Development of regional oceanic and atmospheric modeling
Patrick Marchesiello, Gildas Cambon, Laurent Debreu, Pierrick Penven, Jerome Lefevre, Florian Lemarie
In 2008, the developers of oceanic models from various French institutes (INRIA, IRD, CNRS, Ifremer, SHOM) participated in a first national meeting (Coordinator: L. Debreu, Autrans, October 2008). One objective of this meeting was to unite our efforts and aim for a joint project: COMODO. The French branch of the Regional Oceanic Modeling System, developed at IRD (in collaboration with INRIA) and based at LEGOS, plays an essential role in this joint venture. The first appeal of the model is the sophistication of its dynamic core based on high order numerical methods that minimize the effects of dispersion and diffusion errors, with special care to diapycnal diffusion. The IRD version of ROMS uses the AGRIF library for efficient 2-way nesting (at the fast mode level; figure above). In addition, great efforts are devoted to the model's accessibility. This strategy has lead us to a community of hundreds of users around the world, many in southern countries.
The development of numerical methods with finite differences is guided by a tradeoff between accuracy and cost. In a paper by Sanderson (1998): "order and resolution for computational ocean dynamics", it is shown that the optimal discretization order of accuracy for three-dimensional oceanic models is the fifth order. ROMS and WRF regional models are some of the best examples, for the ocean and the atmosphere respectively. These theoretical considerations have put a limit on the development of finite difference methods. In the future, refinements may be less expected from formal order of accuracy than actual accuracy of space-time numerical schemes. Progress will also be related to the development of physical parameterizations and couplings between various environments, including the wave field and atmosphere.
One aspect of numerical analysis that is of particular interest to us is the assessment of diffusion mechanisms in the context of scheme order, turbulent cascade and submesoscale modeling. The goal is to advance fundamental understanding of the processes of numerical diffusion, define effective resolution of models based on the statistical patterns and contribute to design models for future generation. Follow this link ...
An aspect that remains problematic in regional models is related to the treatment of topography. Terrain-following (sigma) coordinates propose proper bottom boundary conditions that are not subject to any approximation due to discretization, as opposed to the case of geopotential coordinates. This coordinate allows flow sensitivity to the structure of the seabed, such as slope-current interactions, internal tides generation, or benthic boundary layer dynamics. We have shown the fundamental role of topography in few regions and at different scales (Marchesiello et al, 1998; Marchesiello and Middleton, 2000; Marchesiello et al., 2003,. Couvelard et al, 2008), which confirmed the value of sigma coordinates.
But sigma coordinates are not without problems. After advances were made to the pressure gradient computation (Shchepetkin and McWilliams, 2003), our work has recently revealed a new challenge for ocean modeling (Marchesiello et al. 2009a). This is related to the Veronis effect, i.e., an excessive amount of spurious diapycnal diffusion. The Veronis effect is greatly amplified by the orientation of sigma levels with respect to the isopycnals. The effect becomes acceptable at very high resolution (<1 km), but at intermediate resolutions, the advective and diffusive parts of the advection scheme must be separated to redirect diffusion along isopycnals and thus correct the Veronis effect. This approach was consolidated by Lemarié et al. (2012) by including an implicit treatment of vertical fluxes, thus avoiding stability constraints (it effect it provided the first isopycnal hyperdiffusion scheme). But if this technique is efficient for linear schemes, it is not so for nonlinear monotonous schemes (FCT or TVD type schemes that are especially popular with biological modelers). We are thus testing new ideas while refining the actual schemes.
A major development to come is on air-sea coupling. We have addressed the physical problem in relation to cyclone activity in the South Pacific (Jullien et al., 2014), but numerical issues were addressed beforehand (thèse de Florian Lemarié). We used the regional atmospheric model WRF (Weather Research Forcast model) coupled to ROMS. Unlike usual strategies (asynchronous methods), the iterative method of Schwartz decomposition ensures the continuity of the solution to the coupled air-sea interface at an acceptable cost (avoiding using synchronous coupling at very high frequency). It proved important for the stability of the coupled solution.
Figure 1: Path and intensity of Hurricane Erika simulated by the WRF model. (a) forced model by fixed surface temperatures and (b) coupled model ROMS-WRF. Note the differences in intensity of the simulated cyclone and cooling of the ocean along the track of the cyclone.
In contrast, the usual "bulk" formulations of air-sea exchanges that we used so far was not developed on the basis of observations of extreme events (winds greater than 30 m/s). Recent observations show that waves have a significant but complex impact on the oceanic and atmospheric surface layers. In particular, young seas (high frequency waves) can increase the roughness of the ocean (Doyle, 2002), but the layer formed by foam patches ("foam layer") affect exchanges by forming a slippery layer at the interface (Powell et al. 2003). Similarly, sea-spray seems to intensify latent and sensible heat fluxes. Under these conditions, the roughness usually inferred from the work of Charnock in bulk formula is not suitable for extreme air-sea exchanges.
We are also continuing the implementation of wave-current interactions following McWilliams et al. (2004) and Uchiyama et al. (2010). Besides the importance of these interactions for assessing OA dynamics, the parameterization of momentum transfer between waves and currents will also be used to address issues of coastal vulnerability by violent events. Ultimately, we will propose a coupling at three components: air-sea-waves, using the generic coupler OASIS now implemented in ROMS, WRF and soon in WaveWatch.
- Lemarié F., 2009 : Algorithmes de Schwarz et couplage océan-atmosphère. Thèse de l’Université Joseph Fourier, Grenoble, France.
- Marchesiello P. L. Debreu and X. Couvelard, 2009: Spurious diapycnal mixing in terrain-following coordinate models: the problem and a solution. Ocean Modelling, 26, 156-169.
- Marchesiello, P., J.C. McWilliams, and A. Shchepetkin, 2001: Open boundary conditions for long-term integration of regional oceanic models. Ocean Modelling, 3, 1-20.
- Penven P., L. Debreu, P. Marchesiello, and J.C. McWilliams, 2006: Evaluation and application of the ROMS 1-way embedding procedure to the central california upwelling system. Ocean Modelling, 12, 157-187.
- Penven P., P. Marchesiello, L. Debreu, and J. Lefevre, 2008: Software tools for pre- and post-processing of oceanic regional simulations. Environ. Model. Softw., 23, 660-662.
- Sanderson, B. G., 1998: Order and resolution for computational ocean dynamics. J. Phys. Oceanogr., 28, 1271–1286.
- Shchepetkin, A., and J.C. McWilliams, 2005: The Regional Oceanic Modeling System: A split-explicit, free-surface, topography-following-coordinate ocean model. Ocean Modelling, 9, 347-404.
- Shchepetkin, A.F., and J.C. McWilliams, 2003: A method for computing horizontal pressure-gradient force in an ocean model with a non-aligned vertical coordinate. J. Geophys. Res., 108, C3, 3090.
- Skamarock, W. C., J. B. Klemp, 2007: A Time-Split Nonhydrostatic Atmospheric Model for Research and NWP Applications. J. Comp. Phys. special issue on environmental modeling.