OCR Text |
Show CH (i) = Q 2 (i) + Co 2 (i) sx (i) Sy (i) , Where Q (i) is the quadrature spectrum estimate, C9 (i) the cospectrum estimate, an_d Sx (i) and Sy (i) the spectrum estimates ,. all at frequency i. Co~. herence 1s analogous to the square of a correlation coefficient, except that it 1 varies with frequency. 11 :~ ,~ m· The approximate formula for the limiting coherence B at the probability level p is: B = \! 1-p (i) / (m-1) Table 16 shows the coherences at the 1 % and the 5% limits for various degrees of freedom. TABLE 16 Limiting Values on Coherence Significance Level Degrees of Freedom 4 10 20 40 1 % Limit • 89 • 63 • 46 • 33 5% Limit . 80 . 53 . 38 . 27 In the analysis procedures used here, the coherence between the time series records of precipitation rate and a one cycle per hour square wave containing approximately the same total variance, was computed for all seeded periods. It was anticipated that the increase in coherence at one cycle per hour might be significant for seeded periods. During the investigation of natural snowfall spectra were computed from long . time series. An example is shown in Figure 182. The spectrum has been ~- normalized by t2 x 102, since most spectra of snowfall rate records were ju qi found to fall off in spectral density by t2. The spectral analysis for the Base , Camp Station series, includ1.ng the s·ame storm periods as used in the Buffalo Pass series, is shown in Figure 183. The stability of this natural unseeded spectrum can be significantly altered by 269 |