Abstract
Measurements of currents during the 4-month period beginning June 1978 taken at three stations off Ste-Marthe-de-Gaspe in the Gulf of St. Lawrence were subject to time series analyses. Such time series were considered as superpositions of almost periodic and of stochastic components. Variations in the currents due to tidal forcing have been identified by spectral analysis, and both their amplitudes and relative contribution to the total variations were compared. Six cyclical components representing semidiurnal, diurnal and semi-monthly oscillations (M 2, S 2, N 2, K 1, O 1, M f ) have been selected using Mallows’ C P criterion and were incorporated in a harmonic polynomial model. The residual series of the previous adjustment were first tested for their mutual independency and for their stationarity. The backward difference operator was then applied to studentized residual series and then an ARMA model was fitted. It was found that the actual differenced residuals are related to those previous ones with time lags of 16, 17, 21, 33 or 34 hours. Such time lags do not correspond to any known tidal periodicities. It is suggested that other forcing, due to meteorological phenomena for example, seems to be contributing to the dynamics and variability of the Gaspe Current.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bendat, J. S., and A. G. Piersol (1971), Random Data: Analysis and Measurement Procedures, 2nd edition. New York: Wiley Interscience.
Benoît, J. (1980), «Variations temporelles et spatiales du Courant de Gaspé» M.Sc. Thesis, Université du Québec Rimouski.
Benoît, J., M. I. El-Sabh, and C. L. Tang (1985), “Structure and seasonal characteristics of the Gaspe Current”. Journal of Geophysical Research 90, 3225–3236.
Bingham, C., P. Whittle, H. Wold, and J. Shiskin (1978), “Time series.” In International Encyclopedia of Statistics, ed. W. H. Kruskal and J. M. Tanur, pp. 1167–1210. New York: The Free Press.
Bloomfield, P. (1976), Fourier Analysis of Time Series: An Introduction. New York: Wiley and Sons.
Box, G. E. P., and G. M. Jenkins (1976), Time Series Analysis, Forecasting and Control (revised edn.). San Francisco: Holden-Day.
Brillinger, D. R. (1981), Time Series: Data Analysis and Theory (expanded edition). San Francisco: Holden-Day.
Cartwright, D. E. (1982), “Tidal analysis—a retrospect.” In Time Series Methods in Hydrosciences, ed. A. H. El-Shaarawi and S. R. Esterby, pp. 170–188. Amsterdam: Elsevier Scientific Publishing.
Dixon, W. J., ed. (1983), BMDP Statistical Software. Berkeley, CA: University of California Press.
Draper, N. R., and H. Smith (1981), Applied Regression Analysis, 2nd edition. New York: Wiley and Sons.
El-Sabh, M. I., and J. Benoît (1984), «Variabilité spatio-temporelle du Courant de Gaspé.» Sciences et Techniques de l’Eau 17, 55–60.
El-Sabh, M. I., H. J. Lie, and V. G. Koutitonsky (1982), “Variability in the near-surface residual current in the lower St. Lawrence Estuary”. Journal of Geophysical Research 87, 9589–9600.
Forrester, W. D. (1983), Canadian Tidal Manual, Technical Report. Ottawa: Canadian Hydrologic Service.
Godin, G. (1972), The Analysis of Tides. Toronto: University of Toronto Press.
Jenkins, G. M., and D. G. Watts (1968), Spectral Analysis and its Applications. San Francisco: Holden-Day.
Koopmans, L. H. (1974), The Spectral Analysis of Time Series. New York: Academic Press.
Ljung, G. M., and G. E. P. Box (1978), “On a measure of lack of fit in time series models”. Biometrika 65, 297–303.
Marcheterre, M. (1985), «Etude de la dynamique de Courant de Gaspé par l’analyse des séries chronologiques». M.Sc. Thesis, Université de Montréal.
Munk, W. H., and D. E. Cartwright (1966), “Tidal spectroscopy and prediction”. Philosophical Transactions of the Royal Society of London, Series A 259, 533–581.
Tang, C. L. (1979), “Inertial waves in the Gulf of St. Lawrence: a study of geostrophic adjustment.” Atmosphere-Ocean 17, 135–156.
Yevjevich, V. (1972), Stochastic Processes in Hydrology. Fort Collins, Colorado: Water Resources Publications.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Chanut, J.P., El-Sabh, M.I., Marcheterre, M., Roy, R. (1987). A Stochastic Modelling of Tidal Current Measurements. In: MacNeill, I.B., Umphrey, G.J., McLeod, A.I. (eds) Advances in the Statistical Sciences: Stochastic Hydrology. The University of Western Ontario Series in Philosophy of Science, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4792-4_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-4792-4_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8625-7
Online ISBN: 978-94-009-4792-4
eBook Packages: Springer Book Archive