In recent years, machine learning (ML) has been proposed to devise
data-driven parametrisations of unresolved processes in dynamical numerical
models. In most cases, the ML training leverages high-resolution simulations to
provide a dense, noiseless target state. Our goal is to go beyond the use of
high-resolution simulations and train ML-based parametrisation using direct
data, in the realistic scenario of noisy and sparse observations.
The algorithm proposed in this work is a two-step process. First, data
assimilation (DA) techniques are applied to estimate the full state of the
system from a truncated model. The unresolved part of the truncated model is
viewed as a model error in the DA system. In a second step, ML is used to
emulate the unresolved part, a predictor of model error given the state of the
system. Finally, the ML-based parametrisation model is added to the physical
core truncated model to produce a hybrid model.
The DA component of the proposed method relies on an ensemble Kalman filter
while the ML parametrisation is represented by a neural network. The approach
is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled
ocean-atmosphere model. We show that in both cases the hybrid model yields
forecasts with better skill than the truncated model. Moreover, the attractor
of the system is significantly better represented by the hybrid model than by
the truncated model.

本文提出了一种基于机器学习和数据同化的方法，用于从具有噪声和稀疏观测的直接数据中训练基于参数化模型的机器学习模型，在 Lorenz 模型和 MAOOAM 模型中证明，相较于截断模型，该模型具有更好的对系统吸引子的预测能力和更好的预测技能。