Fig. 2.45.5. Functions Rmax (Adr) and Xo max (Adr) for Climax NM data in cycle 22.
From Eq. 2.45.7 we can determine Adr max at which Rmax reaches the biggest value:
what gives Adrmax .= 1.54 ± 0.04%. With this information, we can now correct the Climax NM data of cycle 22 for drifts, with the most reliable amplitude Adr max according to Eq. 2.45.8 and the function R(Xo,Adrmax) is shown in Fig. 2.45.6.
From Fig. 2.45.6 can be seen that the function R(xo,Adrmax) can be approximated with a correlation coefficient 0.99994 ± 0.00003 by a parabola:
where d = 0.000377 ± 0.000002, e = -0.00942 ± 0.00004, and f = -0.906 ± 0.004. By Eq. 2.45.9 we can determine the most reliable value of Xo max corresponding to
what gives Xo max = 12.5 ± 0.1 av. month. At obtained values of Adr max and Xomax the connection between expected and observed CR intensity is characterized by correlation coefficient Rmax (xo max, Adr max ) = 0.9652 (see Fig. 2.45.6).
Results for Kiel NM data. The function Rmax (Adr ) for Kiel NM data (sea level; Rc = 2.32 GV) can be approximated with a correlation coefficient 0.9992 ± 0.0004 by Eq. 2.45.7 with regression coefficients a = 0.0095 ± 0.0001, b = - 0.0250 ± 0.0004, c = - 0.960 ± 0.014, what gives, according to Eq. 2.45.8, Adr max= 1.32 ± 0.04%. Next. we determine R(xo, Adr max ) that can be approximated with correlation coefficient 0.99988 ± 0.00006 by Eq. 2.45.9 with a regression coefficients d = 0.000466 ± 0.000003, e = -0.01191 ± 0.00007, f = -0.897 ± 0.005, that gives, according to Eq. 2.45.10, Xo max = 13.4 ± 0.2 av. months. The obtained values for Adr max and for Xo max are about the same as for the Climax NM. In this case the correlation between the predicted and observed CR intensity is characterized by a coefficient of Rmax (Xo max, Adr max ) = 0.977.
Results for Tyan-Shan NM data. The Tyan-Shan NM (43N, 77E, near Alma-Ata; 3.34 km above sea level, Rc = 6.72 GV) is sensitive to more energetic particles than the Climax NM and the Kiel NM. For the Alma-Ata NM the function Rmax (Adr ) can be approximated with correlation coefficient of 0.9996 ± 0.0002 by Eq. 2.45.7, with regression coefficients a = 0.0149 ± 0.0015, b = -0.019 ± 0.002, c = -0.957 ± 0.009, that gives Adr max= 0.634 ± 0.012% according to Eq. 2.45.8. Next, we determined R(xo,Adrmax ) that can be approximated with a correlation coefficient of 0.9997 ± 0.0002 by Eq. 2.45.9 with a regression coefficients d = 0.000388 ± 0.000004, e =
-0.00845 ± 0.00005, f = -0.917 ± 0.008, that gives, according to Eq. 2.45.10, Xo max= 109 ± 0.2 av. months. In this case the correlation between the predicted and observed CR intensity is characterized by a coefficient of
Results for Huancayo/Haleakala NM data. The Huancayo NM (12S, 75W; 3.4 km above sea level, Rc = 12.92 GV)/ Haleakala NM (20N, 156W; 3.03 km above sea level, Rc = 12.91 GV) is sensitive to primary CR particles of 35-40 GV which is about 2-3 times larger than for the Climax and Kiel NM. For Huancayo/ Haleakala NM the function Rmax (Adr) can be approximated with a correlation coefficient of 0.9998 ± 0.0001 by Eq. 2.45.7, with regression coefficients a = 0.0621 ± 0.0004, b = -0.0165 ± 0.0001, c = -0.978 ± 0.007, which gives Adr max= 0.133 ± 0.002% according to Eq. 2.45.8. Next, we determined R(xo,Adrmax) that can be approximated with a correlation coefficient 0.99998 ± 0.00001 by Eq. 2.45.9 with regression coefficients d = 0.000406 ± 0.000001, e = -0.00842 ± 0.00002, f = -0.935 ± 0.002, that gives Xomax =10.38 ± 0.05 av. months according to Eq. 2.45.10. In this case the correlation between the predicted and observed CR intensity is characterized by Rmax(xomax,Adrmax)= 0 979-
Main results for the inverse problem for the solar cycle 22 on the basis of NM data. The taking into account drift effects (see Fig. 2.45.4) gives an important possibility, using data only for solar cycle 22, to determine the most reliable amplitude Adrmax (at W=75) and the time-lag Xomax (the effective time of the solar wind moving with frozen magnetic fields from the Sun to the boundary of the modulation region on the distance ro ~ uXo max). We found that with an increasing effective CR primary particle rigidity from 10-15 GV (Climax NM and Kiel NM) up to 35-40 GV (Huancayo/Haleakala NM) are decreased both the amplitude of drift effect Adr max (from about 1.5% to about 0.15%) and time-lag Xo max (from about 13 av. months to about 10 av. months). It means that in cycle 22, for the total long term modulation of CR with rigidity 10-15 GV, the relative role of the drift mechanism was 4 x1.5%/25% = 1/4 and the convection-diffusion mechanism about 3/4 (we take into account that observed total 11-year variation in Climax and Kiel NM is 25%, and according to Fig. 2.45.3 the total change of CR intensity owed to drift effects is about 4 times more than the amplitude Adr); for rigidity 35-40 GV
these values were 4 x 0.15%/7% = 1/10 for the drift mechanism, and about 9/10 for the convection-diffusion mechanism. If we assume that the average velocity of the solar wind in the modulation region was about the same as the observed average
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