Abstract. Stochastic subgrid parameterizations enable ensemble forecasts of fluid dynamic systems and ultimately accurate data assimilation (DA). Stochastic advection by Lie transport (SALT) and models under location uncertainty (LU) are recent and similar physically based stochastic schemes. SALT dynamics conserve helicity, whereas LU models conserve kinetic energy (KE). After highlighting general similarities between LU and SALT frameworks, this paper focuses on their common challenge: the parameterization choice. We compare uncertainty quantification skills of a stationary heterogeneous data-driven parameterization and a non-stationary homogeneous self-similar parameterization. For stationary, homogeneous surface quasi-geostrophic (SQG; QG) turbulence, both parameterizations lead to high-quality ensemble forecasts. This paper also discusses a heterogeneous adaptation of the homogeneous parameterization targeted at a better simulation of strong straight buoyancy fronts.

中文翻译：

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Lie 输运和位置不确定性随机平流的数据驱动与自相似参数化

摘要。随机子网格参数化使流体动力学系统的集合预测成为可能，并最终实现准确的数据同化 (DA)。Lie 传输 (SALT) 的随机平流和位置不确定性 (LU) 下的模型是最近的类似基于物理的随机方案。SALT 动力学保存螺旋度，而 LU 模型保存动能 (KE)。在强调了 LU 和 SALT 框架之间的一般相似性之后，本文重点介绍了它们的共同挑战：参数化选择。我们比较了静态异构数据驱动参数化和非平稳同构自相似参数化的不确定性量化技巧。对于静止的、均匀的地表准地转 (SQG; QG) 湍流，两种参数化都可以产生高质量的集合预报。