Downscaling using CDAnet under Observational and Model Noises: The Rayleigh-Benard Paradigm

Abstract

Efficient downscaling of large ensembles of coarse-scale information is crucial in several applications, such as oceanic and atmospheric modeling. The determining form map is a theoretical lifting function from the low-resolution solution trajectories of an infinite-dimensional dissipative dynamical system to their corresponding fine-scale counterparts. Recently, Hammoud et al. (2022b) introduced CDAnet a physics-informed deep neural network as a surrogate of the determining form map for efficient downscaling. CDAnet was demonstrated to efficiently downscale noise-free coarse-scale data in a deterministic setting. Herein, the performance of well-trained CDAnet models is analyzed in a stochastic setting involving (i) observational noise, (ii) model noise, and (iii) a combination of observational and model noises. The analysis is performed employing the Rayleigh-Bénard convection paradigm, under three training conditions, namely, training with perfect, noisy, or downscaled data. The effects of observational and model noise on the CDAnet downscaled solutions are analyzed. Furthermore, the effects of the Rayleigh number and the spatial and temporal resolutions of the coarse-scale information on the downscaled fields are examined. The results suggest that the expected l 2 -error of CDAnet behaves quadratically in terms of the standard deviations of the observational and model noises. The results also suggest that CDAnet responds to uncertainties similar to CDA with an additional error overhead due to CDAnet being a surrogate model of the determining form map.