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.

翻译：在近期工作中，作者开发了一套通用方法，用于校准流体动力学随机偏微分方程中的噪声，其中随机性被引入以参数化次网格尺度过程。在天气与气候预测的不确定性评估中，次网格尺度过程的随机参数化是必要的，用以表征由次网格尺度波动引起的系统性模型误差。先前的方法基于随机参数化增量服从正态分布的假设，采用主成分分析（PCA）技术。本文用生成式模型技术取代PCA技术，从而避免对增量施加额外约束。该方法在随机旋转浅水模型上进行测试，以模型的地势变量作为输入数据。数值模拟表明噪声确实呈现非高斯特性。生成式建模技术在均方根误差（RMSE）、连续等级概率评分（CRPS）和预报等级直方图指标上均取得良好结果。