In the first line of Section A a correlation coefficient of only -0.056, which is scarcely six-tenths of the probable error, means that there is no appreciable relation between the rainfall of a given season and the growth during the following spring and summer. The roots of the sequoias probably penetrate so deeply that the rain and melted snow of the spring months do not sink down rapidly enough to influence the trees before the growing season comes to an end. The precipitation of two preceding seasons, however, has some effect on the trees, as appears in the second line of Section A, where the correlation coefficient is +0.288, or 3.2 times the probable error. When the rainfall of three seasons is taken into account the coefficient rises to +0.570, or 8.7 times the probable error, while with four years of rainfall the coefficient begins to fall off. Thus the growth of these eighteen sequoias on relatively dry slopes appears to have depended chiefly on the rainfall of the second and third preceding rainy seasons. The growth in 1900, for example, depended largely on the rainfall in the rainy seasons of 1897-1898 and 1898-1899.
Section B of the table shows that with 112 trees, growing chiefly in moist depressions where the water supply is at a maximum, the correlation between growth and rainfall, +0.577 for ten years' rainfall, is even higher than with the dry trees. The seepage of the underground water is so slow that not until four years' rainfall is taken into account is the correlation coefficient more than four times the probable error. When only the trees growing in moist locations are employed, the coefficient between
tree growth and the rainfall for ten years rises to the high figure of +0.605, or 9.8 times the probable error, as appears in Section C. These figures, as well as many others not here published, make it clear that the curve of sequoia growth from 1861 to 1910 affords a fairly close indication of the rainfall at Sacramento, provided allowance be made for a delay of three to ten years due to the fact that the moisture in the soil gradually seeps down the mountain-sides and only reaches the sequoias after a considerable interval.
If a rainfall record were available for the place where the trees actually grow, the relationship would probably be still closer.
The record at Fresno, for example, bears out this conclusion so far as it goes. But as Fresno lies at a low altitude and its rainfall is of essentially the Sacramento type, its short record is of less value than that of Sacramento. The only rainfall records among the Sierras at high levels, where the rainfall and temperature are approximately like those of the sequoia region, are found along the main line of the Southern Pacific railroad. This runs from Oakland northeastward seventy miles across the open plain to Sacramento, then another seventy miles, as the crow flies, through Colfax and over a high pass in the Sierras at Summit, next twenty miles or so down through Truckee to Boca, on the edge of the inland basin of Nevada, and on northeastward another 160 miles to Winnemucca, where it turns east toward Ogden and Salt Lake City. Section D of Table 3 shows the correlation coefficients between the rainfall along the railroad and the growth of the sequoias. At Sacramento, which lies fairly open to winds from the Pacific and thus represents the general climate of central California, the coefficient is nearly five times the probable error, thus indicating a
real relation to sequoia growth. Then among the foothills of the Sierras at Colfax, the coefficient drops till it is scarcely larger than the probable error. It rises rapidly, however, as one advances among the mountains, until at Boca it attains the high figure of +0.604 or eight times the probable error, and continues high in the dry area farther east. In other words the growth of the sequoias is a good indication of the rainfall where the trees grow and in the dry region farther east.
In order to determine the degree to which the sequoia record represents the rainfall of other regions, let us select Jerusalem for comparison. The reasons for this selection are that Jerusalem furnishes the only available record that satisfies the following necessary conditions: (1) its record is long enough to be important; (2) it is located fairly near the latitude of the sequoias, 32°N versus 37°N; (3) it is located in a similar type of climate with winter rains and a long dry summer; (4) it lies well above sea level (2500 feet) and somewhat back from the seacoast, thus approximating although by no means duplicating the condition of the sequoias; and (5) it lies in a region where the evidence of climatic changes during historic times is strongest. The ideal place for comparison would be the valley in which grow the cedars of Lebanon. Those trees resemble the sequoias to an extraordinary degree, not only in their location, but in their great age. Some day it will be most interesting to compare the growth of these two famous groups of old trees.
The correlation coefficients for the sequoia growth and the rainfall at Jerusalem are given in Section A, Table 4. They are so high and so consistent that they scarcely leave room for doubt that where a hundred or more sequoias are employed, as in Fig. 5, their curve of growth affords a good indication of the fluctuations of climate in western Asia. The high coefficient for the eleven trees measured by Douglass suggests that where the number of trees falls as low as ten, as in the part of Fig. 4 from 710 to 840 B. C., the relation between tree growth and rainfall is still close even when only one year's growth is considered. Where the unit is ten years of growth, as in Figs. 4 and 5, the accuracy of the tree curve as a measure of rainfall is much greater than when a single year is used as in Table 4. When the unit is raised to thirty years, as in the smoothed part of Fig. 4 previous to 240 B. C., even four trees, as from 960 to 1070, probably give a fair approximation to the general changes in rainfall, while a single tree prior to 1110 B. C. gives a rough indication.
| [TABLE 4] | ||||||
|---|---|---|---|---|---|---|
| CORRELATION COEFFICIENTS BETWEENRAINFALL RECORDS IN CALIFORNIAAND JERUSALEM | ||||||
| (r)=Correlation coefficient (e)=Probable error (r/e)=Ratio of coefficient to probable error | ||||||
| A. Jerusalem Rainfall for 3 Years and Various Groups ofSequoias[27] | ||||||
| (r) | (e) | (r/e) | ||||
| 11 trees measured by Douglass | +0.453 | ±0.078 | 5.8 | |||
| 80 trees, moist locations, Groups IA, IIA, IIIA, VA | +0.500 | ±0.073 | 6.8 | |||
| 101 trees, 69 in moist locations, 32 in dry, I, II, III | +0.616 | ±0.061 | 10.1 | |||
| 112 trees, 80 in moist locations, 32 in dry, I, II, III, V | +0.675 | ±0.053 | 12.7 | |||
| B. Rainfall at Jerusalem and at Stations in California and Nevada | ||||||
| —— 3 years —— | —— 5 years —— | |||||
| Altitude (feet) | Years | (r) | (r/e) | (r) | (r/e) | |
| Sacramento, | 70 | 1861-1910 | +0.386 | 4.7 | +0.352 | 4.2 |
| Colfax, | 2400 | 1871-1909 | +0.311 | 3.1 | +0.308 | 3.0 |
| Summit, | 7000 | 1871-1909 | +0.099 | 0.9 | +0.248 | 2.3 |
| Truckee, | 5800 | 1871-1909 | +0.229 | 2.2 | +0.337 | 3.3 |
| [28]Boca, | 5500 | 1871-1909 | +0.482 | 6.4 | +0.617 | 8.6 |
| Winnemucca, | 4300 | 1871-1909 | +0.235 | 2.2 | +0.260 | 2.4 |
| San Bernardino, | 1050 | 1871-1909 | +0.275 | 2.7 | +0.177 | 1.8 |
| C. Rainfall for 3 Years at California and Nevada Stations, 1871-1909 | ||||||
| (r) | (r/e) | |||||
| Sacramento and San Bernardino | +0.663 | 10.7 | ||||
| San Bernardino and Winnemucca | +0.291 | 2.8 | ||||
Table 4 shows a peculiar feature in the fact that the correlations of Section A between tree growth and the rainfall of Jerusalem are decidedly higher than those between the rainfall in the two regions. Only at Sacramento and Boca are the rainfall coefficients high enough to be conclusive. This, however, is not surprising, for even between Sacramento and San Bernardino, only 400 miles apart, the correlation coefficient for the rainfall by three-year periods is only 10.7 times the probable error, as appears in Section C of Table 4, while between San Bernardino and Winnemucca 500 miles away, the corresponding figure drops to 2.8. It must be remembered that in some respects the growth of the sequoias is a much better record of rainfall than are the records kept by man. The human record is based on the amount of water caught by a little gauge a few inches in diameter. Every gust of wind detracts from the accuracy of the record; a mile away the rainfall may be double what it is at the gauge. Each sequoia, on the other hand, draws its moisture from an area thousands of times as large as