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EAST COAST 3 MODEL Present Sea-Level Durham E-Theses Modelling tidal changes within the wash and Morecambe bay during the Holocene Hinton, A.C. How to cite: Hinton, A.C. (1992) Modelling tidal changes within the wash and Morecambe bay during the Holocene, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/6130/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk The copyright of this thesis rests with the author. No quotation from it should be published without his prior written consent and information derived from it should be acknowledged. Modelling Tidal Changes Within The Wash and Morecambe Bay During The Holocene Volume 1 by A.C. Hinton A Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy Geography Department The University of Durham 1992 2 7 APR 1993 Addendum to Ph.D. thesis 'Modelling tidal changes within The Wash and Morecambe Bay during the Holocene' by A.C. Hinton, 1992. Subsequent to the examination and acceptance of the thesis for the degree of Ph.D., the author discovered that the adjustment to the water depths made for the palaeogeographic simulations for the EC3, WASH, LBM and MBM models was incorrect. This affects the accuracy of the figures in chapter 4, results in chapter 6 and data in the appendices. The reader is referred to Hinton (1995) for corrected results for The Wash. Hinton, A.C. (1995) Holocene tides of The Wash, U.K.: The influence of water-depth and coastline-shape changes on the record of sea-level movements. Marine Geology, 124,87-111. A.C. Hinton, 21st April 1997 The results contained in this thesis are all my own work. Information derived from other sources is acknowledged at the appropriate point in the text. Work presented here has not been published elsewhere. Signed Anne C. Hinton Copyright © 1992 by A.C. Hinton The copyright of this thesis rests with the author. No quota­ tion from it should be published without A.C. Hinton's prior written consent and information derived from it should be acknowledged. The copyright of the bathymetric and label data for the Liverpool Bay and Morecambe Bay tidal models for present sea-level conditions, presented in Appendix 6.1, is held by the Proudman Oceanographic Laboratory, Birkenhead. ABSTRACT Palaeotidal changes are one of the least known factors of the sea-level record variation at the local scale (Shennan, 1986a; Devoy, 1987). This thesis extends knowledge of tidal alterations with sea-level change by means of an approach integrating numerical tidal models with geological stratigraphic data recording former tidal heights. The last 10,000 years. (the Holocene period) were chosen for study due to the sed­ imentary sequence available recording sea-level changes. Two macro-tidal embayments, the Wash and Morecambe Bay, are examined for palaeotidal changes by running a series of seven numerical tidal models from the scale of the north-east Atlantic to that of the bays. In order to obtain results to the required resolution to carry out the work, two new tidal models were developed for the Wash. Tidal model simulations for lowering of sea depths from current bathymetric values without coastline shape changes showed reductions of a maximum of 10% of the sea-level reductions in the bays. Changes to tidal altitudes were not so great for alterations to coastal shape alone, where no modification of present sea depth values was included. A combination of sea depth and coastline changes used in the reconstruction of former tidal height patterns within the embayments showed differences corresponding broadly to the variations in altitude of sea-level index points within the Wash Fenlands, although altitudi­ nal differences are within the model error band for tidal prediCtions. For Morecambe Bay, however, tidal inundation does not occur to altitudes predicted by sea-level index points and it is suggested, following Tooley (1978, 1987), that neotectonic movements may well have influenced the Holocene sea-level record in this area. Better palaeogeographic data are required for more accurate palaeotidal simulations in embayments. Sediment com­ paction is also identified as an area requiring further research in the attempt to explain altitudinal variation of sea-level index points within local areas and so enable regional comparisons of sea-level change to be made. ACKNOWLEDGEMENTS The receipt of a Natural Environment Research Council Studentship held at the Uni­ versity of Durham for a period of three years is gratefully acknowledged. The Studentship was based in the Department of Geography at Durham University and the work presented in this thesis was carried out during that time under the supervision of Dr. Ian Shennan and Dr. Michael Tooley. Use of the facilities in the Geography Department and Computer Centre at Durham and the help of staff from both Departments is much appreciated. This work would not have been possible without the assistance of Dr. Roger Flather and other staff at the Proudman Oceanographic Laboratory, Birkenhead, who provided the tidal model program used in the study. The assistance of staff at the University of London Computer Centre in permitting use of the Cray supercomputer at London for obtaining results from the tidal models employed is also acknowledged with gratitude. Dr. Martyn Waller provided access to Fenland radiocarbon dates and stratigraphic data currently in press and colleagues at Durham, Dr. D. Donoghue and Dr. Y. Zong, provided access to unpublished stratigraphic data for the Wash Penland and Morecambe Bay respectively. Staff at the British Geological Survey in Keyworth and Edinburgh also assisted with useful discussions. Earlier drafts of parts of this thesis were read and commented on by Dr. Shennan, Dr. Flather, Dr. Williams, Dr. Proctor and Dr. Tooley to whom I express my thanks. Dr. W.R. Williams, Mr. P. Dodds and Miss M. Pringle provided assistance with computerised graphics and statistics packages. SYMBOLS USED IN THE TEXT Symbol Meaning (units) a, b Real and imaginary parts of a complex time-varying coefficient c Speed of progression of the tidal wave (metres per second) Cg Phase speed (radians) CD Dimensionless drag coefficient D Total water depth ( h + () E Matrix consisting of values of elements predicted from the model f Nodal factor- adjustment of tidal amplitude made for the 18.61 year nodal cycle of lunar declination fc Coriolis parameter fe Nodal factor of the Equilibrium Tide at time zero F Stress in the x direction FB Bottom stress in the x direction 2 g Gravitational constant (6.67x1o-11 Nm kg-2 ) Ge Phase lag of the Equilibrium Tide at Greenwich (radians) Gy Stress in the y direction GB Bottom stress in the y direction h Mean water depth hmax Maximum bathymetric value in model (metres) hws Smallest model grid width hw Model grid width H Tidal amplitude He Tidal amplitude of harmonic constituent e HO Matrix consisting of values of amplitude and phase of harmonic constituents z, m Number of points at which calculations are made in the latitudinal and longitudinal directions respectively I An unspecified harmonic constituent j, k Constants l Tidal wavelength L Length of bay from sea mouth to head Mass of the earth (5.97x1024 kg) Mass of the moon (7.35x10 22 kg) A point at the centre of the moon n Nodal angle- adjustment of tidal phase made for the 18.61 year nodal cycle of lunar declination Nodal angle of the Equilibrium Tide at time zero A point at the centre of the earth Hydrostatic pressure Atmospheric pressure on the water surface Hydrostatic pressure at a point at depth zd metres below the water surface Symbol Meaning (units) q Depth-mean current vector R Equatorial radius of the earth (6,378 kilometres) Rz Distance from the centre of the earth to the centre of the moon ( 384,400 kilometres) s Coefficient of bottom friction s' An element of space t Time T(t) Tidal level at time t u Latitudinal velocity Uq Component of the depth-mean current in the direction of increasing X u A constant v Longitudinal velocity Vq Component of the depth-mean current in the direction of increasing <P Ve Phase angle of the Equilibrium Tide at time zero (radians) X Latitudinal distance X,Y,Z Points at the surface of the earth y Longitudinal distance z Sea surface elevation Zd Distance below water surface zo, Zo Mean sea-level D.S Grid width D.t, D.T Timestep (seconds) ( Displacement of water level from mean value e North co-latitude (90°- latitude) .\ Wavelength of the progressive wave p Water density (1025kgjm3) a Angular frequency (of a tidal constituent) ae Angular frequency at time zero of a tidal constituent e Tb Bottom stress <P Angle of latitude X East longitude w Angular frequency of the earth's rotation n Gravitational potential at the surface of the earth Dy Gravitational potential at a point Y on the surface of the earth Harmonic Constituents Constituent Speed Meaning M2 28.9841 lunar semi-diurnal tidal constituent M3 43.4 761 lunar third-diurnal tidal constituent M4 57.9682 lunar quarter-diurnal tidal constituent M6 86.9523 lunar sixth-diurnal tidal constituent MS4 58.9841 generated by the interaction of M2 and S2 2MS2 (or Meu2) 27.9682 in shallow water s2 30.0000 solar semi-diurnal tidal constituent CONTENTS Volume 1 Chapter 1.
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