A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Understanding El Niño in ocean-atmosphere general circulation models: progress and challenges

Determining how El Niño and its impacts may change over the next 10 to 100 years remains a difficult scientific challenge. Ocean–atmosphere coupled general circulation models (CGCMs) are routinely used both to analyze El Niño mechanisms and teleconnections and to predict its evolution on a broad range of time scales, from seasonal to centennial. The ability to simulate El Niño as an emergent property of these models has largely improved over the last few years. Nevertheless, the diversity of model simulations of present-day El Niño indicates current limitations in our ability to model this climate phenomenon and to anticipate changes in its characteristics. A review of the several factors that contribute to this diversity, as well as potential means to improve the simulation of El Niño, is presented.