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Erratum
Open Access

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

  • Masayoshi Kozai1Email author,
  • Kazuoki Munakata1,
  • Chihiro Kato1,
  • Takao Kuwabara2,
  • John W. Bieber2,
  • Paul Evenson2,
  • Marlos Rockenbach3,
  • Alisson Dal Lago4,
  • Nelson J. Schuch3,
  • Munetoshi Tokumaru5,
  • Marcus L. Duldig6,
  • John E. Humble6,
  • Ismail Sabbah7,
  • Hala K. Al Jassar8,
  • Madan M. Sharma8 and
  • Jozsef Kóta9
Earth, Planets and Space201668:38

https://doi.org/10.1186/s40623-016-0417-1

©  Kozai et al. 2016

Received: 22 February 2016

Accepted: 22 February 2016

Published: 7 March 2016

The original article was published in Earth, Planets and Space 2014 66:151

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.”

Figure 2
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

 

Nagoya GG

GMDN

NMs

\(T - A\) (%)

 Daily

0.1504

0.1398

0.1090

 Hourly

0.1324

0.1258

–

\(\sqrt{\sigma _{T}\sigma _{A}}\) (%)

 Daily

0.0033

0.0044

0.0062

 Hourly

0.0016

0.0013

–

T / A separation

 Daily

46.2

31.5

17.8

 Hourly

81.2

96.6

–

Success rate (%)

 Daily

73.5

68.7

59.6

 Hourly

58.2

62.0

–

Difference (\(T - A\)) between average \(\xi ^\mathrm{GEO}_z\)s in toward (T) and away (A) IMF sectors, geometric mean (\(\sqrt{\sigma _{T}\sigma _{A}}\)) of the standard errors of \(\xi ^\mathrm{GEO}_z\)s in T and A sectors, “T / A separation” (\(= (T - A)/\sqrt{\sigma _{T}\sigma _{A}}\)) and “success rate” (see text) derived from Nagoya GG-component, GMDN, and NM (Thule–McMurdo) data in 2006–2013 on daily and hourly bases

Notes

Declarations

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Authors’ Affiliations

(1)
Physics Department, Shinshu University, Nagano, Japan
(2)
Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, USA
(3)
Southern Regional Space Research Center (CRS/INPE), Santa Maria, Brazil
(4)
National Institute for Space Research (INPE), São José dos Campos, Brazil
(5)
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Japan
(6)
School of Physical Sciences, University of Tasmania, Hobart, Australia
(7)
Department of Natural Sciences, College of Health Sciences, Public Authority for Applied Education and Training, Kuwait City, Kuwait
(8)
Physics Department, Kuwait University, Kuwait City, Kuwait
(9)
Lunar and Planetary Laboratory, University of Arizona, Tucson, USA

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 66:151View ArticleGoogle Scholar

Copyright

© Kozai et al. 2016

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