EXECUTIVE SUMMARY:
- Measure twice and cut once says the old saw. According to your
highschool math class by averaging N repeated measurements together
you can reduce the error by a factor of 1/sqrt(N).
Hillbillies
generally say the error in the average temperature if N measurements
is still +1C because each thermometer has (for argument's sake) that error.
- But the math formula assumes the measurements are "independent" and
"unbiased".
- One web page tries to average up available met stations to arrive at
an average temp of the earth. The page pointedly maintains it uses
unprocessed temperature data in deg C. Unfortunately the siting of
met stations is not "random". They mostly cluster together around
population centers. They also are not very complete. Even (say)
16000 met stations represent only around 1% of the land's surface,
and much less the total surface of the earth.
- We conduct an experiment with 1000s of met stations from the GHCN v3
dataset. Using larger and larger samples from the TAVG for a given
date we determine how far the sample average is from the average of
all stations for that date. We want to know whether the error is
reducing according to 1/sqrt(N) or maybe is much worse.
- It turns out 80% of the results obtained showed an error of +-8C. It
seems as samples got larger and larger the error rate "got stuck"
and samples larger than ~20 made no improvement to the error bounds
of the average of the TAVG's.
- A power law was fit to the observed trend and showed the error
(ignoring it seemed to get stuck at 8) *seemed* to follow 1/N^0.1 --
a much slower rate of improvement than 1/sqrt(N). Using that
formula showed the error for an average of 6000 or 16000 stations
would still be more than +-5C.
- It seems the "add it up and average" of clustered met stations that
anyway represent only 1% of land area directly (i.e. assuming each
met station faithfully represents the temperature of the surrounding
100 km2) is just junk science.
- By dividing the oceans up into e.g. 2x2 km grids and measuring the
IR from each at nighttime and averaging them all up for a 24 hr
period estimates the average temp of the oceans on the same date as the
dumb method but got a result of 15.85C with a claimed 3 digits of accuracy.
Not surprisingly that compared favorably with other published results.
For non-math types it's sometimes hard to understand that scientists
can calculate the warming trend attributed to AGW without actually
bothering to calculate an explicit "average temperature of the earth".
To many people it seems impossible to calculate rate of increase in X
without calculating X's and looking at how they change over time.
The resolution of the conundrum involves only high school level math.
Each met station on the earth is liable to see the effect of global
warming. If look at a number of them and "average the trends" you tend
to zero in on a very good estimate of the overall trend warming for AGW.
It's also true that each met station also is an approximation of the
average temperature of the earth. It's just that it's a very noisy
estimate. Adding up noisy estimates of something without careful
handling just adds up the noise and eventually swamps the underlying signal.
This is a useful trick lie bloggers and others employed by PR agencies
to fuzz up the public's understanding of what's going on with anything
that might be subject to product liability claims. They add up
disparate numbers and magnify the noise and stand back saying --
"look, nothing to see here".
In the case of the "average temperature of the earth" -- that some
climate denier sites tend to point to as evidence the earth is not
warming and there are no more tornadies, floods, hurricanes and
heatwaves like the newspapers and scientists is sayin -- the dumb way
of calculating this magic number is guaranteed to be way off. Usually
they explicitly say they are using "unprocessed temperature data".
And it's amazing how bad this method is. It's really really laughable.
but as with most science, you have to have an IQ over 90 or have
graduated highschool to get the joke.
Standard highschool math (I met this in year 11) shows you how to
calculate the uncertainty in the calculation of an average of some numbers.
They say if you measure twice you need to cut only once. In some way >averaging 2 measurements is "better" than just one. But how much better?
The highschool math shows you that if you measure something N times
each with an "accuracy" of S then the error in the average of the >measurements is S/sqrt(N). if you take 2 measurements and average then
the error is reduced to 1/sqrt(2) -- about .70, i.e. about a 30%
improvement on 1 measurement. If you measure it 9 times and average
then then error is reduced by almost 70%.
But this formula relies on some assumptions. And the most important is
that the measurements are independent of one another. I.e. if you're
cutting a length of timber you really should stand up, walk around,
come back and measure it again. Not just stand there and look at the
tape measure twice.
To measure the temperature of the earth -- if you wanted to do that --
you would need to measure the temperature of random spots on the
planet at more or less the same time. If each thermometer had an
accuracy of (say) 0.1C then taken 100 "independent" measurements would
reduce the error to 1/sqrt(100) i.e. 1/10 of .1 == .01C.
This was the basic error in the old climate denier claim you cant
measure any temperature better than +-1C. I remember some guy -- let's
call him Brent -- arguing about this basic highschool math for months
before someone must have taken him aside and showed him a school
textbook. He then deleted all those posts he's made because it seemed
at the time he was a college tutor.
But if the temperature measurements are not carefully selected to be
random then the error does not reduce as expected. It can even grow.
So this takes up so the exercise of calculating the "average
temperature of the earth" by summing up the "unprocessed temperature >measurements" from 1000s of (we assume) almost exclusively land-based >stations at some point in time.
We don't expect temp stations to be sited randomly all over the earth.
They are usually, e.g., near population centers and they -- fore sure
-- cluster around latitude 45N.
If you ask only registered voters for one political party their
voting intentions and averaging them out you will not predict the
outcome of too many elections.
But it is incredible just how bad this average of all stations without >twiddling is.
I did an experiment with the GHCN v3 stations. There are 100k of them
in the database, but at any one time only around 7k of them are
active. Picking a random 20th cent date in August I found about 2k of
them had a TAVG measurement for that date.
I made a little program to take averages of random subsets of those
stations, increasing the sample size each time, and plotted out the
average difference between the sample average and the average of all
2k stations for that date.
The results were illuminating:
Samplesize Avg abs err Stddev(AAE)
1 8.16 12.9751
2 12.4845 11.6322
3 16.3943 12.3321
4 15.0626 10.0463
5 14.1675 8.85287
6 13.5807 8.45744
7 13.7353 7.57161
8 13.3503 7.76353
9 11.1113 7.04888
10 12.5444 6.25128
11 10.924 6.76996
12 10.908 6.5558
13 10.6103 5.98467
14 10.8273 5.85623
15 9.36202 5.94612
16 8.82959 5.62549
17 9.90271 6.28352
18 10.0032 6.09971
19 9.3917 5.57505
20 9.87653 5.40169
21 8.59656 5.77514
...
100 8.85012 2.7686
It seems the avg error in the estimate of the global temperature from--
a sample gets stuck at 9 degrees. IOW the average of some sample of
met stations without any fancy fiddling widda numbers is almost +-9C.
IOW the method is truly junk.
Ignoring the error seems to reach ~8 and then gets stuck we can put a
power law through the data and get the approximation avgerror = 13.096
* x^-0.100538.
So for (say) 6000 stations (around the number of active GHCN stations)
in the sample we get 13.096/6000^0.1 = 5.48686 (i.e. approx +-5.5C
error). And for 16000 (supposedly the number of stations used in a
certain web page) 13.096/16000^.1 = 4.97424 (i.e. approx +-5C error).
Given one web page claimed their calculated averaged differed by some
small amount (much less than 1C) from the 30y average it seems the
site is just junk science. They can't tell within +-5C and more likely
within +-8C what the average temperature of the earth is.
On a more careful basis using the avg SST surveyed from satellites and >involving mns of more or less equally spaced samples all over the
earth's oceans the avg temp for the earth on the same day as the
experiment above was 15.85C and .66C above the 30y average centered on
1980. Not surprisingly this corresponds fairly closely with temp anoms >against a 19080s baseline as published by Hadley and NOAA for the period.
On Wed, 25 Aug 2021 13:05:19 +1000, MrPostingRobot@kymhorsell.com...
wrote:
EXECUTIVE SUMMARY:
- Measure twice and cut once says the old saw. According to your
highschool math class by averaging N repeated measurements together
you can reduce the error by a factor of 1/sqrt(N).
Just in case you wondered, that applies using the same device in the
[Unum:]The sky is falling! So is the death rate from climate and weather
related catstrophes.
[ES:]No cite as usual.
Is this another thing you dont know? See, for example https://ourworldindata.org/uploads/2018/04/Global-annual-absolute-deaths-from-natural-disasters-01.png
In alt.global-warming Eric Stevens <eric.stevens@sum.co.nz> wrote:
On Wed, 25 Aug 2021 13:05:19 +1000, MrPostingRobot@kymhorsell.com...
wrote:
EXECUTIVE SUMMARY:
- Measure twice and cut once says the old saw. According to your
highschool math class by averaging N repeated measurements together
you can reduce the error by a factor of 1/sqrt(N).
Just in case you wondered, that applies using the same device in the
Sorry. I dont take technical advice from a silly old fraud that
claims a confidence interval is the same as a correlation.
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