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Why do some places have a bimodal distribution of temperature?
The duration of daylight has a sinusoidal relationship to time of year, with increasing amplitude as you move away from the equator towards the poles. This is the main 'forcing function' determining temperature. If you plot the frequency distribution for a sine curve, it is close to uniform, with fairly steeply shelving shoulders. Superimpose random variation, and you would expect to get an approximately Gaussian distribution - like we get here in the UK.
So - why do some places have a fairly abrupt shift between a colder and a warmer season? I'm not thinking of tropical places with a wet and a dry season, but places well away from the equator. See for example
http://www.bmj.com/cgi/content/full/317/7164/978
which shows a clear bimodal pattern for maximum daily temperature in Yakutsk. Can anyone explain this please? It is said that nature abhors a vacuum, and one manifestation of this is that bimodal distributions tend to arise only as mixtures, e.g. log testosterone levels in adults. So, why do Yakutsk and many other places show this seemingly unnatural pattern?
Robert Newcombe
Newcombe@cf.ac.uk
So - why do some places have a fairly abrupt shift between a colder and a warmer season? I'm not thinking of tropical places with a wet and a dry season, but places well away from the equator. See for example
http://www.bmj.com/cgi/content/full/317/7164/978
which shows a clear bimodal pattern for maximum daily temperature in Yakutsk. Can anyone explain this please? It is said that nature abhors a vacuum, and one manifestation of this is that bimodal distributions tend to arise only as mixtures, e.g. log testosterone levels in adults. So, why do Yakutsk and many other places show this seemingly unnatural pattern?
Robert Newcombe
Newcombe@cf.ac.uk
Views: 269
Comment
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Comment by Robert Newcombe on July 29, 2009 at 2:30am -
OK, this explains why, during a particular season, the distribution can be bimodal. I can't see how this could be the explanation as to why, in some parts of the world, the circannular variation in temperature involves a fairly abrupt switch between colder and hotter weather, which is so marked as to lead to bimodality, as in the BMJ article I cited. Obviously this isn't the pattern we get here in the UK - but it is in many places. Any thoughts?
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Comment by Rob J Hyndman on July 28, 2009 at 5:36pm -
With time series data, bimodal distributions can arise for reasons other than mixtures. For example, some nonlinear time series models are known to produce bimodal distributions. See my 1995 J.Forecasting article
We also get a bimodal maximum temperature distribution in Melbourne, Australia, especially in summer. See my 1996 JCGS article. What happens here is that high pressure systems move slowly across the country and the maximum temperature increases to between 35 and 40 where it sits for a few days. Then a cold front passes through and the temperature suddenly drops, typically by about 15 degrees in 15 minutes. Then we will have a couple of days with the maximum temperature around 20-25 before the next high pressure system comes along.
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