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Erratum to: The spatial density gradient of galactic cosmic rays and its solar cycle variation observed with the Global Muon Detector Network

The Original Article was published on 14 November 2014

Erratum to: Earth, Planets and Space 2014, 66:151 DOI 10.1186/s40623-014-0151-5

Equation (4) in the original paper (Kozai et al. 2014) was incorrect and needs to be multiplied by a factor 2, as

$$\begin{aligned} \xi _z^\mathrm{GEO} = c \cdot \frac{R}{R^T + R^A}. \end{aligned}$$
(4)

Figure 2e and the column “NMs” of Table 1 in the paper which were calculated from Eq. (4) in the paper also need to be corrected. The corrected Fig. 2 and Table 1 are shown below. According to these corrections, a few sentences in the paper need to be reworded as follows. It is noted that all conclusions are not subject to these corrections.

  • Page 6, left column, Line 5

    “mainly due to the small \(T-A\), i.e., the NS anisotropy is significantly smaller than that obtained from the GMDN and GG-component.”

    should be reworded as:

    “due to the large \(\sqrt{\sigma _{T}\sigma _{A}}\) and the small \(T-A\), indicating that the NS anisotropy is smaller than that obtained from the GMDN and GG-component.”

  • Page 7, right column, Line 14

    “If these are the case, the magnitude of the NS anisotropy increases with rigidity and the T/A separation and success rate will also increase if the dispersion remains similarly independent of rigidity. This is in agreement with our results in Table 1, showing that \(T-A\) increases with the rigidity while \(\sqrt{\sigma _{T}\sigma _{A}}\) is almost constant on a daily basis.”

    should be reworded as:

    “This is in an agreement with our results in Table 1, showing that \(T-A\) increases with the rigidity.”

Fig. 2
figure2

Histograms of the NS anisotropy. Each panel displays the histograms of \(\xi _z^\mathrm{GEO}\) on hourly (a, b) and daily (c, d, e) bases derived from the Nagoya GG-component (a, c), the GMDN (b, d), and NM (Thule–McMurdo) (e) data in 2006–2013. Blue and red histograms in each panel represent distributions of \(\xi _z^\mathrm{GEO}\) in toward and away IMF sectors, respectively, while blue and red vertical dashed lines represent averages of the blue and red histograms, respectively

Table 1 \(T-A\), \(\sqrt{\sigma _T \sigma _A}\), T / A separation, and success rate

Reference

  1. Kozai M, Munakata K, Kato C, Kuwabara T, Bieber JW, Evenson P, Rockenbach M, Lago AD, Schuch NJ, Tokumaru M, Duldig ML, Humble JE, Sabbah I, Al Jassar HK, Sharma MM, Kóta J (2014) The spatial density gradient of galactic cosmic rays and its solar cycle variation observed with the Global Muon Detector Network. Earth Planets Space 66:151

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Correspondence to Masayoshi Kozai.

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The online version of the original article can be found under doi:10.1186/s40623-014-0151-5.

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Kozai, M., Munakata, K., Kato, C. et al. Erratum to: The spatial density gradient of galactic cosmic rays and its solar cycle variation observed with the Global Muon Detector Network. Earth Planet Sp 68, 38 (2016). https://doi.org/10.1186/s40623-016-0417-1

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