Reconstructing the long-term cosmic ray intensity: linear relations do not work

Abstract

Abstract. It was recently suggested (Lockwood, 2001) that the cosmic ray intensity in the neutron monitor energy range is linearly related to the coronal source flux, and can be reconstructed for the last 130 years using the long-term coronal flux estimated earlier. Moreover, Lockwood (2001) reconstructed the coronal flux for the last 500 years using a similar linear relation between the flux and the concentration of cosmogenic 10 Be isotopes in polar ice. Here we show that the applied linear relations are oversimplified and lead to unphysical results on long time scales. In particular, the cosmic ray intensity reconstructed by Lockwood (2001) for the last 130 years has a steep trend which is considerably larger than the trend estimated from observations during the last 65 years. Accordingly, the reconstructed cosmic ray intensity reaches or even exceeds the local interstellar cosmic ray flux around 1900. We argue that these unphysical results obtained when using linear relations are due to the oversimplified approach which does not take into account the complex and essentially nonlinear nature of long-term cosmic ray modulation in the heliosphere. We also compare the long-term cosmic ray intensity based on a linear treatment with the reconstruction based on a recent physical model which predicts a considerably lower cosmic ray intensity around 1900.

Heliospheric modulation of cosmic rays: Monthly reconstruction for 1951–2004

“…For many purposes it is important to know the differential energy spectrum of cosmic rays and its temporal variations. For example, the direct use of a linear relation between the energy‐integrated cosmic ray flux and solar activity may lead to large uncertainties in long‐term studies (see details in the work of Mursula et al [2003] and Usoskin and Kovaltsov [2004]). Although it is hardly possible to reconstruct the past cosmic ray spectrum directly, the shape of the cosmic ray spectrum in the vicinity of the Earth can be well approximated by the so‐called force field model [ Gleeson and Axford , 1968; Caballero‐Lopez and Moraal , 2004], which contains only one formal parameter, the modulation potential.…”

Review on dating methods: Numerical dating in the quaternary geology of High Asia

“…In this case, too, solar minima correlate with maxima of the cosmic ray flux measured by terrestrial NMs (Usoskin et al 2008: 442). However, the relationship seems to be complex so that a simple linear extrapolation into the past is not possible (Mursula et al 2001). The scientific effort of taking into account the variations of the cosmic ray flux due to changes in solar activity when calculating the local TCN productivity is therefore still in its early stages (in particular the millennial-scale solar modulation requires further study; Lifton et al 2005: 141) what is clear, at any rate, is that at this stage it cannot possibly mend the inaccurateness of the TCN calculations imposed on High Asia.…”

An empirical model of heliospheric cosmic ray modulation on long-term time scale

“…Kta & Jokipii 2001), resulting in a linear relationship between the modulation potential and OSF. On the other hand, some studies suggest that the relation is not exactly linear or quasilinear (Mursula et al 2003;Alanko-Huotari et al 2006). Alanko-Huotari et al (2006) studied the correlation between / and F over periods of flat or highly tilted HCS and showed that the dependence of / on F varies with the tilt angle.…”