Person:

Huybers, Peter

Errors in the timing assigned to observations degrade estimates of the power spectrum in a complicated and nonlocal fashion. It is clear that timing errors will smear concentrations of spectral energy across a wide band of frequencies, leading to uncertainties in the analysis of spectral peaks. Less understood is the influence of timing errors upon the background continuum. We find that power law distributions of spectral energy are largely insensitive to errors in timing at frequencies much smaller than the Nyquist frequency, though timing errors do increase the uncertainty associated with estimates of power law scaling exponents. These results are illustrated analytically and through Monte Carlo simulation and are applied in the context of evaluating the power law behavior of oxygen isotopes obtained from Greenland ice cores. Age errors in layer counted ice cores are modeled as a discrete and monotonic random walk that includes the possibility of biases toward under- or overcounting. The δ(^{18}O_{ice}) record from the Greenland Ice Sheet Project 2 is found to follow a power law of (1.40 \pm 0.19) for periods between 0.7 and 50 ky, and equivalent results are also obtained for other Greenland ice cores.

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.

A number of previous observational studies have found that the waters of the deep Pacific Ocean have an age, or elapsed time since contact with the surface, of 700–1000 yr. Numerical models suggest ages twice as old. Here, the authors present an inverse framework to determine the mean age and its upper and lower bounds given Global Ocean Data Analysis Project (GLODAP) radiocarbon observations, and they show that the potential range of ages increases with the number of constituents or sources that are included in the analysis. The inversion requires decomposing the World Ocean into source waters, which is obtained here using the total matrix intercomparison (TMI) method at up to 2° × 2° horizontal resolution with 11 113 surface sources. The authors find that the North Pacific at 2500-m depth can be no younger than 1100 yr old, which is older than some previous observational estimates. Accounting for the broadness of surface regions where waters originate leads to a reservoir-age correction of almost 100 yr smaller than would be estimated with a two or three water-mass decomposition and explains some of the discrepancy with previous observational studies. A best estimate of mean age is also presented using the mixing history along circulation pathways. Subject to the caveats that inference of the mixing history would benefit from further observations and that radiocarbon cannot rule out the presence of extremely old waters from exotic sources, the deep North Pacific waters are 1200–1500 yr old, which is more in line with existing numerical model results.

We investigate the stability of marine ice sheets by coupling a gravitationally self-consistent sea level model valid for a self-gravitating, viscoelastically deforming Earth to a 1-D marine ice sheet-shelf model. The evolution of the coupled model is explored for a suite of simulations in which we vary the bed slope and the forcing that initiates retreat. We find that the sea level fall at the grounding line associated with a retreating ice sheet acts to slow the retreat; in simulations with shallow reversed bed slopes and/or small external forcing, the drop in sea level can be sufficient to halt the retreat. The rate of sea level change at the grounding line has an elastic component due to ongoing changes in ice sheet geometry, and a viscous component due to past ice and ocean load changes. When the ice sheet model is forced from steady state, on short timescales (<∼500 years), viscous effects may be ignored and grounding-line migration at a given time will depend on the local bedrock topography and on contemporaneous sea level changes driven by ongoing ice sheet mass flux. On longer timescales, an accurate assessment of the present stability of a marine ice sheet requires knowledge of its past evolution.

Part I presented a Bayesian algorithm for reconstructing climate anomalies in space and time (BARCAST). This method involves specifying simple parametric forms for the spatial covariance and temporal evolution of the climate field as well as ``observation equations?? describing the relationships between the data types and the corresponding true values of the climate field. As this Bayesian approach to reconstructing climate fields is new and different, it is worthwhile to compare it in detail to the more established regularized expectation? maximization (RegEM) algorithm, which is based on an empirical estimate of the joint data covariance matrix and a multivariate regression of the instrumental time series onto the proxy time series. The differing as- sumptions made by BARCAST and RegEM are detailed, and the impacts of these differences on the analysis are discussed. Key distinctions between BARCAST and RegEM include their treatment of spatial and temporal covariance, the prior information that enters into each analysis, the quantities they seek to impute, the end product of each analysis, the temporal variance of the reconstructed field, and the treatment of uncertainty in both the imputed values and functions of these imputations. Differences between BARCAST and RegEM are illustrated by applying the two approaches to various surrogate datasets. If the assumptions inherent to BARCAST are not strongly violated, then in scenarios comparable to practical applications BARCAST results in reconstructions of both the field and the spatial mean that are more skillful than those produced by RegEM, as measured by the coefficient of efficiency. In addition, the uncertainty intervals produced by BARCAST are narrower than those estimated using RegEM and contain the true values with higher probability.

Ocean tracer distributions have long been used to decompose the deep ocean into constituent water masses, but previous inverse methods have generally been limited to just a few water masses that have been defined by a subjective choice of static property combinations. Through air?sea interaction and upper-ocean processes, all surface locations are potential sources of distinct tracer properties, and thus it is natural to define a distinct water type for each surface site. Here, a new box inversion method is developed to explore the contributions of all surface locations to the ocean interior, as well as the degree to which the observed tracer fields can be explained by a steady-state circulation with unchanging surface-boundary conditions. The total matrix intercomparison (TMI) method is a novel way to invert observations to solve for the pathways connecting every surface point to every interior point. In the limiting case that the circulation is steady and that five conservative tracers are perfectly observed, the TMI method unambiguously recovers the complete pathways in- formation, owing to the fact that each grid box has, at most, six neighbors. Modern-day climatologies of temperature, salinity, phosphate, nitrate, oxygen, and oxygen-18/oxygen-16 isotope ratios are simultaneously inverted at 4(^\circ \times 4^\circ) grid resolution with 33 vertical levels. Using boundary conditions at the surface and seafloor, the entire interior distribution of the observed tracers is reconstructed using the TMI method. Assuming that seafloor fluxes of tracer properties can be neglected, the method suggests that 25% or less of the water residing in the deep North Pacific originated in the North Atlantic. Integrating over the global ocean, the Southern Ocean is dominant, as the inversion indicates that almost 60% of the ocean volume originates from south of the Southern Hemisphere subtropical front.

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.

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.

An attempt is made to unravel the dual influences of seawater temperature and isotopic composition upon the oxygen-isotope records of benthic foraminifers from the deep Pacific ((δ^{18}O_{b})). Our approach is to estimate a non-linear transfer function between past sea level and (δ^{18}O_{b}) over the last two glacial cycles, with additional information from the mid-Pliocene. Combining this transfer function with the relationship between temperature and (δ^{18}O_{b}) permits a deconvolution of a (δ^{18}O_{b}) record from the deep Pacific into its temperature and sea-level constituents over the course of the Plio-Pleistocene. This deconvolution indicates that deep Pacific temperature is stable through much of the last glacial (MISs 4 through 2) and then increases by approximately 2 °C during the last deglaciation. This pattern of variability appears to generally be replicated every glacial cycle back to the mid-Pliocene, suggesting a pulse of warming in the deep Pacific on a ∼100 kyr time scale during the late Pleistocene. Thus, according to this partition, there is more ∼100 kyr variability in temperature than in ice variability. Spectral analysis reveals that this variability is likely the product of multiple obliquity cycles rather than a simple 100-kyr signal. The non-linear behaviour of deep ocean temperature, dominated by pulses at 100 kyr time scales, may identify it as a key player in governing the glacial cycles.

One of the many ways that climate change may affect human health is by altering the nutrient content of food crops. However, previous attempts to study the effects of increased atmospheric CO2 on crop nutrition have been limited by small sample sizes and/or artificial growing conditions. Here we present data from a meta-analysis of the nutritional contents of the edible portions of 41 cultivars of six major crop species grown using free-air CO2 enrichment (FACE) technology to expose crops to ambient and elevated CO2 concentrations in otherwise normal field cultivation conditions. This data, collected across three continents, represents over ten times more data on the nutrient content of crops grown in FACE experiments than was previously available. We expect it to be deeply useful to future studies, such as efforts to understand the impacts of elevated atmospheric CO2 on crop macro- and micronutrient concentrations, or attempts to alleviate harmful effects of these changes for the billions of people who depend on these crops for essential nutrients.