Numerical simulations of industrial and geophysical fluid flows cannot usually solve the exact Navier–Stokes equations. Accordingly, they encompass strong local errors. For some applications—like coupling models and measurements—these errors need to be accurately quantified, and ensemble forecast is a way to achieve this goal. This paper reviews the different approaches that have been proposed in this direction. A particular attention is given to the models under location uncertainty and stochastic advection by Lie transport. Besides, this paper introduces a new energy-budget-based stochastic subgrid scheme and a new way of parameterizing models under location uncertainty. Finally, new ensemble forecast simulations are presented. The skills of that new stochastic parameterization are compared to that of the dynamics under location uncertainty and of randomized-initial-condition methods.

工业和地球物理流体流动的数值模拟通常不能求解精确的Navier–Stokes方程。因此，它们包含很强的局部误差。对于某些应用程序（例如耦合模型和测量），需要准确量化这些误差，而总体预测是实现此目标的一种方法。本文回顾了在此方向上已提出的不同方法。在位置不确定性和Lie传输的随机对流作用下，模型应特别注意。此外，本文还介绍了一种基于能量预算的随机子网格方案，以及一种在位置不确定性下参数化模型的新方法。最后，提出了新的整体预报模拟。