A two-way nesting framework for ocean models

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Highlights

  • We present a 2-way nesting framework using largely existing functionality in an ocean code.

  • Open boundary conditions are used to increase stability and avoid coupling at the barortopic level.

  • We test the framework in a baroclinic vortex test case.

  • We also test the framework in a real world application in the Great Barrier Reef.

Abstract

Two-way nesting is becoming a popular method to resolve limited area domains at high resolution. However, implementation of two-way nesting into ocean models is not a trivial process. We present an alternative two-way nesting framework that leverages off existing functionality present in many ocean codes, including arrays to store data exchanged between grids, data exchange protocols and re-gridding. An important element of this is the use of existing open boundary infrastructure to store and apply the data exchanged in two-way nesting, reduce specification error at the boundary and circumvent coupling at the barotropic levels. The resulting two-way system consists of models that operate in isolation of each other and can be considered autonomous in the sense that no overarching coupling infrastructure is required to orchestrate the two-way nesting, and models for respective grids can operate independently with communication achieved only via the sending and receiving of packets of self-describing information.

Introduction

Accurately capturing events at small scales in ocean models is best achieved by increasing the resolution of an ocean model. However, this increases computational demands through an increased number of cells to simulate and stability and accuracy constraints dictating the use of a small time-step. The throughput of high resolution models that cover large areas can be prohibitive, and the technique of nesting high resolution models in larger scale coarser resolution models is a popular approach to circumvent this issue. These models are usually one-way nested, where information only flows from the coarse resolution model (the parent grid) to the high resolution model (the child grid), e.g. Mason et al., 2010, Penven et al., 2006.

Recently, two-way nesting is becoming increasingly used, where information from the child is allowed to propagate back into the parent domain (e.g. Debreu et al., 2012, Cailleau et al., 2008, Jouanno et al., 2008). An excellent review of the issues surrounding two-way nesting can be found in Debreu and Blayo (2008). The process of two-way nesting requires a number of elements to be carried out, and this is typically handled by a coupler, e.g. AGRIF (Debreu et al., 2008).

AGRIF (Adaptive Grid Refinement In Fortran) is a package that facilitates programs written in Fortran to communicate information between parent and child grids, in both a one-way and two-way sense. AGRIF has been implemented in several ocean models, viz, ROMS (Debreu et al., 2012), NEMO (Jouanno et al., 2008) and OPA8.1 (Cailleau et al., 2008). AGRIF consists of a series of model-independent procedures (such as interpolation and update procedures, refinement, clustering and time-integration algorithms) and model-dependent routines that includes the replacement of the main time integration loop of the model with an AGRIF equivalent, and writing an interface routine that transforms the model's configuration file, controlled by keywords. The implementation of such a package into a new model is not a trivial process, however, it needs to be performed only once, after which the benefits of the AGRIF coupling can be realized. The disadvantage is that such a process often diverges ones model code from the core branch.

Many contemporary regional/coastal ocean models codes contain existing functionality that can be exploited to facilitate two-way nesting. In this paper we demonstrate this to be the case using the code described by Herzfeld (2006). This is a mode-split finite difference model based on Blumberg and Herring (1987), using an orthogonal curvilinear Arakawa C grid in the horizontal and ‘z’ or σ coordinates in the vertical. Leapfrog time stepping is used for momentum, and the model is explicit except for the vertical mixing which uses an implicit scheme. A variety of momentum and tracer advection, 2-equation turbulence and open boundary schemes may be used. The 2-way nesting framework developed using this model is applied to an idealized test domain and a real application to demonstrate its utility. The implementation of such a system requires little modification to existing code, and preserves the integrity of the core branch with full backward compatibility. It also results in a system that can leverage functionality inherent in the code that improves the 2-way nesting model solution. This is particularly true of the open boundary infrastructure, especially the application of open boundary algorithms designed to cope with specification error due to boundary data and interior solution mismatches, resulting in increased model stability. The two-way system is also autonomous, in the sense that no overarching coupling infrastructure is required to orchestrate the two-way nesting. The parent and child models run independently as stand-alone implementations (on the same or different processors or machines, using the same or potentially different model codes) without knowing of the other's existence. All communication is achieved only via the sending and receiving of packets of self-describing information.

In Section 2 we review the two-way nesting problem, and articulate the elements required for two-way nesting to operate. We then show how these elements can be accomplished within existing infrastructure inherent in the ocean model. An idealized test case that models the propagation of a baroclinic vortex is introduced in Section 3, after which we demonstrate the functionality of the two-way system. A real application is undertaken in Section 4 and concluding remarks are presented in Section 5 Discussion, 6 Conclusions.

Section snippets

The autonomous two-way system

A simplified view of two-way nesting involves the insertion of a high resolution child grid (ΩC) operating with a small time-step Δt in a coarser resolution parent grid (ΩP) using a longer time-step ΔT, and allowing information from both models to propagate freely over the interfaces of the grids. The procedure is similar to one-way nesting, where the parent model will advance an increment of time (typically ΔT) then the child model will perform many integrations up to this time using boundary

Baroclinic vortex test

The test case chosen to test the two-way nesting system is the baroclinic vortex described by Penven et al. (2006) and used by Debreu et al. (2012). A full description of the test case configuration can be found in Penven et al. (2006) and we summarize the main points here. A baroclinic vortex is embedded in the initial condition where a Gaussian distribution of pressure is imposed (elevated sea level and temperature) having an e-folding length scale of 60 km and initial velocities that are in

Real application

The eReefs initiative seeks to model the whole of the Great Barrier Reef (GBR) on Australia's east coast (Schiller et al., 2014). The hydrodynamic component of this initiative represents the first time that a three-dimensional model is applied at the whole reef scale, from Papua New Guinea to the NSW/QLD border. Many of the issues of interest to managers of the GBR relate to nutrient supply from the catchment into the GBR lagoon, and estuaries joining the GBR lagoon with the catchments are key

Discussion

This study presents a framework capable of performing two-way nesting, largely using existing infrastructure present in a modern ocean code base. While the framework accommodates the elements necessary for two-way nesting, it must still be optimally configured by the user to achieve stable and accurate solutions. This includes optimizing restriction operators, interface separation, conservation and sponge layers (as reported by Debreu et al., 2012); such optimisation is not addressed in detail

Conclusions

The aim of this paper is to contribute two new concepts to two-way nesting methodologies; 1) perform the mechanics of two-way nesting using existing in-code infrastructure without the requirement of overarching orchestration, and 2) use non-reflective open boundary conditions at the dynamic and feedback interfaces to improve the solution. The former has been demonstrated in an idealized and real environment, where in the idealized case a travelling baroclinic vortex is simulated and two-way

Acknowledgements

We gratefully acknowledge the eReefs sponsors for making this research possible. The eReefs project is a collaboration between the Great Barrier Reef Foundation, Bureau of Meteorology, Commonwealth Scientific and Industrial Research Organization, Australian Institute of Marine Science and the Queensland Government, supported by funding from the Australian and Queensland Governments, the BHP Billiton Mitsubishi Alliance and the Science and Industry Endowment Fund.

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