METHOD OF ESTIMATING RAINFALL BY GROWTH OF TREES. 



113 



principal functions: first, it must reduce the mean rainfall to the mean tree growth; second, 

 it must provide a correction to offset the increasing age of the tree; and, third, it must 

 express the degree of conservation by which the rain of any one year has an influence 

 for several years. In a formula of universal application, other factors will play a part, 

 but for a limited group of trees in one locality they can be neglected. In calculating the 



1870 



1880 



1890 



1900 



1910 



V 2.5 

 E 



3 2.0 

 E 

 .E 1.5 



t 1.0 

 o 



O 0.5 

 



20 



Dotted line=Annual precipitation smoothed by 5-year means. 

 Solid line=Annual growtli smoothed by 5 year means 



10 



1910 



Solid line=Actual growth. 



Dotted line=Growth calculated from rainfall 



Tig. 16.— Actual Tree Growth Compared with Growth Calculated from Rainfall. 

 Fig. 17.— Five-year Smoothed Curves of Rainfall and Tree Growth at Prescott. 



formula, the group of ten trees nearest Prescott was used. The first process, namely, the 

 reduction of the mean rainfall to the mean tree growth, was easily accomplished. Ex- 

 pressed in actual figures, the rainfall was about 250 times the average thickness of the rings. 

 This is the general factor K in the formula on the next page. 



The second process, namely, the correction for the age of the tree, was practically 

 omitted in forming the curves here shown, since, judging by the Flagstaff curves, its effect 

 would be very slight in the interval under discussion. In long periods it is an immensely 

 important correction and its effect should always be investigated.* 



The third process, that is, the calculation of the effect of conservation, is far more 

 complicated than the others and its results may be regarded as provisional until a large 

 number of further investigations have been made; yet already very promising results have 

 been obtained, which give an agreement of more than 80 per cent between the calculated 

 curve and the curve derived from actual measurements, as is shown in figure 16. 



There are two features of the conservation factor worth calling attention to: (1) that 

 in this dry climate it appUes better as a coefficient than as an additive term (while there is 

 evidence, as given in a later chapter, that the additive form is better in a moist chmate), 

 and (2) that it gives a prominent place to "accumulated moisture" as commonly used in 

 meteorology. Accumulated moisture is simply the algebraic sum of the amounts by which 



* Over short periods the change may be regarded as linear and a convenient formula ia - = 1 — k(ji — y), 



where ?„ = growth in any year n; Oy = growth in middle year of series, and fc = a constant, which was 0.0043 in the 

 Flagstaff series; in this form it mav be used in the general formula. 



In the Flagstaff curves from 1700 to 1900 the growth proved to be inversely proportional to the square root of 



the time elapsed since the year 1690, and is closely expressed in millimeters by the formula: Tn = / _ 77^? . ' 



Tn is here the tree growth for the year under discussion. 



If G be the mean size of ring, then the factor to be introduced in a general formula becomes 

 9 



10 



GVn - 1690 



