Dr. Hansen’s Statistics

Dr. Hansen’s Statistics


Guest Post by Willis Eschenbach

OK, this post has ended up having two parts, because as usual, I got side-tractored while looking at the first part. It’s the problem with science, too many interesting trails leading off the main highway …

Part The First

I wanted to point out an overlooked part of Dr. James Hansen’s 1988 oral testimony to the US Senate. At the time Dr. Hansen was the Director of GISS, the Goddard Institute of Space Studies. He told the Congresspersonages, or whatever the modern politically correct term is for that class of Politicritters, the following:

The observed warming during the past 30 years, which is the period when we have accurate measurements of atmospheric composition, is shown by the heavy black line in this graph. The warming is almost 0.4 degrees Centigrade by 1987 relative to climatology, which is defined as the 30 year mean, 1950 to 1980 and, in fact, the warming is more than 0.4 degrees Centigrade in 1988. The probability of a chance warming of that magnitude is about 1 percent. So, with 99 percent confidence we can state that the warming during this time period is a real warming trend.


Here is his accompanying graphic …

Now, I am either cursed or blessed with what I call a “nose for bad numbers”. It is a curious talent that I ascribe inter alia to using a slide rule when I was growing up. A slide rule has no decimal point. So if an answer from the slide rule is say 3141, you have to estimate the answer in order to decide if it means 314.1, or 3.141, or .003141, or 31,410. After doing this for years, I developed an innate sense about whether a result seems reasonable or not.

So when I saw Hansen’s claim above, I thought “Nope. Bad numbers”. And when I looked deeper … worse numbers.

First thing I did was to see if I could replicate Hansens’ results. Unfortunately, he was using the old GISS temperature record, made before they were as adjusted as they are today. His statement was that “The warming is almost 0.4 degrees Centigrade by 1987. But in the modern GISS data, I found slightly more warming, 0.5°C.

OK, fair enough. So I went and digitized the dataset above so I could use Dr.Hansen’s data, and it turns out that his “almost 0.4 degrees Centigrade” increase by 1987″ is actually 0.32°C. You can see it in the graphic above. Hmmm … Dr. Hansen’s alarmism is unquenchable. Also, note that Dr. Hansen has spliced into the graphic and discussed the 1988 “annual” average even though at the time he only had a few months of 1988 data … bad scientist, no cookies. Comparisons gotta be apples to apples.

Next, his claim is that there is only one chance in a hundred that the 1987 warmth is a random result. That means his 1987 temperature should be 2.6 standard deviations warmer than the 1951-1980 mean. But once again, Dr. Hansen is exaggerating, although this time only slightly—it’s only 2.5 standard deviations away from the mean, not 2.6.

However, that’s not the real problem. In common with most climate-related temperature datasets, the GISS temperature dataset Hansen used has a high “Hurst Exponent”. This means that the GISS temperature dataset will be what has been called “naturally trendy”. In such datasets, large swings are more common than in purely random datasets.

How much more common? Well, we can actually test that. He’s comparing the 30-year “climatology” period 1951-1980 to the year 1987. So what I did was the exact same thing, but starting in different years, e.g. comparing the thirty-year period 1901-1930 to the year 1937, seeing how unusual that result is, and so on.

When we do that for all possible years of the GISS 1988 dataset, we find that being 2.5 standard deviations away from the climatological mean is not uncommon at all, occurring about one year out of fourteen.

And if we do the same analysis on the full GISS dataset up until today, we find it’s even more common. It has occurred in the historical record about one year out of seven. So Hansen’s “one percent chance” that the 1988 temperature was unusual was actually a fourteen percent chance … more alarmist misrepresentation, which is no surprise considering the source.

Conclusions the First

Regarding the warmth of 1987, which was 2.5 standard deviations warmer than the 30-year climatology average, Hansen claimed that “The probability of a chance warming of that magnitude is about 1 percent.”

In actuality, this kind of warming occurred in the record that he used about once every fourteen years or so … and it occurs in the modern GISS record about once every seven years. So the probability of a chance warming of that magnitude in the GISS temperature record is not one percent, it is between seven and fourteen percent … which means that it is not unusual in any way.

Part The Second

In the process of researching the first part of this post, I realized why there is so much debate about whether Hansen’s predictions were right or wrong. The problem is that we’re living in what the most imaginative and talented cartoonist yclept “Josh” calls “The Adjustocene”

The problem is that Dr. James Hansen is not only the guy who made the 1988 alarmist predictions. He’s also the guy who has been in charge of the GISS temperature record that he has long been hoping would make his prediction come true.

So … here are the changes between the version of the GISS temperature record that Hansen used in 1988, and the 2018 version of the GISS temperature record.

(GISS 2018 data available here. )

Gotta say, those are some significant changes. In the old GISS record (red), 1920 to 1950 were much warmer than in the new record. As a result, in the old record temperatures cooled pretty radically from about 1940 to 1970 … but in the new record that’s all gone.

And things don’t get any better when we add another modern record to the mix. Here’s the Hadley Center’s HadCRUT global average temperature, shown in blue …

Note that HadCRUT (blue) shows the same drop in temperature 1940-1970 that we see in the 1988 version of the GISS temperature record (red). More to the current point, the post-1988 divergence between the HadCRUT and the GISS record is enough to rule out any possibility of determining whether Hansen was right or wrong. The overall trend in the GISS 2018 data is about 40% larger than the trend in the HadCRUT data, so you can get the answer you wish by simply picking the right dataset.

Conclusions the Second

Depending on the dataset chosen, someone can show that Dr. Hansen’s predictions either did or did not come true … it’s the perfect Schrodinger’s Cat of predictions.

Finally, as an aside, just what is an “Institute of Space Studies” doing studying the climate? I’ve heard of “mission creep” before, but that’s more than mission creep, that is extra-terrestrial movement. Don’t know if the Goddard folks have noticed, but there is no climate in space … how about if they go back to, you know, studying the myriad of fascinating things that happen in space, and leave studying the climate to less alarmist folk?

Best regards to all,


Short Version Of My Usual Request:


Digitized Hansen Data from Figure 1:

Year, Anom
1880, -0.403
1881, -0.366
1882, -0.427
1883, -0.464
1884, -0.729
1885, -0.541
1886, -0.461
1887, -0.547
1888, -0.388
1889, -0.184
1890, -0.38
1891, -0.438
1892, -0.44
1893, -0.481
1894, -0.382
1895, -0.408
1896, -0.274
1897, -0.177
1898, -0.38
1899, -0.223
1900, -0.025
1901, -0.086
1902, -0.282
1903, -0.357
1904, -0.493
1905, -0.254
1906, -0.175
1907, -0.45
1908, -0.317
1909, -0.334
1910, -0.313
1911, -0.289
1912, -0.316
1913, -0.254
1914, -0.053
1915, -0.009
1916, -0.258
1917, -0.474
1918, -0.363
1919, -0.197
1920, -0.154
1921, -0.079
1922, -0.143
1923, -0.128
1924, -0.119
1925, -0.097
1926, 0.133
1927, -0.006
1928, 0.066
1929, -0.165
1930, -0.002
1931, 0.085
1932, 0.049
1933, -0.158
1934, 0.047
1935, -0.016
1936, 0.055
1937, 0.17
1938, 0.188
1939, 0.052
1940, 0.111
1941, 0.126
1942, 0.094
1943, 0.034
1944, 0.108
1945, -0.027
1946, 0.035
1947, 0.152
1948, 0.034
1949, -0.018
1950, -0.136
1951, 0.02
1952, 0.071
1953, 0.2
1954, -0.028
1955, -0.069
1956, -0.184
1957, 0.094
1958, 0.113
1959, 0.061
1960, 0.006
1961, 0.077
1962, 0.027
1963, 0.022
1964, -0.264
1965, -0.174
1966, -0.09
1967, -0.024
1968, -0.128
1969, 0.028
1970, 0.034
1971, -0.117
1972, -0.077
1973, 0.168
1974, -0.09
1975, -0.039
1976, -0.235
1977, 0.164
1978, 0.1
1979, 0.131
1980, 0.267
1981, 0.359
1982, 0.058
1983, 0.305
1984, 0.096
1985, 0.053
1986, 0.173
1987, 0.325
1988, 0.562 (five months only)

Superforest,Climate Change

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