A barotropic global ocean model and its parallel implementation on unstructured grids

Unstructured grids can represent the complex geometry of the ocean basin with high fidelity. The lack of development tools supporting irregular grid problems discourages the use of such grids on parallel architectures. The state of the art ocean models are based on logically rectangular grids which makes it difficult to fit the complex ocean boundaries. In this pa- per,we demonstrate the use of unstructured triangular grids for solving a barotropic ocean model in spherical geometry with realistic continental boundaries. The model is based on the shallow water equations with a Coriolis force. A realistic wind forcing and a simple bottom friction term are also included. The numerical method is a cell based upwind finite volume scheme with explicit time stepping. From a parallelization point of view, that means there is only a nearest neighbour communication. A heuristic domain partitioning method was employed to distribute the load among processors. The resulting decomposition resembles 2D grid topo- logy with some long distance communication paths. The model was im- plemented using the PVM message passing library and tested on a cluster of workstations and on an IBM SP2

A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism

Acknowledgments This work was partly supported by joint Engineering and Physical Science Research Council (EPSRC) UK and Technology Foundation STW Netherlands funded SINBAD (EP/J005541/1) project. P. Zheng was supported by the China Scholarship Council during his four-year PhD study at the University of Liverpool. We would like to thank Prof. C.S. Chen of the University of Massachusetts-Dartmouth for providing the source code of FVCOM and also the SWAN developers for developing and providing this open source code. We would also like to thank the staff and personnel involved in collecting and maintaining the DUCK’94 experiment dataset and the anonymous reviewers for their constructive comments and suggestions. Computational support was provided by the Chadwick High Performance Computer at University of Liverpool and also the facilities of N8 HPC Centre of Excellence, provided and funded by the N8 consortium and EPSRC (EP/K000225/1).Peer reviewedPublisher PD

The Oceanographic Multipurpose Software Environment (OMUSE v1.0)

In this paper we present the Oceanographic Multipurpose Software Environment (OMUSE). OMUSE aims to provide a homogeneous environment for existing or newly developed numerical ocean simulation codes, simplifying their use and deployment. In this way, numerical experiments that combine ocean models representing different physics or spanning different ranges of physical scales can be easily designed. Rapid development of simulation models is made possible through the creation of simple high-level scripts. The low-level core of the abstraction in OMUSE is designed to deploy these simulations efficiently on heterogeneous high-performance computing resources. Cross-verification of simulation models with different codes and numerical methods is facilitated by the unified interface that OMUSE provides. Reproducibility in numerical experiments is fostered by allowing complex numerical experiments to be expressed in portable scripts that conform to a common OMUSE interface. Here, we present the design of OMUSE as well as the modules and model components currently included, which range from a simple conceptual quasi-geostrophic solver to the global circulation model POP (Parallel Ocean Program). The uniform access to the codes' simulation state and the extensive automation of data transfer and conversion operations aids the implementation of model couplings. We discuss the types of couplings that can be implemented using OMUSE. We also present example applications that demonstrate the straightforward model initialization and the concurrent use of data analysis tools on a running model. We give examples of multiscale and multiphysics simulations by embedding a regional ocean model into a global ocean model and by coupling a surface wave propagation model with a coastal circulation model

Prospects for improving the representation of coastal and shelf seas in global ocean models

Accurately representing coastal and shelf seas in global ocean models represents one of the grand challenges of Earth system science. They are regions of immense societal importance through the goods and services they provide, hazards they pose and their role in global-scale processes and cycles, e.g. carbon fluxes and dense water formation. However, they are poorly represented in the current generation of global ocean models. In this contribution, we aim to briefly characterise the problem, and then to identify the important physical processes, and their scales, needed to address this issue in the context of the options available to resolve these scales globally and the evolving computational landscape. We find barotropic and topographic scales are well resolved by the current state-of-the-art model resolutions, e.g. nominal 1∕12°, and still reasonably well resolved at 1∕4°; here, the focus is on process representation. We identify tides, vertical coordinates, river inflows and mixing schemes as four areas where modelling approaches can readily be transferred from regional to global modelling with substantial benefit. In terms of finer-scale processes, we find that a 1∕12° global model resolves the first baroclinic Rossby radius for only  ∼ 8% of regions  < 500m deep, but this increases to  ∼ 70% for a 1∕72° model, so resolving scales globally requires substantially finer resolution than the current state of the art. We quantify the benefit of improved resolution and process representation using 1∕12° global- and basin-scale northern North Atlantic nucleus for a European model of the ocean (NEMO) simulations; the latter includes tides and a k-ε vertical mixing scheme. These are compared with global stratification observations and 19 models from CMIP5. In terms of correlation and basin-wide rms error, the high-resolution models outperform all these CMIP5 models. The model with tides shows improved seasonal cycles compared to the high-resolution model without tides. The benefits of resolution are particularly apparent in eastern boundary upwelling zones. To explore the balance between the size of a globally refined model and that of multiscale modelling options (e.g. finite element, finite volume or a two-way nesting approach), we consider a simple scale analysis and a conceptual grid refining approach. We put this analysis in the context of evolving computer systems, discussing model turnaround time, scalability and resource costs. Using a simple cost model compared to a reference configuration (taken to be a 1∕4° global model in 2011) and the increasing performance of the UK Research Councils' computer facility, we estimate an unstructured mesh multiscale approach, resolving process scales down to 1.5km, would use a comparable share of the computer resource by 2021, the two-way nested multiscale approach by 2022, and a 1∕72° global model by 2026. However, we also note that a 1∕12° global model would not have a comparable computational cost to a 1° global model in 2017 until 2027. Hence, we conclude that for computationally expensive models (e.g. for oceanographic research or operational oceanography), resolving scales to  ∼ 1.5km would be routinely practical in about a decade given substantial effort on numerical and computational development. For complex Earth system models, this extends to about 2 decades, suggesting the focus here needs to be on improved process parameterisation to meet these challenges

The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model

The Finite Element Sea Ice-Ocean Model (FESOM) is the first global ocean general circulation model based on unstructured-mesh methods that has been developed for the purpose of climate research. The advantage of unstructured-mesh models is their flexible multi-resolution modelling functionality. In this study, an overview of the main features of FESOM will be given; based on sensitivity experiments a number of specific parameter choices will be explained; and directions of future developments will be outlined. It is argued that FESOM is sufficiently mature to explore the benefits of multi-resolution climate modelling and that its applications will provide information useful for the advancement of climate modelling on unstructured meshes

Simple algorithms to compute meridional overturning and barotropic streamfunctions on unstructured meshes

Abstract. Computation of barotropic and meridional overturning streamfunctions for models formulated on unstructured meshes is commonly preceded by interpolation to a regular mesh. This operation destroys the original conservation, which can be then artificially imposed to make the computation possible. An elementary method is proposed that avoids interpolation and preserves conservation in a strict model sense. The method is described as applied to the discretization of the Finite volumE Sea ice – Ocean Model (FESOM2) on triangular meshes. It, however, is generalizable to colocated vertex-based discretization on triangular meshes and to both triangular and hexagonal C-grid discretizations. </jats:p

Das unstetige Galerkinverfahren für Strömungen mit freier Oberfläche und im Grundwasserbereich in geophysikalischen Anwendungen

Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory. Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing. This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.Für viele geophysikalische Anwendungen spielen Strömungen mit freier Oberfläche und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch für diese Anwendungsszenarien sind große Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit beträchtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten. Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an Flexibilität und sind für paralleles Rechnen gut geeignet. Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher für Strömungen mit freier Oberfläche und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete Stabilitätsanalyse des gekoppelten Modells

A global unstructured, coupled, high-resolution hindcast of waves and storm surge

Accurate information on waves and storm surges is essential to understand coastal hazards that are expected to increase in view of global warming and rising sea levels. Despite the recent advancement in development and application of large-scale coastal models, nearshore processes are still not sufficiently resolved due to coarse resolutions, transferring errors to coastal risk assessments and other large-scale applications. Here we developed a 50-year hindcast of waves and storm surges on an unstructured mesh of >650,000 nodes with an unprecedented resolution of 2-4 km at the global coast. Our modelling system is based on the circulation model SCHISM that is fully coupled with the WWM-V (WindWaveModel) and is forced by surface winds, pressure, and ice coverage from the ERA5 reanalysis. Results are compared with observations from satellite altimeters, tidal gauges and buoys, and show good skill for both Sea Surface Height (SSH) and Significant Wave Height (Hs), and a much-improved ability to reproduce the nearshore dynamics compared with previous, lower-resolution studies. Besides SSH, the modelling system also produces a range of other wave-related fields at each node of the mesh with a time step of 3 hours, including the spectral parameters of the first three largest energy peaks. This dataset offers the potential for more accurate global-scale applications on coastal hazard and ris