NO. 8 HARMONIC PERIODS IN PRECIPITATION — ^ABBOT II 



Figures 5 and 6 give 6-year samples, graphically, of forecasts at 

 Rochester, N.Y., and Nashville, Tenn,, within the interval 1921 

 through 1956. That entire interval has been forecasted. Its forecast 

 has been compared to observed departures from normal, and smoothed 

 by the formula Yo{a + 2b + 4c + 2d + e). I give here only 6-year por- 

 tions of the comparison for I wish to keep this paper as brief as 

 possible. I fear that Smithsonian Publication 4545, on which I placed 

 high hopes, is too long, so that no one but myself ever reads it. The 

 forecasts given in figures 5 and 6 employ all the "World Weather" 

 records. These comprise for Rochester, 1884 through 1956, 72 years, 

 and for Nashville, 1870 through 1956, 86 years. 



Readers may notice that due to the new smoothing formula, this 

 comparison mostly avoids the distressing shifts of prominent features 

 which sometimes amounted to 3 or 4 months in Publication 4390. 

 Both stations are included in the tables given in Publication 4390, 

 and Nashville is illustrated there in figure 29. 



I have preferred to use Nashville forecast, 1950-1956, because it 

 was given 1950-1957 in Publication 4390, plate 3. Now employing 

 the new smoothing formula the new illustration is better. Besides, it 

 shows in 1950 to 1952 shifts and differences in amplitude of features 

 that may have resulted from hydrogen bombing by the U.S.A. and 

 the U.S.S.R. about 1950. I have found similar indications in nearly 

 all of 23 foreign stations I have forecasted. 



Now I proceed to considerations which seem to me to clinch the 

 case for the validity and usefulness of long-range forecasts of pre- 

 cipitation. Figures 7 and 8 give for both Rochester and Nashville: 

 (A) percentage-yearly departures from the mean, 1921 through 

 1956, and 1921 through 1956, respectively, of the total rainfall 

 observed. (B) Departures from the smoothed means (of 72 and 86 

 years respectively) of forecasts, 1921 through 1956. These are com- 

 puted from all monthly records oi 72 and 86 years respectively. 

 (C) Values of (A) smoothed by ^(a + 2b + 4c + 2d + e), and (D) 

 values of (B) smoothed similarly. 



First consider Rochester, figure 7, only. It will be seen from (A) 

 and (B) that the mean of all yearly departures, 1921 through 1956, 

 of (B), involving my forecast, is smaller than that of (A) observed. 

 These results are 9.3 and 11.5 percent. But it is also quite obvious 

 that if one confines attention to large departures, (B) has a much 

 larger advantage over (A). These results support long-range predic- 

 tions somewhat. 



But what really clinches the case for the validity of my forecasting, 

 and all it comprises, is the second pair of curves (C) and (D). For 



