Probabilistic Stack of 180 Plio-Pleistocene Benthic δ18O Records Constructed Using Profile Hidden Markov Models

Abstract:

Stratigraphic alignment is the primary way in which long marine climate records are placed on a common age model. We previously presented a probabilistic pairwise alignment algorithm, HMM-Match, which uses hidden Markov models to estimate alignment uncertainty and apply it to the alignment of benthic δ¹⁸O records to the “LR04” global benthic stack of Lisiecki and Raymo (2005) (Lin et al., 2014). However, since the LR04 stack is deterministic, the algorithm does not account for uncertainty in the stack. Here we address this limitation by developing a probabilistic stack, HMM-Stack. In this model the stack is a probabilistic inhomogeneous hidden Markov model, a.k.a. profile HMM. The HMM-stack is represented by a probabilistic model that “emits” each of the input records (Durbin et al., 1998). The unknown parameters of this model are learned from a set of input records using the expectation maximization (EM) algorithm. Because the multiple alignment of these records is unknown and uncertain, the expected contribution of each input point to each point in the stack is determined probabilistically. For each time step in the HMM-stack, δ¹⁸O values are described by a Gaussian probability distribution. Available δ¹⁸O records (N=180) are employed to estimate the mean and variance of δ¹⁸O at each time point. The mean of HMM-Stack follows the predicted pattern of glacial cycles with increased amplitude after the Pliocene-Pleistocene boundary and also larger and longer cycles after the mid-Pleistocene transition. Furthermore, the δ¹⁸O variance increases with age, producing a substantial loss in the signal-to-noise ratio. Not surprisingly, uncertainty in alignment and thus estimated age also increase substantially in the older portion of the stack.