Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Wednesday, July 8, 2015

Noise reduction and analysis of a long reconstructed record of atmospheric CO2

The CO2 record used last time was presented (largely by interpolation) at 100 year intervals. This provided rather more data than were really needed for the analysis that I had in mind. To produce the plot in yesterday's post, I subsampled the data to produce a record with sample intervals of 1000 years.

The first step is to define regions of stability over each time window. To do this, we reconstruct phase space portraits for each window of data (anywhere from 100 to 200 ky)*.

These graphs have previously been described as looking like they were constructed on an etch-a-sketch. I would say the one on the left looks more like the etch-a-sketch drawings I remember. I would have posted a link to the Zerohedge comments, but the site was down.

Both of the above graphs represent reconstructed phase space plots constructed over a 100-ky window. The one on the left is constructed from a time series with a 100-year sample interval. The one on the right is constructed from a time series with a 1000-year sample window (90% of the data were discarded). At the scale of my investigation, the overall structure of both graphs is the same. The higher resolution data just provides a noisier version of the well-known partially vivisected kangaroo formation.

Many paleoclimate records analyzed in this way commonly show multistability (interpreted as more than one possible equilibria). Multistability may be demonstrated in reconstructed phase space portraits through variable density of observations in phase space.

The above figure shows the successive evolution of the state space through time at 1000 year intervals. Between about 110 and 20 ka, the system evolved through phase space only very slowly--times of slow evolution suggest stability.

Multistability is probably best inferred from phase space density plots. The graph above suggests at least two major areas of stability (perhaps four if you are a splitter rather than a lumper).

Once regions of stability are identified, the next task is characterizing climate by the sequence and timings of the transitions between different regions of stability.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*Note ky = thousand years (i.e., an interval)
ka = thousand years ago (i.e., a specific time)
Similarly, Ma = million years ago, and My = million years (interval)


  1. RE: Your observation

    "A couple of months ago I thought inflation had come to China. But it has really come here. Lots of things have doubled in price in one year."

    1. The exchange rate has been near constant for a year.

    2. Shanghai index went on a wild ride up and some down in a year. I was watching the stock market drop after going up 2.5 times in a year. The western finance pumpers are derisively talking all about it going down x%. I was watching it just before it turned down. Jim Rogers was talking about looking to buy more. He likes to buy low. I was not thinking of it as really bad at all except for the for the latecomers, because it was up a lot.

    So, now you bring up rise in prices which reduces the real gain in the market. What do you think is going on? Do you thing the exchange rate might change? The market might rebound? What did you see. What do you think about it? Can we break the bank of Peking? Is the currency pegged?

  2. The problem with twitter is that the restriction in characters (and the lack of thought about the postings) sometimes leads to ambiguities. By "here", I mean Canada, which I have just returned to. I used to pick up a lot of things (staples, dried fruit, etc.) at bulk barn and have been blown away by the change in prices of some products in less than a year. Some items, however, have scarcely changed in price at all.

    China "pegs" its currency to the US dollar, but episodically changes the peg. I am sure that if they feel it to their advantage, they will alter the peg. The US dollar has risen a lot over the past year.

    In the long run, betting against the Chinese market is probably like betting against the US market in the 19th century. Sure, there were frauds and brief panics where you could lose money, but for the long term, the money was made on the long side.

    I don't think the Chinese market can rebound convincingly until all the people who need to sell have sold. Unfortunately, now that they are not allowed to, it could be a very long time indeed.

  3. I tried analysis of a short reconstructed record of atmospheric CO2 data measured on the top of the volcano.

    I got nifty plots but could not figure out an equation.