Fourier Spectra of Aswan Nilometer data

River Nile at Aswan, taken by Tbachner

The River Nile at Aswan, from Wikipedia

This is the first in a series of posts on the Fourier Analysis of various datasets, some climatological and some not. I actually did these analyses purely for my own pleasure but then a conversation on Climate Audit made me promise to publish them as well.

This post concerns the analysis of the annual Nile level minima as recorded at Aswan from 622-1469 CE (and thus representing one of the longest continuous hydrological datasets in the world).

There have been claims made that the Nile data contained a 22-23 year oscillation that matched the Hale (solar) cycle. But its currently impossible to see whether one correlates well with the other in this data set since the Solar cycle was first systematically logged in the late 16th Century and this dataset only extends to the mid-15th Century.

Trying to find the Aswan Nilometer data online was extremely difficult, but eventually I found an academic using this and other datasets to attempt to measure the Hurst parameter, a measure of Long Term Persistence common in hydrologic datasets.

The original data is found in Hurst.zip from this page: http://www.stats.uwo.ca/faculty/aim/epubs/hurst/default.htm

The following diagrams were generated using Mathcad 14.

First a plot of the data

Now we look at the Fourier Spectrum of the data

and as claimed there is a 22-23 year periodicity in the data.

There is also a slightly stronger 18.4-18.5 year periodicity which could reasonably be associated with the lunar cycle. This lunar cycle appears in many other Fourier spectra including long term tide gauges (which I’ll present sometime soon)

There is also a much more recent dataset taken at Aswan prior to the building of the Aswan dam (in order to assess how big the Aswan dam needed to be to avoid going dry or overtopping).

These are the July-to-June means, Aswan, 1871-1945:

and the Fourier spectrum shows the Saros (lunar) cycle very clearly (the solar cycle not so clear, the short length of the dataset making resolution more difficult)

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