Validity of the hydrostatic approximation at convection-resolving scales: Diagnostic analysis and model intercomparison

The increasing availability of computing power allows the use of kilometer-scale convection-resolving weather and climate models for operational forecasts. One of the open questions at these scales concerns the validity of the hydrostatic approximation, which assumes that vertical accelerations are small compared to the balancing forces of gravity and the vertical pressure gradient. This assumption is valid as long as the ratio of vertical to horizontal length scales of motion is small. Results from previous studies suggest that the horizontal resolution at which the hydrostatic approximation becomes invalid is highly dependent on the particular model, model configuration, and case setup.

 

While most of the previous studies have been conducted with an idealized setup, this work will concentrate on a real-world case. To this end, a few summer days with strong convection over complex terrain in Europe are simulated with the nonhydrostatic regional Consortium for Small-scale Modelling (COSMO) model with horizontal resolutions ranging from 12 km to 275 m. To assess the validity of the hydrostatic approximation, we developed a hydrostatic reconstruction technique and diagnose the vertical wind using the hydrostatic set of equations. The diagnosed values are then compared to the actual nonhydrostatic up- and downdrafts with a statistical analysis of vertical wind speed frequencies for the different resolutions.

 

Results suggest that the diagnosed hydrostatic vertical velocities are very similar to the nonhydrostatic vertical velocities up to horizontal resolutions of 1 km and thus the use of the hydrostatic approximations at these scales still seems to be a valid option.

 

Furthermore, the study contains an intercomparison of precipitation and vertical winds produced by the nonhydrostatic COSMO model and the hydrostatic Integrated Forecast System (IFS) from ECMWF for the same case. The intercomparison supports the previous findings that at resolutions of ∼2 km and ∼4 km the effect of the hydrostatic approximation is negligible. The results also show that a small enough timestep size is essential in order to properly resolve the high vertical velocities associated with convection.