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The paper assesses the difficulties of running an operational NWP model in the resolution range of 3-8 km. In this case, deep convection cells are neither much smaller than the grid box as assumed by most parameterization schemes, nor completely resolved as would be required for them to be treated explicitly. A specific approach is proposed, with an integrated sequential treatment of resolved condensation, deep convection, and microphysics together with the use of prognostic variables. It currently allows for the production of consistent and realistic results at resolutions ranging from a few tens of kilometers down to less than 4 km. Model skill scores and an example of an operational forecast at different resolutions are presented.

† The contribution of C. Smith was written in the course of his employment at the Met Office, UK and is published with the permission of the controller of HMSO and the Queen's Printer for Scottland.Drawing from the results of theoretical studies about the behaviour of constantcoefficients semi-implicit schemes, the dynamical kernel of the Aladin-NH spectral limited-area numerical weather prediction (NWP) model has been modified in order to allow for a stable and efficient integration of the fully elastic Euler equations. The resulting dynamical kernel offers the possibility to use semi-Lagrangian transport schemes together with two-time-level discretizations at kilometric scales for NWP purposes. The main characteristics of the adiabatic part of the model formulation and the space and time discretization are described in this article. In order to illustrate the dependence of the results on adjustable parameters of the dynamical kernel, some real-case dynamical-adaptation forecasts performed with a basic physical parameterization package are presented. The results obtained with this model in real-case experiments fully confirm the conclusions drawn in previous numerical analysis studies. The good quality of the results is found to be compatible with a routine exploitation in a NWP framework. The Aladin-NH dynamical kernel has been used in the operational NWP 'AROME' model since December 2008 at the kilometric scale, with an appropriate physical parameterization package and data assimilation system.

An approach for convective parameterization is presented here, in which grid-scale budget equations of parameterization use separate microphysics and transport terms. This separation is used both as a way to introduce into the parameterization a more explicit causal link between all involved processes and as a vehicle for an easier representation of the memory of convective cells. The equations of parameterization become closer to those of convection-resolving models [cloud-system-resolving models (CSRMs) and large-eddy simulations (LESs)], facilitating parameterization development and validation processes versus a detailed budget of these high-resolution models. The new Microphysics and Transport Convective Scheme (MTCS) equations are presented and discussed. A first version of a convective scheme based on these equations is tested within a single-column framework. The results obtained with the new scheme are close to those of traditional ones in very moist convective cases [like the Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment (GATE) Phase III, 1974]. The simulation of more difficult drier situations [European Cloud Systems Study/Global Energy and Water Cycle Experiment (GEWEX) Cloud System Studies (EUROCS/GCSS)] is improved through more memory due to higher sensitivity of simulated convection to dry midtropospheric layers; a prognostic relation between cloudy entrainment and precipitation evaporation dramatically improves the prediction of the phase lag of the convective diurnal cycle over land with respect to surface heat forcing. The present proposal contains both a relatively general equation set, which can deal continuously with dry, moist, and deep precipitating convection, and separate—and still crude—explicit moist microphysics. In the future, when increasing the complexity of microphysical computations, such an approach may help to unify dry, moist, and deep precipitating convection inside a single parameterization, as well as facilitate global climate model (GCM) and limited-area model (LAM) parameterizations in sharing the same formulation of explicit microphysics with CSRMs.

SUMMARYThe adaptation of a convective parametrization to high resolution has been successfully performed, to a certain point, by refinements in the representation of the entrainment, detrainment and some other features of the original general-circulation-model oriented scheme. But, passing to resolutions below 10 km requires dispensing with some fundamental hypotheses, starting with quasi-equilibrium and the assumption of negligible up-and downdraught mesh fractions. A prognostic scheme has been used for the draughts' vertical velocities and mesh fractions. The prognostic closure of the convective scheme has many benefits, but additional enhancements are required, starting with a coherent treatment of the cloud condensates and a more integrated combination of the different schemes producing condensation, cloud and precipitation.

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SUMMARYWe follow the approach suggested by F. Schmidt to implement a spectral global shallow-water model with variable resolution. A conformal mapping is built between the earth and a computational sphere and the equations are discretized on the latter using the standard spectral technique associated with a collocation (Gaussian) grid. We prove that the only non-trivial conformal mapping which exists between the two spheres is based on the transformation introduced by Schmidt, but the pole of the collocation grid has no longer to coincide with the pole of dilatation. We implement the technique in an explicit model, where only minor modifications to a uniform resolution model are needed. The semi-implicit scheme and the nonlinear normal mode initialization are proved to work satisfactorily. 24-hour forecasts show that the method is successful in dealing with the shallow-water equations and allow us to discuss the potential of the approach.