Project Work Kevin Mersch Report

8/23/2019 Project Work Kevin Mersch Report

1/56

Streamflow Trends in Switzerland

Project Work

by

Kevin Mersch

E-mail: [email protected]

05.12.2011

Supervisor: Dr. P. Molnar


2/56

26.04.10 / NB

Beiblatt zu jeder an der ETH Zrich verfassten schriftlichen Arbeit

Ich erklre mit meiner Unterschrift, das Merkblatt Plagiat(vgl. http://www.ethz.ch/students/semester/plagiarism_s_de.pdf) zur Kenntnis genommen, dievorliegende Arbeit selbstndig verfasst und die im betroffenen Fachgebiet blichen Zitiervorschrifteneingehalten zu haben.

Supervisor ___________________ ____________________________________

Studierender ___________________ ____________________________________

Ort, Datum ___________________ Unterschrift __________________________


3/56

3 Streamflow Trends in Switzerland

Abstract

Mean daily streamflow records from 39 watersheds in Switzerland with a mostlyundisturbed runoff regime are analysed for trends with the MannKendall non-

parametric test in three study periods (1970-1990, 1980-2000, 1990-2010). Thestatistical significance of trends is tested for each station on a seasonal basisand for different streamflow quantiles at a 10% significance level. Identifiedtrends in streamflow are examined and correlated with watershed attributes.

Complex changes in the streamflow regime in Switzerland especially in themore recent periods have been identified, especially in autumn and winter.Particularly the most recent period (1990-2010) experiences a considerable shiftfrom high towards low flows for every quantile in autumn and winter. Theincreasing trend of spring flows is experiencing a decaying development overthe three analysed periods. Summer flows exhibit a decreasing trend, especiallyin magnitude. Behaviour in the summer period is different, indicating both

upward and downward trends. Substantial differences in trends depending onmean basin altitude couldnt be identified for any season but summer, wherestations located between 1000m and 2000m experience increasing trends whichstand in opposition to stations from higher or lower elevations. Winter medianflow of watersheds without glacier remain unchanged, while basins with glaciersface downward trends.

Correlation between mean watershed elevation and trends is strongly depen-dent on season and quantile. Correlation analyses reveal moderate relationshipsbetween streamflow trends and mean basin elevation and glacier coverage. Au-tumn and summer show negative correlation for low flows, resp. moderateflows. In winter high flows show a good correlation with magnitude of trend.

Trends are present in every period for high and low flows. Magnitude de-pends on period and season of interest. Results suggest that, regardless of thetype of environment of watersheds, all basins are subject to streamflow change,specifically in the last 20 years.

Dec 5, 2011 Mersch Kevin Project Work


4/56


Contents

1. Introduction 6

2. Data 8

3. Methods 11

3.1. Mann-Kendall nonparametric trend test . . . . . . . . . . . . . . . . . . . . 113.2. Theil-Sen slope estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3. Spearman rank correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4. Results 14

4.1. Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2. Differences in altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3. Correlation with basin attributes . . . . . . . . . . . . . . . . . . . . . . . . 214.4. Open Quetions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5. Conclusions 23

6. Acknowledgements 25

Literature 26

A. Appendix A 27

A.1. Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.1.1. Basin Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

A.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31A.2.1. Slope estimate results . . . . . . . . . . . . . . . . . . . . . . . . . . 31

A.2.2. Mann-Kendall relative frequency results . . . . . . . . . . . . . . . . 33A.2.3. Altitude groups results . . . . . . . . . . . . . . . . . . . . . . . . . . 35A.2.4. Glacier cover results . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A.2.5. Spearman rank correlation results . . . . . . . . . . . . . . . . . . . 42

A.3. Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

B. Appendix B 50

B.1. Main Matlab Program for Mann-Kendall Theil-Sen . . . . . . . . . . . . . 50B.2. Main Matlab Program for Representative Discharge . . . . . . . . . . . . . 53

List of Figures

1. Representative Discharge [mm/season] for all season of q50 streamflow av-eraged over all stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6



5/56


2. Representative discharge [mm/year] for all season of q50 streamflow averagedover all stations and grouped by station altitude. . . . . . . . . . . . . . . . 10

3. Relative frequencies of high( +) and low(-) flows over all stations for allquantiles and for every period. . . . . . . . . . . . . . . . . . . . . . . . . . 15

4. Slope estimate for all quantiles and for every period. . . . . . . . . . . . . . 165. Slope estimate [mm/season] and standard deviation for 50- and 90-percent

quantiles grouped according to altitude for the period 1990-2010. . . . . . 186. Relative frequencies for 50- and 90-percent quantiles grouped according to

altitude for the period 1990-2010. . . . . . . . . . . . . . . . . . . . . . . . 197. Relative frequencies for 50- and 90-percent quantiles grouped according to

glacier cover for the period 1990-2010. . . . . . . . . . . . . . . . . . . . . . 208. Spearman rank correlation coefficients for mean basin altitude and estimated

slope (a) and MK Z statistic (b) . . . . . . . . . . . . . . . . . . . . . . . . 219. Representative Discharge [mm/season] for all season of q90 streamflow av-

eraged over all stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

10. Representative discharge [mm/year] for all season of q90 streamflow averagedover all stations and grouped by station altitude. . . . . . . . . . . . . . . . 47

11. Estimated slopes [mm/season] and standard deviation for 50- and 90-percentquantiles grouped according to glacier cover for the period 1990-2010. . . . 48

12. Spearman rank correlation coefficients of relative glacier cover and estimatedslope (a) and MK Z statistic (b) . . . . . . . . . . . . . . . . . . . . . . . . 49



6/56


1. Introduction

Trend detection in records of hydroclimatic variables (e.g. air temperature, precipitation,streamflow) contributes significantly to the on-going debate on climate change. So far

the focus of research was on temperature and precipitation rather than on streamflow,giving reason to investigate the latter variable more closely. Records show general increaseof temperature (and precipitation) [(M. Beniston u. Marinucci, 1994)], which have beenrelated to climate change effects. The question arises, if these trends can also (already) bedetected in streamflow data and again, if these trends can be related to climate change. Itis still not clear if and how changes in air temperature and precipitation manifests itself instreamflow. Before this can be investigated, it is first necessary to analyse how streamflowregimes have changed. From the water resources management perspective persisting trendsin streamflow are great importance, particularly trends of extreme events.

Below in figure 1 a representative chart on runoff over the last forty years is shown. Atrend is not obviously detectable with the bear eye; so statistical tools need to be considered

to get a more predicative picture. What can be noticed clearly is the high variation in runoffmagnitude from one season to the other.

Figure 1: Representative Discharge [mm/season] for all season of q50 streamflow averagedover all stations.

The big difference between temperature, precipitation and streamflow is that streamflowis an integrated variable over a watershed. This means that the influence of the first twohydroclimatic variables, which are both point measurements, should to a certain degree be



7/56


noticeable in the integrated value, namely streamflow. Further disadvantage of the firsttwo variables is the high spatial and temporal variability, which can hamper detection ofregional trends.

Switzerland covers an area of 41,284 km2 of which about two thirds is forest and agri-

cultural land. Altitude ranges from 193 m (Lago Maggiore) to 4,634 m (Monte Rosa) andmean annual precipitation reaches about 1480 mm while mean annual runoff is about 960mm (Hydrological Atlas of Switzerland, 19611980). In terms of water resources, 63% ofthe surface water supplies are stored in natural lakes, 35% in glaciers and the remaining2% in artificial lakes. Switzerland lies in four large European watersheds: the Rhine River,draining into the North Sea, the Rhone and Po Rivers, draining into the MediterraneanSea, and the Inn which eventually drains into the Black Sea.

The data and methods are described in Section 2 and 3. Section 4 lists the main resultsaccording to the goals of this project work: first observed streamflow trends are investi-gated, then a correlation analysis between watershed attributes and observed streamflow

trends is conducted. Last some open questions are identified. Finally, the main conclusionsare summarized in Section 5.



8/56


2. Data

Data sources

The analysis of streamflow trends is conducted with data from 39 stations spread aroundthe whole of Switzerland. All these stations provide records of mean daily streamflow rang-ing from 1970 to 2010. More stations were available depending on the period of analysis(52 in total). However, to be consistent in calculations, only stations that provided recordsover the whole of the above-mentioned period were considered. As former trend analysisof streamflow show, trend significance is strongly dependent on flow magnitude and thusseason [Pavel Ya. Groisman u. Karl (2001), (D. P. Lettenmaier, 1991)]. Considering thefacts on Switzerland mentioned in the previous section, snow and ice melt are importantcontributors to runoff seasonality. Streamflow trend analysis on an annual basis mightconceal important information through averaging compared to a seasonal basis [M. Benis-ton u. Marinucci (1994), M.-V. Birsan (2005)]. Hence, seasonality was taken into accountby defining four climatological seasons and analysing them separately (Spring, Summer,Autumn, Winter):

Table 1: Definition of season division

Season Months nr of Days

Spring March - May 92Summer June - August 92Autumn September - November 91

Winter December - January 90

After this, daily streamflows were not analysed directly, but data records were split into

3 periods of each 20 years with 10 overlapping years. This length of period seems to beadequate to capture trends without getting too much variability, which could complicateinterpretation. In this project work shifts in the distribution of daily data are of interest,so the test is applied to quantiles determined at the seasonal timescale. The deciles ofstreamflows as well as minimum and maximum runoff were computed to minimise dataload without losing to much representatitivity. The seasonal qquantile xq(i) of the meandaily flow X is obtained for every season (year) i as the value for which P r(X < x) = q.For instance, the q20-value of a station is the runoff for which 20% of all mean daily flowsfor the given season are below this value. To sum up, in order to identify shifts in thedistribution of mean daily streamflow, a range of 11 quantiles on seasonal bases ( qMIN,qMAX, and q10, q20...q90) were studied for three different observation periods. The analy-sis methods are standard: Mean daily runoff is analysed for trends with the MannKendallnonparametric trend test and the TheilSen slope estimator (both presented in the nextsection).



9/56


Streamflow data used in this work were high resolution records of mean daily discharge.The three main criteria for station selection [M.-V. Birsan (2005)] were:

no substantial influence by water withdrawals for hydropower or other water-usepurposes

spatial independence between station records at least 30 years of continuous and complete observations

Spatial independence for stations located along the same river was ensured by alwayschoosing the upstream station. This offers a good compromise between the assumed in-dependence of station records and a relatively high number of stations [(M.-V. Birsan,2005)].

Alititude groups

In Switzerland 52% of its area lies above 1000 m.a.s.l. and 23% above 2000 m. Froma hydrological perspective, Switzerland can be divided into three distinct runoff regimestypes: Alpine, Midland-Jura, and Southern Alpine (Aschwanden (1985)). So, to get amore detailed picture, the stations were grouped according to the mean altitude of thecorresponding basin, so that they could be compared among each other. Furthermore,the groups were also compared to trends observed by computing all available stations. Inappendix A.1.1 basin attributes and number of stations for each group are listed. For theperiod from 1990-2010 differences according to station altitude were analysed in terms ofslope estimate and relative frequency. To lower data load only two runoff quantiles werelooked at, namely q50 and q90.

Glacier cover

In addition to grouping stations by elevation, they are also divide into a group whichpresent glacier cover and a group which doesnt. Surely both attributes are quite similarand correlated to certain extent. This classification will likely reveal interesting facts,as basins that have an Alpine influence reach a maximum seasonal runoff in spring andsummer. This analysis shall also only consider the 2 quantiles used in the altitude groupsfrom year 1990 to 2010.

Figure 2 shows the same runoff data as figure 1, but with gauging stations groupedaccording to the mean elevation of the corresponding watershed. It highlights that thediffences in flow magnitude related to seasonality is strongly dependent on altitude. Therunoff from basins above 2000m fluctuates considerably compared to the other those oflower stations.



10/56


Figure 2: Representative discharge [mm/year] for all season of q50 streamflow averagedover all stations and grouped by station altitude.

.

For altitude, three groups were formed (0-1000m, 1000-2000m and >2000m), and forglacier cover only two (not glacier covered and partly glacier covered). Neither precipitationnor temperature data were considered, as this work should focus only on the output of therainfall runoff system. Another reason is the relative abundance of assessments on theseparticular values compared to runoff data. (Representative discharge of the q90 streamflow

can be found in appendix A.3).



11/56


3. Methods

Two different statistical tools were used to analyse if streamflow data presented any trends.First, nonparametric slope estimation was used to get an idea of the magnitude of trends

throughout the time series. Also, the Mann-Kendall nonparametric trend test was em-ployed to give the estimated slopes a statistical significance. Simple but robust anddistribution-free tools were preferred. As serial correlation was mostly avoided by dividingdata according to seasons, no pre-whitening was applied to data to discriminate trendsfrom stochastic fluctuations and the influence of serial correlation.

3.1. Mann-Kendall nonparametric trend test

Trend analysis in this project work was conducted with the nonparametric Mann-Kendall(MK) test. This test has been widely used in hydrological studies. It is distribution-free,robust against outliers, and has a higher power than many other commonly used tests[Hess (2001)]. The test, suitable for non-normally distributed data with non-linear trends,should be applied to uncorrelated data [Helsel u. Hirsch (2002)]. Computation of the MKtrend test statistic Z and the identification of statistically significant trends are explainedhereafter. The MK test is applied to time series ofxq(i) with q = 0.1, 0.2,..., 0.9; and alsoto the seasonal minimum xmin(i) and maximum xmax(i), where i = 1,...,n years. Statis-tically significant trends are generally reported at the 10% significance level ( Z/2 = 0.1,two-tailed test). In this study the same significance level will be used to minimize typeII errors. The null and the alternative hypothesis of the MK test for trend in the randomvariable x are:

H0 : P r(xj > xi) = 0.5, j > i,HA : P r(xj > xi)

= 0.5, (twosided test)

The Mann-Kendall statistic S is calculated as

S =n1k=1

nj=k+1

sgn(xj xk) (1)

where xj and xk are the data values in years j and k, respectively, with j > k. sgn() isthe sign function:

sgn(x) =

1, if xj xk > 00, if xj xk = 0

1, if xj xk < 0(2)

Under the null hypothesis the distribution of S can be approximated well by a normal



12/56


distribution (large sample sizes n), with mean S and variance 2S given by:

S = 0, 2S =

n(n 1)(2n + 5)

m

i=1

ti(i)(i 1)(2i + 5)

/18 (3)

This equation yields the variance of S with a correction for ties in data, with ti denotingthe number of ties of extent i. The standard normal variate is used for hypothesis testing,called the MK trend test statistic Z.

Z =

S1S

, if S < 0

0, if S = 0S+1S

, if S < 0.(4)

For a two-tailed test, the null hypothesis is rejected at significance level (Type I error) if

|Z| > Z/2, where Z/2 is the value of the standard normal distribution with an exceedanceprobability /2. Relative frequencies presented in the results section are obtained simplyby dividing the number of Z values for which |Z| > Z/2 applies by the total number ofstations. Low and high flows are reported separately. So, the relative frequency for a givenflow quantile indicates the percentage of stations that prsent a statistical significant trendof of high or low flows.

3.2. Theil-Sen slope estimate

The TheilSen slope estimator is a method for robust linear regression that chooses themedian slope among all lines through pairs of two-dimensional sample points. It is anonparametric method suitable for a nearly linear trend [Helsel u. Hirsch (2002)], andit is more robust than the least-squares estimator because it is much less sensitive tooutliers, meaning that it can tolerate arbitrary corruption of up to 29.3% of the inputdata-points without degradation of its accuracy. It can be significantly more accurate thansimple linear regression and competes well against simple least squares even for normallydistributed data [Wikipedia] . The slope is computed between all pairs i of the variable x:

i =xj xkj k , with j > k (5)

(j = 2,...,n; k = 1,...,n 1)

where i = 1...N. For n values in the time series x this will result in N = n(n

1)/2

values of . The slope estimate b is the median of bi, i = 1...N.



13/56


3.3. Spearman rank correlation

The nonparametric rank-based Spearman correlation coefficient was used to report theresults of correlation analyses. Spearmans is a nonparametric rank-based correlation

coefficient used to estimate the monotone association between two random variables. IfY tends to increase when X increases, the Spearman correlation coefficient is positive. IfY tends to decrease when X increases, the Spearman correlation coefficient is negative.When X and Y are perfectly monotonically related, the Spearman correlation coefficientbecomes 1. It is computed from the difference d between the ranks of independently sortedvariables x and y [Kottegoda (2008)] :

= 1 6n

i=1 d2

n(n2 1) (6)

Under the null hypothesis of no correlation between x and y, the distribution of can be

approximated by a normal distribution with mean and variance 2

given by:

= 0, 2 = 1/(n 1) (7)

The random variables x and y are considered correlated at the significance level if|| > Z/2/

n 1 for a two-tailed test. = 0.1 was chosen for the analysis.

The causal aspects of identified trends in streamflow were investigated by correlationanalyses with 2 basin attributes: mean altitude of the basin and percentage of glaciercover.



14/56


4. Results

The main results are reported in three sections. First, trends in streamflow are analysedfor different seasons and quantiles. Then, differences between groups with different station

altitudes and glacier cover are investigated. Thereafter, relationships between trends andbasin attributes are explored. Ultimately, some open questions are identified and discussedbriefly.

4.1. Trends

As pointed out earlier, choice of study period length is important because it has an impacton trend identification. If a large scale periodic behaviour is present in the records, thelength of analysis period should be chosen in a way that it spans one or more cyclesof this process. A 20 year period is assumed to contain low and high flow periods andtherefore identitified trends should not result from lowfrequency largescale behaviour inthe recorded data. Also, as can be seen in the graphs below, changes in runoff have astrong seasonal dependence and should therefore be considered separately.

Mann-Kendall

Relative frequencies of high and low flows were investigated. In figure 3 up and downtrends are shown for every season and period.

Spring: In the first period high flows are relatively frequent. Up to 40% of the stationsmanifest high flows for all quantiles. However, in the following two periods the frequenciesof high flows exhibit a subsiding development, especially for the lower quantiles. On theother hand, frequencies of low flows tend to increase over the three periods. Still, in

the most recent period quantiles above the median flow (q50) dont display statisticallysignificant low flows.

Summer: In this season there is little change over all periods, except for the frequenciesof low flows from 1980-2000. It seems that the summer of this period had particularlyfrequent low flows. Taken aside this fact, there is no strong significant up- or downwardtrend indicated by the MannKendall test.

Autumn: Autumn shows a similar picture as summer, with the difference that in thisseason an increase of frequent low flows occurs in the last period. Interestingly, the fre-quencies of low flows for the middle period dont follow those of the previous season. Even

high flows frequencies are more numerous after a relative dry summer.



15/56


(a) Spring (b) Summer

(c) Autumn (d) Winter

Figure 3: Relative frequencies of high( +) and low(-) flows over all stations for all quantilesand for every period.

Winter: The first two periods reveal a rising number of high flows in winter. And yet,the last period presents the opposite situation. Frequencies of low flows have increasedconsiderably whereas high flows have practically vanished. This can be an indication of animportant shift of streamflow regime for the winter season.



16/56


Theil-Sen slope estimate

Results for the Theil-Sen slope estimate for each season are shown below in figure 4.

(a) Spring (b) Summer

(c) Autumn (d) Winter

Figure 4: Slope estimate for all quantiles and for every period.

Spring: In the first period (1970-1990) spring flows show an increasing trend for all stream-flow quantiles. The two following periods also demonstrate an increasing trend, but of lowermagnitude. The other 2 periods show a reduced increase and even a decrease for the lowerquantiles.

Summer: Summer flows clearly exhibit decreasing trends in all periods and for all quan-

tiles, except for the maximum flow in the last period. In general the maximum flow insummer is due to heavy rainstorm events, so for the overall picture one can argue thatsummer flows are actively decreasing.



17/56


Autumn: Autumn flows present relatively small changes in the first two periods. Again,there is a significant decrease in the most recent period. Put another way, this most likelyis an indication of a change in the runoff regime.

Winter: Winter season pictures a faint upward trend in the first two periods for all quan-tiles but maximum flow. Similarly to autumn, the trend is inverted in the last period andfor all quantiles (including maximum flow). Indeed, even the maximum flows in winter havesubstantially fallen from an extreme upward trend to a high decreasing trend. Accordingly,this again gives reason to presume a change in the winter streamflow regime.

Frequencies and magnitude

Looking at both frequency and magnitude together, the following can be said:

Spring flows show an increasing trend in both the MannKendall test and the slopeestimate. Moreover both also signal a subsiding development of this trend.

The MK test suggests that in summer, occurrence of high and low flows are moreor less balanced in every period (except for low flows in the middle period), but theslope estimate clearly reveals a decreasing trend.

In summer period from 1990-2010, the maximum flow has a substantial increase butwith a relative low frequency. Also, the frequencies of low flows are higher than thoseof high flows (except for qMIN, q10, q20). In each period low flows outnumber highones in summer, yielding a decreasing trend in runoff.

A clear change is noticeable for the most recent period in both MK test and Theil-Sen estimate. In other words, frequencies of low flows have risen and slope estimates

sketch out a decrease in flow magnitude over all quantiles.

Trends of streamflow in winter trace a similar, maybe even more pronounced, pictureas in autumn. In this season, from 1990-2010, not only frequencies of low flows haverisen, but frequencies of high flows have fall at the same time. Also the slope estimatehas switched from a weak increasing to a decreasing trend.



18/56


4.2. Differences in altitude

For the period from 1990-2010, differences according to station altitude were analysed interms of slope (fig. 5) and relative frequency (fig. 6). To lower data load only two runoff

quantiles were looked at, namely q50 and q90.

Figure 5: Slope estimate [mm/season] and standard deviation for 50- and 90-percent quan-tiles grouped according to altitude for the period 1990-2010.

In spring, all 3 groups show an increasing slope. The summer season is most heteroge-neous with decreasing trends for low and high altitude stations, but an increasing slope forstations located between 1000m and 2000m. Autumn and winter both signal a decreasingtrend for both quantiles. These graphs also show that if a trend is visible (increases ordecreases), it tends to be a more pronounced for the higher quantile q90 (except for sum-mer). While this is true, there is no clearly discernible trend related to the mean elevation

of the watershed when looking at both quantiles.



19/56


Comparing the slope trends with the relative frequencies of high and low flows, revealsthat the trends (slopes) found are endorsed by the Mann-Kendall test. Where springdisplays a positive trend for every altitude, high flows are common whereas low flows arelacking. The previously identified decreasing slope in autumn is matched by frequent low

flows. Particularly in winter for the 90 percent quantile, where slopes are slightly falling,low flows are quite frequent. This indicates that large runoff (q90) in winter is decreasingin magnitude and occur more seldom. To sum up, the mean altitude of a watershed doesnot play a significant role for streamflow regime alteration. Stations from all three altitudegroups exhibit similar behaviour when compared to each other.

Figure 6: Relative frequencies for 50- and 90-percent quantiles grouped according to alti-tude for the period 1990-2010.



20/56


Glacier presence

To further investigate any relation between basin attributes and change in runoff regime,station records were divided into 2 groups depending on whether they presented glacier

cover or not. For these two groups, only the frequencies of high and low flows were consid-ered. The results are shown in figure 7 .

Figure 7: Relative frequencies for 50- and 90-percent quantiles grouped according to glaciercover for the period 1990-2010.

Relative frequencies from both groups coincide most often. In summer, stations with noglacier dont display any trend. In winter stations with glacier cover indicate a decreasingtrend for both quantiles, whereas the other group only exhibits a downward trend for q90.This means that basins with glaciers are facing overall frequent low flows, while basinswithout only experience this trend for large runoff. The median flow of the latter stations

is undisturbed. As seen earlier with elevation, no obvious relation of trend with glacierpresence is detectable.



21/56


4.3. Correlation with basin attributes

In the graphs below (figure8) it is clear that correlation exists, but depends on season andquantile. However for smaller quantiles in winter there mostly is no statistically significant

correlation between mean basin altitude and estimated slope. From the methods section,one can calculate that for a 10% significance level and 39 stations, basin attributes andtrend are considered correlated if || > 0.27.

(a) (b)

Figure 8: Spearman rank correlation coefficients for mean basin altitude and estimatedslope (a) and MK Z statistic (b)

Correlation with estimated slope Positive correlation can be seen for high quantiles inWinter. Summer shows a negative correlation for moderate flows. Lower quantiles correlatenegatively for autumn. Spring has no proper tendency.

Correlation with Mann-Kendall Z statistic No really significant correlation can be seenfor all quantiles in Winter. The other three seasons are similar to the correlation with esti-mated slopes. In summer altitude correlates for moderate flows. Lower quantiles correlate

well for autumn. Again, spring has no clear tendency, displaying positive and negativecorrelations both for high and low flows.



22/56


The Spearman rankbased correlation was also computed for glacier cover.Those corre-lation charts between glacier cover and streamflow trends can be found in appendix A.3.Results are comparable to those of mean basin altitude.

4.4. Open Quetions

As stated earlier, there seems to be a change in streamflow regime in at least 2 out of 4seasons (autumn and winter), especially for when comparing the most recent period withthe two previous ones. Now that changes have been identified, the question arises whatthese changes are due to and if in future these shifts will also be detectable in spring andsummer. Several things have to be investigated:

The assumption that a 20 year period sufficiently captures any large-scale periodicityshould be investigated. As pointed out by (P Pekarova, 2006) dry cycles of 13.5 and28-29 years have been identified (see also P Pekarova (2003)).

Another issue is to assert that these changes are not due to anthropogenic factorsnor emphasised by these. It is arguably nearly impossible to exclude anthropogenicinfluences altogether. If land use (and therfore land cover) changes in some of theanalysed basins this can have influenced the streamflow regime. Also changes in thefluvial systems should be taken into account. The time scale, on which these effectsoccur from external factors, could give an indication on whether they influence trendsor not.

we expect that most of the (natural) watershed changes occur on much longer timescalesthan those studied here, we recognise that they do contribute to hydrological vari-ability

Precipitation and air temperature data (focussing on days with minimum daily tem-perature above melting point) might explain some of the observed trends. Do changesin runoff properly reflect the input to a rainfall-runoff system, namely precipitation.

Changes in net glacier balance should be analysed together with identified trendsto assess whether there is a relationship between both that can be due to climatechange. For instance, glacier retreat will have an impact on land cover which againwill impact runoff.



23/56


5. Conclusions

This project work presents a statistical analysis of trends in mean daily streamflow recordsfrom 39 watersheds in Switzerland with a mostly undisturbed runoff regime for three

study periods (1970-1990, 1980-2000 and 1990-2010). Estimate of trend magnitude andstatistically significant trends were computed for each station on a seasonal basis andfor different streamflow quantiles. Identified trends in streamflow were correlated withwatershed attributes. The main conclusions are as follows:

Trends are present in every period as well for high and low flows. Magnitude dependson period and season of interest.

Particularly the last period (1990-2010) experiences a significant increase of lowerflows in Winter for every quantile. This suggests that winters are becoming increas-ingly dryer over the last 20 years.

In the winter season there is a considerable shift of frequent high flows to frequentlow flows in the last period of analysis (1990-2010).

The increasing trend of Spring flows is experiencing a decaying development over thethree analysed periods.

Summer flows exhibit a decreasing trend, particularly in magnitude. Autumn also reveals a shift in the last period. A decreasing trend in magnitude

matches an increase of statistical significant low flows from 1990-2010.

Winter flows also show a substantial shift in the last period similar to the autumnseason. In Addition to a rising number of low flows, the season presents only veryfew high flows.

There was no discernible dependence of trends related to the mean elevation of theanalysed watersheds.

Basins lacking presence of glacier dont show any trend. Particularly in winter medianflow of watersheds without glacier remains unchanged, while basins with glaciers facedownward trends for both q50 and q90. This trend should be followed closely if itpersists, because it can give an indication on what is happening to precipitation inhigher altitudes.

Correlation between mean watershed elevation and trends is strongly dependent on

season and quantile. No significant correlation was found in spring. Autumn andsummer show negative correlation for low flows, resp. moderate flows. In winter highflows show a good correlation with magnitude of trend (estimated slope).



24/56


The altitude groups followed the same trend patterns as the ones found when com-puting trends from all the available stations.



25/56


6. Acknowledgements

Thanks for the data I received from the Federal Office for the Environment (FOEN orBAFU in german).

Thanks to my supervisor Dr. Peter Molnar, who patiently guided me through this projectwork.Special Thanks to the 2 anonymous reviewers, who helped to improve this report.



26/56


References

[Aschwanden 1985] Aschwanden, Weingartner R. H.: Runoff Regimes in Switzerland.Pub. Gewasserkunde, 1985

[D. P. Lettenmaier 1991] D. P. Lettenmaier, Eric F. W. JAMES R. WALLIS W. JAMESR. WALLIS: A Daily Hydroclimatological Data Set for the Continental United States.In: WATER RESOURCES RESEARCH (1991)

[Helsel u. Hirsch 2002] Helsel, D.R. ; Hirsch, R.M.: Statistical Methods in WaterResources. U.S. GEOLOGICAL SURVEY, 2002

[Hess 2001] Hess, Iyer H. Malm W. A.: Linear trend analysis: a comparison of methods.In: Atmospheric Environment (2001), 10

[Kottegoda 2008] Kottegoda, Rosso R. N.T.: Statistics, Probability, and Reliability forCivil and Environmental Engineers. Bd. 2nd edition. Wiley-Blackwell, 2008

[M. Beniston u. Marinucci 1994] M. Beniston, F. G. M. Rebetez R. M. Rebetez ; Mar-inucci, M. R.: An Analysis of Regional Climate Change in Switzerland. In: Theoreticaland Applied Climatology (1994)

[M.-V. Birsan 2005] M.-V. Birsan, P. Burlando M. P. P. Molnar M. P. Molnar: Streamflowtrends in Switzerland. In: Journal of Hydrology (2005)

[P Pekarova 2003] P Pekarova, J. P. P. Miklanek M. P. Miklanek: Spatial and temporalrunoff oscillation analysis of the main rivers of the world during the 19th20th centuries.In: Journal of Hydrology (2003)

[P Pekarova 2006] P Pekarova, J. P. P. Miklanek M. P. Miklanek: Long-term trends andrunoff fluctuations of European rivers. In: Climate Variability and ChangeHydrologicalImpacts (2006)

[Pavel Ya. Groisman u. Karl 2001] Pavel Ya. Groisman, Richard W. K. ; Karl,Thomas R.: Heavy Precipitation and High Streamflow in the Contiguous United States:Trends in the Twentieth Century. In: Bulletin of the American Meteorological Society(2001)

[Wikipedia ] Wikipedia: Wikipedia. http://de.wikipedia.org, Abruf: 05. Dec 2011

http://de.wikipedia.org/http://de.wikipedia.org/


27/56


A. Appendix A

A.1. Stations

A.1.1. Basin Attributes



28/56

!"#$%&%'

()

ID

NEW_ID

AREA

K-Gravelius

ALTITUDE

SLO

PE

RIV_DENS

MEAN_CN

SOIL

%_ROCK

%GLA

CIER

PREC_ANN

833

2312

48.

5

1.

979

473

2.

6

1406

70.

4

93

0

0

1011

915

2202

261

1.

905

585

13

.6

1223

71.

9

71

0.

1

0

1067

528

2126

78.

9

2.

772

648

11

.3

2095

70.

1

86

0.

3

0

1277

549

2132

342

2.

258

649

11

.6

2522

69.

5

82

0.

2

0

1251

883

2034

392

2.

686

722

7.

3

1693

66.

5

90

0.

1

0

1215

863

2343

59.

9

1.

886

761

1

0

1647

66.

5

97

0

0

1338

650

2159

124

2.

333

842

12

.2

1943

68.

8

76

0.

9

0

1224

479

2122

183

2.

537

924

15

.1

918

68

56

0.

3

0

1284

843

2321

73.

9

1.

7

988

23

.8

3729

72.

1

34

0.

3

0

1816


29/56

!"#$%*%'

()

ID

NEW_ID

AREA

K-Gravelius

ALTITUDE

SLO

PE

RIV_DENS

MEAN_CN

SOIL

%_ROCK

%GLA

CIER

PREC_ANN

698

2187

180

1.

896

1000

17

.2

2138

74.

2

50

4.

3

0

1403

825

2303

493

1.

991

1020

17

.9

2854

72.

7

65

3.

4

0

1723

978

2179

352

2.

079

1069

15

.8

2844

69.

2

71

3.

3

0

1337

822

2300

59.

2

1.

549

1336

1

9

4121

74.

1

39

2.

6

0

2151

1143

2481

227

1.

865

1618

2

9

1352

74.

8

24

19.

4

4.

3

1474

637

2151

344

2.

576

1634

23

.2

1847

74.

3

33

9.

9

3.

4

1408

1127

2150

616

2.

19

1797

25

.5

1950

75.

1

32

14.

6

1.

7

1194

864

2426

105

1.

807

1808

29

.9

2574

78.

5

29

21.

9

0.

3

1396

799

2276

43.

9

1.

916

1815

30

.9

1006

73.

4

19

24.

7

9.

7

1488

750

2232

28.

8

1.

593

1853.

5

25

.9

2380

76

28.

8

14.

6

0

1535

879

2356

25

1.

484

1989

34

.2

1058

84

16

57.

6

0

1807


30/56

!"#$%&%'

(&

ID

NEW_ID

AREA

K

-Gravelius

ALTITUDE

SLOP

E

RIV_DENS

MEAN_CN

SOIL

%_ROCK

%GLAC

IER

PREC_ANN

862

2342

77.

7

1.

744

2012

29.3

1977

73.

2

27

20.

3

7.2

845

387

2109

379

1.

896

2031

30.1

1553

72.

9

20

26.

6

16.

6

1367

614

2141

529

1.

906

2125

27.1

1511

76.

4

22

23.

1

1.2

994

716

2200

164

1.

676

2152

31.8

1268

74.

2

17

33.

3

16.

5

1346

821

2299

20.

6

1.

644

2196

33.6

713

78.

8

10

57

19.

7

1392

877

2355

183

1.

861

2221

24.7

2098

76.

7

21

23.

7

0.8

1038

298

2087

192

1.

949

2277

26.1

2367

77.

8

20

30.

8

5.5

1636

890

2366

14.

1

1.

773

2290

24.3

1772

74.

8

25

15.

9

0

1455

735

2219

35.

7

1.

799

2328

23.8

1069

70.

6

10

36.

6

32.

1

1311

826

2304

55.

3

1.

804

2330

25.3

1304

78.

9

22

31.

8

0

865

866

2346

913

2.

185

2335

27

1524

69.

2

19

26.

8

22.

7

1152

838

2319

26.

9

1.

626

2366

33.8

708

82.

1

10

47.

2

2.6

816

848

2327

43.

3

1.

691

2371

26.9

1732

79.

5

17

34.

7

2.7

990

922

2263

73.

3

1.

624

2548

27.4

1222

81.

4

17

33.

2

0

927

782

2262

107

1.

754

2616

25.4

1290

73.

8

15

38.

1

21.

1

1110

793

2269

77.

8

1.

753

2648

29.6

1256

70

10

37.

5

32.

6

1098

152

2351

778

1.

835

2655

29

1072

67

13

26.

5

29.

3

737

778

2256

66.

5

1.

742

2710

28.3

1192

69.

5

11

37.

1

32.

6

948

792

2268

38.

9

1.

961

2710

22.8

828

64.

4

10

34.

7

45.

7

1737


31/56


A.2. Results

A.2.1. Slope estimate results



32/56

readstations available

spring summer autumn winter 39 44

qmin 0.85 -1.88 -0.45 0.26

q10 1.28 -1.90 -0.40 0.19

q20 1.46 -1.37 -0.41 0.18

q30 1.67 -0.89 -0.37 0.09

q40 1.90 -1.02 -0.19 0.04

q50 1.74 -0.43 0.14 0.03

q60 1.70 0.07 0.42 0.17

q70 2.78 0.30 0.94 0.57

q80 5.28 -0.17 -0.34 1.13

q90 6.53 -0.08 -0.81 1.96

qmax 10.13 -7.40 1.82 20.36


qmin 0.42 -0.16 0.66 0.06q10 0.54 -0.26 0.80 0.21

q20 0.60 -0.28 0.82 0.18

q30 0.14 -1.15 0.87 0.25

q40 -0.23 -2.11 0.88 0.36

q50 -0.62 -3.31 0.89 0.42

q60 0.15 -4.51 0.40 0.42

q70 2.19 -6.06 -0.42 0.58

q80 2.19 -7.99 -0.40 0.66

q90 1.15 -8.96 1.04 0.84

qmax 5.12 -4.47 7.88 5.74


qmin -0.58 0.95 -0.27 -0.22

q10 -0.69 0.57 -0.39 -0.25

q20 -0.21 0.00 -0.56 -0.22

q30 0.38 -0.70 -0.73 -0.26

q40 1.10 -1.09 -1.00 -0.33

q50 1.68 -1.51 -1.57 -0.54

q60 2.50 -1.68 -2.09 -0.64

q70 1.89 -1.78 -3.16 -0.94

q80 3.19 -1.79 -3.83 -1.53q90 3.57 -0.62 -5.43 -2.39

qmax 12.55 7.03 -9.92 -10.32

1970-1990

1980-2000

1990-2010


33/56


A.2.2. Mann-Kendall relative frequency results



34/56

!"#$%&

'

(

'

(

'

(

!"#$

%&'

('

()'

&*'

('

(('

!&+

*&'

*'

(('

&,'

('

-)'

!-+

%)'

('

(&'

&*'

('

-('

!(+

%%'

('

&*'

&+'

,'

,'

!%+

(('

+'

&+'

&('

-&'

('

!*+

-('

('

*'

,'

(&'

('

!)+

&('

('

,'

&+'

(,'

+'

!.+

-)'

('

-)'

&+'

&*'

+'

!,+

%%'

('

-)'

&*'

-)'

+'

!/+

(('

('

&,'

&+'

&+'

+'

!"01

&,'

('

&('

('

-('

+'

!)**+#

'

(

'

(

'

(

!"#$

+'

&,'

,'

&*'

&*'

+'

!&+

+'

&,'

&+'

&('

-('

('

!-+

,'

-&'

*'

-('

&('

,'

!(+

,'

&*'

*'

(&'

('

,'

!%+

&+'

&+'

*'

()'

,'

&+'

!*+

*'

,'

*'

%&'

('

&*'

!)+

&+'

,'

('

%)'

('

&+'

!.+

&*'

*'

+'

*)'

('

&+'

!,+

,'

('

+'

*/'

('

,'

!/+

&*'

,'

+'

*/'

('

,'

!"01

*'

&,'

('

-&'

*'

,'

,-./(,--/

,-0/(1///

,--/(1/,/

,-./(,--/

,-0/(1///

,--/(1/,/

!"#"$%

&

'

&

'

&

'

!"#$

%&

'(&

)*&

%

&

%&

'%&

!'(

(&

'%&

)*&

%

&

%&

'+&

!)(

%&

'%&

'+&

+

&

%&

'%&

!%(

,&

+&

)'&

,

&

(&

)%&

!-(

'(&

'%&

'+&

+

&

%&

)%&

!,(

',&

,&

'(&

%

&

(&

%'&

!*(

'+&

+&

+&

'(

&

(&

%'&

!.(

'%&

+&

+&

'+

&

(&

%*&

!+(

%&

%&

+&

'%

&

(&

%+&

!/(

,&

,&

+&

+

&

(&

)+&

!"01

'%&

,&

+&

(

&

%&

)+&

()%#*+

&

'

&

'

&

'

!"#$

)*&

,&

',&

',

&

+&

)'&

!'(

)'&

,&

)'&

+

&

,&

)%&

!)(

)%&

%&

)'&

+

&

,&

)'&

!%(

)'&

+&

'+&

+

&

,&

',&

!-(

',&

+&

'+&

,

&

%&

)'&

!,(

',&

+&

)'&

%

&

%&

)*&

!*(

'(&

,&

)'&

%

&

%&

)%&

!.(

'(&

+&

%'&

(

&

(&

%'&

!+(

'(&

,&

)%&

(

&

(&

%+&

!/(

+&

,&

'+&

(

&

(&

-'&

!"01

*/&

%&

)%&

(

&

(&

--&

,-./',--/

,-0/'1///

,--/'1/,/

,-./',--/

,-0/'1///

,--/'1/,/


35/56


A.2.3. Altitude groups results



36/56

!"#$%&

'()*+, '-../) 0-1-.+ 2*+1/) '()*+, '-../) 0-1-.+ 2*+1/) '()*+, '-../) 0-1-.+ 2*+1/)

3.*+ 4567 8459: 8459; 845 845:6 45=: 45>4 895


37/56

!

"

!

"

!

"

#$%&

!!"

#"

$$"

#"

%&"

$"

#'(

''"

#"

&'"

#"

%&"

!!"

#)(

(("

#"

)("

#"

'&"

$"

#*(

(("

#"

)("

#"

'("

$"

#+(

(("

#"

*%"

#"

(!"

#"

#,(

(("

#"

'*"

#"

!*"

$"

#-(

!!"

#"

+"

+"

!*"

#"

#.(

(("

#"

+"

+"

'&"

#"

#/(

''"

#"

(&"

+"

$)"

#"

#0(

%%"

#"

+"

+"

%("

#"

#$12

''"

#"

+"

+"

!*"

#"

#$%&

#"

''"

*%"

+"

'&"

!!"

#'(

#"

$*"

%$"

#"

%("

!!"

#)(

#"

%%"

%$"

+"

'&"

$"

#*(

#"

''"

!)"

#"

(!"

$"

#+(

#"

%%"

+"

#"

!*"

$"

#,(

#"

''"

#"

#"

!!"

#"

#-(

#"

''"

#"

+"

!*"

#"

#.(

#"

''"

!)"

+"

%("

#"

#/(

#"

$*"

+"

+"

%&"

#"

#0(

#"

%%"

+"

#"

'("

#"

#$12

#"

#"

#"

+"

(*"

#"

#$%&

#"

!!"

+"

%$"

#"

'&"

#'(

!!"

#"

#"

(&"

#"

'&"

#)(

#"

#"

+"

!)"

#"

'&"

#*(

!!"

#"

+"

#"

$"

!*"

#+(

(("

#"

!)"

#"

(!"

$"

#,(

''"

#"

!)"

#"

'&"

$"

#-(

$*"

#"

+"

#"

%&"

#"

#.(

$*"

#"

+"

#"

#"

#"

#/(

*&"

#"

(&"

#"

$"

#"

#0(

(("

#"

+"

#"

$"

#"

#$12

!!"

#"

!)"

#"

'("

#"

'00(")('(

'0/(")(((

("'((($

'(((")((($

3)((($

456789

'0.("'00(

!

"

!

"

!

"

#$%&

!"

##"

!"

$%

"

!"

#&"

#'(

!"

$$"

!"

#'

"

!"

#&"

#)(

!"

$$"

!"

$%

"

#&"

#&"

#*(

!"

$$"

!"

$%

"

#&"

("

#+(

!"

$$"

!"

#'

"

$#"

!"

#,(

!"

##"

!"

#'

"

##"

!"

#-(

!"

##"

!"

#'

"

$#"

!"

#.(

##"

##"

!"

)

"

$&"

!"

#/(

!"

!"

!"

)

"

#&"

!"

#0(

!"

##"

!"

#'

"

*$"

!"

#$12

!"

**"

!"

$%

"

##"

("

#$%&

!"

$$"

!"

)

"

#&"

#&"

#'(

!"

##"

!"

!

"

$#"

$#"

#)(

!"

##"

!"

$%

"

##"

$&"

#*(

!"

$$"

!"

$%

"

##"

*%"

#+(

!"

$$"

!"

$%

"

##"

+%"

#,(

!"

$$"

!"

*&

"

##"

(*"

#-(

!"

**"

!"

+(

"

("

(*"

#.(

!"

**"

!"

+(

"

!"

%+"

#/(

!"

$$"

!"

((

"

!"

%)"

#0(

!"

##"

!"

&+

"

!"

%)"

#$12

!"

!"

!"

)

"

("

*%"

#$%&

##"

!"

#'"

!

"

#&"

!"

#'(

$$"

!"

$%"

!

"

$#"

("

#)(

##"

!"

$%"

!

"

("

#&"

#*(

!"

!"

)"

!

"

!"

#&"

#+(

!"

!"

$%"

!

"

!"

$#"

#,(

!"

!"

)"

!

"

!"

*$"

#-(

!"

!"

)"

!

"

!"

$#"

#.(

!"

!"

)"

!

"

!"

$#"

#/(

!"

!"

)"

!

"

!"

#&"

#0(

!"

##"

)"

!

"

!"

##"

#$12

!"

##"

#'"

!

"

!"

##"

'00(")('(

'0/(")(((

("'((($

'(((")((($

3)((($

456678

'0.("'00(


38/56

!

"

!

"

!

"

#$%&

!"

##"

!"

$"

%"

##"

#'(

!"

##"

!"

$"

!"

#&"

#)(

!"

''"

!"

$"

%"

##"

#*(

!"

##"

!"

$"

##"

%"

#+(

!"

''"

!"

#("

'#"

%"

#,(

!"

!"

!"

$"

)'"

%"

#-(

!"

!"

!"

#("

)*"

%"

#.(

!"

!"

!"

$"

'&"

##"

#/(

!"

!"

!"

$"

%"

!"

#0(

!"

!"

!"

#("

##"

!"

#$12

##"

!"

#("

#("

##"

!"

#$%&

!"

##"

#("

!"

+'"

!"

#'(

!"

##"

)&"

!"

)'"

!"

#)(

!"

##"

#("

!"

'&"

##"

#*(

!"

##"

'*"

!"

'&"

%"

#+(

!"

##"

'*"

!"

'#"

##"

#,(

!"

!"

#("

!"

##"

%"

#-(

!"

!"

#("

!"

%"

'#"

#.(

##"

!"

$"

!"

%"

)*"

#/(

##"

!"

$"

!"

%"

'&"

#0(

##"

!"

$"

!"

%"

#&"

#$12

##"

!"

!"

!"

##"

!"

#$%&

##"

!"

!"

#("

!"

#&"

#'(

##"

!"

!"

#("

!"

'&"

#)(

##"

!"

!"

$"

!"

'#"

#*(

!"

##"

!"

#("

!"

)'"

#+(

##"

##"

!"

'*"

!"

'&"

#,(

!"

''"

!"

#("

!"

+'"

#-(

!"

++"

!"

#("

!"

)'"

#.(

!"

++"

!"

'*"

!"

)*"

#/(

!"

))"

!"

+%"

!"

)*"

#0(

!"

''"

!"

)&"

!"

'&"

#$12

!"

''"

$"

#("

!"

)*"

'00(")('(

'0/(")(((

("'((($

'(((")((($

3)((($

456578

'0.("'00(

!

"

!

"

!

"

#$%&

!"

##"

$%"

!

"

&%"

'"

#'(

!"

##"

#("

!

"

&$"

'"

#)(

!"

!"

$%"

!

"

&$"

'"

#*(

!"

##"

$%"

)

"

$*"

'"

#+(

!"

!"

#("

)

"

$#"

##"

#,(

!"

!"

)"

)

"

$*"

##"

#-(

!"

##"

)"

!

"

#*"

'"

#.(

!"

##"

)"

)

"

#*"

'"

#/(

!"

##"

$%"

!

"

'"

'"

#0(

!"

##"

!"

!

"

#*"

'"

#$12

%("

!"

)#"

!

"

'&"

'"

#$%&

!"

##"

!"

#(

"

&$"

#*"

#'(

!"

!"

!"

!

"

+$"

#*"

#)(

!"

!"

!"

!

"

+$"

#*"

#*(

!"

!"

!"

!

"

&%"

#*"

#+(

!"

!"

!"

!

"

&%"

##"

#,(

!"

!"

)"

!

"

&%"

'"

#-(

!"

!"

)"

!

"

&%"

'"

#.(

!"

!"

&*"

!

"

+$"

!"

#/(

!"

!"

$%"

!

"

&$"

!"

#0(

!"

!"

)"

!

"

&$"

!"

#$12

!"

!"

&*"

!

"

$*"

!"

#$%&

$$"

!"

!"

#(

"

'"

&$"

#'(

!"

!"

)"

#(

"

'"

&%"

#)(

!"

!"

)"

#(

"

'"

&$"

#*(

!"

!"

)"

$%

"

'"

#*"

#+(

!"

!"

)"

#(

"

!"

&$"

#,(

!"

!"

)"

&*

"

!"

&$"

#-(

!"

!"

)"

#(

"

!"

&%"

#.(

!"

##"

!"

&*

"

!"

&%"

#/(

!"

$$"

!"

''

"

!"

&%"

#0(

!"

++"

!"

''

"

!"

&$"

#$12

!"

'*"

!"

+'

"

!"

&%"

'00(")('(

("'((($

'(((")((($

'0/(")(((

3)((($

456789

'0.("'00(


39/56


A.2.4. Glacier cover results



40/56

spring

summer

autumn

winter

spring

summer

autumn

winter

qmin

-0.

10

0.

90

0.

09

0.

16

-0.

98

1.

00

-0.

58

-0.

55

q10

-0.

14

1.

08

-0.

09

0.

08

-1.

16

0.

14

-0.

64

-0.

53

q20

0.

47

1.

22

-0.

19

0.

12

-0.

79

-1.

06

-0.

88

-0.

52

q30

0.

93

0.

99

-0.

46

0.

07

-0.

09

-2.

15

-0.

96

-0.

55

q40

1.

35

0.

65

-0.

73

-0.

01

0.

88

-2.

58

-1.

22

-0.

61

q50

1.

95

-0.

04

-1.

36

-0.

22

1.

45

-2.

77

-1.

76

-0.

81

q60

2.

74

-0.

60

-2.

37

-0.

38

2.

29

-2.

61

-1.

84

-0.

86

q70

3.

26

-0.

89

-3.

59

-0.

78

0.

71

-2.

54

-2.

79

-1.

07

q80

4.

68

-0.

89

-4.

84

-1.

75

1.

90

-2.

56

-2.

97

-1.

34

q90

5.

61

0.

06

-7.

79

-3.

36

1.

81

-1.

20

-3.

42

-1.

55

qmax

10.

27

13.

79

-10.

00

-

16.

44

14.

50

1.

24

-9.

85

-5.

08

1990-2010

noglacier

glacier


41/56

qmin

6%

17%

0%

48%

qmin

11%

0%

19%

0%

q10

6%

11%

0%

38%

q10

28%

0%

19%

5%

q20

6%

11%

0%

33%

q20

22%

0%

5%

14%

q30

11%

6%

5%

10%

q30

6%

0%

0%

14%

q40

17%

0%

24%

5%

q40

11%

0%

5%

19%

q50

28%

0%

33%

5%

q50

0%

0%

5%

29%

q60

39%

0%

38%

0%

q60

0%

0%

5%

19%

q70

28%

0%

5%

0%

q70

0%

0%

5%

19%

q80

44%

0%

10%

0%

q80

0%

0%

5%

14%

q90

17%

0%

5%

0%

q90

0%

6%

5%

10%

qmax

11%

0%

33%

0%

qmax

0%

6%

10%

10%

qmin

6%

0%

0%

24%

qmin

11%

11%

5%

29%

q10

6%

6%

0%

29%

q10

6%

6%

5%

38%

q20

6%

0%

0%

24%

q20

6%

11%

5%

29%

q30

0%

11%

0%

33%

q30

6%

0%

5%

29%

q40

6%

22%

0%

24%

q40

6%

6%

0%

33%

q50

0%

22%

0%

38%

q50

6%

6%

0%

43%

q60

0%

33%

0%

29%

q60

6%

6%

0%

38%

q70

0%

33%

0%

38%

q70

0%

11%

0%

48%

q80

0%

50%

0%

29%

q80

0%

28%

0%

48%

q90

0%

39%

0%

19%

q90

0%

39%

0%

43%

qmax

0%

33%

5%

24%

qmax

0%

44%

0%

43%

SPRING

SUMMER

AUTUMN

WINTER

1990-2010

1990-2010

1990-2010

1990-2010


42/56


A.2.5. Spearman rank correlation results



43/56

spring summer autumn winter

qmin -0.14 -0.31 -0.06 0.30 1970

q10 -0.27 -0.24 -0.04 0.36 1990

q20 -0.26 0.06 0.07 0.26

q30 -0.25 0.19 0.15 0.32

q40 -0.31 0.16 0.23 0.39

q50 -0.32 0.21 0.30 0.39

q60 -0.26 0.22 0.28 0.22

q70 -0.10 0.24 0.29 -0.18

q80 0.11 0.19 0.18 -0.39

q90 0.04 0.24 0.12 -0.69

qmax -0.41 0.28 0.02 -0.72

qmin 0.32 0.19 0.54 0.32 1980

q10 0.39 0.17 0.33 0.26 2000

q20 0.39 0.20 0.25 0.33

q300.42 0.07 0.16 0.21

q40 0.50 -0.05 0.03 0.18

q50 0.57 -0.09 -0.12 0.27

q60 0.54 -0.17 -0.29 0.39

q70 0.68 -0.33 -0.40 0.36

q80 0.70 -0.59 -0.36 0.31

q90 0.69 -0.52 -0.16 0.20

qmax 0.40 -0.25 -0.01 -0.43

qmin -0.10 0.15 -0.38 -0.25 1990

q10 -0.27 -0.06 -0.41 -0.15 2010

q20 -0.46 -0.27 -0.50 -0.12q30 -0.36 -0.36 -0.37 -0.09

q40 -0.20 -0.38 -0.34 -0.08

q50 -0.18 -0.38 -0.27 -0.04

q60 -0.02 -0.35 -0.08 -0.01

q70 -0.29 -0.32 0.03 0.14

q80 -0.10 -0.20 0.09 0.39

q90 -0.14 -0.09 0.17 0.51

qmax 0.28 -0.26 -0.12 0.49


44/56


qmin 0.06 -0.17 0.03 0.30 1970

q10 -0.08 -0.02 0.02 0.27 1990

q20 -0.17 0.19 0.10 0.20

q30 -0.27 0.22 0.20 0.23

q40 -0.32 0.22 0.34 0.21

q50 -0.34 0.23 0.30 0.20

q60 -0.22 0.22 0.21 0.17

q70 0.05 0.20 0.14 0.09

q80 0.26 0.18 0.13 0.04

q90 0.07 0.31 0.15 -0.14

qmax -0.26 0.30 -0.02 -0.45

qmin 0.43 0.24 0.50 0.17 1980

q10 0.56 0.14 0.35 0.19 2000

q20 0.56 0.10 0.21 0.17

q300.53 -0.01 0.15 0.13

q40 0.56 -0.04 0.05 0.18

q50 0.61 -0.07 -0.17 0.29

q60 0.70 -0.16 -0.30 0.45

q70 0.81 -0.36 -0.44 0.53

q80 0.82 -0.57 -0.41 0.50

q90 0.80 -0.52 -0.23 0.45

qmax 0.53 -0.38 0.05 0.12

qmin -0.17 -0.10 -0.42 -0.32 1990

q10 -0.53 -0.22 -0.41 -0.18 2010

q20 -0.65 -0.38 -0.49 -0.20q30 -0.50 -0.44 -0.39 -0.16

q40 -0.24 -0.35 -0.33 -0.19

q50 -0.07 -0.36 -0.25 -0.20

q60 -0.01 -0.29 0.09 -0.29

q70 -0.52 -0.16 0.21 -0.17

q80 -0.39 -0.03 0.22 0.02

q90 -0.35 0.01 0.23 0.20

qmax 0.55 -0.33 -0.04 0.24


45/56


qmin -0.20 0.26 -0.33 -0.23 1990

q10 -0.22 -0.15 -0.35 -0.21 2010

q20 -0.35 -0.60 -0.37 -0.17

q30 -0.36 -0.66 -0.25 -0.13

q40 -0.28 -0.66 -0.28 -0.13

q50 -0.35 -0.56 -0.42 -0.18

q60 -0.22 -0.45 -0.25 -0.18

q70 -0.22 -0.37 -0.16 -0.10

q80 -0.02 -0.28 -0.09 0.09

q90 -0.21 -0.29 0.16 0.20

qmax 0.15 -0.28 0.01 0.24

qmin -0.35 -0.05 -0.36 -0.29 1990

q10-0.44 -0.36 -0.39 -0.29

2010q20 -0.48 -0.57 -0.47 -0.26

q30 -0.51 -0.63 -0.31 -0.23

q40 -0.40 -0.59 -0.25 -0.25

q50 -0.34 -0.48 -0.34 -0.33

q60 -0.15 -0.39 -0.09 -0.46

q70 -0.33 -0.23 0.02 -0.40

q80 -0.13 -0.16 0.08 -0.33

q90 -0.29 -0.17 0.23 -0.13

qmax 0.41 -0.30 0.12 -0.21

correlationslope-glaciercover

correlationZ-glaciercover


46/56


A.3. Additional Figures

Figure 9: Representative Discharge [mm/season] for all season of q90 streamflow averagedover all stations.



47/56


Figure 10: Representative discharge [mm/year] for all season of q90 streamflow averagedover all stations and grouped by station altitude.



48/56


Figure 11: Estimated slopes [mm/season] and standard deviation for 50- and 90-percentquantiles grouped according to glacier cover for the period 1990-2010.



49/56


(a)

(b)

Figure 12: Spearman rank correlation coefficients of relative glacier cover and estimated

slope (a) and MK Z statistic (b)



50/56


B. Appendix B

B.1. Main Matlab Program for Mann-Kendall Theil-Sen



51/56

1

%

main

file

%select

range

of

records

by

setting

star

t_year

and

end_year

%selct

input

files

by

editing

file_paths

.m

(enter

paths

to

files

&

file

%names)

%%

path

name

vectors

%run

file_paths.m

to

get

file

names

&

pa

ths

file_paths_all

%%

read

data

display('start

read

data');

start_year

=

1990;

end_year

=

2010;

%group

stations

according

to

either

alti

tude

or

slope

or

glacier

cover:

1

=

yes,

0=no

altitude

=

[0;

1000;

2000];

%get

calc

ulations

depending

on

altitude

of

stations

slope

=

[0;

16;

28];

%get

calc

ulations

depending

on

slope

of

stations

glacier

=

[1;

0.1];

%get

calcu

lations

depending

on

slope

of

stations

skipped

=

[1

2

3];

%

stations

where

data

range

is

not

available

for

given

start

&

end

year

station_

list

=

[];

%

stations

with

avail

able

data

%read

data

from

all

stations

with

record

ed

data

for

selected

period

k=1;

for

i=1:length(file_paths)

%read

data

from

file

[runoff_

daily_

date

st_range

st_numbe

r

st_name]

=

read_

data(file_paths{i});

%check

if

data

available

before

sele

ction

if

(start_year

st_range(2))

skipped

=

[skipped

;

st_number

s

t_range];

continue

else

runoff_

daily(:,k)

=

select_

data(runo

ff_

daily_

date,

start_year,

end_year);

station_

list

=

[station_

list;

st_num

ber];

k=k+1;

end

end

%read

basin

attributes

of

stations

[num,txt,raw]

=

xlsread('BasinAttributes

.xls','BasinAttributes','B2:C50');

basin_attr

=

[num(:,2:3)

num(:,5:6)

num(

:,11)];%

get

station

number,

area(km^2),

altitude(m),

slope(%)

%find

basin

area

for

every

station

and

i

nsert

in

station_

list

for

i=1:length(station_

list)

for

j=1:length(basin_attr)

if

(station_

list(i)

==

basin_att

r(j,1))

station_

list(i,2:5)

=

basin_

attr(j,2:5);

end

end

%add

missing

basin

area

stations

to

skipped

stations

list

if

(station_

list(i,2)

==

0)

skipped

=

[skipped

;

station_

lis

t(i,1)

station_

list(i,2)

1];

end

end

display('end

read

data');

%%

process

data

mann

kendall

(Z-value)

a

nd

slope

display('START

process

data');

%Division

into

seasons

2

[lengtth

wi

dtth]

=

size(runoff_

daily);

for

i=1:wid

tth

%for

every

station

%select

one

station

add

date

for

season

division

station

(1:lengtth,1)

=

runoff_

daily(1:lengtth,i);

station

=

add_

date(station,

start_year,

end_year);

%divide

runoff

according

to

season

[spring

,

summer,

autumn,

winter]

=

season_

div(station);

%calcul

ate

quantiles

q_sprin

g

=

quant_calc(spring(2:93,:));

q_summe

r

=

quant_calc(summer(2:93,:));

q_autum

n

=

quant_calc(autumn(2:92,:));

q_winte

r

=

quant_calc(winter(2:92,:));

for

j=1

:1:11

%Ma

nn-Kendall

test

spr

ing_mk_test(j,i)

=

mann_

kendall_test(q_spring(j,:

));

sum

mer_mk_test(j,i)

=

mann_

kendall_test(q_summer(j,:

));

aut

umn_mk_test(j,i)

=

mann_

kendall_test(q_autumn(j,:

));

win

ter_mk_test(j,i)

=

mann_

kendall_test(q_winter(j,:

));

%Th

eil-Sen

slope

spr

ing_ts_slope(j,i)

=

theil_sen_slope(q_spring(j,:)

);

sum

mer_ts_slope(j,i)

=

theil_sen_slope(q_summer(j,:)

);

aut

umn_ts_slope(j,i)

=

theil_sen_slope(q_autumn(j,:)

);

win

ter_ts_slope(j,i)

=

theil_sen_slope(q_winter(j,:)

);

end

end

clear

sprin

g

summer

autumn

winter

clear

q_spr

ing

q_summer

q_autumn

q_winter

clear

stati

on

runoff_

daily_

date

runoff_

daily

%%

calculat

e

frequencies

of

stat.

significant

values

[spring_rel

Freq(:,1),

spring_relFreq(:,2)]

=

freq_Z(spring_m

k_test,0.1);

[summer_rel

Freq(:,1),

summer_relFreq(:,2)]

=

freq_Z(summer_m

k_test,0.1);

[autumn_rel

Freq(:,1),

autumn_relFreq(:,2)]

=

freq_Z(autumn_m

k_test,0.1);

[winter_rel

Freq(:,1),

winter_relFreq(:,2)]

=

freq_Z(winter_m

k_test,0.1);

display('EN

D

process

data');

%%

convert

slopes

to

mm/season

and

calculate

b_mean

display('ST

ART

slope

data');

%

convertf

orm

m3/s

to

mm/season

with

bason

attributes

for

i=1:11

spring_

ts_slope(i,:)

=

spring_ts_slope(i,:)./

transpose(

station_

list(:,2))*3.6*24*92;

summer_

ts_slope(i,:)

=

summer_ts_slope(i,:)./

transpose(

station_

list(:,2))*3.6*24*92;

autumn_

ts_slope(i,:)

=

autumn_ts_slope(i,:)./

transpose(

station_

list(:,2))*3.6*24*91;

winter_

ts_slope(i,:)

=

winter_ts_slope(i,:)./

transpose(

station_

list(:,2))*3.6*24*90;

end

%

remove

in

f

values

skipped_

bas

inatt_missing

=

[];

[le

wi]

=s

ize(spring_ts_slope);

for

i=1:wi

if

(

ab

s(spring_ts_slope(1,i))

==

inf)

spr

ing_ts_slope(:,i)

=

NaN;

sum

mer_ts_slope(:,i)

=

NaN;

aut

umn_ts_slope(:,i)

=

NaN;

win

ter_ts_slope(:,i)

=

NaN;


52/56

3

%make

list

of

missing

basin

attr

ibutes

skipped_

basinatt_missing

=

[skip

ped_

basinatt_missing

;

station_

list(i,1:2)];

end

end

display('END

slope

data');

%%

group

according

to

stations

group_station_

list

=

ones(length(station

_list),1);

%if

no

groups

if

(altitude(1)

==

1)

%if

grouped

by

ele

vation

group_station_

list

=

group_stations(

station_

list,

altitude);

elseif

(slope(1)

==

1)

%if

grouped

by

sl

ope

group_station_

list

=

group_stations(

station_

list,

slope);

elseif

(glacier(1)

==

1)

group_station_

list

=

group_stations(

station_

list,

glacier);

end

[m

n]

=

size(group_station_

list);

for

g=0:4:4*n-1

%for

different

groups

(start

with

0

so

g/4+1==1)

%mean

and

std

of

slope

over

all

stat

ions

%

g+1,+2,+3,+4

g=[1

2

3

4][5

6

7

8][

9

10

11

12]

%

g/4+1

g=[1][2][3][4]

%

2*g/4+1,+2

g=[1

2][3

4][5

6]

for

i=1:11

%b

slope_mean(i,g+1)

=

nanmean(

spr

ing_ts_slope(i,:).*

transpose(group_station_

list(:,g/4+1))

)

;

slope_mean(i,g+2)

=

nanmean(

sum

mer_ts_slope(i,:).*


list(:,g/4+1))

)

;

slope_mean(i,g+3)

=

nanmean(

aut

umn_ts_slope(i,:).*


list(:,g/4+1))

)

;

slope_mean(i,g+4)

=

nanmean(

win

ter_ts_slope(i,:).*


list(:,g/4+1))

)

;

slope_stdev(i,g+1)

=

nanstd(

spr

ing_ts_slope(i,:).*


list(:,g/4+1))

)

;

slope_stdev(i,g+2)

=

nanstd(

sum

mer_ts_slope(i,:).*


list(:,g/4+1))

)

;

slope_stdev(i,g+3)

=

nanstd(

aut

umn_ts_slope(i,:).*


list(:,g/4+1))

)

;

slope_stdev(i,g+4)

=

nanstd(

win

ter_ts_slope(i,:).*


list(:,g/4+1))

)

;

%Z

[spring_relFreq(i,2*g/4+1),

spri

ng_relFreq(i,2*g/4+2)]

=

freq_Z(

spring_mk_test(i,:).*

transpose(

group_station_

list(:,g/4+1)),0.1

);

[summer_relFreq(i,2*g/4+1),

summ

er_relFreq(i,2*g/4+2)]

=

freq_Z(

summer_mk_test(i,:).*

transpose(

group_station_

list(:,g/4+1)),0.1

);

[autumn_relFreq(i,2*g/4+1),

autu

mn_relFreq(i,2*g/4+2)]

=

freq_Z(

autumn_mk_test(i,:).*

transpose(

group_station_

list(:,g/4+1)),0.1

);

[winter_relFreq(i,2*g/4+1),

wint

er_relFreq(i,2*g/4+2)]

=

freq_Z(

winter_mk_test(i,:).*

transpose(

group_station_

list(:,g/4+1)),0.1

);

end

end

display('END

grouping');

%%

spearman

rank

coefficient

%altitude

correlation

spearman_

b_altitude(:,1)

=

spearman_rho(

spring_ts_slope,

station_

list(:,3));

spearman_

b_altitude(:,2)

=

spearman_rho(

summer_ts_slope,

station_

list(:,3));

spearman_

b_altitude(:,3)

=

spearman_rho(

autumn_ts_slope,

station_

list(:,3));

spearman_

b_altitude(:,4)

=

spearman_rho(

winter_ts_slope,

station_

list(:,3));

4

%altitudec

orrelation

spearman_Z_

altitude(:,1)

=

spearman_rho(spring_mk_test,

stat

ion_

list(:,3));

spearman_Z_

altitude(:,2)

=

spearman_rho(summer_mk_test,

stat

ion_

list(:,3));

spearman_Z_

altitude(:,3)

=

spearman_rho(autumn_mk_test,

stat

ion_

list(:,3));

spearman_Z_

altitude(:,4)

=

spearman_rho(winter_mk_test,

stat

ion_

list(:,3));

%glacier

co

verage

correlation

spearman_

b_

glacier(:,1)

=

spearman_rho(spring_ts_slope,

stat

ion_

list(:,5));

spearman_

b_

glacier(:,2)

=

spearman_rho(summer_ts_slope,

stat

ion_

list(:,5));

spearman_

b_

glacier(:,3)

=

spearman_rho(autumn_ts_slope,

stat

ion_

list(:,5));

spearman_

b_

glacier(:,4)

=

spearman_rho(winter_ts_slope,

stat

ion_

list(:,5));

%glacier

co

verage

correlation

spearman_Z_

glacier(:,1)

=

spearman_rho(spring_mk_test,

stati

on_

list(:,5));

spearman_Z_

glacier(:,2)

=

spearman_rho(summer_mk_test,

stati

on_

list(:,5));

spearman_Z_

glacier(:,3)

=

spearman_rho(autumn_mk_test,

stati

on_

list(:,5));

spearman_Z_

glacier(:,4)

=

spearman_rho(winter_mk_test,

stati

on_

list(:,5));

display('EN

D

spearman');

%%

plotting

frequencies

%

%

figure;

%

%

subplot(2

,2,1);

%spring

%

spring_

fr

equencies

=

[frequencies_rel_max(:,1)

frequencie

Project Work Kevin Mersch Report

Documents

Transcript of Project Work Kevin Mersch Report