An Evaluation of the Impact of Horizontal Resolution on Tropical Cyclone Predictions Using COAMPS-TC

Hao Jin Naval Research Laboratory, Monterey, California

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Melinda S. Peng Naval Research Laboratory, Monterey, California

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Yi Jin Naval Research Laboratory, Monterey, California

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James D. Doyle Naval Research Laboratory, Monterey, California

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Abstract

A series of experiments have been conducted using the Coupled Ocean–Atmosphere Mesoscale Prediction System–Tropical Cyclone (COAMPS-TC) to assess the impact of horizontal resolution on hurricane intensity prediction for 10 Atlantic storms during the 2005 and 2007 hurricane seasons. The results of this study from the Hurricane Katrina (2005) simulations indicate that the hurricane intensity and structure are very sensitive to the horizontal grid spacing (9 and 3 km) and underscore the need for cloud microphysics to capture the structure, especially for strong storms with small-diameter eyes and large pressure gradients. The high resolution simulates stronger vertical motions, a more distinct upper-level warm core, stronger upper-level outflow, and greater finescale structure associated with deep convection, including spiral rainbands and the secondary circulation. A vortex Rossby wave (VRW) spectrum analysis is performed on the simulated 10-m winds and the NOAA/Hurricane Research Division (HRD) Real-Time Hurricane Wind Analysis System (H*Wind) to evaluate the impact of horizontal resolution. The degree to which the VRWs are adequately resolved near the TC inner core is addressed and the associated resolvable wave energy is explored at different grid resolutions. The fine resolution is necessary to resolve higher-wavenumber modes of VRWs to preserve more wave energy and, hence, to attain a more detailed eyewall structure. The wind–pressure relationship from the high-resolution simulations is in better agreement with the observations than are the coarse-resolution simulations for the strong storms. Two case studies are analyzed and overall the statistical analyses indicate that high resolution is beneficial for TC intensity and structure forecasts, while it has little impact on track forecasts.

Corresponding author address: Hao Jin, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. E-mail: hao.jin@nrlmry.navy.mil

Abstract

A series of experiments have been conducted using the Coupled Ocean–Atmosphere Mesoscale Prediction System–Tropical Cyclone (COAMPS-TC) to assess the impact of horizontal resolution on hurricane intensity prediction for 10 Atlantic storms during the 2005 and 2007 hurricane seasons. The results of this study from the Hurricane Katrina (2005) simulations indicate that the hurricane intensity and structure are very sensitive to the horizontal grid spacing (9 and 3 km) and underscore the need for cloud microphysics to capture the structure, especially for strong storms with small-diameter eyes and large pressure gradients. The high resolution simulates stronger vertical motions, a more distinct upper-level warm core, stronger upper-level outflow, and greater finescale structure associated with deep convection, including spiral rainbands and the secondary circulation. A vortex Rossby wave (VRW) spectrum analysis is performed on the simulated 10-m winds and the NOAA/Hurricane Research Division (HRD) Real-Time Hurricane Wind Analysis System (H*Wind) to evaluate the impact of horizontal resolution. The degree to which the VRWs are adequately resolved near the TC inner core is addressed and the associated resolvable wave energy is explored at different grid resolutions. The fine resolution is necessary to resolve higher-wavenumber modes of VRWs to preserve more wave energy and, hence, to attain a more detailed eyewall structure. The wind–pressure relationship from the high-resolution simulations is in better agreement with the observations than are the coarse-resolution simulations for the strong storms. Two case studies are analyzed and overall the statistical analyses indicate that high resolution is beneficial for TC intensity and structure forecasts, while it has little impact on track forecasts.

Corresponding author address: Hao Jin, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. E-mail: hao.jin@nrlmry.navy.mil

1. Introduction

More than 50% of the U.S. population is concentrated in coastal regions, according to a National Oceanic and Atmospheric Administration (NOAA) report (Crossett et al. 2008). Many of these populated coastal areas are vulnerable to destructive winds and heavy precipitation associated with tropical cyclones (TCs), along with storm surges, flooding, and landslides, causing anywhere from millions to billions of dollars of property damage each year. For example, the economic loss from Hurricane Katrina (2005) alone exceeded $150 billion (Burton and Hicks 2005) and the financial losses from Superstorm Sandy (2012) were estimated at $60 billion (Associated Press 2012). To mitigate these impacts, it is important to accurately forecast TC track and intensity at sufficiently long forecast lead times. Hurricane track forecasts have improved by 50% in the past 10 years; however, little progress has been achieved for hurricane intensity forecasts during the same period (DeMaria et al. 2007). One main reason for this lack of improvement in the hurricane intensity forecasts is that the track is primarily influenced by the large-scale environment, which has improved steadily through advancements in numerical weather prediction techniques and data assimilation methods. In contrast, the storm intensity and structure changes depend on inner-core dynamics and thermodynamics, and their interactions with the large-scale environment (Davis et al. 2008). These multiscale interactions, which span from vortex to synoptic scales, are inherently nonlinear and remain a major challenge for numerical models. The forecasts of the large-scale environment also have steadily improved, in part, due to the advancement of remote sensing and data assimilation technology. However, observational data near the TC inner core (such as airborne radar and dropsonde), needed for initialization of the three-dimensional vortex structure, are typically very limited or very difficult to use.

Numerical models with grid spacing at 10 km or coarser usually adopt convective parameterizations to represent the subgrid-scale deep convection. It is generally recognized that at high resolution (1–5 km), a great portion of the deep convection can be resolved explicitly using cloud microphysics (Tripoli 1992). Skamarock and Baldwin (2003) found that the kinetic energy spectra are sensitive to the dynamic core, model physics, and grid resolution. The higher cloud-resolving resolution experiments have a −5/3 spectral slope in the kinetic energy spectrum. Generally, global models have insufficient resolution to simulate TC inner-core structure and intensity. A mesoscale-resolving global model used by Shen et al. (2006) simulated Katrina intensity well at ⅛° resolution. Regional models with a large, coarse domain for the TC environment and multiple storm-following nested domains reaching convective-permitting resolution have been adopted for TC research. Recent studies showed that the high-resolution convective-permitting simulations of TCs can better represent the inner-core structure and improve hurricane intensity forecasts (Hendricks et al. 2004; Chen et al. 2007). The results of Rogers (2010) suggested that convective-permitting resolution (1–3 km) may be required for representing the TC inner-core dynamics. Using an idealized framework of the experimental Hurricane Weather and Research Forecast System (HWRF), Gopalakrishnan et al. (2010) found that the simulated storm development and thermodynamic structure are sensitive to the horizontal grid spacing.

The vortex and its associated deep convection are one of the major foci of TC research. Vortex Rossby waves (VRWs), introduced by MacDonald (1968), were found to be propagating on the radial gradient of the vortex near the TC inner core and are related to the secondary circulation. Since then, VRWs have been widely used as a tool to examine the TC inner-core structure and deep convection (Montgomery and Kallenbach 1997; Wang 2002a,b). Gentry and Lackmann (2010) performed sensitivity experiments with grid resolutions ranging from 8 to 1 km for Hurricane Ivan (2004) and concluded that increasing horizontal resolution better resolves the breaking of VRWs, thereby increasing the intensity. Their results indicated that simulations with grid spacing of 4 km or less tend to produce a greater variety of eyewall structures, alternating between polygonal and circular eyewalls, presumably due to the ability to resolve more wavenumbers at higher resolution.

The most reliable measure of TC intensity is arguably the minimum sea level pressure (MSLP), but it is difficult to obtain without direct surface and dropsonde observations or reconnaissance flight data. The maximum surface wind speed (MWS) can be retrieved from satellite observations, although there are resolution constraints with many of the sensors. The relationship between the MWS and the MSLP, known as the wind–pressure relationship (WPR), is also a function of TC environment and structure, varying from case to case. Five different WPRs have been widely used in the operational TC centers for TC forecasts and advisories (Knaff and Zehr 2007). The WPR fit for numerical model results at different resolutions, validated against the operational WPRs, can be used as a metric to evaluate the model performance.

The NOAA Hurricane Forecast Improvement Project (HFIP) was established in 2007 with a 10-year plan to improve 1–5-day hurricane forecasts with a focus on the prediction of intensity. The High Resolution Hurricane (HRH) test, the first HFIP retrospective project, comprises 10 Atlantic TCs during 2005 and 2007 (Developmental Testbed Center 2009). Table 1 lists the six (Emily, Katrina, Ophelia, Phillippe, Rita, and Wilma) TCs in 2005 and the four (Felix, Humberto, Ingrid, and Karen) TCs in 2007, along with their identification number, and the time periods of cases for each storm. This selection of the TCs covers a broad region over the western Atlantic Ocean and a diverse set of TC intensities (Fig. 1). The goal of this study is to identify the potential benefits of increasing model horizontal resolution, ranging from a relatively coarse (with convective parameterization) to a fine grid (with cloud microphysics), and to document the combined impacts of the grid resolution and cloud physics on track, intensity, and structure prediction.

Table 1.

Ten Atlantic TCs during 2005 and 2007 selected for the HFIP HRH test.

Table 1.
Fig. 1.
Fig. 1.

Ten Atlantic TCs during 2005 and 2007 selected for retrospective track and intensity forecasts for the HRH test (Developmental Testbed Center 2009). The major hurricanes (red dots) are tropical cyclones of category 3 and higher (with MWS over 96 kt) based on the Saffir–Simpson hurricane scale, while the nonmajor hurricanes (orange dots) are categories 1 and 2 (with MWS between 64 and 96 kt). The tropical depression (blue dots) has MWS below 32 kt and the tropical storm (yellow dots) has MWS between 32 and 64 kt.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS1) is the operational regional prediction system developed by the Naval Research Laboratory (NRL). A new version of COAMPS has recently been developed for the prediction of TCs (COAMPS-TC2; Doyle et al. 2012). COAMPS-TC is one of the six models that participated in the HRH effort. Each modeling group conducted their own simulations with different configurations, with at least two different grid spacings ranging from 1 to 9 km. Each group interpolated its model results from its native model grid to a standardized uniform latitude and longitude grid for evaluation. The Geophysical Fluid Dynamics Laboratory (GFDL) tracker (Marchok 2002) was used to identify the storm track and intensity from datasets sent from the six groups.

To simulate the multiscale nature of TCs in a computationally efficient manner, multiple two-way nested grid meshes are constructed. The outermost coarse-resolution domain needs to be large enough (HRH guideline is for a grid that covers at least 65° × 65°) to properly represent the large-scale environment and to minimize the lateral boundary impacts. The fine-mesh grid needs to have high enough resolution (on the order of 1–5 km) to resolve the eye, the eyewall, and the secondary circulation. Two independent configurations for COAMPS-TC, one with four nested meshes and the other with three meshes, are used in this study for the 54 cases of the 10 selected storms. The 3-km runs consume about 6 times the computational resources as do the 9-km runs. The objectives of this study are to 1) investigate the impact of increasing horizontal resolution on the track and intensity for Hurricane Katrina; 2) study the TC inner-core structure and verify against satellite observations and the NOAA/Hurricane Research Division’s (HRD) Real-Time Hurricane Wind Analysis System (H*Wind; Powell et al. 1998); 3) apply wave spectrum analysis to the simulated 10-m winds and the H*Wind, and to study the impact of resolution on the resolvable VRW wave energy near TC inner cores; 4) study the resolution impact on TC vertical structure and development; 5) examine the impact of different resolutions on the TC wind–pressure relationship; and 6) evaluate the impact of grid resolutions on TC track and intensity forecasts for all the cases. This systematic evaluation of the impacts of grid resolutions on TC forecasts can provide guidance for model configurations for regional TC prediction.

2. Model overview and configuration

COAMPS-TC consists of data quality control, data assimilation, initialization, a nonhydrostatic atmospheric model, and a hydrostatic ocean model (Chen et al. 2010; Hodur 1997). The Arakawa C grid and the sigma-z vertical coordinate are utilized in the atmospheric model. The Kain–Fritsch cumulus parameterization is used for grid spacing at 9 km or larger, and a modified bulk microphysics parameterization based on Rutledge and Hobbs (1983) is applied on all domains. The planetary boundary layer turbulent mixing scheme is based on a modified 1.5-order Mellor–Yamada scheme (Mellor and Yamada 1974) and includes a mixing length representation following Bougeault and Lacarrère (1989), as well as a dissipative heating parameterization (Jin et al. 2007). The drag coefficient levels off for high winds (Donelan et al. 2004). The surface layer scheme is based on Wang et al. (2002). The model includes shallow convection (Tiedtke et al. 1988) and radiation (Harshvardhan et al. 1987) parameterizations.

Two sets of experiments with different configurations are conducted, both with fixed outermost coarse meshes of 81-km grid spacing and dimensions of 105 × 103. The first set identified as the fine-resolution experiment has three moving two-way nested domains with 27-, 9-, and 3-km horizontal grid spacings, and dimensions of 91 × 91, 169 × 169, and 235 × 235, respectively (Fig. 2). The second set identified as the coarse-resolution experiment has only two moving nested domains of 27 and 9 km, respectively. Both configurations have 40 vertical levels with a model top at 32 km. The model lowest level is at 10 m above the surface.

Fig. 2.
Fig. 2.

COAMPS-TC domains use a Mercator map projection. A 75° × 100° coarse mesh extends from 15°S to 60°N and from 120° to 20°W. The coarse domain is fixed and has an 81-km horizontal gird spacing. The inner three mesh domains have 27-, 9-, and 3-km grid spacings and move with the hurricane center.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The Navy Operational Global Atmospheric Prediction System (NOGAPS) analysis fields are used to provide the first-guess fields for the first forecast (as a cold start) for each storm. The subsequent warm-start runs use the COAMPS-TC forecasts from the previous 12 h for the same storm. A relocation method is used to place the initial vortex at the position issued by the TC warning message from National Hurricane Center (NHC) in the first-guess field. Synthetic observations are constructed based on the NHC warning message and treated as additional radiosonde data to improve the representation of the initial vortex intensity and structure. The NRL Atmospheric Variational Data Assimilation System (NAVDAS; Liou and Sashegyi 2012), a three-dimensional variational data assimilation method, is used in all nests to assimilate the conventional (radiosonde, surface, and aircraft) and satellite observational data. The Navy Coupled Ocean Data Assimilation (NCODA; Cummings 2005) is used to assimilate ocean data, including altimeter, Special Sensor Microwave Imager (SSM/I), Multi-Channel Sea Surface Temperature (MCSST), airborne expendable bathythermograph (AXBT) profile, and ship data. The NOGAPS forecast fields at 1° resolution and 6-h intervals are linearly interpolated both in time and space to provide lateral boundary conditions for the outermost coarse domain at every time step. The forecast lengths vary from 48 to 126 h for different stages of the TC life spans. The simulations are carried out without ocean coupling and the SST generated from NCODA at the initial time does not change during the integration.

3. Katrina simulation

a. Katrina track and intensity forecasts

Simulations of Hurricane Katrina (2005) are used as a case study to highlight the impact of the different horizontal grid spacing (9 versus 3 km) on track and intensity forecasts. Five simulations of Katrina from different initial times (every 24 h from 0000 UTC 25 August to 0000 UTC 29 August 2005) are conducted for both coarse- (9 km) and fine-resolution (3 km) configurations. Overall, the forecast tracks from both configurations are similar and compare well with the TC postseason analysis data (i.e., best track; see Figs. 3a,b). The averaged track errors are 45 nautical miles (n mi; 1 n mi = 1.852 km) at 24 h, 87 n mi at 48 h, 128 n mi at 72 h, 144 n mi at 96 h, and 163 n mi at 120 h. The small differences from the two sets of experiments suggest that using fine resolution has little impact on TC track forecasts, in agreement with the results shown in Gopalakrishnan et al. (2012) using the HWRF.

Fig. 3.
Fig. 3.

Time evolutions of the (a),(b) track; (c),(d) MWS (kt); and (e),(f) MSLP (hPa) from Hurricane Katrina forecasts for the (top) 9- and (bottom) 3-km configurations evaluated against the best track. The best track is in black and the other five colors correspond to the different model initialization times with 24-h intervals. The dots are 6 h apart and the big double circles indicate the landfall time.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

Figures 3c–f depict the intensity forecasts for the five Katrina simulations compared to the best track. The 3-km resolution simulations from 25 to 29 August improve MWS and MSLP forecasts over those from the 9-km simulations. For example, the simulated maximum intensity starting at 0000 UTC August 27 reaches category 5 with a slightly delayed peak in the 3-km simulation (Figs. 3d,f), while the 9-km resolution experiment only reaches category 3 (Figs. 3c,e). The average MWS and MSLP at landfall are about 80 knots (kt; 1 kt = 0.51 m s−1) and 940 hPa, respectively, in the 9-km simulations, versus 110 kt and 920 hPa in the 3-km simulations, respectively, which are closer to the NHC best-track estimates (110 kt and 923 hPa). Both the 3- and 9-km simulations illustrate that the model simulated the timing of the rapid weakening very well after the simulated Katrina makes landfall. The coarse-resolution simulations have a much weaker initial MWS (about a 20-kt drop) and a more unbalanced initial vortex (indicated by a drop in MWS in the first 6 h) than those in the fine-resolution simulations. Overall, the intensities in the 3-km simulations are much stronger (about 30%–40%) than those at 9 km. The results support the notion that the fine-resolution simulations have advantages over the coarse-resolution simulations in intensity predictions for intense storms.

b. Katrina inner-core structure

The vortex structure of Hurricane Katrina is examined in detail for the forecast initiated at 0000 UTC 26 August 2005. The model-simulated radar reflectivity at 72 h and precipitable water at 78 h, computed from the model hydrometeor fields, are compared with satellite images from Geostationary Operational Environmental Satellite-12 (GOES-12) infrared (IR) Tropical Rainfall Measuring Mission (TRMM) 85H and GOES-13 IR Aqua overpasses at the corresponding times (Fig. 4). While the radar reflectivity fields from the two different resolutions have similar features in general, there are several noteworthy differences. The 9-km simulation has a larger eye (a 40-km radius), in contrast to a smaller eye (a 25-km radius) in the 3-km simulation. The relatively thick eyewall of ~150 km (indicated by an area of radar reflectivity exceeding 35 dBZ) in the 9-km simulation is much thicker than the 30-km eyewall in the 3-km simulation, and the latter compares better with the convection captured by the TRMM IR observations (Fig. 4c). The precipitable water in the 3-km simulation also illustrates a smaller eye, a thinner eyewall, and narrower spiral rainbands than in the 9-km simulation. These features are similar to the observation from the Aqua IR overpass (Fig. 4f).

Fig. 4.
Fig. 4.

Radar reflectivity (shaded; dBZ) at 72 h (valid for 0000 UTC 29 Aug 2005) from the (a) 9- and (b) 3-km simulations of Hurricane Katrina, starting at 0000 UTC 26 Aug 2005, compared with (c) the GOES-12 IR TRMM 85H overpass at 0000 UTC. The total precipitable water (shaded; mm) at 78 h from the (d) 9- and (e) 3-km simulations, compared with (f) the GOES-13 IR Aqua overpass at 0600 UTC.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The 10-m winds at 72 h, valid at 0000 UTC 29 August 2005, from the 3-km simulation are much stronger than those from the 9-km simulation (Figs. 5a,b). The distribution of a ring of strong 10-m winds from the 3-km simulation bears closer resemblance to the gridded H*Wind analysis (Fig. 5c), in particular the eye size and the associated eyewall structure. To examine the TC inner-core structure in greater detail, the 10-m winds and H*Wind analysis shown in Fig. 5 are zoomed in over a 160 km × 160 km subdomain near the storm center and displayed in Figs. 6a–c. A more circular TC inner core in the 3-km simulation is evident in contrast to the triangle-shaped core in the 9-km simulation. The large area of stronger wind speed (>90 kt) in the two eastern quadrants in the 3-km simulation is consistent with the structure from the H*Wind analysis. The corresponding relative vorticity from the 3-km, 9-km, and H*Wind simulations (Figs. 6d–f) indicate that the vortex in the 3-km simulation is much more compact and stronger than that in the 9-km simulation, and is closer to the H*Wind analysis. The azimuthally averaged radii of maximum wind (RMWs) are 64 and 41 km in the 9- and 3-km simulations, respectively. The RMW from the 3-km simulation is much closer to the observed RMW from the best track (20 n mi or 37 km; black circles in Fig. 6).

Fig. 5.
Fig. 5.

The 10-m winds (shaded, contour, and vector; kt) from the (a) 9- and (b) 3-km simulations, at 72-h forecast lead time (valid for 0000 UTC 29 Aug 2005), for Hurricane Katrina simulations starting at 0000 UTC 26 Aug, compared with (c) H*Wind analysis (original data from HRD) with the same scales at the same time.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

Fig. 6.
Fig. 6.

The zoomed-in TC inner-core regions (160 km × 160 km box from Fig. 5) of 10-m winds (kt) for the (a) 9-km, (b) 3-km, and (c) H*Wind simulations. The corresponding relative vorticities (10−3 s−1) for the (d) 9-km, (e) 3-km, and (f) H*Wind simulations. The red circles represent the azimuthally averaged RMWs from the simulations and black circles show the RMWs from the best track.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

c. VRW spectrum analysis

As stated earlier, analysis of the VRW associated with TCs can provide additional insight into the TC inner-core structure. An azimuthal VRW spectral analysis of relative vorticity containing wavenumbers 0–3 from both coarse and fine resolutions is performed and verified against the VRW spectrum from H*Wind (Fig. 7). The minimum grid increment to resolve a wave is 4Δx, where Δx is the grid spacing (Grasso 2000). On the other hand, Walters (2000) suggests that 10Δx is required from a practical perspective to represent the true amplitude and its first horizontal derivative in order to fully resolve the wave. Therefore, we consider the azimuthal waves fully resolved if their wavelengths are >10Δx, partially resolved if their wavelengths are between 10Δx and 4Δx, and unresolved if their wavelengths are <4Δx. The 3-km relative vorticity for wavenumber 0 is more compact and stronger than that for the 9-km version, and is closer to that for H*Wind (Figs. 7a–c). The 3-km simulation completely resolves wavenumbers 1–3 over most of the domain (shown by the color-shaded area) with the exception of an area within the 5-km radius. The radii of the partially resolved regions (the nonshaded contours) in the 9-km simulation are in the ranges of 5–14, 10–28, and 15–42 km for wavenumbers 1–3, respectively. The coverage areas of the partially and unresolved waves in the 9-km simulation, represented by the numbers of grid points included, are 9 times as large as those in the 3-km simulation. At the observed RMW (the black circles), the 9-km simulation can resolve waves 1 and 2, but cannot fully resolve wavenumber 3 (Fig. 7j). The results indicate that the high resolution is necessary to resolve higher-wavenumber modes and the associated wave energy near the TC inner-core region.

Fig. 7.
Fig. 7.

Wave spectral analysis of the relative vorticity (shown in Figs. 6d–f) for the (top) 9-km, (middle) 3-km, and (bottom) H*Wind simulations at wavenumbers (a)–(c) 0, (d)–(f) 1, (g)–(i) 2, and (j)–(l) 3. The shaded areas are for the fully resolved waves with their wavelengths >10Δx. The nonshaded contours are for the partially resolved waves (wavelengths between 10Δx and 4Δx) and the white areas are for the unresolved waves (wavelengths <4Δx). The red circles are the RMWs from the simulations and the black circles are for the RMWs from the best track.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The VRW analysis is used here to evaluate the resolution impact on the wave energy. A wave spectral variance analysis has been conducted at the observed RMW (the black circles in Fig. 7) for additional wavenumbers (up to 20) (Fig. 8a). The wave energy is used to denote the wave spectral variances. The total wave energy represented by wavenumbers 0–2 in the 3-km simulation is much higher than that in the 9-km simulation. The 3-km simulation can fully resolve wavenumbers 0–7, and partially resolve wavenumbers up to 20. In contrast, the 9-km simulation can only fully resolve wavenumbers 0–2, partially resolve wavenumbers 3–6, and cannot resolve any higher wavenumbers. The normalized variance analysis of the wave spectrum (Fig. 8b) indicates that the 3-km simulation can resolve 93.8% fully and 6.2% partially of the wave energy, compared to 79.8% and 16.8% in the 9-km simulation, respectively. About 3% of the wave energy in the 9-km simulation carried by high wavenumbers is unresolved and completely lost. Therefore, the 9-km grid spacing is insufficient to fully resolve the TC inner-core structure at wavenumbers higher than 2 at the observed RMW (37 km in this case). A sizable amount of wave energy is lost in the 9-km simulation near the eyewall where the main convective activity occurs. The fine grid spacing of 3 km is essential for resolving the small-scale TC inner-core structure and capturing the TC intensity.

Fig. 8.
Fig. 8.

(a) Wave spectral variances of the relative vorticity at the RMW of the best track (as shown in black circles in Fig. 7) at 72-h forecast lead time from the 3- (red) and 9-km (blue) runs. The solid lines are for the fully resolved waves, and the dotted lines for partially resolved waves. (b) Distributions of the normalized wave spectrum variances for the fully resolved (the solid boxes), partially resolved (the unfilled boxes with solid outlines), and unresolved waves (the boxes with dot outlines). (c),(d) As in (a),(b), but for the RMW from the model.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

Similar wave spectral variance analyses at the model-simulated RMW (64 km for 9-km and 41 km for 3-km) is shown in Figs. 8c and 8d. The wave energy difference between the 3- and 9-km simulations is even larger at wavenumber 0 (Fig. 8c), with the 3-km wave energy about 77% higher than that from the 9-km simulation. Comparing with the wave variances at the observed RMW (Fig. 8a), wavenumber 8 is fully resolved at the simulated RMW (41 km) in the 3-km simulation. Two more wavenumbers (3 and 4) are fully resolved and five additional wavenumbers (7–11) are partially resolved at the simulated RMW (64 km) in the 9-km simulation. The significant contribution of wavenumber 3 in the 9-km simulation can explain the triangle-shaped eyewall (Fig. 6a). The wave spectrum analysis here provides additional evidence that a higher resolution has the capability to represent a greater number of vortex waves and hence retains more details of the eyewall dynamic structure. For the normalized wave spectrum analysis at the simulated RMW (Fig. 8d), the high resolution resolves 94.5% fully and 5.5% partially of the wave energy, while the low-resolution grid has about 86.1% fully resolved, 13.0% partially resolved, and 0.9% unresolved.

d. Azimuthal analysis of TC vertical structure and development

The azimuthally averaged fields for the 9- and 3-km simulations are compared at the 84 forecast hours (Fig. 9). The 3-km simulation has much stronger tangential winds (10 m s−1 higher) in a deeper layer and a smaller eye than in the 9-km simulation. The area of strong tangential winds greater than 50 m s−1 in the 3-km simulation extends up to 13 km above the surface, whereas the 9-km simulation has only a limited area of winds reaching 50 m s−1 at about 5 km. The RMW of azimuthally averaged tangential winds in the 3-km simulation is about 35 km near the surface, which is much smaller than that in the 9-km simulation (about 60 km). The RMW vertical profile from the 3-km simulation (the red line in Fig. 9b) has a more vertical outward slope than that in the 9-km simulation. This result is consistent with the hypothesis of Stern and Nolan (2009) that the outward sloping of the RMW is a function of the size of RMW and the RMW slope increases with increasing intensity and decreasing RMW. Associated with the strong tangential flow in the 3-km simulation is stronger vertical velocity (~2 m s−1) along the inner edge of the more vertically aligned eyewall, relative to its 9-km counterpart (contours in Figs. 9c,d). Correspondingly, the azimuthally averaged equivalent potential vorticity distribution (shaded in Figs. 9c,d) depicts a much stronger, vertically stretched, and organized center in the 3-km simulation. The maximum potential vorticity reaches above 120 PVU at an altitude of 17 km in the 3-km simulation, which is twice as large as that in the 9-km simulation. The condensation heating rate distributions (contours in Figs. 9e,f), closely associated with the vertical velocity, show a much larger value in the 3-km simulation than that in the 9-km simulation. The potential temperature changes from the initial time depict a tighter structure and vertically stretched warm core in the 3-km simulation, compared to the 9-km simulation. The warm-core maximum in the 3-km simulation is found near the maximum potential vorticity and the temperature change reaches 35 K at a 15-km altitude. The upper-level warm core is found to be important in TC intensification (e.g., Zhang and Chen 2012). Therefore, the high-resolution run has stronger vertical motion along the eyewall and induces a larger condensation heating rate, which increases the warm-core temperature. The stronger temperature gradient across the eyewall further intensifies the vortex and its associated circulation. This process, similar to the development of Hurricane Andrew (1992) described in Zhang et al. (2002), provides a stronger positive feedback for the enhanced storm intensity in the 3-km simulation.

Fig. 9.
Fig. 9.

The azimuthally averaged (a) tangential (shaded; m s−1) and radial (contour; m s−1) winds, (c) potential vorticity [shaded; potential vorticity units (PVU)] and vertical velocity (contour; m s−1), and (e) potential temperature change from the initial time (shaded; K) and condensation heating rate (contour; 10−3 K s−1) for the 9-km simulation. (b),(d),(f) As in (a),(c),(e), but for the 3-km simulation. Results are for 84-h forecast lead time, valid at 1200 UTC 29 Aug 2005. The red lines mark the locations of the RMWs at different heights.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

Hovmöller diagrams of the azimuthally averaged fields are shown in Fig. 10. The tangential winds at a 2-km height reach 30 m s−1 at 25 h in the 3-km simulation, 15 h earlier than in the 9-km simulation (Figs. 10a,b). The maximum tangential wind at 2 km reaches above 65 m s−1 in the 3-km simulation, and is stronger than the 50 m s−1 maximum in the 9-km run. The RMW at 2 km in the 3-km simulation is 50 km at 30 h and decreases to 30 km by 90 h, in contrast to an RMW of 50 km at 48 h, which increases to 70 km by 90 h in the 9-km simulation. The vertical motions at the 2-km height are better organized and stronger in the 3-km simulation than those in the 9-km simulation (Figs. 10c,d). Two branches of upward motions, found near the 30- and 50-km radii at 30 h in the 3-km simulation, intensify and merge with time, indicating an eyewall replacement. The condensational heating rates at the 8-km height in both simulations (Figs. 10e,f) are closely linked to the mass of ascent results, which are much stronger in the 3-km simulation than in the 9-km simulation. The core of the hurricane is much warmer (Fig. 10h) and the potential vorticity (Fig. 10j) is stronger due to the more vigorous positive feedback found in the 3-km simulation. A time series of vertical profiles of the azimuthally averaged radial wind at the 150-km radius from the storm center (Figs. 11a,b) shows that the outflow near the 16-km altitude in the 3-km simulation is more intense than that in the 9-km simulation. This result is highly correlated with the time–height distribution of the average vertical velocity at the 100-km radius (Figs. 11c,d), indicative of a better organized secondary circulation pattern in the 3-km simulation.

Fig. 10.
Fig. 10.

Hovmöller diagrams (0–96 h) of the azimuthally averaged fields: (a) tangential wind (shaded; m s−1) and RMW (red line) at 2-km height, (c) vertical velocity (m s−1) at 2 km, (e) condensate heating rate (10−3 K s−1) at 8 km, (g) potential temperature (K) at 8 km, and (i) potential vorticity (PVU) at 8 km for the 9-km configuration. (b),(d),(f),(h),(j) As in (a),(c),(e),(g),(i), but for the 3-km simulation. Forecasts start at 0000 UTC 26 Aug 2005.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

Fig. 11.
Fig. 11.

Time–height distributions of azimuthally averaged radial wind (shaded; m s−1) at the 150-km radius away from the storm center for the (a) 9- and (b) 3-km simulations. The averaged vertical velocity (shaded; m s−1) at the 100-km radius for the (c) 9- and (d) 3-km simulations. Forecasts start at 0000 UTC 26 Aug 2005.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The analysis of the Katrina simulations demonstrates that the simulated hurricane inner-core structure is very sensitive to the horizontal resolution. The finer resolution resolves more details of the inner-core structure associated with the wave energy at higher wavenumbers. Cloud microphysics with greater latent heating release at higher resolution produces a stronger MWS (reaching category 5) and a lower MSLP, which are more consistent with the observations. The high-resolution simulation generates a much smaller and warmer eye, and stronger vertical motion along the inner side of the more vertically oriented eyewall. The representation of the microphysics processes at the higher resolution also produces more realistic features of small-scale convection embedded in the spiral rainbands.

4. Statistics for all cases

a. Wind–pressure relationship

The WPR for all 10 storms, which have over 2000 data points over a wide range of intensities, from tropical storms to category-5 hurricanes, is shown in Fig. 12a for the 9- (blue dots) and 3-km (red dots) simulations, as well as the best track (black dots). The MWS from the best-track data is rounded up to 5-kt intervals. The MSLP distributions of the black dots at a specific MWS value indicate that the corresponding MSLPs may vary due to the size, structure, and location of the storm (Knaff and Zehr 2007). The colored lines are the least squares polynomial fits for each colored dot group. In general, WPRs from both the 9- (blue) and 3-km (red) simulations are close to the best track (black line). The correlations are better for weak storms, but the model underestimates the MWS by 5–10 kt for strong storms. The WPRs from Dvorak (Dvorak 1975), Atkinson (Atkinson and Holliday 1977), and Knaff (Knaff and Zehr 2007) are included for comparison. The Knaff line is based on the best fit using the data from 1974 to 1987. As expected, the black line for the best track is very close to the green line using the Dvorak method, which is the basis for the best track. The 9- and 3-km WPRs are closer to the Atkinson and Knaff methods.

Fig. 12.
Fig. 12.

(a) Scatterplot of MWS (kt) vs MSLP (hPa) from the 9- (blue dots) and 3-km (red dots) configurations, compared with the best track (black dots), along with their polynomial fits. Also shown are the Dvorak (green), Atkinson (dark green), and Knaff (orange) results as polynomial fits. (b) The percentage of binned distributions (every 10 kt) of the MWS for the 9- (blue bars) and 3-km (red bars) simulations and the best track (black bars).

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The percentage distributions of data points in different MWS bins for the 3-km simulations (red dots), the 9-km simulation (blue dots), and the best track (black dots) are shown in Fig. 12b. The peak in the 9-km simulation occurs in the 40-kt bin at a 16% frequency, which is close to the peak of the best track. Less than 7% of the MWS points in the 9-km simulation reach category 3 (MWS > 96 kt), comparing to 20% of the best track, suggesting that the lower-resolution limits the intensity. About 18% of MWS in the 3-km simulation reaches category 3, which is closer to the best track. While the 9-km simulations have few cases reaching categories 4 and 5, the high-resolution simulations do have some capability of simulating these intense storms. The results indicate again that the simulations using a higher resolution are able to produce higher intensities than their 9-km counterparts.

Landsea et al. (2004) found that the number of weak cases outnumbers stronger cases and it is better to bin MSLP values based on MWS before finding the best fit. An intensity-based binned analysis (binned MWS every 10 kt) is used to weight each bin evenly. Three dashed lines represent the polynomial fits to the binned data for the 9- and 3-km simulations and the best track (Fig. 13). The binned best-track profile (black dashed) is closer to Dvorak’s results (green) than to the best track (black) for the stronger storms. The 9-km binned profile (blue dashed) does not fit as well as the 9-km profile (blue). The 3-km binned profile (red dashed) fits the Atkinson and Knaff profiles even better than the 3-km profile (red). The binned method adopted here provides some additional insight when addressing WPRs.

Fig. 13.
Fig. 13.

The colored solid lines are the same as in Fig. 12a. Three more dashed lines are added for the polynomial fits for the binned datasets from the 9- and 3-km simulations and the best track.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

b. Evaluation of TC track and intensity

A statistical analysis of TC track and intensity at various resolutions for multiple research and operational mesoscale models has been performed by the National Center for Atmospheric Research (NCAR) Development Test Center (2009). In this section, we focus on the statistical evaluation of the COAMPS-TC track and intensity forecasts of the 3- and 9-km simulations. The mean absolute errors (MAEs) of track forecasts increase for both resolutions with forecast lead times and reaches 250–300 n mi at the 120-h forecast from a homogeneous sample (Fig. 14a). The track MAEs using different resolutions are very close during the first 36 h and the 3-km simulations have slightly larger track MAEs afterward; however, the difference is not statistically significant. The homogeneous statistics of the track mean error (ME) in the along- and cross-track directions (Fig. 14b) show that the simulated TCs from both the 3- and 9-km simulations move at a similar along-track speed for the first 36 h. The TCs in the 9-km simulations lag behind the observed storms in the last 12 h, while the TCs in the 3-km simulations are ahead. The averaged along-track biases are quite small (less than 20 n mi) with the maximum along-track bias less than 60 n mi. The cross-track biases for both simulations are also small (less than 40 n mi) in the first 4 days. Overall, using high resolution does not improve track forecasts and the difference between the two levels of resolution is not statistically significant.

Fig. 14.
Fig. 14.

Homogeneous comparison of (a) the track MAEs between the 3- (red) and 9-km (blue) configurations. (b) The track MEs in the along- (solid lines) and cross-track (dashed lines) directions from the 3- (red) and 9-km (blue) configurations. The sample sizes are shown above the forecast lead time.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The intensity MAEs and MEs for both the 3- and 9-km simulations are shown in Fig. 15. The MAE from the 9-km simulation is close to that of the 3-km simulation. The errors start from 14–19 kt initially and increase gradually to about 30 kt at 96 h, then decrease to 22 kt at 120 h. Both the 3- and 9-km simulations underestimate the MWSs for all forecast lead times (negative ME values in Fig. 15). The 3-km resolution produces statistically significant smaller intensity biases (by about 5 kt on average) compared to those from the 9-km simulation for all forecast lead times from 6 to 120 h. The results indicate that the high-resolution simulations can improve the intensity bias.

Fig. 15.
Fig. 15.

The homogenous statistics of intensity MAEs (solid lines) and mean errors (dashed lines) from the 3- (red) and 9-km (blue) configurations. The sample sizes are shown above the forecast lead time.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

The statistical analysis for track MAEs, intensity MAEs, and intensity bias can further be categorized in two groups: tropical storms (TSs; MWS < 64 kt) and tropical cyclones (MWS > 64 kt) (Fig. 16). The 9-km TCs have, overall, the smallest track errors. The track MAEs are generally better for TCs than TSs for both the 9- and 3-km simulations. The intensity statistics for the two categories (TC and TS) show that both the 3- and 9-km simulations have much smaller intensity MAEs (20 kt) at the TS stage than at the TC stage (30 kt) during the first 96 h. For strong storms, the intensity MAEs from the 3-km simulations are better than those from the 9-km simulation, except at the initial time and at 96 h. The negative intensity bias from the 9-km simulations indicates underestimated intensity for all forecast lead times for both weak and strong storms. The 3-km simulations underestimate the intensity for both weak and strong storms for the first 60 h, but overestimate the intensity from 72 to 120 h for strong storms. For strong storms, the high resolution reduces the bias by at least 15 kt for 6–60-h forecast lead times.

Fig. 16.
Fig. 16.

(a) Track MAEs, (b) intensity MAEs, and (c) intensity MEs for TS (below 64 kt, light colors) and TC (above 64 kt, darker colors) for the 3- (red) and 9-km (blue) configurations.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00054.1

5. Summary

The COAMPS-TC modeling system is used to simulate 10 Atlantic storms (54 cases in 2005 and 2007) to quantify the impact of horizontal resolution on TC forecasts, as part of the HFIP. Two sets of independent simulations, with coarse (9 km)- and fine (3 km)-grid resolutions, are evaluated. These simulations are configured with two-way interactive moving nested meshes embedded in the fixed outermost domain with an 81-km grid spacing. The Kain–Fritsch convective parameterization is used in this study for the nested domains with grid spacing of 9 km or larger, while cloud microphysics is activated in all nests. While this study focuses on the impact of the two different resolutions on TC prediction, it should be noted that model physics may contribute to some of the differences at the various horizontal resolutions. It is expected that the microphysics would play a more significant role in controlling the cloud processes at 3-km resolution.

The track, intensity, and structure from five Hurricane Katrina simulations are analyzed. The forecast tracks at both 9- and 3-km resolutions are very close to the best track. The high-resolution runs improve the intensity (MWS and MSLP) forecasts by 30%–40% relative to the low-resolution simulations, especially when the storm is relatively strong (of hurricane intensity). The results support the notion that the simulated TC structures are very sensitive to the horizontal resolution. The fine-resolution simulations of Katrina depict more realistic inner-core structures (a circular eye with a small diameter, narrower eyewalls, and more small-scale convection embedded within the spiral bands) than the coarser-resolution simulations, compared to the satellite observations. Additionally, the 10-m winds at 3 km are in closer agreement with the H*Wind analysis than at 9 km. Detailed analysis of the 10-m winds and the vorticity indicates that the 3-km simulation has a more realistic TC inner-core structure (in shape and distribution), a more compact and stronger vortex than the 9-km simulation, and is in closer agreement with the H*Wind results.

The VRW spectrum analysis from H*Wind is used to further evaluate the resolution impact. The degree to which the VRWs are resolved is analyzed through examination of the resolution impact on the wave energy representation. The azimuthal VRW spectral analysis of the Katrina relative vorticity indicates that the 3-km simulation can resolve higher-wavenumber modes in the inner-core region than the coarse-resolution simulation. For example, the percentage of partially resolved and unresolved wave energy in the 9-km simulation is much larger (9 times) than in the high-resolution simulation. The coarse-resolution simulation cannot fully resolve wavenumber 3 at the radius of 20 n mi, which is close to the observed RMW in many of the cases considered. In contrast, the 3-km simulation fully resolves wavenumbers 0–7 at the same radius. The normalized wave spectral analysis at the observed RMW demonstrates that the 3-km simulation can resolve 93% fully and 6.2% partially of the wave energy, compared to the 79.8% and 16.8% predicted by the 9-km simulation, respectively. About 3% of the wave energy, unresolved in the TC inner-core region, is lost in the 9-km simulation. The eyewall shape appears to be closely related to the resolvable waves at the RMW. Fine resolution is necessary to resolve more azimuthal vortex waves, to represent more wave energy, and hence to attain a more detailed eyewall structure.

Compared with the coarse-resolution simulation of Katrina, increasing the resolution produces much stronger vertical motions along the eyewall and larger condensational heating, which increases the warm-core temperature and the temperature gradients across the eyewall, and further intensifies the vortex and its associated circulation. This positive feedback produces higher potential vorticity and is more consistent with the observations from the Hurricane Rainband and Intensity Change Experiment (RAINEX; Houze et al. 2006). The time–height distribution of the azimuthally averaged radial winds at the 150-km radius and vertical velocity at the 100-km radius illustrate the stronger upper-level outflow and a better organized secondary circulation in the 3-km simulation. The impact of resolution on the TC vertical structure and development is significant.

A polynomial fit of the MWS and MSLP from the 9- and 3-km simulations and the best track suggests that the WPRs from the simulations are consistent with the best track in general, although the forecasts have lower MWS values for a given pressure under high wind conditions. The 9-km simulations underestimate the MWS for the same MSLP and have less intense storms compared to the 3-km simulations. The WPRs from the model are closer to the profiles using the Atkinson and Knaff methods. When the binned method is applied to the best fit, the relationship between the 3-km runs is even closer to the Atkinson and Knaff profiles. The comparison of the binned distributions with the best track indicates that the model dynamics and physics at 3 or 9 km still have difficulty with accurately simulating strong storms (MWS over 120 kt).

An increase in horizontal resolution (from 9 to 3 km) does not improve the track forecasts, which is consistent with Davis et al. (2010). The track errors are slightly higher in the high-resolution simulations, but they are not statistically significant. While the intensity MAEs are similar between the two resolutions, the 3-km simulations produce a significantly smaller intensity bias compared to the 9-km simulations. For both simulations the track MAEs are generally better for TCs than for TSs, but the opposite is true with the intensity MAEs. The 3-km simulations perform better in predicting the intensity of strong TCs.

Overall, this systematic evaluation of case studies and statistical analyses supports the idea that the combined impact of grid resolution and cloud physics plays a significant role in TC intensity and structure forecasts for differing horizontal resolutions, whereas it has limited impact on the track forecasts. The VRW spectrum analysis at different resolutions is a good tool to help us understand the importance of VRWs and associated wave energy. The high resolution resolves higher-wavenumber modes of VRWs and associated wave energy near the TC inner core, which is critical for the development of strong TCs.

Acknowledgments

We thank reviewers for their valuable comments and suggestions. The authors appreciate discussions with Dr. Richard Hodur of the Science Application International Corporation, and Drs. Jon Moskaitis and Chi-Sann Liou at NRL. We acknowledge the support of the Office of Naval Research’s (ONR) Program Element (PE) 0602435N, as well as the NOAA-sponsored Hurricane Forecast Improvement Project. The computational resources are provided by the Department of Defense High Performance Computer Modernization Program.

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1

COAMPS is a registered trademark of the NRL.

2

COAMPS-TC is a trademark of the NRL.

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  • Associated Press, 2012: Hurricane Sandy estimated to cost $60 billion. 21 October 2012.

  • Atkinson, G. D., and Holliday C. R. , 1977: Tropical cyclone minimum sea level pressure/maximum sustained wind relationship for the western North Pacific. Mon. Wea. Rev., 117, 421427.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., and Lacarrère P. , 1989: Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon. Wea. Rev., 117, 18721890.

    • Search Google Scholar
    • Export Citation
  • Burton, M. L., and Hicks M. , 2005: Hurricane Katrina: Preliminary estimates of commercial and public sector damages. Center for Business and Economic Research, Marshall University, 13 pp.

  • Chen, S., Campbell T. , Jin H. , Gabersek S. , Hodur R. , and Martin P. , 2010: Effect of two-way air–sea coupling in high and low wind speed regimes. Mon. Wea. Rev., 138, 35703602.

    • Search Google Scholar
    • Export Citation
  • Chen, S. S., Zhao W. , Donelan M. A. , Price J. F. , and Walsh E. J. , 2007: The CBLAST-Hurricane Program and the next-generation fully coupled atmosphere–wave–ocean models for hurricane research and prediction. Bull. Amer. Meteor. Soc., 88, 311317.

    • Search Google Scholar
    • Export Citation
  • Crossett, K. M., Culliton T. J. , Wiley P. C. , and Goodspeed T. R. , 2008: Population trends along the coastal United States: 1980–2008. Coastal Trends Report Series, National Oceanic and Atmospheric Administration, 47 pp.

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  • Fig. 1.

    Ten Atlantic TCs during 2005 and 2007 selected for retrospective track and intensity forecasts for the HRH test (Developmental Testbed Center 2009). The major hurricanes (red dots) are tropical cyclones of category 3 and higher (with MWS over 96 kt) based on the Saffir–Simpson hurricane scale, while the nonmajor hurricanes (orange dots) are categories 1 and 2 (with MWS between 64 and 96 kt). The tropical depression (blue dots) has MWS below 32 kt and the tropical storm (yellow dots) has MWS between 32 and 64 kt.

  • Fig. 2.

    COAMPS-TC domains use a Mercator map projection. A 75° × 100° coarse mesh extends from 15°S to 60°N and from 120° to 20°W. The coarse domain is fixed and has an 81-km horizontal gird spacing. The inner three mesh domains have 27-, 9-, and 3-km grid spacings and move with the hurricane center.

  • Fig. 3.

    Time evolutions of the (a),(b) track; (c),(d) MWS (kt); and (e),(f) MSLP (hPa) from Hurricane Katrina forecasts for the (top) 9- and (bottom) 3-km configurations evaluated against the best track. The best track is in black and the other five colors correspond to the different model initialization times with 24-h intervals. The dots are 6 h apart and the big double circles indicate the landfall time.

  • Fig. 4.

    Radar reflectivity (shaded; dBZ) at 72 h (valid for 0000 UTC 29 Aug 2005) from the (a) 9- and (b) 3-km simulations of Hurricane Katrina, starting at 0000 UTC 26 Aug 2005, compared with (c) the GOES-12 IR TRMM 85H overpass at 0000 UTC. The total precipitable water (shaded; mm) at 78 h from the (d) 9- and (e) 3-km simulations, compared with (f) the GOES-13 IR Aqua overpass at 0600 UTC.

  • Fig. 5.

    The 10-m winds (shaded, contour, and vector; kt) from the (a) 9- and (b) 3-km simulations, at 72-h forecast lead time (valid for 0000 UTC 29 Aug 2005), for Hurricane Katrina simulations starting at 0000 UTC 26 Aug, compared with (c) H*Wind analysis (original data from HRD) with the same scales at the same time.

  • Fig. 6.

    The zoomed-in TC inner-core regions (160 km × 160 km box from Fig. 5) of 10-m winds (kt) for the (a) 9-km, (b) 3-km, and (c) H*Wind simulations. The corresponding relative vorticities (10−3 s−1) for the (d) 9-km, (e) 3-km, and (f) H*Wind simulations. The red circles represent the azimuthally averaged RMWs from the simulations and black circles show the RMWs from the best track.

  • Fig. 7.

    Wave spectral analysis of the relative vorticity (shown in Figs. 6d–f) for the (top) 9-km, (middle) 3-km, and (bottom) H*Wind simulations at wavenumbers (a)–(c) 0, (d)–(f) 1, (g)–(i) 2, and (j)–(l) 3. The shaded areas are for the fully resolved waves with their wavelengths >10Δx. The nonshaded contours are for the partially resolved waves (wavelengths between 10Δx and 4Δx) and the white areas are for the unresolved waves (wavelengths <4Δx). The red circles are the RMWs from the simulations and the black circles are for the RMWs from the best track.

  • Fig. 8.

    (a) Wave spectral variances of the relative vorticity at the RMW of the best track (as shown in black circles in Fig. 7) at 72-h forecast lead time from the 3- (red) and 9-km (blue) runs. The solid lines are for the fully resolved waves, and the dotted lines for partially resolved waves. (b) Distributions of the normalized wave spectrum variances for the fully resolved (the solid boxes), partially resolved (the unfilled boxes with solid outlines), and unresolved waves (the boxes with dot outlines). (c),(d) As in (a),(b), but for the RMW from the model.

  • Fig. 9.

    The azimuthally averaged (a) tangential (shaded; m s−1) and radial (contour; m s−1) winds, (c) potential vorticity [shaded; potential vorticity units (PVU)] and vertical velocity (contour; m s−1), and (e) potential temperature change from the initial time (shaded; K) and condensation heating rate (contour; 10−3 K s−1) for the 9-km simulation. (b),(d),(f) As in (a),(c),(e), but for the 3-km simulation. Results are for 84-h forecast lead time, valid at 1200 UTC 29 Aug 2005. The red lines mark the locations of the RMWs at different heights.

  • Fig. 10.

    Hovmöller diagrams (0–96 h) of the azimuthally averaged fields: (a) tangential wind (shaded; m s−1) and RMW (red line) at 2-km height, (c) vertical velocity (m s−1) at 2 km, (e) condensate heating rate (10−3 K s−1) at 8 km, (g) potential temperature (K) at 8 km, and (i) potential vorticity (PVU) at 8 km for the 9-km configuration. (b),(d),(f),(h),(j) As in (a),(c),(e),(g),(i), but for the 3-km simulation. Forecasts start at 0000 UTC 26 Aug 2005.

  • Fig. 11.

    Time–height distributions of azimuthally averaged radial wind (shaded; m s−1) at the 150-km radius away from the storm center for the (a) 9- and (b) 3-km simulations. The averaged vertical velocity (shaded; m s−1) at the 100-km radius for the (c) 9- and (d) 3-km simulations. Forecasts start at 0000 UTC 26 Aug 2005.

  • Fig. 12.

    (a) Scatterplot of MWS (kt) vs MSLP (hPa) from the 9- (blue dots) and 3-km (red dots) configurations, compared with the best track (black dots), along with their polynomial fits. Also shown are the Dvorak (green), Atkinson (dark green), and Knaff (orange) results as polynomial fits. (b) The percentage of binned distributions (every 10 kt) of the MWS for the 9- (blue bars) and 3-km (red bars) simulations and the best track (black bars).

  • Fig. 13.

    The colored solid lines are the same as in Fig. 12a. Three more dashed lines are added for the polynomial fits for the binned datasets from the 9- and 3-km simulations and the best track.

  • Fig. 14.

    Homogeneous comparison of (a) the track MAEs between the 3- (red) and 9-km (blue) configurations. (b) The track MEs in the along- (solid lines) and cross-track (dashed lines) directions from the 3- (red) and 9-km (blue) configurations. The sample sizes are shown above the forecast lead time.

  • Fig. 15.

    The homogenous statistics of intensity MAEs (solid lines) and mean errors (dashed lines) from the 3- (red) and 9-km (blue) configurations. The sample sizes are shown above the forecast lead time.

  • Fig. 16.

    (a) Track MAEs, (b) intensity MAEs, and (c) intensity MEs for TS (below 64 kt, light colors) and TC (above 64 kt, darker colors) for the 3- (red) and 9-km (blue) configurations.

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