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  • View in gallery

    Minimum central pressure as a function of time for the 8- (purple), 6- (blue), 4- (green), 3- (orange), 2- (red), and 1-km (pink) runs, plotted with best-track observations (black) from the NHC (Stewart 2008). Lowest central pressure for each run is shown in the inset box.

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    Azimuthal- and time-averaged cross sections of positive vertical motion (every 0.25 m s−1) for the (top left) 8-, (top middle) 6-, (top right) 4-, (bottom left) 3-, (bottom middle) 2-, and (bottom right) 1-km simulations, all averaged to 8-km grid spacing and shown from the center of the storm to 150 km away, with a black vertical line placed every 50 km. The brown (white) area denotes ascent greater than 2 (2.5) m s−1. Note that positive and negative values of vertical motion are partitioned before any averaging takes place, in order to prevent cancellation.

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    As in Fig. 2, but with the change in symmetric tangential velocity with pressure (filled every 0.05 m s−1 hPa−1 up to 0.1 m s−1 hPa−1 and then by 0.1 m s−1 hPa−1 thereafter), the horizontal derivative of symmetric potential temperature (contoured in red at 1, 3, and 5 × 10−4 K m−1) and tangential winds (contoured every 10 m s−1 from 50 to 80 m s−1 in black).

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    850-hPa vertical wind component at simulation time 63 h 20 min contoured 0.5 m s−1 up to 5 m s−1 and every 1 m s−1 thereafter for the (a) 8-, (b) 6-, (c) 4-, (d) 3-, (e) 2-, and (f) 1-km runs, with positive vertical motion in warmer colors and negative vertical motion in cooler colors. Purple coloring indicates updraft speed in excess of 5 m s−1. The point maxima (minima) of vertical velocity at this time are 4.66 (−2.54) m s−1 for the 3-km run, 5.58 (−3.34) m s−1 for the 2-km run, and 11.06 (−10.58) m s−1 for the 1-km run.

  • View in gallery

    CFADs of vertical velocity (m s−1) for the (top left) 8-, (top right) 6-, (middle left) 4-, (middle right) 3-, (bottom left) 2-, and (bottom right) 1-km simulations, taken every hour for the last 12 h of the simulation and averaged. Bin size is 0.5 m s−1. The 0.1% of vertical motions are contoured in solid black, 5% are contoured in the dashed line. CFADs are taken from points between 25 and 150 km of the TC center for the 8- and 6-km runs, and between 25 and 100 km for all other simulations.

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    850-hPa PV at 63 h into the simulation scaled by 10−6 and contoured every 5 PVU from 10 PVU, shown for the (a) 8-, (b) 6-, (c) 4-, (d) 3-, (e) 2-, and (f) 1-km runs. Note that both this figure and the next one are representative of the appearance of the PV field at different times throughout the run.

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    As in Fig. 6, but at simulation time 63 h 20 min, 20 min later.

  • View in gallery

    Azimuthal- and time-averaged cross sections of PV (scaled by 10−6 and filled every 5 PVU) and potential temperature (contoured in black every 5 K), plotted as in Fig. 2.

  • View in gallery

    At simulation time 63 h 20 min, composite model-simulated radar for the (a) 8-, (b) 4-, (c) 2-, and (d) 1-km runs. Note that, unlike in previous figures, these images differ in spatial extent, according to the size of the model domains as expressed in Table 1.

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    (a) Temporally averaged variance of 850-hPa PV at the radius of maximum PV (RMPV) in each run, plotted according to wavenumber with colored lines as in Fig. 1. (b) Variance is normalized, such that the value shown is the fraction of the total variance. The inset box shows the averaged 850-hPa RMPV for each simulation. (bottom) Dashed lines correspond to wavelengths less than 10Δx in the azimuthal direction along the circumferences inferred from the average RMPV.

  • View in gallery

    As in Fig. 10b, but segmented by wavenumbers corresponding to azimuthal wavelengths of 10Δx (fully resolved wavenumbers), wavelengths of 4Δx (partially resolved wavenumbers), and the residual or all other remaining wavenumbers.

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Sensitivity of Simulated Tropical Cyclone Structure and Intensity to Horizontal Resolution

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  • 1 North Carolina State University, Raleigh, North Carolina
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Abstract

The Weather Research and Forecasting (WRF) model is used to test the sensitivity of simulations of Hurricane Ivan (2004) to changes in horizontal grid spacing for grid lengths from 8 to 1 km. As resolution is increased, minimum central pressure decreases significantly (by 30 hPa from 8- to 1-km grid spacing), although this increase in intensity is not uniform across similar reductions in grid spacing, even when pressure fields are interpolated to a common grid. This implies that the additional strengthening of the simulated tropical cyclone (TC) at higher resolution is not attributable to sampling, but is due to changes in the representation of physical processes important to TC intensity.

The most apparent changes in simulated TC structure with resolution occur near a grid length of 4 km. At 4-km grid spacing and below, polygonal eyewall segments appear, suggestive of breaking vortex Rossby waves. With sub-4-km grid lengths, localized, intense updraft cores within the eyewall are numerous and both polygonal and circular eyewall shapes appear regularly. Higher-resolution simulations produce a greater variety of shapes, transitioning more frequently between polygonal and circular eyewalls relative to lower-resolution simulations. It is hypothesized that this is because of the ability to resolve a greater range of wavenumbers in high-resolution simulations. Also, as resolution is increased, a broader range of updraft and downdraft velocities is present in the eyewall. These results suggest that grid spacing of 2 km or less is needed for representation of important physical processes in the TC eyewall. Grid-length and domain size suggestions for operational prediction are provided; for operational prediction, a grid length of 3 km or less is recommended.

Corresponding author address: Megan Gentry, Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Raleigh, NC 27695-8208. Email: msgentry@ncsu.edu

Abstract

The Weather Research and Forecasting (WRF) model is used to test the sensitivity of simulations of Hurricane Ivan (2004) to changes in horizontal grid spacing for grid lengths from 8 to 1 km. As resolution is increased, minimum central pressure decreases significantly (by 30 hPa from 8- to 1-km grid spacing), although this increase in intensity is not uniform across similar reductions in grid spacing, even when pressure fields are interpolated to a common grid. This implies that the additional strengthening of the simulated tropical cyclone (TC) at higher resolution is not attributable to sampling, but is due to changes in the representation of physical processes important to TC intensity.

The most apparent changes in simulated TC structure with resolution occur near a grid length of 4 km. At 4-km grid spacing and below, polygonal eyewall segments appear, suggestive of breaking vortex Rossby waves. With sub-4-km grid lengths, localized, intense updraft cores within the eyewall are numerous and both polygonal and circular eyewall shapes appear regularly. Higher-resolution simulations produce a greater variety of shapes, transitioning more frequently between polygonal and circular eyewalls relative to lower-resolution simulations. It is hypothesized that this is because of the ability to resolve a greater range of wavenumbers in high-resolution simulations. Also, as resolution is increased, a broader range of updraft and downdraft velocities is present in the eyewall. These results suggest that grid spacing of 2 km or less is needed for representation of important physical processes in the TC eyewall. Grid-length and domain size suggestions for operational prediction are provided; for operational prediction, a grid length of 3 km or less is recommended.

Corresponding author address: Megan Gentry, Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Raleigh, NC 27695-8208. Email: msgentry@ncsu.edu

1. Introduction

While human forecasters and numerical models have not demonstrated consistent improvement in tropical cyclone (TC) intensity prediction, TC track error has been steadily decreasing for the past several decades (Rogers et al. 2006). Rogers et al. (2006) cite inadequate computational resources to run operational models at sufficiently high spatial resolution, along with incomplete representation of important physical processes, as two reasons for the slow improvement in intensity prediction. As higher-resolution model runs become possible, it is vital to understand how the simulation of physical processes, especially those important to TC intensity, are impacted by changes in horizontal grid spacing. The objective of this study is to analyze simulations of Hurricane Ivan (2004) to determine the sensitivity of TC intensity and structure to grid spacing for grid lengths between 8 and 1 km. Ultimately, we wish to identify the resolution required for dynamical models to provide value-added guidance to operational forecasters.

Although updraft strength and structure differs considerably between squall lines and TCs, resolution sensitivity studies of squall lines hold relevance for both types of systems. Weisman et al. (1997) simulated squall lines with model grid spacing from 1 to 12 km in order to test the sensitivity of organized convective systems to horizontal resolution. They concluded that 4-km grid spacing could reproduce essential features of the structure and evolution of the squall line seen in a 1-km run. Studying deep moist convection, Bryan et al. (2003) focus on grid spacing below 1 km and recommend grid lengths on the order of 100 m to be used as a benchmark in resolution sensitivity studies in order to better represent intracloud motions. This study found no systematic trend in mean vertical velocity with changes in grid spacing. Instead, it found that differences between the model runs stemmed from the ability of the higher-resolution runs to develop grid-scale turbulence. It might be expected that the magnitude of vertical motions would increase as smaller grid spacing is used, as updrafts are more adequately resolved. However, the conclusions of Bryan et al. (2003) suggest that higher resolution could eventually weaken the magnitude of vertical motions as detrimental processes, such as entrainment with grid-scale turbulence, begin to be resolved.

While these earlier studies concentrated on resolution sensitivity in convective systems, the current study is concerned with how changes in grid spacing will affect processes important to TC intensity. In an axisymmetric conception of TC intensification, the ability of the system to deepen depends on the radial convergence of air modified by turbulent fluxes of heat and moisture (Ooyama 1982; Emanuel 1986; Rotunno and Emanuel 1987). The azimuthal circulation contributes to the strength of surface fluxes of heat, moisture, and momentum, and is required to maintain thermal wind balance with the warm core of the system (Ooyama 1982). Asymmetric, intraeyewall physical processes may also play a significant role in determining TC structure and intensity (e.g., Yang et al. 2007). Vortex Rossby waves (VRWs) influence TC structure through phase-locking and breaking as a result of barotropic instability near the radius of maximum wind (RMW). The pools of potential vorticity (PV) formed by the wave breaking can create the appearance of straight-line structures between these pools and the resulting polygonal eyewall structure (Schubert et al. 1999). VRWs also influence TC structure outside of the eyewall, with breaking VRWs stripping off cyclonic PV anomalies from the eyewall. These convectively coupled PV strips can form spiral bands (Chen and Yau 2001). Also, Davis and Bosart (2002) found that the production of PV close to the TC center is sensitive to resolution when using grid spacing between 9 and 3 km, and that this PV generation played a dominant role in the ability of the 3-km run to best reproduce observed intensity during the developing stages of Hurricane Diana (1984).

VRWs have also been theorized to play an important role in TC intensity by mixing low-momentum, high potential temperature (θ) air from the eye into the eyewall (e.g., Schubert et al. 1999). This high-θ air could act as fuel for buoyant updraft cores, which would augment the mass transport of the symmetric moist-neutral ascent, bringing about a state of superintensity, or intensity surpassing that predicted from symmetrical processes (Persing and Montgomery 2003; Cram et al. 2007). However, recent findings by Bryan and Rotunno (2009a) have put the importance of this mechanism into doubt, showing that elimination of the high entropy pool in the lower eyewall resulted in only a small (∼4%) increase in minimum central pressure, and even that change may have been due to a generous definition of the area over which fluxes were suppressed in their model experiments.

The ability of a model to simulate asymmetric intensity processes will depend upon its ability to resolve features on the scale of eyewall vortices and spiral rainbands (e.g., Wang 2009). However, it is worth considering the resolution needed to properly represent the inner core of the symmetric primary circulation. In a 15-yr Atlantic TC climatology, Kimball and Mulekar (2004) found the median value of the RMW to be 55 km. In order for a model to minimally resolve a wave, the wavelength must be ∼4Δx, where Δx is the grid spacing of the model simulation (Grasso 2000). Therefore, it can be argued that grid spacing of 14 km and below may resolve features on the scale of the average-sized RMW for many tropical cyclones, if considering only grid spacing and not other important factors within the model setup, such as diffusion. However, Skamarock (2004) suggests an even finer grid spacing of 7Δx is needed in order to match the observed energy spectra of a given wavelength. It has also been argued that waves are only fully resolved if their scale is as large as 10Δx (Walters 2000). By this criterion, only simulations with grid spacing of 5.5 km may be expected to fully resolve the radial structure of the symmetric primary circulation of an average-sized TC. Extended National Hurricane Center (NHC) best-track data indicate that the average size of Ivan’s RMW during 11–14 September 2004 was approximately 27 km (Demuth et al. 2006). This is somewhat smaller than the median value found by Kimball and Mulekar (2004), but still within the range of RMW sizes considered in that study. By the criteria mentioned above, Ivan’s RMW may be considered to be somewhat resolved with 6.8-km grid spacing and fully resolved with grid spacing of 2.7 km.

Based on either the RMW size indicated by climatology or that of Ivan specifically, the circumference of the eyewall, as computed from the RMW, is considered to be fully resolved in all experiments presented here, according to the 10Δx criteria. The significance of asymmetric, intraeyewall processes, such as VRWs, and spiral rainbands have previously been discussed as processes important to TC intensification (e.g., Wang 2009; Hill and Lackmann 2009). The region inside the RMW is characterized by a large radial gradient of cyclonic shear vorticity, and therefore a large PV gradient. This has implications for VRW formation and propagation, and therefore it is essential that this zone be resolved in order to simulate intraeyewall asymmetric process, such as VRWs. The authors are not aware of a comprehensive observational dataset with which to determine an average spatial scale for this zone of large PV gradient. However, assuming a scale of 10 km or less, it would only be partially resolved by the smaller grid lengths used in this study and 1-km grid spacing or below would be needed to fully resolve it.

If small-scale circulations near the eyewall do provide an additional fuel source for buoyant updrafts, these updrafts must also be represented by the model in order for such an intensification mechanism to operate realistically in the model atmosphere. Eastin et al. (2005) found the median updraft diameter of convective cores to be approximately 2 km with the 90th percentile of cores to be approximately 4 km in diameter (depending on the vertical level being considered). Therefore, the finest grid spacing used in this study, 1 km, can only be expected to somewhat resolve the largest updraft cores. While extension of this study to sub-1-km grid lengths would certainly be valuable, the objective of this study is to provide guidance to both the research and operational communities about model sensitivity to resolution within the range of grid spacing commonly used by these communities at the time of this writing and in the near future.

Hurricane Ivan (2004) was selected for study primarily due to its representative size characteristics, high intensity, and multiple periods of rapid deepening, having intensified to a category 5 storm on three separate occasions before making landfall on the U.S. Gulf coast (Stewart 2008). Based on NHC extended best-track data during this time, the RMW of Ivan is smaller than the median value found by the TC climatology of Kimball and Mulekar (2004), but within the range of storm sizes discussed in that study. Therefore, the results of this study are relevant to many TCs.

2. Methods

a. WRF simulations

The Weather Research and Forecasting (WRF) model (version 2.2; Skamarock et al. 2005) is used for four different simulations of Ivan (Table 1). All runs utilize the same physics options, with no convective parameterization (CP) used on the inner, higher-resolution nests (with the exception of the 12-km nest present during the 4-km simulation). The CP is omitted so that convective motions may be explicitly represented. Furthermore, CP schemes are not generally designed for the finer grid lengths utilized in this study, nor in the inner-core regions of tropical cyclones (Arakawa and Chen 1987; Molinari and Dudek 1992). The use of CP would implicitly account for a portion of the eyewall updraft, thereby weakening the upward branch of the secondary circulation and the compensating grid-scale subsidence within the eye (Gentry 2007, section 3.2). With no CP scheme present, adiabatic warming from increased subsidence produces a warmer core, thereby contributing to a hydrostatic reduction of the cyclone central pressure and increased radial inflow (Emanuel 1986). However, because of the relatively coarse resolution on the outer grids, the Kain–Fritsch (KF; Kain and Fritsch 1993) CP scheme is employed on those domains. Some sensitivity of these results to the CP used on the outer grids can be expected (Warner and Hsu 2000).

The WSM six-class (Hong and Lim 2006) microphysics parameterization and the Mellor–Yamada–Janjic (Janjić 1994, 2002) planetary boundary layer (PBL) scheme are used on all domains for all runs. All options relating to horizontal diffusion and filtering are left as the recommended default settings. These settings include second-order horizontal diffusion on coordinate surfaces. Horizontal eddy viscosity is determined from the horizontal deformation using 2D Smagorinsky first-order closure (Skamarock et al. 2005). Both of these model functions are sensitive to the horizontal grid spacing. Vertical diffusion is represented by the PBL scheme. All domains are initialized at 0000 UTC 11 September 2004 using the 1° Global Forecast System (GFS) analyses and 0.5° real-time global sea surface temperature analysis (Thiébaux et al. 2003). At the time of initialization, the NHC best track lists Ivan’s central pressure as 926 hPa, though the coarse GFS analysis used for initial conditions has a central pressure above 990 hPa (Fig. 1; Stewart 2008). Despite the relatively coarse initial conditions, the TC deepens rapidly on all domains. As all inner nests are initialized at simulation hour 0, all have a poorly resolved vortex to start with and none receive the benefit of having a higher-resolution mother domain to spin up the vortex. In each simulation, one-way nesting between domains is utilized in order to treat each domain as independent from smaller nested domains within; the vortex-tracking moving nest feature is used on the inner domains.

The large discrepancy between the strength of the observed storm and the initial TC in the model could affect the representativeness of the intensification process. However, inclusion of a bogus vortex in the initial conditions would also differ from nature, and by artificially introducing a similar storm structure in all the simulations, this could serve to mask differences that would arise because of resolution. These simulations can be viewed as simulating the intensification of an initial vortex in an environment that is highly favorable to TC intensification.

The domain sizes vary from 640 to 903 km on a side, with the domains that have moving-nest parent domains being necessarily smaller than the parent (Table 1). Although not emphasized here, use of domains sufficient in extent to capture upper-tropospheric outflow and outer-rainband features was deemed essential. The vertical grid spacing is held constant at 46 half-σ levels, with the model top at 50 hPa. The distribution of vertical levels follows Zhang and Wang (2003), who assessed the sensitivity of TC intensity to the placement and number of vertical levels.

Some model sensitivity exists to the time step, as multiple nests from the same run are compared and a 3:1 time step and grid spacing ratio must exist between nested grids (Table 1). A time step of 72 s on the outer domains is used in every case, except with the 3- and 1-km run. In that case, the time step is halved in order to maintain numerical stability. In all simulations, the ratio of time step (in s) to grid spacing (in km) ranges from 2:1 to 4:1. The maximum criterion for numerical stability in WRF suggested by Skamarock et al. (2005) is a 6:1 ratio. Therefore, given that the criterion for numerical stability is met in all simulations and that the time step to grid spacing ratio is similar in all simulations, it is assumed that the sensitivity to time step is significantly smaller than the sensitivity to changes in horizontal resolution.

To further evaluate the validity of this assumption, an additional experiment was performed in which the 8-km simulation was run again with the time step reduced from 24 to 12 s. During this 72-h simulation, the simulation with the shorter time step produced a TC with a minimum central pressure 5 hPa lower than that with a longer time step. In view of this result, no significant emphasis in this study will be placed on central pressure differences of 5 hPa and smaller. Runs with large differences in the time step size generally feature central pressure differences on the order of 10 hPa, larger than the 5 hPa that could be attributed to time step sensitivity (Fig. 1).

b. Azimuthal and temporal averaging

To more clearly isolate differences between the simulations attributable to differences in grid length, a subset of model output variables is azimuthally averaged. This is accomplished by averaging all points within 304 km of the height-varying storm center1 into concentric rings of 8-km width. Thus, output from all simulations is averaged to the same resolution to avoid spatial sampling issues in the comparison of vertical and horizontal winds, as well as minimum pressure. These fields are then temporally averaged every hour from forecast hours 60 to 72, at a time when the simulated Ivan had reached a comparatively steady intensity in all runs. The azimuthally and temporally averaged fields are used to examine the symmetric component of the TC features (and are hereby referred to as the symmetric fields), while the full fields are compared in order to contrast the asymmetric aspects of TC structure.

3. Results

First, the intensity of Ivan in all runs will be compared, followed by a discussion of the eyewall updraft and PV features. In each simulation, Ivan was initialized while located to the south of Jamaica, and subsequently tracked through the gap between the Yucatan Peninsula and the western tip of Cuba. In each experiment, the storm followed a similar track, hence this aspect will not be discussed further.

a. Intensity

Figure 1 presents the time series of minimum central pressure for the six simulations of Ivan, along with the NHC best-track data. The TC in the 1-km simulation exhibits the lowest minimum central pressure, 898 hPa, followed by that in the 2-km run, which reaches 904 hPa. The lowest central pressure in the 3-km run, at 913 hPa, comes the closest to the best-track data during Ivan’s most intense phase, which was ∼910 hPa. However, some overprediction of the observed intensity can be expected in model simulations with a static sea surface temperature as used here, where the effects of cooling due to mixing and upwelling are not represented. Also, like any observational dataset, best-track estimations of minimum central pressure are subject to sampling and instrumentation error, and could have underestimated Ivan’s intensity. This study will mainly be concerned with the structure and intensity of the simulated TCs relative to each other and will make only limited comparisons to best-track observations of Ivan. The lowest central pressures for the 8-, 6-, and 4-km simulations, at 928, 920, and 918 hPa, respectively, are all considerably higher than minimum central pressures in the finer-resolution runs.

Some portion of the reduction of minimum central pressure with decreasing grid spacing is attributable to spatial sampling. As gridcell area decreases, it is more likely that small-scale pressure minima are resolved. However, the magnitude of the lowering of central pressure for a given decrease in grid spacing varies across the spectrum of simulations (Table 2). The smallest increase in intensity per increase in resolution is seen as grid spacing drops from 6 to 4 km, only resulting in a lowest central pressure drop of 2 hPa. But decreasing grid spacing from 4 to 2 km is accompanied by a deepening of 14 hPa. Even when the sea level pressure fields of all runs are azimuthally averaged to 8-km bins, the trend in central pressure as resolution increases remains much the same as when examining values from individual grid cells on the native grid (Table 2). The modest deepening from the 6- to 4-km simulation is unchanged, and the drop in central pressure as grid spacing changes from 4 to 2 km is still 13 hPa. This suggests that differences in the simulations do not result simply from a better-resolved minimum in surface pressure, but that physical processes important to TC intensity are impacted by the resolution changes.

b. Symmetric eyewall updraft

Temporally and azimuthally averaged upward vertical velocity indicate considerable sensitivity of updraft strength and structure to horizontal resolution (Fig. 2). Overall, there is an increase in the averaged ascent as resolution increases. The average ascent throughout the depth of the eyewall updraft is greater than 2 m s−1 in all simulations with grid spacing of 4 km or less. There is less change in updraft strength between the 3- and 1-km runs, with ascent greater than 2.5 m s−1 through much of the depth of the eyewall. The 1-km simulation has the strongest symmetric eyewall updraft, with a small visible area of 3.5 m s−1 or greater updraft speed around the 250-hPa level.

It might be expected that the eyewall updraft in simulations with smaller grid spacing would be stronger relative to that in coarser simulations. However, as implied by Bryan et al. (2003), increased horizontal resolution would eventually begin to resolve processes detrimental to updraft strength, such as entrainment, and could result in a decrease in updraft strength. While this resolution is certainly not achieved in any of these simulations, the 1-km simulation could be approaching this regime. An extension of this study to grid spacing below 1 km would be needed to assess this.

The slope of the azimuthally averaged eyewall updraft decreases noticeably as resolution increases. This is consistent with the system-averaged horizontal winds, which show that, in the finer runs, there is a significant increase in the vertical extent of the stronger horizontal winds (Fig. 3). All simulations with grid spacing below 4 km have distinctly more upright eyewalls in the midlevels, with some sloping of the eyewall outward below 700 and above 200 hPa. Stern and Nolan (2009) found a linear relationship between the outward slope of the RMW and the size of the RMW, both in an observational dataset of three-dimensional Doppler winds and through theoretical development (Emanuel 1986). These findings are also consistent with our simulations. The average size of the RMW for all runs (as defined by the azimuthally and temporally averaged 10-m winds during the last 12 h of the simulation) is listed in Table 3. Consistent with the findings of Stern and Nolan, the RMW is reduced as the outward slope of the eyewall decreases, with the RMW dropping from 63.7 km in the 8-km simulation to 37.5 km in the 1-km run. The exception to this reduction in RMW with grid spacing is the 4-km simulation, which has a slightly larger RMW than the 6-km run. However, this reduction of the eyewall slope with increasing resolution is also corroborated by a study similar to this one conducted by Fierro et al. (2009), a case study of Hurricane Rita (2005) using WRF and utilizing similar grid spacing. Reduction of the RMW with grid spacing has also been noted by other studies (Yau et al. 2004; Davis et al. 2008). A more complete comparison of the temporal evolution of the low-level wind fields is found in Gentry (2007, section 4.1).

To the extent that the primary circulation is in gradient thermal wind balance, we should expect consistency between the vertical slope of the eyewall and the thermal structure of the simulated storms. The gradient thermal wind relation requires that cyclonic flow decrease with height in a warm-core system. For a steady, frictionless, symmetric vortex in a cylindrical coordinate system, the gradient thermal wind is given by
i1520-0493-138-3-688-e1
where Vθ is the tangential wind, r is radial distance from the storm center, the subscript p denotes differentiation along a constant pressure surface, and other terms have their usual meteorological meaning (Gray and Shea 1973). A warm core is associated with decreasing cyclonic winds with height, and an outward-leaning eyewall. This argument is consistent with a Lagrangian perspective, as ascending air parcels in the eyewall experience a reduction of the inward-directed pressure gradient force, leading to an outward centrifugal displacement with increasing height.

To illustrate the relationship between the horizontal thermal gradient and the primary circulation in these simulations, Fig. 3 shows the magnitude of tangential winds, the change in azimuthally averaged tangential velocity with pressure, and the radial gradient of azimuthally averaged potential temperature. There is a robust increase in the uppermost altitude of strong tangential winds in higher-resolution simulations relative to the coarser-resolution runs. Also, the area of decreasing cyclonic winds with height overlaps the region of enhanced radial thermal gradient, as required by (1).

In the coarser-resolution runs, the thermal gradient and corresponding vertical shear exist in a broad area above the strong cyclonic winds. As resolution increases and the RMW decreases, the horizontal potential temperature gradient becomes stronger and more concentrated inside the RMW and the area occupied by the main primary circulation becomes more compact in the horizontal and elongated in the vertical, falling immediately outside the vertical tilt of the region of maximum potential temperature gradient. In the higher-resolution runs, the temperature gradient and shear are present in a narrower zone just inside the area of strong cyclonic winds, at the eye–eyewall boundary, consistent with deeper vertical extension of strong cyclonic winds. Other studies have addressed the degree to which gradient wind balance is applicable to both simulated and observed TCs (Stern and Nolan 2009; Bryan and Rotunno 2009b; Kepert 2006; Zhang et al. 2001). While not a definitive statement of cause and effect, this analysis demonstrates consistent changes in the thermal and dynamical structure with resolution.

c. Full vertical motion field

The complete vertical motion field (including both symmetric and asymmetric components) changes significantly as grid spacing is decreased (Fig. 4). The coarser-resolution simulations exhibit weak ascent surrounding the eye, with relatively few embedded local maxima and no downdrafts evident within the eyewall (Figs. 4a–c). As resolution is increased, the upward vertical velocity maxima become more numerous and smaller in spatial extent, and areas of downward motion appear adjacent to the ring of ascent surrounding the eye (Figs. 4d,e). At 1-km grid spacing the character of the vertical motion field changes considerably, with numerous embedded up and downdrafts that are smaller in spatial scale and much larger in magnitude within the main eyewall region (Fig. 4f).

Further examination of the remarkable increase in the number of isolated up and downdraft maxima also reveals that the maximum in 850-hPa vertical velocity in the 1-km simulation at this time is 11 m s−1. This peak value in the 1-km simulation is similar in magnitude to the strong updrafts reported in the observational studies of Jorgensen et al. (1985), Marks and Houze (1987), Black et al. (1996), and Eastin et al. (2005). Marks et al. (2008) describe updrafts of this magnitude and larger at a very low altitude of 450 m during an aircraft penetration of the eyewall of Hurricane Hugo during a period of rapid intensification.

To examine the distribution of updrafts and downdrafts through the depth of the TC, contoured frequency by altitude diagrams (CFADs;2 Yuter and Houze 1995) for each run are computed every hour for the last 12 h of the simulation and averaged together to produce a time-averaged CFAD (Fig. 5). There is a broadening of the range of vertical motions present as grid spacing is decreased. In all simulations, most vertical velocities are less than 2 m s−1 and there is little expansion of the range of the magnitude of 95% of the updrafts (indicated by the area contained within the 5% contour). In an observational study, Black et al. (1996) did find 70% of vertical motions in all regions of the TC to be 2 m s−1 or less, and that 95% of vertical motions in the eyewall were 5 m s−1 or less. Eastin et al. (2005) found the magnitude of the median convective (mesoscale) vertical velocities of both up and downdrafts to be approximately 2 (0.5) m s−1 within the eyewall, depending on the altitude considered. The CFADs of all simulations show that most vertical velocities are of a magnitude of 2 m s−1 or less, although this study does not parse vertical motions into convective and mesoscale categories.

Most of the variation between the CFADs is tied to broadening of the range of the most intense vertical motions. The magnitude of the most extreme updrafts, indicated by the 0.1% contour, increases by approximately 4 m s−1 as resolution is increased, with the 2-km run having the strongest extreme updrafts. The magnitude of the strongest downdrafts increases by 3 m s−1, with the 1-km run having the most intense downdrafts. Also, as resolution is increased, a broader distribution of vertical motion is present within the lowest 1 km. The presence of stronger updrafts closer to the surface at higher resolution may be physically attributable to improved resolution of smaller-scale updraft roots in higher-resolution simulations. This has implications for vortex stretching and vorticity generation (e.g., Davis and Bosart 2002). Strong vertical motions of several meters per second below 1-km altitude have also been reported in observational studies (e.g., Marks et al. 2008).

d. PV features

The annular tower of PV within the eyewall of the TC is associated with both symmetric and asymmetric processes important to TC strength. Existing in a region of cyclonic shear inside the RMW, the PV annulus is diabatically generated by moist convection in the eyewall region. VRWs propagate along both the positive and negative radial PV gradient on either side of the RMW. Counterpropagating VRWs on the inside and outside edge of the RMW may phase lock and break, forming pools of high PV with a linear segment of PV between (Schubert et al. 1999; Wang 2002).

Examination of high temporal resolution model output reveals that the character of the PV features changes dramatically as resolution increases. This is due, in large part, to the expected sensitivity of fields involving spatial derivates to scale inversely with grid length. Figures 6 and 7 show the PV field at simulation times 63 h and 63 h 20 min, with these times being representative of the attributes of the PV field as seen throughout the runs. As expected, the magnitude of the radial gradient of PV is larger in the finer-resolution simulations with higher values of PV present in the eyewall, both in the full and system-averaged PV fields (Fig. 8). Also, in some cases, the radius of the PV ring itself is smaller, as the RMW generally decreases with grid spacing (Table 3).

The character of the cyclonic PV ring associated with the eyewall exhibits considerable sensitivity to resolution, with the TCs in the higher-resolution simulations experiencing more overt signs of breaking VRWs, such as the exchange of PV anomalies between the eye and eyewall and the appearance of polygonal eyewall segments (Figs. 6 and 7). While the 8- and 6-km simulations show a PV ring with one or two embedded PV maxima, the higher-resolution simulations have numerous PV maxima that are smaller in size and progressively larger in magnitude as grid spacing decreases. In the 2- and 1-km runs, some PV anomalies are observed to break off from the high-PV eyewall region and enter the low-PV environment of the eye (Figs. 6e,f and 7e,f). These events also occur in the 3- and 4-km simulations, but are not present during the time period shown in Figs. 6 and 7. The formation of polygonal eyewall segments is evident in the simulations with 4-km and smaller grid length, also indicative of breaking VRWs in these simulations. Further analysis to establish the presence of VRWs is presented by Gentry (2007, section 4.5.3), where a subjective analysis of the motion of PV features showed the movement of PV features within those simulations to be consistent with the speed of VRWs.

Additional evidence of breaking VRWs is provided by the appearance of PV structures outside the eyewall in higher-resolution simulations, as Rossby wave activity has been linked to the appearance of spiral-banding features emanating directly from the eyewall (Chen and Yau 2001; Wang 2009). While the 8- and 6-km simulations have no PV anomalies of 10 PVU or greater outside the eyewall, PV anomalies of this magnitude do appear at 4-km grid spacing. As grid spacing is further reduced to 1 km, PV anomalies of this magnitude and greater appear more frequently outside the eyewall. The composite model-simulated radar reflectivity also illustrates more developed spiral banding in the higher-resolution simulations (Fig. 9). Note that the extent of the spiral bands is a product not only of the finer resolutions used but also the horizontal extent of the grid (640 km on a side or more as shown in Table 1). In this study, the grid dimensions used are sufficient to include the region of spiral banding, with the exception of spiral bands extending to the northeastern corner of the domain.

Inner-core PV fields within the higher-resolution simulations are observed to take on a greater range of shapes, and to transition more frequently between shapes characterized by polygonal eyewall segments to more circular shapes. Therefore, while polygonal eyewall segments are increasingly common as resolution increases, the higher-resolution simulations also produce more circular PV towers as well (Fig. 7). At 63 h 20 min, the 8- and 6-km simulations still show an oval-shaped PV maximum similar to that shown previously, and the 4-km simulation has a PV structure still dominated by straight-line segments. However, the 3-, 2-, and 1-km simulations have transitioned to more circular shapes, with this transformation being most dramatic in the case of the 1-km run. Overall, the higher-resolution simulations produce a variety of shapes and frequently transition from an appearance dominated by polygonal segments to more circular structures (Figs. 6 and 7). It is hypothesized that these structural changes stem from the ability to resolve a greater range of wavenumbers in the higher-resolution runs. Therefore, a wider variety of VRW wavenumbers are simulated, and this, in conjunction with stronger lateral PV gradients, leads to an increasing likelihood of wave breaking.

e. Spectral decomposition of PV

To quantitatively assess the ability of the finer-resolution runs to simulate higher wavenumber features, a spectral decomposition (SD) is performed of PV at 850 hPa, as outlined in chapter 6 of Panofsky and Brier (1968). A SD is computed from points along the radius of maximum PV3 (RMPV) defined at the 850-hPa level for each hour during the last 12 h of the simulation. These hourly SDs are then time averaged in order to examine consistent trends in the favored wavenumbers in each simulation. Note that this result may vary with altitude and could be significantly affected by the absence of strong vertical shear during this time period, with increased shear favoring wavenumber-1 asymmetry (Reasor et al. 2000). The time-averaged SD for each simulation, plotted for the first 10 wavenumbers, is shown in Fig. 10a. The large amount of variance in the 1-km run is expected, with the higher-magnitude PV anomalies being present in the annular ring of PV associated with the eyewall in that simulation (Figs. 6f and 7f). All other simulations show significantly less variance, with the finer-resolution runs generally producing more variance than the coarser runs at almost every wavenumber. The normalized variance at each wavenumber is also computed in order to determine what percentage of the total variance is found at a given wavenumber (Fig. 10b).

Dashed lines indicate variance at wavenumbers that have a spatial scale smaller than 10Δx (fully resolved) along the circumference of the RMPV. In the coarser-resolution runs, some wavenumbers that are not fully resolved contain a significant amount of variance, over 10% in both the 8- and 6-km runs. The normalized variance is partitioned into the sum of the all wavenumbers with a scale greater than 10Δx along the circumference of the RMPV, those wavenumbers between 10 and 4Δx, and the remaining variance at unresolved wavenumbers (Fig. 11). Again, the 8- and 6-km runs allocate more variance to wavenumbers that are not fully resolved, and simulations with grid spacing of 4 km or less tend to distribute less variance to unresolved wavenumbers. This further supports the previous contention that the higher-resolution simulations have the ability to produce a greater range of resolved VRW wavenumbers; therefore, they are capable of forming a greater variety of eyewall shapes.

It is also possible that higher resolution allows better representation of the axisymmetization process, but investigation of this possibility is not pursued in the current study. However, Möller and Montgomery (2000) did not note significant sensitivity of the axisymmetrization process to resolution when using grid spacings of 2.5 and 5 km in their idealized TC experiments. Finally, we note that observational studies have documented polygonal eyewalls, and it is not implied here that simulated polygonal eyewalls are necessarily unrealistic (e.g., Lewis and Hawkins 1982). The ability for a model to resolve a broader spectrum of wavenumbers does not guarantee that the spectral power would become evenly distributed. Investigation of the physical processes that determine this power distribution are beyond the scope of the current paper.

4. Summary and concluding remarks

This study investigates the sensitivity of the simulated structure and intensity of Hurricane Ivan to horizontal resolution for grid lengths ranging from 8 to 1 km. Hurricane Ivan is chosen because it was an intense storm with representative size characteristics, allowing extrapolation of results to other TCs. All simulations successfully reproduced the track of Ivan. However, within this nested model configuration, it is likely that the outer, coarser nests dictated the TC’s path, producing the steering flow that influenced the storm track. With one-way nesting, the impacts of greater storm intensity on the inner domains did not influence the outer-domain solution.

The objective of this study is to investigate what changes occur in the representation of physical processes important to TC intensity as horizontal grid spacing is varied over operationally feasible grid lengths. According to the typical observed sizes discussed by Kimball and Mulekar (2004), the spatial scale of the RMW would often be fully resolved with a grid length of approximately 6 km. However, observations by Eastin et al. (2005) suggest that grid spacing of 1 km could only partially resolve the largest realistic updraft and downdraft cores within the eyewall. Simulated peak intensity ranges from 12 hPa stronger than observed in the 1-km simulation to 18 hPa weaker in the 8-km run (Fig. 1). As grid spacing is decreased below 4 km, more deepening per decrease in grid spacing is realized, with as much as a 10-hPa reduction in lowest minimum central pressure as grid spacing drops from 3 to 2 km.

The horizontal and vertical character of the eyewall varied considerably over the range of grid lengths investigated. Simulations with grid spacing of 4 km occasionally produce eyewalls characterized by straight-line segments, as well as more circular shapes (Figs. 6 and 7). Also in these simulations, PV anomalies are observed to break off from the high-PV region associated with the eyewall and enter the low-PV environment of the eye. A spectral decomposition of the 850-hPa PV field, performed at the RMPV, finds that runs with a grid spacing of 4 km and below tend to allocate variance in the PV field to wavenumbers that are at least partially resolved (Fig. 11). As grid spacing is reduced toward 1 km, the inner-core PV tower is observed to take on a variety of shapes and is more often circular. This is consistent with higher-resolution simulations producing a greater range of VRW wavenumbers. Although not investigated here, the tendency of the higher-resolution simulations to produce a greater variety of eyewall shapes, both circular and polygonal, may also be related to its ability to represent the axisymmetrization process at finer grid spacing, destroying the PV maxima associated with breaking VRWs and polygonal eyewalls (Möller and Montgomery 2000).

Azimuthally averaged eyewall updrafts are more intense and exhibit a more upright orientation as resolution is increased, with the 1-km simulation exhibiting the strongest eyewall updraft (Fig. 2). As resolution increases, the finer-resolution simulations are characterized by eyewalls that are not only more upright, but also smaller in spatial extent, with the RMW generally reduced with grid spacing (Table 3). This is consistent with the findings of Stern and Nolan (2009), who demonstrated that the outward slope of the RMW with height is directly proportional to the size of the RMW. Within higher-resolution simulations, the TC eyewall is characterized by larger vertical motions and a larger range of vertical motions, as well as higher PV values (Figs. 2, 5, and 8). The anticyclonic vertical shear and vertical tilt of the eyewall are shown to be in agreement with the gradient thermal wind relationship in all cases (Fig. 3). However, anticyclonic shear tends to exist above the strongest cyclonic winds in the case of the coarser runs, but is offset toward the eye–eyewall boundary in the finer-resolution simulations. This is consistent with a deeper vertical extent of strongest azimuthal cyclonic flow.

The sensitivity of physical processes to grid spacing has been discussed, with the goal of suggesting the appropriate grid spacing to be used for operational prediction. It is found that some deepening of the TC does occur as the grid length is decreased from 8 to 6 km. However, the TC structure changes little until the grid spacing drops to 4 km. Even though there is little increase in TC intensity as grid spacing is lowered from 6 to 4 km, the physical processes simulated do appear to change, with polygonal eyewall segments as well as better-developed inner spiral bands appearing more strongly at grid spacing of 4 km and below. As resolution is increased, CFADs show a broadening of the range of the most intense vertical motions (Fig. 5). At grid spacing of 3 km and below, there is a significant drop in minimum central pressure. Also, polygonal eyewall structures and localized, intense updraft cores appear more frequently at the 850-hPa level in the highest-resolution simulations. At 1-km grid spacing, updrafts on the order of 10 m s−1 are present even at lower altitudes (Fig. 4). While updrafts of this magnitude at such low altitudes may seem surprising, they are consistent with the observational study of Hurricane Hugo by Marks et al. (2008). At 1-km grid spacing, an ensemble of isolated eyewall updraft cores appears, along with downdraft cores, within the eyewall at lower levels. Overall as grid spacing is decreased, the structure and evolution of Ivan undergo significant changes, with the finest resolution, the 1-km simulation, exhibiting markedly different structure from the other simulations. This indicates that at these grid spacings, the model solution has not yet converged. This is consistent with the convective system simulations of Bryan et al. (2003), who found that model convergence does not occur even with grid spacing well below 1 km.

After the original submission of this manuscript, the authors were made aware of a similar study by Fierro et al. (2009). That study examined a similar range of grid lengths for the case of Hurricane Rita (2005). Our results exhibit a high degree of consistency with those of Fierro et al., which supports further generalization of the results of both studies. Although findings related to structural and kinematic properties were highly consistent, an important difference is that Fierro et al. (2009) found very similar intensities between runs with different grid spacing, whereas the current study found considerable variation. This may be attributable to the use of two-way nesting in their study, their smaller domain size, or case-dependent factors.

Although simulations from a single case were presented here, some suggestions can be made regarding the more general question of the optimal grid spacing for operational prediction. As the simulated storm tracks are extremely similar, the representation of TC structure and intensity are instead emphasized here. It is apparent that for simulations where it is only necessary to simulate the components of a warm-core, TC vortex with an eyelike structure, 8-km grid spacing is sufficient. In an operational environment, where a correct prediction of track and intensity are critical, grid spacing of 4 and 6 km provide similar performance in this case. However, the results of this case study suggest that even small reductions in grid spacing below 4 km produce larger changes in the representation of intensity. The ability to resolve a larger spectrum of VRWs appears to favor the development of more circular eyewalls, and resolution of spiral bands at 3-km and smaller grid lengths may also improve representation of the intensification process. In order for viable numerical predictions that are able to simulate the full TC intensity, grid spacing no greater than 2 or 3 km should be employed. It should also be noted that the size of the innermost domain should be sufficiently large to allow realistic evolution of the eyewall and surrounding primary circulation, as well as spiral bands and anticyclonic outflow features. This typically requires a grid dimension of at least 500 km. Additional experiments should be performed to explore sensitivity to domain size.

Priorities in a research environment can differ from an operational one, with an emphasis on realistic representation of physical processes and time constraints relaxed for model integration time. If features on the scale of the eyewall itself are to be studied in a research environment, these results suggest that 2 km is the coarsest resolution that should be used. At a grid spacing of 2 km, features within the eyewall (i.e., an ensemble of updraft cores within the eyewall) begin to be somewhat resolved. However, only at 1-km grid spacing, are both updraft and downdraft cores within the lower levels of the eyewall partially resolved. As with any single case, additional simulation comparisons of other storms should be made, and simulations with grid lengths below 1 km should be explored.

Acknowledgments

This research was supported by NSF Grants ATM-0334427 and ATM-0603760, and DOE Grant ER64448, all awarded to North Carolina State University. The authors would also like to thank the Renaissance Computing Institute (RENCI) for making available their computing resources and technical support. The authors are also grateful to Kevin Hill for suggestions on an earlier draft of this manuscript, in addition to assistance with technical tasks. We are grateful to Drs. Frank Marks and Alexandre Fierro for constructive comments and suggestions regarding this study. Drs. Semazzi and Aiyyer of North Carolina State University also provided helpful discussion and suggestions on this work. The authors would also like to thank two anonymous reviewers for their helpful comments on this manuscript. The WRF model is made available by the National Center for Atmospheric Research (NCAR), which is sponsored the National Science Foundation.

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Fig. 1.
Fig. 1.

Minimum central pressure as a function of time for the 8- (purple), 6- (blue), 4- (green), 3- (orange), 2- (red), and 1-km (pink) runs, plotted with best-track observations (black) from the NHC (Stewart 2008). Lowest central pressure for each run is shown in the inset box.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 2.
Fig. 2.

Azimuthal- and time-averaged cross sections of positive vertical motion (every 0.25 m s−1) for the (top left) 8-, (top middle) 6-, (top right) 4-, (bottom left) 3-, (bottom middle) 2-, and (bottom right) 1-km simulations, all averaged to 8-km grid spacing and shown from the center of the storm to 150 km away, with a black vertical line placed every 50 km. The brown (white) area denotes ascent greater than 2 (2.5) m s−1. Note that positive and negative values of vertical motion are partitioned before any averaging takes place, in order to prevent cancellation.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 3.
Fig. 3.

As in Fig. 2, but with the change in symmetric tangential velocity with pressure (filled every 0.05 m s−1 hPa−1 up to 0.1 m s−1 hPa−1 and then by 0.1 m s−1 hPa−1 thereafter), the horizontal derivative of symmetric potential temperature (contoured in red at 1, 3, and 5 × 10−4 K m−1) and tangential winds (contoured every 10 m s−1 from 50 to 80 m s−1 in black).

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 4.
Fig. 4.

850-hPa vertical wind component at simulation time 63 h 20 min contoured 0.5 m s−1 up to 5 m s−1 and every 1 m s−1 thereafter for the (a) 8-, (b) 6-, (c) 4-, (d) 3-, (e) 2-, and (f) 1-km runs, with positive vertical motion in warmer colors and negative vertical motion in cooler colors. Purple coloring indicates updraft speed in excess of 5 m s−1. The point maxima (minima) of vertical velocity at this time are 4.66 (−2.54) m s−1 for the 3-km run, 5.58 (−3.34) m s−1 for the 2-km run, and 11.06 (−10.58) m s−1 for the 1-km run.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 5.
Fig. 5.

CFADs of vertical velocity (m s−1) for the (top left) 8-, (top right) 6-, (middle left) 4-, (middle right) 3-, (bottom left) 2-, and (bottom right) 1-km simulations, taken every hour for the last 12 h of the simulation and averaged. Bin size is 0.5 m s−1. The 0.1% of vertical motions are contoured in solid black, 5% are contoured in the dashed line. CFADs are taken from points between 25 and 150 km of the TC center for the 8- and 6-km runs, and between 25 and 100 km for all other simulations.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 6.
Fig. 6.

850-hPa PV at 63 h into the simulation scaled by 10−6 and contoured every 5 PVU from 10 PVU, shown for the (a) 8-, (b) 6-, (c) 4-, (d) 3-, (e) 2-, and (f) 1-km runs. Note that both this figure and the next one are representative of the appearance of the PV field at different times throughout the run.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 7.
Fig. 7.

As in Fig. 6, but at simulation time 63 h 20 min, 20 min later.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 8.
Fig. 8.

Azimuthal- and time-averaged cross sections of PV (scaled by 10−6 and filled every 5 PVU) and potential temperature (contoured in black every 5 K), plotted as in Fig. 2.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 9.
Fig. 9.

At simulation time 63 h 20 min, composite model-simulated radar for the (a) 8-, (b) 4-, (c) 2-, and (d) 1-km runs. Note that, unlike in previous figures, these images differ in spatial extent, according to the size of the model domains as expressed in Table 1.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 10.
Fig. 10.

(a) Temporally averaged variance of 850-hPa PV at the radius of maximum PV (RMPV) in each run, plotted according to wavenumber with colored lines as in Fig. 1. (b) Variance is normalized, such that the value shown is the fraction of the total variance. The inset box shows the averaged 850-hPa RMPV for each simulation. (bottom) Dashed lines correspond to wavelengths less than 10Δx in the azimuthal direction along the circumferences inferred from the average RMPV.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Fig. 11.
Fig. 11.

As in Fig. 10b, but segmented by wavenumbers corresponding to azimuthal wavelengths of 10Δx (fully resolved wavenumbers), wavelengths of 4Δx (partially resolved wavenumbers), and the residual or all other remaining wavenumbers.

Citation: Monthly Weather Review 138, 3; 10.1175/2009MWR2976.1

Table 1.

The designations and characteristics of different simulations. As the moving-nest feature is used for these simulations, some grids are produced by the same model simulation (such as the 6- and 2-km run). The domain size is expressed in the length of the domain on each side.

Table 1.
Table 2.

Comparison of minimum central pressure, as derived from the full sea level pressure field at its original grid spacing versus the sea level pressure field azimuthally averaged to a common resolution. All values are in hPa.

Table 2.
Table 3.

Comparison of RMW, as derived from the azimuthally averaged 10-m wind every hour and then averaged over the last 12 h of the run. Azimuthal averages are done, in this case, with bins of a width equal to that of the original grid spacing. All values are in km.

Table 3.

1

The storm center is determined at every vertical level by smoothing the geopotential height with a Gaussian filter, with the center defined as the minimum in the filtered field. Therefore, the center is allowed to vary with height, as has been done in other studies (Marks et al. 1992; Lee and Marks 2000; Rogers et al. 2003). At pressure levels where the minimum central pressure of the storm is less than the pressure at that level, the minimum of the Gaussian-smoothed sea level pressure field is used. The filter weights are normally distributed, and the standard deviation of the weight computations was set to a value of 60 points.

2

CFADs are computed from points within 150 km of the TC center in the 8- and 6-km runs, and within 100 km for all other simulations, in order to capture the TC eyewall. As both the RMW and outward slope of the eyewall are reduced as resolution is increased, the area where the main eyewall updraft is present is smaller (Fig. 2). Points within 25 km of the TC center are not included, in order to exclude vertical motions within the eye. Points over land are omitted as well.

3

The radius is determined by the azimuthally averaging PV at 850 hPa, where the SD is computed from points along the RMPV. Again, the minimum in the Gaussian-filtered geopotential height field is used as the center of the TC. The number of points found along the RMPV vary, with as few as 24 points being used in the SD for the 8-km run, and as many as 208 points being used in the 1-km run’s SD.

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