Monday, February 13, 2017

On the Insignificance of Herschel’s Sunspot Correlation | Jeffrey J. Love

William Herschel started to examine the correlation of solar variation and solar cycle and climate. Over a period of 40 years (1779–1818), Herschel had regularly observed sunspots and their variations in number, form and size. Most of his observations took place in a period of low solar activity, the Dalton minimum, when sunspots were relatively few in number. This was one of the reasons why Herschel was not able to identify the standard 11-year period in solar activity. Herschel compared his observations with the series of wheat prices published by Adam Smith in The Wealth of Nations.In 1801, Herschel reported his findings to the Royal Society and indicated five prolonged periods of few sunspots correlated with the price of wheat. Herschel's study was ridiculed by some of his contemporaries but did initiate further attempts to find a correlation. Later in the 19th century, William Stanley Jevons proposed the 11-year cycle with Herschel's basic idea of a correlation between the low amount of sunspots and lower yields explaining recurring booms and slumps in the economy. Herschel's speculation on a connection between sunspots and regional climate, using the market price of wheat as a proxy, continues to be cited. However, according to a study of Jeffrey J. Love of the USGS the evaluation is controversial and the significance of the correlation is doubted:

Jeffrey J. Love (Aug 27, 2013) - Our finding is that Herschel’s hypothesis is statistically insignificant [...] All of the data Herschel discussed in his 1801 paper were collected prior to 1717, during the Maunder Minimum and long before his paper was published. His identification of five durations of time with few sunspots and inflated wheat prices and five other durations that might have had sunspots and which had deflated prices [Herschel, 1801, pp. 313-316] would be an unlikely realization of binary statistics, but it is not clear whether or not Herschel was inspired to state his hypothesis after inspection of these data. Having said this, Herschel acknowledged that predictions based on his hypothesis “ought not be relied on by any one, with more confidence than the arguments ... may appear to deserve” [Herschel, 1801, p. 318]. Today, we have considerably more data than were available to Herschel; these were collected both before and after he stated his hypothesis, and they can be used for both retrospective and prospective testing.  For  London wheat  prices  both before 1801 and, separately, after 1802, binary significance probabilities and Pearson correlations and their effective probabilities are [...] indicative of statistical significance. While solar irradiance may affect global climate, from our analysis of data of the type considered by Herschel, we conclude that historical wheat prices are not demonstrably useful for inferring past sunspot numbers, and, conversely, sunspot numbers are not demonstrably useful for predicting future wheat prices.