The variations of the solar constant and their relation to weather reply to Paranjpe and Brunt
Authors: Abbot C. G. 
Published: July 2010

The author cites five recent papers containing many evidences of solar change ignored by critics. Chief among them, and in the author's opinion unanswerable, are evidences that day to day solar changes profoundly influence temperatures. Between 1924 and 1935 were found 320 dates, the beginnings of sequences of observed rise or of fall of solar radiation. The average march of departures from normal temperatures in four widely separated cities shows opposite trends for 16 days following, respectively, these sequences of rising and falling solar radiation. The separation of temperatures thus produced reaches from 10° to 25°F. Similar curves of temperature departure are found, on the average, in the years 1924 to 1930, to those found in the years 1931 to 1935. Selecting 46 cases of especially large solar changes observed, the temperature effects which followed were in the same phase but about twice as large as usual. A crucial test is given wherein correlation coefficients are computed for the march of temperatures for 16 days after and for 16 days before observed solar changes, as between rising and falling sequences of solar variation. The correlation values are respectively: after, ‐ 54·3±4·9 per cent; before, +11·1 ± 6·0 per cent. The first is 11 times its probable error and therefore significant, the second less than twice its probable error and hence meaningless.

From these studies it appears that day‐to‐day changes averaging 0·7 per cent in solar radiation are presumably real and competent to produce major changes of 10° to 25°F. in temperature in the temperate zone. Such changes may be conventionally represented by the repetition 18 times per year of the day‐to‐day sequence, 3, 6, 9, 12, 14, 12, 9, 6, 3 thousandths calorie in solar radiation.

The author demonstrates that correlation of day‐to‐day solar constant values from different observatories, as relied on by critics, is incompetent to refute the sun's important variability. For the author computes correlation coefficients for 110 days as between the best stations, Montezuma and St. Katherine, obtaining 6 ± 6 per cent. He then loads the values of each station simultaneously with five humps of sequences such as just numerically specified. The two stations are then certainly correlated, and carry assumed solar changes adequate to produce from 10° to 25°F. in temperature departures. The correlation coefficient now becomes 18 ± 6 per cent an increase of 12 per cent, far below what critics require as being evidential.

The author points out that multiplication of values, as in monthly means or in large groupings governed by magnitudes, may sufficiently reduce accidental errors to give trustworthy evidences of solar variation, and cites numerous cases of this sort not referred to by critics.

The author mentions various considerations constantly in his mind but overlooked by critics. He discusses the procedures used in holding the solar constant values to a fixed scale for long range comparisons.

The author points out that critics' disparagement of solar variation by the tabular use of standard deviations proves nothing and is merely reasoning in a circle, since the increase of standard deviations may quite as well be caused by real increase in solar variation as by increase of experimental error. Similarly, increase of correlation coefficients between two stations may be due to increased solar variation rather than experimental interdependence as suggested by critics, for thereby the competitive effects of accidental error are made relatively less considerable.

The author explains in detail the discovery of 12 long periods in solar variation. Critics having claimed on the basis of an equation of Brunt's, that the author's periodicities have impossibly great amplitudes, the author tabulates these periodicities completely, and then synthesizes them for the years 1920 to 1934 and compares the synthetic curve with observed monthly mean values. With a total range of 2 per cent, the synthesized periodicities reproduce the original observations to within an average deviation of 0·2 per cent, hence periodicities cannot have excessive amplitudes as claimed.

The author reiterates his conviction that solar variation is the principal cause of weather changes, and that with annual expenditure of $300,000 for solar observation, principal details of weather might be predicted all over the world from study of solar variation for two weeks in advance.