## 1. Introduction

Observational studies (Nastrom and Gage, 1985; Lindborg, 1999) have shown that kinetic energy (KE) spectra follow a k^{−3} dependence on a large scale (where *k* is the wavenumber) dominated by rotational modes and a transition to a shallower k^{−5/3} dependence on mesoscale and smaller scales, dominated by divergent modes. The k^{−3} dependence on the large scale is well explained by 2D turbulence (Kraichnan, 1967) but an understanding of the mesoscale portion with the k^{−5/3} dependence is still under discussion. Gage and Nastrom (1986) and more recently Tung and Orlando (2003) argue that the −5/3 slope is produced primarily from a forward energy cascade (downscale, from larger to smaller scales), whereas Lilly (1983, 1989) argues that a small amount of the energy injected at small scales (convection or other sources) cascades upscale, producing the shallow spectra.

Spectral analysis is also a powerful tool to assess how the KE is distributed in atmospheric models according to spatial scales and their capacity to reproduce observational spectra (Koshyk *et al.*, 1999). In particular, Skamarock (2004) used spectral analysis to define the effective resolution of the WRF model, i.e. the scale from which the model departs from the theoretical slope, also given by a simulation with a finer grid spacing. Indeed, a part of small-scale energy is damped as it is affected by implicit and explicit diffusion, the tail of spectra showing a rapid decrease of KE. Diffusion is needed to prevent spurious accumulation of energy at 2Δ*x* wavelength, whereas, in nature, the dissipation of energy occurs at scales smaller than 1 mm, which is largely beyond the reach of the resolution used for numerical weather prediction. Skamarock (2004) found an effective resolution for the WRF model around 7Δ*x* for simulations with different horizontal resolutions (varying from 22 to 4 km). KE spectra are also efficient for evaluating whether a model is too diffusive (with too coarse an effective resolution) or not sufficiently diffusive (accumulation of energy at the spectra tails). Whereas model-derived spectra with slopes matching observational spectra do not prove the simulations are realistic, it is a necessary condition but not a sufficient one. Moreover, as underlined by Skamarock (2004), a critically important measure of a numerical weather prediction (NWP) model's accuracy is its ability to resolve features at the limits of its grid resolution.

KE spectra have been largely used to evaluate general circulation models (e.g. Laursen and Eliasen, 1989) or mesoscale NWP models (e.g. Skamarock and Baldwin, 2003) over long periods with a broad range of meteorological situations, or on specific cases like idealized frameworks of squall lines (e.g. Takemi and Rotunno, 2003), supercells (e.g. Fiori *et al.*, 2010), breezes (e.g. Knievel *et al.*, 2007) or baroclinic waves (Waite and Snyder, 2009). However, very few of them deal with real convective cells. Moist convection is very instructive for characterizing a convection-permitting model in terms of filtering and effective resolution, as predictions are strongly dependent on the behaviour of the dynamics of the model, on the physics and also on the interaction between the two.

In this study, KE spectra are first examined from a climatological perspective for the convection-permitting NWP model AROME. Then, special attention is focused on KE spectra for individual convective cells over plains, which can lead to unrealistic strong outflow winds at the surface if strong explicit diffusion is imposed. One of the original features of our study is to compare in this case KE spectra for two mesoscale models–AROME and Meso-NH–which differ only in their dynamics. This allows separation of the numerical filters and subgrid mixing. Sensitivity tests on the explicit diffusion and time step, as well as on the transport and temporal schemes, are conducted to illustrate some damping mechanisms. Indeed, various dampings exist: damping from explicit diffusion, damping from the SI scheme, damping due to the choice of reference temperature profile and reference surface pressure (Simmons and Temperton, 1997), damping from subgrid-mixing, etc. Damping in the model must be controlled in order to obtain a numerical solution as accurate as possible; however, it is worth remembering that some effects are beneficial as damping contributes to ensure numerical stability. The initial spin-up is illustrated to verify that physically realistic fine-scale structures are generated. Finally, analysis of KE spectra for simulations with increasing horizontal grid spacings is conducted with the Meso-NH model on the same convective case, and sensitivity tests on the physical dissipation are led at 500 m horizontal grid spacing to explore the effects of subgrid model mixing in the grey zone of turbulence.

The outline of this paper is as follows. In section 2, the methodology used in this study is explained. In section 3, a climatology of KE spectra is presented for the AROME model. In section 4, KE spectra computed for the convective case are analysed for AROME and Meso-NH, and sensitivity tests on horizontal resolution and PBL parametrization are conducted with Meso-NH. The conclusions are given in section 5.