Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing

Long-term variations in Northern Hemisphere summer insolation are generally thought to control glaciation. But the intensity of summer insolation is primarily controlled by 20,000-year cycles in the precession of the equinoxes, whereas early Pleistocene glacial cycles occur at 40,000-year intervals, matching the period of changes in Earth’s obliquity. The resolution of this 40,000-year problem is that glaciers are sensitive to insolation integrated over the duration of the summer. The integrated summer insolation is primarily controlled by obliquity and not precession because, by Kepler’s second law, the duration of the summer is inversely proportional to Earth’s distance from the Sun.Earth and Planetary Science

Compensation between Model Feedbacks and Curtailment of Climate Sensitivity

The spread in climate sensitivity obtained from 12 general circulation model runs used in the Fourth Assessment of the Intergovernmental Panel on Climate Change indicates a 95% confidence interval of $2.1^{\circ}-5.5^{\circ}C$, but this reflects compensation between model feedbacks. In particular, cloud feedback strength negatively covaries with the albedo feedback as well as with the combined water vapor plus lapse rate feedback. If the compensation between feedbacks is removed, the 95% confidence interval for climate sen- sitivity expands to $1.9^{\circ}-8.0^{\circ}C$,. Neither of the quoted 95% intervals adequately reflects the understanding of climate sensitivity, but their differences illustrate that model interdependencies must be understood before model spread can be correctly interpreted. The degree of negative covariance between feedbacks is unlikely to result from chance alone. It may, however, result from the method by which the feedbacks were estimated, physical relationships represented in the models, or from conditioning the models upon some combination of observations and expectations. This compensation between model feedbacks when taken together with indications that variations in radiative forcing and the rate of ocean heat uptake play a similar compensatory role in models suggests that conditioning of the models acts to curtail the intermodel spread in climate sensitivity. Observations used to condition the models ought to be explicitly stated, or there is the risk of doubly calling on data for purposes of both calibration and evaluation. Conditioning the models upon individual expectation (e.g., anchoring to the Charney range of $3^{\circ} \pm 1.5^{\circ} C$, to the extent that it exists, greatly complicates statistical interpretation of the intermodel spread.Earth and Planetary Science

A Depth-Derived Pleistocene Age-Model: Uncertainty Estimates, Sedimentation Variability, and Nonlinear Climate Change

A new chronology of glaciation, spanning the last 780,000 years, is estimated from 21 marine sediment cores using depth as a proxy for time. To avoid biasing this ‘‘depth-derived’’ age estimate, the depth scale is first corrected for the effects of sediment compaction. To provide age uncertainty estimates, the spatial and temporal variability of marine sediment accumulation rates are estimated and modeled as an autocorrelated stochastic process. Depth-derived ages are estimated to be accurate to within ±9000 years, and within this uncertainty are consistent with the orbitally tuned age estimates. Nonetheless, the remaining differences between the depth and orbitally tuned chronologies produce important differences in the spectral domain. From the d18O record, using the depth-derived ages, we infer that there are weak nonlinearities involving the 100 kyr and obliquity frequency bands which generate interaction bands at sum and difference frequencies. If an orbitally tuned age model is instead applied, these interactions are suppressed, with the system appearing more nearly linear.Earth and Planetary Science

A Test for the Presence of Covariance Between Time-Uncertain Series of Data with Application to the Dongge Cave Speleothem and Atmospheric Radiocarbon Records

[1] Statistical measures of the relationships between time series are generally altered by the presence of errors in timing, i.e., when applied to time-uncertain series. For example, the covariance sampled between two time series which in truth covary will generally be decreased by errors in timing. Most previous work on this subject has sought to maximize some goodness of fit between time-uncertain series either heuristically or through more quantitative methods. However, there is a danger that unrelated records can be made to appear to covary by time adjustment. Here we propose a statistical test for the presence of covariance between time-uncertain series wherein the probability of obtaining a maximum covariance from randomly realized time-uncertain series is assessed using the theory of order statistics. The results of this analytical method provide insight into the influence of timing errors upon covariance and are shown to be consistent with results derived from a Monte Carlo procedure. We apply this methodology to evaluate the covariance between a time-uncertain stalagmite record and atmospheric radiocarbon during the Holocene and find, contradictory to previous interpretation, that there is insignificant covariance between the two at the 95% confidence level.Earth and Planetary Science

Orbital Tuning, Eccentricity, and the Frequency Modulation of Climatic Precession

The accuracy of geologic chronologies can, in principle, be improved through orbital tuning, the systematic adjustment of a chronology to bring the associated record into greater alignment with an orbitally derived signal. It would be useful to have a general test for the success of orbital tuning, and one proposal has been that eccentricity ought to covary with the amplitude envelope associated with precession variability recorded in tuned geologic records. A common procedure is to filter a tuned geologic record so as to pass precession period variability and compare the amplitude modulation of the resulting signal against eccentricity. There is a reasonable expectation for such a relationship to be found in paleoclimate records because the amplitude of precession forcing depends upon eccentricity. However, there also exists a relationship between eccentricity and the frequency of precession such that orbital tuning generates eccentricity-like amplitude modulation in filtered signals, regardless of the accuracy of the chronology or the actual presence of precession. This relationship results from the celestial mechanics governing eccentricity and precession and from the interaction between frequency modulation and amplitude modulation caused by filtering. When the eccentricity of Earth's orbit is small, the frequency of climatic precession undergoes large variations and less precession energy is passed through a narrow-band filter. Furthermore, eccentricity-like amplitude modulation is routinely obtained from pure noise records that are orbitally tuned to precession and then filtered. We conclude that the presence of eccentricity-like amplitude modulation in precession-filtered records does not support the accuracy of orbitally tuned time scales.Earth and Planetary Science

Rectification and Precession-Period Signals in the Climate System

Precession of the equinoxes has no effect on the mean annual insolation, but does modulate the amplitude of the seasonal cycle. In a linear climate system, there would be no energy near the 21,000 year precession period. It is only when a non-linear mechanism rectifies the seasonal modulation that precession-period variability appears. Such rectification can arise from physical processes within the climate system, for example a dependence of ice cover only on summer maximum insolation. The possibility exists, however, that the seasonality inherent in many climate proxies will produce precession-period variability in the records independent of any precession-period variability in the climate. One must distinguish this instrumental effect from true climate responses. Careful examination of regions without seasonal cycles, for example the abyssal ocean, and the use of proxies with different seasonal responses, might permit separation of physical from instrumental effects.Earth and Planetary Science

Feedback Between Deglaciation, Volcanism, and Atmospheric CO2

An evaluation of the historical record of volcanic eruptions shows that subaerial volcanism increases globally by two to six times above background levels between 12 ka and 7 ka, during the last deglaciation. Increased volcanism occurs in deglaciating regions. Causal mechanisms could include an increase in magma production owing to the mantle decompression caused by ablation of glaciers and ice caps or a more general pacing of when eruptions occur by the glacial variability. A corollary is that ocean ridge volcanic production should decrease with the rising sea level during deglaciation, with the greatest effect at slow spreading ridges. CO2 output from the increased subaerial volcanism appears large enough to influence glacial/interglacial CO2 variations. We estimate subaerial emissions during deglaciation to be between 1000 and 5000 Gt of CO2 above the long term average background flux, assuming that emissions are proportional to the frequency of eruptions. After accounting for equilibration with the ocean, this additional CO2 flux is consistent in timing and magnitude with ice core observations of a 40 ppm increase in atmospheric CO2 concentration during the second half of the last deglaciation. Estimated decreases in CO2 output from ocean ridge volcanoes compensate for only 20% of the increased subaerial flux. If such a large volcanic output of CO2 occurs, then volcanism forges a positive feedback between glacial variability and atmospheric CO2 concentrations: deglaciation increases volcanic eruptions, raises atmospheric CO2, and causes more deglaciation. Such a positive feedback may contribute to the rapid passage from glacial to interglacial periods. Conversely, waning volcanic activity during an interglacial could lead to a reduction in CO2 and the onset of an ice age. Whereas glacial/interglacial variations in CO2 are generally attributed to oceanic mechanisms, it is suggested that the vast carbon reservoirs associated with the solid Earth may also play an important role.Earth and Planetary Science

A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part 1: Development and Applications to Paleoclimate Reconstruction Problems

Reconstructing the spatial pattern of a climate field through time from a dataset of overlapping instrumental and climate proxy time series is a nontrivial statistical problem. The need to transform the proxy observations into estimates of the climate field, and the fact that the observed time series are not uniformly distributed in space, further complicate the analysis. Current leading approaches to this problem are based on estimating the full covariance matrix between the proxy time series and instrumental time series over a calibration interval and then using this covariance matrix in the context of a linear regression to predict the missing instrumental values from the proxy observations for years prior to instrumental coverage. A fundamentally different approach to this problem is formulated by specifying parametric forms for the spatial covariance and temporal evolution of the climate field, as well as observation equations describing the relationship between the data types and the corresponding true values of the climate field. A hierarchical Bayesian model is used to assimilate both proxy and instrumental datasets and to estimate the probability distribution of all model parameters and the climate field through time on a regular spatial grid. The output from this approach includes an estimate of the full covariance structure of the climate field and model parameters as well as diagnostics that estimate the utility of the different proxy time series. This methodology is demonstrated using an instrumental surface temperature dataset after corrupting a number of the time series to mimic proxy observations. The results are compared to those achieved using the regularized expectation maximization algorithm, and in these experiments the Bayesian algorithm produces reconstructions with greater skill. The assumptions underlying these two methodologies and the results of applying each to simple surrogate datasets are explored in greater detail in Part II.Earth and Planetary Science

Is There an Orbital Signal in the Polar Layered Deposits on Mars?

Do the polar layered deposits on Mars reflect orbital control or stochastic variability? It is first useful to determine whether an orbital signal would be detected, even if present. An estimate of the uncertainty in the time-depth relationship of the polar stratigraphy shows that nonlinearities in this relationship and noise in the signal will hamper or preclude detection of orbital forcing, even if layer composition is directly proportional to insolation. Indeed, stratigraphic sections of the north polar layered deposits reconstructed from spacecraft images yield no clear evidence of orbital control and are largely consistent with an autoregressive, stochastic formation process. There is, however, a broad rise in spectral power centered on a wavelength of roughly 1.6 m that appears in many of the stratigraphic sections. This bedding may record a time scale associated with processes internal to Mars' climate system, perhaps related to dust storms. Alternatively, if formed in response to variations in Mars' obliquity or orbital precession, the 1.6 m bedding implies that the ~1-km-thick upper north polar layered deposits formed over 30–70 Myr.Earth and Planetary Science

Reconciling Discrepancies between Uk37 and Mg/Ca Reconstructions of Holocene Marine Temperature Variability

Significant discrepancies exist between the detrended variability of late-Holocene marine temperatures inferred from Mg/Ca and Uk37 proxies, with the former showing substantially more centennial-scale variation than the latter. Discrepancies exceed that attributable to differences in location and persist across various calibrations, indicating that they are intrinsic to the proxy measurement. We demonstrate that these discrepancies can be reconciled using a statistical model that accounts for the effects of bioturbation, sampling and measurement noise, and aliasing of seasonal variability. The smaller number of individual samples incorporated into Mg/Ca measurements relative to Uk37 measurements leads to greater aliasing and generally accounts for the differences in the magnitude and distribution of variability. An inverse application of the statistical model is also developed and applied in order to estimate the spectrum of marine temperature variability after correcting for proxy distortions. The correction method is tested on surrogate data and shown to reliably estimate the spectrum of temperature variance when using high-resolution records. Applying this inverse method to the actual Mg/Ca and Uk37 data results in estimates of the spectrum of temperature variance that are consistent. This approach provides a basis by which to accurately estimate the distribution of intrinsic marine temperature variability from marine proxy records.Earth and Planetary Science