Glacial/Interglacial ‘oscillations’: WHY? Time-series analysis SPECMAP 150 ka indicatorsWe now understand how climate has changed over the past few 105 years. Similar basic patterns are seen in most indicators (History:At present, relatively few people doubt that insolation changes play a role in climate change, but there are reasonable questiChanges in the earth's orbital parameters and their influence on radiation receipt at the top of the atmosphere IEccentricity of Present Earth Orbit Around Sun (to Scale)Precession of elliptical orbit (with respect to fixed stars)PrecessionElements of the Earth’s Orbit (Berger, 1981)Precession influence on climate: why 23,000 years not 25,800?Obliquity (tilt)Obliquity change re-apportions radiation between polar regions and tropicsPeriodic changes in orbital geometry modulate solar radiation receipts (insolation)Insolation at 65°N, “June 21”Integrated over a half-year centered on summer, obliquity dominates high latitude insolation and precession dominates lower laSummary: orbital influence on insolation at the top of the atmosphereHow do we make the comparison between these precisely calculable orbital changes and the record of climate change?Oxygen isotopes compared to summer insolation at 65°NFourier time-series analysisFormal definition of the Fourier TransformThe Fourier Transform is reversible:Computation of the Fourier TransformVisual representation of FT as simultaneous equationsSolution to the simultaneous equationsAlternative methodsFT needs “infinite data”; gets it by stacking record end-to-end repeatedlyNyquist Folding Frequency and AliasingHarmonicsDetrending and TaperingPower SpectrumWhat does “power” mean for a climate time series?PeriodogramStatistical significance of the periodogram 1Statistical significance of the periodogram IIDaniell EstimatorStatistical significance of Daniell EstimatorExampleThe problem of frequency resolutionOptimal Spectral Estimation IOptimal Spectral Estimation IICoherence and PhaseCalculating the cross-spectrum, coherence, and phase ICalculating the cross-spectrum, coherence, and phase IICoherence and Phase on the complex plane:Example:Statistical significance of coherence and phaseFrequency Filtering of Time SeriesElements of the Earth’s Orbit (Berger, 1981)Summary: orbital influence on insolation at the top of the atmosphereIntegrated over a half-year centered on summer, obliquity dominates high latitude insolation and precession dominates lower laOxygen isotopes compared to summer insolation at 65°NComputation of the Fourier TransformVisual representation of FT as simultaneous equationsPeriodogramCoherence and PhaseCorrelation does not require CausationHays, Imbrie, & Shackleton (1976) dataHays, Imbrie and Shackleton (1976) outline:Evans and Freeland (1977) Science 198:528-530Molfino (1980) tropical AtlanticBassinot et al. (1994) EPSL 126:91-108Specmap stack compared to ODP 607 vs depthSPECMAP phase wheelImbrie et al. (1992) Last 150 kaClimate black boxReadingDid increasing Northern Hemisphere summer insolation cause the end of the last ice age?MIT OpenCourseWare http://ocw.mit.edu 12.740 Paleoceanography Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Glacial/Interglacial ‘oscillations’: WHY?Time-series analysis12.740 Lecture 4 Spring 2008SPECMAP 150 ka indicatorssource: Imbrie et al. (1992)Image removed due to copyright restrictions.We now understand how climate has changed over the past few 105years. Similar basic patterns are seen in most indicators (with a few loose ends). We can begin to ask the question: Why?• Two approaches:1. "The physics": derive ice ages from first principles. Good luck! (call me when you get there).2. "Correlation (not causation)": look for similarities (coincidences?) between certain driving forces known from first principles and the climate record. Examine the odds that such a correspondence is due to chance. If the odds are good, look into the relevant mechanism in more detail. To be successful, this approach needs: (1) reliable climate record not excessively modified by bioturbation; (2) but the record also needs to be reasonably long so that many cycles are available for statistical tests. Must compromise here! Eventually need to come to an accommodation with “the physics”.History:• ~1840: Agassiz proposed massive continental glaciation; debate ensued which eventually was decided in his favor • ~1860: Croll proposed that changes in the earth's orbital parameters were responsible for glaciation. Theory received a mixed reception.• ~1920 Milankovitch undertook detailed calculations which quantified the expected variations in the earth's orbital parameter and proposed that summer insolation at 65°N was the key [more or less summer insolation => more or less glacial melting]. Theory encountered a mixed reception.• 1950's: Emiliani found stronger evidence for cyclic oscillations; tried to revive Milankovitch. Problem: time scale.• 1960's, 70's: Barbados data (and hence correct time scale) revived interest in Milankovitch hypothesis. Theory was being taken seriously, but it was considered far from proven.• 1976: Hays, Imbrie, Shackleton paper. Overcame most of the resistance to some degree of orbital influence over climate (at least as a "pacemaker" of ice ages).At present, relatively few people doubt that insolation changes play a role in climate change, but there are reasonable questions as to their importance relative to other factors. Even: to what extent is climate actually predictable? Are there significant internal resonances that interact with orbital forcing? What is the origin of large amplitude sub-orbital climate variability? Can we parlay our understanding of past climate change into better predictions of future climate change?Climate models incorporate a lot of first principle physics (e.g. laws of motion, radiation physics, and thermodynamics), but because of the enormous complexity of the system and limited computer capabilities, these models contain less definitive representations of sub-grid scale processes and of poorly understood processes (e.g. convective precipitation and clouds; sea ice formation and melting; relation between soil, vegetation, evaporation, precipitation and river runoff). In the aggregate, these factors are extremely important, so they cannot be left out. Instead they are handled by empirical