Observation error estimation in climate proxies with data assimilation and innovation statistics

Abstract. Data assimilation (DA) has been successfully applied in paleoclimate reconstruction. DA combines model simulations and climate proxies based on their error sizes. Therefore, the error information is crucial for DA to work optimally. However, little attention has been paid to the observation errors in the previous studies, especially when the proxies are assimilated directly. This study assessed the feasibility of innovation statistics, a method developed for numerical weather prediction, for estimating observation errors in climate reconstruction and its impact on reconstruction skills. For this purpose, we conducted offline-DA experiments over 1870–2000. Here, we assimilated stable water isotope records from ice cores, tree-ring cellulose, and corals. We found that the innovation statistics-based approach correctly estimated the observation errors, even with the offline-DA scheme. Although the accuracy of the estimation depended on the sample size and accuracy of the prior error covariance, the estimation generally improved the reconstruction skills. The reconstruction skills with the estimated observation errors were comparable to those with errors defined differently. In contrast with those other methods, however, the innovation statistics-based approach offers an objective and systematic way to estimate observation errors with light computational cost. As such, the innovation statistics-based approach should contribute to improving the reconstruction skills and observation networks.