We compared the long-term variation (1992 – 2017) in solar polar brightening observed with the Nobeyama Radioheliograph, the polar solar-wind velocity with interplanetary scintillation observations at the Institute for Space-Earth Environmental Research, and the coronal-hole distribution computed by potential-field calculations of the solar corona using synoptic magnetogram data obtained at the National Solar Observatory/Kitt Peak. First, by comparing the solar-wind velocity [V\documentclass[12pt]{minimal}
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\begin{document}$V$\end{document}] and the brightness temperature [Tb\documentclass[12pt]{minimal}
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\begin{document}$T_{\mathrm{b}}$\end{document}] in the polar region, we found good correlation coefficients (CCs) between V\documentclass[12pt]{minimal}
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\begin{document}$T_{\mathrm{b}}$\end{document} in the polar regions, CC = 0.91 (0.83) for the northern (southern) polar region, and we obtained the V\documentclass[12pt]{minimal}
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\begin{document}$V$\end{document}–Tb\documentclass[12pt]{minimal}
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\begin{document}$T_{ \mathrm{b}}$\end{document} relationship as V=12.6\documentclass[12pt]{minimal}
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\begin{document}$V = 12.6$\end{document}(Tb−10,667)1/2+432\documentclass[12pt]{minimal}
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\begin{document}$(T_{\mathrm{b}}-10{,}667)^{1/2}+432$\end{document}. We also confirmed that the CC of V\documentclass[12pt]{minimal}
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\begin{document}$T_{\mathrm{b}}$\end{document} is higher than those of V\documentclass[12pt]{minimal}
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\begin{document}$V$\end{document}–B\documentclass[12pt]{minimal}
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\begin{document}$B$\end{document} and V\documentclass[12pt]{minimal}
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\begin{document}$B/f$\end{document}, where B\documentclass[12pt]{minimal}
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\begin{document}$f$\end{document} are the polar magnetic-field strength and magnetic-flux expansion rate, respectively. These results indicate that Tb\documentclass[12pt]{minimal}
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\begin{document}$T_{\mathrm{b}}$\end{document} is a more direct parameter than B\documentclass[12pt]{minimal}
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\begin{document}$B$\end{document} or B/f\documentclass[12pt]{minimal}
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\begin{document}$B/f$\end{document} for expressing solar-wind velocity. Next, we analyzed the long-term variation of the polar brightening and its relation to the area of the polar coronal hole [A\documentclass[12pt]{minimal}
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\begin{document}$A$\end{document}]. As a result, we found that the polar brightening matches the probability distribution of the predicted coronal hole and that the CC between Tb\documentclass[12pt]{minimal}
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\begin{document}$A$\end{document} is remarkably high, CC = 0.97. This result indicates that the polar brightening is strongly coupled to the size of the polar coronal hole. Therefore, the reasonable correlation of V\documentclass[12pt]{minimal}
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\begin{document}$T_{\mathrm{b}}$\end{document} is explained by V\documentclass[12pt]{minimal}
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\begin{document}$A$\end{document}. In addition, by considering the anti-correlation between A\documentclass[12pt]{minimal}
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\begin{document}$f$\end{document} found in a previous study, we suggest that the V\documentclass[12pt]{minimal}
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\begin{document}$T_{\mathrm{b}}$\end{document} relationship is another expression of the Wang–Sheeley relationship (V\documentclass[12pt]{minimal}
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\begin{document}$V$\end{document} – 1/f\documentclass[12pt]{minimal}
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\begin{document}$1/f$\end{document}) in the polar regions.
