California Central Valley, Death Valley May See New Temperature Records Week Of 1 July

[progree]

3. A small little change in average temperatures dramatically increases the number of days with extreme temperatures

Last edited Mon Jul 1, 2024, 11:19 PM - Edit history (1)

if, for example, the average daily high in July in some locale like Phoenix is 105 degrees with a 4 degree standard deviation, and normally distributed:

then the number of July days when the high is 117 or above (3 standard deviations above the mean) is 0.1350% of July days.

In Excel, the formula for finding the area under the normal distribution from 117 to infinity with an average of 105 and standard deviation of 4 is:
=1-NORM.DIST(117,105,4,TRUE)
which gives an answer of 0.001350 which is 0.1350%

OK, so no biggie. So what?

Now lets say that due to climate change so far, the average July daily high temperature has shifted by just 2% to the right, from 105 to 107.1

then the number of July days when the high is 117 or above changes to 0.6662% of July days.

That's a 4.94 fold increase (394% increase) in the number of 117+ degree July days for just a 2% increase in the average.

Shift the average 4% to the right, from 105 to 109.242, and you get 2.622% of July days are 117+, a 19.424 fold increase (1842% increase) in the number of 117+ July days.

More details on the methodology at https://www.democraticunderground.com/1127174636#post1

For the daily highs in July 2023 in Phoenix I used

https://weatherspark.com/h/m/145521/2023/7/Historical-Weather-in-July-2023-at-Phoenix-Sky-Harbor-International-Airport-Arizona-United-States#Figures-Temperature
# Average daily July high in 2023: about 105 degrees, the 10% - 90% confidence bands are about 100 to 110 (reading from the graph). Bandwidth = 10.
# The 10 to 90% confidence interval of the normal distribution is -1.281552sigma to +1.281552sigma
# When the 10 to 90% confidence bandwidth is 10, then
. . the standard deviation, Sigma, is 3.90152: ( 10/2 = 5,   5/1.281552 = 3.90152 )   I rounded to 4 in the above example

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The same principle applies to other climate change events, e.g. the severity of storms or what have you -- a small shift in the average results in a huge increase in the number of extreme events.