TEMPORAL SCALING OF HYDROLOGICAL AND CLIMATE TIME SERIES AND THE LOW FREQUENCY VARIABILITY

Transcription

1 TEMPORAL SCALING OF HYDROLOGICAL AND CLIMATE TIME SERIES AND THE LOW FREQUENCY VARIABILITY Dajela Markovć, Mafred Koch ad Holger Lage 3 Lebz Uversty of Haover Isttute of Meteorology ad Clmatology Uversty of Kassel Departmet of Geohydraulcs ad Egeerg Hydrology 3 Norwega Forest ad Ladscape Isttute

2 OUTLINE Methods The study area ad the data Results Coclusos Varablty scales of the NH crculato dces (NAO, AO) ad clmate tme seres the study bas Correlato maps ( NAO ad AO dces) Varablty modes/scales of precptato ad dscharge tme seres, temporal scalg ad possble log-rage propertes

3 METHODS Wavelet tool (Cotuous extracto of a tme-frequecy formato) (Torrece C., Compo, Bull. Amer. Met. Soc., 998) 0 s j j 0 (s) W W N,..,, s ) (s W W (s) W (s) H ; ) ( ˆ ˆ ) ( N j j j N k t k s k N C t j e s f s W k δ δ ω δ δ ω ψ SSA 0...,, y... X X,...,d ), (, XX S (SVD) ] :...: [X X, ),..., ( ),..., ( ) ( I, T N y X X V U X L N y y X y y Y m k k Ik Ik L N T L N λ Sgular Spectrum Aalyss SSA (Idetfcato the major varablty modes) (Golyada et al., Chapma & Hall, 00) Detreded Fluctuato Aalyss DFA (Determato of the Hurst-scalg expoet) (Hu K., Ivaov P. Che Z., Carpea P., Staley H. E., Phys. Rev. E 64, 000) ~ s F(s) ; ) ( ) ( H 0.5 Ns r F s r Ns s F

4 THE STUDY AREA AND THE DATA Study area: the Germa part of the Elbe Rver Bas Data: Clmate tme seres (95-000) (P, T, p, h, R, C, W) Dscharge tme seres NH crculato dces (NAO, AO)

5 R E S U L T S

6 Varablty scales of the NH crculato dces (NAO, AO) Normalzed global wavelet spectra of the NAO-Idex (gree le) ad the AO-Idex (black le) ad the correspodg 95% cofdece levels assumg a red ose backgroud. Scale averaged wavelet spectra of the NAO- Idex (gree le) ad the AO-Idex (black le) ad the correspodg 95% cofdece level assumg a red ose backgroud: a) -5 yr. b) 6-5 yr.

7 Varablty scales of the clmate tme seres DEGREE AIR TEMPERATURE PRECIPITATION PRESSURE OF CLOUD COVER P T [mm] p C [hpa] [/8] [ C] Perod Perod [year] [year] The average (for the whole study area) extreme mothly tme seres ad the correspodg wavelet spectra

8 Correlato of precptato wth NAO ad AO dces Correlato maps betwee the scale averaged wavelet spectra over the -5 yr. bad: a) NAO-Idex ad precptao; b) AO-Idex ad precptato

9 Varablty modes/scales of precptato ad dscharge tme seres The ormalzed global wavelet spectra for 8 Elbe Rver gages: the gree dashed le correspod to the southers gage (Dresde) ad the thck red le to the orthers (Neu Darchau) The average ormalzed global wavelet power at scales s>yr. Of mea mothly dscharge tme seres from the Elbe Rver Bas versus gage alttude.

10 Varablty modes/scales of precptato ad dscharge tme seres ; Temporal scalg σ [%] Precptato Dscharge σ [%] H r 0.54 H f 0.5 tme Perod [yr.] tme Perod [yr.] 3.7 H r 0.80 H f 0.55 The major SSA varablty modes of the mea mothly precptato ad dscharge aomales at Dresde ad the GWS (wth 95% cofdece levels assumg red ose backgroud) of the dvdual modes.

11 Varablty modes/scales of precptato ad dscharge tme seres ; Temporal scalg tme Perod [yr.] tme Perod [yr.] The major SSA varablty modes of the mea mothly precptato ad dscharge aomales at Dresde ad the GWS (wth 95% cofdece levels assumg red ose backgroud) of the dvdual modes.

12 Varablty modes/scales of precptato ad dscharge tme seres ; Temporal scalg σ [%] σ [%] H r 0.58 H f H r 0.80 H f 0.53 The major SSA varablty modes of the mea mothly areal precptato ad dscharge aomales at Neu Darchau ad the GWS (wth 95% cofdece levels assumg red ose backgroud) of the dvdual modes.

13 Varablty modes/scales of precptato ad dscharge tme seres ; Temporal scalg The DFA fluctuato fucto F as a fucto of scale for the mea dscharge tme seres at at Neu Darchau (black) ad fltered tme seres from ths partcular gage (gree).

14 Varablty modes-groudwater tme seres The major varablty modes of the groudwater tme seres (96-003) ear Dresde (GW54).

15 Approxmate cotuato of the low-f rver flow varablty Seasoal comp. 3% σ Low freq. Comp. 8% σ Q [m 3 /s] tme Mea mothly dscharge tme seres of the Este Rver (Emme) ad the major SSA low frequecy compoet ( )

16 Approxmate cotuato of the low-f rver flow varablty Q [m 3 /s] Este (Emme): Recostructo of the low frequecy sgal for the etre avalable data set (black le), for the testg set (gree le); Approxmate cotuato of the calbrato set (red le), forecast (thck black le) ad the bootstrap cofdece bad (dotted) tme

17 Coclusos Besde the aual cycle, extreme mothly values of T, h, Rs ad Epot do ot have ay other statstcally sgfcat perodc compoets. The tme seres of the W, p ad C have a broad low frequecy dstrbuto but rare sgfcat peaks. The precptato tme seres have spectral peaks at the 7 yr. ad 4 yr. perods whch cocde wth the scales of the NAO varablty; The correlatos betwee the -5 yr. SAWS of the mea mothly precptato ad the NAOad AO-Idces dcate statstcally sgfcat coectos The major varablty scale of the mea mothly Elbe Rver flow dscharge tme seres are 7 yr. ad 4 yr. A comparso of the major low frequecy varablty modes of the bas precptato ad the dscharge at selected outlets cofrms that these cocde well the perod ad approxmately the phase. The percetage of the varace explaed by the low frequecy modes s more tha two tmes larger for the dscharge tha for the precptato. The DFA estmates of the Hurst parameter H of the raw tme seres data dcate log rage persstece for both the bas precptato ad the dscharge. Upo subtracto of the aual sgal ad the major low frequecy SSA compoets from the tme seres, both precptato ad the dscharge, reveal that the estmates of H>0.5 for raw seres have othg to do wth the log rage memory.

18 Thak you for your atteto