WPL UNC-CH

Detecting the spectrum of the Atlantic’s thermo-haline circulation

Deconvolved climate proxies show how polar climates communicateE. Reischmann, X. Yang, J.A. Rial

Wave Propagation Laboratory Department of Geological Sciences

Deconvolution has long been used in science to recover an input given a system’s impulse response and output. In this study, we applied spectral divi-sion deconvolution to select, polar, δ18O time series to investigate the possible relationship between the climates of the Polar Regions, i.e. the equivalent to a climate system’s ‘impulse response.’ While the records may be the result of nonlinear processes, deconvolution remains an appropriate tool because the two polar climates are synchronized, forming a Hilbert transform pair. In order to compare records, the age models of three Greenland and four Ant-arctica ice cores have been matched via a Monte Carlo method using the methane-matched pair GRIP and BYRD as a basis for the calculations. For all twelve polar pairs, various deconvolution schemes (Wiener, Damped Least Squares, Tikhonov, truncated singular value decomposition) give consistent, quasi-periodic, impulse responses of the system. Multitaper analysis reveals strong, millennia scale, quasi-periodic oscillations in these system responses

function is generally of longer period than the south to north transfer function. High amplitude power peaks at 5.0ky to 1.7ky characterize the former, while the latter contains peaks at mostly short periods, with a range of 2.5ky to 1.0ky. Consistent with many observations, the deconvolved, quasi-periodic, transfer functions share the predominant periods known to exist in the data, some of which are likely related to solar forcing (2.5-1.0ky), while some are probably indicative of the internal oscillations of the climate system (1.6-1.4ky). The approximately 1.5 ky transfer function may represent the internal periodicity of the system, per-

-ings.

Introduction

Polar Isotope Data Deconvolution

Deconvolution of Model With Known Internal Oscillation

Stochastic Van Der Pol Oscillator Model Deconvolution

Discussion and Conclusions

Data and Methods

Since deconvolution may produce spurious results no matter how carefully regularized, it is important that the results be guided and supplemented with the use of models of the polar climate

adjustable parameters, the model uses two frequency modulated (FM) carrier signals 100ky in duration to represent each polar ice core record (e.g., Rial and Saha 2011). Comparison with the transferfunctions from the data shows that the results are consistent, and retrieve the input internal oscillating frequency, validating the use of deconvolution.

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MTM spectra of North to South transfer functions

BP filter used prior to deconvolution: 1e-04 to 0.001Freq

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The dataset for this study is three Greenland and four Antartic δ18O ice core proxy records from the National Oceanic and Atmospheric Adminstration.We create 12 combinations of cores, which are age-model matched via the Monte Carlo method (Blunier et al. 2007) and have Milankovitch-related

the north-to-south and south-to-north directions, using the four seperate methods of deconvolution mentioned above. Deconvolution is an appropriate operation to apply because of the linear relation characteristics described above (Rial, 2012). The spectra of the transfer functions are then analysed for predominant oscillating frequencies which could show underlying mechanisms of oscillation. A Saltzman (2001) basedmodel for the last 100 kilo-years is then analysed to demonstrate that the

of the Thermohaline circulation.

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Figures 6 and 7: Multi-taper spectra of the deconvolved transferfunctions obtained from each of the pairs of records named. The inset shows the same data in log-log plot for a the signal-to-noise level comparison. The spectra of the N-to-S transferfunctions are strongly peaked at 1.7ky, while the spectra of the S-to-N transfer functions show prominent power peaks at 2.5ky, 1.5ky and 1.2ky, all of which are close to the periodicities reported for Holocene solar and internal forcing (Bond et al. 1999;Darby et al. 2012; Sorrel et al. 2012). Theoretically, the spectra should be the inverses of each other. This is shownin Fig. 8 via the deconvolution of NGrip from DomeC in blueand DomeC from NGrip in grey. Maxs and mins are inversely aligned.

Figure 2: The Saltzman (2001) model for sea ice and icean temperature interaction for 5-20kya as compared to the data. The model is composed of four equations, maintainingthe oscillator behavior of the system (via pendulum displacement and velocity terms) while characterizes the ocean/ice interactions, with three adjustable parameters (Milankovitch forcing magnitude, noise level, and linking strength). (RIal and Saha 2011)

Fig. 5: Spectra of Fig 4’s transfer functions with highlighted prominent periods. Once again, the frequencies are in the range of those stated by Bond et. al to be related to the thermohaline circulation.

Loglog Plot

circulation, which has a proposed period within the range of those found in our analysis. The thermohaline circulation here would provide a mechanism of connection between the poles, through which the polar climates communicate with each other. This is consistent with our previous work studying the synchronizationof the polar climates, all of which requires a strong coupling between the poles across the ocean and atmosphere. Much further study on the global dynamics of the atmosphere-ocean-cryosphere system during the ice ages is needed before any statement of mechanism can be put forward.

Main Frequencies: 4,11,12,18,24,25 = 3750, 1364,1250,833,625,600 yr

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MTM spectra of South to North transfer functions

BP filter used prior to deconvolution: 1e-04 to 0.001Freq

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AcknowledgmentsNational Science Foundation: Paleoclimate and P2C2 programsTHe J.S. McDonnell Foundation: 21st Century Initiative on Complex Science.The Geological Sciences Department, UNC-Chapel Hill

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Blunier, Thomas, et al. "Synchronization of ice core records via atmospheric gases." Climate of the Past Discussions 3.1 (2007): 365-381.Bond, Gerard C., et al. "The North Atlantic's 1‐2 Kyr Climate Rhythm: Relation to Heinrich Events, Dansgaard/Oeschger Cycles and the Little Ice Age." Mechanisms of global climate change at millennial time scales (1999): 35-58.

sea-ice drift." Nature Geoscience (2012).Oh, Jeseung, Elizabeth Reischmann, and J. A. Rial. “Polar Synchrony and the Climatic History of Antarctica Deduced from Greenland’s (in Press).” Quaternary Science Reviews (2013).Rial, J. A. “Synchronization of Polar Climate Variability over the Last Ice Age: In Search of Simple Rules at the Heart of Climate’s Complexity.” American Journal of Science 312, no. 4 (2012): 417–448.Rial, J. A., and R. Saha. “Modeling Abrupt Climate Change as the Interaction Between Sea Ice Extent and Mean Ocean Temperature Under Orbital Insolation Forcing.” Abrupt Climate Change: Mechanisms, Patterns, and Impacts (2011): 57–74.Rial, J. A., and M. Yang. “Is the Frequency of Abrupt Climate Change Modulated by the Orbital Insolation?” Ocean Circulation: Mechanisms and Impacts-Past and Future Changes of Meridional Overturning (2007): 167–174.Saltzman, Barry. Dynamical paleoclimatology: generalized theory of global climate change. Vol. 80. Access Online via Elsevier, 2001.

References

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Fig. 3: Both directions of trans-fer functions for the TIkhonov Deconvolution Method for a reasonable regularization factor.

Fig. 4 : The four deconvolution -

tion of the Saltzman Model between 5 and 20 kya.