As finer resolutions become possible in numerical modeling, it has become increasingly common to turn off the cumulus parameterization scheme in favor of explicit simulation of convection. To the author's knowledge, the grid spacing at which it is appropriate to do so in a tropical cyclone (TC) case has not been systematically investigated. Therefore, this study examines the sensitivity of explicit model simulations of Hurricane Ivan (2004) to changes in horizontal grid spacing, when grid spacing between 12 and 2 km is used.
As grid spacing decreases, the minimum central pressure of Ivan deepens, droping by approximately 20 hPa as grid spacing decreases from 4 to 2 km. However, the 8-, 6-, and 4-km simulations have intensity differences of only around 10 hPa between them. The structure shown by model-simulated radar, as well as model-simulated satellite infra-red (IR) temperatures, shows that the eyewall of the coarser resolution simulations (12- to 6-km) is highly asymmetrical and elliptically-shaped, with two large maxima (minima) in reflectivity (cloud top temperature) rotating about the TC center. The 4- and 2- km runs have more circular eyewalls, with more numerous and larger maxima (minima) in reflectivity (cloud top temperature) embedded within the eyewall, as well as better developed spiral bands.
Temporal and spatial averaging, done at a given radius over azimuth, show the system-averaged quanitites in cross-section and reveal differences in the structure of the TC core and eyewall. The finer resolution simulations have larger updrafts and more subsidence within the eye. However, the warming of the eye, relative to the other runs, is confined to the upper levels of the troposphere. The eyewall of the TC in the finer resolution runs slopes radially outward less with height, as the horizontal temperature gradient changes little with height, compared with the coarser simulations. This lack of warming in the lower- and mid-levels of the TC eye indicates a ventillation mechanism at work in the finer resolutions, acting to mix high potential temperature air (&thetas;e) from the eye into the eyewall. Such air could act as a fuel source for buoyant convection within the eyewall (Persing and Montgomery 2003; Eastin et al. 2005b; Yang et al. 2007)
Fine-scale eyewall and eye features are examined at high temporal resolution in order to further analyze changes in the TC structure as grid resolution increases. Wind, &thetas;e, and potential vorticity (PV) anomalies in the finer resolution simulations tend to be smaller in size and larger in magnitude, especially in the 2-km simulation. The PV field in the 2-km simulation appears to have several wave-like features moving throughout the eyewall, suggesting that smaller-scale processes, such as vortex Rossby waves (VRWs) and buoyant convection, areat least partially resolved at this grid spacing. VRWs, waves that propagate along a PV gradient, are further explored as a possible ventillation mechanism acting in the lower TC eye. The presence of VRWs is tested by visual analysis, as well as by a subjective estimate of the motion of PV features and a PV budget. Both of these analyses show the properties of these PV features to be consistent with the theoretical and observed properties of VRWs. A spectral decomposition of kinetic energy shows that the higher resolution simulations distribute energy to specific wavenumbers where organized wave motions are simulated. However, the coarser runs distribute lower amounts of power over more wavenumbers, some of which are not even fully-resolved at that grid spacing.
There is some convergence in the model solution for the basic TC structure and intensity at grid spacings between 8- and 4-km, suggesting that these grid spacings might be appropriate for an operational NWP environment. For research purposes, where the time needed for numerical integration is less constrained, 4-km is the largest grid spacing that could be considered appropriate to partially resolve physical process within the eyewall. However, as the minimum central pressure of the 2-km simulation is significantly deeper than all other simulations, small-scale physical processes important to the intensification of a TC are clearly being resolved in this run that are not well-resolved in coarser runs.