I’ve been collecting a few interesting curves from the 1/f generator at uBurns.com and here is a selection showing the kinds of features that are typical of 1/f noise and which we regularly see being mistaken for “something”.
Note
First all references to “forecasts” is just my attempt at humour. It is 1/f noise, but such noise makes it impossible to forecast and it’s ridiculous to attempt to do so.
The plots are:

• Top left: simulated raw data 1/f noise (equivalent to yearly global temperature)
• Top right: Smoothed raw data (equivalent to decadal smoothed global temperature)
• Bottom left: distribution of first half of raw data
• Bottom right: distribution of second half of raw data.

Trends

Habitat of error: IPCC report and almost every alarmist website.
A very common characteristic of 1/f noise is that there will appear long-term trends. These are just the coincidental juxtaposition of smaller trends which happen all to go the same direction, but they clearly confuse some academics who cannot understand that such trends are perfectly natural.

Continue reading →

Across at uBurns.com, a slow trickle of people have been looking at the page giving me a total of 221 page views. So, I thought there was enough data to do some preliminary stats.
First to recap: the climatic temperature data has a 1/f frequency response showing that natural variation can be modelled by 1/f noise. So assuming all the variation is natural we should be able to model climate with 1/f noise. But little has been written on the statistics of 1/f so it is difficult to know how it will behave. So, I have created a simple 1/f noise generator at uBurns.com and am using this to get data.
To do this, I’ve split the 1000 or so data points of each trial into 16 “buckets” and recorded the average value and slope of each bucket for each trial.
The predictions I made were as follows:

Variance increases proportional to square root.

As predicted the variance (sum of squares) of the 1/f noise (shown above in blue) increases with each successive “bucket” so that the increase is proportionate to the square root of the number of points (or in this case buckets). It’s not a perfect fit, but it looks like it’s heading that way. Continue reading →