Mesoscale Impacts of Explicit Numerical Diffusion in a Convection-Permitting Model

In convection-permitting simulations, the spectrum of resolved motions is truncated near scales where convection is active. An "energy gap" between resolved and unresolved motions does not exist, such that the upscale and downscale fluxes of energy across the spectrum are affected by the representation of turbulence as well as (implicit and explicit) numerical diffusion. In the current study, a systematic analysis is undertaken of the role of explicit numerical diffusion in simulations of diurnal convection over a large Alpine region, using the Consortium for Small Scale Modeling (COSMO) mesoscale model. Results are explored by using energy spectra and by diagnosing the physical and dynamical contributions to the bulk mesoscale heat budget. In addition, a linear analytical model is employed to assess different formulations of numerical diffusion. Consistent with previous studies the authors find that diffusion may strongly affect the energy spectrum and the formation of precipitation. Besides the direct impact on convective intensity and cloud distribution, they demonstrate that diffusion has an upscale influence and ultimately affects the mesoscale dynamics. Diffusion reduces the bulk Alpine net heating on a scale of O(100 km). It is hypothesized that this upscale influence is primarily due to the following factor: multiple triggering of orographic convection over a complex mountain range leads to mountain-scale diurnal signals in vertical velocity that are sensitive even to scale-selective diffusion. The simulations show that, in agreement with linear stability theory of convective growth, convective amplification is most sensitive to numerical diffusion of buoyancy and horizontal momentum components on near-surface model levels. If horizontal diffusion is not accomplished by a physically based parameterization and if the application of noise-reducing (e.g., monotonic) advection schemes proves to be insufficient to obviate the amplification of numerical noise, a necessary minimum of explicit diffusion is found to improve (i.e., decrease) the upscaling of energy to the mesoscale.