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This framework generates spatially coherent uncertainty fields that effectively capture variability related to atmospheric flow and orographic features. By harnessing the probabilistic capabilities inherent in diffusion models, DDPM-ML is able to learn intricate uncertainty structures from ensemble data and reconstruct the cross-scale uncertainty relationships between the coarser-resolution ERA5 ensemble data assimilation (ERA-EDA) and the finer-resolution CARRA2  dataset. Comprehensive details regarding the methodology, input data, and uncertainty quantification procedures are provided in this documentation of the method:https://confluence.ecmwf.int/display/CKB/Copernicus+ Copernicus pan-Arctic + Regional +Reanalysis+%28CARRA2%29%3A+Uncertainty+Estimation+Reanalysis (CARRA2): Uncertainty estimation method

Upon learning the uncertainty structures via the DDPM-ML framework, uncertainty estimates can be generated for the deterministic CARRA2 reanalysis. The trained model produces flow-dependent uncertainty fields by downscaling ERA5 ensemble information onto the high-resolution CARRA2 grid and its associated orography. Although applying this approach to the entire 40-year CARRA2 record presents significant computational challenges, we demonstrate the methodology using data for 2019. In the absence of an intrinsic ensemble prediction system for CARRA2, this dataset represents a pragmatic advancement toward providing uncertainty information to the CARRA2 user community.

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