Analysis of geophysical time series using discrete wavelet transforms: An overview

Lecture Notes in Earth Sciences

Volumn 112, Issue , 2008, Pages 61-79

  Percival, Donald B ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Arctic sea ice; Haar wavelet; Ice cores; Maximal overlap discrete wavelet transform; Multiresolution analysis; Wavelet spectrum; Wavelet variance

Indexed keywords

EID: 48949098181     PISSN: 09300317     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-78938-3_4     Document Type: Article

References (33)

1. Goupillaud, P., Grossmann, A. and Morlet, J. (1984). Cycle-octave and related transforms in seismic signal analysis. Geoexploration, 23, 85-102.
2. Grossmann, A. and Morlet, J. (1984). Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM Journal on Mathematical Analysis, 15, 723-736.
3. Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, 41 909-996.
4. 2(R). Transactions of the American Mathematical Society, 315, 69-87.
5. Mallat, S.G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.
6. Mallat, S.G. (1989). Multifrequency channel decompositions of images and wavelet models. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37, 2091-2110.
7. Percival, D.B. and Walden, A.T. (2000). Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge, UK.
8. Torrence, C. and Compo, G.P. (1998). A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79 61-78.
9. Pelgrum, H., Schmugge, T., Rango, A., Ritchie, J. and Kustas, B. (2000). Length-scale analysis of surface albedo, temperature, and normalized difference vegetation index in desert grassland. Water Resources Research, 36, 1757-1766.
10. Lark, R.M. and Webster, R. (2001). Changes in variance and correlation of soil properties with scale and location: Analysis using an adapted maximal overlap discrete wavelet transform. European Journal of Soil Science, 52, 547-562.
11. Labat, D., Ababou, R. and Mangin, A. (2001). Introduction of wavelet analyses to rainfall/runoffs relationship for a karstic basin: The case of Licq-Atherey karstic system. Ground Water, 39, 605-615.
12. Massel, S.R. (2001). Wavelet analysis for processing of ocean surface wave records. Ocean Engineering, 28, 957-987.
13. Rybák, J. and Dorotovič, I. (2002). Temporal variability of the coronal greenline index (1947-1998). Solar Physics, 205, 177-187.
14. Barbosa, S.M., Fernandes, M.J. and Silva, M.E. (2006). Long range dependence in North Atlantic sea level. Physica A: Statistical Mechanics and its Applications, 371, 725-731.
15. Cornish, C.R., Bretherton, C.S. and Percival, D.B. (2006). Maximal overlap wavelet statistical analysis with application to atmospheric turbulence. Boundary-Layer Meteorology, 119, 339-374.
16. Steel, E.A. and Lange, I.A. (2007). Using wavelet analysis to detect changes in water temperature regimes at multiple scales: Effects of multi-purpose dams in the Willamette River basin. River Research and Applications, 23, 351-359.
17. Flato, G.M. (1995). Spatial and temporal variability of Arctic ice thickness. Annals of Glaciology, 21, 323-329.
18. World Meteorological Organization (2007). Sea-Ice Information Services in the World. (3rd ed.), World Meteorological Organization, Geneva, Publication 574.
19. Percival, D.B., Rothrock, D.A., Thorndike, A.S. and Gneiting, T. (2008). The variance of mean sea-ice thickness: Effect of long-range dependence. Journal of Geophysical Research - Oceans, 113, C01004, doi:10.1029/2007JC004391.
20. Rothrock, D.A., Percival, D.B. and Wensnahan, M. (2008). The decline in arctic sea-ice thickness: Separating the spatial, annual, and interannual variability in a quarter century of submarine data. Journal of Geophysical Research - Oceans, 113, C05003, doi:10.1029/2007JC004252.
21. Karlöf, L., Winebrenner, D.P. and Percival, D.B. (2006). How representative is a time series derived from a firn core? A study at a low accumulation site on the Antarctic plateau. Journal of Geophysical Research - Earth Surface, 111, F04001, doi:10.1029/2006JF000552.
22. Mondal, D. and Percival, D.B. (2008). Wavelet variance analysis for gappy time series. Annals of the Institute of Statistical Mathematics under revision.
23. Percival, D.B. and Mofjeld, H.O. (1997). Analysis of subtidal coastal sea level fluctuations using wavelets. Journal of the American Statistical Association, 92, 868-880.
24. Jach, A., Kokoszka, P., Sojka, J. and Zhu, L. (2006). Wavelet-based index of magnetic storm activity. Journal of Geophysical Research - Space Physics, 111, A09215, doi:10.1029/2006JA011635.
25. Barbosa, S., Silva, M.E. and Fernandes, M.J. (2006). Wavelet analysis of the Lisbon and Gibraltar North Atlantic Oscillation winter indices. International Journal of Climatology, 26, 581-593.
26. Barnes, R.J., Baxter, S.J. and Lark, R.M. (2007). Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform. Soil Biology and Biochemistry, 39, 295-310.
27. França, C.A.S. and De Mesquita, A.R. (2007). The December 26th 2004 tsunami recorded along the southeastern coast of Brazil. Natural Hazards, 40, 209-222.
28. Chun, S.J., Liu, Y.Z. and Sung, H.J. (2007). Multi-resolution analysis of the large-scale coherent structure in a turbulent separation bubble affected by an unsteady wake. Journal of Fluids and Structures, 23, 85-100.
29. Wang, Y. (2006). Selected review on wavelets in statistics. In Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of His 65th Birthday (J. Fan and H.L. Koul, eds.). Imperial College Press, London, pp. 163-182.
30. Percival, D.B., Sardy, S. and Davison, A.C. (2001). Wavestrapping time series: Adaptive wavelet-based bootstrapping. In Nonlinear and Nonstationary Signal Processing (W.J. Fitzgerald, R.L. Smith, A.T. Walden and P.C. Young, eds.). Cambridge University Press, Cambridge, UK, pp. 442-470.
31. Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.
32. Mallat, S.G. (1999). A Wavelet Tour of Signal Processing (2nd ed.). Academic Press, San Diego.
33. Maraun, D., Kurths, J. and Holschneider, M. (2007). Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significance testing. Physical Review E 75, 016707.