## Selvam: Universal Inverse Power Law Distribution for Indian Region Rainfall

Space-time fluctuations of meteorological parameters exhibit selfsimilar fractal fluctuations. Fractal space-time fluctuations are generic to dynamical systems in nature such as fluid flows, spread of diseases, heart beat pattern, etc. A general systems theory developed by the author predicts universal inverse power law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution is in close agreement with observed fractal fluctuations of all size scales in the monthly total Indian region rainfall for the 141 year period 1871 to 2011.

Universal Inverse Power Law Distribution for Indian Region Rainfall

From: A. Mary Selvam

[v1] Fri, 3 May 2013 09:52:00 GMT (434kb)

arXiv:1305.1188 [physics.gen-ph]

The Gaussian probability distribution used widely for analysis and description of large data sets underestimates the probabilities of occurrence of extreme events such as stock market crashes, earthquakes, heavy rainfall, etc. The assumptions underlying the normal distribution such as fixed mean and standard deviation, independence of data, are not valid for real world fractal data sets exhibiting a scale-free power law distribution with fat tails (Selvam, 2009). There is now urgent need to incorporate newly identified fractal concepts in standard meteorological theory for realistic simulation and prediction of atmospheric flows.

I guess this isn’t about skewing the normal distribution to the right with the general change of the measured parameters, rather trying to recognize the extreme outliers which could be the basis for disaster modelling and safety limits for infrastructure and such. In other words, predicting the frequency of events that are outside the results of normally (skewed or not) distributed climate models. Way too advanced maths for me.

My understanding is the same as yours.

Hmmm … we have data here ….

ftp://www.tropmet.res.in/pub/data/rain/iitm-regionrf.txt

As for the math regarding that data, she (?) basically just binned the data and then calculated a probability distribution (number of events in the bin divided by the total number events). Straight forward stuff.

The inverse power model is described above, the key being P = τ^-4*σ. Sigma σ is derived from the standard deviation of the binned data.

But what about tau τ? It’s in the intro …

“the golden mean (τ 1.618)”http://en.wikipedia.org/wiki/Golden_ratio

http://en.wikipedia.org/wiki/Golden_mean_(philosophy)

“Beauty is truth, truth beauty,” — that is allYe know on earth, and all ye need to know.

That should be sufficient to reproduce the results …

ok, missed the link to the paper somehow. τ – 1.618 seems to come up in so many places, once i found someone linking it to electron orbitals (only some of them), and another amateur study by someone else linked it to planetary orbits.