Adaptation of classical tidal harmonic analysis to nonstationary tides, with application to river tides

Journal of Atmospheric and Oceanic Technology

Volumn 30, Issue 3, 2013, Pages 569-589

  Matte, Pascal ^a,b   Jay, David A ^a   Zaron, Edward D ^a  

^a Portland State University   (Canada)

^b CENTRE EAU TERRE ENVIRONNEMENT   (Canada)

Author keywords

Hindcasts; Regression analysis; Rivers; Software; Spectral analysis models distribution; Tides

Indexed keywords

CORRELATED NOISE MODEL; ESTIMATION PROCEDURES; HINDCASTS; NONSTATIONARY SIGNALS; RAYLEIGH CRITERION; REGRESSION COEFFICIENT; ROOT-MEAN SQUARE ERRORS; SPECTRAL ANALYSIS/MODELS/DISTRIBUTION;

COMPUTER SOFTWARE; COVARIANCE MATRIX; HARMONIC ANALYSIS; REGRESSION ANALYSIS; RIVERS; TIDES; TIME DOMAIN ANALYSIS; TIME SERIES; WATER LEVELS;

TIDAL POWER;

COVARIANCE ANALYSIS; ERROR ANALYSIS; HARMONIC ANALYSIS; HINDCASTING; MATRIX; OCEAN TIDE; REGRESSION ANALYSIS; RIVER FLOW; SOFTWARE; SPECTRAL ANALYSIS; SUBTIDAL ENVIRONMENT; WATER LEVEL;

COLUMBIA RIVER;

EID: 84875665564     PISSN: 07390572     EISSN: 15200426     Source Type: Journal    
DOI: 10.1175/JTECH-D-12-00016.1     Document Type: Article

References (46)

1. Amin, M., 1983: On perturbations of harmonic constants in the Thames estuary. Geophys. J. Roy. Astron. Soc., 73, 587-603.
2. Amin, M., 1985: Temporal variations of tides on the west coast of Great Britain. Geophys. J. Roy. Astron. Soc., 82, 279-299.
3. Amin, M., 1993: The mutual influence of tidal constituents in the presence of bottom stress. Estuarine Coastal Shelf Sci., 37, 625-633.
4. Aubrey, D. G., and P. E. Speer, 1985: A study of non-linear tidal propagation in shallow inlet/estuarine systems. Part I: Observations. Estuarine Coastal Shelf Sci., 21, 185-205.
5. Bottom, D. L., C. A. Simenstad, J. Burke, A. M. Baptista, D. A. Jay, K. K. Jones, E. Casillas, and M. H. Schiewe, 2005: Salmon at river's end: The role of the estuary in the decline and recovery of Columbia River salmon. NOAA Tech. Memo. NMFS-NWFSC-68, 246 pp.
6. Buschman, F. A., A. J. F. Hoitink, M. van der Vegt, and P. Hoekstra, 2009: Subtidal water level variation controlled by river flow and tides. WaterResour. Res., 45, W10420, doi:10.1029/2009WR008167.
7. Byrd, R. H., J. C. Gilbert, and J. Nocedal, 2000: A trust region method based on interior point techniques for nonlinear programming. Math. Program., 89A, 149-185.
8. Codiga, D. L., 2011: Unified tidal analysis and prediction using the UTide Matlab functions. University of Rhode Island Graduate School of Oceanography Tech. Rep. 2011-01, 59 pp.
9. Daniell, P. J., 1946: Discussion of "On the theoretical specification and sampling properties of autocorrelated time-series." J. Roy. Stat. Soc., 8 (Suppl.), 88-90.
10. Darwin, G. H., 1891: Bakerian lecture: On tidal prediction. Philos. Trans. Roy. Soc. London, A182, 159-229.
11. DiLorenzo, J. L., P. Huang, M. L. Thatcher, and T. O. Najarian, 1993:Dredging impacts onDelaware estuary tides. Proceedings of the Third International Conference, M. L. Spaulding, Ed., Vol. 3, Estuarine and Coastal Modeling, ASCE, 86-118.
12. Doodson, A. T., 1921: The harmonic development of the tidegenerating potential. Proc. Roy. Soc. London, 100A, 305-329.
13. Dronkers, J. J., 1964: Tidal Computations in Rivers and Coastal Waters. North-Holland Publishing Company, 518 pp.
14. Foreman, M. G. G., 1977: Manual for tidal heights analysis and prediction. Pacific Marine Science Rep. 77-10, 58 pp.
15. Foreman, M. G. G., and R. F. Henry, 1989: The harmonic analysis of tidal model time series. Adv. Water Resour., 12, 109-120.
16. Foreman, M. G. G., J. Y. Cherniawsky, and V. A. Ballantyne, 2009: Versatile harmonic tidal analysis: Improvements and applications. J. Atmos. Oceanic Technol., 26, 806-817.
17. Gallo, M. N., and S. B. Vinzon, 2005: Generation of overtides and compound tides in Amazon estuary. Ocean Dyn., 55, 441-448.
18. Godin, G., 1972: The Analysis of Tides. University of Toronto Press, 264 pp.
19. Godin, G., 1984: The tide in rivers. Int. Hydrogr. Rev., 61, 159-170.
20. Godin, G., 1985: Modification of river tides by the discharge. J. Waterw. Port Coastal Ocean Eng., 111, 257-274.
21. Godin, G., 1999: The propagation of tides up rivers with special considerations on the upper Saint Lawrence River. Estuarine Coastal Shelf Sci., 48, 307-324.
22. Horsburgh, K. J., and C. Wilson, 2007: Tide-surge interaction and its role in the distribution of surge residuals in the North Sea. J. Geophys. Res., 112, C08003, doi:10.1029/2006JC004033.
23. Huber, P. J., 1996: Robust Statistical Procedures. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 68, 2nd ed. Society of Industrial and Applied Mathematics, 67 pp.
24. Jay, D. A., 1991: Green's law revisited: Tidal long-wave propagation in channels with strong topography. J. Geophys. Res., 96 (C11), 20 585-20 598.
25. Jay, D. A.,2009: Evolution of tidal amplitudes in the eastern Pacific Ocean. Geophys. Res. Lett., 36, L04603, doi:10.1029/2008GL036185.
26. Jay, D. A., and E. P. Flinchem, 1995: Wavelet transform analyses of nonstationary tidal currents. Proc. Fifth Working Conf. on Current Measurement, St.Petersburg, FL, IEEE, 100-105.
27. Jay, D. A., and E. P. Flinchem, 1997: Interaction of fluctuating river flow with a barotropic tide: A demonstration of wavelet tidal analysis methods. J. Geophys. Res., 102 (C3), 5705-5720.
28. Jay, D. A., and E. P. Flinchem, 1999:Acomparison of methods for analysis of tidal records containing multi-scale non-tidal background energy. Cont. Shelf Res., 19, 1695-1732.
29. Jay, D. A., and T. Kukulka, 2003: Revising the paradigm of tidal analysis - The uses of non-stationary data. Ocean Dyn., 53, 110-125.
30. Jay, D. A., K. Leffler, and S. Degens, 2011: Long-term evolution of Columbia River tides. J. Waterw. Port Coastal Ocean Eng., 137, 182-191.
31. Kukulka, T., and D. A. Jay, 2003a: Impacts of Columbia River discharge on salmonid habitat: 1. A nonstationary fluvial tide model. J. Geophys. Res., 108, 3294, doi:10.1029/2003JC001829.
32. Kukulka, T., and D. A. Jay, 2003b: Impacts of Columbia River discharge on salmonid habitat: 2. Changes in shallow-water habitat. J. Geophys. Res., 108, 3294, doi:10.1029/2003JC001829.
33. LeBlond, P. H., 1978: On tidal propagation in shallow rivers. J. Geophys. Res., 83 (C9), 4717-4721.
34. LeBlond, P. H. 1979: Forced fortnightly tides in shallow rivers. Atmos.- Ocean, 17, 253-264.
35. LeBlond, P. H., 1991: Tides and their interactions with other oceanographic phenomena in shallow water (review). Tidal Hydrodynamics, B. B. Parker, Ed., Wiley, 357-378.
36. Leffler, K. E., and D. A. Jay, 2009: Enhancing tidal harmonic analysis: Robust (hybrid L1/L2) solutions. Cont. Shelf Res., 29, 78-88.
37. MathWorks, 2012: R2010a MathWorks documentation. [Available online at http://www.mathworks.com/help/releases/R2010a/ helpdesk.html.]
38. Munk, W. H., B. Zetler, and G. W. Groves, 1965: Tidal cusps. Geophys. J. Roy. Astron. Soc., 10, 211-219.
39. Nidzieko, N. J., 2010: Tidal asymmetry in estuaries with mixed semidiurnal/diurnal tides. J. Geophys. Res., 115, C08006, doi:10.1029/2009JC005864.
40. Parker, B. B., 1991: The relative importance of the various nonlinear mechanisms in a wide range of tidal interactions (review). Tidal Hydrodynamics, B. B. Parker, Ed., Wiley, 237-268.
41. Parker, B.B. 2007: Tidal analysis and prediction. NOAA Special Publ. NOS CO-OPS 3, 378 pp.
42. Pawlowicz, R., B. Beardsley, and S. Lentz, 2002: Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput. Geosci., 28, 929-937.
43. Pugh, D. T., and J. M. Vassie, 1976: Tide and surge propagation offshore in the Dowsing region of the North Sea. Dtsch. Hydrogr. Z., 29, 163-213.
44. Shaw, A. G. P., and M. N. Tsimplis, 2010: The 18.6 yr nodal modulation in the tides of southern European coasts. Cont. Shelf Res., 30, 138-151.
45. Speer, P. E., and D. G. Aubrey, 1985: A study of non-linear tidal propagation in shallow inlet/estuarine systems. Part II: Theory. Estuarine Coastal Shelf Sci., 21, 207-224.
46. Waltz, R. A., J. L. Morales, J. Nocedal, and D. Orban, 2006: An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math. Program., 107, 391-408.