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2. Bivariate analysis The second approach involved the computation of correlation coefficients and serial regression coefficients for the prediction of growth incre- ments based on single monthly climatic values and seasonal climatic values. The Pearson product- moment correlation coefficients based on monthly climatic data are presented in Figures 3 through 5. The values are in general agreement with Fritts' results for ponderosa pine growth patterns. Precipitation-tree ring correlation coefficients are nearly all positive; temperature-tree ring correlation coefficients are generally negative. The tree ring growth is best correlated with precipitation and temperature in winter (November through February) and late spring (especially June) in the San Juans. The serial regression coefficient b is given by S. D. tr b = r S. D. cl where r = product-moment correlation coefficient. S.D.tr = standard deviation of growth layer widths, S.D.cl = standard deviation of the climatic parameter (temperature or precipitation). The serial re- gression coefficients for the four-season set using the Durango data and the three study sites are plotted in Figure 6. For an example of the inter- pretation of the temperature and precipitation plots shown in Figure 6, consider spring precipitation at SJS-2. The regression coefficient read from the graph is +.06. This means that for each inch of spring precipitation above/below normal the tree ring width in that year will be increased/decreased 0.06 mm about the mean tree ring width. All four seasons +.6 +.4 +.2 0 -.2 I- -A- z -.6 w <..> ~ LL. W 0 <..> z 0 +.6 ~ +.4 ..J +.2 w 0 a:: a:: -.2 0 <..> -.4 -.6 shown in Figure 6 affect the size of the growth layer and the factors are cumulative. A prediction equation for annual growth width was developed using the serial regression coefficients for seasonal precipitation shown in Figure 6. The coefficient values are shown in Table 6 below. Prediction Results Since Durango is outside the target area, its climatological data should reflect the regional temperature and precipitation characteristics. Effects of cloud seeding should not be expected in the weather record. Thus, if the winter orographic 'snow augmentation program has been effective, there should be a difference between actual ring widths and those predicted based on the historical climate- tree ring relationship. Prediction of annual growth widths for each study site using each of the two regression equations are shown in Table 7. The differences between the sites in predicted values are striking whereas the diff- erences in results between the two predicted values are relatively small in each case. The predicted ring width was not significantly different from the actual value. This is especially true for SJS-1. Although the weather modification sample is far too small to be conclusive, this suggests that at SJS-1 the variability in tree-ring width is most influenced by temperature and precipitation. The high positive residuals for station SJS-2 indicate that the weather regime in that area for the seeded years is somewhat different from the climatic data set for Durango. It is interpreted that if the weather regime influencing SJS-2 has been changed, the growth response of the trees at SJS-2 is reflecting this change. The large residuals for SJS-3 confirm PRECIPITATION X A - ---- --~--- --t--~-- - --1--"[-,- -1- - 1- -0 -- --T --~-~-------------------------~----- A Tree-Ring Sites SJS I - A SJS 2 - 0 SJS 3 - X TEMPERATURE --------------------~-------------- o 6 t ' _ J __ ~ _ ~ _ _ ~ _ _ ~ _ -; _ _X_ _ _ _ _ __L _.J._ -t--~- _ _ __1 x x .x X X I I I \ Jly. Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun. Jly. Aug. Sep. Figure 3. Monthly correlation coeffieients of Durange precipitation and temperature with San Juan study tree ring sites (SJS): SJS-1, SJS-2, and SJS-3. Values outside dashed line indicate signif- icance at 0(= 0.05 level. 76