Stochastic coupling of climate variables and ice volume over the Late Pleistocene glacial cycles

Abstract

Understanding the interactions between ice sheets and global climate forcings over geological timescales is essential for projecting their future. Previous studies have highlighted the role of ice dynamics and climate interactions in establishing the 100,000-year glacial cycles, particularly regarding the growth of the North American ice sheet. Researchers have reconstructed consistent time series for ice volume, temperature, and carbon dioxide by applying inverse forward modeling to benthic oxygen isotope records. Here we model the stochastic behavior of paleoclimate time series to evaluate the coupling between climate variables during the Pleistocene glacial cycles. We quantify the behavior of these time series using multifractal time-weighted detrended fluctuation analysis, which differentiates between near-red-noise and white-noise behavior below and above the 100,000-year glacial cycle, respectively, in all records. This study builds upon the work of Keyes et al. [Chaos vol. 33, 093132 (2023)] by incorporating ice volume into a five-variable model that includes carbon dioxide, methane, nitrous oxide, and temperature, along with intervariable coupling terms to capture potential relationships among these variables. Our analysis shows that ice volume, carbon dioxide, and temperature have a stabilizing effect upon each other. To test our model, we compute response functions for each pair of variables and compare these with empirical data, confirming our predictions regarding intervariable stability and coupling. This study provides a comprehensive overview of glacial-interglacial dynamics and highlights the role of cryosphere-climate feedbacks in shaping Earth's climate evolution.

Figures (8)

• Figure 1: Carbon dioxide, methane, temperature, nitrous oxide, and ice volume time series. (a) Original time series, (b) normalized fluctuations time series relative to the slowly varying mean. Here BP denotes before present and m.l.s.e denotes meters sea level equivalent.
• Figure 2: Frequency spectra of (a) original time series and (b) normalized fluctuations time series relative to the slowly varying mean.
• Figure 3: Logarithmic plots of the fluctuation functions for (a) original time series and (b) fluctuation time series with the slowly varying behavior removed. The vertical dotted black lines show the 23.5 kyr periodicity used in the later modeling section.
• Figure 4: (a) Stability coefficient for the one-dimensional model and the net stability coefficient for the five-dimensional model, defined as $a_{i,5D}$(net) $= a_{i,5D} - \sum_{j} b_{ij}$, and coupling coefficients for the five-dimensional model. In the legend, the generic symbol $b_{x}$ represents the influence of variable $x$ on the other variables. (b) Noise amplitude coefficients for one- and five-dimensional models.
• Figure 5: Comparison of (a) periodic standard deviations, (b) probability density functions, and (c) autocorrelation functions between the data and one-variable (top rows) and five-variable (bottom rows) models.