## 2 Data and Methods  
### Data  
The Hong Kong Observatory collects data on nearly 100 automatic weather stations, including data on surface air temperature, wind speed, wind direction, rainfall, etc. The data utilized in this article include the daily average temperature, daily maximum temperature, and daily minimum temperature data of the 14 sites: Ta Kwu Ling (TKL), Lau Fau Shan (LFS), Wetland Park (WLP), Shek Kong (SEK), Tai Mo Shan (TMS), Sha Tin (SHA), Tate's Cairn (TC), King's Park (KP), Hong Kong International Airport (HKA), Hong Kong Observatory (HKO), Sha Lo Wan (SLW), Peng Chau (PEN), Cheung Chau (CCH), and Waglan Island (WGL) (Table 1). For simplicity, in the following discussion, we refer temperature to as surface air temperature, unless otherwise specified. The temperature data of these stations contain missing data points (Table 1), which implies difficulties for extracting target signals by using the Lanczos filter or other commonly used \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Automatic** & \multicolumn{2}{c}{**Position**} & \multicolumn{2}{c}{**Length of Data Record**} & \multicolumn{2}{c}{**Number of Missing Values**} \\ \cline{2-7}
**Weather** & **Latitude** & **Longitude** & **Starting** & **Number of** & **Mean** & **Max/Min** \\
**Station** & **N** & **E** & **Date** & **Data Points** & **Temperature** & **Temperature** \\ \hline Ta Kwu Ling & \(22^{\circ}\) & \(114^{\circ}\) & & & & & \\ (TKL) & \(31^{\prime}43^{\prime\prime}\) & \(09^{\prime}24^{\prime\prime}\) & 14 October 1985 & 13,593 & 1091 & 1043 \\ \hline Lau Fau Shan & \(22^{\circ}\) & \(113^{\circ}\) & & & & \\ (LFS) & \(28^{\prime}08^{\prime\prime}\) & \(59^{\prime}01^{\prime\prime}\) & 16 September 1985 & 13,621 & 222 & 147 \\ \hline Wetland Park & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (WLP) & \(28^{\prime}00^{\prime\prime}\) & \(00^{\prime}32^{\prime\prime}\) & 10 November 2005 & 6261 & 13 & 7 \\ \hline Shek Kong & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (SEK) & \(26^{\prime}10^{\prime\prime}\) & \(05^{\prime}05^{\prime\prime}\) & 4 November 1996 & 9554 & 342 & 293 \\ \hline Tai Mo Shan & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (TMS) & \(24^{\prime}38^{\prime\prime}\) & \(07^{\prime}28^{\prime\prime}\) & 1 December 1996 & 9527 & 231 & 179 \\ \hline Sha Tin & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (SHA) & \(24^{\prime}09^{\prime\prime}\) & \(12^{\prime}36^{\prime\prime}\) & 1 October 1984 & 13,971 & 154 & 111 \\ \hline Tate’s Cairn & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (TC) & \(21^{\prime}28^{\prime\prime}\) & \(13^{\prime}04^{\prime\prime}\) & 1 December 1997 & 9162 & 106 & 66 \\ \hline King’s Park & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (KP) & \(18^{\prime}43^{\prime\prime}\) & \(10^{\prime}22^{\prime\prime}\) & 1 July 1992 & 11,141 & 25 & 7 \\ \hline Hong Kong & \(22^{\circ}\) & \(113^{\circ}\) & & & & \\ International Airport (HKA) & \(18^{\prime}34^{\prime\prime}\) & \(55^{\prime}19^{\prime\prime}\) & 1 June 1997 & 9345 & 0 & 31 \\ \hline Hong Kong & \(22^{\circ}\) & \(114^{\circ}\) & & & & & \\ Observatory (HKO) & \(18^{\prime}07^{\prime\prime}\) & \(10^{\prime}27^{\prime\prime}\) & 1 April 1884 & 50,678 & 2557 & 2557 \\ \hline Sha Lo Wan & \(22^{\circ}\) & \(113^{\circ}\) & & & & \\ (SLW) & \(17^{\prime}28^{\prime\prime}\) & \(54^{\prime}25^{\prime\prime}\) & 25 February 1993 & 10,902 & 691 & 591 \\ \hline Peng Chau & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (PEN) & \(17^{\prime}28^{\prime\prime}\) & \(02^{\prime}36^{\prime\prime}\) & 1 June 2004 & 6788 & 53 & 32 \\ \hline Cheung Chau & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (CCH) & \(12^{\prime}04^{\prime\prime}\) & \(01^{\prime}36^{\prime\prime}\) & 30 March 1992 & 11,234 & 98 & 44 \\ \hline Waglan Island & \(22^{\circ}\) & \(114^{\circ}\) & & & & \\ (WGL) & \(10^{\prime}56^{\prime\prime}\) & \(18^{\prime}12^{\prime\prime}\) & 22 August 1989 & 12,185 & 811 & 665 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information about 14 automatic weather stations employed in this study.