Abstract
Hydrological discharge time series are known to depict low-frequency oscillations, long-range statistical dependencies, and pronounced nonlinearities. A better understanding of this runoff behaviour on regional scales is crucial for a variety of water management purposes and flood risk assessments. We aimed at extracting long-term components which influence simultaneously a set of southern German runoff records.
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References
M.R. Allen, L.A. Smith, Monte Carlo SSA: Detecting irregular oscillations in the presence of colored noise J. Clim. 9, 3373–3404 (1996)
M. Bernstein, V. de Silva, J.C. Langford, Y.B. Tenenbaum, Graph Approximations to Geodesics on Embedded Manifolds, Technical report, Stanford University, Stanford (2000); [available from http://Isomap.stanford.edu/BdSLT.pdf] (Accessed Jan. 2006)
I. Borg, P. Groenen, Modern Multidimensional Scaling (Springer, New York, NY, 1997), p. 471
D.S. Broomhead, G.P. King, Extracting qualitative dynamics from experimental data. Physica D, 20, 217–236 (1986)
F. Camastra, Data dimensionality estimation methods: A survey. Pattern Recognit., 36, 2945–2954, (2002)
T.F. Cox, M.A.A. Cox, Multidimensional Scaling, (Chapman & Hall/CRC, Boca Raton, FL, 2001), p. 308
V. de Silva, Y.B. Tenenbaum, Global versus local methods in nonlinear dimensionality reduction, in S. Becker, S. Thrun, K. Obermayer ed. by Advances in Neural Information Processing Systems 15, (MIT Press, Cambridge, 2002), pp. 705–712
B. Diekrüger, M.J. Kirkby, U. Schröder (eds.), Regionalization in Hydrology vol 254 (IAHS Publications, Wallingford CT, (1999)
E.W. Dijkstra, A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269–271 (1959)
J.B.Elsner, A.A. Tsonis, Singular Spectrum Analysis. A New Tool in Time Series Analysis, (Plenum Press, New York, NY, 1996) p. 164
A.J. Gámez, C.S. Thou, A. Timmermann, J.Kurths, Nonlinear dimensionality reduction in climate data. Nonlinear Processes Geophys., 11, 393–398 (2004)
M. Ghil, M.R. Allen, M.D. Dettinger, K. Ide, D. Kondrashov, M.E. Mann, A.W. Robertson, A. Saunders, Y. Tian, F. Varadi, P. Yiou, Advanced spectral methods for climatic time series, Rev. Geophys. 40, 1–25 (2002)
N. Golyandina, V. Nekrutkin, A. Zhigljavsky, Analysis of Time Series Structure: \(\textsc{Ssa}\) and related techniques, Monographs on Statistics and Applied Probability, 90, (Chapman & Hall/CRC, Boca Raton, FL, 2001), p. 305
W.W. Hsieh, Nonlinear principal component analysis by neural networks. Tellus, 53(A), 599–615 (2001)
W. Hsieh, K. Hamilton, Nonlinear singular spectrum analysis of the tropical stratospheric wind, Q J R Meteorol. Soc. 129, 2367–2382 (2003)
H.E. Hurst, Long-term storage capacity of reservoirs, Trans. Am. Soc. Civil Eng., 116, 770–808 (1951)
M. Kirby, Geometric Data Analysis. An Empirical Approach to Dimensionality Reduction and the Study of Patterns (Wiley, New York, NY, 2001), p. 363
E. Koscielny-Bunde, J.W. Kantelhardt, P. Braun, A. Bunde, S. Havlin, Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies. J. Hydrol. 332, 120–137 (2006)
M.A. Kramer, Nonlinear Principal Component Analysis Using Autoassociative Neural Networks. J. Am. Inst. Chem. Eng. (AIChE), 37, 233–243 (1991)
H. Lange, K. Bernhardt, Long-term components and regional synchronization of river runoffs, in Hydrology: Science and Practice for the 21st Century ed. by B. Webb et al. (British Hydrological Society, 2004), pp. 165–170. ISBN 1-903741-10-6 (Accessed Jan. 2006)
M. Mahecha, Linear and Nonlinear Dimensionality Reduction in Spatial and Temporal Ecological Data Sets, Diploma Thesis, University of Bayreuth, (2006)
B.B. Mandelbrot, Multifractals and 1/f noise, (Springer, New York, NY, 1999), p. 442
B.B. Mandelbrot, J.R. Wallis, Robustness of the rescaled range R/S in the measurement of noncyclic long-run statistical dependence, Water Resourc. Res., 5, 967–988 (1969)
D. Markovic, M. Koch, Wavelet and scaling analysis of monthly precipitation extremes in Germany in the 20th century: Interannual to interdecadal oscillations and the North Atlantic Oscillation influence, Water Resourc. Res. 41, W09240, (2005)
A. Montanari, R. Rosso, M.S. Taqqu, A seasonal fractional ARIMA model applied to the Nile River monthly flows at Aswan, Water Resourc. Res. 36, 1249–1259 (2000)
P. Pekárova, P. Miklánek, J. Pekár, Spatial and temporal runoff oscillation analysis of the main rivers of the world during the 19th–20th centuries. J. Hydrol. 274, 62–79 (2003)
S.T. Roweis, L.K. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science, 290, 2323–2326 (2000)
O. Samko, P. Rosin, D. Marshall, Selection of the optimal parameter value for the Isomap algorithm, Pattern Recognit. Lett. (2006)
A. Saxena, A. Gupta, A. Mukerjee, Non-linear Dimensionality Reduction by Locally Linear Isomaps, L N C S, 3316, 1038–1043 (2004)
T. Shun, C. Duffy, Low-frequency oscillations in precipitation, temperature, and runoff on a west facing mountain front: A hydrogeologic interpretation, Water Resourc. Res. 35, 191–201 (1999)
J.B. Tenenbaum, Mapping a manifold of perceptual observations, in Advances in Neural Information Processing Systems, Vol. 10, ed. by M. Jordan, M. Kearns, S. Solla (MIT Press, Cambridge, 1998), pp. 682–687
J.B. Tenenbaum, V. de Silva, J.C. Langford, A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290, 2319–2323 (2000)
Acknowledgments
The authors are grateful to the Bavarian Environment Agency and the Global Runoff Data Centre for providing the runoff data investigated. This work has been supported by the German Federal Ministry of Education and Research (BMBF) within the research project “Scaling Analysis of Hydrometeorological Time Series” (grant no. 03330271).
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Mahecha, M.D., Lange, H., Lischeid, G. (2011). Long-Term Structures in Southern German Runoff Data. In: Kropp, J., Schellnhuber, HJ. (eds) In Extremis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14863-7_12
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DOI: https://doi.org/10.1007/978-3-642-14863-7_12
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