Temperature History

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Temperature History

• An Application of Trigonometric Functions

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San Antonio Average Temperatures 1890 - 1899
Source http//www.srh.noaa.gov/ewx/html/cli/sat/
satmontemp.htm
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(No Transcript)
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Average Temperature 1890s
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Some Things to Notice

• Average of all temperatures 69
• Average of highest annual temps 84
• Average of lowest annual temps 53
• Cycle seems to repeat itself every 12 months
  (surprise -)

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Could we model this behavior?

• Choice might be a sine function

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Average Temperature 1890s vs model
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Not Quite

• Too low.
• Remember the average of all temps for the decade?
  Lets change our equation a bit. Vertical shift
  69

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Average Temperature 1890s vs model rev 1
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Closer, but

• Our curve cycles too much
• Recall that the period of Sine is 2p (approx
  6.28..), but we want to have a period of 12
  months

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Average Temperature 1890s vs model rev 2
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Better, but

• Were still about four months out of phase

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Average Temperature 1890s vs model rev 3
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Not Bad

• Except for a couple of months (Jan 1892, Dec
  1898, Feb 1899) the function we modeled matches
  fairly well
• Shall we compare it against another decade?

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Average Temperature 1930s vs model rev 3