Bill Scheftic Feb 2nd 2008 Atmo595c

Bill Scheftic Feb 2nd 2008 Atmo595c

Review: White Noise and Red Noise ` ` Hasselman s noise forced climate External Climate forcings: Insolation Cycles Mechanisms for continuous climate variability Stochastic/Coherence resonance Modified random walk Diffusion ` Huybers and Curry (2006) Methods Results ` Discussion

The ocean SST anomalies can be represented as the integral response to short time-scale random forcings. d (< y > + y ' ) =< v( y0, x(t )) > +v' ( x' (t )) dt ` Var ( y ' ) = 2 Dt 1 D = cov(v' (t + τ ), v' (t ))dτ 2 Follows the assumption that τx << τy (Frankignoul and Hasselman 1977)

` ` Variability in insolation greater in polar regions Temperature max lags insolation max Forcing of climate dependent on accumulation of insolation. A function of summer duration and intensity

Stochastic Resonance T2 T4 U (T ) = + TA sin(ωt ) 2 4 dt du = + η (T ) dt dt Represents a periodic signal and noise that combine to push the state of the system between two stable points. (Moss 1991; Benzi et al. 1983) (Hizanidis 2005)

Coherence Resonance dtt = Tt Tt 3 + εtt τ + Dηt dt ` Feaures: Bistability Delayed Feedback (Pos. or Neg.) Noise (Pelletier 2003)

Time-rate of change of δ18o deep-sea sediment core. White to 100 kyr, blue noise at lower frequencies ` ` ` Random walk is constrained by a no-ice and max-ice boundary, where memory is erased Spectrum has ~ f-2 power law characteristic. Dominant time-scale is 400 before rednoise walks to threshold. Past 400 noise is white (blue forcing (Wunsch 2003)

Realistic memory of SSTs can be simulated through a two-layer (mixed and deep) heat diffusion model. Tn 2Tn T F = Kn 2 = F0a=realistic gt0 +(~ζ 1/f) ` This model was able to produce t z t z characterization of the annual to centennial timescale spectrum. (Fraedrich et al. 2004)

Spectral Estimates and β 3 window Thomson s Multitaper Estimates were weighted by freq. resolution of proxy. β estimated with leastsquares fit to log-log plot. ` Autobicoherence fraction of power between (ω1,ω2, ω1+ ω2) for ω1+ ω2 (Elgar and Guza 1988)

` What is the importance of figure e? Does figure f suggest a connection between the annual and extra-annual time periods?

` What is the input noise for the Milankovitch periods? Why is there a difference between the annual to centennial slope vs. the centennial to 100 kyr slope?

` ` ` The 3 primary features of the instrumental temperature spectra (the power law, annual period energy, and interrannual energy) are all tightly linked. Continuum more energetic near timescale and locations of high solar variability. The insolation cycles are the forcing for climate, whereas the continuum represents the dynamic interaction between a noisy input and memory. What would the background continuum look like in the absence of annual or Milankovitch variations? (Huybers and Curry 2006)

` ` ` ` ` ` ` ` ` ` Benzi, R., G. Parisi, A. Sutera, and A. Vulpiani, 1983: A theory of stochastic resonance in climatic change. SIAM Journal of Applied Mathematics, 43, 565-578. Elgar, S., and R. T. Guza, 1988: Statistics of Bicoherence. Transactions on Acoustics, Speech, and Signal Processing, IEEE, 36, 1667-1668. Fraedrich, K., U. Luksch, and R. Blender, 2004: 1/f model for long-time memory of the ocean surface temperature. Physical Review E, 70, 037301. Frankignoul, C., and K. Hasselman, 1977: Stochastic climate models, Part II Application to sea-surface temperature anomalies and thermocline variability. Tellus, 29, 289-305. Hasselman, K., 1976: Stochastic climate models, Part I. Theory. Tellus, 28, 473-485. Hizanidis, J., 2005: Stochastic Resonance and Coherence Resonance. Technical University of Berlin. [available online at http://wwwnlds.physik.tu-berlin.de/~hizanidis/ ] Huybers, P., 2006: Early Pleistocene glacial cycles and the integrated summer insolation forcing. Science, 313, 508-511. Huybers, P., and W. Curry, 2006: Links between annual, Milankovitch and continuum temperature variability. Nature, 441, 329-332. Moss, F., 1991: Stochastic resonance: A signal + noise in a two state system. 45th Annual Symposium on Frequency Control, IEEE. Pelletier, J. D., 2003: Coherence resonance and ice ages. J. Geophys. Res., 108, D20, ACL 11. Wunsch C., 2003: The spectral description of climate change including the 100 ky energy. Climate Dynamics, 20, 353-363.