Prediction of galactic cosmic ray intensity variation for a few (up to 10-12) years ahead on the basis of convection-diffusion and drift model

We determine the dimension of the Heliosphere (modulation region), radial diffusion coefficient and other parameters of convection-diffusion and drift mechanisms of cosmic ray (CR) long-term variation, depending on particle energy, the level of solar activity (SA) and general solar magnetic field. This important information we obtain on the basis of CR and SA data in the past, taking into account the theory of convection-diffusion and drift global modulation of galactic CR in the Heliosphere. By using these results and the predictions which are regularly published elsewhere of expected SA variation in the near future and prediction of next future SA cycle, we may make a prediction of the expected in the near future long-term cosmic ray intensity variation. We show that by this method we may make a prediction of the expected in the near future (up to 10-12 years, and may be more, in dependence for what period can be made definite prediction of SA) galactic cosmic ray intensity variation in the interplanetary space on different distances from the Sun, in the Earth's magnetosphere, and in the atmosphere at different altitudes and latitudes.

sphere relative to the processes on the Sun, will be ln where X=r u, X E =1 AU u, X o =r o u, and n (R, X o , β, r E , t) exp is the expected galactic CR density at the Earth's orbit, in dependence of the values of the parameters X o and β.Regression coefficients A (R, X o , β, t 1 , t 2 ) and B (R, X o , β, t 1 , t 2 ) can be determined by correlation between observed values ln (n (R, r E , t)) obs and the values of X E , calculated according to Eq. ( 2), for different values of X o and β.In Dorman et al. (1997a,b) three values of β=0, 0.5, 1, have been considered; it was shown that β=1 strongly contradicts the CR and SA observation data, and that β=0 is the most reliable value.Therefore, we will only consider here this value.

Influence of drift effects on the time lag in odd and even cycles
We suppose that the observed long-term cosmic ray modulation is caused by two processes: the convection-diffusion mechanism (e.g.Dorman, 1959;Parker, 1963;Dorman, 1965), which does not depend on the sign of the solar magnetic field, and the drift mechanism (e.g.Jokipii and Davila, Fig. 1.The first and second approaches of the different influence of drift effects on the observed time lag in odd and even cycles: "CD" is convection-diffusion modulation with a total change of 20% (as about in Climax NM data), "CD+DR2" and "CD+DR1" are "observed", including convection-diffusion and drift modulations; "DR2-4%" and "DR1-4%" are supposed drift effects with amplitude A dr =4% (right ordinate).

Fig. 2.
Drift effect according to the third approach for A dr =2% (at W =75).
1981; Jokipii and Thomas, 1981;Lee and Fisk, 1981;Kota and Jokipii, 1999;Burger and Potgieter, 1999;Ferreira et al., 1999) which gave the opposite effects with a changing sign of solar magnetic field.For the convection-diffusion mechanism we will use the model described in detail in Dorman et al. (2001).We will consider three approaches of drift effects.Two of them are shown schematically in Fig. 1.It can be seen from Fig. 1 that in both approaches drift effects in even cycles lead to a decrease in the time lag and in odd cycles to an increase in the time lag in comparison with that expected in convection-diffusion modulation.The first approach also leads to an increase in the width of the CR maximum, from an even to odd cycle, but does not change the value of the CR maximums.The second approach does not change the width of the CR maximums but leads to a relative increase in the CR maximum, from an even to odd cycle, and a decrease from an odd to even cycle (see Fig. 1).This result contradicts the supposition that the CR intensity out of the modulation region is constant in time.But we cannot exclude this model from consideration and discussion: there can be some additional modulation out of the Heliosphere in periods of solar magnetic field A>0, and no modulation in periods A<0 (e.g.only at A<0 can be good direct connection of the IMF with the interstellar magnetic field).In the third approach (see Fig. 2) we suppose that the drift effect is proportional to the value of tilt-angle T (see references above on drift effects in galactic CR).
Data were on tilt-angles only for the period between May 1976−September 1993.On the basis of these data it was found that there was a very good connection between T and W : for yearly data T =0.363W +13.06 • with correlation coefficient 0.973, for monthly data T =0.316W +16.42 • with correlation coefficient 0.882, and for 11 months of smoothed data T =0.349W +13.52 • with correlation coefficient 0.955.We used 11 months of smoothed data of W and the amplitude A dr of drift effects normalized to W =75 (average value of W for the period between January 1953−November 2000).For information on reversal periods we used as follows (according to the Internet): August 1949±9 months, December 1958±12 months, December 1969±8 months, March 1981±5 months, and June 1991±7 months.The drift effect according to the third approach for the period January 1953-November 2000 is shown in Fig. 2 for A dr =2% (at W =75).We calculated the correlation coefficients between expected integrals F , determined by Eq. (2), with observed "LNCL11M" and "LNHU/HAL11M", as well as for these integrals corrected on drift effects according to the first, second and third models with different amplitudes of the drift effect from 0.15% up to 4%.As example, in Table 1 are the results of the determination of X o max and the correlation coefficients for the third model for solar cycles 19, 20, 21, and 22.It can be seen from Table 1 that for odd cycles, increasing of the drift effects leads to a decrease in X o max but for even cycles situation is inverse: with an increasing in the drift effects X o max increases.In Figs. 3 and 4        10-15 GV) and for Huancayo/Haleakala NM (sensitive to 35-40 GV).From Fig. 3 it can be seen that for Climax NM the region of the crossings of the dependences X o max (A dr ) for the odd cycles with the dependences for the even cycles is very small: 13≤X o max ≤16.5, 1.7%≤A dr ≤2.3%.
For Huancayo/Haleakala NM this region is also very small: 13≤X o max ≤18, 0.23%≤A dr ≤0.43% (see Fig. 4).Let us note that for the first and second approaches, the regions of crossings are much bigger than for the third drift approach.Thus, we came to the conclusion that the more reliable is the third drift approach and the amplitude of the drift effects is about 2% for Climax NM and about 0.25-0.3%for Huancayo/Haleakala NM.

Principles of cosmic ray intensity prediction on the basis of solar activity data and convection-diffusion and drift model
In Fig. 5 a comparison of observed long-term CR variation and corrected on drift effects, according to the third model with amplitude 2% (at W =75) for Climax NM (the long-term variation of drift effects for this case was shown in Fig. 2) is shown.Thus, we came to the conclusion that for primary CR with a rigidity of 10-15 GV the relative role of drift effects is about 20% in periods of high solar activity and negligible near solar minimums.For CR with rigidity 35-40 GV, the relative role of drift effects is about 3 times smaller.
From Fig. 5 it can be seen that on the basis of SA data, taking into account convection-diffusion and drift modulations, a very good prediction of CR intensity change can be made, with a correlation coefficient between the observed and predicted intensities of about 0.97.

Prediction of cosmic radiation for few years ahead
At the onset of the cycle there is no information on the values X o max and A dr for this cycle, but the type of cycle (odd or even) is known and we can use published predicted values of sunspot numbers for a few years ahead.NM (effective rigidity of primary particles 10-15 GV) and A dr ≈0.25% for Huancayo/Haleakala NM (35-45 GV).We came to the conclusion that for Climax NM (effective rigidity of primary particles 10-15 GV) the convection-diffusion mechanism gives about 80% of the observed modulation and a drift mechanism of about 20%; for Huancayo/Haleakala NM (effective rigidity of primary particles 35-45 GV) the relative role of drift effects is about 3 times smaller.By regression coefficients of Eq. ( 1), estimated for X o max ≈15 av.months and A dr ≈2% for Climax NM, and A dr ≈0.25% for Huancayo/Haleakala NM we determined the expected convection-diffusion modulation in 1996-1999 only on the basis of monthly sunspot numbers.By adding the expected drift effects, we determined the "predicted" CR intensity.
Comparison with observed data gives correlation coefficients 0.988 and 0.986 for Climax NM and Huancayo/Haleakala NM, accordingly.If it is a good prediction of SA for about one solar cycle, correspondingly, then the prediction on the CR intensity variation can be made for about 10-12 years ahead. Fig.1.

Fig. 1 .
Fig.1.The 1-st and 2-nd approaches of the different influence of drift effects on the observed time-lag in odd and even cycles: CD is convection-diffusion modulation with total change 20% (as about in Climax NM data), CD+DR2 and CD+DR1 are "observed", included convection-diffusion and drift modulations; DR2-4% and DR1-4% are supposed drift effects with amplitude % 4 = dr A

Table 1 .
Values of max o X(in av.months, bold) and correlation coefficients for observed data (0%) and corrected on drift effects with different amplitudes according to the 3-rd model.
dependences X o max (A dr ) for Climax NM (sensitive to primary particles with rigidity

Table 1 .
Values of X omax (in av.months, bold) and correlation coefficients for observed data (0%) and corrected drift effects with different amplitudes, according to the third model.