In these cases, if one wants to know whether it is related with the spatial pattern changes or not, MWF may help substantially to get some idea for the spatial changes of the signal. MWF should be used with care; MWF can have problems near the begenning and end of a record as other filtering methods, and MWF generally has smaller temporal resolution than conventional band-pass filters having wider pass-band. These disadvantages can be overcome, by analysing with EOFs and conventional band-pass filter complementary as shown above. Consequently, if one uses MWF for a proper problem with enough care, MWF would be helpful significantly.
Acknowledgements
We thank R.E. Thomson, B.Qiu, Y.Tourre, W.B.White, and R.-H.Zhang for preprints and reprints. Some figures are produced with the GrADS developed by B.Doty. This study is supported by grants from the Japanese Ministry of Education, Culture and Science.
References
Baker, C.B., Eischeid, J.K., Karl, T.R. and H.F.Diaz. 1995: The quality control of long-term climatological data using objective data analysis. Preprints of AMS Ninth Conference on Applied Climatology, Dallas, TX., January 15-20.
Dettinger, M.D. & D.R.Cayan, 1995: Large-scale atmospheric forcing of recent trends toward early Snowmelt Runoff in California, J.Climate, 8, 606-623.
Farge, M. 1992: Wavelet transforms and their applications to turbulence. Ann.Rev. of Fluid Mech 24, 395-457.
Ghil, M. , and R.Vautard, 1991: Interdecadal oscillations and the warming trend in global temperature time series, Nature, 350, 324-327.
Gu, D.F., and S G H. Philander, 1997: Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics. Science, 275, 805-807.
Hanan, E.J. 1970: Multiple Time Seies. Wiley.
Hare, S.R., and R.C. Francis, 1995: Climate change and salmon production in the Northeast Pacific Ocean. In Ocean climate and northern fish populations. Canadian Special Publication of Fisheries and Aquatic Sciences,. Edited by Beamish R.J. pp357-372.
Kondo, J., 1988: Volcanic eruptions, cool summers and famines in the northeastern part of Japan. J.Climate 1, 775-788.
Jin, F.-F., 1997: A theory of interdecadal climate variability of the North Pacific ocean-atmosphere system. J.Climate 10, 324-338.
Kawamura, R, 1994: A rotated EOF analysis of global sea surface temperature Variability with interannual and interdecadal scales. J.Phys.Oceanogr., 24, 707-715.
Latif, M. and T.P.Barnett, 1994: Causes of decadal climate variability over the North Pacific and North America. Science, 266, 634-637.
