Externalizing the lateral-boundary conditions from the dynamic core in semi-implicit semi-Lagrangian models

Research is still undertaken to develop so-called transparent lateral boundary conditions (LBC) for limited-area numerical weather prediction models. In the widely used semi-implicit semi-Lagrangian schemes, this naturally leads to LBC formulations that are intrinsically intertwined with the numerics of the dynamic core. This may have profound consequences for the implementation and the maintenance of future model codes. For instance, scientific development on the dynamics may be hindered by constraints coming from today's choices in the LBC formulation and vice versa. Building further on the work of Aidan McDonald, this paper proposes an approach where (1) the LBCs can be imposed by an extrinsic numerical scheme that is fundamentally different from the one used for the dynamic core in the interior domain and (2) substituting one such LBC scheme for another is possible in a manner that leaves the Helmholtz solver unmodified. It is argued that this concept may provide the necessary frame for formulating transparent boundary conditions in spectral limited-area models. Since this idea touches all aspects of the LBC problem, its feasibility can only be established by a rigorous systematic approach. As a first step, this paper provides promising experimental support in a one-dimensional shallow-water model

Well-posed lateral boundary conditions for spectral semi-implicit semi-Lagrangian schemes : tests in a one-dimensional model

The aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme and (ii) the implications of such a lateral boundary treatment for the semi-Lagrangian trajectory computations at the lateral boundaries. Straightforwardly imposing boundary conditions in the gridpoint-explicit part of the semi-implicit time-marching scheme leads to numerical instabilities for time steps that are relevant in today's numerical weather prediction applications. It is shown that an iterative scheme is capable of curing these instabilities. This new iterative boundary treatment has been tested in the framework of the one-dimensional shallow-water equations leading to a significant improvement in terms of stability. As far as the semi-Lagrangian part of the time scheme is concerned, the use of a trajectory truncation scheme has been found to be stable in experimental tests, even for large values of the advective Courant number. It is also demonstrated that a well-posed buffer zone can be successfully applied in this spectral context. A promising (but not easily implemented) alternative to these three above-referenced schemes has been tested and is also presented here

Alternative formulations for incorporating lateral boundary data into limited area models

Limited-area models (LAMs) use higher resolutions and more advanced parameterizations of physical processes than global numerical weather prediction models, but suffer from one additional source of error-the lateral boundary condition (LBC). The large-scale model passes the information on its fields to the LAM only over the narrow coupling zone at discrete times separated by a coupling interval of several hours. The LBC temporal resolution can be lower than the time necessary for a particular meteorological feature to cross the boundary. A LAM user who depends on LBC data acquired from an independent prior analysis or parent model run can find that usual schemes for temporal interpolation of large-scale data provide LBC data of inadequate quality. The problem of a quickly moving depression that is not recognized by the operationally used gridpoint coupling scheme is examined using a simple one-dimensional model. A spectral method for nesting a LAM in a larger-scale model is implemented and tested. Results for a traditional flow-relaxation scheme combined with temporal interpolation in spectral space are also presented

M-theory on AdS_4xM^{111}: the complete Osp(2|4)xSU(3)xSU(2) spectrum from harmonic analysis

We reconsider the Kaluza Klein compactifications of D=11 supergravity on AdS_4x(G/H)_7 manifolds that were classified in the eighties, in the modern perspective of AdS_4/CFT_3 correspondence. We focus on one of the three N=2 cases: (G/H)_7=M^{111}=SU(3)xSU(2)xU(1)/SU(2)xU(1)'xU(1)''. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fre') with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4)xSU(3)xSU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N=2 compactifications. Furthermore, it is a necessary comparison term in the AdS_4/CFT_3 correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the AdS/CFT correspondence than in the S^7 case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hypercharges that we obtain in the present article. The investigation of the match is left to future publications. Here we provide an exhaustive construction of the Kaluza Klein side of our spectroscopy.Comment: 65 page

Jean-François Geleyn, fondateur et premier directeur de programme d'Aladin

Jean-François Geleyn has been leading the international Aladin consortium from 1990 until 2010, first informally and then later, as the Program Manager. This consortium was a collaboration of 16 European and North-African national meteorological institutes that developed and maintained the Aladin numerical-weather prediction system. While many people contributed to this collaboration, its outstanding success was the result of Jean-François Geleyn's tireless efforts, his exceptional intellect and his unique human dedication to the program. His efforts formed the basis for the collaboration with the Hirlam consortium that ultimately led to a new consortium of 26 countries for numerical weather prediction

FOREWORD BY ALADIN PROGRAM MANAGER

FOREWORD BY ALADIN PROGRAM MANAGE

Simulating model uncertainty of subgrid-scale processes by sampling model errors at convective scales

Ideally, perturbation schemes in ensemble forecasts should be based on the statistical properties of the model errors. Often, however, the statistical properties of these model errors are unknown. In practice, the perturbations are pragmatically modelled and tuned to maximize the skill of the ensemble forecast. In this paper a general methodology is developed to diagnose the model error, linked to a specific physical process, based on a comparison between a target and a reference model. Here, the reference model is a configuration of the ALADIN (Aire Limitée Adaptation Dynamique Développement International) model with a parameterization of deep convection. This configuration is also run with the deep-convection parameterization scheme switched off, degrading the forecast skill. The model error is then defined as the difference of the energy and mass fluxes between the reference model with scale-aware deep-convection parameterization and the target model without deep-convection parameterization. In the second part of the paper, the diagnosed model-error characteristics are used to stochastically perturb the fluxes of the target model by sampling the model errors from a training period in such a way that the distribution and the vertical and multivariate correlation within a grid column are preserved. By perturbing the fluxes it is guaranteed that the total mass, heat and momentum are conserved. The tests, performed over the period 11–20 April 2009, show that the ensemble system with the stochastic flux perturbations combined with the initial condition perturbations not only outperforms the target ensemble, where deep convection is not parameterized, but for many variables it even performs better than the reference ensemble (with scale-aware deep-convection scheme). The introduction of the stochastic flux perturbations reduces the small-scale erroneous spread while increasing the overall spread, leading to a more skillful ensemble. The impact is largest in the upper troposphere with substantial improvements compared to other state-of-the-art stochastic perturbation schemes. At lower levels the improvements are smaller or neutral, except for temperature where the forecast skill is degraded