Computationally efficient evaluation of Earth System Models in the presence of complex uncertainties

Comparing Earth System Model (ESM) simulations with in-situ, lab, and remote sensing measurements often involves analytically intractable uncertainty structures for example due to observational uncertainties, internal variability in the climate system, and limitations of ESMs. With increasing resolution of models, ensemble sizes, length of simulations, and number of observations, this can create computational bottlenecks. Making use of Monte Carlo techniques in a data cube architecture, we present a python package for efficient propagation of complex uncertainties in model-data comparison. Additionally, the package contains functionalities for visualizations of uncertainties and the computation of probabilistic score functions. Our focus is on measurement operators, in particular so-called proxy system models that map ESM output onto proxy measurements for transient paleoclimate simulations. Proxy system models contain multiple sources of autocorrelated and non-Gaussian uncertainties due to complex proxy-climate relationships, chronological uncertainties, and processes perturbing the recorded climate signal during the sedimentation of the proxy. Thereby, we connect data cube methods for processing climate simulations with analysis techniques for point data such as those stemming from time series of paleoclimate proxy records. We demonstrate our approach by quantifying the discrepancies of temperature and forest cover changes between global proxy networks and transient simulations from the Last Glacial Maximum to present-day. Given the ongoing shift in the paleoclimate modelling community from equilibrium time-slice towards long transient simulations, our work can help integrate the evaluation of simulations from the Paleoclimate Modelling Intercomparison Project (PMIP) into CMIP7 model benchmarking. Additionally, the implemented methods are transferable to other types of observations that are subject to analytically intractable uncertainty structures.