小波分析在水文学中的应用-地球科学期刊2

㄀2 ㄀1⧗⾥ V ol.2No.12012 3 Scientific Journal of Earth Science [SJES] Mar. 2012 PP .27-33 © 2011 American V-King Scientific Publishing, L TD⊶ ∈ Ёⱘ ⫼ē⊇ ⿟ 䰶䌘⑤Ϣ⦃ ⿟㋏ˈ⊇ 䚥 451191㽕˖ Ϗ ԅ Շ ē ԅ Շ ԅ ē΄ ԙ Ӿ ԅ d· Ϗ Fourier έ · ιԅ ҄ ē Ϗ c Ϗc c Љ Љ ͱԉ ԅ d ē ѻ Ϗ ё ѻ ԅϢ ԅԙ d 䬂䆡˖ Ϗ ĢFourier έ Ģ ĢApplication of Wavelet Analysis in HydrologyJianfeng Zhang, Wenlu WangDepartment of Resources and Environmental Engineering, Henan Institute of Engineering, Zhengzhou, China, 451191zjfldp@Abstract: Due to the good ability of localization of time-frequency, which is suitable for frequency analysis in unstable time series, the wavelet analysis is widely used in scientific research in many fields. After the explanation of essential differences between wavelet analysis and Fourier transform, the paper summarizes the status-quo of Wavelet analysis’applications in period analysis, filtering, trend analysis, singularity detection, and forecasting in hydrology. Problems and deficiencies of wavelet application in hydrology are figured out in the end.Key words: Wavelet Analysis;Fourier Transforms; Hydrology; Time Series㿔∈ ∈䌘⑤乚 Ёⱘ 䯈 ˈ ⇨䈵ǃ ⧚⦃ ǃҎ㉏⌏ ㄝӫ ㋴ⱘ DŽ 㗠ˈ∈ ∈䌘⑤ 䴲㒓 ǃ ǃ䱣 䴲 〇 ㄝ⡍⚍ˈԚ г ⱘ 䍟 DŽ ∈ ∈䌘⑤ 䯈 ˈFourier Փ⫼ ⊯ⱘϔ⾡ ⊩DŽԚ Fourier 䗖⫼Ѣ〇 ˈ䖭Փ ∈ 䌘 䳔㽕䖯㸠 〇 ⧚ˈ㗠䖭⾡ ⧚ 㛑Ӯ 乥䈅ⱘ⭌ 㗠䗴 䇃 DŽ ⊶ ⱘ ѢϞϪ㑾 ˈ ⫼ϔϾ ⱘԌ㓽 ⿏ ⿃ ぎ䯈L 2(R)ⱘϔ㒘 ˈℸ ⿄Ў ⊶DŽ 20Ϫ㑾80 ҷЁ ˈ⊩ 䋼⠽⧚ Morlet њ ⊶ [1]DŽⱘ䖥20 䞠ˈ ⊶ ⧚䆎 њЄ 䗤⏤ ❳DŽ԰ЎFourier ⱘ ˈ ⊶ ⬭њFourier ⱘӬ⚍ˈ 㸹њFourier Ϟⱘϡ䎇DŽ Ҟˈ ⊶ 㒣 ⊯ⱘ ⫼ њ 乚 ˈ ⧚[2, 3]ǃ⫳⠽[4, 5]ǃ⠽⧚[6, 7]ǃ∈ [8-10]ㄝDŽ⬅Ѣ ⊶ 㛑 ⱘ 䴲 〇 䯈 ˈ 乥⥛ ӑⱘ 䯈 ԡ⡍ ˈ䖥20 ˈ ⊶ ∈ Ё њ䞡㽕԰⫼ њ䆌 ⷨお ˈЏ㽕㸼⦄ ∈ ⱘ ǃ䍟 ǃ ⲥ⌟ǃ乘⌟乘 䱣 ῵ ㄝDŽ1Fourier Ϣ ⊶⊶ Fourier ⱘ ⸔Ϟ 䍋 ⱘˈ䖭 䳔㽕ҟ㒡Fourier ⱘὖ DŽӫ ⶹˈϔϾ ⱘ⊶ ҹⳟ ⬅䆌 ϡ 乥⥛ǃϡ ⱘㅔ䇤⊶ 㗠 ⱘDŽFourier ˄῵ ˅԰䇤⊶ 㾷ǃ ⱘ ⱘ [11])(t f DŽ䆒 ˈ ⱘFourier Ў˖ēԉ Ϗ ԅ PP .27-33 © 2011 American V-King Scientific Publishing, L TD-28- ³ f f dt e t f F t i Z Z )()( (1)✊ˈFourier ˄ 㗙 ˅ⱘ Ͼ乥⥛ ӑ㾚Ў ⱘǃ 䰤 Ԍⱘ䇤⊶П ˈ䖭ѯ乥⥛ ӑ ⱘ Ͼ 䯈 ϞDŽ ℸˈFourier Ͼ 䯈 乥⥛⡍ ⱘ 䗄DŽ⊶ ϢFourier 䋼Ϟⱘ ˖ ϡ 乥⥛ Ϟˈ ⊶ 㾷Ў 䯈 ԡ 㛑ⱘ 䰤䭓 ⊶ П DŽ ⊶ ϸϾ ˖ a 䯈ԡ㕂 b ˖)(1)(,a b t at b a \\ (2)䗮䖛 a ˈѻ⫳ϡ ⱘĀ ⊶āˈҢ㗠 ҹⷨお ⱘϡ 乥⥛ ӑ˗㗠䗮䖛 b ⱘ ҹ䇗 䯈䕈Ϟӏ 䯈 㒭 ⱘ乥⥛ ӑDŽ ℸˈ ⊶ 㛑 ⱘ 䗄䴲 〇 ⱘ乥⥛⡍ DŽ )(t s ⱘ䖲㓁 ⊶ ˖³ f f dt a b t at S b a W )(*1)(),(\ (3) Ёˈ*㸼⼎ 䕁DŽ䖲㓁 ⊶ ⱘ㒧 䴶Ϟ ϔϾㄝ 㒓 ˈ乥⥛Ўy 䕈ˈ ⥛˄㛑䞣power ˅Ўz 䕈ˈ 䯈Ўx 䕈DŽ∈ Ёˈ∈ 䯈 ˄ ϟ∈ԡǃ ⌕ǃ䰡∈ǃ㪌 ㄝ˅ Т䛑 䴲 〇ⱘˈ Ӏⱘ乥⥛ ӑ䛑Ӯ䱣 䯈㗠 [12, 13]2.1∈DŽ ℸˈⷨお㗙ℷ ⫼䖭ϔ乥⥛- 䯈⡍ ⊶ ⊯ⱘ ⫼ њ ǃⒸ⊶ǃ䍟 ǃ ⲥ⌟ǃ乘⌟乘 䱣 ῵ ㄝDŽ2 ⊶ ∈ Ёⱘ ⫼∈ Ёˈ 䰡∈ǃ⏽ ⌕ⱘ Ѣњ㾷 ⱘ∈ 㸵 ∈ ⦃DŽ⬅Ѣ ⊶ 㛑 䯈 ⱘ 乥 䚼 ⡍ ˈ ҹⳟ ӏ 䯈ⱘԡ㕂ˈ ⹂ⱘ⹂ ⱘ ˈ↨ ⥛䈅 ⊩䅵ㅫ ⱘ 〇 [14]ˈ ℸˈ 㛑 䱣 䯈ⱘ DŽ1993 ˈKumar [10, 15] ⫼ℷѸ ⊶ ⷨお䰡∈ ⱘ ⡍ ⦄ˈ䰡∈ 䯈 䰡∈⊶ ⱘ㞾ⳌԐ ⡍ ˈ㄀ϔ⃵ ⊶ ∈ 䯈 ЁDŽ㑾 㧡[16]⫼ 㽓 ⊶ њ 1908-1997 䗤 䰡∈ⱘ ⡍ ⦄ˈ20Ϫ㑾 50 ҷ ˈ䰡∈Џ㽕㸼⦄Ў20-30 Ϟⱘ⊶ ˗60 ҷ㟇Ϫ㑾 ˈ䰡∈⊶ ҹ10 5-7 ЎЏDŽ䗮䖛 ⊶ ⦄ˈ 䰡∈ 28 ǃ7.4 2 ⱘ ˈ Ё28 ӑЎЏ DŽ㒣䖛Ϣ ➉䈅 ⊩ǃ ⥛䈅 ⊩ҹ EOF ˄㒣偠ℷѸ ˅ ⊩ 㒧䆎ⱘ ↨ˈ 䆕њ ⊶ ҹ⫼ 䯈 Ё ⱘЏ㽕 DŽⷨお ⒊ ϟ∈䕧䖤 ⡍ ˈMassei 䗮䖛 ↨䰡∈ǃ ϟ∈ԡǃ⌥⌞ ⬉ ⥛ㄝ 䯈 ⱘ ⊶ [17]DŽ㒧 㸼 ˈ䰡∈ Ϣ ϝ㗙ⳌԐⱘ㒧 ˗⡍ ⌥⌞ ⱘ⊶ 催 ձ䌪Ѣ䰡∈DŽ 㗙䇈 ˈ ϟ∈⌥⌞ ҹ ⱘ⼎䏾 ⒊ㅵ䘧⌕DŽ԰㗙䖯㗠䗮䖛 ⊶䗚 㾷њ ϟ∈ԡⱘ催乥 Ԣ乥 ӑ˄ ⒊∈ⱘ 䗳⌕ 䗳⌕˅ˈ㒣 ↨ ϟ∈ԡ 䯈 ⱘ催乥 ӑ ⌥⌞ ˈ ⦄Ѡ㗙⊶ 㡃 ˈ䇈 ⌥⌞ г㛑⫼ ϟ∈ⱘ 䗳⌕ 䗳⌕DŽ⬅Ѣ ⊶ ㋏ Ϣ 䯈 ⊶ 㒓 ㋏[18, 19]ˈ ⊶㋏ ⱘ њ 䯈 ⱘ⊶ ⡍ ˈ ℸˈ ҹⳈ 䗮䖛 ↨ϡ ⱘ ⊶ ㋏ ӀП䯈ⱘⳌѦ ㋏DŽṕ ⍋[20]ㄝ䗮䖛 ⊶ њ咘⊇⑤ 1955-1999 ⌕䞣ˈ㒧 ⼎⑤ ⌕䞣 ϔϾ䕗 ⱘ䍟 乍ҹ 7-8ǃ3-4 ϸϾ 㨫 ˈ 䍟 乍ϢϸϾ 㨫 ⱘ ⌕Є ⱘ ӑˈг Ϟϝ⃵ ⌕ⱘḍ DŽ䗮䖛 ⌕ǃ⇨⏽ǃ䰡∈Џ ӑ ⊶㋏ ⱘ ↨ ⦄ˈ⑤ ⌕䞣䍟 乍 ⇨⏽ 㟈ˈ㗠䰡∈ⱘ⊶ њ ⌕ⱘϸϾ 㨫 DŽScientific Journal of Earth Science [SJES] PP .27-33 © 2011 American V-King Scientific Publishing, L TD -29-2.2∈ Ⓒ⊶䗮 ˈ ⌟ⱘ 䯈 㹿 ∵ ⱘˈЎњ ⳳ ⱘ ˈ ⾡ ⧚⧚䆎ǃ ⊩ ϔ ϟ䖯㸠Ⓒ⊶ǃԄ䅵 ⱘ ҹ䖙䗳 [21, 22]DŽӴ㒳ⱘⒸ⊶ ⊩ Ⓒ⊶ǃ Ⓒ⊶ǃ Ⓒ⊶ㄝ[11]ˈ䖭ѯⒸ⊶ ⊩㛑 䗖⫼Ѣ㒓 ϡ ㋏㒳ˈ 㽕∖ 䯈 〇ⱘDŽ⬅Ѣ䖭ѯ ⊩䛑 䩜 ԧⱘⒸ⊶ ⊩ˈ Ӏ 㛑⫼Ѣ 乥 䞡 䴲 㗙≵ 䞡 ⱘ DŽ 䰙Ϟˈ⬅Ѣ ǃ⇨ ǃ⌕ ϟ 䴶 Ҏ㉏⌏ ㄝ䇌 ㋴ⱘ ˈ∈ 䗮 䴲〇 ǃ催 ⱘ䴲㒓 䱣 䖛⿟[23, 24]DŽ ∈ 䖯㸠⍜ ⧚㛑 催 ⱘ 䴴 ⱘ㊒ [12]DŽ䗮 ˈ 䑿 ҹ Ўϸ䚼 ˖䚼 催乥ⱘ ӑˈԢ乥 ⫼ ӑDŽ Ѣℸˈ䗮䖛 ⱘ ⊶ 㾷ˈ 催ǃԢ乥 ⾏ˈ✊ ḍ 䳔㽕䗝 ϔϾ 䗖ⱘ䭹 ˄threshold ˅ Ⓒ䰸ˈ ⧚ ⱘ ҹ䞡 ˈҢ㗠 ⦄ ⾏DŽ⥟ӆ⇥[25] ⫼Ѡ⃵ ˄QSLF ˅ ⹂ 䭹 ˈ ϔϾ 催 ⱑ ⱘϸϾℷ 㒘 ῵ 䖯㸠њⒸ⊶䆩偠DŽ Т 㹿 䰸ˈ ↨Ў15.1dB ˈ ⲞЎ10.1dB ˈ䞡 ⱘ⊶ Ϣ ϔ㟈DŽ⥟⾔ [26] ⫼ ⊶⍜ ⊩ⷨおњ∈ 䯈 ⱘ佅 㘨㓈 ˈ䅵ㅫ㒧 㸼 ˈ㒣䖛⍜ ∈ 䯈 ⱘ佅 㘨㓈 ↨⍜ 䰡ԢˈЎ⏋≠∈ ㋏㒳Ё ⱘ⍜䰸 կњϔ⾡ ⱘ䗨 DŽⷨお䞡 䴦 ⒊ ϟ⊇∈ԡЁˈ [27]2.3∈ 䍟䗮䖛 ⊶⍜ ⱘ ⊩ ⒥њ∈ԡ 㒓ˈ ⍜ ⱘ 㒓 ⬭њ ⱘЏ㽕㒚㡖DŽ㒣䖛 ⍜ 䯈 Ⳍ ˈ⍜ ⱘ㞾Ⳍ ㋏ ˈ ⱘ㞾ⳌԐ DŽ䱣ⴔ 䯈ⱘ 䭓ˈ∈ ⱘ Ϟ ϟⱘ ˈ䖭⾡ ⿄Ў䍟 DŽ∈ 㽕㋴ 䍟 ∈ ⦃ⷨおⱘ䞡㽕 ˈ 㒣㹿䆌 㗙 ⊼[28, 29]DŽ⬅Ѣ∈ ⱘ ˈ Ӏ 䲒 ϔ㞾✊䖛⿟ Ѣ㞾✊⊶ 䖬 ⹂ ⡍ ⱘ 䍟 DŽ䩜 䖭ϔ䯂乬ˈ њӫ ⱘ䍟 䆞 ⊩DŽ䗮 䍟 ӑ ⊩ ⒥ ⊩[12]ǃMann-Kendall ⾽⃵Ⳍ Ẕ偠⊩[30-33] 䍟 Ẕ偠⊩[12, 34]ㄝDŽ ⊶ 䕼 㛑ˈ 㛑䆚 ∈ ⾡催Ԣϡ ⱘ乥⥛ ӑˈϡ ϟⱘԢ乥 ӑ 㸼⼎∈ 䆹 ϟⱘ 䍟 DŽ䖭 Ӵ㒳 ⊩ ϡ ⱘDŽ⥟ [12]䖤⫼㋻ Ѡ⃵ḋ ⊶ ϝ䮼 キ ⌕䖯㸠5㑻 䗳 ⊶ 㾷DŽ䗮䖛 ㄀Ѩ㑻Ԣ乥 ⱘ䞡 ⦄ˈ20Ϫ㑾 30 ҷ ⌕ 䍟 ˈ30 ҷ 60 ҷ ⌕ 䍟 ˈ70 ҷ 21Ϫ㑾 ⌕ ⱘ 䍟 DŽLiu [35]2.4∈ Ẕ⌟⫼ ⊶ ⊩ⷨおњ咘⊇ ⋹∈ キ1950-2002 ⌕-≝⎔⠽ 䯈 DŽҪ䗮䖛 㾷Ў催乥 Ԣ乥 ӑ ⱘ 䍟 DŽ㒧 ⼎ˈ咘⊇ ⌕-≝⎔⠽䛑 ⱘϟ䰡䍟 ˈ䖭⾡ϟ䰡ⱘ䍟 ⑤Ѣ ⇨ ⱘ Ҏ㉏⌏ ˈ ⊓咘⊇ ∈ⱘ䕀 DŽ∈ ϔ 㞾✊ ⇨ ӊϟⱘѻ⠽ˈ Ё ⾡ ӊ ⫳ ˈ 䯈 Ӯ ⦄䍟 ǃ䏇䎗 さ ⦄䈵ˈ䖭ѯ⦄䈵 ∈ Ё㹿 Ў ˈ Ё⿄Ў ˄singularity ˅DŽ ⫼䖭ѯ ⱘ∈ 䖯㸠乘⌟乘 ˈ 㛑䗴 䕗 ⱘ DŽ ℸˈ さ ⚍ⱘԡ㕂ⱘẔ⌟ ∈ ⱘϔϾ䞡㽕 DŽ⬅Ѣ ⊶ ϔ⾡ 乥 䕼 ⊩ˈ 乥 䛑 㸼 䚼⡍ ⱘ㛑 ˈ ℸˈ 䗖 ⲥ⌟ Ёⱘ ӑDŽ ⊶ ⲥ⌟ ⊩ 㒣 ⊯ⱘ ⫼ њ Ͼ乚 ˈ Ẅ 䱰ⲥ⌟[36, 37]ǃⳂ ⌟[38]ǃ ⧚[39, 40] [41]ㄝDŽēԉ Ϗ ԅ PP .27-33 © 2011 American V-King Scientific Publishing, L TD-30- ⱘさ ⚍ 䚼 DŽさ ⚍ ҹ Ўϸ㉏˖ϔ㉏ Ѣさ Ё ⚍ⱘ 䚼 ⿄さ ⚍ˈ ϔ㉏ Ѣさ Ё ⚍ 䚼 ⿄ⱘさ ⚍DŽ㢹⫼ϔϾ 䚼 ⿄ 䚼 ⿄ⱘに Ϣ䖭ϸ㉏ 䚼さ ⿃ˈ ҹ さ ⚍ⱘԡ㕂[42])(t x DŽ㒣䖛Ẕ㋶ ⊶㋏ ⱘ῵ ⚍˄ ⊶ Ў ⒥ ⱘϔ䰊 ˅ Ẕ㋶ ⊶㋏ ⱘ䖛䳊⚍˄ ⊶ Ў ⒥ ⱘѠ䰊 ˅ˈ ҹẔ⌟ ⱘさ ԡ㕂 䋼DŽ Ϟ 䞛⫼Lipschitz ˄ Lip ˅ 䗄 ⚍ⱘ DŽ䆒 0t 䰘䖥 ϟ⡍1,)()(00 d n n h A h t p h t x n D D (4)⿄ )(t x 0t ⱘLip ЎD ˗A Ўϔℷ ˗h Ўϔ ⱘ ˗n p 䖛0t ⚍ⱘn ⃵ 乍 DŽLip 㸼 њ )(t x Ϣn ⃵ 乍 Ⳍ↨ ⒥⿟ ⱘ ˈLip 䍞 ˈ䆹⚍ⱘ ⒥ 䍞催ˈ 㑺 ˗ Пˈ䆹⚍ⱘ 䍞 DŽ[43]2.5∈ 乘⌟乘Ѣ ⊶ ϢLipschiz ⊩ њ咘⊇䴦䪰 キ1723-2000 ✊ ⌕ 䯈 DŽ 㸼 ˈ䴦䪰 キ ⌕ 278 䖛⿟Ёˈ ⫳њ10⃵䕗 ⱘさ ˈ↣⃵さ ⱘ㉏ ⿟ 䛑 ϡ ˈ Ёˈ 䯈㣗 䍙䖛10 ҹϞⱘさ ⚍ 3⃵ˈ 1760ǃ1967 1989 ˗㗠䖥50 ҹ さ ⫳ⱘ乥⥛ DŽ䙧㞾 ⫼ ⱘMorlet ⊶ⷨおњ㽓 䖥50 䰡∈ 䯈 DŽ䗮䖛 ⊶㋏ ⱘⳌԡ 䰡∈ Ё さ ⚍ⱘԡ㕂DŽⷨお ⦄ˈ 䰡∈ⱘ ⊶ Ⳍԡ Ϟˈ8 1 5Ͼ ⱘϡ ˈ䖭ѯ ⱘ㒧 ⚍Ў1951ǃ1959ǃ1964ǃ1976 1984 ˈ䇈 䖭ѯ Ё㽓 䰡∈ DŽ∈ 乘⌟῵ ⷨおϔⳈ ∈ ⱘ䞡㽕 DŽ ⌟∈ 䯈 ˈ ⱘ ⏍≵њ∈ 䯈 ⳳ ⱘ ⡍ ˈ⡍ њ ⱘ㞾Ⳍ 㒧 [12]ˈҢ㗠Փ ῵ 乘⌟䇃 DŽ ℸˈ њ Ѣ ⊶⍜ ⱘ䱣 ῵ ⫼Ѣ∈ 乘⌟ЁDŽϔ⾡ ⊩ ˈ佪 ⷨおⱘ∈ 䖯㸠 ⊶Ⓒ⊶˄⍜ ˅˗✊ 䞡 ⍜ ⱘ˗ ḍ ⍜ ⱘ⡍ ゟ 䗖ⱘ䱣 ῵ [44]ˈ 㞾 ῵ ˄AR ˅DŽ ϔ⾡ ⊩ ˈ佪 ˈ 䯈 䖯㸠 㑻 㾷ˈ ⱘ催乥 Ԣ乥 ˗✊ ˈ ⫼㞾 ῵ ˄AR ˅ ⒥ ῵ ˄MA ˅ㄝ䩜 〇 ⱘ䱣 ῵ ῵ 催乥 ˈ⫼BP ⼲㒣 㔥㒰῵ Ԣ乥 ῵ ˗䅽 催Ԣ乥῵ 㓐 ˈ 㒜῵ DŽϰ [45] ⊶ ǃ㞾 ῵ ϢBP ⼲㒣 㔥㒰῵ 㒧 䍋 ˈ⫼ 乘⌟ Ҁ㽓䚞⌙ ϟ∈∈ԡDŽ佪 ϟ∈ԡ 䯈 䖯㸠 ⊶ 㾷ˈ 㑻催乥 Ԣ乥 ˗✊ 䖤⫼AR ῵ 催乥 䖯㸠῵ ˈ⫼BP ⼲㒣 㔥㒰῵ Ԣ乥 䖯㸠῵ DŽϢ ⣀Փ⫼AR ῵ ⼲㒣 㔥㒰῵ Ⳍ↨ˈ ⊶ 㒧 ῵ BP ⼲㒣㔥㒰῵ ㊒ 㽕 DŽ԰㗙г⡍ ˈ ⊶ 㾷 䴲㑻 䍞 䍞 ˈ䳔㽕ḍ 䰙 ⹂ DŽⒸ⊶ ῵ ⱘ ⊩ЁˈЎ䙓 ⍜䰸 䖛 ⱘ ⫼催乥 ӑˈ⥟ ϔ㠀 䖯㸠ϔ㑻Mallat ⊶ 㾷DŽҪ ⷨお䭓∳ キ1890-2000 ⌕䞣䌘 ˈ䞛⫼Db3ℷѸ ⊶ 䖯㸠њ 㾷ϔ㑻 㾷ˈ⬅Stein Ԅ䅵⊩䅵ㅫњ㄀ϔ ⊶㋏ ⱘ䭹 䖯㸠⍜ DŽ⫼⍜ ⱘ ⌕䌘 ゟњ 㡖 㞾 ῵ ˈ῵ 乘⌟ⱘ㒧 Ϣ ⌟䌘 㡃 DŽ3㒧䆎⊶ ⧚䆎 㒣㹿 ⊯ⱘ ⫼ њ∈ Ёˈ ϢӴ㒳 ⊩Ⳍ↨ 䕗 ⱘӬ ˈ 䖥20 ⱘ ⫼䖛⿟Ё њ ⱘ DŽ ⊶ ⧚䆎䖬 Ѣ 䰊↉ˈ ∈ Ёⱘ ⫼䖬 ┰ ˈ䖬 䆌 ԰䳔㽕⏅ ⷨおDŽḍ ⊶ ∈ Ё ⫼ⱘ⦄⢊ˈⳂ 䳔㽕㾷 ⱘ䯂乬 㒻㓁 ⱘ ˖Scientific Journal of Earth Science [SJES] PP .27-33 © 2011 American V-King Scientific Publishing, L TD -31-1˅ ⊶ ⱘ䗝⫼ ⊶⧚䆎㾷 Ⳍ 䯂乬ⱘ ˈ佪 䳔㽕㾷 ⱘ ⊶䗝 ⱘ䯂乬DŽ㗠 䰙ⱘ ⫼䖛⿟Ёˈ 䇜 ⊶䗝 ⱘ䯂乬ˈ䗝 ⊶ⱘ䱣 䕗 DŽ ℸˈ䳔㽕ḍ ∈ 㽕㋴ 䯈 ⱘ⡍⚍ˈ 䅼䗖 Ѣ∈ 䅵ㅫ 乘⌟ⱘ ⊶ ˈ 䩜 ϡ ⱘ∈ ∈䌘⑤ⱘ䯂乬 ゟϔ ⊶ 䗝 ⱘℹ偸DŽ2˅ 䞣⫼ ⊶ ⊩ⷨお∈ 䖛⿟Ёˈ㔎 䞣 ˈ ϟҙҙձ䴴㾖 ⹂ ҹ ⱘⳌ DŽ ℸˈ䳔㽕䩜 ∈ 䯈 ˈⷨお ⱘ⡍ ˈ⹂ 㚠 ⱘ㉏ ˈ✊ ⷨお ⱘ 㨫 Ẕ偠 ⊩DŽ3˅Ⳍ⫼ ⊶ ⷨおϡ ∈ П䯈ⱘ ㋏ ˈ䗮 䞛⫼ⱘ ⊶ ㋏ П䯈ⱘⳌ ҷ DŽ䖭⾡ ⊩ⳳ ⊶㋏ Ϣ ⊶ ℷ↨ⱘ↡ ⊶ 䇈 ℷ⹂ⱘˈԚ 䡈Ѣ ⊶ⱘ ḋ ˈ䖭⾡ҷ ↨ⱘ ϡ 䗖ⱘDŽ ℸˈ Ⳍ 䯂乬ⱘⷨお ˈ ⡍ 乥⥛ ӑ䖯㸠 ⊶䗚 ˈ Ⳉ ↨ϡ 䯈 ϔ乥⥛ ӑDŽⳂ ˈ ⇨䈵 Ё ⦄ⱘⳌ ⊶ ϔϾ ⱘ䗝 DŽ4˅ ⊶Ϣ⼲㒣㔥㒰ǃ 䱣 ⧚䆎ㄝ㗺 ϔϾ ⱘ ⊩ˈ ҹ ⾡ ⊩ⱘӬ⚍ˈЎ∈ 乘⌟ կ ㊒⹂ⱘ乘⌟ ⊩DŽ㗗 ⤂[1]Grossman, A. and J. Morlet,Decomposition of Hardy functions into square integrable wavelets of constant shape[J].SIAM Journal onMathematical Analysis, 1984, 15(4): 14.[2]Antoshchuk, S., A. Nikolenko, O. Babilunga, et al., Image Contour Analysis Using Iterative Search Algorithms Based on WaveletTransform[J].2009 Ieee International Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, 2009: 390-393.[3]Padilla, P., J.M.Gorriz, J. Ramirez, et al., Alzheimer's diseases detection in functional images using 2D Gabor wavelet analysis (vol 46, pg556, 2010)[J].Electronics Letters, 2010, 46(14): 1038-1038.[4]Li, J.L., Y . J iang, and R. Fan. Recognition of biological signal mixed based on wavelet analysis. in Proceedings of UK-China SportsEngineering Workshop. 2007. Liverpool: World Academic Union (World Academic Press).[5]Horihata, S., Z. Zhang, T. Imamura, et al., Biological Signal Analysis by Independent Component Analysis Using Complex WaveletTransform[J].International Journal of Wavelets Multiresolution and Information Processing, 2010, 8(4): 595-608.[6]Bartosch, T. and J. Wassermann, Wavelet coherence analysis of broadband array data recorded at Stromboli volcano, Italy[J].Bulletin ofthe Seismological Society of America, 2004, 94(1): 44-52.[7]Alexandrescu, M.M., D. Gibert, J .L. Le Mouel, et al., An estimate of average lower mantle conductivity by wavelet analysis ofgeomagnetic jerks[J].Journal of Geophysical Research-Solid Earth, 1999, 104(B8): 17735-17745.[8]Labat, D., R. Ababou, and A. Mangin, Wavelet analysis in karstic hydrology. 1st part: univariate analysis of rainfall rates and karstic springrunoffs[J].Comptes Rendus De L Academie Des Sciences Serie Ii Fascicule a-Sciences De La Terre Et Des Planetes, 1999, 329(12): 873-879.[9]Partal, T., Wavelet Transform-Based Analysis of Periodicities and Trends of Sakarya Basin (Turkey) Streamflow Data[J].River Researchand Applications, 2010, 26(6): 695-711.[10]Kumar, P. and E. Foufoulageorgiou, A Multicomponent Decomposition of Spatial Rainfall Fields .1. Segregation of Large-Scale andSmall-Scale Features Using Wavelet Transforms[J].Water Resources Research, 1993, 29(8): 2515-2532.ēԉ Ϗ ԅ[11]䚥⊏ⳳ,⊶䈅 ⸔[M]. Ҁ: 䳛 ⠜⼒, 1979.[12]⥟ ,ϕ , 䎗⏙,∈ ⊶ [M]. Ҁ: Ϯ ⠜⼒, 2005.[13]Ḗ ,䫊㣅 ,䰜 ,ㄝ,∈ [M].℺∝: Ё⾥ ⠜⼒, 2008.[14]Daubechies, Ten lectures on wavelets[M]. Philadelphia: Capital City Press, 1992.[15]Kumar, P. and E. Foufoulageorgiou, A Multicomponent Decomposition of Spatial Rainfall Fields .2. Self-Similarity in Fluctuations[J].Water Resources Research, 1993, 29(8): 2533-2544.[16]㑾 㧡,䈋 ,䇶⚃ , 䖥ⱒ ⇨ ⱘ 䯈 [J].⛁ ⇨䈵 , 1999(01): 49-56.[17]Massei, N., J.P. Dupont, B.J. Mahler, et al., Investigating transport properties and turbidity dynamics of a karst aquifer using correlation,spectral, and wavelet analyses[J]. Journal of Hydrology, 2006, 329(1-2): 244-257.[18]Torrence, C. and G.P. Compo, A practical guide to wavelet analysis[J]. Bulletin of the American meteorological society, 1998,79(1):61-78.[19]Farge, M., Wavelet Transforms and Their Applications to Turbulence[J]. Annual Review of Fluid Mechanics, 1992, 24: 395-457.[20]ṕ ⍋, ӳ, ϛ , ㄝ, 咘⊇⑤ ⌕䞣ⱘ 㾘 ㋴[J]. 㓬, 2008, No.70(04): 280-289.[21]Chang, S.G., B. Yu, and M. Vetterli, Spatially adaptive wavelet thresholding with context modeling for image denoising[J].IEEETransactions on Image Processing, 2000, 9(9): 1522-1531.[22]Berkner, K. and R.O. Wells, Smoothness estimates for soft-threshold denoising via translation-invariant wavelet transforms[J]. Appliedand Computational Harmonic Analysis, 2002, 12(1): 1-24.[23] ,咘⊇⌕ ✊ ⌕ ⡍ 乘⌟[D].2005, : 䛑.[24] ⬭ , ∳Ϟ␌ ⌕ ⡍ 乘⌟ⷨお[D].2006, : 䛑.[25]⥟ӆ⇥, , , ㄝ, Ѣ ⊶ ⱘ ⍜ [J].⊇ Ϯ , 2000(05): 48-51.[26]⥟⾔ , 㒗㒻 , 䌍 , Ѣ ⊶⍜ ⱘ∈ ㋏㒳⏋≠⡍ 䆚 [J].㋏㒳 ⿟⧚䆎Ϣ 䏉, 2008(02): 170-175.[27] , 㩟 , , ㄝ, ⒊ ϟ⊇∈ 䯈 ⊶⍜ ⧚[J].Ҏ⇥䭓∳, 2009, 40(21): 45-46+65.[28]Thomas, A., Spatial and temporal characteristics of potential evapotranspiration trends over China[J]. International Journal of Climatology,2000, 20(4): 381-396.[29]Burn, D.H. and M.A.H. Elnur, Detection of hydrologic trends and variability[J]. Journal of Hydrology, 2002, 255(1-4): 107-122.[30]Kendall, M.G., Rank correlation methods[M]. London: Griffin, 1975.[31]䰜ҕ , ⊫, , ㄝ, ⫬㙗⊇㽓 䖥50 ⇨䈵 ∈ ⱘ 䍟 [J]. , 2002(02): 163-170.[32]Mann, H.B., Nonparametric Tests against Trend[J]. Econometrica, 1945, 13(3): 245-259.[33] , 䚥㑶 , 咘⊇⌕ ∈ ⦃㽕㋴ 䍟 [J].㞾✊䌘⑤ , 2003(02): 129-135.[34] 㧠 , 咘䫺䨿, ∈ 䯈 䍟 ⊩ [J].䭓∳ ⿟㘠Ϯ 䰶 , 2007, No.92(04): 35-37.[35]Liu, S.G., H.L. Zhu, and G.F. Ma, Changing trend of runoff and sediment transport in the lower Yellow River: Wavelet analysis, inProceedings of the Ninth International Symposium on River Sedimentation, 1-4, 2004: 1768-1772.[36] ↙, 䰜⼢, ⒵, ㄝ, ⊶ 䱰䆞 Ё㸼 ⚍ⱘ ⫼[J]. ⬉ ⿟, 2005(04): 55-57.[37]催㤷, Խ䴦, 㩟 㤷, ㄝ, Ѣ ⊶ ⱘ⬉Џ䕈 ⧚[J]. ( ⠜), 2010, 40(04):1025-1028.[38]Huang, X.Y., B. Gao, F.Q. Han, et al., Wavelet singularity analysis of radar target disappearing and capture[J]. Wavelet Analysis and ItsApplications (Waa), V ols 1 and 2, 2003: 903-908.[39]Lun, D.P.K., T.C. Hsung, and Y.F. Ho, Wavelet singularity detection for image processing[J]. 2002 45th Midwest Symposium on Circuits PP.27-33 © 2011 American V-King Scientific Publishing, L TD-32-。