Analysis and modeling under uncertainty are increasingly critical for robust scientific simulations. Physics-based model simulations cannot resolve the mathematical model exactly, typically leaving out fine scales, which are either approximated or not represented. This results in uncertainties in their outputs that need to be characterized. A variety of stochastic methods have been developed to address these errors and uncertainty in order to better describe complex systems. In this symposium we discuss new developments in sub-grid stochastic models, multiscale aspects, model reduction techniques, and the effect they have on Bayesian inversion and data assimilation applications.
08:30
Statistical space-time characterization of sub-grid air-sea exchanges variability including scale information
Julie Bessac | Argonne National Laboratory | United States
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Julie Bessac | Argonne National Laboratory | United States
Adam Monahan | University of Victoria | Canada
Hannah Christensen | University of Oxford | United Kingdom
Nils Weitzel | Karlsruhe Institute of Technology | Germany
We present a statistical space-time characterization of the sub-grid variability of air-sea exchanges driven by wind. Many physical phenomena happen at scales below the resolution of the discretization of the physics-based model; however, these phenomena interact with the resolved scales. Hence, quantifying the influence of the sub-grid scales on the resolved scales is needed to better represent the entire system. We evaluate the difference between the true turbulent fluxes and those calculated using area-averaged wind speeds. We investigate a space-time characterization of this discrepancy with the goal of developing a stochastic wind-flux parameterization. A locally stationary space-time statistical model is used to characterize and model this error process. The space-time structure is proposed in a scale-aware fashion meaning that the space-time correlation ranges depend on the considered resolution. The scale-aware capability enables to derive a stochastic parameterization at any given resolution and to characterize statistically the space-time structure of the error process across scales. The study is performed on high-resolution simulations on a domain that extends across the Indian Ocean into the West Pacific.
09:00
Machine learning for sub-grid parameterizations in Earth system and hydrodynamic simulations: Stochastic parameterization, uncertainty quantification, and online learning
Nathan Urban | Los Alamos National Laboratory | United States
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Nathan Urban | Los Alamos National Laboratory | United States
I discuss several applications of machine learning to enhance sub-grid parameterizations in atmosphere and ocean simulations: (1) Nonparametric conditional density estimation by using normalizing flows for cloud parameterization in global atmospheric models that is trained on cloud resolving simulation data; (2) Hybrid physical-Gaussian process parameterizations of vertical mixing in global ocean models that are trained on large eddy simulation data; and (3) a neural network representation of hydrodynamic artificial viscosity numerical schemes which, although not strictly a subgrid variability problem, suggests new approaches to online training of data-driven parameterizations by using differentiable programming.
09:30
Stochastic modelling of large-scale fluid flows
Etienne Memin | INRIA | France
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Etienne Memin | INRIA | France
I will describe a formalism, called modeling under location uncertainty (LU), to derive in a systematic way large-scale stochastic representations of fluid dynamics. This modeling takes into account the neglected small-scale effects in the evolution laws through the introduction of a random field. The resulting dynamics is built from a stochastic representation of the Reynolds transport theorem. We will show how to derive systematically stochastic representations of flow dynamics. We will give several examples of simulations obtained by such systems and how an ensemble of such realizations can be used in data assimilation or for uncertainty quantification. This formalism leads to turbulence modeling and provides (i) a natural subgrid tensor expression that represents the mixing of the resolved components by the unresolved components; (ii) a multiplicative random term associated to an energy backscattering; and (iii) a modified advection that depicts a so-called turbophoresis phenomena that tends to drive fluid particles from regions of high turbulence toward areas of lower turbulent kinetic energy. We will focus on this last term and show its relevance to describe several physical situations such as wall-law velocity profiles or wave mean-current interaction and the apparition of the so-called vortex force. This will put an emphasis on the importance of modeling the unresolved components' inhomogeneity.
10:00
- CANCELED - Towards A Probabilistic Earth-system model
Timothy Palmer | University of Oxford | United Kingdom
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Timothy Palmer | University of Oxford | United Kingdom
Kristian Strommen | University of Oxford | United Kingdom
The truncation of the true climate system to a finite grid introduces a large source of uncertainty from unresolved sub-grid scale processes. While parametrizations are usually developed to account for these unresolved processes, it relies on introducing a number of assumptions that are not always valid, effectively introducing an additional layer of uncertainty in any model prediction. In medium-range and seasonal forecasts using numerical models, the use of stochastic schemes has become widespread as a means to sample such uncertainties, leading to improved spread, errors and reliability of forecasts. Recent studies indicate that stochasticity can also improve the long-term projections, including the mean climate, variability and crucial dynamical processes. On the shorter time-scales, atmospheric variability dominates and hence the first stochastic schemes were implemented within the atmospheric component of models. The stochastic schemes, implemented within the coupled climate model EC-Earth, form the basis for the first `Probabilistic Earth-system model’, which is a model with stochasticity in all the major components. We will give an overview of the impact of stochasticity in climate models so far, followed by an introduction to this stochastic version of EC-Earth. The first results from climate simulations using this model are presented, showing notable improvements to many key mean state variables, including surface temperature, precipitation and cloud cover.