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Abstract. Robust, proxy-based reconstructions of relative sea-level (RSL) change are critical to distinguishing the processes that drive spatial and temporal sea-level variability. The relationships between individual proxies and RSL can be complex and are often poorly represented by traditional methods that assume Gaussian likelihood distributions. We develop a new statistical framework to estimate past RSL change based on nonparametric, empirical modern distributions of proxies in relation to RSL, applying the framework to corals and mangroves as an illustrative example. We validate our model by comparing its skill in reconstructing RSL and rates of change to two previous RSL models using synthetic time-series datasets based on Holocene sea-level data from South Florida. The new framework results in lower bias, better model fit, and greater accuracy and precision than the two previous RSL models. We also perform sensitivity tests using sea-level scenarios based on two periods of interest – meltwater pulses (MWPs) and the Holocene – to analyze the sensitivity of the statistical reconstructions to the quantity and precision of proxy data; we define high-precision indicators, such as mangroves and the reef-crest coral Acropora palmata, with 2σ vertical uncertainties within ± 3 m and lower-precision indicators, such as Orbicella spp., with 2σ vertical uncertainties within ± 10 m. For reconstructing rapid rates of change in RSL of up to ∼ 40 m kyr−1, such as those that may have characterized MWPs during deglacial periods, we find that employing the nonparametric model with 5 to 10 high-precision data points per kiloyear enables us to constrain rates to within ± 3 m kyr−1 (1σ). For reconstructing RSL with rates of up to ∼ 15 m kyr−1, as observed during the Holocene, we conclude that employing the model with 5 to 10 high-precision (or a combination of high- and low-precision) data points per kiloyear enables precise estimates of RSL within ±∼ 2 m (2σ) and accurate RSL reconstructions with errors ≲ 0.7 m. Employing the nonparametric model with only lower-precision indicators also produces fairly accurate estimates of RSL with errors ≲1.50 m, although with less precision, only constraining RSL to ±∼ 3–4 m (2σ). Although the model performs better than previous models in terms of bias, model fit, accuracy, and precision, it is computationally expensive to run because it requires inverting large matrices for every sample. The new model also provides minimal gains over similar models when a large quantity of high-precision data are available. Therefore, we recommend incorporating the nonparametric likelihood distributions when no other information (e.g., reef facies or epibionts indicative of shallow-water environments to refine coral elevational uncertainties) or no high-precision data are available at a location or during a given time period of interest. 

Abstract. The penultimate deglaciation (PDG, ∼138–128 thousand years before present, hereafter ka) is the transition fromthe penultimate glacial maximum (PGM)to the Last Interglacial (LIG, ∼129–116 ka).The LIG stands out as one of the warmest interglacials of the last 800 000 years (hereafter kyr),with high-latitude temperature warmer than today and global sea level likely higher by at least 6 m.Considering the transient nature of the Earth system,the LIG climate and ice-sheet evolution were certainly influenced by the changesoccurring during the penultimate deglaciation.It is thus importantto investigate, with coupled atmosphere–ocean general circulation models (AOGCMs),the climate and environmental response to the large changesin boundary conditions(i.e. orbital configuration, atmospheric greenhouse gas concentrations, ice-sheet geometry and associated meltwater fluxes) occurring during the penultimate deglaciation. A deglaciation working group has recently been set up as part of the Paleoclimate Modelling Intercomparison Project (PMIP) phase 4, with a protocolto perform transient simulations of the last deglaciation (19–11 ka; although the protocol covers 26–0 ka).Similar to the last deglaciation, the disintegration of continental ice sheets during the penultimate deglaciation led to significant changesin the oceanic circulation during Heinrich Stadial 11 (∼136–129 ka).However, the two deglaciations bear significant differences in magnitude and temporal evolution of climate and environmental changes. Here, as part of the Past Global Changes (PAGES)-PMIP working group on Quaternary interglacials (QUIGS), we propose a protocol to perform transient simulations of the penultimate deglaciationunder the auspices of PMIP4.This design includes time-varying changes in orbital forcing, greenhouse gas concentrations, continental ice sheets as well as freshwater input from the disintegration ofcontinental ice sheets.This experiment is designed for AOGCMs to assessthe coupled response of the climate system to all forcings.Additional sensitivity experiments are proposed to evaluate the response to each forcing.Finally, a selection of paleo-records representing different parts of the climate system is presented, providing an appropriatebenchmark for upcoming model–data comparisons across the penultimate deglaciation.