before which the system is confined to the small yellow circle; and after which the system exhibits greater variability with a bias to a somewhat lesser extent. After 2004, as we saw last time, the system has been evolving towards a new state with smaller area covered. At this point we cannot predict where the next area of stability is.
There are those who predict that the Arctic is heading for ice-free conditions in a matter of a few years. Alternatively, we may be observing part of a multi-decade (or longer) oscillation, and that there may be a non-zero stable state somewhere near or below the present-day observed sea-ice extent.
To investigate this possibility, we consider records of Russian sea ice extent compiled by the Arctic and Antarctic Research Institute since the 1930s based on observational methods. As this paper was published a few years ago, the analysis of the hand-drawn charts has only been completed until 2005, although more up-to-date charts can be located on the AARI site. Below I have the reconstructed phase space portrait for autumn sea-ice extent (which I'm guessing compares to the September sea-ice record above) in the Russian Arctic.
There are appear to be two areas of attraction in the above graph--at about 4 million sq km, which characterized sea ice area from about 1950 to the end of the 1970s--and a second at about 4.5 million sq km, which characterized the system from 1980 until 2004. The final year suggests a drop in area of autumnal sea ice, and if the decline since then is anything like our first plot, we would expect the current state to be near the bottom left corner of the graph.
The Russian observations are consistent with other Arctic climate records which suggest a period of cooling until the late 1970s. This idea suggests that there is long-term variability in ice extent, with periods of cooling alternating with periods of warming. However, the current losses in ice extent are greater than any observed back to the 1940s. If we are to argue that the current warming is part of a long-term natural cycle, then it must be on the order of century-scale or longer.
Today I present to you reconstructed phase space portraits, using the time-delay method, from some longer Arctic sea ice records, found here and here (pdf). The last record I looked at went back to 1979. The one below begins at 1972.
As in the earlier article, I have used a two-year lag.
There are some interesting differences we note with the slightly longer record. First of all, there appears to be a behavioural change at about 1989, before which the system is confined to the small yellow circle; and after which the system exhibits greater variability with a bias to a somewhat lesser extent. After 2004, as we saw last time, the system has been evolving towards a new state with smaller area covered. At this point we cannot predict where the next area of stability is.
There are those who predict that the Arctic is heading for ice-free conditions in a matter of a few years. Alternatively, we may be observing part of a multi-decade (or longer) oscillation, and that there may be a non-zero stable state somewhere near or below the present-day observed sea-ice extent.
To investigate this possibility, we consider records of Russian sea ice extent compiled by the Arctic and Antarctic Research Institute since the 1930s based on observational methods. As this paper was published a few years ago, the analysis of the hand-drawn charts has only been completed until 2005, although more up-to-date charts can be located on the AARI site. Below I have the reconstructed phase space portrait for autumn sea-ice extent (which I'm guessing compares to the September sea-ice record above) in the Russian Arctic.
There are appear to be two areas of attraction in the above graph--at about 4 million sq km, which characterized sea ice area from about 1950 to the end of the 1970s--and a second at about 4.5 million sq km, which characterized the system from 1980 until 2004. The final year suggests a drop in area of autumnal sea ice, and if the decline since then is anything like our first plot, we would expect the current state to be near the bottom left corner of the graph.
The Russian observations are consistent with other Arctic climate records which suggest a period of cooling until the late 1970s. This idea suggests that there is long-term variability in ice extent, with periods of cooling alternating with periods of warming. However, the current losses in ice extent are greater than any observed back to the 1940s. If we are to argue that the current warming is part of a long-term natural cycle, then it must be on the order of century-scale or longer.
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