# Quantifying Age and Model Uncertainties in Paleoclimate Data and Dynamical Climate Models with a Joint Inferential Analysis

## TL;DR

This paper introduces a joint inferential approach to paleoclimate data analysis that simultaneously estimates age models, climate reconstructions, and model parameters, addressing uncertainties overlooked by traditional multi-stage methods.

## Contribution

It develops a comprehensive joint inferential framework for climate reconstruction, model calibration, and age estimation, improving accuracy over multi-stage approaches.

## Key findings

- Joint analysis captures full uncertainty in age and climate estimates.
- Results differ significantly from multi-stage analyses, affecting scientific conclusions.
- Age estimates align with previous studies but include full uncertainty quantification.

## Abstract

A major goal in paleoclimate science is to reconstruct historical climates using proxies for climate variables such as those observed in sediment cores, and in the process learn about climate dynamics. This is hampered by uncertainties in how sediment core depths relate to ages, how proxy quantities relate to climate variables, how climate models are specified, and the values of parameters in climate models. Quantifying these uncertainties is key in drawing well founded conclusions. Analyses are often performed in separate stages with, for example, a sediment core's depth-age relation being estimated as stage one, then fed as an input to calibrate climate models as stage two. Here, we show that such "multi-stage" approaches can lead to misleading conclusions. We develop a joint inferential approach for climate reconstruction, model calibration, and age model estimation. We focus on the glacial-interglacial cycle over the past 780 kyr, analysing two sediment cores that span this range. Our age estimates are largely in agreement with previous studies, but provides the full joint specification of all uncertainties, estimation of model parameters, and the model evidence. By sampling plausible chronologies from the posterior distribution, we demonstrate that downstream scientific conclusions can differ greatly both between different sampled chronologies, and in comparison with conclusions obtained in the complete joint inferential analysis. We conclude that multi-stage analyses are insufficient when dealing with uncertainty, and that to draw sound conclusions the full joint inferential analysis must be performed.