Abstract
Horton's hierarchical and fractal analysis of channel circumference reveals that tidal-channel systems in the Dutch Wadden Sea have similar branching patterns. Channel systems have the same characteristics as three- to four-times branching networks. The branch lengths of these channels decrease logarithmically. The channel systems can be regarded as ‘statistical self-similar fractal’ networks, considering the natural variability in branch lengths and channel positions. Branching of channels does not continue below the 500 m scale. The channel-system circumference length is logarithmically related to the tidal prism and drainage area. The similarity of the channel systems, regardless of their size, relative amount of intertidal flats, and tidal amplitude, points to a self-organising nature. All processes depend on the feedback between morphology and hydrodynamics. At first sight, the channel systems can be regarded as an ebb-driven drainage network, governed by erosion. However, flood-dominated net sedimentation occurs in large parts of the drainage basins and modifies the ebb-driven network. The complex interaction of hydrodynamic and morphodynamic processes in tidal basins limits the applicability of process-based models. Behaviour-oriented modelling has a wide applicability and can be improved using the fractal geometry as the dynamical equilibrium morphology. The fractal-network geometry can also be used for stochastic reconstructions of fossil tidal-channel systems, when only limited observations are available.
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References
Archer, A.W. & S.F. Greb 1995 An amazone-scale drainage system in the early Pennsylvanian of central North America-J. Geology 103: 611-628.
Van Bendegom, L. 1949 Beschouwingen over de grondslagen van kustverdediging. Internal report Rijkswaterstaat, Hoorn
Buijsman, M.C. 1997 The impact of gas extraction and sea level rise on the morphology of the Wadden Sea. WL Delft Hydraulics report no. H 3099.30, Delft
Cowell, P.J. & B.G. Thom 1994 Morphodynamics of coastal evolution. In: Carter, R.W.G. & C.D. Woodroffe (eds) Coastal Evolution, Late Quaternary Shoreline Morphodynamics. University Press, Cambridge: 33-86
Dalrymple, R.W. 1992 Tidal depositional systems. In: Walker, R.G. & N.P. James (eds) Facies Models, Response to Sea Level Change. Geol. Assoc. Canada: 195-218
Dean, R.G. & T.L. Walton 1975 Sediment transport processes in the vicinity of inlets, with special reference to sand trapping. In: Cronin, L.E. (ed.) Estuarine Research, Vol 2: Geology and Engineering. Academic Press, New York: 129-150
De Boer, P.L., A. van Gelder & S.D. Nio 1988 Tide-influenced sedimentary environments and facies (Sedimentology and petroleum geology). Reidel, Dordrecht, The Netherlands
Dieckmann, R., M. Osterthun & H.W. Partenscky 1988 A comparison between German and North American tidal inlets. In: Proc. 21st Coast. Engng. Conf. ASCE, 3, New York, 199: 2681-2691
Escoffier, F.F. 1940 The stability of tidal inlets-Shore and Beach 8: 114-115
Horton, R.E. 1945 Erosional development of streams and their drainage basins; Hydrophysical approach to quantative morphology-Geol. Soc. Am. Bull. 56: 275-370
Hume, T.M. & C.E. Herdendorf 1990 Morphologic and hydraulic characteristics of tidal inlets on a headland dominated low littoral drift coast, Northeastern New Zealand-J. Coast. Res., Spec. Iss.: Proc. Skagen Symp.: 527-563
Van der Kreeke, J. 1990 Can multiple inlets be stable?-Estuarine, Coastal and Shelf Science 30: 261-273
Van der Kreeke, J. 1992 Stability of tidal inlets; Escoffier's analysis-Shore and beach 50: 9-12
Leopold, L.B., M.G. Wolman & J.P. Miller 1964 Fluvial processes in Geomorphology. Freeman, San Francisco
Louters, T. & F. Gerritsen 1994 The riddle of the sands: a tidal system's answer to a rising sea level. Rapport RIKZ-94.040, Ministry of Public Works, The Hague
Mandelbrot, B.B. 1967 How long is the coast of Britain?, statistical self-similarity and fractional dimension-Science 156: 636-638
Mandelbrot, B.B. 1982 The fractal geometry of nature. Freeman, San Francisco
Maritan, A, F. Colaiori, A. Flammini, M. Cieplak & J.R. Banavar 1996 Universality Classes of Optimal Channel Networks-Science 272: 984-986
O'Brien, M.P. 1931 Estuary tidal prisms related to entrance areas-Civil Engineering 1: 738-739
Oost, A.P. 1995 Dynamics and sedimentary development of the Dutch Wadden Sea with emphasis on the Frisian Inlet: a study of the barrier islands, ebb-tidal deltas, inlets and drainage basins. Geol. Ultraiectina 126, PhD Thesis Utrecht
Oost, A.P. & P.L. de Boer 1994 Sedimentology and development of barrier islands, ebb-tidal deltas, inlets and backbarrier areas of the Dutch Wadden Sea-Senckenbergiana Marit. 24: 65-115
Postma, H. 1961 Transport and accumulation of suspended matter in the Dutch Wadden Sea-Netherlands J. Sea Res. 1: 148-190
Rankey, E. & L. Watney 1996 Of the making of earth science models there is no end..., Introduction to the NES meeting. In: Numerical Experiments in Stratigraphy, An International Workshop, University of Kansas, Kansas, Abstract Volume: 17-33
Reineck, H.E. 1995 Randpriele-Senckenbergiana Marit. 26: 37-43
Richardson, L.F. 1961 The problem of contiguity: An approach of statistics of deadly quarrels-General Systems Yearbook 6: 139
Rigon, R., A. Rinaldo & I.G. Rodriguez-Iturbe 1994 On landscape self-organization-J. Geoph. Res. 99: 11971-11993
Rijkswaterstaat 1980 Dieptelijnen kaart Waddenzee en Eems Dollard (scale 1:100 000), Meet en Adviesdienst Delfzijl, Delfzijl
Sha, L.P. 1989 Cyclic morphologic changes of the ebb-tidal delta, Texel Inlet, the Netherlands-Geol. Mijnbouw 68: 35-48
Shreve, R.L. 1969 Stream lengths and basin areas in topologically random channel networks-J. Geology 77: 397-414
Smart, J.S. 1979 Determinism and randomness in fluvial geomorpholgy-EOS 60: 651-655
Van der Spek, A.J.F. 1995 Reconstruction of tidal inlet and tidal channel dimensions in the Frisian Middelzee, a former tidal basin the Dutch Wadden Sea. In: Flemming, B.W. & A. Bartholoma (eds) Tidal Signatures in Modern and ancient sediments. Spec. Publ. Int. Ass. Sediment. 24: 101-119
Stark, C.P. 1991 An invasion percolation model of drainage network evolution-Nature 352: 423-425
Stive, M.J.F., M. Capobianco, Z.B. Wang & P. Ruol 1996 The dynamics of microtidal lagoons and adjacent coasts. In: 8th Internat. Biennial Conf. Physics Estuaries Coastal Seas, Extended Abstracts. Netherlands Centre Coastal Research, The Hague, the Netherlands: 103-105
Stølum, H.H. 1996 River-meandering as a self-organization process-Science 271: 1710-1713
Van Straaten, L.M.J.U. 1954 Composition and structure of Recent marine sediments in the Netherlands-Leidse Geol. Mededel. 19: 1-110
Van Straaten, L.M.J.U. 1964 De bodem der Waddenzee. In: Anderson, W.F., J. Abrahamse, J.D. Buwalda & L.M.J.U. Van Straaten (eds) Het Waddenboek. Thieme, Zutphen: 75-151
Van Straaten, L.M.J.U. & Ph.H. Kuenen 1958 Tidal action as a cause of clay accumulation-J. Sediment. Petrology 28: 406-413
Turcotte, D.L. 1992 Fractals and chaos in geology and geophysics. University Press, Cambridge
Van Veen, J. 1950 Eb-en vloedschaar systemen in de Nederlandse getijdewateren-Tijdschr. Kon. Ned. Aardrk. Gen. 67: 303-325
Voss, R.F. 1988 Fractals in nature: From characterization to simulation. In: Peitgen, H.O. & D. Saupe (eds) The Science of Fractal Images. Springer, New York
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Cleveringa, J., Oost, A.P. The fractal geometry of tidal-channel systems in the Dutch Wadden Sea. Geologie en Mijnbouw 78, 21–30 (1999). https://doi.org/10.1023/A:1003779015372
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DOI: https://doi.org/10.1023/A:1003779015372