Understanding recent German regional hydro-climatic Variability by means of modern Tools of stochastic Time-Series Analysis.

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1 Undertanding recent German regional hydro-climatic Variability by mean of modern Tool of tochatic Time-Serie Analyi Manfred Koch Department of Geohydraulic and Engineering Hydrology, Univerity of Kael, Germany Keyword: Climate change, Germany, precipitation, treamflow, NAO, wavelet analyi, Hurt parameter

2 Abtract For Germany, recent regional climate model have predicted ignificant eaonal change of temperature and precipitation for the coming century that will require regional adjutment of the management of water reource. Notwithtanding, it till not clear whether the recently oberved warming trend, namely in the lat decade, i jut an outlier in the oberved hydro-meteorological time erie with it well-known tochatic nature, or whether it i jut part of a long-term trend pattern that ha already been ongoing over mot of the 20th century. To undertand the variability of tochatic hydro-climatic time erie technique, uch a the Continuou Wavelet Tranform (CWT), Detrended Fluctuation Analyi (DFA) and Singular Spectrum Analyi (SSA) have been applied to variou hydro-meteorological data recorded over mot of the 20th century throughout Germany. A it i now commonly recognized that the oberved variability of uch climatic record can be characterized by a non-tationary tochatic proce with a few periodic or nearly periodic component acting within time- cale that range from annual, over decadal, centennial to millennial and even longer time period, the goal i to undertand the exact nature of the tochatic proce, namely, whether the variou oberved periodicitie are an inherent property of the time erie or if they are triggered by external event that act on more or le regular time-cale. Periodicitie and the degree of peritence - a indicated by the calculation of the Hurt parameter with DFA - acting up to the decadal cale are retrieved. Cro-correlation of the oberved hydro-climatic time erie with the North Atlantic Ocillation (NAO) - whoe tele-connective effect on the European weather pattern on the inter-decadal cale ha been urmied for ome time, indicate a trong influence of the NAO on the long-term precipitation, though with omewhat different local effect throughout Germany. Extending the named analyi tool to dicharge erie in everal river bain provide further evidence of uch tructural break in the time-erie variability over Germany between the firt and econd half of the 20th century. While thee reult can omewhat be taken a indicator of ome climate change that ha been taking place in thi country recently, the abnormal weather condition experienced here in the lat decade may then alo be explained more a an inter-decadal intermittency phenomenon rather than a evidence for a long-term climatic trend.

3 Overview 1. INTRODUCTION 1.1 Obervational indicator of poible climate change in Germany over the lat century 1.2 Variability of hydro-meteorological time-erie in Germany and their teleconnective correlation with large cale circulation pattern 1.3 Scale of variability and change of climate 1.4 Future climate prediction for Europe 2. METHODS 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.1 Study area and data 3.2 Wavelet analyi of precipitation pattern 3.3 Etimation of Hurt parameter and analyi of long-term memory with DFA 3.4 Correlation of the precipitation with NAO 4. ANALYSIS OF ELBE RIVER FLOW 4.1 Motivation and approach 4.2 Wavelet analyi of the Elbe river dicharge 4.3 Temporal change of the Hurt parameter 5. CONCLUSIONS

4 1. INTRODUCTION 1.1 Obervational indicator of poible climate change in Germany over the lat century Change in annual mean temperature, moothed with a 11- year window Change in annual precipitation, (Baur curve) moothed with a 11- year window.

5 1. INTRODUCTION 1.2 Variability of hydro-meteorological time-erie in Germany and their teleconnective correlation with large cale circulation pattern Change in annual precipitation, (top panel) (Baur curve) and of the winter month NAO-index (ea- level preure difference between the Azoreanticyclone and the Iland-depreion), (bottom panel) (Hurrel, 1995). The precipitation and the NAO index are moothed with a 11-year and 5-year window, repectively.

6 1.3 Scale of variability and of change of climate Scale of variability and of change of climate

7 1.4 Future climate prediction /Global Calculation of global warming for a range of climate model under the SRES A2 emiion cenario which aume no action i taken to reduce emiion Predicted global warming at the end of the 21t century accourding to the HADCM3 climate model with a buine-a-uual emiion cenario (IS92a). Average warming i 3.0 C CCSR/NIES: Japan Center for Climate Sytem Reearch, CCSR/NIES AGCM + CCSR OGCM Model CCCma: Canadian Center for Climate Modelling and Analyi, CGCm2 Model CSIRO: Commonwealth Scientific and Indutrial Reearch Organiation, CSIRO-Mk2 model Hadley Centre: Hadley Centre for Climate Prediction and Reearch, HADCM3 model GFDL: Geophyical Fluid Dynamic Laboratory, R30 Model MPI-M: Max Planck Intitute für Meteorologie, ECHAM4/OPYC coupled model NCAR PCM: National Center for Atmopheric Reearch, PCM model NCAR CSM: National Center for Atmopheric Reearch, CSM Model

8 1.4 Future climate prediction /Europe Temperature change in 0 C for 2080 relative to the average Summer precipitation change in in % for 2080 relative to the average * From 1990 to 2100, the global average temperature i projected to increae by 1.4 and C for Europe For Europe 1 2 % increae per decade in annual precipitation in northern Europe to 1 % per decade decreae in outhern Europe (in ummer, decreae of 5 % /dec

9 1.4 Future climate prediction /Germany / Remo Annual temperature change in 0C for relative to Winter and Summer precipitation change in % for relative to average While the average annual precipiation may not vary too much in the future, there are ignificant eaonal variation, with longer drought in the ummer but more wetne i => Adjutement required for agriculture

10 2. METHODS = = = = = = = = n 2 j 2 j n 2 n 2 n n 1 0 () W 1 W N 1,.., n, ) ( W W () W () H ; ) ( ˆ ˆ ) ( 2 1 N n j j j N k t n i k k n N C t j e f W k δ δ ω δ δ ω ψ Wavelet tool (Continuou extraction of a time-frequency information) (Torrence C., Compo, Bull. Amer. Met. Soc., 1998) Scale averaged wavelet pectrum Global wavelet pectrum Local wavelet coefficient

11 2. METHODS (cont.) The Hurt Parameter (caling exponent) H Dicovery of longterm correlation in the dicharge of the Nile river (Hurt, 1951) Rn* = Rn/S ~ N H R= range; S= tandarddeviation (Q -Qm) dt Mn mn Rn time H < 0.5: antiperitence H = 0.5: Gauian (Brownian noie) H > 0.5: long-memory, fbn H > 1: fbm, nontationary

12 2. METHODS (cont.) Autocorrelation tunction (time-domain) ρ(k) ~L(k) k -α, a k, α = 2-2H Powerpectrum (frequency-domain) P(f) ~ f -β, a f 0 β = 1 -α = 2H -1 H = (β + 1)/2 Lag Detrended Fluctuation Analyi, DFA (Hu K. et al., Phy. Rev. E 64, 2000) 1) Y ( i) = 2) 2 N 3) 4) F 2 i k = 1 1 ( r) = 1 F( ) = 2N ( x k i= 1 2N r= 1 x) Removal of trend Y 2 F 2 [( r 1) + i] ( r) 0.5 Typical example for the three method F( ) ~ H

13 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.1 Study area and data German precipitation tation ued in the tudy, with tation height indicated.

14 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.2 Wavelet analyi of precipitation pattern Precipitation erie and wavelet calogram for tation Schwerin, plit into two time pan (left) and (right). Thick black-line contour in the calogram delineate the 95% -level of tatitical ignificance with repect to the red-noie hypothei.

15 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.2 Wavelet analyi of precipitation pattern Hamburg Hohenpeißenberg Precipitation erie and wavelet calogram

16 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.2 Wavelet analyi of precipitation pattern Global wavelet pectrum for Hamburg. Solid thick line i the overall global pectrum and the other one repreent global wavelet pectra for the pecified data time window Global wavelet pectrum for Hannover and Potdam In the early 20 th century the monthly precipitation in Hamburg i characterized by high-frequency ocillation, with period of 1, 2 and 4 year, while from the mid 20 th century on, only the 1-year ocillation remain ignificant, and a maller 21-year ocillation peak i recognizable. Similar for mot of the other tation

17 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.4 Etimation of Hurt parameter and analyi of long-term memory with DFA Dominant period obtained with the wavelet analyi and the Hurt parameter computed with the DFA. Vertical bar denote the portion of the variance explained by the dominant ocillation in the time-erie with period T= 3-7 yr, T=7-8 yr and T> 10 yr. Colour of the quare denote the range of the DFA-etimated H. Note a poitive correlation of H >0.5 (long-term memory) with period of dominant ocillation, particularly in northern Germany Effect of NAO with interdecadal dominant period

18 3. VARIABILITY ANALYSIS OF 20 th CENTURY PRECIPITATION OVER GERMANY 3.4 Correlation of the precipitation with NAO Wavelet pectrum for the winter NAO index ( ) Global wavelet pectra of the NAO (green line) and the AO Cro-wavelet pectrum for monthly extremal precipitation (Hannover) and the NAO index

19 4. ANALYSIS OF ELBE RIVER FLOW 4.1 Motivation, data and approach Data: Climate time erie ( ) (P, T, p, h, R, C, W) Dicharge time erie Elbe river bain with topography NH circulation indice (NAO, AO)

20 4. ANALYSIS OF ELBE RIVER FLOW 4.2 Wavelet analyi of the Elbe river dicharge Monthly extremal dicharge time-erie and wavelet pectra for Dreden and Neu Darchau. Black contour around the peak denote the 95% confidence level againt red noie.

21 4. ANALYSIS OF ELBE RIVER FLOW 4.2 Wavelet analyi of the Elbe river dicharge Normalized global wavelet pectra for 8 Elbe River gage: green dahed line correpond to the outhern gage (Dreden) and thick red line to the northern gage (Neu Darchau) Scale-averaged wavelet pectra (SAWS) for Dreden for the large-cale band (j = 1.8; n = 15.6 yr) (olid line) and the annual-cycle band (j = 0.97; n = 1.01 yr.) (dahed line). Average normalized global wavelet power at cale >2yr. for mean monthly dicharge erie veru gage altitude.

22 4. ANALYSIS OF ELBE RIVER FLOW 4.3 Temporal change of the Hurt parameter Note a continuou increae of the etimated Hurt parameter H over the tudied time interval, from about H~0.5 (white noie) at the beginning of the 20 th century, to H> 0.80 at it end, with value for the average H for the total record omewhere in between. Wherea H up to the middle of the lat century i 0.71<H<0.76, it jump up to H >0.80 after that time. Hypothei of a izeable change in the caling- and long-range-dependence property of the Elbe dicharge omewhere in the middle of the lat century hould be accepted.

23 5. CONCLUSIONS To look for evidence of poible climate change in Germany over the 20 th century with repect to alteration in precipitation and treamflow, a long-term tochatic time-erie analyi uing the wavelet tool for the frequency- time localization and the detection of their dominant ocillation a well a in the NAO index i carried out. Similarity of the NAO index variability with that of the precipitation and with that of the Elbe river dicharge itelf i a clear indicator that German long-term hydro-climate i affected remotely by thi hemipherical index. The caling propertie of the hydro-climatic time-erie, a determined by the DFAcomputed Hurt parameter H, reveal important apect of the long- term peritence of the precipitation acro the country and of the Elbe river dicharge. H turn out to be time-dependent over the coure of the 20 th century, with a continuou increae of H over the tudied time interval, from about H~0.5 (white noie) at the beginning, to H> 0.80 (long-range memory) at the end of the 20 th century. Thu, notwithtanding uncertaintie in the exact time-localization of thee nontationaritie of H, the idea of a certain change of the Elbe dicharge caling property, i.e. increaed peritence and variability, occurring omewhere in the middle of the lat century i to be accepted. Whether thi i jut an inter-decadal intermittency phenomenon or a hint of a longterm climatic trend i another tory.