A Study of the Effect of Resolution on the Properties of Modelled Atmospheric Flow Over Orography

An accurate representation of flow over orography using numerical simulation techniques is clearly dependent on the resolution of the model used. Flow over well-resolved hills can be expected to be well represented, while features close to the model grid scale are likely to be poorly described. As a result, some numerical weather prediction models apply a smoothing to their resolved orography fields. The most appropriate smoothing method is however not well established. Here, we investigate which scales of orography (relative to the model grid scale) can be adequately represented in numerical simulations. Since the results obtained are potentially sensitive to the flow regime, a wide range of cases has been considered. These include neutral flow over two dimensional ridges and three dimensional hills, of varying heights. Stable, gravity wave, flow with varying Froude number, to include both `flow over' and `flow around' the hill has also been examined. The results have been analysed both qualitatively, with respect to the general features of the flow, and quantitatively, for example via the total force on the surface due to gravity wave and turbulent form drag.

Well-resolved simulations (typically 20 grid points per hill) have been performed using the BLASIUS numerical model for each of the different cases studied. This is a fully non-linear, three-dimensional finite difference model, incorporating a first order turbulence closure. A series of simulations were then performed where the number of grid points per hill was gradually decreased in order to observe where the results diverge from those obtained for the well-resolved simulations.

In all cases, a good description of the orographic form drag (75% of the value calculated for the well resolved cases) is obtained when as few as six grid points are used to escribe the hill. Simulations with four points per hill give results which remain to be qualitatively reasonable but only capture approximately 50% of the drag of the well resolved hills. In contrast, if only two grid points are used to represent the hill, the description of the flow is worse than that obtained if the hill was omitted from the model completely.

These results suggest that smoothing should be used to remove orography with scales less than twice the model grid spacing , but that the smoother used must be scale selective so that it has a relatively small effect on larger scale orography, in particular for hills larger than six times the model grid spacing. This is not the case for many commonly used smoothers such as the 1-2-1 filter. However, if scales four times the model grid length are resolved, which is advantageous for some flow features, then enhancing the subgrid drag to allow for the fact that hills of this scale are probably only contributing 50% of the true drag, should be considered. This contrasts with the standard approach in numerical weather prediction models where the subgrid parameterisations are assumed to only have to deal with scales smaller than those of the explicitly resolved orography.