1862 HadCRUT coverage
During the “cold” year of 1862, HADCrut’s thermometers covered less than 10% of the Earth, yet they report temperature anomalies from 1862 within 0.001C. Their reported precision is about five orders of magnitude larger than their accuracy. What a complete joke.
1: Global Temperature Record - Phil Jones
global temperature hadcrut febraury 2012, temperature of the earth 1862
Good point. I am sure you are aware that this must be the artifact of taking and average and reporting it to the number of decimal places on the calculator. Typical noobe mistake. Which is my impression of stat skills of the visible Climatology Clowns Crowd
SG – Again I commend you for discussing the importance of significant digits.
E.g. If I had a millimeter ruler, I could measure the length of an object to the nearest mm (e.g. 4 mm), but could probably guess to the nearest tenth of a mm (e.g. 4.3 +/- 0.1 mm). If I measured 10 similar objects, it would be inappropriate to conclude that their avg length was, say 4.37634 mm.
Thermometer readings, even digital ones (not present in 1880), should follow the same rules. That “avg” daily temps are taken to be the simple avg of the daily high and low temps introduces large errors – you can’t even legitimately report an avg temp to the nearest degree, let alone tenth of a degree. Perhaps one could do this if took continuous data measurements (say, 48 readings per 24 hrs).
Take three readings: 9.1, 8.9, and 9.2
What is the average reading? 9.0666666666666666666…….
How many digits should be reported?
Take three readings: 9.1000, 8.9000, and 9.2000
What is the average reading? 9.0666666666666666666…….
How many digits should be reported?
My best guess: If you think you know the answer, you’re probably wrong.
1st year physics . . .
http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
Another example: I have 1000 thermometers. Each of them has an uncorrelated calibrated accuracy of +/-1C at 100C and a resolution of .01C. They’re placed in a sand bath set at 100C and ten measurements are taken with each thermometer. For simplicity’s sake we’ll say they’re all computer controlled and triggered simultaneously with the same sampling rate.
After averaging the ten measurements for each thermometer the results are sorted. The lowest average reading is 99.698 and the highest is 100.320. Here are some other results:
26th lowest = 99.813
51st lowest = 99.845
101st lowest = 99.875
251st lowest = 99.929
500th lowest = 99.992
500th highest = 99.992
251st highest = 100.061
101st highest = 100.109
51st highest = 100.153
26th highest = 100.182
What can we say about the sand bath’s ‘true’ temperature at a 95% confidence interval?
What can we say about the sand bath’s ‘true’ temperature at a 90% confidence interval?
Cool. A statistics problem. Not sure how it relates to the accuracy of the global temperature record, and I’m over 2 decades past my college statistics class, but I’ll take a crack at this problem (but I expect the correct answer with rationale will be provided so that I learn something).
First, I’m not sure what 100C +/- 1 C means. Is this +/- 2 SD? Doesn’t matter.
Next, the resolution is to the nearest 0.01 C, but the avg of 10 readings is reported to the nearest 0.001 C? I think you can only report the avg to the nearest 0.01 C.
Anyway, I’ll assume the readings are as stated.
I’ll also assume the sand bath temperature distribution is homogeneous, or that if it is heterogeneous, that the thermometers are evenly distributed.
The numbers as given are not exactly a normal (Gaussian) distribution, and the mean and median do not match, and so I can only approximate my answer. Had I been given every data point, a precise mean with confidence interval could be calculated.
Avg sand bath temp (90% confidence interval): 99.992 +/- 0.154.
Avg sand bath temp (95% confidence interval): 99.992 +/- 0.1845 (extra digit is for the next calculation below).
Given the thermometer resolution to the nearest 0.01 C,
90% – 99.99 +/- 0.15.
95% – 99.99 +/- 0.18.
I am going to watch the Superbowl now.
Confidence Intervals! Maybe you could analyse some of them for Phil Jones. Let’s get back on topic – which is the left-hand side of the graph at the top of the page. If you worked out confidence intervals based the global distrubution of thermometers in 1862 it would only get worse.
Avg of 9.1, 8.9, and 9.2 as data measurements is 9.1.
Avg of 9.1000, 8.9000, and 9.2000 is 9.0667.
Avg of 9.1, 8.9, and 9.20000000000 is 9.1.
Individual weather station temperature readings are accurate to how many decimals? Is the “avg temp” the integral of the temp vs. time curve divided by 24 hrs, and the air heat content is properly adjusted for humidity, or is it simply the avg of the high and low temps during the 24 hr period?
Why in Chicago do we get city temps on the weather forecast from O’Hare (official Chicago station), Midway, and the lakefront? It is because they are all different by up to several full degrees depending on cloud cover, humidity, wind speed and direction, UHI effect, precipitation, etc. As least we don’t have to adjust for altitude change in flatland.
HadCruT suffers the same disease as GISS, temperature revisionism: http://www.skyfall.fr/?p=122
It woul just be bad had it not be used in the successive IPCC reports.
I think that graph is completely misleading.
Remember it doesn’t actually show temperature it shows a deviations from an arbitrary temperature range via average.
And to get an average you will always have temperatures higher and lower than the average
Hence the name average.
What would be intresting is just a plain graph showing global temperatures, not a deviation from global temperatures based on an arbitrary time series.
The graph is a statisticle trick based on a mis understanding of the creation of an average.