Generative Modelling of Stochastic Rotating Shallow Water Noise

• URL: http://arxiv.org/abs/2403.10578v1
• Date: Fri, 15 Mar 2024 09:30:29 GMT
• Title: Generative Modelling of Stochastic Rotating Shallow Water Noise
• Authors: Dan Crisan, Oana Lang, Alexander Lobbe,
• Abstract summary: This paper develops a generic methodology for calibrating the noise in fluid dynamics partial equations where the differentiality was introduced to parametrize subgrid-scale processes. The parameterization of sub-grid scale processes is required in the estimation of uncertainty in weather and climate predictions, to represent systematic model errors arising from subgrid-scale fluctuations. The methodology is tested on a rotating shallow water model with the elevation variable of the model used as input data. The numerical simulations show that the noise is indeed non-Gaussian.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent work, the authors have developed a generic methodology for calibrating the noise in fluid dynamics stochastic partial differential equations where the stochasticity was introduced to parametrize subgrid-scale processes. The stochastic parameterization of sub-grid scale processes is required in the estimation of uncertainty in weather and climate predictions, to represent systematic model errors arising from subgrid-scale fluctuations. The previous methodology used a principal component analysis (PCA) technique based on the ansatz that the increments of the stochastic parametrization are normally distributed. In this paper, the PCA technique is replaced by a generative model technique. This enables us to avoid imposing additional constraints on the increments. The methodology is tested on a stochastic rotating shallow water model with the elevation variable of the model used as input data. The numerical simulations show that the noise is indeed non-Gaussian. The generative modelling technology gives good RMSE, CRPS score and forecast rank histogram results.

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