I want to ask you for advice. In a preliminary study published in 2009 at the State University of Mordovia, Russian Federation (Климатические изменения в пойме Балта-Брэилей.), I analyzed, using software Benoit , fractal analysis distribution curves of mean annual and mean monthly temperatures ( of Braila meteorological station) for the period 1878-1964 (before impoundment of wetlands of Braila), compared the period 1964-2007 (after damming, when the wetlands of Braila became polder and suffered intense anthropogenic change by draining, clearing, leveling, irrigation, pesticide and fertilizer use specific chemical intensive agriculture).
Fractal analysis of annual and monthly distribution curves of Braila meteorological station temperature before and after damming reflect the upward trend after damming the fractal dimension distribution values within a year. This indicates an increase in complexity (due to global climate change), the existence of many degrees of freedom that may materialize in the occurrence of more frequent risk factors. For example: the annual thermal distribution curve fractal dimension increased from 1.100 before to 1.109 after damming. I noticed the same trend for precipitation and evapotranspiration and. I await your comments.
The basic idea is a good one, but you’ve got to realize that there are three fundamentally different scaling regimes: the weather regime (below about 10 days), the low frequency weather regime (10 days to 10-30 yrs) and the climate regime, 10-30 yrs to 50- 100 kyrs. Also, fractal dimensions are not the best way of characterizing the regimes, fluctuations are best, and Haar wavelets are a good compromise. For a review, see the following (you can download with the link).
Lovejoy, S., D. Schertzer, 2012: Low frequency weather and the emergence of the Climate. In Complexity and Extreme Events in Geosciences, Eds. A. S. Sharma, A. Bunde, D. Baker, V. P. Dimri, AGU monographs (in press).
http://www.physics.mcgill.ca/~gang/ftp.transfer/New.galley.2A_2011GM001087.SL.24.2.12.pdf
It is not evident to me how you would demonstrate the significance of this -- do you have some underlying theoretical explanation? Why would you use fractal analysis as opposed to some more traditional time series analysis or multivariable regression where you might be able to say something about statistical significance? I am just asking -- I don't know enough about fractal analysis to make a meaningful comment other than that.
Dear colleague I am according with Finley, it depends of the software used. Remember that each software use specific variables, so you need find your response on this model used. But the analyses fractal if necesary to compare wiht either the others results or others time series analysis multivariables regression (depend of the sowftware used),
The basic idea is a good one, but you’ve got to realize that there are three fundamentally different scaling regimes: the weather regime (below about 10 days), the low frequency weather regime (10 days to 10-30 yrs) and the climate regime, 10-30 yrs to 50- 100 kyrs. Also, fractal dimensions are not the best way of characterizing the regimes, fluctuations are best, and Haar wavelets are a good compromise. For a review, see the following (you can download with the link).
Lovejoy, S., D. Schertzer, 2012: Low frequency weather and the emergence of the Climate. In Complexity and Extreme Events in Geosciences, Eds. A. S. Sharma, A. Bunde, D. Baker, V. P. Dimri, AGU monographs (in press).
http://www.physics.mcgill.ca/~gang/ftp.transfer/New.galley.2A_2011GM001087.SL.24.2.12.pdf
If you want to see a difference of complexity between different time series you could use some entropy measures like aproximate entropy (ApEn). If not, you should use wavelets like Lovejoy said.
Thank you for advice. We performed analyzes on time series analysis or multivariable regression and then I wanted to see if fractal analysis indicates the same issues. I analyzed a fractal dimension and Hurst exponent relation. I did not done other fractal analysis on other datasets. What we do is only a preliminary study. You take into account the guidance received and I will analyze the database strings and using Haar wavelets and ApEn. Do you mind if when I make determinations, I will require an advice?
My experience with estimating self-similarity measures such as "fractal dimensions" is that, except you have really clear and really many data, you cannot estimate a fractal dimension to 1% accuracy...
plot the differentiated scaling curve and see where, how broad and how exactly determined the plateau is...
Moreover, I agree with above comments that it will be hard to draw conclusions from the results (even if you have
evidence that the dimension changes) for the underlying system.
Fractal analysis of time series usually aims at establishing measures of persistence, i.e. whether some reliable periodicities and, most usually, long term correlations can be found hidden in the data. For climate and/or meteorological series, reliable data obtained from instrumental records form rather short series, and as M Timme points out, accuracy is greatly diminished. On data stemming from proxy reconstructions, there are some added problems...
I would suggest that after reduplicating, boostrapping and other statistical refinements, a multifractal analysis could be performed. Regime changes could then be read in the log-log plots.
See e.g. Kantelhardt J et al. (2002) Multifractal detrended fluctuation... Physica A 316, pp.87-114
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