Intellectual Merit: Stratigraphic alignment is the primary way in which long marine climate records (105-107years) are placed on a common age model. However, currently there are no techniques for quantifying the uncertainty associated with these alignments. This project will build probabilistic models of an automated stratigraphic alignment algorithm for paleoclimate records as a means of characterizing this uncertainty. The development of this uncertainty analysis is important because the relative timing of climate responses (derived from stratigraphic alignment) is frequently used to evaluate causal relationships within the climate system. Therefore, this study will also assess the effects of alignment uncertainty on these evaluations. Additionally, a probabilistic algorithm will be created for age model development through orbital tuning. The improved accuracy and error estimates for paleoclimate age models that result from this work will improve estimates of the climate system?s sensitivity to changes in radiative forcing.
The original software developed by PI L. Lisiecki uses dynamic programming to find the optimal alignment of paleoclimate records based on user-defined parameter settings and produces one best-fit alignment with no uncertainty analysis. The new version will provide users with alignments sampled in proportion to their probability and will provide error bars for the estimated relative ages at each point in the alignment. Specifically, this project will develop two probabilistic versions of the alignment algorithm (pairwise and multiple) in the form of (pair and profile) Hidden Markov models (HMM) and develop a probabilistic HMM for creating orbitally tuned age models for paleoclimate data. The algorithm for age model development will incorporate knowledge gained about sedimentation rate variability from the pair and profile HMM algorithms. All three algorithms will be applied to create a new stack model of benthic δ18O records (a proxy for global climate) with uncertainty estimates which include data noise, alignment uncertainty and age model uncertainty. This "probabilistic stack" is scientifically important because it will yield uncertainty estimates for a widely used measure of past climate change. This project also aims to develop statistical methods to characterize the shapes of the posterior distributions of stratigraphic alignments and orbital tuning. This alignment problem is in a large class of discrete high dimensional problems that often have complex multimodal solution spaces which are difficult to characterize. To date the characterization of these spaces has been limited to a point estimate(s) and Bayesian confidence limits around these high-D estimates. In this project novel methods will be developed for the identification of clusters from multiple modes in these high-D spaces and characterize them as specific probabilistic models using both direct samples from the posterior distribution and the probabilities of each sampled value. Given the limited utility of point estimates and confidence limits in such high-D spaces, these probabilistic characterizations of posterior spaces will greatly improve the ability to describe such posterior spaces. Broader Impacts: The current version of the alignment software developed by PI Lisiecki has been downloaded by users in many different countries and applied to a wide variety of data in many publications. The new software and δ18O stack with uncertainty analysis will be posted on the NOAA NCDC website, on Lisiecki's personal website, the Brown CCMB web server. The new software will improve stratigraphic alignments and estimation of their uncertainty, which ultimately will lead to a better understanding of the climate system and better climate change predictions. The alignment problem is one of many problems in discrete high-D inference, including: the prediction of RNA secondary structures; the characterization of segmental duplications in primate genomes; and stochastic context free grammars in linguistics. This work on the characterization of discrete high-D posterior spaces will have a direct impact in all of these other areas and beyond. This proposal will train undergraduate and graduate students and a post-doc in both stratigraphy and mathematical statistics. This proposal will also broaden participation of under-represented groups by supporting a female PI at the start of her career.
Intellectual merit: There is a growing demand for uncertainty assessment in climate and paleoclimate studies, driven in part by the need to assess the likelihood of various climate changes in the near future. There are, of course, many sources of uncertainty in paleoclimate reconstructions. For long climate records (>40,000 years) from ocean sediment cores, age estimates are a large source of uncertainty that has generally only been estimated qualitatively. However, age estimates are quite important if one wishes to understand the cause-and-effect sequence and rate of climate responses. Our work aimed to develop improved age models and quantitative age uncertainty estimates for two methods of estimating ages: (1) correlation between ocean sediment cores records and (2) correlation between the climate response and well-dated forcing mechanisms (changes in the seasonal distribution of solar radiation associated with Earth’s orbital geometry). This project was successful in generating uncertainty estimates for age models that use the first technique. We used an established statistical techniques (Hidden Markov models) and radiocarbon age estimates of sediment accumulation-rate variability to generate age uncertainty estimates for the correlation of paleoclimate records between ocean sediment cores. We found that relative age uncertainty typically ranges from 5000-15,000 years, depending on the resolution (sample spacing) of the records. Additionally, certain time intervals within individual records can have age uncertainties of 20,000-30,000 years. It is important to be aware of such large age uncertainties when trying to interpret the causes and consequences of climate responses during these intervals. An additional important application of our work is the ability to calculate the probability that a climate event observed in one sediment core occurs before or after an event observed in a different core. Which event occurred first or whether events are potentially simultaneous has important implications for trying to understand the causes of the climate events. With respect to developing uncertainty estimates for ages generated from the second technique (correlation with well-dated orbital changes), work is still on-going. Broader impacts: This grant provided support for an early-career faculty member, and provided professional training for two graduate students (both of whom have now received their PhDs) and a postdoctoral scholar. It additionally helped broaden participation of under-represented groups in the STEM fields as one faculty member, one graduate student, and the postdoctoral scholar were women. Our results were disseminated to the scientific community in prestigious peer-reviewed journals and at an international scientific conference. All current and future data and software products are/will be freely distributed to the public through university websites and the NOAA National Climatic Data Center.
