Assimilation of Written Climate and Weather Records into Paleoclimate Reanalysis using a Non-Linear Forward Model

Recent reanalysis products offer unprecedented insights on past climates, but the paleoclimatic proxies that they assimilate are unevenly distributed in space leading to substantial simulation uncertainties over certain regions. In that context, written climate and weather records -- or docu proxies --  covering the past 2,000 years offer promising insights to complement natural proxies. However, docu proxies are also subject to a range of biases and error sources, for instance related to the cultural, technological background of the author and the prevailing need to convert qualitative observation to quantitative data assimilation input. These challenges require careful consideration when assimilating docu proxy into climate products, many of which employ a Bayesian Hierarchical approach with a forward model intended to translate climate models' initial estimates into a space that is compatible with the (natural or docu) proxy. Currently, docu proxy assimilation uses multivariate linear models for this transition, but the presence of perception biases within docu proxies suggests that linearity assumptions may not be suitable. To address this, we propose a non-linear forward model that better replicates docu proxy characteristics, aiming for more accurate assimilation. Leveraging the DOCUCLIM database and Last Millennium Reanalysis, we assess the efficacy of this non-linear approach.