Transition Probabilities of Noise-induced Transitions of the Atlantic Ocean Circulation

The Atlantic Meridional Overturning Circulation (AMOC) is considered to be a tipping element of the climate system. As it cannot be excluded that the AMOC is in a multiple regime, transitions can occur due to atmospheric noise between the present-day state and a weaker AMOC state. For the first time, we here determine estimates of the transition probability of noise-induced transitions of the AMOC, within a certain time period, using a methodology from large deviation theory. We find that there are two types of transitions, with a partial or full collapse of the AMOC, having different transition probabilities. For the present-day state, we estimate the transition probability of the partial collapse over the next 100 years to be about 15%, with a high sensitivity of this probability to the surface freshwater noise amplitude

A Staggered Grid Multi-Level ILU for steady incompressible flows

We present a parallel fully coupled multi-level incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed in [1]. In this paper, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the wellknown 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

A staggered‐grid multilevel incomplete LU for steady incompressible flows

Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this article, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation

The Kuroshio Current in the North Pacific displays path changes on an interannual-to-decadal time scale. In an idealized barotropic quasi-geostrophic model of the double-gyre wind-driven circulation under stochastic wind-stress forcing, such variability can occur due to transitions between different equilibrium states. The high-dimensionality of the problem makes it challenging to determine the probability of these transitions under the influence of stochastic noise. Here we present a new method to estimate these transition probabilities, using a Dynamical Orthogonal (DO) field approach. In the DO approach, the solution of the stochastic partial differential equations system is decomposed using a Karhunen–Loève expansion and separate problems arise for the ensemble mean state and the so-called time-dependent DO modes. The original method is first reformulated in a matrix approach which has much broader application potential to various (geophysical) problems. Using this matrix-DO approach, we are able to determine transition probabilities in the double-gyre problem and to identify transition paths between the different states. This analysis also leads to the understanding which conditions are most favorable for transition

Symbiotic Ocean Modeling Using Physics-Controlled Echo State Networks

We introduce a “symbiotic” ocean modeling strategy that leverages data-driven and machine learning methods to allow high- and low-resolution dynamical models to mutually benefit from each other. In this work we mainly focus on how a low-resolution model can be enhanced within a symbiotic model configuration. The broader aim is to enhance the representation of unresolved processes in low-resolution models, while simultaneously improving the efficiency of high-resolution models. To achieve this, we use a grid-switching approach together with hybrid modeling techniques that combine linear regression-based methods with nonlinear echo state networks. The approach is applied to both the Kuramoto–Sivashinsky equation and a single-layer quasi-geostrophic ocean model, and shown to simulate short-term and long-term behavior better than either purely data-based methods or low-resolution models. By maintaining key flow characteristics, the hybrid modeling techniques are also able to provide higher quality initial conditions for high-resolution models, thereby improving their efficiency. Key Points We propose a symbiotic ocean modeling framework in which models of different complexities benefit from each other Unresolved processes are represented through hybrid machine learning methods using data from the symbiotic framework Hybrid correction strategies with imperfect physics as control input improve the representation of key long-term flow propertie