Numerical bifurcation analysis of a 3D turing-type reaction–diffusion model

We perform a numerical study of a two-component reaction-diffusion model. By using numerical continuation methods, combined with state-of-the-art sparse linear and eigenvalue solvers, we systematically compute steady state solutions and analyze their stability and relations in both two and three space dimensions. The approach gives a more reliable and complete picture than previous efforts based on time integration schemes and is also typically much more efficient in terms of computing time. We are therefore able to produce a rich bifurcation diagram showing a variety of solution patterns and transitions

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

Using the VBARMS method in parallel computing

The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li, Saad and Sosonkina [NLAA, 2003] for solving general nonsymmetric linear systems. The parallel VBARMS solver can detect automatically exact or approximate dense structures in the linear system, and exploits this information to achieve improved reliability and increased throughput during the factorization. A novel graph compression algorithm is discussed that finds these approximate dense blocks structures and requires only one simple to use parameter. A complete study of the numerical and parallel performance of parallel VBARMS is presented for the analysis of large turbulent Navier-Stokes equations on a suite of three- dimensional test cases

The GEOTRACES Intermediate Data Product 2014

The GEOTRACES Intermediate Data Product 2014 (IDP2014) is the first publicly available data product of the international GEOTRACES programme, and contains data measured and quality controlled before the end of 2013. It consists of two parts: (1) a compilation of digital data for more than 200 trace elements and isotopes (TEIs) as well as classical hydrographic parameters, and (2) the eGEOTRACES Electronic Atlas providing a strongly inter-linked on-line atlas including more than 300 section plots and 90 animated 3D scenes. The IDP2014 covers the Atlantic, Arctic, and Indian oceans, exhibiting highest data density in the Atlantic. The TEI data in the IDP2014 are quality controlled by careful assessment of intercalibration results and multi-laboratory data comparisons at cross-over stations. The digital data are provided in several formats, including ASCII spreadsheet, Excel spreadsheet, netCDF, and Ocean Data View collection. In addition to the actual data values the IDP2014 also contains data quality flags and 1-? data error values where available. Quality flags and error values are useful for data filtering. Metadata about data originators, analytical methods and original publications related to the data are linked to the data in an easily accessible way. The eGEOTRACES Electronic Atlas is the visual representation of the IDP2014 data providing section plots and a new kind of animated 3D scenes. The basin-wide 3D scenes allow for viewing of data from many cruises at the same time, thereby providing quick overviews of large-scale tracer distributions. In addition, the 3D scenes provide geographical and bathymetric context that is crucial for the interpretation and assessment of observed tracer plumes, as well as for making inferences about controlling processes