### Why We Cannot Predict Rainfall Extremes - Chaos, Lies and Butterlies

 Edward Lorenz
How accurate are weather forecasts?  Not very.

Call it chaos or call it the 'butterfly effect' - http://en.wikipedia.org/wiki/Butterfly_effect - it is "the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state."

This is the name given by Edward Lorenz (23 May 1917 – 16 April 2008), an American mathematician, meteorologist, and pioneer of chaos theory.  He was not consulted the the Weather Gone Wild authors, or others who hang their hat on faulty science .. maybe because he is dead and because science is secondary to crafting sensational journalism.

In practice the butterfly effect means we can't predict future extremes (like rainfall) that cause flooding.  Nope. All we can practically predict is weather will regress to its mean, but highs and lows we won't know.  Per the Wikipedia butterly effect article (or anyone who plans picnics based on weather):

"Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range (approximately a week in the case of weather) since it is impossible to measure the starting atmospheric conditions completely accurately. "
 Example 1-3 month precipitation forecast

In practice do we just predict weather to be average?  Yes. Environment Canada has predictions months in advance.  Here is the 1-3 month precipitation forecast:
http://weather.gc.ca/saisons/image_e.html?img=s123pfe1p_cal&bc=prob

And the 10-12 month forecast:
http://weather.gc.ca/saisons/image_e.html?img=s101112pfe1p_cal&bc=prob

White on the map means precipitation will be 'average'.  Or as Environment Canada puts it on the main page (http://weather.gc.ca/saisons/prob_e.html):

 Example 10-12 month precipitation forecast
"The occurrence of the white colour areas over Canada is more predominant for precipitation forecasts, which are generally less skillful than temperature forecasts, and increases with forecast range at longer lead times. The increasing occurrence of areas coloured in white over Canada implies diminishing ability of the forecasting system to make reliable and accurate predictions in these regions."

Look at the example to the right - ITS ALL WHITE, meaning in 10-12 months we can expect average precipitation  .. that is recurrence, trending back to the mean.  Any extremes get washed out in the predictions.

What about short time periods within the predicted month? Well, climate models do not have the temporal precision to drill down to minutes and hours because they have daily times steps.  Some day they likely will simulate smaller time steps, but don't confuse precision with accuracy - extra decimal places that infer precision in the output do not mean the overall number is close to reality.

So you have to ask yourself how you can predict changes in 5 minute and 1 hour extreme rainfall intensities 50 years from now with any accuracy. Climate modellers will suggest that you can but reputable scientists, like professor emeritus Edward Lorenz, would tell them its just lies and butterflies.

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."  — Albert Einstein, Sidelights on Relativity (1920)

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