Abstract
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.
Highlights
Geophysical fluid dynamics and other turbulent flows cover a wide range of spatial and temporal scales
The limited resolution of these numerical simulations introduces unknown errors which are continuously amplified during the course of the simulation and which compound with the measurement errors to the extent that the simulations model the true chaotic nature of fluid dynamics
This paper develops the Stochastic advection by Lie transport (SALT) and location uncertainty (LU) models which coexist in a single family of stochastic schemes
Summary
Geophysical fluid dynamics and other turbulent flows cover a wide range of spatial and temporal scales (see, e.g. FoxKemper, 2018). Numerical studies for the implementation of the SALT subgrid parameterization are discussed in Cotter et al (2019a, 2018) for a 2D Euler model and two-layer 2D QG dynamics. A first study on employing SALT dynamics for data assimilation is provided in Cotter et al (2019b) In both LU and SALT frameworks, the velocity is decomposed into a random large-scale component, w, and a timeuncorrelated component, σ B = σ dBt /dt. – Section 3 begins by presenting the deterministic and stochastic surface quasi-geostrophic (SQG) models, their numerical setup, and simulation parameters. These are followed by detailed discussions of uncertainty quantification skills in Sect. The discussion can focus on the parameterization choices in this timely application
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