By Antonio Navarra (auth.), Hans von Storch, Antonio Navarra (eds.)

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Stochastic climate models remain testable, however, by focusing on energy levels and, if atmospheric observations are available, cause-to-effect relationships (Müller and Frankignoul, 1981). g. by the changes in the orbital parameters of the earth), or reflect the chaotic nature of the climate subsystem. 6: SST anomalyspectrum at Ocean Weather Station 1(59 0 N, 19°W) for the period 1949-1964, with 95% confidence interval. The smooth curve is the stochastic model prediction. (From Frankignoul and Hasselmann, 1976).

This mode accounts for 12% of the variance. Also shown is the climatological SST distribution (thin contours). Bottom: Spectrum of EOF 2. The thin line represents a background red noise spectrum and its 95% confidence limit. (From Deser and Blackmon, 1993). 6 Chapter 3: Climate Spectra and Stochastic Climate Models Variability in the Ocean Interior Few long time series are available in the ocean interior, so that the spectral characteristics are virtually unknown below the surface at periods longer than a few years.

For a stable solution, the matrix Vij must be negative definite. Since for t ~ t lll , v~ acts as a white noise generator, Eq. 11) represents a multivariate first-order Markov process. 12) k,l = with the matrix T (ilI - V)-l (I is the unit matrix). 14) where >. is the feedback. 4: Sea Surface Temperature Anomalies 39 which can even be tested when no simuItaneous information is available on the weather forcing. 11), providing more stringent signatures than the power spectra. 15) which yields the cross correlation between X and Y.

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