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.

近期工作中，作者们开发了一种通用方法，用于校准流体动力学随机偏微分方程中的噪声，其中随机性是用于参数化子网格尺度过程的。该方法在天气和气候预测的不确定性估计中需要随机参数化子网格尺度波动引起的系统模型误差的表示。本文中，PCA 技术被生成模型技术取代，这使我们能够避免对增量施加额外的约束。该方法在使用模型的高度变量作为输入数据的随机旋转浅水模型上进行了测试，数值模拟表明噪声确实是非高斯分布的。生成模型技术给出了良好的 RMSE、CRPS 分数和预测等级直方图结果。

随机旋转浅水噪声的生成建模

Generative Modelling of Stochastic Rotating Shallow Water Noise

Stochastic parameterizations account for uncertainty in the representation of
unresolved sub-grid processes by sampling from the distribution of possible
sub-grid forcings. Some existing stochastic parameterizations utilize
data-driven approaches to characterize uncertainty, but these approaches
require significant structural assumptions that can limit their scalability.
Machine learning models, including neural networks, are able to represent a
wide range of distributions and build optimized mappings between a large number
of inputs and sub-grid forcings. Recent research on machine learning
parameterizations has focused only on deterministic parameterizations. In this
study, we develop a stochastic parameterization using the generative
adversarial network (GAN) machine learning framework. The GAN stochastic
parameterization is trained and evaluated on output from the Lorenz '96 model,
which is a common baseline model for evaluating both parameterization and data
assimilation techniques. We evaluate different ways of characterizing the input
noise for the model and perform model runs with the GAN parameterization at
weather and climate timescales. Some of the GAN configurations perform better
than a baseline bespoke parameterization at both timescales, and the networks
closely reproduce the spatio-temporal correlations and regimes of the Lorenz
'96 system. We also find that in general those models which produce skillful
forecasts are also associated with the best climate simulations.

本研究使用生成对抗网络（GAN）机器学习框架开发了随机参数化模型，通过评价天气和气候时间尺度上的模型运行结果，发现一些 GAN 配置表现更好，能够紧密地再现 Lorenz'96 系统的时空相关性和模式。