Acknowledgements

The authors would like to express our sincere thanks to Prof. Seiichi Kanari for his fruitful comments at the beginning of this study. The comments for the original version of the manuscript from an anonymous reviewer and the editor, Dr. Satoshi Sakai, are quite helpful to improve the present paper. This study is partly supported by grants from Hokkaido University, from Center for Climate System Research at University of Tokyo, and from the Japanese Ministry of Education, Culture and Science.