Learning dominant physical processes with data-driven balance models

Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only applies in asymptotic regimes where there is a strict separation of scales in the physics. Here, we automate and generalize this approach to non-asymptotic regimes by introducing the idea of an equation space, in which different local balances appear as distinct subspace clusters. Unsupervised learning can then automatically identify regions where groups of terms may be neglected. We show that our data-driven balance models successfully delineate dominant balance physics in a much richer class of systems. In particular, this approach uncovers key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

High order numerical schemes for transport equations on bounded domains

This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite difference approximations of the transport equation with nonzero incoming boundary data that achieve the best possible convergence rate in the maximum norm. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at the incoming boundary. Optimal convergence rates are obtained by combining sharp stability estimates for extrapolation boundary conditions with numerical boundary layer expansions. We illustrate the results with the Lax-Wendroff and O3 schemes.

Marginal Instability and the Efficiency of Ocean Mixing

The mixing efficiency of stratified turbulence in geophysical fluids has been the subject of considerable controversy. A simple parameterization, devised decades ago when empirical knowledge was scarce, has held up remarkably well. The parameterization rests on the assumption that the flux coefficient Γ has the uniform value 0.2. This note provides a physical explanation for Γ = 0.2 in terms of the “marginal instability” property of forced stratified shear flows, and also sketches a path toward improving on that simple picture by examining cases where it fails.

A scale invariance criterion for geophysical fluids

<p>Scale invariance of geophysical fluids is investigated in terms of a scale invariance criterion. It was developed by Schaefer-Rolffs et al. (2015) based on the implication that each scale invariant subrange shall have its own criterion. Two particular cases are considered, namely the synoptic scales with a significant Coriolis term and a case at smaller scales where the anelastic approximation is valid. The first case is characterized by a constant enstrophy cascade, while in the second case small-scale fluctuations of density, pressure, and temperature are taken into account. In both cases, the respective scale invariance criteria are applied to simple parameterizations of turbulent diffusion. It is demonstrated that only dynamic approaches are scale invariant.</p>

Validation of Earth rotation time series by comparison of their sub-daily to sub-monthly excitation signal with simulated geophysical fluid model excitations

<p>Time-variations in the orientation of the solid Earth are largely governed by the exchange of angular momentum with the surface geophysical fluids of atmosphere, oceans, and the land surface. Modelled fields of atmospheric winds, atmospheric surface pressure, ocean currents, ocean bottom pressure, and terrestrial water storage allow calculating effective angular momentum (EAM) functions that can be compared to geodetic angular momentum functions (GAM) derived from observed Earth Orientation Parameters (EOP) via the Liouville equation. Especially in the high-frequency range, currently available global geophysical fluid models provide highly reliable information about angular momentum transfers that determine the orientation changes of the Earth.</p><p>In this contribution, we investigate the extent to which the modelled Earth rotation angular momentum functions processed at GFZ can be used to evaluate time series of EOP processed from different geodetic space techniques at periods between 2 and 60 days. We therefore compare the time series from various sources that are based on individual techniques (e.g., VLBI[TD1], GNSS, SLR, and DORIS) only, and also combined solutions that are processed at different institutions (e.g., JPL, GFZ, BKG[TD2], DGFI-TUM) or published by international services (e.g., IERS, IGS, IVS[TD3] ). By calculating differences from all possible pairs of EAM and GAM and by utilizing both band-pass filtering and spectral analysis techniques, we will elaborate the systematic differences between excitation functions from different sources that are expected to help identifying deficits in geodetic data processing and/or numerical modelling.</p>