Observation Error Estimation in Climate Proxies with Data Assimilation and Innovation Statistics

Data assimilation (DA) has been successfully applied to reconstruct paleoclimate. DA statistically combines model simulations and climate proxies based on their error sizes and distributions Therefore, these errors play a crucial role in DA to work properly. However, they have been treated rather crudely in previous studies, especially when the proxies are assimilated directly. This study aims to improve the paleoclimate reconstruction skill by estimating observation errors accurately. For this purpose, offline data assimilation experiments for the last 100 years were conducted. Here, stable water isotope ratios recorded in ice cores, tree ring cellulose, and corals were assimilated. We first show the reconstruction skills' sensitivity to the observation errors and then, we estimate observation errors using innovation statistics. Lastly, we show the impact of estimating observation errors on reconstruction skills.