Sad if sticks

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Sad if sticks

Postby Weatherlawyer » Fri Apr 18, 2008 8:55 pm

I didn't want to ask this in the Calc forum as it is likely to engender lots of useful advice about the various "If" algorithms.

If you were working on climate statistics and wanted to determine how many rainy days there are likely to be in any given year for any give region, the maths is relatively simple. I imagine you'd just divide the number of days in the year by the number of wet ones. Ad much the same idea to get monthly analysis or weekly etc.

So what slants do you put on the maths to do analysis over a longer time period?
As far as I can tell you'd only end up with a ratio of one in 6 or 10 or 27 or whatever it turns out to be.

So how do you go about ruling out what happens with sunspots or phases of the moon? What sort of If functions could you utilise?
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Re: Sad if sticks

Postby squenson » Sat Apr 19, 2008 1:44 pm

If I understand well your question, you want to know how to describe a phenomenon like "How often are there sunspots?" by a ratio. Contrary to the 'rainy day' this looks like a continuous process, so how can we define such ratio? I suggest:
1. Define a time interval -- let's say one hour as an example
2. Observe the sun during one hour. If you see a sunspot, put a 1, if not put a 0. Repeat this step several times.
3. Make the sum of all your 1's, and divide by the number of hours of observation. Call the result p, which is a number between 0 and 1.

If the observation is done over a large number of time intervals (many days or even weeks in my example), the result in step 3 represents the probability that a sunspot appears during one hour. What is the probability that there is no sunspots during n hours? If p is the probability of a sunspot, (1-p) is the probability of no sunspot, so (1-p)^n is the probability of no sunspots during n hours*, so 1 - (1-p)^n is the probability to see at least one sunspot during a period of n hours.

*: I assume that the events (in our case, the measure of sunspots during one hour) are independent of each others: like a dice roll, the result of the next roll does not depend on the previous one. In such case, the probabilities can be multiplied together.
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Re: Sad if sticks

Postby Weatherlawyer » Sat Apr 19, 2008 6:47 pm

It is the sort of thing I was describing.

Climatologists use a variety of best guesses to date good and bad growing years. I don't know how they can tell when a year was good for getting a lot of rain/sun, -or bad for getting too much but that's not the point.

A long time ago there was a theory that sunspots were related to the weather. Meteorologists and astronomers proved that wrong but how would they fall over in their calculations if there is an IF factor?

IF the sunspot is high latitude; IF there are a set of sunspots; IF they are so and so many degrees apart. How could you put that into a programme to calculate climate probabilities?

The same goes for ruling out things like lunar phases. Obviously the first thing you'd look at would be weather related to the type of phase. How would you introduce alternative "extenuating circumstances"?
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Re: Sad if sticks

Postby squenson » Sat Apr 19, 2008 9:09 pm

What you describe is called "correlation". You try to link two (or more) events and see if they happen at the same time. The type of graph "XY (scatter)" in Calc is good for such visual representation. For example, you could put on the x axis the number of millimeters of rain and on y axis the phase of the moon (0 being a new moon and 28 the next one). If the data looked aligned, then you have correlation. If they looked all around, then there is no correlation. While writing this answer, I found an excellent description on wikipedia: http://en.wikipedia.org/wiki/Correlation
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Re: Sad if sticks

Postby Weatherlawyer » Mon Apr 21, 2008 11:50 am

squenson wrote:What you describe is called "correlation".
http://en.wikipedia.org/wiki/Correlation


I know what it is called and why it does it but I can't waste time not understanding the maths.

Do you think you could pot and explanation of the thinking behind those calculi; not the maths so much as the logic? Looking at equations just freezes me up. TIA.

I had a stab at it with the stuff I am working on and I got this:

There is a basic common value [ρx,y] for any examples of variable behaviour: X and Y.

It correlates to the [for example] expected weather with random background low value seismic disturbances: E.

That could well vary to a standard deviation [σx and σy] where [for example] a modest hurricane [σx] would produce a series of not very low Lows instead of a Col of some 1010 mb [σy].

Which, if you wanted to get technical would equate to:
ρx,y = cov(X,Y)/σxσy = E((X - μx)(Y — μy))/σxσy

Which is as far as I could push that particular envelope with my limited grasp of maths.

http://en.wikipedia.org/wiki/Correlation

And which I posted here:
http://groups.google.com/group/uk.sci.weather/browse_frm/thread/e447ef84fbbc1ec9#
... where it will doubtless languish for a century and an half.
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Re: Sad if sticks

Postby foxcole » Wed Apr 23, 2008 5:42 am

You're asking the wrong people.

Weather calculations are not logic per se (unless you're a master of chaos theory) but a summation of historical data, data already collected and recorded, plotted, graphed, interpolated and extrapolated. No guesswork except for the usual methods of averaging over time. If you access that data, you presumably have the same means to 'predict' and program weather trends. The Old Farmers Almanac uses that method successfully. Check out their pages on How We Predict the Weather and The Art, Science, and Accident of Predicting the Weather.
Cheers!
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Re: Sad if sticks

Postby Weatherlawyer » Sat Apr 26, 2008 2:39 pm

No I am not asking the wrong people. It is general discussion after all.
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Re: Sad if sticks

Postby foxcole » Mon Apr 28, 2008 8:43 pm

Weatherlawyer wrote:No I am not asking the wrong people. It is general discussion after all.

Yes, it's a general discussion forum, but my point was that the information you're trying to calculate isn't pure calculation, it's based on collected data. How many people here have access to that data? And nobody can just assume or guess what data is available, and no one can suggest how to manipulate data without knowing what information the data offers. I pointed to some publicly available summaries, but those summaries had to come from raw data. The kinds of questions you're asking can't be answered here because any such guesswork would provide meaningless numbers, so it would be a futile exercise to try.
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