Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ff by ff ects may ratios, the ff Sciences ff Discussions Earth System ects on runo Hydrology and ff ratio, representing the timing of the ff 812 811 ects ecosystems and human activities. Recently, ff and basin precipitation are investigated for changes and variability of ff Further there is evidence of coincident changes in trend direction (change points in In this study, changes of the annual cycle of hydrological variables are analysed for It has been found that the annual phase of runo This discussion paper is/has beenSystem under Sciences review for (HESS). the Please journal refer to Hydrology the and corresponding Earth final paper in HESS if available. increasing importance of snowand on mainly governs the the basin temporal variability water of balance the annual with timing of elevation hydrological is1971 regimes. and apparent 1988) in snow meltratio influenced is basins. significantly In correlated thesetemperature with basins phase the the changes timing timing of are of the evenexplain temperature, runo amplified. the and Interestingly, low temperature e frequent e variability offirst the change second point change can point not untilbe be today. considered. explained However, the by temperature alone and other causes have to phase and amplitude, are required. hydrological regime, is subject to considerablewith year-to-year variability, basins being concurrent in similaridentified, hydro-climatic conditions. whereby Two basin distinct elevation basin classes has have been been found to be the delimiting factor. An there is a needregimes and to to quantitatively understand how describeriver climatic basins the changes on control variability the the in regional seasonal scale. water the budget timing of of27 hydrological river basins in Saxony/Germany.ratio Thereby of monthly series runo oftheir basin annual runo periodicity over thethe period means 1930–2009. of Approximating harmonic the annual functions cycle gave by acceptable results, while only two parameters, The timing of the seasonsthere strongly is e increasing evidencespring of seasons changes detected in in phenological thetemperature, records, timing earlier advanced snow seasonal of melt timing the or of streamflow seasons, surface timing. such For as water resources earlier management Abstract Hydrol. Earth Syst. Sci.www.hydrol-earth-syst-sci-discuss.net/8/811/2011/ Discuss., 8, 811–853, 2011 doi:10.5194/hessd-8-811-2011 © Author(s) 2011. CC Attribution 3.0 License. Long term variability of thehydrological annual regime and sensitivity to temperature phase shifts in Saxony/Germany M. Renner and C. Bernhofer Dresden University of Technology, Faculty ofInstitute Forestry, of Geosciences Hydrology and and Hydrosciences Meteorology – – Department ofReceived: Meteorology 13 January 2011 – Accepted:Correspondence 14 to: January 2011 M. – Renner Published: ([email protected]) 21 JanuaryPublished 2011 by Copernicus Publications on behalf of the European Geosciences Union. 5 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , ) ). ) and 1995 ) note 2006 ( KLIWA , ). Further, 2009 2009 , ( 2010 Hodgkins et al. ( Thomson ; Dose and Menzel ´ ery et al. 1962 Stine et al. D , ; Huybers and Curry Stahl et al. 1995 Court ); , 2009 ( ). Even though these measures are rel- Thomson 2005 813 814 , ´ ery et al. ) report, concerned about long term changes D and seasonal changes by monthly data ( ); . This is mainly introduced by basin evapotranspi- ). Generally annual flows do not show significant and precipitation. ff ff 2003 ( ff ). Still, it is common practise, to assume stationarity 2005 2010 ( ). The resulting annual phases and amplitudes describe , 2005 Stewart et al. , ). Mostly it is concluded that these trends are a result of KLIWA ; 1999 , 2010 2005 ) found tendencies of advanced seasonal timing. , , ). The Stahl et al. in Southern Germany concludes with the recommendation to jointly ; Stewart et al. 2009 ff ( Loucks et al. 2009 ). However, there is increasing evidence of changes in the timing of the Thompson , 2008 , Stahl et al. 2005 , Fiala Regonda et al. ). Based on station and gridded data of surface temperature, ; ; Stine et al. There is a range of measures that can be used to directly estimate the timing of Relatively few studies have studied the variability of the annual cycle, being the Consequently, there is a need to estimate the timing of hydrological regimes, its vari- Water resources management has to deal with the seasonality of hydrological Franke et al. Maniak 2004 in regional runo analyse seasonal changes of runo annual streamflow regimes, suchof as annual discharge the in timing a of given the month or annual half maximum, flow the dates fraction ( ied for long records of surface temperatures ( 2003 atively simply and easily understood, thesehydrological metrics regimes are only such useful as forthat very those pronounced synoptic dominated events by may snowmelt. climate, dominate e.g. such warm measures spells rather in winter than or long late term seasonstrongest precipitation. changes signal in in climate recordsBy at using mid a to harmonic high representation latitudes of ( the annual cycle, this variability has been stud- Hydrological studies concernedout with CE changes usually analyse in annual2003 streamflow runo within regionstrends, through- but spatially coherent trends innounced separate are months have positive been streamflow reported. trendsin Most in spring pro- winter ( months, followed by negative trends ability and to check for long term changes, which could possibly violate the stationarity changes of the phase intant temperature when considering needs the to regional be impacts assessed. of This climate is and1.2 especially land impor- use change. Seasonal changes in hydrologic records ( precipitation ( assumption of the annual cycle of hydrologic records. Furthermore, the sensitivity of warmer winters which ingional turn climate lead studies also to changes an in earlier winter onset precipitation of have been snow ascertained melt. e.g. Moreover, in re- of monthly statistics andfor thus water stationarity resources management, of e.g. the( the whole use of annual the cycle Thomas-Fiering in simulationseasons model design from studies various disciplines.reported Earlier e.g. streamflow by timing and snow melt has been phenological studies provide evidence of( earlier spring season, e.g. and the resulting hydrological regime. regimes. Generally demand and waterability availability are of out water of phase, isdelivery i.e. systems when lowest increases the (summer) the avail- need thecal to processes correctly demand ( estimate is the seasonality highest. of hydrologi- This pressure on water of several processes inducedceiving by catchments. meteorological Looking forcing at the andhas water a the balance small properties of seasonal typical ofthe cycle basins the pronounced compared in seasonality re- CE, to of precipitation its runo ration, variation resulting and in would lower alone flows during nothigher summer elevations, account and snow for early accumulation autumn. andter snow Also and at melt spring. catchments produce at higher Besidesin flows the in local soils, late climate, evaporative win- catchment demand properties of such vegetation as and water human storage water management moderate 1.1 Motivation In nival and pluvial catchmentsvariable and but distinct river seasonal basins hydrological of regime. Central Europe This (CE) hydrological we regime observe is a a result 1 Introduction 5 5 15 25 20 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . ) ) 2 φ er- ff 2008 ( ). Using 1997 , erent methods ects are partly ff ff ratio. ff Bernhofer et al. West and Harrison ) compared four di 2005 ( 816 815 ). From the observed changes they deduce erent basins more comparable. The series of ˇ s et al. ff ratio. The climatologic behaviour of the timing is 2009 ff ( Palu ) and the resulting annual phases represent a timing ratio is a direct measure of seasonal water availability and 2009 ( ff ratio, the ratio of discharge and basin precipitation. The sea- ects are more pronounced in Saxony than in other regions in ff ff Franke et al. ratio are filtered for their annual periodicity by the harmonic method Stine et al. ff In general there are two ways to accomplish this task. First, there are form free To resolve these issues, a reliable measure for the timing, being valid over di a good approximation toparameters. the periodic The signal, second at approachmonic the are functions. cost, Fourier however, These form of are modelsand estimating generally which many amplitude. defined are by These based only parameters onand two are are har- parameters: economic a in natural the terms representation phase of ( of parameter the estimation seasonal ( cycle without a subjective definitionfilter of the annual the cycle seasons. fromthe the timing Therefore, data of and methods to the are gain seasons. a necessary time to variant parameter whichmodels, defines which use some seasonal factor to describe the periodic pattern. This yields transform). They found goodthe agreement annual between phase is these a methods robust and and concluded objective way that to estimate the onset of seasons. of temperature, annual temperatures anddriving monthly processes snow governing depths, the we changes aim in to the identify timing of the the runo 2 Methods 2.1 Annual periodic signal extraction The aim is to estimate the timing of the annual cycle from a geophysical time series several long temperature series, for estimating the temporal evolution ofplex the annual demodulation phase via (sinusoidal Hilbert model fitting, Transform, com- Singular Spectrum Analysis and the Wavelet measure of the regimethen of analysed the by circular runo descriptive statistics.is The being interdecadal addressed variability by of a theage. qualitative timing method, Together with namely a cumulative correlation departures analysis of to the observed aver- climate variables, such as timing described in monthly runo sonal fluctuation of runo as being a normalisation it makes di The objectives of this paperhydrological are regimes (1) for to a derivetheir interdecadal a range variability climatology and of of (3) river the tolocally determine timing coherent basins the patterns of throughout proximal of the processes the Saxony; annual governing observed the (2) changes in to timing. evaluate ent hydrological regimes isemploy needed. the So basin instead runo using streamflow records directly, we that climate change e Germany. Generally a positive trendis in the reported, number of combined droughtscompensated with during at growing intensified the season annual heavy level by precipitation. increased winter precipitation. These1.4 e Objective and structure densely populated with aboutThe 4.3 climate Mio. inhabitants is andmaritime characterised covers western by an European climate area two to of theleads main continental 18 to 413 factors. climate km a of eastern temperate First, Europe,Second, warm which there and there humid is is climate aborder an with with transition orographic cool elevations of winters factor gradually and the climate due increasing warm and to observed from summers. the trends 100 mand have mountain been up summarised ranges described to by in at 1200 detail m. the by Southern Recently, the sidering each month separately. 1.3 Regional climate in Saxony The Free State of Saxony is situated at the southeastern border of Germany. It is the timing of the annual cycle and its range, based on the whole cycle instead of con- 5 5 20 15 10 25 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ff (1) (2) (3) (4) (5) ) is P / Q ratio is a Thompson ff denoting the ratio ( is derived by: 0 ff t t as follows: ) and Y t ratio (RR). It repre- set X ff ff have been computed. 1995 ( t and both are allowed to 0 f ) has been used to analyse sums over a period of 5 years ff 2000 Thomson , are computed for each period from ratio in this analysis. x erent hydrological regimes. for each month ff A ff ratio naturally reflects key processes of 1 1 + t + ff change slowly over time and remove the t the complex demodulate Q P t ) for hydrological quantities, a pronounced + 0 + Bloomfield t t f 818 817 φ P Q + + and basin rainfall, the runo 1 1 − 2009 − ff t t ( and P by using various filters. In this work a simple mov- Q t t Y = A is a residual component which has no component at t and amplitude is the phase at frequency t ). t ) analysed trends in the phase of surface temperatures  φ 4 φ , ) observed at the basin outlet from the amount of precipitation 0 t 2009 Stine et al. ff )) ( t , ratio is a direct measure of water availability of a basin, and + ratios RR t Y ) and ( t (  ff ( ff 3 x + ) 12 t (top) depicts monthly rainfall and runo /Re ratio and its annual phase ) assumes that ) φ 1 t ff πit/ Y ) are demeaned monthly observations, with an o . + ) is applied separately for each calendar year in the record to gain a ( 2 t 0 t 5 0 t e . Then for a given frequency Stine et al. 2000 0 ( 5 0 f Im 5 . f + πif . ( is the amplitude, 0 2 1 t = X 11 t ( erent from an harmonic such as a cosine function. − t . , the amplitudes and phases over time are derived from the complex demodu- | ff x A t cos( t ratio, Fig. t exp 2 Y ) analysed the seasonality of precipitation over the British isles. Y 12 tan | A ff x by applying Eqs. ( = = = = = To illustrate the procedure of deriving a timing measure for the annual cycle of the A better quantity is the ratio of runo Moreover the runo Equation ( The method of complex demodulation ( The idea behind complex demodulation is to write a time series Recently, t t t X X 1999 φ runo for an example basin.shown In as the grey bottom line. graph,also the heavy Due rain resulting events monthly to in runo snowmonthly summer running melt may runo the induce spikes ratio in is the larger record. than Therefore, 1 three- in late winter time, the basin water balance.tion, Most the important actual are basin the evapotranspirationsnow and seasonal pack. the characteristics storage Over of and the precipita- release year of these water processes in form soil a or pronouncedis seasonal therefore cycle. an importantnormalisation quantity which allows in to water compare management. quite di Lastly, the runo seasonal cycle suitableregime for in a Central harmonic Europequite representation has di is distinct seasonal needed. features, it While is the notsents the runo very fraction balanced of runo and for a certain period. The regime of the runo These are depicted asfor bold estimation blue of the line annual and cycle. are generally smoother and better suitable To apply the method of series of annual phases andgood amplitudes. agreement Because with of more the complexthe methods, simplicity annual this of phases method this of method has temperature and and been the used runo to2.2 estimate The runo shift in seasons from long temperature records by X ( where change over time. Thefrequency term Y A Y middle of the month.Y Phase From late: Bloomfield a likely climatology of the phase estimates. on a global perspective.and They amplitudes: used the Fourier transform to compute annual phases where high frequency components from ing average filter has been chosen, whereby several filters have been tried to resemble 5 5 15 20 10 25 10 20 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (7) (8) (9) (6) ]. For π,π − Kleiber and Stewart et al. ). 2001 ( between two circular cc ρ , the circular mean and vari- n ,...,α 2 the streamflow is summed over a pe- ,α 1 50 α Q ratio, an independent metric, the half-flow ff , 820 819 . 2 ) 2 ). ! ¯ ) β )) i i − α ) α i ¯ β 2001 Jammalamadaka and Sengupta β , − are in fact circular variables in the range of [ cos( i cos( 1 1 β sin( φ n n = = 1 i i X X = ( n i / ) + )sin( i P . ¯ 2 α ) α 2 ) )) α − ¯ i α i α sin( α − 1 sin( i n = i α X sin( = . : sin( 1 π y

1 β n being the respective circular averages. For a full treatment of circular = 2 i = sin( X ), where the focus is on the analysis of regression residuals and their n i ¯ ( 1 β = P ) have been chosen. Half-flow dates are for example used by φ/ n i v u u t and ) erences in some years, whereby the phase estimate shows less fluctuations . 50 1 n P arctan . The annual phases 2008 α α ff and Q 1 50 365 , − = q ) to analyse streamflow timing changes and their link to seasonal temperature . Already for this short period, it can be seen, that both timing measures can have ¯ Q 1 α ¯ = α 1 = cos( = Another metric used in this work is the circular correlation There are many simple graphical methods available for this purpose, with simple As any circular variable can be represented as point on the unit circle, the starting Considering a set of angular observations The estimated cosine functions are depicted as dash-dotted lines in the bottom graph To compare the derived timing of runo = 2 cc α Jammalamadaka and Sengupta 2005 ρ vectors statistics the reader is referred to stability over time. However, thewhereby its method stationarity can is also assessed. be directly applied to a time series, σ with for nonstationarities suchAs as decadal trends changes orlinear structural of trends changes the and significance of mean testingsensitivity the may may of be the mean be not linear or useful expected trendfor here. to variance. from more the Another complex estimation climatic drawback trend period. is variables, patterns the Therefore, and it simple analyse is the necessary low to frequencymoving look variability. averages and cumulativethis sums paper. of The standardisedZeileis CUSUM variables method (CUSUM) is used often in used in econometric literature ( 2.4 Detection of nonstationarities, trends andTo analyse change the points variability of the estimated annual phase angles it is necessary to check point to derive correctnates statistics is to transform the angularx variable into polar coordi- ance are computed as follows: ( of Fig. 2.3 Descriptive circular statistics Circular variables have certainthe properties, coincidence of such “beginning” as andpropriate the the and arbitrary “end”. special choice treatment Therefore, linear is of statistics needed origin may to and be derive inap- correct conclusions from the data convenience the phasedoy angles are transformed to represent thedates day ( of year( (doy): changes in Northern America.riod, To e.g. compute one hydrological year,computed, starting when at 50% the 1 orderived November. more half-flow Then of dates the the half-flow ofFig. annual date the sum is illustrative have example passed arelarge the shown di river in gauge. thethan The upper sub plot of 5 5 20 15 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) 1 1975 ( series signifi- ff (mm/month) using Brown et al. ff ). However, ), based on the continuous se- series, no obvious reason has been 2002 1979 N) has been chosen for the spatial ff , , ◦ –52 ◦ Pettitt ; 822 821 E, 50 ratio has been used. For 8 runo in the Ore Mountains has been altered by water ◦ Zeileis et al. 1986 ff , ff . Most stations are within the Mulde River basin (15) –16 2 ) have been detected by the Alexandersson and Pettitt ◦ 2 ). This was verified by using several temporal aggrega- 2009 , . , chapter 4.6). For a few runo 2 Alexandersson ratio show to converge with increasing aggregation periods (half ff 2005 ( data Stine et al. ff IKSE The station network density has changed dramatically throughout time. Currently To check for influences of the changing network, three data sets have been prepared. The discharge data have been converted to areal monthly runo It is also possible to test the stationarity of such CUSUM processes. Under the Null One set only withother stations covering set the which full consists period of without all longer missing observations periods, available an- at a time step and another set The geographical domaininterpolation (11.5 and station data selection. there is one station availableup in the to database 111 since in 1858,From the 12 the 1930’s. stations since 1950’s Due 1891 the to1990. rising World network Since War 2000 has II the improved were network to only density has 20 374 been stations in decreased available 1951 to in 354 to 1945. in a 2008. maximum of 873 in found for the detected inhomogeneities.to These basins are where usually a not dam aserrors has severe (for as been example compared built, changes and in are the most rating probably curve related due3.2 to to measurement cross section Precipitation changes). data and the map in Fig. or are tributaries of the Upper Elbe (6). Detailed information may be found in Table cant inhomogeneities (cf. Table homogeneity tests ( ries as well as forare separate most months. severe. Whereby twothe Both series, 1970s. Streckewalde inhomogeneities and are Neundorf, Traditionally, river relatedmanagement runo to facilities, reservoir such as constructions damsdrainage during for systems drinking for water forestry supply, andsee weirs e.g. water for management hydro of power, the various mining activities, the respective catchment area.tion test Then procedure. As the referenceand data series secondly have a the weighted been mean catchments subject of runo to neighbouring catchments a homogenisa- period 1930–2009. Theranging stations between 37 cover and large 5442 km parts of Saxony, with catchment areas estimates of runo monthly to quarterly). 3.1 Runo Due to extensive hydraulic19th engineering century, projects a since densein the network Saxony. industrial of We revolution have hydrologic in chosen gauging the 27 stations river has gauge been stations, established which all almost fully cover the Hypothesis of no structuralthe change Standard the Brownian limiting Motion.can fluctuation be Then process used the is for significance probability assumed testing of to ( crossing be some boundary line tion levels, which resulted in no essential change for temperature. The annual cycle temperature and snow depthsriver have basin been average values. spatially All interpolated proceduresfilter to are the based be on annual able monthly periodic data, to components asresolution compute of the the ( method to time series does not need higher temporal 3 Data The analysis comprises dischargeclimatic series data of series 27 suchstation as river data precipitation, gauges used temperature throughout within andcedure, Saxony this snow which and study depth has have records. been firstto used been The exclude to subject anomalous detect to series possible from a structural the homogeneity analysis. changes test in Further, pro- the climatic data series such and as rainfall, note that these boundarygraphically lines check “should the be CUSUM regarded graphs. as yardsticks” and recommend to 5 5 25 15 20 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , ratio Theil ff . There is 2 ) (iii) cover most of 0.05 level then the ratio of the selected = ff α 1994 , ratios ranging between 0.3 ff ratio shows a distinct seasonal ff ratio is presented in Fig. ff ). Monthly basin average precipitation is 0.01 level then the series has been flagged 824 823 = 2009 ratio exhibits a low-frequent periodicity. Look- , α ff Peterson and Easterling ) of 1500 m raster size using an automatic Ordinary ratios ff ratio series, two distinct peaks are generally found, one 2008 ratio is shown, as an example, for the gauge at Licht- , ff ff ratio in mountainous basins in the South, having a runo Hiemstra et al. ff erenced series ( ff Jarvis et al. . The three-monthly running runo 3 . 3.2 ) has been established. Then the residuals have been interpolated onto an aggre- A time series of the runo Based on the station dataset a spatial interpolation for each month has been com- Based on these stations a homogeneity test procedure has been conducted. De- To gain some insight inbasins, the general a spatial map behaviour of of the the runo long term average runo pattern, while the 2-yearing running at runo the spectra ofat the an runo annual and the other at the semiannual frequency (not shown). 4.1 Time series of basin runo and 0.4 and are characterisedcontrast to by the lower higher precipitation, basins, higher larger evapotranspiration bodies and of in groundwater due toenwalde unconsolidated in rock. Fig. 4 Results generally a higher runo up to 0.6,soil which depths. is The due basins in to the higher hilly precipitation, North have lower lower evapotranspiration runo and limited the region since 1950.basin average On have average been 163 computedin similar series Sect. to are the available. methods described For for both precipitation elements the The network of climate1930 stations 9 long in temperature the seriesagain domain have reduced has been to available, also this 38 changedmate increased in stations. during to 2008. 47 time. Additionally, in a A 1961 Since dense few and network snow of depth snow observations depths are has been available from established in cli- 3.3 Temperature and snow depths puted. First a linear height1950 relationship using a robust mediangated based SRTM grid regression ( ( then computed by thegression average and of OK of the the respectivelowest residuals grid has root-mean-square been cells. errors chosen, as (RMSE) Thebased this among method method on showed of monthly other to station height methods, have data the re- in sets. a cross-validation fail the hypothesis of stationarityas at suspect. the Finally, alation, set i.e. of without 299 any precipitation290 suspect series from series. have 1950–1990 been There with left 170 are for in 83 spatial the stations interpo- last during decade. the 1930’s, about Bartlett test for changesall in these the three variance tests andseries reject has the the been Alexandersson hypothesis flagged homogeneity as ofbeen suspect. test. no done Next change using If an at iterative a the homogeneityare weighted test selected series procedure according of has to about 4correlation 5 criteria: of reference the (i) stations. di not Referencethe inhomogeneous stations record from of previous test the (ii) candidateAlexandersson best station homogeneity and test (iv) and are the close Pettitt to test the have candidate. been Then applied. both, the If both tests Kriging (OK) procedure ( two sets, meeting thei.e. requirement from that 1950–1990. the This series set contains used 368 must stations. cover atpending on least the 40 meta years, databreakpoints available using a the part Kruskal-Wallis of rank these sum stations test has for been changes tested in for the known location and the which has been used in the analysis. This last set is a compromise between the other 5 5 20 10 15 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , . In 3 ) are ratios Wilks . ff 0.5). RR 2010 ¯ ratios. This − , φ ff erence is smaller 0.2 to ff Hennig ratios and yield an 2 , displaying circular ; R ff 3 2005 ratios, single events such , ¨ uck. While the higher ele- ff ratio of representative basins erences in standard deviation ff ff erences are found for the circular ¨ ) are a way to depict the empirical onigsbr ff ratio 2010 ff , 826 825 . Naturally, lower basins appear to have an 4 0.3 days per 100 m elevation change. erence in the phase between mountainous basins ± ff Kaufman and Rousseeuw ). When using monthly runo ), the smoothed phase estimates are derived by complex ) and a simple moving average filter. Both are converted into ratio, its annual phase is also quite dependent on the basin 2 Lund and Agostinelli , the results of a basin classification, using the robust method 2009 2009 ( ff ( bin , column Stine et al. presents annual phase estimates of the runo Stine et al. 3 5 ) has been performed based on the circular correlation matrix of the annual phase Circular density plots ( Figure Independent from the cluster analysis, a Principal Component Analysis (PCA) ( Similarly to the runo In Table As independent comparison to the annual phases estimated from RR, the basin estimates from each basin. Two dominantexplained modes variance have for been the found, first withand and 68% its second and principal mode, 13% component respectively. generally Thereby1, reflects the while the first the mountainous mode basins second ofin mode cluster cluster explains group most group of 1. themountainous This temporal basins result, evolution have especially of the a thevariability. first lower common The dominant basins temporal first eigenmode, evolution supports principalwalde, of that component show their a as timing period wellearlier of as and timing late the decadal but timing representative large from basinlate variability about Lichten- timing in 1960–1970, in the the followed 1970s, by 1980s.these which a trend Since is features period then followed will a with by be trend discussed another towards in period earlier the timing of next is subsection. noted. Causes of 2006 the highest basins linearly decreasing with decreasing elevation ( of cluster groupmethod 1 of and 2.demodulation using While Eq. ( the annual values have been estimated using the correlation between both timing metrics. Here weak positive correlations are found for doy. The graphslarge exhibit the year-to-year variability, temporal which evolutiongroup. is of In coherent the general annual with1980. a phase catchments In period and of addition of there a the is largersuch relatively same a temporal larger as cluster variability di Lichtenwalde is andvated found lower basins in of basins the cluster such period groupphases as 2 1950– of appear K cluster to 1 appear have earlier.combined a with During later lower other than variability. periods average the phase, phase the di annual frequency distribution of circular data. For two periods of 30 years length (1950–1979 Here the standard deviationdecreased of from the 23.7 to annual 17.9 phases days,is when estimated mainly using for due three-monthly moving monthly to runo runo less55.2). extreme years, Descriptive while keeping statisticsaverage the and for standard overall each deviations phase of average basin the (54.4 annual are to phase given estimates in inelevation, column Table which can be seen in Fig. As a next stepmethod annual of phases andas amplitudes summer have rain been storms computedreliable or by timing low applying estimation monthly the and rainfall thus and increases larger the streamflow, variability may of prevent the a estimated phases. found a strong linear relation of 5.6 of partitioning around medoids ( tend to decrease with higher elevations. Larger di 4.2 Variability of the annual phase of runo earlier timing than higher basins, which is due to earlier snow melt in winter/spring. We Mountains with a snowThe melt average regime phase in and this14 a group days. distinct is Basins seasonal 1 grouped cyclean March into peaking (doy group cluster 60) in average 1 and phase March. appearsituated has at to in a the have the standard an 13 lower deviation hilly earlier February. of ranges seasonal of The cycle Saxony, basins with with belonging aaverage less to half-flow dominating date this snow and group regime. itsgeneral are standard the deviation are half shown flowand in dates about column 35 are 4 days of later in Table higher on elevated basins. average, Also with the about di 44 days in lower basins provided. The classificationoptimal is number based of on clusters of the two. time Cluster series 2 represents of mountainous runo basins in the Ore 5 5 25 15 20 10 10 15 25 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | of RR φ cient of ratio has ffi ff ratio and the ff ¨ uck of cluster 1, erences for the ff erences between ratio to the annual ff ff ratio than earlier ones. erences. So late years ¨ ect of a change in the onigsbr boxplots of the monthly ff ff ects of temperature due ff 8 annual average tempera- ff C, while there are increas- ◦ 7 ratio. The slope of the regression ff , reflects these di 8 ratio, it is interesting to check for direct links 828 827 , column 6 and plotted against average basin ff 3 0.05 level, marked bold. There is significant positive cor- . T = φ α , column 5, with significant correlations, i.e. being significantly 3 . Again, there is a distinct height dependence, which is increasing with 9 ratios and larger variability in February to April are apparent in late years ff 0.01 per 100 m basin height. For mountainous basins, we found a coe ratio are depicted for early and late years. One representative basin from cluster . The annual phase of basins of cluster 2 (19 basins) is generally more pro- ± 6 ff erent from 0 at the A simple linear regression allows to assess the average e It is interesting to note that the correlation of the phase of runo Next a direct comparison of the annual phases of temperature and runo To check for direct temperature timing dependence, early years have been classified The average phase of the annual cycle of temperature for the climate station Dresden ff phase of temperature online for the each timing basin of is reported the in runo Table each basin in Table di relation found in mountainousdecays towards basins the lower belonging basins. toof This course cluster might the be group minor caused 2.to by importance several the of reasons, timing The snow, the of secondly first correlation dynamics. evapotranspiration is indirect and e other reasons such as surface – ground water of 5 days, amountsregime. to a decrease of 15 days in theaverage basin timing temperatures is of in the oppositeare annual direction also and hydrological notable about correlations half with monthly intime. average magnitude. temperatures, There but However, the these change average with Marchsimilar temperature magnitude, shows than to have a correlation to and delay snow melt towards March and April. been done. To assess a direct,correlation linear has link been between computed these fromannual angular the variables, phase annual the phase of circular of the the monthly basin basin runo average temperature. The results are detailed for elevation in Fig. 0.37 about three in magnitude, which means that a decrease of the phase of temperature are characterised by distinct colder winters, which lead to increased snow accumulation And the opposite istemperature, true which for is the superimposed in months Fig. October till December. The average monthly having annual phases below thephases in first the quartile last (approx. quartile (approx. doyruno later 198) than and doy 204). late In years1 Fig. having and 2 has been selected.larger As runo can be seen forcompared the river to gauge K earlyearly years. and At late the yearsmonths April are river till much gauge August, more with Lichtenwalde late pronounced, the years with di having an significant higher di runo is the 20 Julyterm (doy variability 200) of and the hasthe annual a 1990’s phase there long of is term a temperatureextreme standard decline years is deviation (2006 in relatively of very the constant, 4 late, average however, and of days. in 2007 about very The 5 early) long days, observed. concluding with the most 4.3 Correlation to the annual phase ofHaving temperature analysed the phasebetween of climatic the variables, runo especially temperature.tures In and Fig. the annual phaseThe of annual temperature average temperature for for the thising climate period temperatures station is since about Dresden the 8.9 are end shown. of the 1980s. Fig. nounced, with lesscontrast late basins years of and clustertendency its towards 1 less mean (8 very early is basins) years moved moved in the towards towards second later earlier period after seasons seasons. 1980. and there In is a and 1980–2009) and all basins of cluster 1 and 2, the circular density is presented in 5 5 10 15 25 20 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ratio, ff 0.25 for snow erent from 0 at = ff 2 ratio in snow melt R ff and annual temperatures T φ around 1960. ratio. However, the correlation, RR ff φ ratio using the Fourier decomposition ratio ff ff 830 829 ratio at Lichtenwalde/Zschopau is shown with the ratio series. Further the phase angle computed ff ratio. As there are no linear trends found over the ff ff 0.19 for winter average snow depths and = 2 . Thereby the time and the magnitude of departure (referring to the 3 R 0.55) and a similar temporal evolution, which can be seen exemplary ) of the two largest peaks are noted. Significant change points based ratio reaches the significance level in 1971, so there is some evidence = ff 2 11 R , where the phase of runo and determined change points, i.e. peaks in the CUSUM graphs are listed for 0.1 level are marked bold. In 6 basins significant change points have been 0.05 level ( . For a stationary variable without any temporal trend or change of the mean it 10 = = RR 11 α α φ These trend patterns for all three observation variables are found at every basin in Having identified the links of temperature, snow depth and runo Again the river gauge Lichtenwalde is used to show the results of this approach in We checked some annual statistics, such as winter average snow depths and snow most of the variabilityas of day the of runo year gives a natural understanding of the timing of the hydrograph/water 5 Discussion 5.1 Estimation of the timing ofThe the estimation runo ofprovides the an annual phase objectiveharmonic of measure function runo of describes the the seasonal timing fluctuations accurately of enough and the explains hydrological regime. The fitted basins the first peak in 1971basins is larger the than 1988 the peak, following peakis coinciding in more 1988. with pronounced However, a in (Aue, some changeNeundorf). Streckewalde, point Zwickau, Within in and the lower to situated athere basins, seems minor there to is degree be not Dohna a such and common a clear negative departure trend pattern, of but the Ore Mountains, belonging tofor cluster group 2. The resultseach of basin in structural Table change tests y-axis in Fig. on the OLS-based CUSUMthe test, i.e. withdrawing thedetected, null all hypothesis having of their no headwaters change in at the upper Ore mountains. In most of these there is another peak inthe 1988, trend followed pattern by of anot the decline. the annual It phase peak is of in verypeaks, temperature 1971. interesting even also though to reveals However, the note, the the significance that annual 1988 levels graph basin are peak, for temperatures not but the reveals reached. a snow significant The depth structural CUSUM in change, graph also of March in the reflects 1988. both the temporal evolution of low frequent changes of the mean. So it can be seen, that to reject the stationarity hypothesis. Beside significance testing the graph also reveals is expected that thephase line of will runo fluctuate around zero. Here we observe that the annual time series of average Marchat snow head depth of measured the at basin. the station Fichtelberg situated influenced basins, it is nowterns investigated, found if these in variables the mightwhole phase explain period, of the trend runo decadal pat- cumulative variations standardised and anomalies. deviations from the meanFig. are analysed using cover duration). Instead the averagecorrelation snow ( depth in Marchin appears Fig. to have the largest a detailed look at snowof depth snow observations depth is observations interesting. hascompute been Since established basin 1950 in averages. a Saxony, dense which network is dense enough to cover duration for linkse.g. to for the annual the phasethe basin of station Lichtenwalde runo Fichtelberg, andthe the is corresponding not snow very depth high observations and at also not significant di Most of the basinslation in to cluster the group annual 2higher phase appear altitudes. of to temperature It have and is atemperature have instead clear positive larger acts that and parts as temperature significant of a alone corre- their trigger does for catchment not snow at precipitation influence and the snow runo melt. Therefore, 4.4 Trend analysis in snow dominated basins 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . 11 , ects Bar- 6 ff ratios ff ) yield a 5 Stahl et al. ) and thus and Fig. 3 ratio, the phase 2005 ect of increasing , ff ff ratio to the annual to interannual vari- ratio? . 5 ff ff 50 Q ratio is stronger and more yield two cluster groups/two ff Mote et al. ratio, cf. Table RR ) found eye-catching trends of ff φ erent sensitivities to temperature. 2008 ff ( ratio . As there is a smooth transition of the ff ff Fiala ratio. However, this correlation is only half in ), indeed a decreasing trend in the phase of 831 832 ff ): (a) choice of the period when half-flow dates 2010 ( ). Moreover, the phase angles have been compared 2009 ect river runo ( ff erences are due to three factors which are in accordance 2009 ( ff Stahl et al. a robust measure for changes in seasonality of hydrological ´ ery et al. D . It is clear that this height dependence is an e RR 4 φ erent hydrological regimes. Stine et al. ff ) state that rising temperatures possibly lead to earlier timing of the ratio, as well as its phase is very much dependent on basin elevation, . ff RR the CUSUM is plotted for the series of the phase of runo 2005 and Fig. φ ( 3 11 ratio is found for mountainous basins of cluster 2, see Fig. ) and for the nearby Czech Republic ff . Especially for mountainous basins there is some evidence to believe that there The employed approach in this paper allows to examine shifts in the seasonal cycle, It is clear that the sensitivity to temperature found at higher basins is due to snow In Fig. Again the basin elevation distinguishes the di So, finally with Phase estimates derived by the method of complex demodulation (cf. Fig. RR 2010 φ are non-stationary signals in the timing estimate of runo based on the whole annual cycle instead of looking at single months. For CE of temperature, of March snow depths and the annual average temperature separately. snow and low land basins, whereby each group has its distinct temporal evolution of ( storage and release in winter.nett This et relationship al. has beenhydrologic often regime. cited in We literature. foundcorrelated indeed, with that the annual the phase annualmagnitude of basin compared runo temperature to is the negatively cle, phase the of timing temperature. relationship Considering betweenrelevant than temperature the the and whole one runo annual with cy- annual temperatures. To answer this question a quantitative correlationof analysis the and a low qualitative frequent assessment variability has been done. Most interesting isphase the of correlation temperature. of Almostcular the all correlation, annual basins which appear is phase again to of dependent have on a runo basin positive elevation. and significant cir- relevance of snow storagegreater and water release. volumes The than natural any storage human of made water reservoir in ( snow a increasing streamflow in winter, especially infrom March, April while to June. decreasing in From the springin perspective months of the an phase annual cycle of theseperiod the trends imply (1962–2004) cycle, a towards as change earlierruno timing of streamflow. Considering the same 5.3 Does temperature explain trends in seasonality of runo and (ii) PCA based on thedominant circular correlation principal matrix of components. These refer to mountainous basins, dominated by 5.2 Variability of the annual phaseAverage of runo runo cf. Table changes in snow pack directlyproperties e with basin elevationHowever, it two independent is methods, hard (i) to cluster assign analysis based the on correct monthly group runo for a few basins. the one of regimes has been gained.water availability and This it can measure be may regarded as have an practical interesting regional relevance hydro-climatic signal. for seasonal are being used, e.g.ations in the streamflow hydrological magnitude;basins year; and compared (c) to (b) higher the sensitivity basins less leadshalf of pronounced to flow significant seasonal dates. influences cycle Still, of the single at events low lower on frequent the variability reflected by half-flow dates is similar to cycle between di similar, but smoothed temporal evolutioning compared the to method the of annual phase estimates us- availability during the year. The measure allows to compare the timing of the annual snowmelt dominated basins, withaltitude. correlation However, between for both basins measures aton lower increasing an altitude annual with basis. half-flow dates These di to do the not seem conclusions to of be useful with the simpler measure, the half-flow dates. There has been a good agreement for 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 ), 1998 , resulted ect is that RR ff φ ). However, the erent catchments ratio. That means ff ff ects of this inhomo- ). ff 2007 , 2009 , erent precipitation input sets, ff ratio coincides with the phase Thompson and Wallace ) have prevailed. Negative NAO ff Philipona et al. Baines and Folland 834 833 0.2) and only very extreme and enduring NAO − characteristics. Without detailed information it is ff ratio. This peak in the CUSUM graph for ff ect streamflow timing in Saxony. ff erences have been found. One reason for this small e erent sets of input stations have been prepared. One set with stations ff ff ratio is relatively weak ( ff ect may result in late snow melt. In addition, there is some evidence of ff and rainfall series. When we assume that these errors lead to an abrupt but ratio was similar to basins without such changes in the runo ff ff ected. Last there is some uncertainty in the estimation of the timing of the annual cycle So we can conclude that beside a range of uncertainties in the various steps of the Another source of uncertainty is the estimation of basin precipitation. Beside the spa- In two basins strong inhomogeneities have been detected which are most probably First of all there may be measurement errors or inhomogeneities in the observed The other peak in 1971, which might indicate significant nonstationary behaviour, ff http://www.cgd.ucar.edu/cas/jhurrell/indices.data.html or less independent river basins, the main features are repeated in di study of the spatial interpolation during periods of highusing observation the network density. approximation ofthat a the harmonic fitted function sinusoids to arefrom not the a always data. sinusoidal optimal. form. One And To check verycomplex can for demodulation few see the years has from reliability completely been of deviate Fig. used thephase, to detected which estimate trends, showed the the good temporal method agreement changes of to of the the other annual method. analysis, the method proved to be quite robust. Moreover, having this large set of more the requirement that the series usedWhen must comparing cover the at resulting least annual 40only phases years, of i.e. marginal these from di di 1950–1990. the errors of the spatialstations interpolation is do increased not e.g. decrease significantly from when 30 the to number 290. of This has been verified by a cross validation that the periodic signal has not been altered stronglytial in most interpolation cases. error, whichof is changes ideally of normal the distributed,geneity, observation we three network had di to over time. facewhich the To covered problem check the for e fullsisted period of all without observations longer available at missingin a the periods, time analysis. step another and This set the set which final has set con- been which a has compromise been used between the other two sets, meeting a result of anthropogenic influencesmining such activities as have dam impacted construction runo andimpossible management. to correct Also for such changes.dataset Therefore, without these a records correction. have beenruno However, we kept in note the that the anomalies of the phase of the indices are said to bring cold winter weather to Europe ( a circulation patterns may e 5.4 Uncertainty and significance of theWhen results dealing with real data,results uncertainties it come is into necessary play. to For list the the interpretation sources of of the uncertaintyruno and to examine theirconstant relevance. change of the mean, the cyclic behaviour and thus the phase is unlikely to be which in e a global climateoverall shift correlation during to the this winterphase period of time runo NAO ( index to the first principal component of the only coincides withthat the the CUSUM impact graph ofone for the snow of timing depths several of relevant indeparture temperature of processes late on the which winter. phase the of infrom timing runo That two of combination periods means hydrological explain with regimes theboth late is periods above timing remarkable during average negative the( winter 1960s time (1961–1965, North 1969–1971). Atlantic oscillation During (NAO) indices undergo structural changes atWe found the that same the timeof peak and temperature, in might the annual late even averagechanges 1980s temperatures explain in of and such temperature the the a may runowith snow be trend. aerosols depth related over CE to in since drastic March. 1980, changes see e.g. These towards ( less air pollution The coincidence of peaks in the CUSUM graphs indicate that the respective elements 5 5 25 20 10 15 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 815 ect of ects of ff ff ¨ ucksichtigung 832 ¨ uchler W.: Klimamono- characteristics. ratio have been analysed ff ff , precipitation, snow depths and ff time series and the German Weather Service ratio are not random or catchment specific, ¨ ansel S., Mellentin U., K ff ff 836 835 ¨ antzschel, J., Harmansa, S., Pluntke, T., Geidel, ¨ ur Umwelt und Landwirtschaft (Hrsg.), p. 211, 2008. erent basins may further reduce the probability of this 833 ff erent hydrological regimes in Saxony. ratio has been central in the analysis. This measure is shown to ff ratio explains the opposite linear trends in winter and spring found ff ff This work was kindly supported by Helmholtz Impulse and Networking ratio than the magnitude of the annual temperature. This study also con- 822 ff ¨ ur Sachsen (KLIMOSA) – Untersuchung und Visualisierung der Raum- und Zeit- 817 ¨ achsisches Staats-Ministerium f Climate, 20, 2721–2744, 2007. S 675, 1986. K., Surke, M., Prasse,graphie H., f Freydank, E.,struktur H diagnostischer Zeitreihender der Witterungsextreme Klimaelemente und der unter Wetterlagen. besonderer In: Ber Sachsen im Klimawandel – eine2000. Analyse, availability in snow-dominated regions, Nature, 438, 303–309, 2005. The sensitivity to the timing of temperature interestingly only explains the long term The main findings are that (i) there are interdecadal changes of the mean and vari- Baines, P. and Folland, C.: Evidence for a rapid global climate shift across the late 1960s, J. Bernhofer, C., Goldberg, V., Franke, J., H Bloomfield, P.: Fourier analysis of time series: an introduction, Wiley-Interscience, 2nd edn., Alexandersson, H.: A homogeneity test applied to precipitation data, Int. J. Climatol., 6, 661– References Barnett, T., Adam, J., and Lettenmaier, D.: Potential impacts of a warming climate on water gases will probably continue toserious reduce consequences snow in depth the in intra-annual low variations mountain in rangesAcknowledgement. runo in CE, with Fund through HelmholtzGRADE). Interdisciplinary Graduate We School furtherand for Geology acknowledge Environmental (LfULG) Research the for(DWD), (HI- Czech Saxon providing Hydro-meteorological the Service State (CHMI) runo (UNESCO-IHE) for Agency is providing gratefully climate for acknowledged data. for Environment, Micha reading Werner and Agriculture improving the manuscript. changes in thefound. phase Moreover of the timing temperature ofof within the the temperature runo snowmelt cycle dominated hasfirms more basins the influence previous has finding, on that been thebasins. impacts timing of Future climate climate change changes are as stronger expected in due mountainous to continued release of greenhouse on climate impacts on hydrological systems, it is notable that an amplified e these changes relate toforest changes die-back in expected atmospheric in circulation, the air 1970s pollution trough or 1990s. e In the course of the discussion hypothesis. Therefore, itremoval is of recommended seasonality to areedge be these required. careful structural changes when Also ofseasonal seasonal hydraulic the time statistics design series annual models. cycle or studies by should using time acknowl- variant, e.g.departures dynamic of the meanthe annual early timing since 1970s 1980. iswould most The be probably structural very related change interesting, observed to but in changes out in of the the scope late of winter this snow study, cover. to investigate It how strong temperatures within snowmelt influenced basins.in the It phase has of runo been discussedby previous that studies the on trend streamflow changes.significance Moreover level these of changes rejecting are the almostrepetition at hypothesis of the of these stationarity of trends the in annual di cycle, but the A hydro-climatic dataset oftemperature monthly from values 1930–2009 ofony/Germany. has runo Long been term establishedby seasonal filtering for the changes 27 annual of period basinsannual the using cycle throughout a runo of harmonic runo Sax- function.be The applicable variability to of the the di timing of ance of the annual phase and (ii) the timing is directly sensitive to the phase of annual change points found in thebut phase a of result runo of a changing climate. 6 Conclusions with similar climatic and hydrologic properties. This last argument underlines that the 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ff = http: ; last http:// 825 832 814 , ; last access: 814 826 814 815 , http://srtm.csi.cgiar.org 814 814 831 ¨ urttemberg und Bayern, Institut , 831 814 http://CRAN.R-project.org/package 822 , 813 816 823 838 837 ¨ usse in Baden-W ; last access: 10 January 2011, 2003. 823 814 813 ` 833 y, P.: Shifts of seasons at the European mid-latitudes: last access: 10 January 2011, r package version 2.0–3, 832 , 823 ¨ ofel, C., and Heuvelink, G.: Real-time automatic interpolation fpc; 814 = , http://www.hydrol-earth-syst-sci.net/14/2367/2010/ ´ odar, J.: Streamflow trends in Europe: evidence from a dataset 814 813 821 ´ 820 a, D., and Tichavsk , 813 813 819 ; last access: 10 January 2011, r package version 0.4, 2010. 822 820 825 ; last access: 10 January 2011, 2005 (in German). ˇ s, M., Novotn ¨ ur Wasserwirtschaft und Kulturtechnik (Karlsruhe). Abteilung Hydrologie, Mannheim, 5194/hess-14-2367-2010, ogy over the western United States, J. Climate, 18,S., 372–384, 2005. Fendekova, M., andof near-natural J catchments, Hydrology and Earth System Sciences, 14,10 2367–2382, January doi:10. 2011, 2010. gases forced rapid warmingdoi:10.1029/2008GL036350, in 2009. Europe since the 1980s, Geophys. Res. Lett., 36, L02806, series, Int. J. Climatol., 14, 671–679, 1994. 1979. Natural fluctuations correlated withL12805, doi:10.1029/2005GL022838, the 2005. North Atlantic Oscillation, Geophys. Res. Lett, 32, http://www.ikse-mkol.org/uploads/media/IKSE-Elbe-und-ihr-Einzugsgebiet-2005-Kap4-6. pdf International Center for Tropical Agriculture (CIAT). Available at: North America, B. Am. Meteorol. Soc., 86, 39–49, 2005. Inc, 2001. access: 10 January 2011, 2008. Berlin, 2005. variability, Nature, 441, 329–332, 2006. f Planning and Management: An Introduction toParis, Methods, 2005. Models and Applications, UNESCO, rivers in the period 1961–2005, J. Hydrol. Hydromech., 56,senschaftliche 133–140, Zeitschrift 2008. der TU Dresden, 58, 32–38, 2009. of ambient gamma doseand rates Geosciences, 35, from 1711–1721, the 2009. dutch radioactivity monitoring network, Computers Wiley’s Series in Probability and Statistics, John Wiley and2008. Sons, New York, 2005. //www.kliwa.de/download/KLIWAHeft3.pdf circular 45, W04426, doi:10.1029/2008WR006975, 2009. Change Biology, 10, 259–272, 2004. CRAN.R-project.org/package 2010. JZ067i011p04335, 1962. timing changes in pluvial, nival, and glacial rivers of western Canada, Water Resour. Res, England over the 20th century, J. Hydrol., 278, 244–252, 2003. tionships over time, Journal149–192, of 1975. the Royal Statistical Society. Series B (Methodological), 37, ´ ery, S., Stahl, K., Moore, R., Whitfield, P., Menounos, B., and Burford, J.: Detection of runo Stewart, I., Cayan, D., and Dettinger, M.: Changes toward earlier streamflow timing across Stahl, K., Hisdal, H., Hannaford, J., Tallaksen, L. M., van Lanen, H. A. J., Sauquet, E., Demuth, Regonda, S., Rajagopalan, B., Clark, M., and Pitlick, J.: Seasonal cycle shifts in hydroclimatol- Philipona, R., Behrens, K., and Ruckstuhl, C.: How declining aerosols and rising greenhouse Pettitt, A.: A non-parametric approach to the change-point problem, Appl. Stat., 28, 126–135, Peterson, T. and Easterling, D.: Creation of homogeneous composite climatological reference Palu Kaufman, L. and Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. Jarvis, A., Reuter, H., Nelson, E., and Guevara, E.: Hole-filled seamless SRTM data version 4, Mote, P., Hamlet, A., Clark, M., and Lettenmaier, D.: Declining mountain snowpack in western IKSE: Die Elbe und ihr Einzugsgebiet, Internationale Kommission zum Schutz der Elbe (IKSE), Jammalamadaka, S. and Sengupta, A.: Topics in circular statistics, World Scientific Pub Co Maniak, U.: Hydrologie und Wasserwirtschaft: Eine Einfhrung fr Ingenieure, Springer Verlag, Huybers, P. and Curry, W.: Links between annual, Milankovitch and continuum temperature KLIWA: Langzeitverhalten der mittleren Abfl Loucks, D., van Beek, E., Stedinger, J., Dijkman, J., and Villars, M.: Water Resources Systems Lund, U. and Agostinelli, C.: circular: Circular Statistics, Fiala, T.: Statistical characteristics and trends of mean annual and monthly dischargesFranke, of J., Czech Goldberg, V., and Bernhofer, C.: Sachsen im Klimawandel Ein Statusbericht, Wis- Kleiber, C. and Zeileis, A.: Applied econometrics with R, Springer Verlag, New York; 1. edition, Hennig, C.: fpc: Fixed point clusters, clusterwise regressionHiemstra, P., Pebesma, and E., Twenh discriminant plots, Dose, V. and Menzel, A.: Bayesian analysis of climate change impacts in phenology, Global D Hodgkins, G., Dudley, R., and Huntington, T.: Changes in the timing of high river flows in New Court, A.: Measures of Streamflow Timing, J. Geophys. Res., 67, 4335–4339, doi:10.1029/ Brown, R., Durbin, J., and Evans, J.: Techniques for testing the constancy of regression rela- 5 5 30 25 20 15 30 25 10 10 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , RR 2 831 , denotes the 826 , 821 833 elev 825 , 823 819 821 817 , , , 814 818 814 , , 813 817 , denotes catchment area in km 816 , gives the number of missing months. area 814 , miss 813 839 840 826 ratio and ff ¨ oder Schwarze Elster 248 300 0.30 36 816 ¨ oha Mulde 663 644 0.47 0 ¨ ollnitz Upper Elbe 168 211 0.21 24 ¨ ob. Wasser Spree 284 195 0.29 12 ¨ oha Mulde 688 385 0.50 0 ¨ uglitz Upper Elbe 555 198 0.46 9 ¨ oltzsch Weiße Elster 518 155 0.46 12 817 , River stations analysed over the period 1930–2009. The column Merzdorf/D Grossdittmannsdorf/R Koenigsbrueck/PulsnitzGroeditz/L Schwarze Elster 274 92 0.34 26 station/riverElbersdorf/WesenitzBautzen/Spree majorNiederstriegis/Striegis basinPorschdorf/LachsbachKirnitzschtal/Kirnitzsch Upper Elbe elevGoeritzhain/Chemnitz Mulde areaGolzern/Mulde Upper ElbeNossen/Freib. Spree Mulde Upper RR 317 ElbeWechselburg/Zwick. Mulde miss Mulde 227Neundorf/Gottleuba 378 0.37 MuldeMylau/G 374 381 267 Mulde 283 154 0.43 357 0 Mulde 0.36 0.36 Upper 410 276 Elbe 0 0.37 13 491 532 0 2107 0.47 485 24 493 0.46 481 585 133 5442 0 0.43 0.42 0 0.42 0 12 0 Dohna/M Adorf/Weiße ElsterLichtenwalde/ZschopauWolfsgrund/ChemnitzbachZwickau/Zwick. Mulde Mulde MuldeBorstendorf/Fl Weiße Elster Mulde 599 629 618 171 1575 0.36 37 0.47 631 0.60 35 1030 0 0.46 2 12 Pockau/Fl Hopfgarten/ZschopauNiederschlema/Zwick. MuldeAue/Schwarzwasser MuldeStreckewalde/Preßnitz MuldeRothenthal/Natzschung Mulde Mulde Mulde 705 701 759 0.52 529 0.50 742 744 12 770 362 206 0 0.54 0.47 75 0.58 0 0 0 814 , structural change in linear regression models, J. Stat. Softw., 7, 1–38, 2002. Vol. 59, Academic Press, 2nd edn., 2006. York, 2nd edn., 1997. Isles and neighbouring areas, J. Hydrol., 224, 169–183, 1999. 813 Nederlandse Akademie Wetenchappen Series A, 53, 386–392, 1950. height and temperature fields, Geophys. Res. Lett., 25, 1297–1300, 1998. western North America, J. Climate, 18, 1136–1155, 2005. temperature, Nature, 457, 435–440, 2009. Zeileis, A., Leisch, F., Hornik, K., and Kleiber, C.: strucchange: An R package for testing for Wilks, D. S.: Statistical Methods in the Atmospheric Sciences, International Geophysics Series, West, M. and Harrison, J.: Bayesian forecasting and dynamic models, Springer Verlag, New mean basin elevation in meters above sea level, Thompson, R.: A time-series analysis of the changing seasonality of precipitation in the British Thomson, D.: The seasons, global temperature, and precession, Science, 268, 59–68, 1995. Table 1. denotes the long term average runo Theil, H.: A rank-invariant method ofThompson, linear D. and and Wallace, polynomial J.: regression The analysis,(Parts Arctic 1–3), Oscillation signature in the wintertime geopotential Stine, A., Huybers, P., and Fung, I.: Changes in the phase of the annual cycle of surface 5 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2 p σ 0.62 0.44 0.58 0.86 0.83 1.14 0.78 0.80 − − − − − − − − 2 1988 1.11 1971 1.23 1971 1.12 1988 1.24 1988 0.85 1988 1.07 1982 peak 1 1 1943 p − denotes the phase 1.4 σ 1.29 1.34 1.46 1.49 0.91 1941 1.37 1.14 1941 0.941.28 1960 0.45 1973 0.43 0.840.56 1959 1960 0.50 0.93 1960 0.97 1944 0.33 − − − − − − − − − RR ¯ φ 1 1971 1988 19881988 0.95 1971 0.93 1971 1958 19881971 1.091971 1.16 1971 1988 0.75 0.75 19881971 0.681971 0.71 1971 1988 0.50 0.57 19881992 0.85 0.57 1970 1952 0.71 19711971 0.931971 0.85 19881971 0.68 1988 0.69 1.12 1988 0.76 1988 0.60 0.78 1957 1940 1941 1981 0.45 0.48 0.49 0.47 0.48 0.44 0.51 0.44 0.45 0.35 0.78 0.43 0.43 0.55 0.49 0.47 0.42 0.48 0.47 1961 0.57 0.540.64 1985 0.48 1961 0.480.54 1978 0.54 0.51 1985 large inand March June 1980s 1960–1985 weak inhomogeneity winter 1960–1970, September 1980 weak, 1950–1970 mainly winter half-year strong inhomogeneity 1980s Tcoef peak ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± the strength of the linear link between cient and its standard deviation. The ffi , c b 3 3 a 3 cc e 0.5 2.21 0.4 1.86 Tcoef ρ 0.53 2.62 0.510.58 2.53 3.01 0.48 2.34 0.470.53 2.05 0.52 2.76 0.48 2.28 2.12 0.530.46 1.93 3.18 0.48 2.08 0.490.48 2.08 2.4 0.46 2.12 0.510.45 2.13 2.11 0.23 1.13 0.35 1.42 0.25 1.13 0.28 1.39 3 hm is the circular correlation between the annual d 3 50 842 841 18 20 20 19 20 21 21 20 20 21 20 20 24 24 22 21 21 20 17 0.21 0.91 20 19 0.152022 0.76 0.16 0.96 23 1924 0.19 0.82 17 0.11 0.5 cc ¯ Q ρ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 3 and ¨ 50 ollnitz dam ¯ Q 15 hm stream, largest: Eibenstock dam 1976, 14 hm construction 1967 1974–1984 83 hm 1973–1976, 55 hm RR 16 7 Apr 18 9 Apr 18 14 Apr 19 14 Apr 17 8 Apr 2016 12 Apr 17 5 Apr 5 Apr 17 31 Mar 1716 2 Apr 4 Apr 13 27 Mar 20 4 Apr 1616 3 Apr 15 4 Apr 18 27 Mar 15 12 Apr 31 Mar 14 1 Apr 17 1 Apr 1815 30 Mar 15 Mar 16 30 Mar 16 29 Mar 1615 26 Mar 25 Mar 15 28 Mar ¯ φ Dam ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Preßnitz Dllnitzsee Eibenstock Rauschenbach ¨ ollnitz D ratio and temperature. In column ¨ obauer Wasser May 60–70s ¨ oha Rauschenbach dam ff is denoted as the regression slope coe T denotes the respective bin assigned by the cluster analysis, φ Inhomogeneous discharge series. Statistics of the river gauge stations analysed, sorted according to basin elevation. The bin Groeditz/L Merzdorf/D Goeritzhain/ChemnitzPockau/Fl change in mean about 1970 station/riverStreckewalde/Preßnitz damNeundorf/Gottleuba construction reason dam construction inhomogeneity Niederstriegis/StriegisWechselburg/Zw. Mulde various dams up- changes in mean 1950–1970 and Rothenthal 2 8 Mar Streckewalde 2 12 Mar Aue 2 14 Mar Niederschlema 2 8 Mar Hopfgarten 2 6 Mar BorstendorfPockau 2 2 Mar 2 5 Mar Zwickau 2 6 Mar Wolfsgrund 2 26 Feb AdorfLichtenwalde 2 3 Mar 2 28 Feb Dohna 2 26 Feb Mylau 2 20 Feb GolzernNossenWechselburgNeundorf 2 2 25 26 2 Feb Feb 21 Feb 2 25 Feb Goeritzhain 2 15 Feb Kirnitzschtal 1 11 Feb Porschdorf 1 21 Feb BautzenNiederstriegis 2 14 1 Feb 12 Feb Elbersdorf 1 14 Feb Groeditz 1 11 Feb GrossdittmannsdorfKoenigsbrueck 1 12 Feb 1 13 Feb stationMerzdorf bin 1 7 Feb RR http://de.wikipedia.org/wiki/Talsperre http://en.wikipedia.org/wiki/Gottleuba http://de.wikipedia.org/wiki/Talsperre http://de.wikipedia.org/wiki/Talsperre http://de.wikipedia.org/wiki/Talsperre Table 3. column average as calender dayhalf-flow and date its is respective given circular standard in deviation column inφ days. The average phases of runo years of the two largestdeviation peaks is in given cumulative in standardised the anomalies last plots 4 and columns. their Further respective explanations are given in the text. a b c d e Table 2. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ratio ff 2006 2006 ratios is given 85 0.81 78 = ff = = 2 φ R 50

Q Germany ratios of the basins 2005 2005 ff ) of the respective year 50 66 0.84 are computed as doy and 111 = Q = = Groeditz 2 φ ● 50 R RR Q φ ● 2004 2004 Bautzen Kirnitzschtal 0.2 0.3 0.4 0.5 0.6 73 0.86 ● 11 = = ● = ratio, three-monthly moving runo of a sample period from the station at 2 φ 50 R ff Q ff ● ● Runoff Ratio Koenigsbrueck ● Porschdorf ● 2003 2003 Time ● Neundorf Elbersdorf Dohna 104 45 0.91 844 843 = = = 2 φ 50 R Q Wolfsgrund ● Rothenthal ● lakes river gage river river Grossdittmannsdorf 2002 2002 Nossen Merzdorf ● ● ● ● Pockau ● ● ● 0.9 59 101 ● = Hopfgarten = ● = 2 φ ● R 50 Q Streckewalde Borstendorf Lichtenwalde Niederstriegis Goeritzhain Golzern ● ● ● 2001 2001 ● ● Aue 50 km 83 0.93 73 = = = 2 φ ● fitted annual sinusoid fitted annual catchment rainfall runoff monthly runoff ratio RR average 3−month moving R 50 Wechselburg Q Niederschlema Adorf Zwickau ● ●

2000 2000

Mylau

1.0 0.5 0.0 250 150 50 2.0 1.5

0 km

runoff ratio Q/P ratio runoff rain, runoff [mm/mon] [mm/mon] runoff rain, Map of the study area and long term average basin runo Top: monthly data of precipitation and runo Fig. 2. investigated. Fig. 1. Lichtenwalde. The vertical dotted lines depict the half-flow date ( the annual correlation of the fitted sinusoid’s to the three-monthly running runo and its value is denotedand as doy. the Bottom: resulting monthly annual runo sinusoidal fits.below. The annual phases Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ●● ●● ●● ●● ●● ●● 700 ●● ●● ●● ●● ●● 600 ●● 2000 ●● ●● ●● ●● ●● 500 ●● ●● 400 ●● ●● ●● ●● ●● 300 ●● ●● basin average elevation [m asl] elevation basin average cluster 1 cluster 2 ratio (left) and dependence of the 200

● ● ●●

1980 ff

50 45 40 75 70 65 60 55 average streamflow timing [doy] timing streamflow average 846 845 ●● ●● ●● ratio at Lichtenwalde, Zschopau. 1960 ●● ●● ●● ff 700 ●● ●● ●● ●● ●● 600 ●● ●● ●● ●● ●● ●● 500 ●● ●● 400 ●● ●● ●● 1940 ●● ●● 300 ●● ●● 3 − month MA MA 2 − year basin average elevation [m asl] elevation basin average cluster 1 cluster 2

200

● ● ●●

0.6 0.5 0.4 0.3 0.2

0.8 0.6 0.4 0.2 1.4 1.2 1.0

average runoff ratio [−] ratio runoff average runoff ratio, Q / P / Q ratio, runoff Height dependence of long term average runo Time series of the monthly runo average streamflow timing (right). Fig. 4. Fig. 3. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ● ● ● ● ● ● ● ● ● ● ● 2000 ● ● ● ● ● ● ● ● ● ● ● ● Lichtenwalde, cluster 2 Lichtenwalde, MA filter demodulate, complex cluster 1 Koenigsbrueck, MA filter demodulate, complex ● ● ● ● ● ● ● ● 0 2 equals doy 91 for example. ● 1980 ● ● ● π/ ratio, estimated for the basins of cluster ● ● ● ff ● ratio at 2 selected representative gauging ● ● ● ff ● ● ● ● ● ● 848 847 π ● + π 2 2 3 ● ● ● 1960 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● π ● ● ● ● ● 1940 ● cluster 1, 1950 − 1979 cluster 1, 1980 − 2009 cluster 2, 1950 − 1979 cluster 2, 1980 − 2009 ● ● ● ● ● ●

●

●

0 120 100 80 60 40 20 phase as doy as phase Time series of the annual phase of runo Circular kernel densities of the phase of runo Fig. 6. 1 and 2 anddensities. for Here two angular periods units each. are being A used, whereby bandwidth of 80 has been used to estimate the circular stations. Fig. 5.

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

average monthly temperature [°C] temperature monthly average

20 15 10 5 0 −5 −10 −15 Phase [doy] Phase

of climate

230 220 210 200 190 T ● ● ● ● φ ● Nov ● ● ● ● ● ● ● ● Sep ● ● ● ● ● 2000 Jul ● ● ● 198 ● ● ●

204

May ● ● ¨ uck, Pulsnitz (cluster 1); Right: < day > day T ● T φ φ ● ● Mar ● ● early late ●

¨ Jan

onigsbr 1980

3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 runoff ratio, Q / P / Q ratio, runoff ratio, depending on early years with the annual

Time

average monthly temperature [°C] temperature monthly average ff

850 849

20 15 10 5 0 −5 −10 −15 ● 1960 ● ● ● ● Nov ● ● ● ● ● ● Sep ● ● ● ● ● Jul ● ● ● 1940 ● 197

204 annual average temperatures average annual phases of temperature annual

May ● ● ● ● < day > day T ● T φ φ ● ● ● Mar ●

● early late

10 9 8 7 6 5 ● ●

Jan

Temperature [°C] Temperature

3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0

Boxplots of the seasonal cycle of runo Annual average temperatures (dashed) and annual phases of temperature runoff ratio, Q / P / Q ratio, runoff Fig. 8. phase of temperature belowgrey the and 1st quartile black and linesthe late denote corresponding years the beyond axis the averageLichtenwalde, on 3rd Zschopau monthly the (cluster quartile. temperature 2). right. The for bold late Left and subplot: early years, K with Fig. 7. station at Dresden. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ● _ _ ● ● _ _ _ _ 2000 ● ● _ _ _ _ ● _ _ 700 ● _ _ standard deviation) between ● ● _ _ _ _ ● _ _ ± ● _ _ 600 ● _ _ 1980 cient ( ● _ _ ffi ● ● _ _ _ _ ● ● _ _ 500 _ _ ● _ _ time in years ● 852 851 400 ● _ _ _ _ ● _ _ ● _ _ 1960 ● _ _ ● _ _ 300 ● basin average elevation [m asl.] elevation basin average _ _ ratio at Lichtenwalde compared with the March average ● _ _ ff 200 ● _ _

1940

2 1 0 4 3

March average snowdepth, Fichtelberg snowdepth, March average Lichtenwalde phase of runoffannual ratio,

slope phase RR vs. phase T [day/day] T phase vs. RR phase slope

100 50 0 250 200 150

Annual phase of runo phase [doy] / average snowdepth [cm] snowdepth average / [doy] phase Height dependence of the regression slope coe snowdepth series at11-year the moving mountain averages. climate station at Fichtelberg. The bold lines depict the Fig. 10. Fig. 9. annual phases of streamflow and temperature. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2000 1980 ratio at Lichtenwalde compared with the ff Time 853 1960 0.05) for a stationary process are denoted as horizontal lines at the = 1940

phase runoff ratio phase temperature depth March snow Temperature average Annual

α

−0.5 −1.0 −1.5 1.5 1.0 0.5 0.0 Empirical fluctuation process fluctuation Empirical CUSUM Analysis of the annual phase of runo annual phase of temperature, annualThe significance basin levels temperatures ( and the March average snow depth. top and bottom of the graph. Fig. 11.