Abstract
The scope of this research effort was to examine the effect of water management practices and land use changes on river flow over the last 3 decades, to identify the dominant trends in the discharge and precipitation time series and to examine the interrelationship between these two parameters. In order to accomplish these aims, the annual discharge time series of seven (7) major rivers in Greece were compared to the annual precipitation of the corresponding watersheds. This comparison was achieved through trend analysis of each time series, which involves the determination of basic statistical characteristics (normality, homogeneity, stationarity). Due to lack of satisfactory discharge time series at the downstream parts of each catchment examined, the results from E-HYPE pan-European hydrological model was used (European – HYdrological Predictions for the Environment). The main outcome of this work concludes that there is no consistent, single trend for the entire study period for any of the investigated rivers, while there are some wet and dry periods in the data which are very clear in all catchments and coincide at a temporal level. The main dry periods were at the end of the 1980s and the beginning of the 2000s. There is also a prolonged wet period during the last decade for all study catchments.
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References
Iglesias A, Garrote L, Flores F, Moneo M (2007) Challenges to manage the risk of water scarcity and climate change in the Mediterranean. Water Resour Manag 21:775–788
Zacharias I, Dimitriou E, Koussouris T (2005) Integrated water management scenarios for wetland protection: application in Trichonis Lake. Environ Model Softw 20:177–185
Sofios S, Arabatzis G, Baltas E (2008) Policy for management of water resources in Greece. Environmentalist 28:185–194
Moschou EC, Batelis SC, Dimakos Y, et al (2013) Spatial and temporal rainfall variability over Greece. In: 5th EGU Leonardo conference – Hydrofractals 2013 – STAHY’13, Kos Island, Greece, European Geosciences Union, International Association of Hydrological Sciences, International Union of Geodesy and Geophysics
Hellenic Ministry for the Environment Physical Planning and Public Works (2008) National reporting to the fourteenth & fifteenth sessions of the Commission for Sustainable Development of the United Nations (UNCSD 14-UNCSD 15), Athens
Mimikou M, Baltas E (2013) Assessment of climate change impacts in Greece: a general overview. Am J Clim Chang 2:46–56
Atay I (2012) Water resources management in Greece: perceptions about water problems in the Nafplion area. Independent thesis Advanced level, Stockholm University
Jarboe JE, Haan CT (1974) Calibrating a water yield model for small ungaged watersheds. Water Resour Res 10:256–262
Machiwal D, Jha MK (2006) Time series analysis of hydrologic data for water resources planning and management: a review. J Hydrol Hydromech 54:237–257
Burn DH, Hag Elnur MA (2002) Detection of hydrologic trends and variability. J Hydrol 255:107–122
Liarikos K, Maragou P, Papagiannis TH (2012) Nationwide land cover mapping and land cover changes in Greece during 1987–2007. WWF, Athens
European Environmental Agency (EEA) (2014) Corine Land Cover 2006. http://www.eea.europa.eu. Accessed 10 Apr 2014
Skoulikidis N, Economou A, Gritzalis K, Zogaris S (2009) Rivers of the Balkans. In: Tockner K, Uehlinger U, Robinson CT (eds) Rivers of Europe, 1st edn. Elsevier, London
Donevska K (2006) Report on second communication on climate and climate changes and adaptation in the Republic of Macedonia-Section: vulnerability assessment and adaptation for water resources sector. Ministry of Environment and Physical Planning, Skopje
Koutsoyiannis D, Andreadakis A, Mavrodimou R et al (2008) Support on the compilation of the national programme for water resources management and preservation. National Technical University of Athens-Department of Water Resources and Environmental Engineering, Athens
National Statistical Institute of the Republic of Bulgaria (NSI) (2011) Environment 2009. National Statistical Institute of the Republic of Bulgaria, Sofia. http://www.nsi.bg/sites/default/files/files/publications/Environment2009.pdf. Accessed 3 May 2014
Yildiz D (2008) Water report- our need for a national water policy. National Association of Industrialists and Businessmen-USİAD, Ertem Matbaa, Ankara
Climate Prediction Center/National Centers for Environmental Prediction/National Weather Service/NOAA/U.S. Department of Commerce (2014) CPC global summary of day/month observations, 1979-continuing. Research Data Archive at the National Center for Atmospheric Research, Computational and Information Systems Laboratory. http://rda.ucar.edu/datasets/ds512.0/. Accessed 16 Apr 2014
Arheimer B, Dahné J, Donnelly C et al (2012) Water and nutrient simulations using the HYPE model for Sweden vs. the Baltic Sea basin – influence of input-data quality and scale. Hydrol Res 43:315–329
Strömqvist J, Arheimer B, Dahné J et al (2012) Water and nutrient predictions in ungauged basins: set-up and evaluation of a model at the national scale. Hydrol Sci J 57:229–247
Beven K (2012) Rainfall-runoff modelling: the primer. Wiley, Chichester
Krause P, Boyle DP, Bäse F (2005) Comparison of different efficiency criteria for hydrological model assessment. Adv Geosci 5:89–97
Singh J, Knapp HV, Demissie M (2004) Hydrologic modeling of the Iroquois River watershed using HSPF and SWAT. Illinois State Water Survey, Champaign
Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models. Part I – a discussion of principles. J Hydrol 10:282–290
Legates DR, McCabe GJ Jr (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35:233–241
Kolmogorov AN (1933) Sulla determinazione empirica di una legge di distribuzione. G dell’Istituto Ital degli Attuari 4:83–91
Lilliefors HW (1967) On the Kolmogorov–Smirnov test for normality with mean and variance unknown. J Am Stat Assoc 62:399–402
Shapiro ASS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika 52:591–611
Machiwal D, Jha M (2012) Hydrologic time series analysis: theory and practice. Springer, The Netherlands
Massey FJ Jr (1951) The Kolmogorov–Smirnov test for goodness of fit. J Am Stat Assoc 46:68–78
Fernando DAK, Jayawardena AW (1994) Generation and forecasting of monsoon rainfall data. In: 20th WEDC conference on affordable water supply and sanitation, Colombo
Von Neumann J (1941) Distribution of the ratio of the mean square successive difference to the variance. Ann Math Stat 12:367–395
Buishand TA (1982) Some methods for testing the homogeneity of rainfall records. J Hydrol 58:11–27
Chernoff H, Zacks S (1964) Estimating the current means of a normal distribution which is subjected to change in time. Ann Math Stat 35:999–1018
Gardner LA Jr (1969) On detecting changes in the mean of normal variates. Ann Math Stat 40:116–126
Dahmen ER, Hall MJ (1990) Screening of hydrological data: tests for stationarity and relative consistency. ILRI publication no. 49. ILRI, Wageningen
Snedecor GW, Cochran WG (1989) Statistical methods. Wiley-Blackwell, New Jersey
Haan CT (2002) Statistical methods in hydrology. Iowa State University Press, Ames
Shahin M, Van Oorschot HJL, De Lange SJ (1993) Statistical analysis in water resources engineering. A.A. Balkema, Rotterdam
Kendall MG (1975) Rank correlation methods. Charles Griffin and Company, London
Mann HB (1945) Nonparametric tests against trend. Econometrica 13:245–259
Lehmann EL (1975) Nonparametrics: statistical methods based on ranks. Holden-Day, San Francisco
Sneyers R (1990) On the statistical analysis of series of observations, Technical note no. 143. World Meteorological Organization, Geneva
Spearman C (1904) The proof and measurement of association between two things. Am J Psychol 15:72–101
Yue S, Pilon P, Cavadias G (2002) Power of the Mann–Kendall and Spearman’s rho tests for detecting monotonic trends in hydrological series. J Hydrol 259:254–271
McGilchrist CA, Woodyer KD (1975) Note on a distribution-free CUSUM technique. Technometrics 17:321–325
Sen PK (1968) Estimates of the regression coefficient based on Kendall’s Tau. J Am Stat Assoc 63:1379–1389
Moriasi DN, Arnold JG, Van Liew MW et al (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50:885–900
Vangelis H, Spiliotis M, Tsakiris G (2010) Drought severity assessment based on bivariate probability analysis. Water Resour Manag 25:357–371
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Annexes
Annexes
1.1 Annex I
Statistical criteria of E-HYPE model performance by comparing the observed (o) and predicted (p) data of a sample size (n)
Mean error ME: \( \mathrm{ME}=\frac{\Sigma_{i=1}^n\left({o}_i-{p}_i\right)}{n} \)
Mean absolute error MAE: \( \mathrm{ME}=\frac{\Sigma_{i=1}^n\left|{o}_i-{p}_i\right|}{n} \)
Mean absolute percentage error MAPE: \( \mathrm{ME}=\frac{\Sigma_{i=1}^n\left|\frac{o_i-{p}_i}{o_i}\right|}{n}\times 100 \)
Root mean squared error RMSE: \( \mathrm{ME}=\sqrt{\frac{\Sigma_{i=1}^n{\left({p}_i-{o}_i\right)}^2}{n}} \)
Pearson’s correlation coefficient R: \( R=\frac{\Sigma_{i=1}^n\left({p}_i-\overline{p}\right)\left({o}_i-\overline{o}\right)}{\sqrt{\Sigma_{i=1}^n{\left({p}_i-\overline{p}\right)}^2\ }\sqrt{\Sigma_{i=1}^n{\left({o}_i-\overline{o}\right)}^2}} \)
Squared correlation coefficient R 2: R 2 = R 2
Nash–Sutcliffe coefficient of efficiency Nr: \( \mathrm{Nr}=1-\frac{\Sigma_{i=1}^n{\left({o}_i-{p}_i\right)}^2}{\Sigma_{i=1}^n{\left({o}_i-\overline{o}\right)}^2} \)
1.2 Annex II
1.2.1 Normality Tests
Kolmogorov–Smirnov (KS) test: KS = sup x |F*(x) − Fn(x)|, where sup stands for supremum, Fn(x) is theoretical cumulative distribution function of the normal distribution function and F*(x) is the normal empirical distribution function of the data, with known mean μ and standard deviation σ.
Lilliefors (LF) test: LF = max x |F*(x) − Sn(x)|, where Sn(x) is the sample cumulative distribution function of the normal distribution function and F*(x) is the empirical distribution function, with the sample mean \( \mu =\overline{x} \) and the sample variance s 2 defined with denominator n − 1.
Shapiro–Wilk (SW) test: \( \mathrm{SW}=\frac{{\left({\Sigma}_{i=1}^n{a}_i{x}_i\right)}^2}{\Sigma_{i=1}^n{\left({x}_i-\overline{x}\right)}^2} \), where x i stands for ordered (increasing ordered) sample values and a i stands for constants generated from the means, variances and covariances of the order statistics of a sample of size n from a normal distribution.
1.2.2 Homogeneity Tests
von Neumann test: \( N=\frac{\Sigma_{i=1}^{n-1}{\left({x}_i-{x}_{i+1}\right)}^2}{\Sigma_{i=1}^n{\left({x}_i-\overline{x}\right)}^2} \), where x i is the hydrologic variable constituting the sequence in time, n is the total number of hydrologic records and \( \overline{x} \) is the average of x i .
Cumulative deviations test: Sensitivity to the departures from homogeneity is defined by the following statistic:
\( Q={\mathrm{max}}_{0\le k\le n}\left|{S}_k^{\ast \ast}\right| \), where S * * k is the rescaled adjusted partial sums.
\( {S}_k^{\ast \ast }={S}_k^{\ast }/{D}_x \), k = 1, 2, …, n, where \( {S}_k^{\ast }={\Sigma}_{i=1}^k\left({x}_i-\overline{x}\right) \), k = 1, 2, …, n, and D x the sample standard deviation.
High values of Q are an indication for non-homogeneity.
The homogeneity can also be tested with the following statistic:
Bayesian Test: \( U=\frac{1}{n\left(n+1\right)}{\Sigma}_{k=1}^{n-1}{\left({S}_k^{\ast \ast}\right)}^2 \), for p k independent of k.
\( A={\Sigma}_{i=1}^{n-1}{\left({Z}_k^{\ast \ast}\right)}^2 \), k = 1, 2, …, n, for p k proportional to [k(n − k)]−1. Z ** k is the weighted rescaled partial sums, \( {Z}_k^{\ast \ast }=\left[{\left\{k\left(n-k\right)\right\}}^{-1/2}{S}_k^{\ast}\right]/{D}_x \).
1.2.3 Stationarity Tests
t-test: To apply this test, the annual time series is divided into two (or more) subseries of size n 1 and n 2 (n 1+n 2 = n):
\( {t}_s=\frac{\left|{\overline{x}}_2-{\overline{x}}_1\right|}{S\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \), \( S=\sqrt{\frac{\left({n}_1-1\right){s}_1^2+\left({n}_2-1\right){s}_2^2}{n-2}} \), where \( {\overline{x}}_1 \), \( {\overline{x}}_2 \), s 21 and s 22 are the estimated means and variances of the first and the second subseries, respectively.
Mann–Whitney test: To apply this test, the annual time series n t is divided into two (or more) subseries of size n 1 and n 2 (n 1+n 2 = n), and a new series z t (t = 1, 2, …, n) is defined by arranging the original data (n t ) in increasing order of magnitude:
\( u=\frac{\Sigma_{t=1}^{n_1}R\left({n}_t\right)-{n}_1\left({n}_1+{n}_2+1\right)/2}{{\left[{n}_1{n}_2\left({n}_1+{n}_2+1\right)/12\right]}^{1/2}} \), where R(n t ) is the rank of the observation n t in ordered series z t .
1.2.4 Trend
Mann–Kendall test: The Mann–Kendall statistic S compares each value of the series (x t ) with all subsequent values (x t+1) and is defined as
\( S={\Sigma}_{t^{\prime }=1}^{n-1}{\Sigma}_{t={t}^{\prime }+1}^n\operatorname{sgn}\left( xt-{x}_{t^{\prime }}\right) \), where sgn is the signum function, \( \operatorname{sgn}\left( xt-{x}_{t^{\prime }}\right)=\left\{\begin{array}{c}\hfill 1,\mathrm{if}\ {x}_t>{x}_{t\hbox{'}}\hfill \\ {}\hfill 0,\mathrm{if}\ {x}_t={x}_{t\hbox{'}}\hfill \\ {}\hfill -1,\mathrm{if}\ {x}_t<{x}_{t\hbox{'}}\hfill \end{array}\right. \)
Based on Mann [41] and Kendall [40], when n ≥ 8, the statistic S is approximately normally distributed with the mean m and the variance V as follows: E(S) = 0, \( V(S)=\frac{1}{18}\left[n\left(n-1\right)\left(2n+5\right)-{\Sigma}_{i=1}^g{e}_i\left({e}_i-1\right)\left(2{e}_i+5\right)\right] \), g is the number of tied groups, and e i is the number of data in the ith tied group.
The standardised test statistic Z is defined as \( Z=\frac{S+m}{\sqrt{V(S)}}. \)
Spearman’s Rho: The Spearman’s Rho D statistic is defined as
\( D=1-\frac{6{\Sigma}_{1=1}^n{\left[R\left({X}_i\right)-i\right]}^2}{n\left({n}^2-1\right)} \), where R(X i ) is the rank of ith observation X i in the sample size n.
Under the null hypothesis that the time series has no trend, it can be shown that the statistic t s has a Student’s t-distribution with n–2 degrees of freedom. Here, t s is defined as \( {t}_{\mathrm{s}}=D\sqrt{\frac{n-2}{1-{D}^2}}. \)
Sequential Version of the Mann–Kendall Test (Mann–Kendall Rank Correlation Test): The sequential version of the Mann–Kendall test is calculated so that rank (x i ) > rank (x j ) (i > j). The t statistic is calculated as \( t={\Sigma}_{i=1}^n{n}_i \). The distribution of t is assumed to be asymptotically normal with the following expectation: \( E(t)=\mu =\frac{n\left(n-1\right)}{4} \) and \( \mathrm{Var}(t)={\sigma}^2=\frac{n\left(n-1\right)\left(2n+5\right)}{72}. \)
The null hypothesis that there is no trend is rejected for high values of the reduced variable |u(t)|, which is calculated as \( u(t)=\frac{t-E(t)}{\sqrt{\mathrm{Var}(t)}} \). The statistic u′(t) is computed backwards starting from the end of the time series.
CUSUM Test: The test statistic Vk is defined as \( {V}_k={\Sigma}_{i=1}^k\operatorname{sgn}\left({x}_i-{x}_{\mathrm{median}}\right) \), k = 1,2, …, n, where x median is the median value of the x i data set and sgn(x).
Sen’s Slope Estimator: The Sen’s slope estimation test is defined for a season g as \( \beta =\mathrm{Median}\left(\frac{x_i-{x}_j}{i-j}\right) \), i < j, where Q is the slope between points x i and x j , x i is data measurement at time i and x j is data measurement at time j.
It is defined as the estimator β which is the median overall combination of record pairs for the whole data set and is resistant/robust to the extreme observations or outliers. The positive value of the β connotes the slope of the upward trend and negative value for the downward trend [29].
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Mentzafou, A., Dimitriou, E., Papadopoulos, A. (2015). Long-Term Hydrologic Trends in the Main Greek Rivers: A Statistical Approach. In: Skoulikidis, N., Dimitriou, E., Karaouzas, I. (eds) The Rivers of Greece. The Handbook of Environmental Chemistry, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/698_2015_446
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