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    Domain used in WRF simulation of Hurricane Dennis. Outer grid has a horizontal resolution of 27 km, inner grids have resolutions of 9, 3, and 1 km. Two-way interactive domains were used for the three coarsest resolutions. The innermost 1-km nest followed the vortex center.

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    Schematic of vertical resolution of the 55 uneven vertical levels used in model simulations. Enhanced resolutions used in boundary layer, melting layer, and in the layer between 11 and 14 km.

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    Observed (NHC) and simulated (WRF) location of observed center of Hurricane Dennis. Solid black lines connect each observed center location with coincident simulated location.

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    Observed (NHC) and simulated (WRF) minimum central SLP and maximum 10-m wind speed as a function of time for Hurricane Dennis.

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    (a) Reflectivity measured by NOAA P-3 lower fuselage radar at z = 4.2 km during penetrations through Hurricane Dennis between 0145 and 0245 UTC 7 Jul. (b) Reflectivity computed from WRF model fields at 0300 UTC 7 Jul at z = 4.25 km. (c) Reflectivity computed from WRF model fields at 0000 UTC 8 Jul at z = 4.25 km.

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    (a) Column-integrated graupel mass content derived from simulated model fields at 2120 UTC 7 Jul. (b) Infrared image obtained at 2245 UTC 7 Jul by Geostationary Operational Environmental Satellite (GOES). (c) 85-Ghz brightness temperature measured by SSM/I satellite at 2349 UTC 7 Jul.

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    (a) Cumulative CFAD of Z derived from NASA EDOP measurements composite from period between 0001 and 0129 UTC 8 Jul. (b) Cumulative CFAD of Z derived from WRF simulation of Dennis between 0000 and 0300 UTC 7 Jul, using hourly output. Contours represent cumulative frequencies relative to all 1-km grid points with Z > −5 dBZ. (c) As in (b), but for period from 0000 to 0300 UTC 8 Jul.

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    Maximum reflectivity anywhere in vertical column derived using simulated WRF fields for (a) 1200 UTC 7 Jul, (b) 2100 UTC 7 Jul, (c) 0300 UTC 8 Jul, and (d) 1200 UTC 8 Jul. Black circle represents a radius of 75 km centered on the eye of Dennis.

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    (a) CFAD of simulated w between 0000 and 0300 UTC 8 Jul; contours represent frequencies (%) of the occurrence of w within bins of width 1 m s−1 for all 1-km grid points with Z ≥ −5 dBZ. (b) Number of data points that went into construction of CFAD at each height. (c) As in (a), but for contours generated without applying a threshold of Z ≥ −5 dBZ. (d) As in (b), but without applying a threshold of Z ≥ −5 dBZ.

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    CFAD of simulated w computed by (a) averaging data obtained 9 h before RI at 0000 UTC 8 Jul and (b) averaging data obtained 9 h after RI. Contours represent frequencies (%) of the occurrence of w within bins of width 1 m s−1 for all 1-km grid points with Z ≥ −5 dBZ. (c) Difference plotted is the CFAD of w during RI minus the CFAD of w before RI.

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    Outlier (99.9th percentile) of w distribution as function of distance from center of eye of Hurricane Dennis and time at altitudes of (a) 6 and (b) 14 km. Values derived using azimuthal averages of derived cloud fields.

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    Outlier (99.9th percentile) of graupel mixing ratio as function of time and height, obtained using fields within a radius of 75 km of eye of simulated Hurricane Dennis. Contours of 99.9th percentile of vertical velocity distribution are superimposed.

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    (a) Outlier (99.9th percentile) of w distribution as function of time and height, obtained using fields obtained within a radius of 75 km of eye of simulated Hurricane Dennis. (b) Average w obtained within the same distance.

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    (a) Cumulative contour frequency distributions of w as a function of time for simulations of Hurricane Dennis. Frequencies calculated using data obtained within 75 km of eye of Dennis and at an altitude of 14 km. Broadening of distribution in 24 h before best estimate of RI at 0000 UTC 8 Jul 2005 seen. (b) Red and blue lines indicate the total number of downdrafts and updrafts that were present at each altitude level, respectively.

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    (a) Average latent heating occurring in w bins of width 1 m s−1 as a function of time, for all grid points within 75 km of eye and at altitudes between 8 and 16 km. (b) As in (a), but average aggregate latent heating in each velocity bin, determined by adding latent heating for all grid points whose w is within a specified range and dividing by the number of grid points, shown. (c) Average total latent heating (total latent heating divided by number of grid points) as a function of time.

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    Outliers (99.9th percentile) of w distribution (contours) and of latent heating distribution (colors with scale given on right-hand side of plot) as a function of time and height. Outliers calculated using simulated model fields within 75 km of eye of Hurricane Dennis.

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    Total updraft airmass flux for all points within 75 km of eye of Hurricane Dennis as a function of time and height for (a) convective regions, (b) stratiform regions, and (c) all regions.

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    Total net upward hydrometeor mass flux for all points within 75 km of eye of Hurricane Dennis as a function of time and height for (a) convective regions, (b) stratiform regions, and (c) all regions. Hydrometeor upward mass flux determined by multiplying updraft speed by hydrometeor mass content, meaning terminal fall speeds of hydrometeors not considered in calculation.

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    Contribution of weak (w < 2 m s−1), moderate (2 < w < 6 m s−1), and strong (w > 6 m s−1) updrafts to total upward hydrometeor mass flux for all points within 75 km of eye of Hurricane Dennis for (a) all altitudes, (b) z < 1.5 km, (c) 1.5 < z < 6 km, and (d) z > 6 km.

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    (a) Area of convective bursts within a distance of 75 km of eye of Hurricane Dennis as a function of time using definitions of Reasor et al. (2009), Rogers (2010), and Montgomery et al. (2006). (b) Average distance of burst from eye of Dennis.

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    Temporal evolution of azimuthal dependence of 99.9th percentile of w at (a) z = 6 km and (b) at z = 14 km. All points within 75 km of eye of Dennis used in determining w distribution as function of azimuthal angle.

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Vertical Velocity and Microphysical Distributions Related to Rapid Intensification in a Simulation of Hurricane Dennis (2005)

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  • 1 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
  • | 2 Department of Atmospheric Sciences, University of North Dakota, Grand Forks, North Dakota
  • | 3 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
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Abstract

A 1-km Weather Research and Forecasting model simulation of Hurricane Dennis was used to identify precursors in vertical velocity and latent heating distributions to rapid intensification (RI). Although the observed structure qualitatively replicated data obtained during P-3 and Earth Resources-2 (ER-2) flights, the simulated reflectivity was overestimated. During the 6 h preceding RI, defined as 0000 UTC 8 July 2005 close to the time of simulated maximum central pressure deepening, the asymmetric convection transformed into an eyewall with the maximum 10-m wind speed increasing by 16 m s−1.

Contour by frequency altitude diagrams showed unique changes in the breadth of simulated vertical velocity (w) distributions before and after RI. Outliers of w distributions at 14 km preceded RI onset, whereas the increase in w outliers at 6 km lagged it. Prior to RI there was an increase in the upward flux of hydrometeors between 10 and 15 km, with increased contributions from w > 6 m s−1. Increases in lower-level updraft airmass fluxes did not lead RI, but the 14-km positive w outliers were better indicators of RI onset than positive w averages. The area of convective bursts did not strongly increase before RI, but it continually increased after RI. Latent heating was dominated by contributions from w < 2 m s−1, meaning increases in positive w outliers before RI did not cause the increase in latent heating seen during RI. The location of convective bursts and outliers of positive and negative w distributions contracted toward the eye as the simulated Dennis intensified.

Corresponding author address: Greg McFarquhar, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory Street, MC 223, Urbana, IL 61801. E-mail: mcfarq@atmos.uiuc.edu

Abstract

A 1-km Weather Research and Forecasting model simulation of Hurricane Dennis was used to identify precursors in vertical velocity and latent heating distributions to rapid intensification (RI). Although the observed structure qualitatively replicated data obtained during P-3 and Earth Resources-2 (ER-2) flights, the simulated reflectivity was overestimated. During the 6 h preceding RI, defined as 0000 UTC 8 July 2005 close to the time of simulated maximum central pressure deepening, the asymmetric convection transformed into an eyewall with the maximum 10-m wind speed increasing by 16 m s−1.

Contour by frequency altitude diagrams showed unique changes in the breadth of simulated vertical velocity (w) distributions before and after RI. Outliers of w distributions at 14 km preceded RI onset, whereas the increase in w outliers at 6 km lagged it. Prior to RI there was an increase in the upward flux of hydrometeors between 10 and 15 km, with increased contributions from w > 6 m s−1. Increases in lower-level updraft airmass fluxes did not lead RI, but the 14-km positive w outliers were better indicators of RI onset than positive w averages. The area of convective bursts did not strongly increase before RI, but it continually increased after RI. Latent heating was dominated by contributions from w < 2 m s−1, meaning increases in positive w outliers before RI did not cause the increase in latent heating seen during RI. The location of convective bursts and outliers of positive and negative w distributions contracted toward the eye as the simulated Dennis intensified.

Corresponding author address: Greg McFarquhar, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory Street, MC 223, Urbana, IL 61801. E-mail: mcfarq@atmos.uiuc.edu

1. Introduction

Landfalling hurricanes have major impacts on humankind through economic devastation and loss of life, especially from widespread inland flooding caused by intense rain (Rappaport 2000). To reduce the societal consequences of a hurricane’s destruction, more accurate forecasts of strength, intensity, and precipitation are required. Although Rogers et al. (2006) showed that official 48-h tropical cyclone (TC) track forecast errors have decreased by nearly 45% over the past 15 yr, there has been no significant improvement in the National Hurricane Center (NHC) official intensity forecasts in the last 30 yr (Aberson 2008). Further, precursors to the rapid intensification (RI) that some hurricanes undergo (Holliday and Thompson 1979; Kaplan and DeMaria 2003) have not been well identified. A complete understanding of TC physics and the interactions of processes at various scales does not exist, nor are the processes or scales playing the dominant role in TC intensification fully understood.

On the cloud scale, latent heating and cooling govern TC intensity, but knowledge of their detailed three-dimensional structure remains limited (Zhang et al. 2002). Transformations between vapor, liquid, and ice can produce latent heat. However, a quantitative understanding of the distribution of cloud microphysical processes (e.g., riming, melting, evaporation, and sublimation) and their role in the creation of updrafts and downdrafts releasing this energy is lacking. Isolated, inner-core, intense updrafts, termed convective bursts, may play a role in TC intensification (Steranka et al. 1986; Montgomery and Enagonio 1998; Nolan et al. 2007; Rogers 2010). The reflectivity cores associated with these bursts have been detected by airborne radars and satellites (Reasor et al. 2009; Cecil et al. 2010; Guimond et al. 2010; Fierro and Reisner 2011), but observational sampling limitations, both spatially and temporally, continue to hinder interpretation of their statistics and how the associated microphysical processes evolve with TC intensity change. In addition, axisymmetric convective rings in the eyewall have been implicated as a precursor to RI in models and observations (Nolan and Grasso 2003; Nguyen et al. 2008; Harnos and Nesbitt 2011), providing for a contrasting view that axisymmetric eyewall convective coverage and latent heating in low environmental vertical wind shear may be more important in providing for RI than isolated intense eyewall convection and heating.

Recent field projects—such as the Fourth Convection and Moisture Experiment (Kakar et al. 2006), the Tropical Cloud Systems and Processes (TCSP; Halverson et al. 2007) Experiment, the Genesis and Rapid Intensification Processes experiment, and the Hurricane Rainband and Intensity Change Experiment (Houze et al. 2006)—provide unique data on the structure of TCs. However, the observations obtained represent snapshots of TCs at specific stages in their life cycles, and they need to be supplemented with a process-oriented understanding that can be obtained through numerical simulations.

Coupled atmosphere–ocean models have the capability to improve prediction of feedbacks between microphysical processes that govern the distribution of latent heat and atmosphere–ocean interactions (e.g., evaporation from the ocean surface) that ultimately drive hurricanes. Adding more physical basis to model parameterizations is a key to improving TC prediction. For example, upgrades to microphysics schemes (Ferrier 2005), improved air–sea momentum and enthalpy flux parameterizations (Davis et al. 2008), and assimilation of loop current and warm-core eddies in ocean initial conditions in the 2006 Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model reduced intensity errors by 13% for reruns of 2005 TCs (Bender et al. 2007). However, work remains, as the improved model by Bender et al. (2007) did not capture the RI of Hurricanes Dennis and Emily.

A multiscale understanding of the environmental and storm internal processes modulating changes in TC intensity is needed. Houze et al. (2006) hypothesized that fluctuations in TC intensity come from changes in the dynamics and interactions of the eye, eyewalls, and rainbands, the patterns of which are always evolving. Rodgers et al. (1998) showed that latent heat release concentrated by locally intense convection around TC centers usually precedes intensification by several hours. Because TC burst updraft speeds are not often observed directly by aircraft, increases in total lightning flash rates can serve as an indicator for increases in TC intensity over a wide area. Price et al. (2009) demonstrated a significant correlation between total lightning frequency and maximum sustained winds in 56 different hurricanes. A modeling study (Fierro et al. 2007) also demonstrated a correlation between TC intensification and total lightning flash rate, since total lightning requires updrafts that are strong enough to produce and loft both graupel and liquid water. However, Thomas et al. (2010) found an increase in the frequency of cloud-to-ground lightning in the inner core also occurs prior to and during the weakening of TCs. Thus, the relationship between the distributions of convective bursts, latent heating, lightning, and RI has yet to be well established.

The parameterization of microphysics is important in investigations of the precursors to RI. Lord et al. (1984) and Lord and Lord (1988) showed that the extent and intensity of the cooling initiating and maintaining model downdrafts is determined by the horizontal advection and fall speeds of snow and graupel, and conversion rates between hydrometeor species. Studies have suggested that cloud-resolving models at resolutions of approximately 2–3 km overpredict precipitation and graupel compared to radar and radiometer observations for particular storms (e.g., McFarquhar et al. 2006; Rogers et al. 2007)—a problem that may be partially alleviated by using improved microphysics schemes (Schneider et al. 2006). Thus, particular attention is paid here to the use of improved microphysics schemes (e.g., Thompson et al. 2008). Microphysical processes alone, however, do not control intensity and rainfall potential; rather, large-scale forcing (e.g., vertical wind shear), mesoscale dynamics, and ocean thermal properties are also critical. Hence, our results must be interpreted in the context of such factors.

In this paper, a numerical simulation of Hurricane Dennis (2005) conducted using the Weather Research and Forecasting (WRF) model at cloud-resolving resolution is used to identify potential precursors in distributions of vertical velocity w and latent heat to its modeled RI. Further, the evolution of these simulated distributions with changes in TC intensity is examined. Statistics from the high-resolution simulation of Dennis regarding the distributions, magnitudes, vertical structures, durations, proximities to the vortex center of convective bursts, and their trends as precursors to RI are also described. The remainder of the paper is organized as follows. Section 2 gives an overview of Hurricane Dennis, whereas section 3 describes the WRF simulations of Dennis. Section 4 discusses the results of the simulation, and section 5 summarizes the most important findings of the study.

2. Observations of Hurricane Dennis 2005

Hurricane Dennis (2005) was chosen to investigate how distributions of latent heat affect the kinematics, dynamics, and interactions of the eye and eyewall for a number of reasons. First, it was observed by instruments, such as the National Aeronautics and Space Administration (NASA) Earth Resources-2 (ER-2) Doppler radar (EDOP) and the Advanced Microwave Sounding Unit (AMSU), on the NASA ER-2 (Guimond et al. 2010) and by the National Oceanic and Atmospheric Administration (NOAA) P-3 Doppler radar at three different life cycle stages during TCSP. Through comparison of observed and modeled fields, these data can help assess how well WRF is representing the physical processes occurring in Dennis. Second, Dennis underwent RI during its life cycle. Third, Dennis was an intense TC that reached category 4 on the Saffir–Simpson scale, and hence was capable of producing intense damage had its track taken it over a populated area. Therefore, understanding the causes and consequences of its RI has important societal ramifications because improved intensity forecasts can assist policy makers in evacuation decisions.

Beven (2005) describes the synoptic history of Dennis. It originated from a tropical wave that moved off the coast of Africa on 29 June 2005. It began to organize on 2 July and became a tropical depression over the southern Windward Islands at 1800 UTC 4 July. On 5 July, the NASA ER-2 and the NOAA P-3 flew a coordinated mission into Dennis shortly after it had intensified into a tropical storm, noting a large circulation and convective regions scattered around all of its quadrants. As the system moved west-northwest on 6 July, a subsequent mission was flown by the ER-2 and P-3 as Dennis transitioned into a category 1 hurricane. Thereafter, Dennis rapidly intensified with the central pressure falling 31 hPa in 24 h as it struck southeastern Cuba as a category 4 hurricane. Dennis weakened to category 1 status while traversing Cuba. The final coordinated flight of the ER-2 and P-3 over the eastern Gulf of Mexico on 9 July took place while Dennis was gradually intensifying after crossing Cuba. Within a few hours of the final coordinated flights, Dennis reintensified rapidly with a central pressure drop of 37 hPa in 24 h, 11 hPa of which occurred in only 1.5 h. Dennis weakened to category 3 before making landfall over Santa Rosa Island, Florida.

Rogers (2010) used the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5; Grell et al. 1995) to simulate Hurricane Dennis with 1.67 km horizontal resolution. He found the onset of simulated RI was linked to an increase in the area of convective precipitation in the inner core of the storm and with an increase in the updraft mass flux in the lowest 1.5 km, associated with updrafts with speeds of about 1–2 m s−1. However, 6 h prior to RI there was a period of enhanced updraft mass flux in midlevels associated with updrafts with speeds greater than 5 m s−1 inside the radius of maximum winds. Output from a simulation of Dennis conducted with WRF reported here is used to further assess how the distributions, magnitudes, vertical structures and durations of convective bursts, and their proximities to the vortex center vary with the life cycle stage. Comparison to the simulation by Rogers (2010) is also made. Bryan et al. (2003) showed that coarsely resolved updrafts are numerically damped at resolutions larger than 100–200 m; thus, there will inevitably be some discrepancies between studies with different resolutions and with observations made in hurricanes (e.g., Black et al. 1996; Heymsfield et al. 2010). One must be aware of such resolution differences when making comparisons.

3. WRF simulation of Hurricane Dennis (2005)

The Advanced Research WRF (ARW) dynamical core version 3.0.1 was used to simulate Dennis. The model domain and grid spacing used are shown in Fig. 1. Three nested two-way interactive domains with horizontal resolutions of 27, 9, and 3 km were initialized with GFDL’s Global Forecast System (GFS) fields. An innermost 1-km nest followed the vortex center using the 700-hPa vorticity. The WRF fields above the boundary layer were nudged every 3 h toward the GFS analyses with the NOAA/GFDL vortex structure superimposed following the approach of Stauffer and Seaman (1994). For the first 15 h, nudging of winds, temperature, and water vapor was done for the 27- and 9-km domains; on the 3-km domain, only wind nudging was applied. After 15 h, nudging was limited to only winds. The four-dimensional data assimilation was necessary to provide the 1-km domain the most accurate boundary conditions; otherwise, the observed and simulated track deviated in the vicinity of the Caribbean islands, resulting in landfall that inhibited Dennis’s RI.

Fig. 1.
Fig. 1.

Domain used in WRF simulation of Hurricane Dennis. Outer grid has a horizontal resolution of 27 km, inner grids have resolutions of 9, 3, and 1 km. Two-way interactive domains were used for the three coarsest resolutions. The innermost 1-km nest followed the vortex center.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

The Kain–Fritsch convective parameterization (Kain 2004) was used on the outermost domain, while the Thompson et al. (2008) microphysics scheme was used on the three inner domains. The Thompson scheme predicts the mass mixing ratio of water vapor, cloud water, rain, cloud ice, snow, and graupel, and prognoses cloud ice number concentration. Its use of a variable intercept parameter (which helps define the size distribution) as a function of mass mixing ratio is more consistent with observations (McFarquhar and Black 2004) than conventional microphysics schemes and is less expensive than fully double-moment schemes. The following additional parameterizations were used: the Yonsei PBL scheme with Cd and Ck TC modifications (Hong et al. 2006), the Dudhia (1993) shortwave radiation scheme, and the Rapid Radiative Transfer Model (RRTM) longwave radiation scheme (Mlawer et al. 1997). Following Kimball and Dougherty (2006) and Fierro et al. (2009), enhanced vertical resolution at the surface and outflow levels was used to better resolve processes in these layers. Enhanced vertical resolution was also used near the melting level to resolve microphysical processes affecting latent heating and cooling. Figure 2 shows the resolution of the 55 vertical levels used in the simulation.

Fig. 2.
Fig. 2.

Schematic of vertical resolution of the 55 uneven vertical levels used in model simulations. Enhanced resolutions used in boundary layer, melting layer, and in the layer between 11 and 14 km.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

During the course of defining a simulation that reasonably reproduced the track and intensity of Dennis, several problems with WRF were encountered and fixed. The use of quilting—namely, the dedication of some processors to handle the input and output of data—was needed to use data assimilation with high temporal resolution output; however, a problem with quilting in WRF was encountered. Because of the reliance on boundary conditions from the data assimilation for environmental steering, a fix to the quilting problem, released in WRF, version 3.0.1 (WRFV3.0.1), was necessary to prevent premature interaction of the simulated Dennis with Jamaica. A change to the vortex-following algorithm of WRF was also needed. In the original code, when the search for a vortex position spanned the entire 1-km domain, there was sometimes unnecessary detection of the impact of the Caribbean topography located near the periphery of the 1-km domain. By limiting the initial vortex search to a predefined radius, successful vortex following was realized.

In spite of these improvements to WRF, a consistent underprediction of Dennis’s intensification was obtained when using the 1° GFS analyses for initial conditions. Thus, the GFDL fields (Kurihara et al. 1993), which provide both axisymmetric bogus vortices consistent with observations and ⅙° resolution that limits vortex interpolation errors relative to the GFS, were used. A new method for merging necessary soil parameters from the GFS with the improved GFDL vortex was incorporated into the WRF preprocessing system, which refined the terrain resolution from 27 to 3 km.

Finally, it was found that unrealistic surface pressure mesoscale features associated with nesting could prolong almost an hour after nesting with WRFV3. Although sixth-order diffusion reduced the amplitude of the noise, there was still an impact on the intensification rate and residual. Thus, all analysis was performed several hours after nesting times in order to avoid contaminated analysis. The nesting was also done earlier in the simulation so that it would not have an impact on the intensification of the storm.

All fields were output at 2-min resolution for later analysis. In addition to the temperatures, velocities, pressure perturbations, and mass mixing ratios and concentrations of the different hydrometeor species, the reflectivity Z and latent heat terms were also calculated. The Z was derived from the mass mixing ratios of rain, snow, and graupel, consistent with the assumptions in the Thompson et al. (2008) microphysics scheme. The latent heating terms were also consistent with the assumptions in the microphysics codes.

4. Model Results

a. Simulated track and intensity

Figure 3 shows the observed and simulated track of Dennis. Although the assimilation of radar data could possibly improve the simulated track and intensity further (Pu et al. 2009), such data are not used here to avoid the possibility of assimilated vertical velocity masking the role of modeled physical processes in determining precursors to RI. There is a southern bias in the simulated track before 600 UTC 8 July, and an eastward bias after Dennis made landfall on Cuba. The average track error between 0000 UTC 6 July and 1200 UTC 8 July was 57 km, with maximum and minimum errors of 79 and 31 km at 1800 UTC 6 July and 0000 UTC 8 July, respectively. In contrast, Pu et al. (2009) had track errors ranging between 75 and 90 km, depending on the type of data assimilation used.

Fig. 3.
Fig. 3.

Observed (NHC) and simulated (WRF) location of observed center of Hurricane Dennis. Solid black lines connect each observed center location with coincident simulated location.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

The observed and simulated minimum central pressure and 10-m maximum wind speeds of Hurricane Dennis are shown in Fig. 4. Although the simulated minimum central pressures average 12.4 hPa higher than those observed and the maximum surface wind speeds average 8.3 m s−1 lower than those observed between 0000 UTC 6 July and 1200 UTC 8 July, both the observations and simulations show Dennis intensified over the plotted period. The average simulated intensification rates of 18.1 and 26.9 m s−1 day−1 are within 28% and 25% of the observed intensification rates of 25.1 and 35.7 m s−1 day−1.

Fig. 4.
Fig. 4.

Observed (NHC) and simulated (WRF) minimum central SLP and maximum 10-m wind speed as a function of time for Hurricane Dennis.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

To identify precursors of RI in the simulated fields, it was necessary to define the timing of the start and end of simulated RI. This was done using the pressure and wind fields at 2-min resolution. Using the Holliday and Thompson (1979) definition of RI—namely, a decrease in the minimum central pressure of at least 42 hPa over a 24-h period—the onset of the earliest 24-h RI occurred at 1310 UTC 7 July and the latest at 1550 UTC 7 July 2005. The maximum deepening of 43 hPa began at 1530 UTC 7 July.

Alternate definitions of RI exist and give different periods for its onset. For example, defining RI as a period when surface wind speeds increase by 15.4 m s−1 [30 knots (kt)] over a 24-h period (Kaplan and DeMaria 2003) gives a range of possible onsets from 0310 UTC 6 July to 1650 UTC 7 July. The maximum increase in the simulated 10-m wind speed over any 24-h period started at 0850 UTC 7 July with a 27.7 m s−1 (54 kt) increase in speed. The timing of RI can also be determined by examining pressure and wind speed changes over shorter periods that may permit identification of storm internal processes, operating on shorter time scales than environmental factors, which lead to RI. The maximum simulated wind speed increase over any 6-h period was 18.5 m s−1 (36 kt) starting at 0330 UTC 8 July, whereas it was 12.8 m s−1 (25 kt) for the 3-h period starting at 0410 UTC 8 July. In terms of minimum central pressure, the maximum simulated deepening over any 6-h period was 19 hPa beginning at 0100 UTC 8 July; the maximum simulated deepening over any 3-h period was 12 hPa beginning at 0320 UTC 8 July.

Although a discussion of the optimum definition of RI is beyond the scope of this paper, it is apparent that alternate definitions give different times for the onset of simulated RI. For this paper, the onset of simulated RI is defined within ±3 h of 0000 UTC 8 July 2005, encompassing most of the shorter-time-duration definitions of RI, which are appropriate for modeling studies investigating the role of storm internal processes occurring at fine time scales on RI.

This timing and rate of RI differs from that used in other studies of Dennis and from that observed. Rogers (2010) used 1800 UTC 6 July as the RI onset because his peak simulated winds increased from 37 m s−1 at that time to 54 m s−1 by 1200 UTC 7 July (an 18 m s−1 increase over 18 h). A corresponding drop in minimum central sea level pressure (SLP) also occurred. The simulation presented here did not exhibit the same rates of RI. The timing of RI used herein corresponds to a second intensification observed before Cuban landfall at 0600 UTC 8 July. Here, the time defined as the start of modeled RI, 0000 UTC 8 July, had the largest discrepancy in observed and simulated intensity, with the observed Dennis not intensifying at that time. But, exact agreement in the timing and spacing of observations and simulations cannot be expected. Thus, examination of differences in modeled fields before and after 0000 UTC 8 July permits the identification of processes responsible for RI in the model. Further, because the simulated intensity at this time is similar to that when the observed storm intensified, the comparison is reasonable. Rogers (2010) did not extend his simulation to the time of RI used in this study, which also corresponds to the second observed intensification of Dennis. Although direct comparison between studies at the same time is not possible, it is still useful to identify similarities and differences in how modeled fields vary before and after RI for the two studies.

b. Observed and simulated cloud distributions

The simulated hydrometeor fields were first evaluated against observations using observations of Z, visible and infrared imagery, and other passive and active remote sensors. The Z observed by the NOAA P-3 radar at a height z of 4.2 km between 0145 and 0245 UTC 7 July is compared against the simulated Z for z = 4.25 km at 0300 UTC 7 July in Fig. 5. Because of uncertainties induced by calibrations and attenuation, the P-3 radar data are only used to qualitatively compare observed and simulated Z. The structure of the observed and simulated storm are similar, in that the highest Z occurs in the southern half of the eye and in rainbands to the south of the vortex center, which are located over Haiti. In addition, there is a line of intense Z about 240 km to the north of the eye in Figs. 5a,b. The simulated Z at 0000 UTC 8 July (Fig. 5c) is also compared to that observed at 0300 UTC 7 July because the intensities are similar at those times, and hence depict a similar stage in evolution. However, the modeled Zs at that time are still larger than those observed and the spiral rainbands do not occur at the same positions and orientations.

Fig. 5.
Fig. 5.

(a) Reflectivity measured by NOAA P-3 lower fuselage radar at z = 4.2 km during penetrations through Hurricane Dennis between 0145 and 0245 UTC 7 Jul. (b) Reflectivity computed from WRF model fields at 0300 UTC 7 Jul at z = 4.25 km. (c) Reflectivity computed from WRF model fields at 0000 UTC 8 Jul at z = 4.25 km.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

The observed and simulated storm are also compared in Fig. 6, where the simulated column total modeled graupel amount at 2120 UTC 7 July is plotted with both infrared satellite imagery and 85-GHz brightness temperatures measured by the Naval Research Laboratory Special Sensor Microwave Imager (SSM/I) at 2245 UTC 7 July. The 85-GHz brightness temperature is sensitive to scattering by precipitation-sized ice hydrometeors (Spencer et al. 1994), which are represented as graupel in WRF. Strong updrafts can loft both large graupel and ice particles to levels where the 85-GHz weighting function peaks, which is around 8–10 km in altitude. In both the 85-GHz image and the plot of simulated graupel amount, there are peaks in the signal in a broad area about 250 km west of the eye, in a band running in a southwest–northeast orientation to the south of Dennis’s eye, and in the eyewall in the northeast quadrant and immediately to the north.

Fig. 6.
Fig. 6.

(a) Column-integrated graupel mass content derived from simulated model fields at 2120 UTC 7 Jul. (b) Infrared image obtained at 2245 UTC 7 Jul by Geostationary Operational Environmental Satellite (GOES). (c) 85-Ghz brightness temperature measured by SSM/I satellite at 2349 UTC 7 Jul.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

A quantitative comparison of observed and simulated statistical radar properties is also needed. Statistical tools, such as contoured frequency by altitude diagrams (CFADs; Yuter and Houze 1995) were used to compare the relative frequency of occurrence of how observed and simulated Z changed with height, when averaging over periods when the simulated and observed Dennis had similar intensities so as to compare the same evolution stage. Cumulative CFADs of Z observed between 0001 and 0129 UTC 7 July and Z computed from model simulations at a similar time (0000–0300 UTC 7 July) and evolution stage (0000–0300 UTC 8 July) are shown in Fig. 7. Guimond et al. (2010) describe the characteristics of the EDOP used to construct the observed CFADs, noting that Z is corrected for attenuation using the surface reference technique (Iguchi and Meneghini 1994). Similar to the TC simulations of McFarquhar et al. (2006) and Rogers et al. (2007), the frequency of the largest Z, especially above the melting layer, is overpredicted for both simulation times. For example, whereas 3.0% of Z exceeds 25 dBZ at 10 km in the simulation, this occurs less than 0.1% of the time in the observations. Even though the NASA ER-2 only overflew a small portion of Dennis, this is a strong indication of a systematic offset in the simulated Z, suggesting the model did not capture all the processes responsible for the evolution of the precipitation field. This occurs even though the Dennis simulation used a more sophisticated microphysics scheme than the earlier study of McFarquhar et al. (2006), suggesting that the overprediction of graupel may be caused by factors in addition to microphysics.

Fig. 7.
Fig. 7.

(a) Cumulative CFAD of Z derived from NASA EDOP measurements composite from period between 0001 and 0129 UTC 8 Jul. (b) Cumulative CFAD of Z derived from WRF simulation of Dennis between 0000 and 0300 UTC 7 Jul, using hourly output. Contours represent cumulative frequencies relative to all 1-km grid points with Z > −5 dBZ. (c) As in (b), but for period from 0000 to 0300 UTC 8 Jul.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

The apparent overestimate of Z and graupel content by the model might suggest the model is operating in an environment where the instability is overestimated, but this is not the case. The sources of convective available potential energy (CAPE) determined from the WRF model fields using a parcel based on averaged values in the lowest 500 m were compared against observed CAPE estimated from rawinsonde releases at Key West, Florida; Nassau, Bahamas, and San Juan, Puerto Rico. WRF exhibited consistently lower CAPE than the observations, rather than the reverse. Thus, the overestimate of graupel and heavy precipitation is occurring because of some other unknown reason.

Figure 8 shows four snapshots of the column maximum Z of the simulated Dennis at times ranging from 12 h before the onset of RI (0000 UTC 8 July) to 12 h after its onset. This framework emphasizes the extreme values of Z because the maximum value anywhere in the column is displayed. It is difficult to discern a change in the spatial frequency of occurrence of Z for the two times before RI (Fig. 8a at 1200 UTC 7 July and Fig. 8b at 2100 UTC 7 July) compared to the 2 times during RI (Fig. 8c at 300 UTC 8 July and Fig. 8d at 1200 UTC 8 July). However, there is a change in the eyewall structure with a closed eye seen during RI. In the next step, statistical distributions of simulated w were examined in order to identify precursors of this RI.

Fig. 8.
Fig. 8.

Maximum reflectivity anywhere in vertical column derived using simulated WRF fields for (a) 1200 UTC 7 Jul, (b) 2100 UTC 7 Jul, (c) 0300 UTC 8 Jul, and (d) 1200 UTC 8 Jul. Black circle represents a radius of 75 km centered on the eye of Dennis.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

c. Distributions of vertical velocities before and after RI

Figure 9 shows CFADs of simulated w obtained by averaging fields between 0000 and 0300 UTC 8 July. The different colors represent the percentage of w greater than the indicated value, and both the updrafts and downdrafts are treated separately. The top and bottom panels differ, in that the top panel shows the relative frequency of occurrence of positive and negative w relative to all 1-km grid points with Z ≥ −5 dBZ, whereas the bottom panel is relative to all grid points. The −5-dBZ threshold corresponds to the approximate minimal detectable Z by EDOP. When the threshold is applied, there are fewer data points that contribute to the distributions at higher altitudes with only 40% of the points having Z ≥ −5 dBZ at 10 km and 2% at 15 km. The frequency of most intense simulated updrafts increases for higher altitudes in Fig. 9a but not in Fig. 9b because the number of included data points decreases for Fig. 9a but not for Fig. 9b. The difference in techniques for calculating CFADs may explain why McFarquhar et al. (2006) found increases in updraft distributions with height for their simulations of Hurricane Erin, whereas Rogers et al. (2007) did not for simulations of Hurricanes Bonnie and Floyd.

Fig. 9.
Fig. 9.

(a) CFAD of simulated w between 0000 and 0300 UTC 8 Jul; contours represent frequencies (%) of the occurrence of w within bins of width 1 m s−1 for all 1-km grid points with Z ≥ −5 dBZ. (b) Number of data points that went into construction of CFAD at each height. (c) As in (a), but for contours generated without applying a threshold of Z ≥ −5 dBZ. (d) As in (b), but without applying a threshold of Z ≥ −5 dBZ.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Convective bursts have been hypothesized to be a cause of RI in TCs. However, to examine the distributions, magnitudes, vertical structures, durations, proximities to the vortex center of simulated convective bursts, and their trends as precursors to RI, a definition of a convective burst is required. Alternate definitions have been proposed: (i) Reasor et al. (2009) defined convective bursts as prominent downshear-left clusters exhibiting 2–6-km average w > 5 m s−1 and 2-km Z > 30 dBZ; (ii) Rogers (2010) stipulated the averaged positive w needed to exceed 5 m s−1 between 700 and 300 hPa; and (iii) Montgomery et al. (2006) defined a convective hot tower as a tower with w > 1 m s−1 extending from 1 to at least 15 km. Because some of the aforementioned studies were based on observations and others on modeled fields, the dependency of modeled w on model resolution (Bryan et al. 2003) may also cause differences in identification of convective bursts. In this study, no attempt is made to determine the optimum definition for a convective burst. Instead, all definitions are used for easy comparison with past studies. Regions of enhanced w in CFADs of w are also regarded as potential convective bursts.

Cumulative CFADs of simulated w for Z ≥ −5 dBZ within a radius of 75 km of the vortex center for 9 h before the onset of simulated RI and for 9 h during its onset are shown in Fig. 10. With 2-min model output, 271 times went into the creation of each CFAD. Although there is much similarity in the CFADs before and during RI, there are noticeable differences in the outliers, such as those represented by the 0.01% of 0.1% outliers. These differences, highlighted in Fig. 10c, show that the positive simulated w distribution broadened before RI for z > 11 km but contracted for z < 6 km.

Fig. 10.
Fig. 10.

CFAD of simulated w computed by (a) averaging data obtained 9 h before RI at 0000 UTC 8 Jul and (b) averaging data obtained 9 h after RI. Contours represent frequencies (%) of the occurrence of w within bins of width 1 m s−1 for all 1-km grid points with Z ≥ −5 dBZ. (c) Difference plotted is the CFAD of w during RI minus the CFAD of w before RI.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

The simulated w distributions are not stratified according to the distance away from the eye in Fig. 10. To establish how these simulated distributions varied with distance from the vortex center, the 99.9th percentile of the positive w distributions as a function of time and distance from the vortex center for altitudes of 14 and 6 km is shown in Fig. 11. For times before 1200 UTC 6 July, the outliers frequently exceeded 12–16 m s−1 at 6 km and 20 m s−1 at 14 km. However, this is before the simulated storm organized into a tropical storm. Subsequently, the outliers were typically less than 8–12 m s−1 until about 0000 UTC 7 July, when the simulated Dennis started to deepen more rapidly. At this time, the 99.9th percentile positive simulated w began to increase, especially within the 75-km radius used to construct Fig. 10. The increases of the outliers to values of 20–24 m s−1 at 14 km preceded the onset of RI, whereas their increases to values of 16–20 m s−1 at 6 km occurred at the same time or lagged the onset of RI. However, the outliers at both 14 and 6 km converged toward the center of the simulated Dennis prior to RI. This convergence toward the eye is inevitably associated with a tightening of the eyewall, consistent and a shift in the radius of maximum wind inward with time and with the stronger storm. The outliers at 6 km only exceeded 12 m s−1 after the onset of RI.

Fig. 11.
Fig. 11.

Outlier (99.9th percentile) of w distribution as function of distance from center of eye of Hurricane Dennis and time at altitudes of (a) 6 and (b) 14 km. Values derived using azimuthal averages of derived cloud fields.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Figure 12 shows the 99.9th percentile outlier of graupel mixing ratio as a function of height and time derived from simulated fields within 75 km of the eye of Dennis. Contours of the 99.9th percentile of the positive simulated w distribution are superimposed. The outliers of the graupel mixing ratio increase markedly after the onset of RI because more graupel is generated by the increase of the intense lower-level positive w after the onset of RI. The increase in the outliers of graupel mixing ratio also corresponds to the time when there is a shift from an upper-level to a lower-level increase in the 99.9th percentile positive w. This suggests that precipitation (graupel) loading has reduced the outliers of positive w after the onset of RI. This is opposite of the effect suggested by Lord and Lord (1988), who found that more rapid production of graupel prevented the horizontal spreading of the melting processes, producing narrower and stronger updrafts and downdrafts, the latter of which slowed storm intensification. The increase of large graupel mixing ratios after RI also suggests that there should be a corresponding increase in lightning after the onset of RI, contrary to the 24-h lag found by Price et al. (2009). Future investigations are needed to determine the generality of our findings from the simulation of Hurricane Dennis.

Fig. 12.
Fig. 12.

Outlier (99.9th percentile) of graupel mixing ratio as function of time and height, obtained using fields within a radius of 75 km of eye of simulated Hurricane Dennis. Contours of 99.9th percentile of vertical velocity distribution are superimposed.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Precipitation loading, however, is not the sole contributor to height-dependent trends in simulated w distributions. An increase in the radial gradient of the inner-core simulated water vapor mixing ratio resulted from moistening within 50 km of Dennis’s eye and drying for radii greater than 50 km prior to RI (figure not shown). This corresponded to a reduction in simulated relative humidity but a pronounced increase in simulated midlevel convective available potential energy (figure not shown), which was either a forcing for or a manifestation of the upper-level precursor updrafts.

The evolution of the outliers of the positive simulated w distributions is compared against that of the average in Fig. 13. Consistent with earlier figures, the increase in outliers at 14 km precedes the onset of simulated RI, whereas the increase in outliers at 6 km lags it. The outliers of the upper-level positive w decrease after RI as does the altitude at which the maximum outlier occurs. Trends in average positive w differ. Although the average positive w at levels near 14 km increases before RI onset, there are continuing increases afterward. There are also increases in average positive w at lower levels during and after RI, but not before. Figure 14, which shows a cumulative contour frequency by time diagram for both updrafts and downdrafts within 75 km of the eye at a height of 14 km, illustrates that these interpretations are not restricted to the choice of the 99.9th percentile as outlier. If another high percentile was chosen to represent the outliers, such as 99.5th, 99th, or 98th, then similar conclusions are reached, namely, an increase in the outlier before RI followed by a subsequent decrease. Thus, there is a difference in the behavior of the outliers and averages of w. In contrast, Rogers (2010) did not find that outliers of w at levels higher than 8 km led the RI for his simulation of Dennis; the enhanced resolution between 11 and 14 km for the simulations reported here would have better resolved processes occurring at this level. The narrowing of the upper-tropospheric w distributions during RI could be related to increased precipitation loading. The next section investigates the relationship between the w and latent heating distributions.

Fig. 13.
Fig. 13.

(a) Outlier (99.9th percentile) of w distribution as function of time and height, obtained using fields obtained within a radius of 75 km of eye of simulated Hurricane Dennis. (b) Average w obtained within the same distance.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Fig. 14.
Fig. 14.

(a) Cumulative contour frequency distributions of w as a function of time for simulations of Hurricane Dennis. Frequencies calculated using data obtained within 75 km of eye of Dennis and at an altitude of 14 km. Broadening of distribution in 24 h before best estimate of RI at 0000 UTC 8 Jul 2005 seen. (b) Red and blue lines indicate the total number of downdrafts and updrafts that were present at each altitude level, respectively.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

d. Distributions of latent heating before and after RI

The relationship between TC intensification and latent heat release is not straightforward. Adler and Rodgers (1977) suggested TC intensity and latent heat release were correlated, but Marks (1985) showed changes in the intensity of Hurricane Allen had little effect on latent heat release. In contrast, Rodgers et al. (1998) hypothesized greater amounts of latent heating in the mid- to upper troposphere intensified Hurricane Opal through the generation of kinetic energy as convective bursts increased eyewall buoyancy, and Sitkowski and Barnes (2009) showed the deepening of Hurricane Guillermo was correlated with a spiraling in of the northern eyewall, leading to a net increase in latent heating. Thus, further investigations of latent heat release and how it contributes to TC intensity change are warranted.

To investigate the relationship between positive w and latent heating at upper levels in the simulated Dennis, the average latent heating in clouds having positive w within the range specified on the horizontal axis as a function of time is plotted in Fig. 15a. The contributions in w bins to the average aggregate latent heating, with the total latent heat plotted on the right-hand side, is shown in Fig. 15b. The average aggregate latent heating in each velocity bin is computed by adding the latent heating for all grid points whose w is within the specified range, and dividing by the number of grid points within 75 km of the eye and at altitudes between 8 and 16 km. Lower altitudes were not included because no precursor w to RI was noted at such levels; however, latent heating for lower altitudes is discussed below.

Fig. 15.
Fig. 15.

(a) Average latent heating occurring in w bins of width 1 m s−1 as a function of time, for all grid points within 75 km of eye and at altitudes between 8 and 16 km. (b) As in (a), but average aggregate latent heating in each velocity bin, determined by adding latent heating for all grid points whose w is within a specified range and dividing by the number of grid points, shown. (c) Average total latent heating (total latent heating divided by number of grid points) as a function of time.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

As expected, there is larger average simulated latent heating for higher positive w. For instance, 6 h after the onset of RI clouds with w of 4 m s−1 had average latent heating of about 20.8 K h−1, whereas those with w of 15 m s−1 about 90.5 K h−1. More intense positive w generates larger latent heating because a larger upward flux of vapor and condensate generates more condensation, freezing, and deposition. Interestingly, the average latent heating varies as a function of time within the same w bin. For example, for the 6 h before the onset of RI 12–13 m s−1 ws are associated with an average latent heating of 87.8 K h−1, but the 6 h after the onset of RI are associated with an average latent heating of 115.0 K h−1. This is explained by the variation in altitude at which the 12–13 m s−1 w occurs. For the 6 h before RI, the average altitude of 12–13 m s−1 w was 11.4 km, whereas it was 10.4 km after RI. The increased abundance of water vapor at lower altitudes, and the consequent increased cloud water amounts and riming rates (not shown) explain the higher heating rates for the same positive w.

The plot of average aggregate latent heating in Fig. 15b shows that even though the average latent heating in Fig. 15a is higher for more intense w, substantial contributions to the aggregate latent heating actually come from the weaker updrafts. For example, for w < 4 m s−1 there is an average aggregate latent heating of 1.7 K h−1 during the onset of RI between 2100 UTC 7 July and 0300 UTC 8 July, and of 1.9 K h−1 after its onset between 0300 and 1200 UTC 8 July. In contrast, Fig. 15a shows that between this important range of 0 < w < 2 m s−1, the average latent heating per grid cell is at the low end of the scale at less than 480 K day−1.

One can also investigate how latent heating as a whole (for all w) changed before and during RI. The right-hand plot in Fig. 15c illustrates that the average total latent heat released per grid point increased dramatically both before the onset of RI with increases from 1.3 K h−1 at 1800 UTC 6 July to 2.7 K h−1 at 0000 UTC 8 July and after its onset with a further increase to 3.6 K h−1 at 1400 UTC 8 July.

The contributions of individual processes (condensation, freezing, and deposition) to latent heating were examined by plotting process-specific latent heating in w bins of width 1 m s−1 for different height levels as a function of time (cf. Fig. 15b). Freezing contributed less to the total latent heating than did deposition and condensation. However, the latent heat released by freezing (or fusion) increased at heights of 6 and 7 km approximately 12 h before RI when the stronger updrafts started to occur in the upper troposphere (i.e., at 1200 UTC 7 July). There was a decrease in the amount of fusion in the 3 h before 0000 UTC 8 July, after which there was further increases associated with the RI of the simulated Dennis. Thus, whereas fusion is not a major contributor to the total amount of latent heating, further investigation was performed to investigate its potential role in initiating RI.

Figure 16 summarizes the relationship between the outliers of w and latent heating as a function of altitude and time, where the 99.9th percentiles have been calculated from values within 75 km of the eye of the simulated Dennis. As in Fig. 12, the outliers of w increase before the onset of RI and decrease thereafter for altitudes above about 6 km, with the altitude of their maxima lowering after RI. Their maximum values also seem to decrease with time after RI. In contrast, the outliers of latent heating markedly increase with time after the onset of RI, especially at an altitude of 5 km near the freezing level but also for altitudes below 11 km. This again shows that although the outliers of the w are precursors of RI, they are not the source of the majority of latent heating associated with its onset. Interestingly, there is a strong increase in the 99.9th percentile of latent heating from both fusion and condensation immediately before the RI at 0000 UTC 8 July.

Fig. 16.
Fig. 16.

Outliers (99.9th percentile) of w distribution (contours) and of latent heating distribution (colors with scale given on right-hand side of plot) as a function of time and height. Outliers calculated using simulated model fields within 75 km of eye of Hurricane Dennis.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Figure 16 also shows an increase in latent heating at lower levels down to 1.5 km at times starting around 0600 UTC 8 July after the onset of RI. There is no increase in latent heating at such levels before the onset of RI. In contrast, Rogers (2010) found that the immediate cause of RI in his simulation of Hurricane Dennis was a significant increase in updraft mass flux, particularly in the lowest 1.5 km accomplished primarily by updrafts on the order of 1–2 m s−1, before RI.

There were multiple differences in the setup of WRF for simulations reported here and those of Rogers (2010). Rogers used Goddard microphysics and Blackadar PBL schemes as opposed to the Thompson et al. (2008) microphysics and Yonsei PBL schemes used here. He used 36 vertical layers instead of 55, and he did not use enhanced resolution between 11 and 14 km. His use of the GFS analyses differs from that of the GFS analyses plus GFDL vortex fields used here. These differences are no doubt responsible for some of the variations noted in model fields and timing of RI, and give an indication of the uncertainty associated with prediction from state-of-art models.

To facilitate a comparison with Rogers (2010), model output is partitioned into convective, stratiform, no-rain, and other categories. Figure 17 shows a time–height cross section of the updraft airmass flux for all points within 75 km of the eye of the simulated Dennis, and for points within 75 km that were identified as convective and stratiform. Consistent with Rogers (2010), the largest mass flux and the largest absolute increase in mass flux before RI occurs at low levels in convective regions. At upper levels between about 11 and 13 km, there is an increase in mass flux right around the time of RI occurring in convective regions. The increase in mass flux seen about 6 h before RI in the stratiform area is not as prominent in the total mass flux plot because of smaller contributions from stratiform areas.

Fig. 17.
Fig. 17.

Total updraft airmass flux for all points within 75 km of eye of Hurricane Dennis as a function of time and height for (a) convective regions, (b) stratiform regions, and (c) all regions.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

However, a different view emerges when the net upward motion of hydrometeors is examined. The net hydrometeor upward mass flux is shown in Fig. 18 for the convective, stratiform, and all regions; the fall velocities of the hydrometeors have not been included in the net hydrometeor mass flux in Fig. 18. The largest increase in hydrometeor upward mass flux occurs 3 h before the RI at altitudes between 10 and 15 km, and is primarily caused by motions in the convective region. There is also a small increase in updraft mass flux at altitudes between 3 and 5 km, but no major increase for heights below 1.5 km. Thus, it is hypothesized that the hydrometeor mass transported to upper levels in convective regions prior to RI leads to more cooling in downdrafts that are subsequently produced, which in turn have a role in creating low-level airmass updrafts seen in both Fig. 17 and in the study of Rogers (2010). It is not known whether this increase in hydrometeors being transported to upper levels occurred in the Rogers (2010) simulation. Nevertheless, a plausible explanation for how the increase in hydrometeor mass flux leads to RI is suggested. Figure 19 examines the fractional contributions of different w to net hydrometeor upward mass flux for different altitudes as a function of time. For low levels (z < 1.5 km), the bulk of the mass flux is concentrated in the weak (w < 2 m s−1) and moderate (2 < w < 6 m s−1) updraft ranges, consistent with radar studies of Florida cumulonimbus (Yuter and Houze 1995). The fractional contributions of the strongest updrafts (w > 6 m s−1) integrated over all height levels initially contribute less than 20% to the total mass flux, but they start to steadily increase 24 h before RI, with a spike in contributions approximately 3 h before its onset. The strong updrafts contributing to the hydrometeor mass flux come from higher (z > 6 km) and midlevels (1.5 < z < 6 km) rather than low levels (z < 1.5 km). After the onset of RI, the strongest updrafts for z > 6 km decline to an approximately 40% contribution of the hydrometeor upward mass flux, while the contributions for 1.5 < z < 6 km continue to increase to approximately 50%. The increase in the contributions from strong updrafts to the updraft mass flux at low levels begins only after RI, suggesting this increase is a response rather than a cause of the RI. This analysis of upward hydrometeor mass flux differs from that presented in Fig. 19 in Rogers (2010), where only net upward airmass flux was plotted.

Fig. 18.
Fig. 18.

Total net upward hydrometeor mass flux for all points within 75 km of eye of Hurricane Dennis as a function of time and height for (a) convective regions, (b) stratiform regions, and (c) all regions. Hydrometeor upward mass flux determined by multiplying updraft speed by hydrometeor mass content, meaning terminal fall speeds of hydrometeors not considered in calculation.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Fig. 19.
Fig. 19.

Contribution of weak (w < 2 m s−1), moderate (2 < w < 6 m s−1), and strong (w > 6 m s−1) updrafts to total upward hydrometeor mass flux for all points within 75 km of eye of Hurricane Dennis for (a) all altitudes, (b) z < 1.5 km, (c) 1.5 < z < 6 km, and (d) z > 6 km.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Finally, these results are put into the context of how the area of the simulated convective bursts varies with time in Fig. 20a. Three different definitions of convective burst are used: (i) the Reasor et al. (2009) without the restriction to downshear left clusters, (ii) the Rogers (2010), and (iii) the Montgomery et al. (2006) definitions. Because these definitions are applied to simulations with 1-km horizontal resolution, the horizontal scale of any feature defined as a burst is necessarily 1 km as well. The first two definitions yield very similar convective burst areas, both of which are substantially larger than the area computed by the Montgomery et al. (2006) definition. For the Reasor et al. (2009) and Rogers (2010) definitions, the area of convective bursts increases to about 150 km2 12 h before RI and then decreases to 75 km2 6 h before RI. Subsequently, there is a spike in the area of convective bursts to 200 km2 about 3 h before RI, followed by a decrease and then a continual increase after RI, reaching a maximum convective burst area of 300–350 km2 at the end of the simulation. The fluctuation in the area of bursts in the 24 h before RI suggests there is no strong correlation between the convective burst area and RI; however, there seems to be a clear increase in the convective burst area after RI. This is somewhat different from Rogers (2010), who found the distribution of the number of bursts was nearly constant with respect to time, with the exception of a couple of times of increased bursts.

Fig. 20.
Fig. 20.

(a) Area of convective bursts within a distance of 75 km of eye of Hurricane Dennis as a function of time using definitions of Reasor et al. (2009), Rogers (2010), and Montgomery et al. (2006). (b) Average distance of burst from eye of Dennis.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

Figure 20b shows the average distance of the convective burst from the eye of the simulated Dennis. This decrease of this distance with time is consistent with the temporal evolution of the radius of maximum wind (figure not shown), which decreased from 60 km at 1200 UTC 7 July, to 30 km at the time of RI (0000 UTC 8 July), and to 20 km at 1800 UTC 8 July. This strong decrease of maximum wind radius before RI and gradual decrease after RI is somewhat different from Rogers’s (2010) study, which showed the peak in average tangential winds contracted from 70 to 30 km after RI. Thus, although it is clear that the increase in upper-level distributions of w and of updraft mass fluxes preceded the occurrence of RI in the simulations of Dennis presented here, it does not mean they were necessarily the cause of it. Molinari and Vollaro (2010) point out that RI is a multiscale process where the rapid development of an intense cell within a region of efficient latent heating (cf. Nolan et al. 2007; Vigh and Schubert 2009) may follow the development of a new circulation center downshear of a precipitation shield, giving a favored region for cell formation downshear of the new center. Thus, it was necessary to determine how azimuthal distributions of w changed before and after RI.

e. Azimuthal distributions of vertical velocity before and after RI

To investigate if axisymmetric convective rings in the eyewall are potential precursors to RI in the simulation of Hurricane Dennis, Fig. 21 plots the temporal variation of the azimuthal dependence of the 99.9th percentile of w at z = 6 and z = 14 km. All points within 75 km of the eye of the simulated Dennis are used in the creation of the plot. An asymmetrical distribution of the outliers is seen, with the most intense outliers to the north and east of the eye before RI, and to the north and west of the eye after RI. These trends are seen regardless of whether Z > −5 dBZ is used to threshold the data.

Fig. 21.
Fig. 21.

Temporal evolution of azimuthal dependence of 99.9th percentile of w at (a) z = 6 km and (b) at z = 14 km. All points within 75 km of eye of Dennis used in determining w distribution as function of azimuthal angle.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-016.1

An azimuthal variation in Z often relates to vertical wind shear. Both the WRF simulation of Dennis and analysis values contained higher environmental shear values compared with the mean Atlantic basin shear value for storms undergoing RI (9.5 kt; Kaplan and DeMaria 2003), and those values remained high for the duration of the RI period. Shear values calculated from 200 to 850 hPa 200–800 km from the storm center from the Statistical Hurricane Intensity Prediction Scheme (SHIPS) analysis (DeMaria and Kaplan 1994) were 16.6, 14.4, and 18.7 kt for 1200 UTC 7 July, and 0000 and 1200 UTC 8 July, respectively. Values calculated from WRF output for the same times were 15.1, 10.7, and 16.3 kt.

5. Summary

A high-temporal resolution simulation of Hurricane Dennis 2005 was conducted with WRF using a sophisticated microphysics scheme (Thompson et al. 2008) to identify precursors in the distributions of vertical velocities and latent heating to rapid intensification (RI). Comparison against observations obtained by instruments on the NOAA P-3 and NASA ER-2 during a similar evolution stage showed that the simulation qualitatively represented the observed structure of the storm even though the simulated reflectivity was overestimated compared to observations. Thus, the results from the simulations were used to make the following conclusions about precursors to the RI of the simulated Hurricane Dennis:

  1. The definition of RI is a function of whether changes in minimum central pressure or maximum surface wind speed are examined and of the time interval over which these changes are examined. For numerical simulations with high temporal resolution output, definitions based on changes occurring over 3-h intervals are appropriate because changes in distributions of hydrometeors, vertical velocity, and latent heating, which ultimately cause RI, are occurring over similar time scales. Identifying the precursors of RI is dependent on its definition.

  2. Outliers of w distributions (e.g., 99.9th or 99.99th percentiles) are better indications of simulated RI onset than are averages of vertical velocities. In particular, increases of the outliers to values of 20–24 m s−1 at 14 km preceded the onset of RI, whereas increases to values of 16–20 m s−1 at 6 km occurred at the same time or lagged the onset of RI. The outliers also converged toward the center of the simulated Dennis before its RI.

  3. Although changes in the outliers of the w distributions are precursors to RI, ws in the 90th–99.99th percentiles have a minimal effect on aggregate latent heating because they do not occur sufficiently frequently. The latent heating is dominated by contributions from smaller ws less than about 2 m s−1.

  4. The onset of simulated RI is manifested by an accompanying increase in the latent heating and in the area of convective bursts. There is no clear increase in the convective area before the onset of RI.

  5. Outliers of vertical velocity distributions at discrete levels are needed to identify convective bursts rather than outliers within confined columns.

  6. Immediately prior to simulated RI, there is an increase in the upward hydrometeor mass flux at altitudes between 10 and 15 km. However, the largest increase in updraft mass flux occurs after RI. Levels with z < 1.5 km make small contributions to the upward hydrometeor mass flux. However, these levels contribute significantly to the net updraft airmass flux, which is seen to increase during and after the start of RI.

  7. The fractional contributions of the strongest updrafts (w > 6 m s−1) initially contribute less than 20% to the total upward hydrometeor mass flux, but their contributions increase to nearly 50% before RI and then only decrease at the end of the simulation when Dennis starts to make landfall. The increased contribution of the strong updrafts to upward hydrometeor mass flux comes from contributions at higher (z > 6 km) and midlevels (1.5 < z < 6 km) rather than from low levels.

Future studies should examine the implications of the upper-level rapidly accelerating updrafts for RI. In addition, the timing and location of convective bursts relative to the penetrative downdrafts and their resulting impacts on the latent heating distributions should be examined. Simulations with more sophisticated microphysics packages should be conducted in order to determine if the systematic overestimate of Z seen here and in simulations of other hurricanes can be alleviated, and whether such changes will impact any of the conclusions above on the precursors of RI.

Acknowledgments

This work was supported by Grant NNX09AB82G from the NASA Hurricane Science Research Program and from Grant NNG05GR61G from the Tropical Cloud Systems and Processes (TCSP) mission. The model simulations and much of the analysis were conducted by graduate student Eric Meyers, who received support from the Grant NNX09AB82G, the NASA Earth and Space Science Fellowship NNX08AU92H, and from the American Meteorological Society Industry/Government Graduate Fellowship. Computing resources were obtained from the TeraGrid Computational Resources Allocation TG-ATM060008N using computers at the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana–Champaign. We acknowledge the Naval Research Laboratory for the GOES-12 infrared imagery accessed from online (http://www.nrlmry.navy.mil/tcdat/tc05/ATL/04L.DENNIS) and the Hurricane Research Division of NOAA for the P-3 LF composite radar data accessed online (through http://www.aoml.noaa.gov/hrd/Storm_pages/dennis2005). We appreciate the comments of John Molinari, Rob Rogers, and two anonymous reviewers, which improved the manuscript.

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