Gassmann A.,Max Planck Institute For Meteorologie
Journal of Computational Physics | Year: 2011
C-grid discretizations based on a hexagonal or triangular mesh can be investigated with the help of a planar trivariate coordinate system, where the vector components are either defined tangentially (hexagonal C-grid) or perpendicularly (triangular C-grid) to the coordinate lines. Inspecting the Helmholtz decomposition of a vector in case of the linearly dependent trivariate coordinate description reveals insights into the structure and stencil of the discretized divergence and vorticity on such grids. From a vector Laplacian, which is consistent with the Helmholtz decomposition, a general formulation for the inner product operator at grid edges can be derived. Thus, the vector reconstruction of the tangential wind for the Coriolis term in the shallow water equations can be given even for a slightly distorted tesselation as present on icosahedral spherical grids.Furthermore, a rigorous comparison of the triangular and the hexagonal C-grid linear shallow water equations is performed from a theoretical and also from an experimental viewpoint. It turns out that the additional degree of freedom in the height field in the triangular C-grid case compared to the hexagonal C-grid is responsible for the decoupling of divergence values on upward and downward directed triangles. This problem occurs especially for small Rossby deformation radii, and practically requires additional explicit diffusion. In contrast, the hexagonal C-grid discretization has remarkable similarity to the quadrilateral C-grid case in the wave dispersion properties and eigenvector structure. Numerical experiments performed with that option proved resilent. © 2011 Elsevier Inc.
Giraldo F.X.,Naval Postgraduate School, Monterey |
Restelli M.,Max Planck Institute For Meteorologie
International Journal for Numerical Methods in Fluids | Year: 2010
We extend the explicit in time high-order triangular discontinuous Galerkin (DG) method to semi-implicit (SI) and then apply the algorithm to the two-dimensional oceanic shallow water equations; we implement high-order SI time-integrators using the backward difference formulas from orders one to six. The reason for changing the time-integration method from explicit to SI is that explicit methods require a very small time step in order to maintain stability, especially for high-order DG methods. Changing the timeintegration method to SI allows one to circumvent the stability criterion due to the gravity waves, which for most shallow water applications are the fastest waves in the system (the exception being supercritical flow where the Froude number is greater than one). The challenge of constructing a SI method for a DG model is that the DG machinery requires not only the standard finite element-type area integrals, but also the finite volume-type boundary integrals as well. These boundary integrals pose the biggest challenge in a SI discretization because they require the construction of a Riemann solver that is the true linear representation of the nonlinear Riemann problem; if this condition is not satisfied then the resulting numerical method will not be consistent with the continuous equations. In this paper we couple the SI time-integrators with the DG method while maintaining most of the usual attributes associated with DG methods such as: high-order accuracy (in both space and time), parallel efficiency, excellent stability, and conservation. The only property lost is that of a compact communication stencil typical of time-explicit DG methods; implicit methods will always require a much larger communication stencil. We apply the new high-order SI DG method to the shallow water equations and show results for many standard test cases of oceanic interest such as: standing, Kelvin and Rossby soliton waves, and the Stommel problem. The results show that the new high-order SI DG model, that has already been shown to yield exponentially convergent solutions in space for smooth problems, results in a more efficient model than its explicit counterpart. Furthermore, for those problems where the spatial resolution is sufficiently high compared with the length scales of the flow, the capacity to use high-order (HO) time-integrators is a necessary complement to the employment of HO space discretizations, since the total numerical error would be otherwise dominated by the time discretization error. In fact, in the limit of increasing spatial resolution, it makes little sense to use HO spatial discretizations coupled with low-order time discretizations. Published in 2009 by John Wiley & Sons, Ltd.
Smith D.M.,UK Met Office |
Eade R.,UK Met Office |
Pohlmann H.,UK Met Office |
Pohlmann H.,Max Planck Institute For Meteorologie
Climate Dynamics | Year: 2013
There are two main approaches for dealing with model biases in forecasts made with initialized climate models. In full-field initialization, model biases are removed during the assimilation process by constraining the model to be close to observations. Forecasts drift back towards the model's preferred state, thereby re-establishing biases which are then removed with an a posterior lead-time dependent correction diagnosed from a set of historical tests (hindcasts). In anomaly initialization, the model is constrained by observed anomalies and deviates from its preferred climatology only by the observed variability. In theory, the forecasts do not drift, and biases may be removed based on the difference between observations and independent model simulations of a given period. Both approaches are currently in use, but their relative merits are unclear. Here we compare the skill of each approach in comprehensive decadal hindcasts starting each year from 1960 to 2009, made using the Met Office decadal prediction system. Both approaches are more skilful than climatology in most regions for temperature and some regions for precipitation. On seasonal timescales, full-field initialized hindcasts of regional temperature and precipitation are significantly more skilful on average than anomaly initialized hindcasts. Teleconnections associated with the El Niño Southern Oscillation are stronger with the full-field approach, providing a physical basis for the improved precipitation skill. Differences in skill on multi-year timescales are generally not significant. However, anomaly initialization provides a better estimate of forecast skill from a limited hindcast set. © 2013 Crown Copyright.
Stevens B.,Max Planck Institute For Meteorologie
Journal of Fluid Mechanics | Year: 2010
Mixing processes at cloud boundaries are thought to play a critical role in determining cloud lifetime, spatial extent and cloud microphysical structure. High-fidelity direct numerical simulations by Mellado (J. Fluid Mech., 2010, this issue, vol. 660, pp. 5-36) show, for the first time, the character and potency of a curious instability that may arise as a result of molecular mixing processes at cloud boundaries, an instability which until now has been thought by many to control the distribution of climatologically important cloud regimes. © 2010 Cambridge University Press.
Mikolajewicz U.,Max Planck Institute For Meteorologie
Climate of the Past | Year: 2011
A regional ocean general circulation model of the Mediterranean is used to study the climate of the Last Glacial Maximum. The atmospheric forcing for these simulations has been derived from simulations with an atmospheric general circulation model, which in turn was forced with surface conditions from a coarse resolution earth system model. The model is successful in reproducing the general patterns of reconstructed sea surface temperature anomalies with the strongest cooling in summer in the northwestern Mediterranean and weak cooling in the Levantine, although the model underestimates the extent of the summer cooling in the western Mediterranean. However, there is a strong vertical gradient associated with this pattern of summer cooling, which makes the comparison with reconstructions complicated. The exchange with the Atlantic is decreased to roughly one half of its present value, which can be explained by the shallower Strait of Gibraltar as a consequence of lower global sea level. This reduced exchange causes a strong increase of salinity in the Mediterranean in spite of reduced net evaporation. © 2011 Author(s).