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

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

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